Demo a Course Session
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Demo Video Transcripts
00:00:15:15 OK, how are we doing?
00:00:19:11 How are you?
00:00:23:09 Maybe the snow's going away. That's a good thing. One can hope. Could be worse. We could be back East. I hear it's really bad.
00:00:33:11 Ready? We have virtual attendance. See, that's not bad.
00:00:36:15 And then it's ice. And I just-- I talked to a-- was supposed to meet with the guy for lunch today. And he's stuck in Columbus, Ohio. He's not even sure if his flight's going to get-- plane's going to get out today. So, OK, questions?
00:00:57:01 I'm going to say this probably poorly, but is there something called a indemnification clause about being-- from contract-- your contract-- I know I'm saying it wrong.
00:01:09:17 No, indemnification, so in general, it's whoever is indemnified, they're protected against legal actions under certain circumstances. So it's like indemnified and hold harmless. So that if a client-- I mean, we're-- I'm trying to give a decent example.
00:01:40:25 If you're in a contractual relationship but the other party behaves in a certain way that's reckless and irresponsible, there would be, presumably, clauses in the contract that would indemnify you from harm if things were brought forth. So I mean, just things like contractors are responsible for putting together storm water, erosion control plans. We would review those. But if it wasn't properly maintained, we'd be indemnified, I guess.
00:02:21:16 Was this a particular-- just something that popped into your mind? I was reading contract docs this morning. And part of the construction fitting, construction-- I think contract docs that said we'd do some observation had that clause in there at the end. So that way, I think if there's something wrong, we, as engineers, wouldn't get sued. The city would pay for our indemnification of that. I was trying to figure out what that--
00:02:45:05 So it would just be protecting and holding harmless for actions by others that we wouldn't be held responsible for, outcomes that happened. And it may come up again as we-- as we get more into the general conditions. Let's make sure we try and maybe catch that. OK, good. Other questions.
00:03:15:24 So I was going to share with you the Lewiston project here. We'll just go to overhead. I'll show a few things. As I've already told you, it's Lewiston, so that-- so here's the bid form, just to kind of get a sense of it. You can see in this case, your opening bids. There were four addenda. so when it was received, the number, initials, those types of things.
00:03:41:17 But what went South in this project is this particular language here. So this is under vertical turbine pumps. So a water pump, this was a water booster pump station. Under work included, so this is a technical spec, we haven't arrived at technical specs yet, but we will. And so they say in here, work included, "as a bid alternate, the contractor may propose vertical inline pumps."
00:04:12:04 And then the spec points the bidder to a particular section for the 50 and 100 gallon minute application only. If selected, the inline pumps shall be installed over the can. So these were pumps, cans that were already in place at the pump station, which should be covered with a blind flange as shown in the drawings.
00:04:33:15 The base-- so then it does say the base bid shall be for providing vertical turbine can pumps, which was the original spec one. And then any costs associated with providing and installing inline pumps shall be borne. So you read that, so you say, first you say, as a bid alternate, and then-- but then it clarifies then it says, well, but the base bid is for the vertical turbine can pumps, not the vertical turbine inline pumps, so slightly different.
00:05:08:01 So does allow for that. Not language I would have chosen. It led to, let's see, so here's the bid. So it was just it-- it was a lump sum project. Yeah, so the bidder shall list below the total lump sum bid prices. So this was a $1.8 million lump sum project, which is beyond my comfort range. That's a lot of money for a lump sum.
00:05:42:28 But no opportunity. It doesn't speak to base bid. It doesn't speak to alternate. But the technical specifications, which are part of the bidding documents, did speak to that. So they wrote in there their dollar amount. Then they said deduct $98,700 if vertical inline pumps are used. So they just wrote it in there because it was referred to in the technical specification.
00:06:07:18 So the bid form didn't account for a base bid. Didn't list alternates. And we've looked at the bid form in your document. And it's got that type of structure. So contractor, a very creative smart contractor, saw that opportunity. If we look at the total prices here, I'm not going to give you the names, although it really doesn't matter. This was several years ago.
00:06:33:19 And so you can see, so there's the-- there was their bid. It took them down to $1.719 million. You can see two other contractors observed the same, but they were not-- it wouldn't have dropped them to low bid. But you can see, so this is low bid, the apparent low bid with the deduct. Contractor 2 didn't deduct. And so you can see $1.818 versus $1.750. So this is number one, versus number two. Number one didn't list that. Number two did, these ones.
00:07:07:00 So now they're in a pickle, right? Because the technical specifications stipulated base bids, stipulated alternate. The bid form didn't include for it. Contractors address that, some of them. I won't-- I'll just read you from the letter. So during the bid process, so this is a letter from the contractor to the city, because they're hearing the bids might be rejected.
00:07:34:27 During the bid process, we conducted a thorough analysis of the bid contract documents provided by the city and project engineer of record, which again, is required in the instructions to bidders, in the bid form, thorough analysis. In the case of this project, the contract specification stated a bid alternative at the contractor's choice. It was clear at the contractor's choice.
00:07:55:00 This is clearly indicated in spec section, as copied below. And then the specs acknowledge the alternate is that the contractor's choice and not a requirement for the bid proposal. They found it in the best interest of the city. So they tried to make the compelling argument, you opened the door, you stipulated it, and then-- and then you're in this-- now you got yourself in a bind, because the bid form doesn't account for it.
00:08:21:07 And they didn't stipulate in the instructions to bidders how they might address that. So all of those things should have been covered. This is construction bidding 101 quite frankly. And the outcome was a rejection of all bids on basically a $2 million project. My understanding is the next time around, prices went up. And so it costs the city. And that low bidder, I mean, there are several good contractors out there.
00:08:48:26 That one in particular is a very good contractor, didn't bid. Walked away from it. And so there are consequences to our failures in putting together bid documents. And so, again, that's just 101. If you're going to develop a tech spec that allows for an alternative, you need to immediately put a note in your bid form somehow to catch it later on as you're developing that.
00:09:14:04 So that was a pretty bad one. And it cost-- it cost the city money. It cost the engineer money. So anyway, interesting one. So I'm sure there's more out there like that, unfortunately. So questions? Yeah.
00:09:32:11 What do you think is the leading factor for having-- for spec? Do you think is the transportation costs, like hauling equipment, or labor shortage?
00:09:45:29 So let me-- so we better understand your question, and I'll try and repeat for EOC. What actually in--
00:09:51:16 When bidding out a job, what is the biggest factor that makes it cheapest compared to more expensive?
00:09:58:23 Like for a contractor? I mean, it's going to vary by type of project, street project, underground utility project, where you're located. Mobilization costs are obviously expensive. Pipe materials can be expensive. Excavation is pretty fixed, probably. It's just equipment and labor. Pipe materials can vary substantially.
00:10:22:10 In today's world, I mean, who knows? Asbestos-- or asphalt concrete, any of the materials for road construction. So I'd say it's highly-- it's going to vary project to project on what drives the costs. And proximity-- certainly mobilization costs can affect things. Although we, again, we typically cap that as-- and most contractors will come in at, say, 5% pretty close to the cap on mobilization, et cetera, demobilization.
00:10:56:14 There's no one thing, though. So I'm not I'm not waffling. It's just highly variable, depending on the project. And these-- but these are the things that we do our best to stay on top of. It's one of the many hats we wear as engineers. Is we're doing the technical design, technical specifications, contract, thinking about pricing.
00:11:16:26 Making sure we're not gold-plating projects. I mean, this situation, this project in Colfax, now we're finding out that with new energy efficiency requirements in the state of Washington, it's requiring pump suppliers to upsize motors in order to get in the motors of a similar efficiency curve. And they're not maximum efficiency at maximum horsepower.
00:11:41:28 And so here we are, we've pulled out a system that's 75 horsepower. And unless we want to derate the capacity of the well, which really isn't desirable, we're probably going to have to bump to 100 horsepower, because you don't-- there isn't an 80 horsepower or 85 horsepower motor. It's 75 to 100.
00:11:59:09 So now we're in this-- we hadn't seen this coming. It was-- and trying to-- first thing you do is you let the client know, hey, energy standards in Washington might bump us to 100 horsepower. But then we got to go back and we got to look at all the electrical equipment. And what sort of domino effect does that have on the design and the cost, right?
00:12:22:29 It's a difficult-- it's an increasingly difficult environment to project design projects. OK, other questions? OK, so we left off here on this slide 29. This is unit pricing and contract management.
00:12:50:04 And this is one, I'm going to do my best to explain or give you an example on cash allowances. I'm going to-- you don't need to bounce to 14.03, but I will really quickly. If I go to instructions to bidders, get rid of that. 14.03, there's a little-- so in the instructions to bidders, for cash allowances, the bid price shall include such amounts as the bidder deems proper for contractor's overhead, et cetera.
00:13:23:15 So they're stipulating what's in a cash allowances piece. And then are there extra handouts? You want to pass one back to the back? Just pass one, just float one back. Oh, OK, OK, good. So it was here, and then gone, and then here? Somebody saved it for you? OK, that's good. That's good.
00:13:50:10 You got some friends back there. That's good. Because I wasn't going to pay one for you. And you can't ask for it in the next class either. I'm kidding. So here, so it's spelling out to the contractor, if there is a unit price contract, a line item for allowances, you would spell those out in your technical specifications.
00:14:14:24 And then it's also further covered. And we will spend some time-- I'll hit on Article 11 right now. But we'll come back to it more than once, because there is a lot of information there. But if we go to 11.02. Again, you don't need to bounce around here. Shortly, maybe we'll jump there for a while.
00:14:34:14 But this cash allowances contractor agrees. So in there, yeah? Sure. So I jumped to general conditions article 11, 11.02. sorry, I was-- it's one of the challenges, slides, I don't want to cut a whole bunch of stuff from the EJCDC into the slides. So we have to bounce back and forth. And I feel like Logan's still hasn't tapped his.
00:15:01:16 I honestly don't know what to do--
00:15:04:19 What time is it?
00:15:10:04 Yeah, so here's where it's spelled out, everything. And actually, article 11 in the general conditions, we'll come back to. Because one of my former grad students shared with me a really useful story about how to-- experience on how to deal with things like this. But here, contractor agrees that cash allowances include the cost to contractor of materials, equipment required by, to be delivered to the site, and all applicable taxes, and contractor's costs for doing all these things.
00:15:39:27 So it's right there in the general conditions on everything that needs to be the contractor if there is something for cash allowances. And so, sorry, we'll bounce back to the slides for a minute. What is it? It's a lump sum that you would put. You would just have a line item and a unit price contract. You would pay it off typically on a lump sum basis you can pay percent of, I suppose, that provides the owner with a general item to pay contractor for extras.
00:16:12:17 Maybe there's some uncertainty during the design, the contractor-- the owner's not quite sure what they might want to purchase, so funds to buy stuff later. And it could be-- I mean, it could be instrumentation. Hey, they'd like to-- we had a-- when we were closing, I wasn't involved with it, when the wastewater treatment plant project in Culdesac was being closed out, they had some money left over.
00:16:41:07 And so I helped the engineer work to buy some instrumentation. So they could do some of their own analytical work. They bought a spectrophotometer for nitrogen testing, which was pretty useful. They had some funds left over. So those types of things, you could envision that. Maybe you put it as an alternate in your bid.
00:17:01:26 But it's just that-- it just gives you some, if the owner wants, if there's maybe some things that might be desired, it allows the owner to have the contractor buy stuff, whatever that stuff may be. Now, that all being said, I mean, not that I've bid out hundreds of projects, but I've never used cash allowances.
00:17:24:17 But it's there. It's there. It's nice to know. It's good to know that you have that flexibility, that you could write that into a contract. And the general conditions cover that. So you're well covered if you want to do that.
00:17:41:08 Let's see, go to the next one, OK unbalanced bid. So this is an interesting one. And this is the handout. We'll take a glance at that. So what is it? So this is overpricing one or more items in a unit price bid. So this wouldn't be in a lump sum, because a lump sum is one number.
00:18:02:23 It's often called penny bidding. And we'll see an example where it literally was penny bidding. Why might a contractor do this? They might employ unbalanced to conceal some pricing strategies from contractors. Maybe there's-- they see an opportunity where they can frontload something, where they get a lot of money out of-- they sort of-- basically, what they're doing is they're putting together their whole bid, putting together their bid with all the unit price items.
00:18:36:06 And then they might end up-- they might see up front that there's maybe some uncertainty in quantities, the engineer screwed that up. So they can put a large number by that. And then-- and then balance it out somewhere else by putting a low unit price for an item that they then can be compensated. So they'll actually make a lot of money out of one particular item. So it's unbalanced. It's not equitably bid.
00:19:05:19 Again, believing the quantity estimates are inaccurate. So there might be a windfall. So you jack up that particular price. But in order to secure the bid or hopefully win the bid, they would elsewhere put in a really low price on an item. And there is some case law, we're not going to jump into that, other than just a case study.
00:19:26:19 Now, one of the things is, it's obviously-- if you go look at IB 19.01, and I'm not-- I'm not going to drag you there, I'm going to go there myself, but just point something out. It's minor, but it's I've covered it in the slides. If we look at 19.01, owner reserves the right to reject any and all bids, including unbalanced.
00:19:54:27 So we are-- so it's stipulated in the instructions to bidders if it's unbalanced, that the owner can reject based on that. Yup?
00:20:07:26 How do they determine whether it's unbalanced?
00:20:12:21 No, no, so good question, how do they determine? So not from the engineer's estimate, you just look at it. So let's just take a minute and look at this one I gave you. See if you-- just kind of-- anything look-- take a few minutes and just look at this handout here, this transmission line project. We've got five bids in there, plus the engineer's estimate. So obviously, I was not penny bidding. So you can ignore the engineer's estimate.
00:20:44:07 But-- So you think item 16, additional cost for--
00:20:54:27 He estimates $200, but you put $24.
00:20:59:06 So you're saying I was penny bidding? You think I'm unbalanced?
00:21:02:17 No, I thought it would be-- jacking down that one.
00:21:05:20 But remember, so this is-- so this is a good one to point out. So Rock ex, we didn't this-- I gave that example earlier. We didn't know if we would have rock ex. We had 2 and 1/2 miles of pipeline. We wanted to be able to pay the contractor if they encountered-- so we just said, gosh, we think there's 100 cubic yards of rock excavation.
00:21:27:11 And let me further clarify, in the payment section, in the measurement and payment section, it is made very clear what is rock excavation. There is certain equipment that has to be used if the rock is to-- so if the rock can be just-- rock excavation isn't rock, isn't just all rock. It's very specific to-- it would spell out the type of equipment necessary to excavate said material.
00:21:56:09 That would qualify under rock excavation. So we throw-- we just throw one in there. And rock ex can be expensive, because it's expensive equipment. And so remember Logan, the point is-- so here, this would be a situation where you might interpret penny bidding or unbalanced bidding, so maybe they would increase the price substantially, right?
00:22:24:04 Because they're like, wow, we actually think that it's going to be a lot. And so we see an opportunity to make some money. And so then elsewhere, they would reduce the price. In this case, given the uncertainty, we hadn't-- we hadn't shown on the drawings. If you knew somewhere where there was rock, you would spell it out.
00:22:42:15 You would provide that information in your supplementary general conditions. You would provide that information. You would provide geotechnical information in the bidding documents. We didn't do that. We just sort of put it out there as speculative, just to cover it. So in this case, it wasn't deemed unbalanced. And we didn't see anything that would suggest penny bidding elsewhere to-- because the low contractor was Skyline there.
00:23:11:25 They were at $20. That's, wow, that's cheap. You want to rock ex for us for $20, we're OK with that. That's a good price. It's on the contractor. It's not our fault that you underbid or underpriced that particular item. Anything else sort of jump out?
00:23:33:13 I was looking at item 22, buried 2 inch diameter conduit. Seeing a little bit of a misbalance there on Skyline and Mesa compared to everyone else.
00:23:45:02 So again, so what we're looking for then, so at $8, I mean, 2 inch diameter conduit, I mean, that's-- that we said there was 1,000 feet. We had good numbers on it. That's just what they thought it was going to be. So then you would look elsewhere. So you're saying maybe that's low. So did they did they counterbalance somewhere else to make money up front?
00:24:10:19 And again, we didn't see anything. And one of the takeaways here is just because the engineer's estimate and all the other numbers, the unit prices, are different and widely variable doesn't make it unbalanced. Doesn't make it penny bidding. So hold on a second, David. I think I had-- Willow were you?
00:24:29:18 No, I rethought that.
00:24:32:19 Would it be the control valve vault 13.
00:24:35:18 Number 13, OK. So we said 30. I mean, they're all about the same, really, and expensive. That was a particularly expensive-- and one way to-- one sort of the-- one value of the engineers estimate is, again, we aren't penny bidding or unbalanced bidding when we put together an engineer's estimate. So if they're in the ballpark, pretty close, if they're similarly seeing an expense, then you're OK with that.
00:25:04:13 And so number 13, we're at $30k, lowest-- the low bidder was $40, $40, you work away across. Particularly, what you're looking for-- I mean, just looking at Skyline, because they were the low bid. So I wouldn't-- Jade had one.
00:25:21:26 Oh, I was going to say Stanley contracting seems a little odd with all of their numbers. They're all weird dollar values. And then you get to a very large amount, I guess not large.
00:25:34:09 Yeah, you know, I honestly never quite-- I mean, although actually, if you look at the prices, I mean this is one, there's not a huge $872 to $928, not a huge range. I mean, they-- however, I've never been on the side of putting together an actual bid for construction. I've never worked for a general contractor. I mean, yeah, their numbers were-- I think one thing you would do is you would look at your two low bidders, thank goodness we didn't end up with low bid, change order low bid king there.
00:26:15:28 We were very grateful for that. Because this is the contractor that would go out and buy equipment when he found a project that he liked, and then sell it when the project was over, and was a true pleasure to work with. But you just get these-- you get-- oddities doesn't mean unbalanced or penny bidding. You're always going to see variable. And different contractors are going to employ different approaches.
00:26:41:19 And there might be-- it might be subtle, but it's been really hard to prove. It would have to be-- and when we look at a case study, it would have to be really egregious. So one more.
00:26:52:25 I was just looking at line 15, because Mesa's, their estimate was $15,000, and then the next highest was $3.
00:27:00:29 Yeah, that was abandonment. I mean, that does seem like a lot of money. And so-- but you think about, OK, I'm trying to remember where the phasing-- that was later stages of the project. So one of the things we're looking for in unbalanced is have they-- are they trying to get a lot of money upfront at the initial part of the project, and then balanced their bid to be competitive by lowering a price elsewhere.
00:27:35:01 So really, they're getting a whole bunch of money out of item 4, whatever it might be. But really, that's going to cover the cost of item 12, which comes later in the project, different strategies. So I will tell you, I've never seen it. I've never had it happen. I've never seen an unbalanced bid. I've never seen penny bidding.
00:27:55:25 I don't know that it's really actively pursued by contractors. But if we go back to the slides, so it's just good, because it's-- one of the things is looking at-- you're looking at these, you've got a couple of bid tabs now. You've got that one and the one I gave the other day on the pumping station.
00:28:15:10 You can see the difference in prices. It's just-- they just are. And you don't know what's going on behind the scenes. And as long as-- one of the things you do look for in pricing, particularly for the low bid, is it-- are there particular items that are significantly lower than everybody else and the engineer's estimate?
00:28:39:03 Again, because we're really trying to think through. We're not trying to get creative in the engineer's estimate to get some frontend money, or move things around, or whatever, look at the quantities. We're trying to literally predict what we think it's going to cost. And so if you get some that are significantly different, that could be a red flag.
00:29:03:26 But the red flag in that case is maybe they don't understand what the work entails. That would be a red flag, if they've really underbid something that you have illustrated and described in the drawings, and in the specs, it is really significant, whether it's equipment, I mean, whatever it might be, that would be a red flag.
00:29:29:22 So if we kind of go back to the slides here. So this is one, this was several-- obviously, several years ago. OK, this was in Boston. We had two bidders, $18 million, $20 million. The low bid had this literal penny bidding, a penny per square foot for temporary sheeting. And again, just as we've got in our instructions, the bidders commission could reject an unbalanced.
00:30:02:25 Boston went ahead, low bid, I mean, $2 million, that's not chump change. I mean, but then the Department of Labor and Industry for the state said the bid had to be rejected. Said it was-- they did find, though, so what was interesting is they said it's unbalanced. It's not unbalanced-- because there was no-- when you see a penny, you've got to go look for a counterbalance, because it's somewhere there.
00:30:33:15 And there was no counterbalance. But the Department of Labor and industry had a policy, that word's key, had a policy against penny bidding. And said that's not realistic. I mean, you can't accept that, because that's not really what it's going to cost. Boston said whatever the words they chose and moved forward, right? Went to a judge, judge determined that the low bid was not unbalanced or front loaded.
00:31:08:01 Judge concluded that Boston could not move forward with that. Again, we're talking $2 million, that's not a small amount of money. So it goes to a higher court, because that's what happens. And the higher court is ruling over policy. DLI can establish policy. They can't make rules.
00:31:27:17 So a policy and a rule are different. Legislature in this case hadn't given them that authority. All the rules come from the legislature. And then the departments enforce the codified rules. And ultimately, the judge said, look, that's fine, that's your policy. But it's a policy. It's not a rule.
00:31:51:13 Another appeal, claimed the judge had the power to prohibit penny bidding. And ultimately in the end, low bidder was just more creative, saw an opportunity. Wasn't unbalanced, wasn't frontend loaded. So those would be grounds for rejection. She had a more creative contractor, didn't think that temporary sheeting was going to be all that important somehow.
00:32:17:14 Maybe they'd factored it in elsewhere, but it wasn't obvious. And DLI and second low bidder had confused equal footing, which is a principle in contract law, with creative bidding to all bidders. So everybody had an equal footing. One got more creative. Why are you penalizing the more creative bidder?
00:32:37:29 And you could almost apply this case study here to the Lewiston situation. You had three contractors that were more creative, and it would have saved the city money. Unfortunately, the city hadn't properly-- or the engineer hadn't properly developed the bid form. So yeah, I've never seen it. Looking for-- I don't know how many of these are actually out there. But it's good to know.
00:33:06:09 I mean, it's one thing. I mean, we do scrutinize prices. We look for things that could be a red flag, that we think could cause problems should the contract be executed. And I think one more important one is-- I mean, the pricing is important. So it can be-- I wouldn't call it necessarily penny bidding, but low bidding, or underappreciating the required work, not that they have an unbalanced or loaded elsewhere, they just didn't actually understand the work. Those are the things that we look for. OK, Logan.
00:33:41:12 Talk about frontend loading. Is there anything in the sense of backend loading?
00:33:46:25 No, I mean, I've not heard of it. A frontend would make-- I think, the things where contractors are-- they're looking to exploit, perhaps, is underestimate of quantities, which is why we have to get our-- if we're going to do unit price, we need to measure super careful and very clearly articulate how measurement and payment. And then get it right in the bid form.
00:34:10:05 Because if we don't, a contractor might see that, they might jack up that price, but it's a low. It's a low quantity. But then when the real quantities come into play, boom, lots of money. But backend, I don't think there's really any-- I don't know why a contractor would necessarily do that. They're looking more for exploiting weaknesses in the bid form, and maybe getting some money upfront so they're less up bank during the project. Other questions? Yeah, Alex.
00:34:43:14 You may have hit on this. But how-- how are items-- in a lump sum contract, how is a contractor paid off of that? They're not going to get it all at once, I know they're going to slowly stagger it. But the unit price is pretty obvious. However much you put in, you keep quantities, you pay them that amount. But lump sum, I'm a little unsure how they get paid.
00:35:05:29 How does a contractor get paid under a lump sum contract? Excellent question. It's percent completion. It's a judgment call. But we'll see that. So we'll get to that later as well. But yeah, no, good point. I mean, how do you pay? You pay on percent complete. But the-- it's going to be subjective. It's going to be subjective. And the engineer has some weight in that.
00:35:32:17 Yeah, I mean, I much prefer unit price contracts for so many reasons. I mean, it's just-- one is it gives you the flexibility to add work if the bids come in low, which nowadays, they really aren't. But there was a time when they did. And you could add work to a project. And then it's so much easier to pay. And you're not getting into disputes.
00:35:59:11 OK, let's see where we are here. So different type of contract, so we've talked about lump sum. We've talked about unit price. This would be a cost plus contract. This is where you're paying for the actual work. You're paying-- you're actually paying for the labor, the materials, and supplies, plus a percentage or fee, that fee basis, that's the overhead and profit.
00:36:23:25 So you're actually pulling them apart. We're going to just pay you for the work. And then we're going to have an agreed upon percentage or fixed fee that's your overhead and profit, rarely used, more emergency project. Where you just say we need to get a contractor on board. We had-- during some flooding in '96, there were-- the city of Amity in Oregon, the whole Yamhill water-- or Yamhill River went over its banks.
00:36:52:24 And ended up totally silting in their raw water intake for their water plant. And so we had to bring a contractor on board in that situation. And we didn't have time to bid it. We were able to just hire a contractor, under a structure like this. We'll just pay you for the work you do. And then we have an agreed upon percentage or fixed fee. So those types of-- that's where you would use it.
00:37:17:00 You could use it in difficult or unique projects. We had-- that was actually the same contractor. It was the city of Hood River. It was actually design build project. So the engineer was partnered with the contractor. But sort of similar, we'll talk about that more later, and then I have a guest lecturer at some point later in the semester who's very knowledgeable in these alternate delivery methods, including design build.
00:37:46:19 But this was a situation where we had springs that the city had developed back in the early 1900s. We knew next to nothing about what we were going to see. And so as the-- we were doing preliminary design with the contractor for the city. And then there came a point where then the owner was able to work with the contractor to negotiate a sort of a similar cost plus type contract, given all the uncertainties.
00:38:18:29 Because we didn't know what to expect. And thankfully, one of our myriad designs is what we used. Not the one we put on the drawings, but one of the ones we'd actually talked through, which was useful. It was actually a lot of fun. If you can get into a design build project, that can be with a contractor, it can be a lot of fun.
00:38:39:04 OK, so here's-- I'm going to just talk about-- and we'll go look at some general conditions here to walk through this. So again, an engineer friend of mine had a project up in northern Idaho. They were-- it was a sewer project. It was a cured in place. So this was a special-- very specialized work. It was a contractor that would-- it was-- I don't know if it was Insituform or Gelco. I don't know who or what the contractor was, but-- who it was.
00:39:08:28 But they're pulling a liner. They're repairing a pipe in place, cured in place. So they're not excavating or removing the pipe. They're not-- they're not pipe bursting, pulling a new one in. They're just pulling a liner in. And then they actually can-- it's a particular chemical structure. And then they heat it up. And it creates a whole new pipe, if you will.
00:39:33:19 So they went to the contractor and said, hey, we'd really like to add some work to the project. But the project didn't have line item unit price on some excavation. So they had the contractor, again, was not an excavation project, had to go find a sub. And then they submitted a price. So they found a subcontractor who can do the excavation. They went, submitted the price to the owner.
00:40:01:25 And then the general contractor passed along the cost, so it was a cost plus type contract, but a 20% markup for overhead, admin, profit, et cetera. So the question is, do you just-- do accept it? Do you pay them the 20%? So this is where we need to go-- I'll let you get to general condition.
00:40:24:19 Actually, we'll go to Article 12 in the General Conditions, which is change of contract price or change in contract times. I'll let you find that. So this is page EJCDC C-700 page 46, at the bottom. So here's one. I mean, this is a real situation. And this engineer had to navigate it.
00:40:56:20 So if we look at 12.01.C, 12.01.C.1.a, that's where you start. So here's a change of contract price. That's what this was. You were asking for a change order. The contract may be only changed by a change order. So that's a formal document. It's in capital letters purposely. It's defined in Article 1 of the General Conditions.
00:41:23:14 Contractor's fee, that's what we're speaking of here, the contractor's fee for overhead and profit shall be determined as follows. So the general conditions in the contract that have been signed for allows-- I mean, it gives you clarity on how to deal with that. You can be a mutually accepted fixed fee, which wasn't the case.
00:41:48:12 If a fixed fee is not agreed upon, then a fee based on the following percentages of the various portions of the cost of the work for costs incurred under 11.01.A, et cetera, shall be 15%. Well that's not 20%. Contractor just did 20%, didn't adhere to the contract at all, 15%.
00:42:14:09 But then if-- so if we look at-- so C-- that's C.2.a, right? But then, it gets a little more gray. For costs incurred under 11.01.A 1 and 2, it's 15%. But if it's A.3, it's 5%. So it's either 15 or 5. But now, we have to go look at 11.01.A.1, A.2, and A.3.
00:42:54:20 So A.1 gets into some great-- spells it out in great detail, the cost of the work means the sum of all costs. You get all these-- one of the things you're seeing is it doesn't repeat. It says except as those excluded in 11.01.B. So you have to look at 11.01.B. So you're doing a little bouncing around, which can be frustrating.
00:43:20:11 When the value of any work, covered by a change order or a claim, which is different than a change order, is based on the cost of the work, the cost to be reimbursed will only be those-- will be only those additional or incremental costs required because of the change because of the event giving rise to the claim, except as otherwise may be agreed in writing, such costs should be the amounts no higher than those prevailing in the local.
00:43:49:18 That's subjective, right? Shouldn't be those that it would not exceed prevailing. So we've got payroll costs. I'm going to scroll through this really quickly. A whole bunch of them, costs excluded. But then C, so here's-- when all the work performed is performed on the basis of cost plus, so we have two different ones-- so it was 15% if it was A.1, which is payroll costs, what was it? A.1 and 2, I forget? Or yeah, A.1 and 2, right?
00:44:32:28 So it's 15% on top of what the contractor is proposing if what the contractor is proposing is payroll costs and materials and equipment, furnished and incorporated into the work. So that's 15%. But then, if we look at C, as set forth in the agreement. So all sorts of-- I mean, it's clear but not clear.
00:45:06:28 So again, the first part deals with payroll costs, materials. So the challenge that he faced was what do you do, right? Clearly, it's not 20%. Right from the get go, it's not 20%. But is it 15%? Or is it 5%?
00:45:26:12 His conclusion, based on the contract that was in play, is that the general conditions indicated 5% was the right number. Now, the contractor is not required to execute the change order. You invite-- you ask for a change order. You ask them to perform extra work. But if the price isn't agreed upon, it doesn't happen. So nothing is-- nothing is requiring the contractor to accept the terms.
00:45:54:05 Of course, the contractor in this case wasn't super thrilled about 5% for whatever reason, especially, it wasn't really their expertise. They had to really-- they had to bring on a sub. They'd have liked to get a little bit more out of the deal. And they countered with 12%. And they ultimately did settle on 12%.
00:46:16:16 So a little bit of negotiation, owners involved on that. They decided there would be some direct coordination work in the field and the office. So direct payroll costs, so there would have been-- it would have required payroll costs of the general contractor to, actively in the field, oversee the work performed by the subcontractor that was being brought into play. And so that would lean you toward the 15%.
00:46:47:06 But 15% didn't feel quite right. And they settled on 12%. So you could see where, depending on what you're asking, it could go either way. But the nice thing is, at least the general conditions cover us. And they allow for a discussion and a negotiation. We're not held to whatever dollar amount the general contractor wants to do.
00:47:18:11 And so I'll just-- I'm going to read this verbatim. So this is what he said. The rest of the story here that you won't find guidance on in EJCDC, and that I'm sure you're familiar with, from my experiences, is the give and take of construction and the need to pick battles. He goes, I didn't want to be too much of a stickler, because-- I'm going to make sure he's not using inappropriate words, anything I don't want to put on tape, didn't want to be too much of a stickler, because they were are really helping the owner by taking on the subcontractor and agreed to do so even though they typically don't.
00:47:54:07 Again, this was a very specialty contractor that they don't do excavation. So this was very much a favor to the owner. They'd also done some additional TV work on the lines that we thought we might add to the project that we ultimately didn't based on-- so there were some-- apparently some work that they didn't get paid for that was originally part of the bid. They weren't planning on claiming that additional work anywhere else. So even though they had some time.
00:48:25:23 So it was ultimately in the best interest to not make this a big deal. The city didn't pay a premium for the markup. But our generals still came out with something. So ultimately, it was a win-win. So that's the general conditions give us a lot of direction. But there is still that negotiating with contractors. A win-win, you want it to be a win for the owner.
00:48:48:04 And the other way to think about it, because again, the contractor could have said, no, it's not it's not our bailiwick. It's not in our world. We don't want to do this. So then you would have to prepare bid documents, go out to bid, bid the work, and then go through that whole process.
00:49:05:11 So all the engineering costs, so there's a lot of extra costs that would have been incurred if the general contractor said no, we don't like your terms. We're not going to do this. So you have to factor that in, as well. What's the alternate approach? And is that more expensive? Or is this a very expedient way, and so you compromise.
00:49:29:26 So I think those kind of stories are interesting to share. Let's see where are we at on slides? I got beeped. I'll let you look at-- I would encourage you, because I fully expect to have at least a question on the exam that speaks to 11.01, our general condition 11 and general condition 12. So you should be looking at those as you think about the exam. And we will pick up right there on Monday. Have a good weekend.
00:00:21.550 -- OK, a couple things as we get started. The first one is we
00:00:26.828 -- have the last lab assignment.
00:00:31.670 -- And so this one is going to be a bus differential protection lab
00:00:35.349 -- and so the on campus students is pretty much going to be a
00:00:39.028 -- similar setup to what you did before. You just need to read
00:00:42.424 -- through this and then work with the TA. As far as if you're
00:00:46.103 -- going to, I think you all of you have groups that you've been
00:00:49.782 -- doing the labs with the TA. If you want to stick with those
00:00:53.461 -- groups in those times. If you wanted to negotiate a different
00:00:56.574 -- time, then you just need to communicate with him about that.
00:01:02.040 -- Until you have a system and you're going to look at fault
00:01:05.628 -- at a couple of different places, this is actually
00:01:08.319 -- should be a little bit shorter than the last, quite a bit
00:01:11.907 -- shorter than the last lab.
00:01:14.920 -- And so you're really just going to look at several
00:01:17.710 -- different cases.
00:01:19.710 -- Look at the behavior with this.
00:01:22.940 -- The Engineering Outreach Lab is going to be similar.
00:01:26.730 -- So this is just the description of the entering outreach lab.
00:01:31.580 -- And so it's a little bit more complicated system, but it's
00:01:34.616 -- still the same basic idea.
00:01:36.980 -- And also you have some information about the CT
00:01:40.410 -- ratio that's was used for this.
00:01:44.480 -- And then this is using that.
00:01:47.590 -- Relay model that the differential relay model we
00:01:50.462 -- talked about. So again this is a low impedance restrained
00:01:54.052 -- differential element, so it's not. It's not a high
00:01:57.283 -- impedance differential element.
00:02:01.530 -- If anyone has fair time and wants to create their own
00:02:05.369 -- creative all the create this, it wouldn't be that hard to
00:02:09.208 -- create a lab for the restraint for the high impedance
00:02:12.698 -- differential elements. We just haven't had a chance to put
00:02:16.188 -- together the simulation files.
00:02:18.800 -- So anyway, it's the same idea you read in the data files.
00:02:24.470 -- Very similar to the handout that we talked about with the lecture
00:02:28.310 -- last week. All of this stuff we're reading the comtrade file,
00:02:31.830 -- and so where this really starts to differ a little bit is
00:02:35.670 -- towards the end of it. Once we've got the phasers, so we've
00:02:39.510 -- got the things where we're looking at the voltages in the
00:02:43.030 -- currents, and then we have the operating restraint current, and
00:02:46.230 -- so one thing that's different from the handout before is now
00:02:50.070 -- the. In this case, there's no.
00:02:53.660 -- Nothing where you put in a multiplier to imitate
00:02:56.297 -- saturation. The simulation data that you're using for this now
00:02:59.227 -- actually has saturation in it.
00:03:01.850 -- And the case is that you'll be doing for the on campus
00:03:05.450 -- students in the lab. You're actually going to be doing
00:03:08.450 -- these with an RTS simulation instead of using the model
00:03:11.450 -- power system, and so that the RTS will have setae. Models
00:03:14.750 -- that include saturation, but you're still going to be
00:03:17.450 -- setting the actual physical relay.
00:03:21.310 -- And then one of the things that this is going to show is the
00:03:25.664 -- basically the how they operate. Quantity changes. So basically
00:03:28.463 -- as it reads through samples, this thing is moving and then it
00:03:32.195 -- works its way up and then it has some final value it goes to and
00:03:36.860 -- so you can as you look at these different cases once you enter
00:03:40.903 -- the slope setting you can actually look at a little bit
00:03:44.324 -- how the how the value evolves and when you look at the case
00:03:48.367 -- with the saturation you can actually see how it.
00:03:51.300 -- Now the saturation changes what it's what the relay
00:03:54.171 -- element is seeing too, and so this was a case for an
00:03:57.999 -- internal fault, so it grows quickly.
00:04:02.860 -- So any questions about that?
00:04:09.170 -- Hey are there any questions from the last lecture?
00:04:12.680 -- Yeah, so in the last lecture when you talk about the high
00:04:16.832 -- impedance plus differential protection, you mentioned that
00:04:19.254 -- for an external fault. Once one of the see T starts to saturate
00:04:23.752 -- it will dive deeper into saturation, right? So my
00:04:26.866 -- question is how will that?
00:04:29.160 -- To how will that city begin to saturate? Like because?
00:04:33.660 -- The currents are all balanced, right? I mean based on the
00:04:37.972 -- culture of slow, so part of it's too far into this into the
00:04:43.460 -- hand out so.
00:04:47.760 -- That's the internal fault. So for the external fault part of
00:04:51.148 -- it's going to be the case that.
00:04:54.690 -- We've got this one. This is 1 heck external fault, right? So
00:04:58.338 -- this is seeing the current from all of the other feeders or
00:05:01.986 -- other lines going through it, and so depending on what the
00:05:05.330 -- burden is for this one.
00:05:07.800 -- Oh that 'cause there's going to be?
00:05:12.460 -- The relay and the and some of the winding resistance is going
00:05:16.084 -- to be dominant. Burden that affect saturation in this one in
00:05:19.406 -- a lot of ways.
00:05:21.210 -- So if this one, if there's a fault with a lot of DC offset,
00:05:25.088 -- especially then this one is going to start to saturate.
00:05:27.858 -- 'cause this is seeing the most current. I thought there is only
00:05:31.182 -- one button then that's the one at the end. Well, remember that
00:05:34.506 -- the burden and we look at ACT when we look at burden.
00:05:40.260 -- Mr Lead wire.
00:05:48.530 -- So the first thing we're going to have is the CT winding
00:05:51.338 -- resistance. And it's so. So in this case the Siti
00:05:54.649 -- winding resistance is going to be the most significant
00:05:57.088 -- one, because once we get to the terminals of the see T.
00:06:07.470 -- We're basically connecting each of the CTS.
00:06:12.750 -- In parallel on the secondary side, right and then once
00:06:16.320 -- they once we have this parallel combination, then
00:06:19.176 -- that's going. Then we have the rest of the lead wire.
00:06:25.200 -- And we have the relay out here.
00:06:30.540 -- But there's the secondary current on the secondary
00:06:33.404 -- winding, and the CT is still going to see.
00:06:37.340 -- All that current, right? The current when they sum
00:06:40.328 -- to 0 between.
00:06:44.320 -- We put in a third CT just to kind of.
00:06:49.030 -- Illustrate this a little bit more.
00:06:58.680 -- When I talk about connecting them together right, this is
00:07:01.940 -- where they sum to 0, right? So if it's if it's an
00:07:05.852 -- external fault.
00:07:12.350 -- So let's say that this is the one with.
00:07:18.870 -- The external fault, right? So that's going to have.
00:07:23.100 -- Let's say we have current going this way and this one. Each of
00:07:26.948 -- these are going to have their share feeding it right, so this
00:07:30.500 -- one is going to be the sum of this plus this and so at this
00:07:34.940 -- point here. They're going to sum
00:07:37.224 -- to 0. But this one, each one of these is going to have its own
00:07:42.072 -- fault current share the fault current, it's it's
00:07:44.628 -- carrying. It's going to go
00:07:46.048 -- through this resistance. And so basically what's going to
00:07:49.888 -- drive that start driving in this one in the saturation is
00:07:53.936 -- going to be a combination of the voltage drop across this
00:07:57.984 -- plus the ACE asymmetric current due to the DC offset.
00:08:03.130 -- Remember that as we talked about with on the BH
00:08:07.030 -- characteristic, the DC offset is shifting you in One
00:08:10.540 -- Direction and the BH characteristic.
00:08:17.450 -- And so when we look at this.
00:08:21.080 -- So under normal conditions.
00:08:23.650 -- It's going to be doing something like this, right? And
00:08:26.760 -- if we have a fault with no set without significant saturation?
00:08:31.480 -- It's going to be doing some like this, and so if we have well
00:08:36.324 -- size CTS we may only see behavior that looks like this.
00:08:40.730 -- But for a bus situation, sometimes it's hard to get
00:08:44.380 -- around that, but if we add.
00:08:47.510 -- The.
00:08:52.590 -- The DC offset.
00:08:54.830 -- I did not draw that very well, sorry. So we may start out with
00:09:00.248 -- something like this. Then the
00:09:02.183 -- next cycle. It's going to be working like this and it's going
00:09:06.480 -- to be following that DC offset, so it's going to push it into
00:09:10.302 -- saturation. Discuss. The flux loops are being pushed this way
00:09:13.242 -- by the DC offset.
00:09:15.870 -- And in some cases with a combination of the of a large
00:09:20.286 -- current and going through this resistance in a DC
00:09:23.598 -- offset, this one may start to go into saturation an.
00:09:29.390 -- Lessina cycle.
00:09:31.800 -- Possibly quite a bit less in the cycle.
00:09:35.790 -- And so that's why that's why even though you on the surface,
00:09:39.606 -- you would say that there shouldn't be much voltage across
00:09:42.786 -- this, because these current sum to zero and the voltage drop
00:09:46.284 -- across this should normally be negligible. But what's going to
00:09:49.464 -- happen is that the combination of that fault current going
00:09:52.644 -- through this winding resistance and the DC offset starts this
00:09:55.824 -- one into saturation. And then that mismatch current through.
00:10:00.130 -- That saturation goes through this, and because of that
00:10:03.577 -- compensating resistor that's going to drive this voltage up.
00:10:08.730 -- But because this is the one that's already starting to
00:10:12.290 -- saturate and has a lower impedance than it's, it's
00:10:15.494 -- going to tend to make this voltage collapse and keep
00:10:19.054 -- these from rising.
00:10:28.560 -- Like I said, it's not. That's a very good question. 'cause it's
00:10:32.280 -- there's a lot of things that are not intuitively obvious when we
00:10:36.000 -- look at the high impedance bus
00:10:37.860 -- differential. Because we're basically using something that's
00:10:42.662 -- inherently nonlinear to work.
00:10:57.580 -- Any other questions for my son?
00:11:06.790 -- OK, so then we're going to start on. Next, we're going to start
00:11:11.223 -- talking bout transformer protection and I talked to I did
00:11:14.633 -- a very quick introduction to some of the some of the issues
00:11:18.725 -- and the difference.
00:11:20.960 -- Things were gonna talk about.
00:11:21.870 -- We're going to talk about. Fall protection of the
00:11:25.190 -- transformer itself for faults inside the transformer.
00:11:29.680 -- And then we're also going to look at protecting the
00:11:32.850 -- transformer, firm external conditions, and
00:11:34.435 -- this can include faults external to the
00:11:36.654 -- transformer. Boy, the transformer is carrying
00:11:38.556 -- the fault currents that goes that go to it.
00:11:47.680 -- And then there are Transformers introduce a number of unique
00:11:51.640 -- challenges that we'll talk about as we go through this.
00:11:56.550 -- So in some ways it will start out looking at a concept similar
00:12:01.308 -- to what we looked at with the bus protection. So we're going
00:12:05.700 -- to a lot of the internal fault protection for Transformers.
00:12:09.360 -- Starts with the idea of restrained low impedance
00:12:12.288 -- differential element, so it's kind of build time. We start. I
00:12:16.314 -- started with the bus protection.
00:12:29.630 -- And so one of the things that the bear in mind as we talk
00:12:35.748 -- about transformer protection is when we talk about bus
00:12:39.681 -- protection. Fast protection has a bus fault or misoperation
00:12:43.614 -- where a bus gets tripped when it shouldn't can have very severe
00:12:48.858 -- operational. Consequences for our power system. So bus faults
00:12:52.556 -- are actually fairly rare.
00:12:54.760 -- Fat faults that cause were and the bigger concern is as
00:12:59.028 -- generally going to be external faults that caused the bus
00:13:02.908 -- protection to miss operate.
00:13:06.160 -- And so that's why the restrained differential element, the high
00:13:09.640 -- impedance differential element, have so there so much efforts
00:13:12.772 -- gone into developing and optimizing those at the relay
00:13:15.904 -- vendors is because they are very high consequences operationally
00:13:19.036 -- to the system in the short term.
00:13:24.130 -- Transformer failures, on the other hand.
00:13:44.050 -- Can have longer time consequences.
00:13:54.730 -- And that's because there are longer replacement times.
00:13:59.700 -- And in most cases, if an internal fault happens in a
00:14:04.560 -- transformer.
00:14:06.370 -- There is a good chance that it's going to evolve to the point
00:14:10.348 -- where it's not something that's very simply repaired. In some
00:14:13.408 -- cases there are still a number of cases where they're caught
00:14:16.774 -- fast enough, or it could be repaired simply, but if it gets
00:14:20.446 -- to severe faults and you'll have a fire in the transformer, then
00:14:24.118 -- it can be very severe.
00:14:27.950 -- And so there are a number of things. The number of strategies
00:14:32.750 -- that try to minimize the impact of transformer faults.
00:14:49.760 -- So one of the big ones is finding ways to reduce the
00:14:53.252 -- likelihood of them happening.
00:15:05.320 -- And so part of what a lot of this comes down to is.
00:15:10.900 -- Track external events.
00:15:31.620 -- And it's really the life of the installation. That's a
00:15:34.010 -- big issue.
00:15:35.620 -- So one of the things that I mentioned is that we have two
00:15:39.741 -- directions. We're gonna go to, and they actually are related to
00:15:43.228 -- each other. So one of the big things that is a has a
00:15:47.349 -- consequence for Transformers is.
00:16:06.620 -- Meeting of the installation will have a big impact on
00:16:09.700 -- how the life or how long that installation is going
00:16:12.780 -- to be good.
00:16:23.030 -- Transient overvoltages is another another issue.
00:16:44.770 -- So what are some of the things that are going to
00:16:47.168 -- cause a transformer? Cause heating in a transformer?
00:16:51.350 -- So let's think about a transformer for a second
00:16:53.690 -- we have.
00:16:56.970 -- So I'm just going to draw a single phase core.
00:17:01.570 -- So as we've talked about where we have a single phase core
00:17:05.410 -- and have the low voltage winding on the inside, an will
00:17:08.930 -- have a higher voltage winding wrapped around the outside of
00:17:12.130 -- it, right? And then we'll take those out to the bushings.
00:17:16.690 -- And as I mentioned earlier, we don't. You don't see a
00:17:20.397 -- transformer core just sitting out open in the air, right?
00:17:24.360 -- And so usually this is going to be.
00:17:32.140 -- In a tank.
00:17:37.710 -- Anna's tank is going to be.
00:17:45.730 -- Filled with oil, right? So usually it's going to be some
00:17:48.271 -- sort of a dielectric oil.
00:18:02.600 -- Is also used as a coolant.
00:18:08.650 -- And so you may look at a name plate for a transformer, an it
00:18:13.914 -- may say that you have a transformer that's rated at 15
00:18:18.050 -- MVA, 20 MVA.
00:18:20.300 -- 25 NBA
00:18:23.920 -- so why would why would there be 3 MVA ratings for the
00:18:27.712 -- same transformer?
00:18:34.120 -- Different cooling stages. It's different cooling stages, so
00:18:37.424 -- this is going to be.
00:18:40.720 -- Basically, entirely passive cooling.
00:18:45.100 -- So there is going to be there will be radiator fins or on the
00:18:49.510 -- side of this case on the side of
00:18:52.030 -- that tank. This is going to be.
00:19:03.070 -- Going to be pumps used to circulate oil to cool the
00:19:06.029 -- transformer or cool the oil so it's going to circulate because
00:19:08.988 -- there are going to be.
00:19:11.010 -- Different spots in the winding that are hot spots said certain
00:19:14.156 -- certain points are going to be
00:19:15.872 -- hotter than others. And so if you don't circulate the coolant,
00:19:19.424 -- there will be a little bit of natural convection, but you're
00:19:22.262 -- going to. Those hot spots are not going to be cooled as well.
00:19:26.580 -- And then this is going to be pumps.
00:19:31.090 -- Plus
00:19:32.920 -- running cooling fans that are blowing error basically across
00:19:36.997 -- the radiator so that the radiator works more efficiently.
00:19:45.810 -- So depending in some cases people will just run these
00:19:49.220 -- all the time. In some cases they'll based on the load
00:19:52.971 -- conditions, they'll start and stop this equipment.
00:19:56.890 -- And if you have a transformer that's always lightly loaded,
00:19:59.290 -- they may not. Run it as. Run to run them very much at all.
00:20:15.100 -- So other things that could cause heating.
00:20:23.270 -- So I want to be carrying harmonic currents.
00:20:38.460 -- Do you know external loads?
00:20:48.380 -- So for example, if we have a transformer that one of
00:20:52.153 -- the loads.
00:20:54.110 -- Is.
00:20:59.190 -- A dialed dialed rectifier.
00:21:04.740 -- And then we have a voltage source converter.
00:21:09.580 -- Anyway, have an induction motor.
00:21:17.060 -- If.
00:21:19.260 -- This doesn't have any compensation.
00:21:28.570 -- The current strong by this drive are going to look
00:21:30.800 -- something like this.
00:21:34.920 -- And so this is going to have 5, seven, 1113 and
00:21:39.463 -- basically multiples of 6 plus or minus one.
00:21:47.670 -- Is there going to have other loads here? But this
00:21:50.100 -- transformer is going to be carrying this current plus
00:21:52.287 -- whatever loads are here.
00:21:57.000 -- And carrying those harmonic currents increases Eddy current
00:22:00.808 -- losses in the transformer core.
00:22:04.480 -- And so that the transformer is going to run hotter.
00:22:23.280 -- And so they actually you can actually get.
00:22:27.470 -- K factor rated.
00:22:35.920 -- So basically these K factors are more of a derating factor.
00:22:41.170 -- And so if you have, if you know you're going to be supplying
00:22:45.642 -- harmonic loads, you can buy a transformer that has basically
00:22:49.082 -- an extra factor in its MVA rating to be able to deal with
00:22:53.554 -- harmonics. If you're not, if you don't have a transformer
00:22:58.028 -- that has any K rating an you start supplying harmonics,
00:23:01.848 -- then usually you can. There's there are formulas from the
00:23:05.668 -- IEEE standards that talked about how you derate the
00:23:09.106 -- transformer, so instead of being a 15 MVA transformer, it
00:23:12.926 -- may actually be a 12 MVA transformer due to the extra
00:23:17.128 -- heating from the harmonics.
00:23:19.820 -- And so when someone buys a transformer, usually you're.
00:23:24.470 -- Part of the data for when you sign the contract with the
00:23:28.019 -- supplier and stuff like that is saying well, this is. This has a
00:23:31.568 -- 30 year design life for this as a 25 year design life.
00:23:35.850 -- If you routinely overheat the transformer, you may take years
00:23:39.750 -- off of that life.
00:23:41.870 -- So we had an outreach student awhile back that worked at an
00:23:46.334 -- industrial facility that was basically with zinc smelter.
00:23:50.010 -- And so they had a lot of very large rectifier loads and so
00:23:54.924 -- they had Trent. They bought Transformers that had.
00:23:59.340 -- 30 year old designlife
00:24:01.880 -- Then they push them kind of right. It may be a slightly
00:24:07.520 -- beyond their NBA ratings.
00:24:10.240 -- And then they gave this heavy harmonic loading. So they
00:24:13.060 -- lasted about 10 years.
00:24:18.790 -- An that fit and when I say lasted about 10 years, they had
00:24:24.237 -- a fault, and so if I did so by heating the insulation, you end
00:24:30.103 -- up causing the you decrease the lifespan of the installation and
00:24:34.712 -- your moral an it's more likely to fail by having our fault. And
00:24:40.159 -- so that's why this external event, external condition stuff
00:24:44.349 -- matters from the from the transformer Protection POV.
00:24:52.670 -- So transformer protection will usually track the loading on a
00:24:56.900 -- transformer an if the transformer is overloaded, and
00:25:00.284 -- then there are formulas you can use to figure out how much
00:25:05.360 -- that's affected the life.
00:25:10.980 -- And so some other things that will go into this are going
00:25:13.776 -- to be over excitation.
00:25:23.720 -- So on a transformer over excitation basically means
00:25:26.400 -- a steady state.
00:25:34.200 -- However, voltage that means you're partially saturating.
00:25:57.850 -- Angene why the transformer is going to produce more
00:26:01.478 -- harmonics because of this? Because this is a steady state
00:26:05.438 -- sinusoidal condition, these will be only odd harmonics.
00:26:11.110 -- And often the 5th harmonic is usually going to be the one
00:26:14.674 -- that's used as sort of the main detection detector for that.
00:26:21.140 -- But again, because you're saturating the core.
00:26:26.070 -- What does that? What does it mean when you saturate
00:26:28.960 -- the core more deeply?
00:26:35.050 -- More excited, you have more expectations, well over
00:26:37.938 -- expectations. We have more expectation right? But what
00:26:40.826 -- losses go up?
00:26:44.480 -- The winding losses go up, or so we're going to increase
00:26:50.200 -- hysteresis losses.
00:26:54.180 -- Remember, hysteresis losses are basically proportional to
00:26:56.672 -- the area of the hysteresis loop it follows, so if you're
00:27:00.588 -- over exciting the transformer, your loop has a bigger bigger
00:27:04.148 -- area, so the losses are going to be higher.
00:27:24.780 -- Another one that's a big factor are through faults, which means
00:27:29.345 -- that the transformer.
00:27:52.160 -- So basically, one of the things that also gets tracked is how
00:27:56.120 -- many, how many faults is this transformer supplied? What is
00:27:59.420 -- the magnitude of the fault
00:28:01.070 -- current bin? Because. Oh through fault can cause very substantial
00:28:05.092 -- heating. It may not. It's not going to last very long, but
00:28:08.764 -- it's going to take a long time. It's going to take awhile quite
00:28:12.742 -- awhile for the transformer to cool down from that.
00:28:37.870 -- So even frequent large motor starting or if the transformer
00:28:42.020 -- is supplying current to energize other Transformers.
00:28:48.500 -- So for example when.
00:28:53.020 -- I think their procedures have changed a little bit, but at
00:28:56.771 -- Grand Coulee there's a pumped hydro storage facility that
00:28:59.840 -- has very large synchronous Motors. They generally only
00:29:02.568 -- start those Motors once a day because the thermal shock on
00:29:06.319 -- the Motors every time they start them is so much that
00:29:10.070 -- they can't start them more often.
00:29:14.040 -- They redid that facility.
00:29:17.610 -- And within the last.
00:29:20.130 -- Eight years, so I think they've redone it, so
00:29:23.019 -- it's not quite as harsh.
00:29:26.260 -- But so basically all of these things get tracked.
00:29:45.910 -- They predict lifespan loss and we're going to. We're going to
00:29:48.814 -- come back and talk about the over some of these issues and
00:29:51.982 -- how and how this factors into the transformer protection later
00:29:54.622 -- in the course. I want to talk about internal faults. First,
00:29:57.526 -- we're going to come back to
00:29:59.110 -- this. That a good resource for this. Our textbook does a pretty
00:30:03.945 -- good job with this, but also the IEEE 30 C 3791.
00:30:08.770 -- Also another good one for this and or there's some
00:30:11.730 -- other references. We'll talk about a little bit later.
00:30:21.310 -- And So what I want to start talking about is now protection.
00:30:27.370 -- For internal faults.
00:30:33.170 -- And will be going through this over the next couple
00:30:35.320 -- of lectures.
00:30:45.020 -- And so I guess that's one other sort of structural
00:30:47.990 -- thing. When we look at.
00:30:51.370 -- Large Transformers again.
00:31:13.460 -- I felt it evolved to the point where there's
00:31:15.485 -- a fire can cause long.
00:31:19.490 -- As I said, long repair times.
00:31:23.550 -- And so some of the things that you'll see in a substation, for
00:31:29.205 -- example for large transfer transmission substations
00:31:31.815 -- especially often you'll see single phase Transformers used,
00:31:35.295 -- and so you'll see.
00:31:40.310 -- Three single phase units, and actually they are often going
00:31:43.810 -- to be 3 winding Transformers as we talked about earlier in
00:31:47.660 -- the semester.
00:31:49.800 -- And so they're going to have their own individual tanks.
00:32:00.700 -- And when you look at the substation.
00:32:04.490 -- You'll see a wall that's been placed.
00:32:09.980 -- Between the Transformers.
00:32:13.120 -- So what's the purpose of that wall?
00:32:16.130 -- Prevent fire from cleaning, so these are.
00:32:20.530 -- Firewalls raise more of the archaic usage of the term
00:32:24.070 -- instead of the one that's now everyone uses when they talk
00:32:27.964 -- about software.
00:32:29.990 -- And so this is basically if this one has a fault, and as
00:32:34.072 -- a fire, the idea is that this is that this is going
00:32:37.840 -- to basically make it less likely for any for the heat
00:32:41.294 -- in the flames to get to this transformer, so it fails to.
00:32:49.730 -- And a lot of utilities will
00:32:52.352 -- have. A limited number of spare Transformers that they
00:32:56.392 -- can put in to replace a failed transformer.
00:33:00.350 -- So.
00:33:03.620 -- This was probably almost 15 years ago. Now there was a
00:33:08.328 -- transformer fault at a 500 kva. Think it's a 500KV substation in
00:33:13.464 -- the Southwest. An they did not have.
00:33:18.530 -- Firewalls between the single phase transformer, so they lost
00:33:22.364 -- all three phases. They had their spares close enough that it
00:33:27.050 -- actually scorched the paint off of the tanks, but they actually
00:33:31.736 -- didn't lose the spares.
00:33:36.820 -- But because they lost all three and they only had three spares,
00:33:41.392 -- then they had to scramble to try to get spares from other people.
00:33:46.345 -- And I know that one of the utilities in the northwest
00:33:50.536 -- sentence pairs and they had all sorts of issues because these
00:33:54.727 -- were 500 kva Transformers, Oran, high MVA ratings. Just
00:33:58.156 -- transporting them was difficult.
00:34:04.410 -- And I think even transporting the spares
00:34:06.867 -- took like several months.
00:34:17.190 -- So then actually one of the things that the.
00:34:21.070 -- US Department of Energy in the Department of Homeland
00:34:24.814 -- Security been working on in the last several years, is
00:34:28.974 -- basically trying to form a kind of a national database
00:34:33.134 -- of transformer spares and also trying to increase the
00:34:36.878 -- inventory of spares so that if there is something like.
00:34:42.950 -- High energy electromagnetic pulse from a nuclear weapon or a
00:34:47.550 -- major Geo Geo magnetic.
00:34:50.070 -- A disturbance for the gym geomagnetically induced currents
00:34:53.454 -- caused transformer failures that they've got something that they
00:34:57.261 -- can go to restore power in some
00:35:00.222 -- areas quickly. Relatively quickly.
00:35:05.270 -- OK, so let's now start talking a little bit more about the
00:35:08.798 -- Internal fault protection.
00:35:16.340 -- Really, the first line for this is going to be
00:35:19.390 -- differential protection.
00:35:27.600 -- So as I said, much like what we were just talking
00:35:31.285 -- about with the.
00:35:33.640 -- Boss protection for the restrained low impedance
00:35:38.078 -- differential protection.
00:35:42.100 -- So let's start out looking at a transformer that.
00:35:47.170 -- We have a YY connection.
00:35:51.350 -- And so, let's say it's.
00:35:55.330 -- 3:45 KV. 2.
00:36:00.110 -- 138 KV.
00:36:07.700 -- And so for the moment, let's just say it's a.
00:36:11.870 -- 2 winding Transformers. So we're going to have
00:36:14.102 -- three leads coming out.
00:36:34.210 -- Now I have see T is on each phase and will just look at one
00:36:38.110 -- phase for the moment.
00:36:47.100 -- And so we start out saying, OK, well, this looks a lot
00:36:50.436 -- like what we talked about when we anytime we talked
00:36:53.216 -- about differential protection. So we're going to
00:36:55.162 -- have current if we have current going this way.
00:37:02.630 -- Then we're going to have.
00:37:06.340 -- Secondary current. That's going to circulate like this, and.
00:37:12.870 -- I op should be about 0, right? That would be. That's
00:37:17.666 -- what we would expect.
00:37:23.200 -- Now, unlike the virus protection, we've got a number
00:37:27.574 -- of factors that complicate this.
00:37:44.360 -- So what do you think? Some of the complicating factors
00:37:46.660 -- might be?
00:37:49.540 -- Configuration. Well, let's say they will stick with the
00:37:53.020 -- YY for the moment.
00:37:56.010 -- If it's why Delta that, that will add, that will be the next
00:37:59.195 -- challenge, will talk about after we finish this one.
00:38:03.450 -- CD accuracy. Find CD accuracy.
00:38:07.640 -- So ciety accuracy, but there's actually something
00:38:09.831 -- before that. One is going to be the CT ratios.
00:38:37.200 -- So we may not get apart. We may not get a perfect
00:38:40.284 -- cancellation of.
00:38:42.410 -- So let's say that just for making this easier, let's say
00:38:46.172 -- that this was a 2 to one ratio.
00:38:54.770 -- So let's say that this was 500KV and this was 250KV just
00:38:58.598 -- for nice numbers. Even though the 2:50 is not something
00:39:01.788 -- you'd run across much.
00:39:04.660 -- Then we would say OK. Well then this. Let's say that
00:39:07.608 -- this is 1000 to one CT and this is going to be what?
00:39:15.290 -- Or 1000 to 5C T, and that's what would this
00:39:17.760 -- would need to be then.
00:39:24.010 -- Remember, this is.
00:39:26.200 -- Two to one is the effective voltage transformation
00:39:28.680 -- ratio, so the current goes the opposite, right?
00:39:32.170 -- So this one would need to have 500 to 5 setes.
00:39:37.110 -- So that would be one that would be an example of a
00:39:39.894 -- good cancellation. So let's say that this was.
00:39:44.450 -- 500KV to 250KV.
00:39:50.810 -- And the cities were.
00:39:53.330 -- 1000 to 5
00:39:56.690 -- in. 500 to 5 so that's something that you could pretty easily.
00:40:00.320 -- Fine cities.
00:40:03.260 -- To cancel that right?
00:40:06.340 -- If we look at 3:45 to 138.
00:40:13.080 -- That's not going to be so easy to find CTS that give
00:40:16.572 -- you a good cancellation on that. So even if this was
00:40:19.773 -- even if these were still.
00:40:22.920 -- Thousands of five.
00:40:27.930 -- This would need to be basically 1000 times.
00:40:33.640 -- 38 / 345.
00:40:37.240 -- To five.
00:40:43.830 -- And chances are that's not going to be a nice stock
00:40:47.108 -- number that you're going to be able to buy in. SNS ET.
00:40:56.510 -- And so it's one that we're we'll talk about a solution for that,
00:41:01.424 -- but this is basically going to
00:41:03.692 -- be. Having
00:41:06.760 -- taps on the relay.
00:41:10.600 -- So watch mechanical relays. What they had was they had multiple
00:41:13.625 -- tap points where you could
00:41:15.000 -- connect. The inputs from the transformer for the differential
00:41:19.010 -- and you could partly correct for that mismatch to a degree you
00:41:23.690 -- couldn't. You could not connect 4 correct for it perfectly, but
00:41:27.980 -- you could. You could go a long ways towards correcting it.
00:41:33.160 -- What we'll see in probably not today. We may. I don't know if
00:41:37.697 -- we get to the example today, what you'll see in
00:41:41.187 -- microprocessor relays now that's just a number, so it's just a
00:41:45.026 -- scaling factor, so you can. So basically you as you enter the
00:41:49.214 -- stuff into the relay for setting it, you're entering the
00:41:52.704 -- information so the relay calculates that tap and you
00:41:55.845 -- don't even have to answer. Calculate it yourself so you say
00:41:59.684 -- OK, here is the MVA rating. Here's the voltage rating.
00:42:03.680 -- And then at the relay says OK and this is the rated
00:42:06.980 -- current and just basically calculates it for you.
00:42:11.830 -- And then you also put the seat. The actual CT ratios 'cause it
00:42:15.444 -- puts that in as a correction to.
00:42:27.670 -- Another thing you'll see in a lot of large power Transformers
00:42:31.080 -- is they have taps, right?
00:42:34.410 -- So we may see.
00:42:37.830 -- 500KV to 250KV.
00:42:42.510 -- Anne, this could be we could
00:42:46.392 -- have. Plus 2 1/2% + 5%
00:42:58.620 -- And these could also have some different apps. So if
00:43:01.930 -- you start putting.
00:43:04.060 -- If you and so in some cases, these maybe.
00:43:08.340 -- For lower power ones, these may be on load. Tap
00:43:11.695 -- changing Transformers where they can be changed. In other cases
00:43:14.745 -- the transformer has to be D energized for crew to come in
00:43:18.405 -- and change that tag.
00:43:22.870 -- What is that tap change due to the differential current?
00:43:32.540 -- You just change the ratio of the transformer, right? So you've
00:43:36.984 -- gone to the effort of correcting for compensating for this, this
00:43:41.428 -- ratio and the CT ratios. Now you just threw that off because you
00:43:46.680 -- changed the transfer. The power transformation ratio by 2 1/2%.
00:43:59.070 -- Then another one would be.
00:44:25.660 -- The transformer is always going to draw some magnetizing current
00:44:28.480 -- if it's energized right.
00:44:32.250 -- And this is something that's.
00:44:34.160 -- Going into the transformer and not coming out.
00:44:44.190 -- And as we talked about last time, this might be 2 to 4%,
00:44:48.948 -- maybe 5% of the rated current.
00:45:07.230 -- It will be higher if the transformer is over excited.
00:45:13.210 -- So there's really two things that you need to look at with
00:45:16.414 -- over. Excitation is going to be.
00:45:18.830 -- If the over excitation is severe enough and last long enough you
00:45:23.114 -- want to trip the transformer.
00:45:25.910 -- But you don't want to trip it because you think it's an
00:45:29.414 -- internal fault, so you don't want to trip at the instant it
00:45:32.918 -- happens. So there's some tradeoffs on that, and the
00:45:36.460 -- harmonic content of that's going to be a factor in how
00:45:39.595 -- the relay responds to it.
00:45:44.120 -- Now there's another issue that you have to worry about
00:45:46.480 -- with magnetizing current.
00:45:51.280 -- What would that be?
00:45:58.370 -- So we have magnetizing inrush current.
00:46:09.250 -- So if you energize a transformer.
00:46:23.570 -- You're going to see a current that's going to
00:46:25.568 -- start out looking like this.
00:46:28.260 -- And it may take a second or two
00:46:31.508 -- to. One at one to two seconds to get down to the normal
00:46:36.314 -- magnetizing current.
00:46:40.990 -- So are people familiar? Why Transformers exhibit
00:46:43.867 -- this behavior?
00:46:52.120 -- So it goes down, it goes back to our hysteresis characteristic.
00:46:57.400 -- So the transformer is going to when it's operating is
00:47:00.650 -- going to be.
00:47:03.580 -- Following something that looks like this, right? So if this is
00:47:07.507 -- B versus H.
00:47:10.670 -- This is proportional to voltage. This is proportional to current.
00:47:15.790 -- So every time you go through a sinusoidal cycle, it's going to
00:47:18.982 -- trace this curve, right?
00:47:22.010 -- And so when you deenergize the transformer, you deenergize
00:47:26.042 -- nearer at a current 0, right?
00:47:29.630 -- And so when the current goes to zero, you're going to be
00:47:32.654 -- somewhere up here. And so there's going to be some trapped
00:47:36.706 -- flux on the core.
00:47:38.830 -- When it's deenergized and depending on where you were in
00:47:42.030 -- that hysteresis cycle, when the breaker contact cleared or what
00:47:45.230 -- the power factor of the current
00:47:47.150 -- was. Usually the final invoice and normal routine operation
00:47:51.948 -- when I want to Transformers.
00:47:54.940 -- D energize you open one side, then you open the other ones
00:47:59.476 -- you're interrupting, basically just magnetizing current with
00:48:02.122 -- the final. The energizing of the transformer.
00:48:06.540 -- When you re energize it.
00:48:09.140 -- How is voltage related to flux in a transformer?
00:48:13.830 -- So V is equal to NDF DT, right? So the flux in the voltage or 90
00:48:19.014 -- degrees out of phase with each other. But you can so that the
00:48:23.226 -- voltage here at some point in a sinusoidal voltage waveform you
00:48:26.790 -- can map that the flux when you energize it. So when you're when
00:48:31.002 -- you close a circuit breaker, there's going to be some
00:48:34.242 -- basically effective flux that you're you're trying to impose
00:48:37.158 -- on that core. So if you're lucky and you and you pose a circuit
00:48:41.694 -- breaker in the effective flux for the point on waiver, you're
00:48:45.258 -- closing. It's about what you trapped on the core.
00:48:48.680 -- Then there's not really going to draw any current.
00:48:53.430 -- If you're unlucky and you had trap works up here and you're
00:48:56.562 -- closed when you're somewhere down like this, now the
00:48:58.911 -- transformer is going to draw a lot of current to try to
00:49:02.043 -- equalize that flux. And after magnetizing inrush current.
00:49:06.320 -- And it's very nonlinear current.
00:49:09.000 -- And so this has a lot of harmonic content. The
00:49:12.210 -- generally it's going to be dominated by second and
00:49:15.099 -- then 5th and so on. But it's going to have more
00:49:18.630 -- even harmonics where the over excitation is only
00:49:21.198 -- going to be odd.
00:49:25.610 -- How's the modern steels that they're using in newer
00:49:29.615 -- Transformers? Do not have a sharper second harmonic
00:49:32.839 -- characteristic. They still draw big magnetizing currents, but
00:49:35.135 -- now there's not as clear a second harmonic, and we'll talk
00:49:38.292 -- about some of the issues with that later in the.
00:49:42.650 -- Not this, not later today, but next week or
00:49:45.570 -- the week after next.
00:49:49.040 -- So you've got these very large currents again, they're just
00:49:51.940 -- going into the transformer.
00:49:57.860 -- And so you know, if you're doing
00:49:59.764 -- a normal. Registration of the transformer. Not something
00:50:02.364 -- following like Re closing in a fault. You might have this side
00:50:06.312 -- open and you energize this side and so now you're seeing current
00:50:10.260 -- San people have measured currents as high as 15 per unit.
00:50:16.260 -- If there are a lot of lights, limits that is partly whether
00:50:19.596 -- the surrounding power system can supply that much current.
00:50:22.098 -- If there's too much impedance in the power system that won't
00:50:25.156 -- supply it.
00:50:28.120 -- And so you're doing. You have a differential element. You're
00:50:31.140 -- going to see. Let's say it's something more normal, like 5 to
00:50:34.764 -- 7 per unit for a second.
00:50:37.980 -- So in electromechanical relays.
00:50:41.570 -- One of the things that they did initially was basically turn off
00:50:46.274 -- the differential element until the inrush current period was
00:50:49.802 -- over. They still had issues where if you had two
00:50:53.199 -- Transformers that were close together and you energized one
00:50:55.638 -- when the other one was on, sometimes you had a sympathetic
00:50:58.619 -- trip of the different of the differential element for the one
00:51:01.600 -- that was already energized.
00:51:07.180 -- Professor, I have a question on this one, so
00:51:09.952 -- there is no saturation really, it's just the.
00:51:13.740 -- The core trying to reach that
00:51:15.876 -- flux level. But there's no saturation, so as.
00:51:21.150 -- It face it, it started has sort of a saturation effect because
00:51:24.966 -- of where it pushes the flux, but there really isn't any true
00:51:28.782 -- saturation of the core in this.
00:51:31.560 -- So why isn't it sinusoidal?
00:51:35.990 -- So when you think about the iron in the core right, you
00:51:40.423 -- basically have a bunch of magnetic domains that want to be
00:51:44.174 -- in random directions, right? So let's say that because of the
00:51:47.925 -- trap flux, they're all pointing
00:51:49.630 -- this direction. And for the inrush you're trying to flip
00:51:53.712 -- them all to go back. Basically you want the flux to go this
00:51:58.249 -- way, so you need to flip all
00:52:00.692 -- these domains. And.
00:52:03.920 -- They don't, simply.
00:52:06.420 -- Follow a nice thing in sinusoidal behavior as they flip
00:52:09.250 -- on this. So there's some resistance. I'm really
00:52:12.652 -- oversimplifying this, but basically it's it's a
00:52:15.186 -- magnetic. The nonlinear magnetic behavior of the core
00:52:18.082 -- that keeps it from looking sinusoidal.
00:52:25.980 -- And this harmonic, and So what we're going to see in a little
00:52:30.426 -- bit, is that to try to minimize
00:52:32.820 -- this effect. The second harmonic is often used as a
00:52:37.252 -- as a signature, so if the second harmonics above a
00:52:40.942 -- certain threshold.
00:52:43.030 -- Then it's got the relay will block the differential
00:52:46.189 -- element, so you can either do harmonic blocking or harmonic
00:52:49.699 -- restraint, which is basically making the slope steeper.
00:52:53.590 -- Now, this raises an interesting thing. From a relay point of
00:52:57.572 -- view. We talked about digital filters, right? So here we
00:53:01.192 -- talked about second harmonic. I talked about fifth Harmonic when
00:53:04.812 -- I talked about over excitation detecting over excitation.
00:53:09.520 -- So remember what we talked about with digital filters? If
00:53:12.270 -- we're using cosine filters.
00:53:14.730 -- Well, the is the what is a cosine filter due to harmonics.
00:53:19.866 -- What's the gain about cosine filter 0, right? So the relay
00:53:24.574 -- needs a separate.
00:53:26.820 -- Cosign filter that if you want to measure second harmonic or
00:53:30.582 -- you want to measure 5th harmonic or any of the others, you need
00:53:35.028 -- to have some separate filter elements that are going
00:53:38.448 -- to calculate those.
00:53:40.160 -- Because the normal cosine filter using for your protection
00:53:43.400 -- calculations is going to have a gain of zero and block those.
00:53:49.450 -- And when you start getting up to 5th or 7th, now you're
00:53:52.450 -- starting to get up to the range where the low pass filters,
00:53:55.450 -- anti aliasing filters also going to have an effect on
00:53:57.950 -- them.
00:54:03.460 -- So when you talk about residual magnetism, why doesn't it die
00:54:07.387 -- out? So if I'm.
00:54:09.370 -- I'm switching off or closing opening the breaker in front of
00:54:13.286 -- the transformer at equals to zero. Eventually the residual
00:54:16.490 -- magnetism should die out, right? If I'm not energizing it back in
00:54:20.762 -- let's say days or weeks. So does it die out and not? It does
00:54:25.746 -- decay OK, so basically it's a it's a thermal process. So
00:54:29.662 -- basically these are going to try to randomize if the car is warm
00:54:34.290 -- when you demagnetize it, then they tend to randomize faster
00:54:37.850 -- than if the core is cool as the core as a transformer cools that
00:54:42.834 -- slows down the rate.
00:54:44.460 -- That randomization OK, but even if it's gone to zero an you
00:54:48.900 -- closing your somewhere up here still we're going to have
00:54:52.970 -- some issues on that.
00:54:57.930 -- Awhile back, well actually one of the Masters students here who
00:55:01.989 -- works at Sweitzer. Now guy named Doug Taylor looked at using a DC
00:55:06.786 -- source to preflex the transformer so you could put
00:55:10.476 -- the trap flux at a known at a known point and then if you have
00:55:16.011 -- Breakers with individual phase control then you can control
00:55:19.332 -- when you close them.
00:55:22.220 -- They also are using variations of that an like.
00:55:28.760 -- There's been a lot of stuff looking at that in Europe, for
00:55:32.324 -- example, in some of the offshore wind farms where they basically
00:55:35.591 -- are in a system that can't supply that magnetizing current
00:55:38.561 -- to magnetize the core, because there isn't a source strong
00:55:41.531 -- enough to provide it out there.
00:55:44.090 -- And so they want to be able to close the Transformers with no
00:55:48.276 -- inrush. And so rather than pre flexing the cores, they're
00:55:52.692 -- looking at trying trying to dissipate the flux in the
00:55:56.960 -- core so that they can bring it to zero, and then they do
00:56:02.004 -- individual phase control on the Breakers to minimize the inrush.
00:56:07.670 -- Also the whole pre fluxing minimize trying to get the
00:56:10.730 -- known side of inrush makes a big difference. If you have a
00:56:14.402 -- five legged core versus the three legged core.
00:56:18.190 -- So when you see the anticipated, basically they figure out at
00:56:21.644 -- what time or what voltage at what point in the voltage the
00:56:25.412 -- breaker was opened, and then based on that they calculate the
00:56:28.866 -- residual magnetism and the decay, and then they open
00:56:31.692 -- individual phases at different times. Or they close them, they
00:56:34.832 -- close them at specific times. OK, so the Breakers are always
00:56:38.286 -- going to try to open it. A natural current 0. Sure, an
00:56:42.054 -- there are actually some big problems if you don't open it in
00:56:45.822 -- natural current 0, because then you can get very big.
00:56:49.350 -- Transient response if you do a current shopping.
00:56:53.590 -- So the parasitic capacitance of the winding will interact
00:56:56.560 -- with the magnetizing branch, and you can see like 2 / 2
00:57:00.520 -- per unit voltage.
00:57:03.600 -- Even if you're chopped like half an amp.
00:57:11.700 -- That's a topic more for you. See 524 though.
00:57:20.290 -- OK, so any other questions related to the magnetizing.
00:57:24.950 -- Current behavior.
00:57:27.630 -- So these are all things that need to be accounted for in
00:57:31.758 -- creating the differential element an in setting like
00:57:34.510 -- the slope and the minimum operate current.
00:57:39.090 -- The other one to look at is going to be the transformer
00:57:42.342 -- phase shift.
00:57:49.760 -- So I started out drawing a YY transformer.
00:58:00.000 -- So the other thing we have to look at is Delta Y.
00:58:04.150 -- Or why Delta Transformers?
00:58:22.310 -- And so in North America there's an ANSI IEEE standard so that
00:58:27.926 -- the phase shift is generally very predictable, right?
00:58:33.330 -- And what's the standard?
00:58:37.720 -- Sorry. The high side is leading by $30.
00:58:59.020 -- So V line the neutral in the high voltage side leads
00:59:01.902 -- vilanda neutral in the low voltage side by 30 degrees.
00:59:06.370 -- The Power systems textbook I used when I was an undergrad
00:59:10.055 -- gave the impression that whenever you had a Y Delta
00:59:13.405 -- transformer or the Y side always led the Delta side by 30 degrees
00:59:17.760 -- because the author in.
00:59:20.620 -- All the cases he had run across the Y side was always
00:59:24.328 -- a high voltage transformer, 'cause he'd always worked in
00:59:27.109 -- transmission and never worked in distribution.
00:59:38.430 -- And so. So one of the effects were going to have
00:59:42.274 -- obviously is the 30 degree phase shift this also.
00:59:58.400 -- The Delta Y connection also
00:59:59.820 -- impacts the. Turns ratios right. So now you've got this other
01:00:03.574 -- sqrt 3 that gets put in there in addition to having.
01:00:11.110 -- The voltage transformation ratio.
01:00:14.910 -- That sqrt 3 shows up in the current so that reflects
01:00:18.320 -- back to the CTS.
01:00:23.620 -- And let's say that we have a Delta Y grounded transformer.
01:00:28.640 -- So this side.
01:00:41.830 -- When we're measuring the phase currents, there's going to be 0
01:00:45.537 -- sequence current on this side, but there won't be on this side.
01:00:53.200 -- And so even some Even so, one of the things that you have to be
01:00:57.550 -- careful of his solutions to try to fix this phase shift.
01:01:01.490 -- And fix this also after account for this. So I said that they
01:01:05.871 -- are one of the solutions that people did for less mechanical
01:01:09.578 -- relays. Had to have an extra step added to it because of
01:01:14.094 -- the zero sequence kind.
01:01:26.250 -- So if we have a transformer.
01:01:47.130 -- So we can look at the CTS.
01:01:51.140 -- So for electromechanical relays.
01:02:00.880 -- The common solution in this for this was going to.
01:02:06.860 -- To use the CT connections to help cancel for the cancel this.
01:02:12.520 -- And so.
01:02:16.250 -- So one option.
01:02:31.830 -- Would be to connect the CTS on the Y grounded side in Delta.
01:02:38.340 -- And the CTS and the Delta side and Y.
01:02:57.440 -- You need to make sure you connect the Delta properly to
01:03:01.092 -- cancel the shift. But So what that means is that the that the.
01:03:07.110 -- Phase currents that the Delta phase currents.
01:03:12.580 -- Well, include the zero sequence current that's going
01:03:15.148 -- to circulate in that Delta, but then the line currents
01:03:18.358 -- coming off the Delta which go to the differential relay
01:03:21.568 -- will not have.
01:03:23.640 -- That current
01:03:29.600 -- morning your device is running low on memory.
01:03:37.470 -- So one of my colleagues has a sledgehammer. He brings the
01:03:40.737 -- class for people whose cell phones make noise during class.
01:03:47.100 -- The new phone is trying to shut it down.
01:03:52.290 -- And so this is so, you still will run across substations that
01:03:57.018 -- have the CTS wired this way from the electromechanical relays.
01:04:03.920 -- And then a second option.
01:04:16.440 -- Would be the connect.
01:04:18.660 -- This it is an Y and this it isn't Delta.
01:04:24.240 -- So yes, there's a problem with this one, right?
01:04:30.810 -- So now the.
01:04:35.270 -- The differential element on this, the current that goes to
01:04:38.140 -- the differential an element from this side, it's going to include
01:04:41.297 -- zero sequence current. The one in this one won't, right.
01:04:45.970 -- So this one is going to need.
01:04:55.020 -- So basically this one needed an auxiliary set of current
01:04:58.210 -- Transformers that would block the zero sequence current by
01:05:01.081 -- basically circulating it in the auxiliary Transformers and
01:05:03.633 -- not have a go to the differential element.
01:05:26.570 -- So now if you go to a substation where it's new
01:05:31.553 -- construction and it's designed not anticipating
01:05:34.271 -- that there's going to be microprocessor relays
01:05:37.442 -- protecting this.
01:05:47.680 -- Now the seats are going to be why on both sides and there
01:05:51.632 -- will be a ground reference in the seat path.
01:06:19.860 -- And it will also the CTA will basically perform calculations.
01:06:24.340 -- To compensate for the phase shift an it's going to
01:06:28.920 -- perform another calculation to remove I 0.
01:06:35.480 -- And these are actually going to be matrix multiplications.
01:06:48.380 -- So I have a handout that.
01:06:51.350 -- Maybe I will pass it out today. You need to
01:06:53.950 -- remember to bring it.
01:06:57.250 -- Don't be sorry.
01:07:13.600 -- And so.
01:07:18.360 -- This first calculation is basically.
01:07:23.660 -- Typical calculation that you would see.
01:07:27.220 -- Done in the relay.
01:07:29.840 -- For the.
01:07:32.120 -- As an intermediate step for going to the
01:07:35.264 -- differential element.
01:07:37.540 -- So you're gonna have.
01:07:40.570 -- You're going to have the primary currents. Then they're going to
01:07:44.112 -- be divided by the current
01:07:45.722 -- transform transformation ratio. Remember, these are
01:07:48.686 -- why connected.
01:07:54.000 -- And then there's also going to be this tap calculation, and
01:07:57.744 -- the other hand out goes into more detail about the how this
01:08:01.488 -- tap is calculated. And then there's going to be a correction
01:08:06.020 -- matrix, so the correction matrix the output is going to be the
01:08:09.920 -- secondary current with the phase and zero sequence correction.
01:08:16.110 -- And so the current from both windings are going to. So this
01:08:20.190 -- is actually. This would be the primary side, and then we're
01:08:23.930 -- going to secondary sidewinding. So this is actually.
01:08:27.470 -- The power transformer primary.
01:08:53.070 -- And then the correction matrix, or a number of correction matrix
01:08:58.240 -- we can do. And so when I say matrix zero, that is using the
01:09:04.820 -- IC Clock terminology. So if we think about o'clock, we're going
01:09:09.990 -- to have 12369, etc and then 12.
01:09:13.890 -- 12 is also equal to 0, right?
01:09:19.820 -- And so if we have a Y connection with, if you say
01:09:24.212 -- that we have basically our phase, a voltage is going to
01:09:28.238 -- be here at an angle of 90 degrees. That's our zero
01:09:32.264 -- position.
01:09:37.340 -- And so the Matrix Zero is assuming we have a Y
01:09:40.783 -- connection and we're not trying to do any reversal of
01:09:43.913 -- the voltages, so this will be just the identity matrix.
01:09:53.370 -- And then where matrix one is the one o'clock position and this is
01:09:59.129 -- one that in.
01:10:00.540 -- South America is often referred to as the DAB and
01:10:03.490 -- this would be a Delta.
01:10:08.250 -- AV connection so that means that the first winding of the
01:10:11.583 -- Delta is connected from A to B. The second line will be to
01:10:15.522 -- see the third one will be see to a. This gives you remember
01:10:19.461 -- North America. You're limited to either plus 30 degrees or
01:10:22.491 -- minus 30 degrees when you're going from Y to Delta. So all
01:10:26.127 -- we care about in North America is going to be the D1
01:10:29.763 -- in the D11 connection.
01:10:33.240 -- And then we have the D11 connection, and so if we
01:10:37.398 -- compare these all it's doing is exchanging
01:10:40.044 -- which rows are have the.
01:10:43.410 -- Then have the different column combinations.
01:10:47.840 -- And so, well, we'll talk about this a little bit more, applying
01:10:52.172 -- it in the other example.
01:10:54.970 -- And then, as I mentioned, we have that we need that zero
01:10:58.054 -- sequence removal matrix too.
01:11:03.900 -- And so that's what this one does.
01:11:08.460 -- And so this is mathematically reproducing
01:11:10.410 -- the effect of the current circulating in the Delta.
01:11:20.750 -- Anworth this what this is coming from?
01:11:24.700 -- A very good reference for summarizing this is.
01:11:31.420 -- A paper that was written by.
01:11:35.230 -- I group from Basler Electric John Horack.
01:11:37.659 -- Actually, I have a link to on their class links web
01:11:41.476 -- page. I have a link to webpage it he's got put
01:11:45.293 -- together an extensive web page was protective
01:11:47.722 -- relaying. Related links.
01:11:51.260 -- And so I did not. I gave you copy. It's, uh, some of the
01:11:54.676 -- pages from this paper. I have links to the whole paper on
01:11:57.604 -- the course web page. That's the on campus students. There
01:12:00.044 -- were some of the pages that I'm going to talk to talk
01:12:02.972 -- about today and next time.
01:12:06.810 -- So this is just showing sort of the connection information
01:12:10.070 -- as a reference for the rest of this paper.
01:12:16.410 -- So.
01:12:18.450 -- He has uppercase letters to indicate the primary lowercase
01:12:22.635 -- to do the secondary.
01:12:25.520 -- And then he has the third of the terminal ends an the.
01:12:31.060 -- So this would be the polarity end of the wine,
01:12:33.656 -- and this is the nonpolarity end of the winding.
01:12:40.150 -- And so. This is one of the things that you go through.
01:12:45.030 -- You're going to find different people in different places, use
01:12:48.580 -- somewhat different notation so we see UV WABC.
01:12:52.070 -- And so on.
01:12:59.290 -- And so if we wanted to build a YY transformer in a typical
01:13:05.166 -- North American connection so when we see the W1W 2W3, those
01:13:10.138 -- are referring to the winding.
01:13:14.330 -- The windings of the six windings that produced the
01:13:17.372 -- three phase transformer.
01:13:21.590 -- And then it's not very obvious, but these are his
01:13:24.910 -- polarity marks for those windings.
01:13:28.910 -- And so H1X1 this is high voltage. This is
01:13:31.664 -- low voltage and so on.
01:13:34.330 -- And so mapping these this is how they would map.
01:13:39.870 -- Tell the two winding sets.
01:13:47.510 -- And so winding one and winding 4 on the same course.
01:13:50.282 -- So these two are going to be in phase with each other.
01:13:55.700 -- And so you can use this to build the diagram for how
01:13:59.168 -- the transformer ones relate to how the windings relate
01:14:01.769 -- to each other.
01:14:06.900 -- And so then he goes on to look at.
01:14:15.830 -- So the basically the Y zero is the one that's most
01:14:19.669 -- common in North America.
01:14:24.100 -- And so we can look at things that change polarities by so
01:14:27.556 -- the Y four is now we're shifting things down to the
01:14:30.724 -- 4:00 o'clock by putting winding one connected to Phase
01:14:33.316 -- V.
01:14:35.850 -- White and then we can just look at all these different
01:14:39.546 -- combinations. WHI Six is just reversing the polarity so the
01:14:42.906 -- polarity marks reversed unwinding one.
01:14:47.440 -- And so this is another one that is more of an industrial
01:14:51.076 -- power systems one, but you'll sometimes see Transformers
01:14:53.500 -- with wired opposite of the polarity marks.
01:14:57.580 -- Then he goes through the same thing with Delta windings.
01:15:02.450 -- So the. And so next time we'll go back and look at
01:15:06.270 -- this in terms of a Y Delta transformer. How we do the
01:15:09.054 -- plus 30 if the Y is a high side, how we do the minus 30?
01:15:12.534 -- If the why is the low side?
01:15:17.010 -- And so this paper goes on to kind of lead into deriving
01:15:21.402 -- those connection matrices.
01:15:24.560 -- And so we'll finish talking about this paper next time, and
01:15:28.014 -- then we'll talk about the.
01:15:31.130 -- Example handout so that we're going to apply these
01:15:34.622 -- connection matrices to measurements for a fault.
01:15:38.450 -- We can look at an internal fault or an external fault. We
01:15:42.458 -- can also look at what happens if somebody accidentally left
01:15:45.798 -- ascete shorted in the substation and how that plays
01:15:48.804 -- through these connection matrices.
01:15:51.560 -- So with that, well, any questions before we stop.
01:15:55.730 -- OK, and just a reminder for the outreach students.
01:15:58.115 -- There is no class on campus next week, so there will be
01:16:01.295 -- no new lectures for a week.
01:16:05.650 -- OK, that's all done.
Okay, welcome back.
We're going to jump back into this cost accounting.
The first topic under the business essentials left off last time getting ready to talk about overhead, so let's see.
So overhead this is, let's sit there in my notes.
This is the this is the most uncertain part of product and service cost.
How do we assign overhead to this cost of goods sold concept?
As an example, at the University of Idaho here we do research.
Our overhead is roughly 50%.
I know that may seem high to some people, but I also know like it at the national labs it may go up to 100 a 125%.
You know, it can be a lot, lot larger than that.
All rates actually set by the federal government because they do that for all universities and they look at the cost of your facilities, they look at your administrative costs, support staff, things of this nature.
And in fact here it's called F and A facilities and administration and they they have a formula they use and Add all that up and come up with that indirect rate.
I also another another example.
I also know that in general, if you look at the budget of the university, about 45% of the expenditures of the university go to the academic colleges like the College of Engineering, the College of Architecture and so forth College of Science.
The other 55% is non academics.
So it would be like the grounds, the facilities and buildings, heating, cooling, Provost, office athletics, the research office, HR, you know, president, all these other kinds of things that make a university operate so that you know that's not exactly overhead in the same sense as this 50%.
But it kind of just give you a sense that or appreciation that that the cost is never just direct and there's always other costs associated with direct cost to give you that final cost of something.
Now if you're a company with a single product or perhaps a single kind of service, you know traditional method of just slapping on a percentage is good enough.
Generally that's not that's not the best way to go.
In fact even at the university if you think of the indirect of the F and A as like a almost like a tax on your direct cost, when money comes into the university it comes with with variations in that money comes.
Say a company pays for sponsored research.
They're going to pay about 50% for the F and A.
If it's something on the order of a just a specific service to procure something, it'll get taxed at 10%.
If money is coming from another state agency, it's limited to 20%.
In a way.
As a student in, you're paying tuition.
You're essentially paying 55% if you want to think about it from that 4555 split.
In fact, probably a little more because the cost of the academic colleges has administration built into it as well.
So if you looked at just the cost of your professor versus other things, you might be paying a little higher indirect.
But anyway, the bottom line is that there's always these other other things that cost money that are not direct cost of the product or service.
We have to account for that if a company has multiple products, each one is sort of redundant here, but each one has different level of resources to produce it.
So a better method is to account for be more specific about accounting fed overhead to give you more complete and a better better picture.
So here's some some simple allocations of direct cross.
So let's say you have a plantwide overhead rate, you can add up all the indirect charges.
So faculty managers, salaries, office support, depreciation for buildings, equipment related to production, office support, utilities, training, safety, maintenance, da, da, da, DA of the last year.
This is kind of what I was saying about the federal government calculating the F and A for the university.
They they have the specific things that they look up for our school and then you divide it by the total person hours spent last year to obtain an hourly overhead charge.
So that's what you would put on top of your your hourly rate and then you add this to the product involved based on labor hours needed.
So that's one way of of of accounting for this.
Then there's a departmental overhead rate so that the nature of the work performed determines that overhead rate.
If it's a machining department, then you might look at say, machining hours.
If it's assembly department, you might look at the direct labor hours involved in the in the assembly.
So there's, you know, there's different ways to account for this, which leads us into this topic called activity based costing.
So the notion here is that in in a BC you're attempting to assign overhead cost by using number of allocation bases each representing a major activity that causes the overhead costs.
Example would be like setting up machines, meeting meeting pages to a hospital, scheduling production, performing blood tests, billing customers, preparing shipments, DA, DA, DA, DA, right.
So you have all these activities and you're trying to assign essentially you're trying to assign an indirect or an overhead to those activities because they're all different, they're all going to take different non direct expenditures to make happen.
So here's, here's an example from an income statement you can see you know sales revenue, cost of goods sold, gross margin.
Essentially what you're trying to do is you're trying to trace the, you try to trace the indirect support cost and to activities and then on to products.
And again, this says most most useful with numerous diverse products and especially if the indirect cost make up a large fraction of the total cost of goods sold, especially if you're you're not, you're not dominated by the direct costs, ABC becomes even more important some some key terms.
There's what's called cost objects.
Again, I don't expect you to memorize these.
I'm just trying to give you an appreciation for the lingo.
There's, you know, these are like targets for applying activity based costing.
So your products, your service, your customers, that's your your, your objects.
Then there's the activity.
These are this, it says they're homogeneous groups of work.
That's pretty, pretty verbose explanation, but again you're accounting, your machining, forging design these activities, you know all these tasks that are very similar, they provide an activity and and the idea here is that you need a second activity if the overhead that supports that activity becomes significantly different.
And so that's going to give you because that's going to give you a distinction.
I mean if if you have the same overhead you might just have it be 1 activity and then you have your your drivers in your pools.
So these your drivers and your metrics used to measure the extent of an activity and the pool is the organizational unit supplying the value added activities.
OK, well, let's look at a couple of examples because it's not that clear.
All right, cost drivers.
Storage, like you know, could be like the square footage of of storage space needed for an activity.
Maybe there's loading, there's material movements.
These are things that are not direct cost, but you know, loading, unloading, transporting, picking up, setting down setups, inspections, maybe.
Could be machining, could be transportation, driving around, processing invoices, numbers of production.
These are all things that drive costs.
Now notice because some of you have a, you have a background lien, I'm not talking about those that are value added or those that are wasteful.
I'm just saying these are just cost drivers.
So these are things that they did, they drive cost, they add cost to the product.
OK, some you might try to get rid of, but they're but the but these are what's associated with it.
And then you have your pools, these be your plant, your office support, your maintenance, marketing, design, development, procurement, plant engineering and so forth.
These are things that you know if you're a call center, these are, I mean a profit center.
These are things in your call centers that are leading towards your overhead.
That's why I think you should now, you should be able to now it should be sort of making sense here.
You have as a, as a as a profit center, you've got say products or services with direct cost of service here then.
But now you have all these other support services that are you need them.
But what you're trying to do is you're trying to allocate the cost of those activities onto your products.
So the basis, so various activities are needed to create and support products and services.
Each activity is measured by the applic, by the applicable cost driver and cost pool supply the activities needed for the products and services.
So the cost assigned only to those products and services requiring the applicable activity and then activities consume cost pools.
So again, this is a lot of lingo here.
To put it in simple, more layman's term, all these support activities, training, HR, whatever you mean you need them you can't function without that stuff Okay.
You have to allocate that to your direct cost as a way of coming up with the cost of the goods sold definition.
So when you think about it from that perspective, all this kind of accounting jargon, you know it just gives you an appreciation of what that really what that is all right.
Some of the value added by activity based costing if you when you go through an activity based cost and exercise you, you actually get a clearer picture of which cost objects generate profitability or losses.
So this is, this is one that I've I've observed this to be fairly critical here.
A lot of times companies will, they'll provide a whole variety of products and a whole variety of services and not have a very good grasp of how they contribute to the profitability of the organization, especially if you're in a lower competitive environment.
It it's just doesn't get to be that significant.
I know we've tried a little bit of this at the university to try to grasp a little bit about distinctions between degree programs and so forth.
For example, not, not necessarily using this terminology.
By using these principles and the the idea here is to you're trying to maximize profit by focusing on what products and what services you provide when.
If you just slap on one general overhead rate everything, it really masks the dependency of that product on these indirect services.
And can you can be you can put in you know an appropriate overhead rate on everything when you determine what you're going to sell a product for and still be losing money because you haven't specifically attributed to that product based on the services it provides.
So this also by going through a BC you can identify areas for continuous improvement and possibly eliminate non value add activity.
So in other words, if you find that you go through an ABC analysis and suddenly instead of putting 50% overhead on this particular line of product, you've got to put 90% on it.
Well, maybe you're maybe you're actually going to be losing money by producing that.
And so that's an opportunity to make changes, to get to get it to be profitable because you don't want to be losing money.
Now you know, people argue that Okay Costco loses, they lose money on their rotisserie chickens and maybe that's true, but it's it is, But it's a real marketing gimmick.
So they put in the back of the store.
So you have to go back there to get your get your Costco chicken, right.
So you know there are some instances like that where it becomes part of your brand and part of what you do.
You also might be in a situation where, yeah, you might be even with a BC and in a better understanding of the indirect costs associated with a particular product, you know you're losing money on that.
But you've got to maintain that at a competitive cost to your customer because you don't want them going someplace else because you don't carry this segment of the product.
You know, you may be making all these pieces of protective equipment, but you decide you can't carry this lower end because you're not making money.
Well, now you're fortune or customer to go someplace else to get that.
And what if they get intrigued by another supplier?
So there's there's a number of decisions that go along with this kind of gets back to what I told you the very first or second lecture that you know all all these decisions you make are subjective.
You've got, you've got information that's provided to you as engineering manager.
And so the ABC analysis may tell you that you've got the, you've got an unprofitable product in your in your family of products.
But you still make the decision to lose money on that because you feel it's essential for overall business.
And that's fine, OK.
Just as long as you know why you're doing it.
And that's one of the things that a BC does.
It helps make these things known, give you more information, more detailed information, so you can make better decisions.
Let's look at this, this application of in XYZ manufacturing.
This this is on page 150 or so of your textbook.
So says here.
XYZ company with 10 million annual sales makes components for the automotive industry.
The key processes include forging and machining and the operating activities are buying steel bars, checking the steel bars and moving the storage.
When needed for an order, workers move the bars in bins of 20 to 25 to an area where the bars are sandblasted and cut the length.
The bars are forged to shape and then move to an in process storage.
For each forging procedure, the bars are moved from the in process storage to the forging area, then back to the in process assessed storage.
After the final forging, the bars are moved to the machining area where they're finished.
Sent the finished goods storage and find the finished goods, go to the shipping area to be sorted, packet loaded onto the trucks and delivered to customers.
So immediately you see an opportunity for the T bar accountings or the T accounts.
So here's these 7, excuse me, these seven activities.
And you know, you might look at that and say, well, there's a lot of wasted activities going on here, which I would agree with, but we're not going to get into that right now.
We're just going to look at this from an ABC perspective.
So before ABC, the company used a traditional approach to overhead, just tacking the percentage on to each labor hour.
So you have the seven activities, there's labor associated with all seven.
They know how many hours each one takes and they just slapped on a percentage to get the cost of each of those.
Now we're going to implement active based costing.
So we look at set up only assigned to parts which were produced by the equipment forging the press operating cost based on the press hours production, labor cost based on labor hours, induction heating cost based on parts weight, the machining or just the machine hours worked material movements.
It was the cost to sign based on the cost per move.
And then the raw material procurement and ordering was the cost of associated with the actual cost on the records.
What is it actually?
What does it actually cost to do that?
And as you might guess, each of these things set up 4G machining, material movement, raw materials, they're all they take different levels of activity and support and so they're going to have a different overhead rate.
So here's the again, this is Table 6 two in your text.
So you can see you have your forging press hour cost, your machine hour cost, heating and so forth.
And then you can see there's just looking at the foraging, there's things that are directly attributed cost depreciation, utilities, manufacturing, supplies, outside repairs.
And then there's distributions, there's maintenance, building grounds, manufacturing, engineering, commodity overheads, some have supervision.
All these together give you a total cost which results in a particular rate per hour.
And so you were to get a different, you're going to get different basically different overhead rate for forging than you're going to have for machining because you have, you know different different support costs associated with those.
So what was the results of this particular exercise?
Well, the the company's sales tripled and it's profit increased fivefold due to a more profitable mix of contracts by an improved price quoting process consistent with the actual cost structure made over by the ABC.
Now there's a lot in that in that comment from your author because or I should say there's a lot of assumptions made there.
One, they were able to, they were they were able to get more money for certain products.
So there was some elasticity in that price, which was good.
They most likely change the product mix.
He didn't didn't want a lot of details here, but they most likely change the product mix, maybe they change product volumes and so forth.
A number of things that had to go into because the ABC doesn't do this for you.
The ABC provides direction and then you have to go in and take action based on the ABC analysis.
So let me let me say that again, activity based costing does not triple your sales, increase your profits and so forth.
It just shows you the opportunities you then have to go in and make that happen.
But at least you've got an idea of of what your opportunities are.
You know you may have been overpricing a particular product because it's heavily relied on forging and more than another product and so it had a much higher overhead than it needed to have.
And now you can bring the price down which makes you more competitive with your with everybody else and get your volumes up and overall profitability.
I don't know, but all I'm saying is that what the ABC does is it, it presents opportunities, provides guidance, but you still have to go in there and take action on that.
So the isolation of and measurement of material movement costs result in operational changes for increased efficiency.
So these are some results of this implementation targeting process improvement.
So this is kind of getting where I was just starting to say activity based costing can be used to identify activities that would benefit from process improvement.
This is sometimes called activity based management and this focuses, this involves focusing on activities to eliminate or reduce waste, decrease processing time, reduce defects.
You know you might just gets back to what I was saying a little bit earlier.
You might look at all that material handling going on and go, my gosh this is adding a lot of cost to this step.
Can we do something, maybe reduce batch sizes, maybe move things directly to work in process, not put them inventory and pull them out again, some things like that that that sort of your weaknesses have been revealed by the ABC activity.
So ABC is applied across a diverse group of industries, not just manufacturing.
It's kind of the simple example that I've presented here, but it's certainly used in other places.
So you basically, you know you need to decide what you're going to improve and again that that comes about where primarily you see discrepancies between the overhead rate that you got from a BC versus the traditional one overhead rate for everything.
So decide what you're going to approve, determine the right set of activity rates that drive those costs, decide what you're going to improve using things like theory of constraints or lean or whatever benchmarking and then you know fixing, fixing the issues.
I thought I'd I'd just sort of just dropped a term on you there.
I'll just briefly briefly mention this idea of theory constraints.
Some of you may have heard of the, the guy Goldrot kind of attributed with this idea of theory constraints.
This was really, you know initially popular back in my gosh, probably back in the 90s I think.
But it's this idea of looking at your, looking at your, look at your process and identifying the bottleneck, where is your process constrained and then focusing on that constraint and making improvements.
So it's no longer your constraining process and and then relooking at your entire process to identify the new constraint.
And so by focusing on your constraints, your main constraint or your bottleneck, you can improve the profitability of the entire process.
So I remember this would have been Mac probably in the early 2000s.
There's a company I was working with called you may have heard of it's called J Bill and they were they were basically losing losing money on a surface mount line And so I went there to to help them look at that the we we basically applied their constraints.
We looked at the production process and what was happening is by watching the the flow of material through all these steps, there was a setup for testing and it became quickly obvious that that was the the constraint or the bottleneck in this process.
It was actually dumb easy to determine because there's all sorts of crap piled up piled up before in front of this waiting to get into this testing setup and and so we went and looked at that made some changes to speed up that constraint or other words, that bottleneck and improve the flow of material so that it was no longer the IT was it was still the bottleneck.
We never did figure out a way to get rid of that without significant capital investment, but it was it was still much improved and so it really didn't make that much difference.
We were trying to make another steps of the process until we got that one solved.
That was that was the real kicker right there is by using this idea of theory of constraints to know where to focus in interesting interesting story the the end result of that was the the the real problem had nothing to do with production, had nothing to do with the inspection station.
What it really had to do was was sales practices.
So what was happening was that the salespeople, in order to meet their quarterly goals, see if I I'm trying to remember this correctly, in order to meet their quarterly goals, they were heavily discounting product the last few weeks of of the quarter.
I think it was 1/4 process.
And and so by doing this, what they were inadvertently doing, it was sort of like this, this idea of Pavlov's dog.
They were basically training their customers to wait until the price dropped to place orders.
And So what was happening was that by doing that they were getting, you know, this level of orders coming in and all of a sudden the last few weeks orders went up and then when the new quarter started and the prices went back up, guess what happened, orders dropped down.
And so they were inadvertently introducing huge variabilities into their process by by this sales tactic and so poor, poor production that there's no way they could keep up during that window of time.
And that that was the real problem.
Interesting interesting situation.
So I got got distracted there.
Process improvement examples.
So here's some other examples given to you by the author.
There's a like in a Medical Center used activity based costing to improve one of the most expensive and error prone processes within the nursing unit that's ordering, distributing and administering medicine.
It showed that 43% of the nursing operating operating costs involved medical related activities.
They did a recall so that so the ABC just showed that right that's what it's shown but it didn't it didn't solve the problem it didn't make any improvements.
It just said hey we got a lot of overhead a lot of things going on with this particular activity.
Then they applied root cause analysis and what they found was the biggest problem was Allegibly or say this right.
The basically when the when the physicians faxed their their prescriptions to the pharmacy you couldn't read the thing.
And I think we've all have seen that this scribble that goes on.
I mean I just got a I just got a prescription for a rash a few weeks ago and the directions on the bottle are totally different than what the physician told me during my office visit.
I had to call back in and get and I'm sure what happened is they couldn't, they couldn't read what was scribbled down.
So yeah, so I've seen this directly.
Anyway, they they did, they figured out.
And So what they did in this case is they replaced the fax machine with a much better one that made it easier to read what the scribble that the physicians were turning in.
And that decreased a lot of these followup calls, which these followup calls were part of the overhead that was now attributed to this process, which before it wasn't put on there before.
So again, this is a way of using a BC as a way of identifying opportunities for process improvement, not making the improvements, but where the opportunities lie, some of the limitations of activity based costing the cost of implementing and maintaining an activity based system may outweigh the benefits less.
Like it's like any any process that you've got at your organization, you have to look at the cost of managing that, whether it's doing the FM EA, whether it's doing the ABC, it's the T accounts, whatever.
You know, look at the cost benefit of the implementation.
And then the ABC implementation relies on a number of critical assumptions, specifically that the cost of an activity cost pool is proportional to its activity measure.
That's not always the case.
It's not always just the time and you may need to include a distinction between manufacturing and selling and administrative expenses.
In other words, you may need to get more down into the guts.
Not just how many hours does this take multiplied by an hourly rate, but look what what are those kinds of hours and and be a little more fine grained than that.
There's you can you can do this in all levels of detail.
There's obviously you can just put a simple Excel together to track your activity.
You can buy activity based costing software that operates on computers that will just take inputs and magically provide reports and things for you.
There's all sorts of ways to implement this.
So you know, I'm mostly concerned that you understand just the concept of a BC and what it actually does for you more than you can actually, you know, do an analysis and calculate numbers and calculate exact overheads.
If if if you're actually going to get into it at work, you'll have, you'll have a lot more concerns to deal with what we talked about in this class, it's just to get you familiar with that process.
So in summary, activity based costing can improve the accuracy of product cost in, in a whole number of ways.
It can increase the number of cost pools.
Your cost pools can be more homogeneous.
You can use a variety of activity measures.
It highlights the activities that could benefit most from improvement initiatives.
And you know it's still, as I said before, it still requires we apply our engineering management judgment to the problem at hand.
We still have to decide, you know, we've got, we got an opportunity here, what we could do about it.
But what this does do is does give you an analysis process with a little more fidelity to decide where to make improvements.
And you know, when you just slap on a single percentage overhead to all products or all activities, you're just not going to get that insight that you'll get from a BC.
And so again, depending on the size of your organization, you may find accountants that you can nerd out with on this.
But I think just what we've discussed and what's in your text at least give you an appreciation that you can least communicate now with your peers at your organization on this okay risk analysis.
So we're going to take the next half hour and I'd like to kind of talk about this topic a bit.
Again, going back to this notion of variation.
We live, we live in a very uncertain world.
We don't know what's going to happen.
The future Lord knows when the pandemic hit Nobody.
Nobody could predict that.
Well, at least not not, you know, months in advance, you know things, things just happen.
And so the future is more or less uncertain.
You have events, you have you know the economy.
There's different countries involved, competitive factors, technological breakthroughs.
I was just listening to report this, actually found this a little bit fascinating where Microsoft is coming up with a different kind of search engine.
So just instead of you know putting terms in your in your Bing, which is pretty lousy these days and having it come up with a list of websites that you can search, you can actually in natural language entering your question you know what What would be a good dinner to make my wife for Valentine's Day here in a couple weeks and it'll come back with a personalized response.
So total total shift and actually using using the web because really when you get down to it you're, you know that's really more what you're looking for.
You could you could Google in, you know Valentine's dinner and get some websites and search around trying to figure out what makes a good dinner.
But to actually ask a question have it come back when the answer that's that's pretty cool.
You know that's that's a technological breakthrough and and we and if you think back just even in your lifetime you've seen these you know I see things like you know cell phones and all that.
I mean all these kind of breakthroughs, they change.
They do change the future.
So you have all this uncertainty that goes on.
How do you estimate cost?
How do you estimate task completion dates, manpower requirements, the customer needs, market share, all these kind of things?
How do you estimate these things when you have all this uncertainty going on?
And obviously, the further out you have to look, the less certain it is.
But the reality is you can't.
You can't ignore the uncertainty.
Don't mean you can, and we often do, but to your peril.
So the more sophisticated you can get at understanding that uncertainty, the better your initial estimates can be.
So let's let's start off talking about this notion of risk.
So risk is a measure, I'm just going to read this because every words important here.
Risk is a measure of the potential variability of an outcome from its expected value.
So a couple key things here.
It's a measure.
So we we're trying to quantify this, we're trying to quantify risk potential variability because we don't know what that variability is, but the potential for variability of an outcome from its expected value.
So you expect one thing, but there's potential of getting another that's your risk.
And so typical applications of risk analysis are cost of products, cost of services, schedules, you know you're you're, you're, you're getting things all set up to move into a new facility and you're making purchases because you got six month lead time, you got eight-month lead time, you got things like this going on.
You're making these investments because your new facility is going to be done September 1st and you want to gear up so you can start to occupy it.
Well, there's a risk, okay, because September 1st is your expected value, but it could be October 1st.
I, as I said in my in my opening lecture, you know, I last year went up to Coeur d'Alene to run EU of I campus with a expected end date of December.
The reality was the following August there was a risk and we experienced that everywhere in our life.
We experienced that.
And typically the risk decreases as you get closer to the actual thing at hand.
The risk is greater when you get further out into the future.
Sort of intuitively should you should see that.
So what are some common techniques that we do to account for risk?
Well, first there's contingency factors and we're going to, we're going to talk about each of these in more detail, but you have contingency factors which again we'll just, we'll just go there as we get to them.
You have simulations, there's sensitivity analysis, decision trees, diversification, there's fuzzy logic systems, there's other things other than this, but these are just a handful of techniques that we're going to address today that give you some ways to account for that risk that's involved in the uncertainty of the of the future.
So first thing, contingencies.
I mean, there's both empirical and subjectivity to this approach.
Based what you're doing is you're adding a lump sum to the total budgeted cost to account for Lord knows what.
A lot of times that's 515%.
This contingencies factor is less for repeated projects and more for new programs.
If you don't have any prior judgment, she might put a larger contingency on it.
Just as an example what I've dealt with at here at EU of I, all facility projects carry mandatory contingency of 10%.
So when I was I, you know I had, I've done several facilities, I did a something called the Think tank.
It's a student services center here on campus.
Built a coffee shop for the students, put in, did remodels on various things and so I had to deal with facilities, put a engine lab in across the hall.
Each of these cases I worked with an architect, we designed plans, we came up with initial costs and facilities always made me put 10% slap on top of that.
Trying to think, yeah, there was this pretty standard.
And what was what was interesting there is because for the most part, the most part these projects were built with donations from corporations and alumni And so I had to go out and raise the money for for making these changes.
And if there was a it was you got a little frustrating because there was a project like when I did the when I did the conference room, I knew you know I had I had like 35,000 that was earmarked from one of our donors that wanted that project done and I made the estimates.
I knew what was going to cost.
We designed it to fit there.
They still made me come up with another 3 1/2 thousand in the budget before they would proceed work, you know, so I had to do some juggling around, put the money in, did the work and I can then took it back out.
So didn't have.
You don't have to spend the contingency, but you have to have this in.
And again that's they're doing that because you know, I'm, I'm estimating these costs here in April, but they're not going to get around to making the changes until September.
And so they're trying to put in this little buffer contingency in case things go awry because there is uncertainty.
And you know, back when I did that, things were pretty stable.
Had I done that last year, they probably would have been called a little short because you know, construction costs were going up, labor's going up, all this inflation, it wouldn't even been good enough.
So there's a, there's good justification for for contingency.
And again, it's it's just this idea of trying to manage risk in an uncertain future because what is the risk?
The risk is that I have the money, I want to do the remodel.
They get the bids, boom, you can't do it because you don't have the money.
Or they start the work the vendor has committed to a price and then they're getting towards the end.
They realize they're losing money, they may start taking shortcuts and other things.
And I've actually, when I worked at the at the Westinghouse, we would actually work with our vendors.
And you just said this might be crazy, but it makes sense.
Give me a minute here.
We work with our vendors.
If they underestimated the job, we would actually work with them to increase their bid so that they didn't get caught shortchanged.
Because we were so obsessed with the quality of the work that was getting done.
We wanted to make sure that we weren't just going with a lowcost bidder, but we were going with with the we were establishing a contract that was going to it was it was going to get done and a way we wanted it done.
So that was that way of dealing with this risk of of the future and this uncertainty of the future.
But again, this is, this is a pretty common thing.
You'll probably see this in your activity, just throw a contingency on it.
There's also this idea of risk analysis by simulation.
So risk can be graphically illustrated by a probability distribution function.
And I think everybody here has had some statistics.
You understand this idea of a probability distribution function, but we're we're going to go over a couple of cases that your offer does just to illustrate this.
So there's three cases.
There's this case of treasury bills.
The second case is what he calls blue chip corporate stocks in this third case of real estate investment and they both, they all have different probability distribution functions and then what we'll show that graphically in a in a in a minute here.
So yield on the 10 year T bill.
So if you look at the rate or the OR the yield on a on a T bill, it changes constantly.
And I and I went out on the Internet.
Now this was not Microsoft's AI search process.
It didn't give me this, this.
I had to do this the oldfashioned way of just Googling tenure T bill and looking through a bunch of stuff and finding this.
But you can see the if you look, if you go back to where this graph starts back in 54, ironically here's my lifespan.
You can see where it how it's changed over time.
In fact I remember right here this is actually when I built, when I bought my first house T-bills were 15%, right.
So that was that was a time of very high inflation.
You think we have inflation today.
I paid 11 1/2 percent on my very first home loan.
And so you can see where it it, it varies over time and it's gone down it's and historically we're actually at pretty pretty low rates.
This goes through 2019.
So since then it's it has jumped up, has jumped up in recent years.
But the the notion here is that yeah, this may change over over decades and years, but once you purchase that, once you purchase that bond, it's done, it's set and it's not going to change.
So you may purchase it for 10%, you may purchase it you know back here, you may purchase it for 5%, you may purchase it at 2% if you did it recently.
But once you've once you've got it, it's said it's not going to change for the for the ownership of that.
So that that has very, very little risk associated because it's a pretty certain future for that particular investment.
You bought it for 5% a year from now it's going to, it's going to give you 5% two years from now, 5%, three years, 5%, whatever, whatever the duration is that you've you've paid for.
On the other hand, a little more risky would be your classic blue chip corporate stock.
So here's your stock in Home Depot, for example.
So let's assume you've got a rate of return of 8% on that blue chip stock.
Now I know, don't don't criticize me yet, but I do know the stock market goes up, it goes down, we agree.
But if you look at this over a longer period of time, 8% is pretty reasonable.
And so yes, market conditions will change that.
If you go back last year, yeah, you lost money on that blue chip stock, but you go back to you before that you got it, you got quite a bit.
But this, this, this risk is represented by a normal distribution.
So that's your probability distribution.
It's, it's normal.
And then you go to a more classic return on investment in real estate, let's assume that's say 15%.
Now you actually returns will be a little bit less because you have taxes, you have upkeep, could even go down.
Real estate never goes down, but you actually did go down in.
I remember in 20/10/2011 it went down but it could also go up.
It can go up significantly.
I sold my house in 20 or 23, so my house and when I moved to Coeur d'Alene in 22 I sold it for way too much money, but then again I bought another one for way too much money.
So hopefully it balances out, but so you do have these anomalies, but over time it tends to be a little, little more stable.
It's also got a normal distribution that represents it.
So if you look at these three cases, you've got, you've got a graphical distinction.
So here's your here's your case one, this is your T bill.
This is essentially saying hey, there's there's there's no risk here.
It's, it's, it's just locked in.
So for whatever duration you purchased that for, you're going to, you're going to get that.
However, if you look at your classic blue chip stock, you got a normal distribution, but theoretically you're going to, it's going to be a little more stable.
You're going to get 8% most of the time.
Sometimes the market conditions will be such that you'll get 10/12/13 percent, especially if you you look at this from the perspective of mutual fund, that's going to decrease your standard deviation.
But there will be times when you'll get less in that and they'll also be times when it could be negative.
And then you'll look at your real estate.
You're going to have a wider distribution, but you know there's the potential for greater return.
So you could, you could really make some money here on your real estate, especially if you can sell it for development purposes.
There's also the possibility where you're going to lose significant money because taxes, insurance and so forth, and it just sits there and does nothing for you.
It's just sits there.
Maybe you get a few dollars from a local farmer to raise crops, but otherwise you're just paying money out and get nothing.
Nothing's coming in.
So this represents greater risk of that particular investment.
So again this, that's this this notion of the risk.
So simulation of risk data we tend to make 3 point estimates to get this these distributions that will model this risk data.
So like in scheduling a lot of times what you'll do is you'll come up with minimum, most likely and maximum values.
That could be for cost of components, task completion dates and project like critical path method or whatever.
You'll do these three-point estimates there's there are some probability functions that you can use to represent these metrics for determining risk, like normal distributions, triangular, Poisson, and so forth.
And then you create a model to compute the total cost or the total compute completion time, whatever it is you're trying to estimate.
So, for example, here's your classic normal distribution.
Don't worry too much about the equation here, it's just.
Showing you that it's really used a lot of times when you know any kind of variation around the means seems to be somewhat random or you really don't understand what the causes are.
You just know that it varies kind of like like the real estate example, you know you get too far out in the future, you just you don't know and So what what's what happens is what's going to happen And so you can just represent that with a normal distribution.
Sometimes you'll use a a triangular distribution.
You can do this especially when you want to emphasize the most likely value.
So that's where your emphasis lies.
So you'll you'll you'll use that or it's just simply easy to implement And then there's a beta distribution.
I remember once using this when we were looking at repairs.
So you know the the function of repairing a product really falls under a like an exponential or beta distribution much better than it does under a normal distribution.
And that's because there's just a lot of uncertainty with repairs and sometimes certain repairs just take a lot more time.
So you'll get this, this kind of distributions that shows you there.
It's sort of a, you know, a most likely amount of time would be .25, but there's cases where you just can't figure out what's going on.
You just can't get it fixed in your having to order parts and repair thing or fix things before you repair it and you'll get some of these really outliers.
This might be a better distribution for that particular situation.
And then what you're going to do is you're going to simulate this risk data.
So you want to use PC based risk analysis software in your office, gives you some examples, crystal ball risk and so forth.
I personally haven't used any of these PC based systems, so I can't tell you much about it just using Excel.
But you can also what a lot of these will do is just do a Monte Carlo simulation.
So you might just do like in this case like 10,000 samplings on a computer, because you can really, you can really look at all sorts of variations on this uncertainty and these these results will be more realistic and descriptive than just throwing a contingency on there.
So for example, the way this works is you have for whatever your probability distribution is, you can convert that or these programs will convert that to a cumulative cost curve.
And So what this will do is you, you start off and you, you know, you might say, geez, how do I want to illustrate this?
You might have a certain cost of raw materials, certain labor rate, whatever.
And you throw that in there.
And based on your probability distribution that you modeled that parameter with, you'll just pick up, you'll pick a particular instance off of that curve.
And then you'll run your model on that.
And then you'll generate another random number and that will put you on a different point in this curve.
Then you run that model for that instance and then you pick another random number.
So the key here is you have this random number generator that randomly picks instances on your probability distribution that you used to simulate that process and you repeat this thousands of time and the end result is you get a set of end results of minimum, maximum, most likely and scenarios.
And so because of this, what we call this risk pooling, the total cost will have a lower overall risk than the risk associated with individual components which will in in in turn reduce your contingency cost giving you know giving you better a better estimation because you know let let's face it the the when you throw in a contingency cost typically what's what's happening there is people and organizations tend to pick the worst case scenario they're they're you want to cover your *** make sure you don't get in trouble.
Nobody really cares if you save a few dollars but if you mess up everybody cares.
So you tend to be a little more conservative on these things and you're you're left with this higher burden Now you're putting the bid together, you're trying to go out and get that work.
You you know you've got, you got a facilities work project, you're trying to get done, you got a bid going in, you got you have a contingency.
And in fact what that does is put if it's too high, you're not going to get the job.
But if somebody has gone through and done this more sophisticated simulation risk analysis, so they're going to get a more accurate analysis of the risk associated with that and likely come in with a lower bid and get that work and will they be taking on more risk?
They're taking on the risk that's associated with the most likely scenario of the unlikely future.
So that's the value of doing that.
So this gives you this.
The simulation makes explicit the uncertainties in the input variables.
It promotes a more reasoned estimate of the procedures.
It gives you an opportunity to simultaneously look at a whole variety of inputs and in the end allows you to make decisions based on a more fuller understanding the risk based implications.
Again, back to that initial comment, all decisions are subjective.
You can do this, you can get better quantitative information, but in the end you got to decide what you're going to do with that information.
But the but the notion here is that you can you can come in with a contingency to account for the risk of the uncertainty of the future at a lower rate than just slapping on the company standard don't get caught with your pants down.
Very conservative 1015% that's slapped on top.
OK so that's the the value of going through this approach.
Then there's a, let me see what see what I do here.
Yeah, I think I'm going to do, I'm going to go ahead and just stop here because I have this example.
It's going to take a little bit too long.
We'll go ahead and just stop here and then we'll next lecture, we'll pick up with this example from the, the chem plant in in Rossford.
OH, outside of Toledo.
00:00:30.200 -- Yes.
00:00:33.030 -- So today we will continue discussion about the
00:00:35.870 -- modified, all the method and Runge Kutta methods. So we
00:00:39.420 -- will talk about the formulas and then accuracy and so on.
00:00:43.325 -- So I give you hand out and the problem. I'll use it
00:00:47.585 -- today so that we can cover a little bit faster. And then
00:00:51.845 -- I'll spend time on other material. OK, so.
00:00:58.460 -- In there you remember in all this method in order to go from
00:01:03.751 -- point X&YN to point XN plus one 1 + 1, essentially with another
00:01:09.042 -- next index, we only use information from the previous
00:01:12.705 -- point. So in a modified or leave use information from 2 points
00:01:17.589 -- and we use oil as step to go to the point X N + 1 NU N +
00:01:24.915 -- 1. This is predicted point.
00:01:27.950 -- And then be available slope at the predicted point and we use a
00:01:33.059 -- slope at initial, not initial. But the point that we start
00:01:37.382 -- start from and then we average these slopes defined slope
00:01:41.312 -- alone, which we find essentially construct line right tangent
00:01:44.849 -- line and then we find approximation at the next step.
00:01:48.779 -- So I also wrote this method last
00:01:51.530 -- time. So you can either define predictor which is the Oilers
00:01:57.000 -- step and then this is slope at.
00:02:01.370 -- .1 right and here we have slope at .2 and then we average slopes
00:02:07.082 -- and this is how we find the next. The next point all we can
00:02:12.794 -- write down these slopes explicitly. So K1 is a slope at
00:02:17.282 -- point. XNYN and then we use it to March to find point you and
00:02:22.907 -- plus one. Then we find K2 slope at the second point and then we
00:02:27.793 -- take every to the slopes defined. And if you don't want
00:02:31.632 -- to use K1K2 and just write this in terms of an even without you
00:02:36.518 -- N + 1, then you just write explicitly all the expressions
00:02:40.357 -- for you and plus one. So this is a first step. Predictor
00:02:44.894 -- does not change and in the second step in the character.
00:02:48.970 -- You have your own plus one equals UN plus H / 2, so you
00:02:53.702 -- take average. This is your slope at point XYN. This is your point
00:02:58.096 -- and you X N + 1 right here. This is your predicted point. U N + 1
00:03:03.842 -- essentially just written
00:03:04.856 -- explicitly. OK.
00:03:09.510 -- Modified the oldest method uses two term approximation from the
00:03:13.990 -- Taylor series right. The constant term and the linear
00:03:18.022 -- term. The modified Euler method uses. Also next terms uses
00:03:22.502 -- quadratic term in the Taylor expansion, so if we go back to
00:03:27.878 -- their tail expansion then modified Euler will use up to
00:03:32.358 -- age squared term. So this means that the first time that you
00:03:37.734 -- neglect will be proportional to
00:03:39.974 -- H cube. Right next will be age to the 4th. Each of the 5th and
00:03:45.450 -- if H is small then this will be a dominant term. So air local
00:03:50.070 -- error over one step will be proportional to H cube.
00:03:54.290 -- And then you find cumulative error after multiple steps right
00:03:58.000 -- after. If you're going from zero to X final, then the error will
00:04:02.823 -- be proportional to age squared, so similar usually you lose one
00:04:06.904 -- order when you sum the errors you find cumulative error. So
00:04:10.985 -- since modified term all this but it matches the 1st three terms
00:04:15.437 -- in the Taylor series up to and including termination squared,
00:04:19.147 -- the local area is proportional to each cube, but the cumulative
00:04:23.228 -- error is proportional to age
00:04:25.083 -- squared. So if air is proportional to H squared
00:04:28.998 -- and instead of H, you take H / 2, what would happen
00:04:32.910 -- with the error?
00:04:35.610 -- As will decrease by approximately 1 force, right? So
00:04:38.265 -- if you see so, this is a way how you can check that your method
00:04:42.690 -- is quadratic. So this means that your method is quadratic,
00:04:45.935 -- so your error is proportional to each squared. Let's say you
00:04:49.180 -- write a program and how would you verify that? Yes, the method
00:04:52.720 -- is programmed correctly. So what you can do you take you take a
00:04:56.555 -- test problem for which you know exact solution, so you can look
00:05:00.095 -- at the error because error would be the difference between exact
00:05:03.340 -- solution and numerical solution. So you go from.
00:05:06.430 -- Initial time to some final time final point, and you compute
00:05:11.457 -- solution at the final point.
00:05:14.530 -- And you look at the error right? And then you decrease error by
00:05:18.391 -- half and look how the error will change. So if error bill
00:05:21.955 -- decreased by half, this means that you have a linear method.
00:05:26.250 -- If it decreased by quarter, than its accuracy is quadratic.
00:05:32.310 -- OK. So this is a way to verify that your program is correct,
00:05:37.448 -- and then once you verify your code then you can change
00:05:41.034 -- equation. You can change function, then you can more or
00:05:44.294 -- less thing that your program is reliable, computes correctly, so
00:05:47.554 -- this is what happens with the error. Is H decreased by half
00:05:51.466 -- then the arrabelle because by a factor of four and just for
00:05:55.704 -- comparison. Again for all this method it's a linear
00:05:58.638 -- convergence. So if you decrease age by half your error will also
00:06:02.550 -- decrease approximately by half.
00:06:05.710 -- OK.
00:06:11.410 -- And so essentially we know the methods we just. I can just
00:06:15.442 -- rewrite it may be in the way that is more convenient for
00:06:19.810 -- programming. So if we want to solve initial value problem with
00:06:23.506 -- some initial condition. So what do we need? We need initial
00:06:27.202 -- condition right? So X not, why not? We also know we need to
00:06:31.570 -- know the step size and how many steps we have to perform right
00:06:35.938 -- function F is known. So once you have equation you can find
00:06:39.970 -- function F so again.
00:06:41.420 -- Then before you need to compute 'cause you have some homework
00:06:46.051 -- that you have to actually implement by hand or using
00:06:50.261 -- Calculator. So write down the formulas before you substitute
00:06:54.050 -- values right so?
00:06:56.320 -- You can, we can use either write this in terms of predictor
00:07:00.256 -- corrector or we can use this slopes K1K2 to write the method
00:07:04.192 -- so XN plus 1 = X N plus H. So every time you increment by H
00:07:09.440 -- right and also we can write
00:07:11.408 -- that. H is X final minus X starting divided by number of
00:07:17.326 -- steps right or number of steps is X final minus 0 / H right?
00:07:23.150 -- So if you know number of steps you know initial point
00:07:28.142 -- terminal point then you can find step size or vice versa.
00:07:32.718 -- If you know step size you can find number of steps.
00:07:39.730 -- OK, predict this step is just the oldest method.
00:07:43.490 -- Right and then corrector? So predicted allows you to find
00:07:46.940 -- this predictive point you N + 1 and then corrector will find
00:07:51.080 -- slopes at both points and average them to find exponent.
00:07:55.210 -- OK, and again Alternatively this is using the K1K2 and but
00:07:59.687 -- essentially the same.
00:08:01.550 -- OK, so whatever way you prefer, you can use.
00:08:08.170 -- OK, any questions here.
00:08:14.070 -- So let's look at the example.
00:08:16.890 -- So in this example you have to implement modified order in.
00:08:23.520 -- And solve the problem in 2
00:08:24.972 -- steps. So equation is Y prime equals X + y -- 1 squared.
00:08:30.250 -- Initial condition by 0 = 2. So find Y at. So you start from X
00:08:35.575 -- equals. O you go to X = 0.2 in two steps means that step
00:08:42.728 -- step sizes. 0.1 right again, it's a 0.2, so H is 0.2
00:08:49.380 -- -- 0 / / 2 zero point 1 which is written here.
00:08:56.710 -- Initial condition X00Y0 stole from here number of steps two
00:09:02.050 -- and then H you find.
00:09:06.260 -- Their function function F function F is the right inside
00:09:09.760 -- of your equation.
00:09:12.550 -- OK, and I know it's tempting to write down right away their
00:09:17.230 -- solutions, but take some time. Just write down the formulas in
00:09:21.520 -- terms of X&YN, it's easier than to substitute. I mean, if you
00:09:26.200 -- program something then you just program with indices and then it
00:09:30.490 -- computable repeat, write your computations. But when you do by
00:09:34.390 -- hand then you have to keep track of X0X1Y0Y1 and then here you
00:09:39.460 -- have you also UN to worry about.
00:09:43.700 -- So you write down the formula. So this is your next.
00:09:46.850 -- Approximation of X. This is your predicted value just
00:09:50.540 -- using the Euler's method, because this is your function
00:09:54.230 -- F at X&YN and then.
00:09:57.420 -- This is your next approximation.
00:10:00.110 -- By using the previous and the average of slopes.
00:10:04.030 -- OK.
00:10:06.520 -- So for all this method to go from one point to another, you
00:10:11.109 -- do one is 1 stage method because you only use one point for the
00:10:16.051 -- modified order, it is 2 stage because you have predictor an
00:10:19.934 -- you have character. So each step has two parts.
00:10:24.160 -- OK.
00:10:26.920 -- So if we take so here, we have N equals.
00:10:33.010 -- Zero, so when N = 0, I have X 1 = X O plus H. We find 0.1,
00:10:40.462 -- which is what supposed to be predicted point Yuan Yuan plus
00:10:45.016 -- one. Will you one and then it's Y0 plus HX0Y0 and you substitute
00:10:50.398 -- values you get 2.1. So this is your predicted value and then
00:10:55.366 -- you can use it in the next stage
00:10:58.678 -- defined. Correction, OK, so this is your essentially. This is the
00:11:02.650 -- same as what you have here.
00:11:05.450 -- So it might be more beneficial to use key one key two if you
00:11:10.014 -- want to reduce time on writing because you have to rewrite
00:11:13.600 -- this. And this is your slope at the predicted point. Again, just
00:11:17.512 -- write down X0Y0X1U one before you substitute values, because I
00:11:20.772 -- mean you see that becomes messy.
00:11:29.940 -- OK, so then we substitute values and we obtain approximation. So
00:11:33.845 -- so we did two stages, but this is the first step.
00:11:38.670 -- OK, it's not 2 steps first step. So now we use N = 1 and
00:11:45.525 -- this allows us to find X2U2 and Y2. So X2 is exam plus H, so
00:11:52.380 -- we have you too is a prediction using the Oilers step from Point
00:11:58.321 -- X one U-1 and then you do is correction with average of
00:12:03.805 -- slopes. Again as you see, right down X one U1X1X2U2 and so on.
00:12:09.880 -- And then approximate and then substitute values.
00:12:16.130 -- So finally so this is our approximation of a solution at
00:12:19.639 -- 0.2, and again this is not exact value, right? It's only
00:12:23.148 -- approximation because we use out of infinitely many terms in the
00:12:26.657 -- Taylor series, we only use 3.
00:12:29.290 -- So H is finite, right? So definitely we have an error. OK,
00:12:33.442 -- so schematically what is going on here? You start. Your initial
00:12:37.248 -- condition was at 02 right? This is your point.
00:12:42.180 -- Predictor brings you to point X one U-1.
00:12:47.560 -- You find slope at this point at X1. You want you find slope at
00:12:54.224 -- X0Y0. You average corrector gives you point X1Y1.
00:12:59.420 -- This is your first step, but
00:13:01.412 -- still stages. Then again from point X1 U one you find
00:13:06.648 -- predictor X2U2 right YouTube means has index as Y two. So
00:13:11.510 -- please different letter. But it is the same index and then
00:13:16.372 -- you've added slopes at X 11X2U2 average them and this
00:13:20.792 -- gives you correct correction point X2Y two again two stage
00:13:25.212 -- but it's one step.
00:13:31.180 -- OK.
00:13:33.760 -- Any questions here?
00:13:36.930 -- So example have either Euler or modified Euler method to
00:13:40.870 -- implement by hand, which means the step size will be generously
00:13:45.204 -- large, maybe like one or something that doesn't require
00:13:48.750 -- because you cannot use calculators for the test there
00:13:52.296 -- 'cause I don't know which device you bring mini. Something
00:13:56.236 -- computer that has access online and so on. So the algebra will
00:14:00.964 -- be simple enough that you can do
00:14:03.722 -- by hand. But for me, even if you have to perform 2 steps.
00:14:08.650 -- I need to see that yes, you know what is initial
00:14:11.411 -- condition. What is the next point and so on. So it will
00:14:14.423 -- not be a lot of steps, but at most Euler or modified Euler.
00:14:18.810 -- OK, your homework has more steps to perform, so you're welcome to
00:14:23.358 -- use whatever calculators computers to get the values, but
00:14:26.769 -- you have to write down. Then you can probably minimize number of
00:14:31.317 -- things that you write.
00:14:33.600 -- OK, your project Modeler project is based on
00:14:36.888 -- implementing these methods actually not implementing.
00:14:39.354 -- Using them to solve problems because the
00:14:42.231 -- programs functions are available on the course
00:14:45.108 -- websites. You just have to.
00:14:49.070 -- Maybe on Monday I'll bring the laptop so I'll show you where
00:14:52.646 -- files are and how to use them.
00:14:57.500 -- OK so next method.
00:15:00.250 -- To consider is so called 1st order on the quota method.
00:15:06.320 -- And the idea here is the falling. So we saw from their
00:15:10.880 -- modified all the method that if we use information from two
00:15:15.060 -- points then we get more accurate
00:15:17.340 -- approximation. Right, so can we use more points to get the even
00:15:22.577 -- more accuracy and the question the answer is yes. So in this
00:15:27.101 -- case we use four points.
00:15:29.560 -- So we go from .1.
00:15:32.980 -- 2.2 Essentially this is your order step. We get point .2.
00:15:38.645 -- Then we use this slope K2 to go to .3.
00:15:44.670 -- We use the .3 slope. Do you go to .4 and then we take weighted
00:15:50.790 -- average of the slopes at this
00:15:53.238 -- point? OK, so OK.
00:15:57.250 -- Um?
00:16:00.400 -- So which points we use? We use
00:16:03.529 -- point X. We use point in the middle of this interval at X N +
00:16:08.925 -- H / 2 and here we have two points to use and we also use
00:16:13.050 -- point at X = N + 1.
00:16:16.350 -- So do we? Do we give the same weight essentially the sum of
00:16:21.316 -- slopes over 4? No, we give twice more weight at points
00:16:25.518 -- in the middle.
00:16:36.200 -- And this is last page that you have an I I did not print. I
00:16:42.095 -- have a few more pages, but.
00:16:45.910 -- I'll explain what we have here. So if you have.
00:16:51.170 -- Probably let me use, maybe this so you don't
00:16:55.094 -- have this page, but this is a recap of the last page, so you
00:16:59.672 -- have to want to solve the 1st order equation with some given
00:17:03.596 -- initial. So I'll bring a copy of
00:17:05.885 -- this next time. So what you do you find the slope at .1. This
00:17:11.178 -- is where you start.
00:17:13.540 -- Then you match half step to .2 using this slope.
00:17:19.110 -- So you have you have X N + H over to you. This is your X
00:17:25.462 -- displacement an in. Why you do Oilless step with step size H of
00:17:30.623 -- it but slow K1.
00:17:33.320 -- So once you have this point, you use this point
00:17:37.380 -- to evaluate slope.
00:17:39.970 -- So I compute slope K2 and I find
00:17:43.858 -- .3. By marching again from KXAN half step and using alone Def
00:17:50.700 -- line with slope Cato.
00:17:53.650 -- OK, this gives me point X 3.3, so from .3 then we match full
00:18:00.090 -- step to find point for using Slope case 3.
00:18:05.020 -- Once you have all these four slopes, you have weighted
00:18:08.630 -- average so you have you give weight 1 to the first point and
00:18:13.323 -- to the last point, but two weights to the .3 and two and
00:18:18.016 -- three. So overall you have for slopes six slopes. So you divide
00:18:22.348 -- age by 6.
00:18:24.130 -- So this is your average weighted slope.
00:18:28.090 -- OK, and then you can write this slope like even if you don't
00:18:32.640 -- know this. So you use information from four points. OK
00:18:36.140 -- to find, so this is a full stage
00:18:38.940 -- method. Anne.
00:18:43.250 -- In order to go from X&YN 2 X N + 1 one plus one, it is still
00:18:49.098 -- using only one previous point, right essentially, but it does
00:18:52.538 -- it in four in four stages.
00:18:55.260 -- OK.
00:19:01.760 -- OK, So what I can say here is there wrong accoutre
00:19:08.756 -- force order matches there?
00:19:14.230 -- The local error in their own decoder 1st order method is of
00:19:18.406 -- order H as a power 5.
00:19:21.980 -- OK, but when you find cumulative error then you lose one order
00:19:27.476 -- and then overall the error is.
00:19:31.300 -- Proportional to H is about four and you can. You can appreciate
00:19:35.116 -- it if H is let's say 0.01 to 10 to the point is the power of
00:19:40.204 -- negative one right? All this method will have error also of
00:19:43.702 -- the order of 10 to the minus
00:19:45.928 -- one. Right modified order will have error to the order 10 to
00:19:50.999 -- the minus. Two but longer code will have error of the order 10
00:19:56.205 -- to the minus four right? So you see that it's occasionally.
00:20:00.180 -- Logic difference in the in the accuracy. So all this method in
00:20:03.744 -- order to get the same accuracy.
00:20:06.480 -- You need to use smaller H. Ruby code allows you to use larger
00:20:11.992 -- step size. Because the error is small and So what you save,
00:20:17.542 -- you save the number of steps. But again, remember that one
00:20:21.634 -- step of the longer quota has
00:20:23.866 -- four stages. So at each stage you have to evaluate function
00:20:28.565 -- and function evaluation may be consuming, so that's so. That's
00:20:32.015 -- why it's not very cheap method because at every step you have
00:20:36.155 -- four function evaluations.
00:20:39.020 -- OK.
00:20:40.850 -- How do we check that method is first order accurate? If we
00:20:45.686 -- decrease H by half, their level decreased by a factor of.
00:20:55.410 -- If H is replaced with H / 2, so the arrabelle decreased
00:20:59.622 -- by a factor of.
00:21:03.430 -- 22 to the power. 416 right so this is, you see, is a
00:21:08.929 -- significant difference between this method and that method OK?
00:21:14.650 -- Which method you would like to use if you have
00:21:17.570 -- to solve your problem?
00:21:22.740 -- So you have a choice. You have three methods and you have to
00:21:27.095 -- implement MCF thread programs, foiler for modified or Lefranc
00:21:30.110 -- equal to which method you would start with.
00:21:33.900 -- If you want to solve the problem that you don't know
00:21:36.595 -- solution about anything about.
00:21:39.660 -- Probably oil it while it's easy to implement, its lately least
00:21:43.037 -- accurate, but it's easy to implement, and for example, if
00:21:46.107 -- you programmed at an, you see that it doesn't work. Maybe
00:21:49.484 -- there is no point of investing time, right? But if you know
00:21:53.168 -- that yes solution exists, an that gives you what you need,
00:21:56.545 -- you can start with all the method just to get a feeling of
00:22:00.536 -- what solution is going to do. But then if you need to have
00:22:04.527 -- more accuracy, or let's say if you have to compute for long
00:22:08.211 -- time and maybe. Many points then you probably would use on
00:22:12.492 -- GeForce order method. Matlab in fact has so called variable
00:22:15.782 -- Force 5th order method ricotta which allows us to change the
00:22:19.401 -- step size depending on the estimate of the error. So they
00:22:23.020 -- have some estimate of the error in air is small. Then
00:22:26.639 -- you can use largest largest step. If estimate becomes
00:22:29.600 -- large then you decrease the time step so it's not
00:22:32.890 -- constant, is not the same method that would be
00:22:35.851 -- considered here.
00:22:37.550 -- OK, I mean whatever Matlab built-in function solver.
00:22:42.500 -- OK, so an example and I'll have this available on the course
00:22:47.564 -- website and then I'll give you a hand out next time just to show
00:22:53.472 -- you what is going on in this ricotta method. So if we
00:22:58.958 -- want to solve this initial value problem starting from .12 and
00:23:03.600 -- finding oh at 1.4 in two steps using force ordering decoder
00:23:08.242 -- method, so two steps means that.
00:23:11.460 -- What is H we go from 1 to 1.4.
00:23:15.900 -- Each is.
00:23:19.750 -- So age is 1.4 -- 1 / / 2, so this will give us.
00:23:27.190 -- Zero Point 4 / 2 will be 0.2, right? So this is your step size
00:23:32.515 -- capital N number of steps is 2 inside of each step. How many
00:23:37.130 -- stages do you have?
00:23:39.330 -- Four stages right? So 4th function evaluations. So for
00:23:42.480 -- each stage you have to write K1K2K3K four and then the
00:23:46.330 -- weighted average to find next
00:23:48.080 -- approximation. So K1K2K64 will be different for
00:23:51.738 -- inside of each step.
00:23:55.390 -- OK, so H with no envy, no initial condition. X Zero is
00:23:59.626 -- one, XY0 is 2 OK, what is a function function is X + sqrt y.
00:24:04.921 -- This is your function F so F of XNYN is X N + sqrt y N.
00:24:12.780 -- OK, and then you carefully substitute these values, right?
00:24:16.263 -- I mean it's OK for demonstration purposes, so you probably want
00:24:20.520 -- to have this done by computer right? Unless function is simple
00:24:24.777 -- that you can, you can do it. OK, so gave one is a slope at first
00:24:30.969 -- point. In this case at X0Y0, right? You find Cato is you
00:24:35.613 -- March, you replace X with 0 + H to point in between and Y zero.
00:24:41.418 -- You follow The Cave one slope.
00:24:45.130 -- Right, so this is your X value. This is your why value once you
00:24:48.882 -- have them, you substitute them in the function, so you replace
00:24:51.830 -- X with this. Why is that?
00:24:54.140 -- Annual value it so this gives you slope K2 then use K2 here to
00:24:59.768 -- find .3 again. X is just half step away while zero plus K 2 *
00:25:05.798 -- H / 2 This is your ex. This is your Y value you put in the
00:25:12.230 -- function you evaluate. Finally K 4 you much full step.
00:25:16.890 -- Use slope case 3. This is your X value. This is your.
00:25:20.694 -- Why will you find slope K 4? You take weighted average.
00:25:24.181 -- You get next approximation.
00:25:31.380 -- OK, so now what you found you found.
00:25:37.130 -- X1 is 1.2 and Y one is 2.5201.
00:25:45.570 -- So now you use this.
00:25:47.540 -- To do another step so we have two steps here to do.
00:25:51.350 -- Right, so we have this and then again K1K2K3K four. But now
00:25:56.990 -- instead of X0Y0 you have X1Y1.
00:26:00.690 -- Just indexes shifted and so on, so I'll have this online and
00:26:05.034 -- I'll bring this on Monday.
00:26:09.020 -- OK, any are there any questions yes.
00:26:14.720 -- This is based on.
00:26:17.670 -- Next one you just. Right, you found this one from the previous
00:26:22.220 -- right step and then you just keep it the same, but you keep
00:26:26.640 -- adding. So what I do OK, I have formulas dependent on X&YN
00:26:30.720 -- right? So here I had to use.
00:26:34.040 -- My end was zero.
00:26:37.050 -- So I replace end with zero everywhere before I try to
00:26:41.285 -- compute anything. So in the next stage I have to use N equals.
00:26:46.910 -- 1.
00:26:48.560 -- OK so I replace.
00:26:51.160 -- SNV X1 Y end with Y1 and similarly everything else but
00:26:56.011 -- K1K2K3 will be different now from the previous case from the
00:27:00.862 -- previous step. So I have F of X1Y1 compared to.
00:27:06.930 -- F of X0Y0 I have for K2 I have F of X1 plus HY one plus K 1 * H
00:27:14.250 -- / 2 I have here with HO, but this key one and escape one of
00:27:19.740 -- the same. OK, so at every state at every step you
00:27:24.894 -- K1K2K3K four will be different, so he probably
00:27:28.142 -- technically we have to write down another index an, but
00:27:32.202 -- it just will increase. It will be very cumbersome. So
00:27:36.262 -- so all slopes are different. So for each step you
00:27:40.322 -- recompute your slopes.
00:27:44.870 -- OK, that's why.
00:27:47.280 -- Write this before you implement your substitute values.
00:27:52.260 -- OK, right X 0X1YY1Y2 and so on.
00:28:00.600 -- This will not be on the test.
00:28:04.540 -- OK, but it is in the homework so you have to do it.
00:28:10.850 -- OK, any other questions?
00:28:16.150 -- So more about numerical methods. So we teach a
00:28:20.236 -- course which is now taught between three department's
00:28:23.868 -- mathematics, physics, and engineering is typically
00:28:26.592 -- chemical genius teaching and then so this method are
00:28:30.678 -- studied in more details, but not only this, but also
00:28:35.218 -- root, finding methods, argon values, eigenvectors,
00:28:37.942 -- solving linear systems. So maybe I should write so.
00:28:47.210 -- More about.
00:28:58.720 -- Anne.
00:29:01.050 -- 428 and there's also so this physics for 28 and engineering.
00:29:07.850 -- So it is the same course. I mean, of course the also
00:29:12.602 -- graduate version.
00:29:15.760 -- 529 I think and physics.
00:29:20.070 -- 528 So it's slightly dependants who is teaching, but we cover
00:29:24.437 -- the same material, so professors from different departments POV
00:29:28.010 -- alternate, but we have the same syllabus to follow.
00:29:36.920 -- No, normally you choose whatever flavor you want on
00:29:40.664 -- your transcript, but that's the only difference.
00:29:46.810 -- OK questions.
00:29:51.800 -- So.
00:29:53.810 -- I'll start Chapter 3, which is linear equations of
00:29:57.689 -- higher order.
00:30:16.410 -- So far we've dealt only with first order linear equations,
00:30:20.940 -- but we will look at their methods that will allow us to
00:30:26.376 -- solve equations of high order and linear equations do not
00:30:30.906 -- require. Coefficients to be constantly constant, but we will
00:30:35.444 -- for simplicity we will start with questions of miss
00:30:39.656 -- constantly efficients. OK, so let's just recall the definition
00:30:43.868 -- of the linear equation of ends order so linear.
00:30:51.720 -- And order.
00:30:54.120 -- Differential equation. Has function derivative, second
00:30:58.768 -- derivative, and so on up the derivative order NPL linearly in
00:31:04.675 -- the equation so?
00:31:07.440 -- Hey Ann.
00:31:13.720 -- Plus a N -- 1.
00:31:21.670 -- Loss etc plus a 2X.
00:31:25.550 -- D2Y T X ^2.
00:31:29.040 -- Plus a one of X.
00:31:34.190 -- Plus a 0 times function Y
00:31:37.382 -- equals. Some function that does not depend on why.
00:31:44.150 -- So remember.
00:31:46.460 -- How, how, how we define linear function we defined in a
00:31:50.673 -- function is a X + B right? So your independent variable AP is
00:31:55.652 -- linearly means raised to the power one. So now in the linear
00:32:00.248 -- differential equation you have the same but for the function
00:32:04.078 -- derivative, second derivative and up to the ends of the
00:32:07.908 -- derivative. These are the functions of X only.
00:32:11.540 -- Right then they don't involve why dependence are
00:32:14.716 -- of X is right inside.
00:32:18.020 -- Can be 00 but linearity means that you don't have y ^2.
00:32:22.604 -- Don't have y * Y prime and so on so they appear linearly
00:32:27.952 -- same way as X appears in the linear function.
00:32:32.770 -- In this case, we multiply by constant in the equation. In
00:32:36.268 -- the case of, the equation, coefficients can be functions
00:32:39.130 -- of X at most.
00:32:41.960 -- OK. So if.
00:32:46.070 -- Oldest coefficients.
00:32:51.390 -- Constants.
00:32:57.190 -- Then we have equations with constant coefficients.
00:33:00.960 -- Then differential equation is.
00:33:05.460 -- A linear.
00:33:08.260 -- Differential equation with.
00:33:13.190 -- Constant.
00:33:18.560 -- Coefficients. And these are, these equations are
00:33:23.016 -- typically easier to solve. Otherwise equation has
00:33:26.103 -- variable coefficients.
00:33:36.630 -- This differential equation is.
00:33:41.680 -- Linear, viz.
00:33:48.200 -- Variable coefficients.
00:33:53.330 -- OK.
00:33:55.070 -- If you have a linear equation an if right hand
00:33:59.190 -- side is identically zero, then we have linear
00:34:02.486 -- homogeneous equation and in fact homogeneous equation
00:34:05.370 -- only can be introduced for linear equations. I mean
00:34:09.078 -- sometimes can be introduced for nonlinear, but typical
00:34:12.374 -- is for linear equations.
00:34:15.830 -- Then
00:34:19.440 -- linear differential equation.
00:34:22.060 -- Is homogeneous.
00:34:29.190 -- Otherwise.
00:34:35.270 -- Linear differential equation is.
00:34:42.490 -- Nonhomogeneous
00:34:47.710 -- let's look at some examples that we've just trying to classify
00:34:51.593 -- and then to analyze the order if it is linear. If it is
00:34:56.182 -- homogeneous or non homogeneous.
00:35:01.010 -- So Y double prime plus X y = 0. So what is the
00:35:05.716 -- order of this equation?
00:35:09.740 -- 2nd order.
00:35:12.000 -- Is it linear or nonlinear?
00:35:16.800 -- Linear right? Because XY is multiplied by a function of
00:35:21.040 -- XY, double prime is multiplied by one. So linear is a
00:35:25.704 -- sensitive linear. Is it homogeneous or non
00:35:28.672 -- homogeneous?
00:35:32.050 -- Homogeneous because there is no function that only depends on X
00:35:36.428 -- rated 0 so homogeneous.
00:35:42.100 -- Coefficients are constant or variable.
00:35:46.930 -- Variable because we have X right? So this.
00:35:55.180 -- Variable coefficients. OK.
00:35:59.730 -- What about this equation?
00:36:03.530 -- X ^2 y double prime minus two XY prime plus Y to the XY equals
00:36:10.640 -- two X -- 1.
00:36:13.550 -- Order
00:36:15.760 -- 2nd. Is it linear or nonlinear?
00:36:25.740 -- OK, so we have Y times each of the XY prime times minus two XY
00:36:30.630 -- double prime times X squared. We have termed it depend on why
00:36:34.868 -- is it in this form?
00:36:38.870 -- That you have derivatives multiplied by at most
00:36:41.350 -- functions of X.
00:36:43.760 -- Yes, so it is linear, right?
00:36:46.730 -- Is it homogeneous since it is linear or not homogeneous?
00:36:51.860 -- None, because we have to explain this one.
00:36:56.590 -- So, nonhomogeneous? And coefficients are variable
00:37:00.892 -- variable right? Because we have functions so this.
00:37:07.660 -- Variable coefficients.
00:37:12.280 -- OK, next example.
00:37:15.440 -- Is 2 Y triple prime minus three Y prime plus seven Y equals
00:37:22.499 -- luxury four X ^2 -- 1?
00:37:26.490 -- OK, the order of the equation is 3 third order.
00:37:35.940 -- Is it linear or nonlinear?
00:37:42.440 -- Huh?
00:37:43.970 -- Linear or nonlinear?
00:37:47.530 -- Why is it nonlinear?
00:37:52.610 -- We have function multiplied by 7 derivative multiplied by
00:37:57.002 -- negative three, so the order to multiply by two.
00:38:03.220 -- Linear.
00:38:07.420 -- What is in here an is 3.
00:38:10.950 -- Look for linear equation. You have function multiplied by at
00:38:14.430 -- most, so this may be
00:38:16.518 -- constant. Or maybe some function of X. This functional effects
00:38:20.159 -- may be nonlinear, but we look at the look at the YY prime Y
00:38:24.373 -- double prime up to the highest order derivative, not in terms
00:38:27.684 -- of X in terms of Y.
00:38:30.880 -- OK. So equation is.
00:38:34.260 -- Linear.
00:38:36.670 -- Since it is linear, is it homogeneous or homogeneous?
00:38:41.910 -- Non, because of the logarithm of X ^2. So nonhomogeneous
00:38:46.250 -- and coefficients are.
00:38:48.580 -- Constant rate with constant coefficients.
00:38:54.990 -- OK and last example.
00:38:59.640 -- White triple prime my plus 2Y double prime
00:39:04.216 -- minus y * Y prime +7.
00:39:08.920 -- The order is.
00:39:11.750 -- So the order. 3rd order.
00:39:16.710 -- Linnaean olenia.
00:39:21.560 -- Nonlinear because we have y * y prime right nonlinear.
00:39:28.920 -- We cannot say if it is ominous nonhomogeneous because we don't
00:39:33.980 -- have linearity to say this.
00:39:38.200 -- OK.
00:39:40.660 -- So big chunk of this course will be devoted on the 2nd order well
00:39:45.924 -- probably not sister going to order, so essentially it's
00:39:49.308 -- easier probably to solve 2nd order equations, especially when
00:39:52.692 -- you consider with variable coefficients. But the method
00:39:55.700 -- that we will develop for equations with constant
00:39:58.708 -- coefficients can be easy.
00:40:00.470 -- Applied to the 2nd order first Order 5th order intense order I
00:40:06.086 -- will have 19th order example to consider. So yes.
00:40:15.070 -- It is defined only for linear for linear equations, so.
00:40:21.530 -- I've seen some definitions that say if identical is zero
00:40:24.950 -- solution satisfies equation, then you can think of this as
00:40:28.370 -- homogeneous. In this case it won't be because if you have
00:40:32.132 -- zero then this is 0. This is non 0 but typically homogeneous is
00:40:36.578 -- only for linear equations because you have some relation
00:40:39.656 -- to linear algebra. So linear systems, linear equations so
00:40:42.734 -- that's the reason. So once you may have a question on the
00:40:47.180 -- test to classify equation equations and then so similar
00:40:50.258 -- like we we've done here.
00:40:52.400 -- You look at the order if it is linear then you can think
00:40:56.716 -- it's homogeneous, nonhomogeneous, but if it's
00:40:58.708 -- not linear then you just stop.
00:41:01.720 -- OK.
00:41:06.820 -- OK, so let's start with second order linear
00:41:10.396 -- homogeneous equations so.
00:41:15.190 -- So we consider 2nd.
00:41:19.420 -- Modern.
00:41:24.600 -- Linear homogeneous differential equations.
00:41:30.280 -- We will first address the problem when we have none of
00:41:34.031 -- them, we have homogeneous equation. Once we know how
00:41:37.100 -- to solve homogeneous then we will study how to solve
00:41:40.510 -- nonhomogeneous equations because there are different
00:41:42.556 -- methods how to address this problem. OK, so in general,
00:41:45.966 -- if you have second order linear equation then you can
00:41:49.376 -- write it in just using some coefficients which are
00:41:52.445 -- functions of X.
00:41:55.200 -- A1 of X.
00:41:57.440 -- Divide the X + A zero XY homogeneous. This means very
00:42:03.776 -- inside is 0.
00:42:15.190 -- And so let's look at example and then we will try to establish
00:42:20.546 -- some properties of solutions to the homogeneous equations.
00:42:25.750 -- So example is.
00:42:38.500 -- Let's let's let's do 2 examples, so example a.
00:42:43.530 -- X ^2 D two YG X ^2 -- 2 X divided X.
00:42:51.680 -- Plus plus two y = 0.
00:42:54.760 -- So you can see it is second order, right?
00:42:58.620 -- It is linear 'cause you have y * 2 divided you exams minus 2X and
00:43:03.480 -- this is also linear term and it is not just homogeneous because
00:43:07.368 -- there is no function that only depends on X and not multiplied
00:43:11.256 -- by wire derivative and.
00:43:13.310 -- My first statement is that the X ^2.
00:43:17.680 -- Is a solution of this equation.
00:43:21.770 -- How do we? How do we verify that this function is a solution?
00:43:27.300 -- We have the substitute and check if you get identity right. OK,
00:43:30.840 -- So what do we have? If X squared is a solution, what is the
00:43:34.970 -- derivative of this solution?
00:43:37.500 -- 2X and 2nd derivative will be 2, so we have X ^2 * 2 -- 2
00:43:44.572 -- X times. Two X + 2 times function. So do we have 0?
00:43:51.430 -- We have two X ^2 -- 4 X squared plus two X squared
00:43:55.863 -- right, so cancels so 0 = 0. So this means that X squared
00:44:00.296 -- is a solution of the equation. What happens if we?
00:44:05.020 -- Multiply this function by constant.
00:44:09.370 -- By some arbitrary constant.
00:44:13.130 -- The claim is that this is also a solution.
00:44:18.740 -- So C One is an arbitrary constant.
00:44:25.870 -- Indeed.
00:44:27.990 -- 1st Order derivative will be 2 C 1X and 2nd order derivative will
00:44:32.839 -- be 2C1, right?
00:44:35.290 -- So we have X ^2 * 2 C 1 -- 2 X times 2C. One X
00:44:43.162 -- + 2 * y C One X ^2.
00:44:48.260 -- C1 is present in all the terms, right and otherwise
00:44:51.760 -- you have two X ^2 -- 4 X squared X squared, so this
00:44:56.660 -- is also zero. So again, if you take a solution of a
00:45:00.860 -- linear homogeneous equation multiplied by arbitrary
00:45:02.960 -- constant, you still get the solution, so this will be
00:45:06.460 -- still a solution.
00:45:08.850 -- So similarly.
00:45:11.370 -- And you can verify that X is a solution.
00:45:18.240 -- The first derivative is.
00:45:20.930 -- One second derivative is 0, right? So we have X ^2 * 0
00:45:26.819 -- plus. I'm sorry minus.
00:45:32.040 -- Minus two X * 1 + 2 times function you can see that
00:45:37.318 -- this is 0.
00:45:40.060 -- And if I multiply this solution by an arbitrary constant, I also
00:45:44.452 -- get a solution.
00:45:49.450 -- Let's say C 2 * X is a solution.
00:45:55.110 -- And we can verify this by substitute and so again, second
00:45:58.883 -- derivative will be 0, so we have X, y ^2 * 0 -- 2 X times C 2
00:46:05.057 -- + 2 * C Two X.
00:46:07.860 -- Zero and finally, if you consider linear combination of
00:46:12.225 -- these two functions.
00:46:14.860 -- In linear combination is you multiply function by constant by
00:46:19.410 -- different constant and you add
00:46:21.685 -- so C1. X ^2 + C two X is.
00:46:27.720 -- Also a solution.
00:46:33.150 -- OK, let's let's verify, because probably those cases are easy to
00:46:36.560 -- see. This one is a little bit tricky. OK, so we have X squared
00:46:40.900 -- times second derivative. What is the 2nd derivative here?
00:46:45.460 -- To see one right plus zero.
00:46:48.830 -- Minus two X times first order
00:46:51.908 -- derivative 2C1X. Plus C2.
00:46:56.020 -- And plus two times functions, so C One X ^2.
00:46:59.830 -- Plus it 2X.
00:47:02.870 -- Do we have here?
00:47:06.240 -- So if I look at terms with C1.
00:47:10.270 -- I have two X ^2 -- 4 X squared, two X squared, they cancel.
00:47:18.040 -- In terms with C2.
00:47:21.470 -- Minus two XY2 plus to exit to
00:47:24.837 -- also cancel. Right, and this is here.
00:47:29.070 -- So 0 = 0.
00:47:36.510 -- So what we showed here is that if you have linear homogeneous
00:47:41.178 -- equation an if you have solutions, you form linear
00:47:44.679 -- combination. So you multiply by constants and you add and you
00:47:48.958 -- have you keep them arbitrary. Then result is also a solution
00:47:53.237 -- to this equation.
00:48:01.930 -- So maybe just another example be.
00:48:05.740 -- G2Y G X ^2 +
00:48:09.486 -- 3. Divide X + 2 * y = 0 again. This is second
00:48:17.322 -- order equation. Linear homogeneous coefficients are.
00:48:22.880 -- Constant variable so 2nd order.
00:48:29.390 -- Linear homogeneous.
00:48:34.050 -- With constant coefficients.
00:48:39.860 -- And the claims here are that E to the minus X is a solution. So
00:48:44.615 -- at this point I'm not saying how we find them, we will. We will
00:48:49.053 -- know this soon, but let's just check. So if you have it to
00:48:53.491 -- the minus X derivative will be minus E to the minus X second
00:48:57.612 -- derivative will be with the plus sign, right? So you have either
00:49:01.416 -- the minus X + 3 * E to the minus X minus sign plus two times
00:49:06.488 -- function E to the minus X.
00:49:10.010 -- You get 0 right, and similarly if you multiply by constant.
00:49:16.900 -- Is a solution.
00:49:20.190 -- That I will not verify, but you can see that this is also
00:49:23.284 -- straightforward to do.
00:49:27.080 -- And then another solution here available is E to the minus, 2X
00:49:32.864 -- is a solution.
00:49:38.360 -- And if we multiply by constant, it is a -- 2. X is a solution.
00:49:45.230 -- And finally, linear combination is.
00:49:50.340 -- Also a solution.
00:49:53.260 -- OK.
00:49:56.540 -- So the result is how much time do I have left?
00:50:05.830 -- One minute. OK, so I'll I'll write the just result
00:50:09.690 -- so theorem.
00:50:12.320 -- So principle.
00:50:15.760 -- Of linear superposition?
00:50:22.460 -- It only works for linear homogeneous equations, so given.
00:50:28.790 -- 2nd order equation.
00:50:39.160 -- 2nd order.
00:50:42.280 -- Linear.
00:50:44.550 -- Homogeneous equation.
00:50:51.200 -- If. Why one of XY2 of X?
00:50:56.650 -- Our solutions.
00:51:01.250 -- Of this differential equation.
00:51:05.810 -- Then
00:51:08.050 -- their linear combination.
00:51:15.580 -- C1Y one of X + y two Y2FX is also solution
00:51:21.212 -- of the same equation.
00:51:37.400 -- See once you're here.
00:51:41.630 -- C1C2 are arbitrary constants.
00:51:50.360 -- And similar result holds 4th order equations, right? So this
00:51:54.430 -- doesn't change. OK, so I guess I'm out of time, any questions?
00:52:01.690 -- OK, thank you and drive safely.
00:00:21.260 -- Alright, good morning.
00:00:22.202 -- Welcome to class city.
00:00:23.460 -- You got your homework turned in?
00:00:25.340 -- How was the assignment? Do OK with it.
00:00:29.170 -- How was the airfoil problem the long?
00:00:34.050 -- But solvable.
00:00:34.688 -- Just kind of have to be patient
00:00:36.921 -- as you work your way through it.
00:00:39.240 -- OK, so since you're here right now,
00:00:40.970 -- I will tell you next time we
00:00:42.503 -- have a midterm next Thursday.
00:00:43.930 -- We have mentored.
00:00:45.007 -- There will be an airfoil problem on the exam.
00:00:48.200 -- So study that up.
00:00:49.276 -- We'll review it a little bit later on today,
00:00:51.830 -- OK? Alright I have.
00:00:54.616 -- I have colleagues here at the university
00:00:57.292 -- and some friends in the law school.
00:00:59.620 -- That's probably a bad sign,
00:01:01.420 -- right that I have lawyer friends.
00:01:05.130 -- And I always ask, you know,
00:01:07.130 -- do you do you bring up current
00:01:09.265 -- events in your classes?
00:01:10.790 -- You know they're always the Supreme
00:01:12.854 -- Court litigation stuff going on?
00:01:14.450 -- I hear no all the time.
00:01:16.450 -- It takes too much work.
00:01:18.120 -- We do not do that in gas tax.
00:01:20.780 -- OK, just to be clear,
00:01:22.450 -- so.
00:01:25.150 -- This is. The seven minutes of terror.
00:01:29.460 -- OK, the perseverance Lander
00:01:30.888 -- that landed on Mars last week.
00:01:33.030 -- So I thought that I would go through
00:01:35.854 -- step by step to let you know what's
00:01:38.812 -- going on and then watch a video of it.
00:01:41.950 -- Just 'cause I'm the teacher, right?
00:01:44.096 -- And I say we could watch videos,
00:01:46.590 -- we're going to watch videos, all right.
00:01:49.092 -- Let's check this out.
00:01:50.520 -- So 10 minutes before landing,
00:01:52.300 -- the shell comes off and this
00:01:54.346 -- is what the Lander looks like,
00:01:56.590 -- and you can see that it maneuvers itself.
00:01:59.850 -- OK, now it's 8 minutes to entry.
00:02:01.870 -- Gets balance right here.
00:02:02.958 -- What kind of body would we call that right
00:02:05.550 -- there, that kind of rounded surface?
00:02:09.750 -- That's a blunt body. OK,
00:02:12.520 -- that's how that's how any kind of spaceship.
00:02:18.460 -- Enters the atmosphere with a blunt body and
00:02:21.100 -- we'll see that once it starts to enter.
00:02:23.630 -- Look at this, although they
00:02:25.170 -- don't draw it as a shock.
00:02:27.180 -- We know because we are experienced
00:02:29.352 -- gas dynamicist that is a
00:02:31.554 -- shockwave that occurs right there
00:02:33.274 -- and notice that's a peak heating.
00:02:35.290 -- OK, let's look at some of these numbers.
00:02:39.140 -- Here it is 78 miles in altitude
00:02:42.262 -- above the Martian surface.
00:02:44.430 -- Look at this velocity 13,000.
00:02:47.670 -- Mph. Let's move in.
00:02:52.573 -- That is about 5900 meters per second, OK?
00:03:00.730 -- And let's see here.
00:03:02.322 -- So I did a little bit of calculation here.
00:03:06.760 -- The Martian atmosphere temperature.
00:03:08.512 -- Obviously it ranges like
00:03:10.264 -- every other atmosphere,
00:03:11.870 -- but kind of a standard temperature
00:03:15.272 -- is 60 degrees Centigrade below 0.
00:03:18.410 -- Minus 60 pretty cold, so that is 213
00:03:22.210 -- Kelvin enters at 5900 meters per second.
00:03:25.730 -- It's Martian atmosphere is primarily
00:03:28.170 -- carbon dioxide is about 95% carbon dioxide,
00:03:31.548 -- and so it's gamma is about 1.3
00:03:34.831 -- and its molecular weight is 44.
00:03:37.930 -- So we can calculate RA 314 divided
00:03:41.038 -- by 44 and it works out 'cause you
00:03:44.993 -- know how to calculate Mach numbers.
00:03:48.430 -- This works out to be a Mach number of 25.6.
00:03:53.910 -- Entering the atmosphere.
00:03:58.570 -- That's moving. That's moving OK,
00:04:00.990 -- so one of the one of the one of the
00:04:03.975 -- primary designs for this blunt body is that
00:04:07.951 -- you're traveling on Mach number of 25.6.
00:04:10.940 -- Tell me do parachutes work
00:04:12.895 -- very well in a lot #25.6 no.
00:04:15.720 -- OK, we will talk actually a little
00:04:18.303 -- bit later on in the semester that
00:04:21.516 -- there are some supersonic parachutes.
00:04:24.050 -- OK, there are some,
00:04:25.506 -- but this is not designed to do that.
00:04:28.390 -- So what the blunt body does is
00:04:30.721 -- that it absorbs that kinetic
00:04:32.582 -- energy and slows it down.
00:04:34.550 -- OK, so it's moving that amount #25.
00:04:37.080 -- Here's where it heats up that peak
00:04:39.460 -- heating and then it starts to decelerate,
00:04:42.150 -- and then finally finally it starts
00:04:44.244 -- to slow down and what it can do
00:04:47.223 -- this hypersonic aero maneuvering
00:04:48.731 -- what it does is kind of vibrate.
00:04:51.200 -- So it goes like this and it
00:04:53.657 -- converts that kinetic energy into.
00:04:55.650 -- Thermal energy and slows down.
00:04:57.510 -- That's what this maneuvering is.
00:04:59.360 -- And then finally.
00:05:00.803 -- Begins to deploy a parachute.
00:05:03.210 -- Does that at 400 meters per second.
00:05:05.980 -- Now, if you think in air that's
00:05:08.696 -- a little over Mach one,
00:05:10.730 -- it turns out for the Martian atmosphere and
00:05:14.098 -- these times it's a little bit over Mach one,
00:05:17.470 -- so it turns out that this supersonic,
00:05:20.240 -- but not real high,
00:05:21.820 -- not like hypersonic.
00:05:23.010 -- A parachute begins to deploy,
00:05:24.990 -- then the heat shield that
00:05:26.970 -- protected the spacecraft.
00:05:28.160 -- Right here, drops off.
00:05:29.988 -- OK falls off and then over here.
00:05:33.290 -- This is kind of neat.
00:05:35.210 -- The shell drops off and then there's
00:05:37.975 -- a little radar system right there
00:05:40.454 -- in that beams down to the surface to
00:05:43.756 -- determine the best place to land.
00:05:46.150 -- So it's like an autopilot.
00:05:48.140 -- It's like it's like an auto,
00:05:50.530 -- an artificial intelligence system.
00:05:52.602 -- That search arounds figures
00:05:54.674 -- out the best place to land OK?
00:05:57.420 -- Starts to collect that data and
00:05:59.706 -- then this shell drops off right
00:06:02.030 -- here and the Lander starts to
00:06:04.190 -- descend to starts to descend.
00:06:06.280 -- Excuse me, comes down,
00:06:07.776 -- it's got 4 little rockets right here
00:06:10.480 -- and these are called cold gas thrusters.
00:06:13.210 -- That's pressurized gas there,
00:06:14.902 -- so it's not necessarily a combustion
00:06:17.507 -- process starts to descend right here and
00:06:20.020 -- then it deploys what's called a sky crane,
00:06:22.830 -- so this hovers right here with those rockets,
00:06:25.910 -- and what the sky crane does.
00:06:28.380 -- Is that it lowers the Lander CABI
00:06:30.606 -- wires so that the Lander lands,
00:06:32.790 -- and then it cuts those wires in the sky,
00:06:35.840 -- crane falls away and you have
00:06:37.730 -- soft landing on the surface?
00:06:41.890 -- First off, if you're an engineer,
00:06:43.400 -- you can't look at that and say
00:06:45.213 -- that is not absolutely awesome.
00:06:47.230 -- To see that in action OK Now is actually.
00:06:49.980 -- That's kind of a complicated process if you
00:06:52.188 -- think of everything that's going on there,
00:06:54.550 -- you know one of the few seniors here that
00:06:57.016 -- learn about the Kiss principle, right?
00:06:59.125 -- Keep your design simple so that they work.
00:07:01.570 -- This is actually a pretty
00:07:03.090 -- complicated process.
00:07:03.700 -- Past Mars Landers.
00:07:06.030 -- Past Mars Landers actually have a
00:07:08.022 -- kind of a balloon on the outside
00:07:10.452 -- number of balloons that cover this in,
00:07:12.870 -- so that when it lands,
00:07:14.580 -- it actually bounces on the
00:07:16.230 -- surface of Mars until it stops.
00:07:18.340 -- Then the balloons deflated, opens up.
00:07:20.390 -- Then you have a Lander,
00:07:22.100 -- so spirit and opportunity landed like that.
00:07:24.500 -- OK, so.
00:07:26.460 -- That the pretty complicated
00:07:27.820 -- sort of landing process.
00:07:29.180 -- Now let's watch the video.
00:07:30.880 -- They actually in fact I heard
00:07:32.896 -- this on the news is that is that
00:07:35.661 -- in part of the design process,
00:07:37.680 -- they told a couple of engineers say hey,
00:07:40.400 -- listen,
00:07:40.804 -- would it be kind of cool to take high def?
00:07:44.890 -- Pictures,
00:07:45.179 -- High resolution pictures of the
00:07:46.624 -- landing process so they actually went.
00:07:48.450 -- I want to see RadioShack that kind
00:07:50.585 -- of dates me so they went to off
00:07:53.100 -- the shelf cameras and were able to
00:07:55.232 -- put it on the Lander so that you
00:07:57.360 -- can see the landing in process.
00:08:00.400 -- Dumb question, would you like to see it?
00:08:03.570 -- I thought so, so here we go.
00:08:05.630 -- So now that you know.
00:08:07.100 -- So now that you know the landing process,
00:08:09.450 -- let's see what we got here and fly
00:08:11.482 -- right maneuver where the spacecraft
00:08:13.007 -- will jettison the entry balance
00:08:14.612 -- masses in preparation for parachute
00:08:16.198 -- deploy and to roll over to give the
00:08:18.563 -- radar a better look at the ground.
00:08:23.330 -- Public it indicates she's deployed.
00:08:26.610 -- The navigation has confirmed that
00:08:28.390 -- the parachute has deployed an.
00:08:30.170 -- We're seeing significant
00:08:31.235 -- deceleration in the velocity.
00:08:32.660 -- Our current velocity is 450 meters
00:08:34.658 -- per second at an altitude of about 12
00:08:37.545 -- kilometres from the surface of Mars.
00:08:42.310 -- He tilts up. Perseverance is now,
00:08:45.000 -- so she was dropping off these
00:08:47.010 -- and then literally on Mars.
00:08:48.750 -- Just allow both the radar and the
00:08:50.920 -- cameras to get their first look
00:08:52.991 -- at the surface current velocity
00:08:54.771 -- it 145 meters per second at an
00:08:57.263 -- altitude of about 10 Columbia 9
00:08:59.321 -- 1/2 kilometers above the surface.
00:09:03.160 -- Now that's pretty cool to see that close.
00:09:06.420 -- Picture in that sort of definition of
00:09:08.667 -- the Martian surface. That's pretty neat.
00:09:14.260 -- And if you look on the bottom,
00:09:16.470 -- you can kind of see it's.
00:09:18.370 -- It gives the step filter contract about
00:09:20.540 -- players entry .3 meters that there
00:09:22.546 -- should come out altitude 7.4 kilometers
00:09:24.574 -- now has radar lock on the ground.
00:09:26.580 -- Current city is about 100 meters per second,
00:09:29.110 -- 6.6 kilometres of the surface.
00:09:35.220 -- President is continuing to
00:09:36.888 -- descend on the parachute.
00:09:38.560 -- We're coming up on the initialization of
00:09:41.507 -- terrain relative navigation and subsequently
00:09:43.641 -- the priming of the landing engines.
00:09:46.060 -- Our current velocity is about 90 meters per
00:09:49.724 -- second at an altitude of 4.2 kilometers.
00:09:53.320 -- Now, whether or not your geologist,
00:09:55.090 -- you could look at that surface
00:09:56.692 -- and say that there's windblown.
00:09:58.340 -- You can see the guys mentioned
00:10:00.086 -- that the reservation system has
00:10:01.595 -- produced a valid solution here,
00:10:03.060 -- and part of strain out the navigation water
00:10:05.500 -- or liquid that was there be a nominal.
00:10:07.780 -- We have timing of the landing engine's.
00:10:15.160 -- Back Shell survival at sea is 83
00:10:17.589 -- meters per second at about 2.6
00:10:19.838 -- kilometers from the surface of Mars,
00:10:22.110 -- we have confirmation that the
00:10:23.940 -- back shell has separated.
00:10:25.410 -- We are currently performing
00:10:26.870 -- the divert maneuver.
00:10:27.970 -- Travelocity is about 75 meters per
00:10:30.256 -- second at an altitude of about a
00:10:32.874 -- kilometre off the surface of Mars.
00:10:34.920 -- Here, in safety Bravo.
00:10:38.090 -- We have completed our
00:10:39.770 -- terrain relative navigation.
00:10:41.030 -- Current speed is about 30
00:10:43.130 -- meters per second altitude,
00:10:44.810 -- about 300 meters off the surface of Mars.
00:10:50.680 -- We have started our constant
00:10:52.570 -- velocity accordion, which means
00:10:54.084 -- we are conducting the skycrane,
00:10:55.970 -- so this is where the sky Crane
00:10:58.616 -- maneuver deploys at it drops,
00:11:00.510 -- there's the Lander right there?
00:11:02.400 -- I mean, that's that is totally cool,
00:11:05.040 -- 20 meters off the surface.
00:11:13.220 -- And you see that in the top view,
00:11:15.220 -- that's the that's the sky cream.
00:11:16.720 -- Rocky go delta.
00:11:18.148 -- Captain confirmed persevered
00:11:19.576 -- safely on the surface of Mars,
00:11:22.130 -- ready to begin seeking
00:11:23.930 -- the sands of past life.
00:11:29.220 -- There you go.
00:11:32.380 -- How great is that?
00:11:33.828 -- And that is pretty cool.
00:11:35.640 -- And since you are,
00:11:37.088 -- since you were all gas dynamicist's,
00:11:39.260 -- you know you could figure out the
00:11:42.186 -- aerodynamics of a good portion
00:11:44.444 -- of everything that we saw there.
00:11:47.210 -- In a couple of weeks actually,
00:11:49.100 -- starting next week,
00:11:50.528 -- we'll learn about rocket nozzles.
00:11:52.910 -- OK, and how they work good.
00:11:56.780 -- Any questions at all for get going?
00:11:58.950 -- Is it not a beautiful day
00:12:00.600 -- for gas at the office today?
00:12:02.670 -- It is awesome, OK?
00:12:05.420 -- Thursday is an exam at the end of class.
00:12:08.480 -- Today we will have a little review
00:12:11.360 -- an what's going to be on the exam,
00:12:13.920 -- but I want to just rehash
00:12:15.780 -- expansion waves to make sure
00:12:17.462 -- you've got that down expansion,
00:12:19.360 -- which are very important concept.
00:12:21.400 -- OK so.
00:12:23.500 -- Recall that an expansion wave
00:12:25.810 -- occurs when you have a supersonic
00:12:28.231 -- flow that turns away from itself,
00:12:30.650 -- so it's coming down this way
00:12:32.828 -- known as the mod numbers.
00:12:35.010 -- One goes through goes through
00:12:36.995 -- a turn away from itself.
00:12:38.980 -- There are some questions
00:12:40.568 -- last time after class,
00:12:42.160 -- so I just want to clarify
00:12:44.542 -- this that this line,
00:12:46.130 -- this leading Mauchline in this
00:12:48.205 -- trailing Mauchline constitute
00:12:49.450 -- what's called an expansion fan.
00:12:51.290 -- OK, those are expansion waves that.
00:12:53.810 -- That occur when a supersonic
00:12:56.005 -- flow turns away from itself.
00:12:58.200 -- OK, this leading Mauchline,
00:12:59.992 -- then that's the front edge of that fan,
00:13:03.470 -- and it occurs at this Mach angle.
00:13:06.540 -- Musa one OK?
00:13:09.470 -- It's it's the air turns through this
00:13:11.990 -- fan once it leaves the fan then it
00:13:14.769 -- falls the wall as it comes down here OK.
00:13:17.890 -- In the turning angle Delta OK,
00:13:20.590 -- recall a number of things.
00:13:22.840 -- The flow is isentropic.
00:13:24.640 -- No losses.
00:13:25.540 -- That means the stagnation pressure
00:13:27.790 -- remains constant across that turn,
00:13:30.040 -- their model number goes up.
00:13:33.190 -- It accelerates,
00:13:33.940 -- in fact,
00:13:34.690 -- I mentioned nozzles rocket nozzles will learn
00:13:37.357 -- how expansion waves work in rocket nozzles,
00:13:39.870 -- and that's how they that's how a
00:13:42.201 -- nozzle can produce supersonic flow.
00:13:44.320 -- Since the model number goes up,
00:13:46.550 -- the pressure goes down,
00:13:48.030 -- static pressure goes down,
00:13:49.510 -- static temperature goes down,
00:13:51.350 -- so these temperature and pressure ratios
00:13:54.182 -- right here are both less than one.
00:13:56.420 -- OK, again,
00:13:57.056 -- as you're going through problems,
00:13:58.650 -- make sure that you've got that.
00:14:01.850 -- That when you calculate those numbers
00:14:03.602 -- that your pressure and temperatures are
00:14:05.476 -- all trending in the right directions.
00:14:07.450 -- OK, if you haven't seen it already
00:14:09.445 -- in your homework problems,
00:14:10.870 -- but I've seen it all the time in exams.
00:14:13.670 -- You're under the pressure.
00:14:14.878 -- You gotta get the problem solved and
00:14:17.060 -- you accidentally invert a number.
00:14:18.640 -- Or you read it wrong.
00:14:20.200 -- OK,
00:14:20.540 -- check and make sure that all those
00:14:22.920 -- pressure temperature Mach number
00:14:24.332 -- values are going in the right direction.
00:14:26.670 -- OK.
00:14:28.710 -- Good we showed then what the
00:14:31.032 -- Prandtl Meyer angle was and it is.
00:14:33.400 -- It's a fictitious angle.
00:14:34.828 -- OK so it's not like as an angle.
00:14:37.740 -- You can take your protractor
00:14:39.540 -- out and measure it in the flow.
00:14:42.070 -- It's a mathematical construct that occurs
00:14:44.590 -- for every Mach number greater than one.
00:14:47.480 -- OK,
00:14:47.824 -- and as you learn in your in your homework
00:14:51.004 -- that you could go through the book
00:14:53.573 -- or go through com prop and be able
00:14:56.444 -- to figure out what that value of
00:14:58.840 -- Theta is that parental Meyer angle.
00:15:00.970 -- And this is the big relationship right here.
00:15:04.580 -- That the turning angle.
00:15:06.292 -- Right there is related to the
00:15:08.946 -- difference in the parental Myer angles.
00:15:12.100 -- OK. Alright, and this is this is
00:15:14.564 -- the key relationship right here.
00:15:16.420 -- When you're solving expansion weight
00:15:17.885 -- problems, you know any two values.
00:15:19.650 -- If you know the downstream Mach
00:15:21.360 -- number and the turning angle,
00:15:22.870 -- you can get the upstream Mach number.
00:15:24.920 -- If you know the upstream Mach number
00:15:26.901 -- in the downstream Mach number,
00:15:28.440 -- you get the turning angle.
00:15:29.900 -- If you know the turning angle
00:15:31.562 -- in the upstream Mach number,
00:15:33.120 -- you can get announcement number.
00:15:34.590 -- OK, so you'll be able to deduce
00:15:36.522 -- two pieces of information and
00:15:38.168 -- from this relationship right here
00:15:40.043 -- you can get the third OK.
00:15:42.030 -- Straight forward there.
00:15:46.230 -- OK, shock expansion theory.
00:15:48.054 -- You use this when you solve problems, OK?
00:15:54.360 -- So again, I don't want you to use
00:15:57.120 -- the airfoil function on com prop.
00:15:59.500 -- I want you to be able to look at
00:16:01.831 -- an airfoil like this and determine
00:16:04.504 -- if you have oblique shockwaves.
00:16:06.840 -- If you have expansion ways all
00:16:09.420 -- based on the geometry of the turn
00:16:12.395 -- right here and the angle of attack.
00:16:15.120 -- OK, let's let's, let's talk about.
00:16:17.160 -- Let's talk about a problem here real
00:16:19.505 -- quickly to make sure you've got this down.
00:16:22.260 -- 'cause this is, this is an issue
00:16:24.514 -- that comes up many times here.
00:16:26.680 -- Let's say you have a triangular
00:16:28.720 -- shaped airfoil.
00:16:29.400 -- OK, and then we'll just put
00:16:31.494 -- this at an angle of attack of 0.
00:16:34.160 -- So looks like this.
00:16:35.520 -- It's a symmetric airfoil.
00:16:39.930 -- Looks like this here and you have some
00:16:42.314 -- Mach number that's greater than one.
00:16:44.400 -- And let's say that we have a
00:16:46.647 -- turning angle here of 10 degrees
00:16:48.601 -- just to pick a number, OK.
00:16:50.590 -- K alpha is equal to 0,
00:16:53.290 -- so zero angle of attack there.
00:16:55.290 -- What kind of waveform do
00:16:56.955 -- you see at the bottom?
00:17:01.400 -- Nothing. What's the pressure that
00:17:03.725 -- acts on the bottom right there?
00:17:06.620 -- It's whatever your that's greater than one.
00:17:08.730 -- It's whatever your piece
00:17:09.934 -- of one is right there.
00:17:11.440 -- Whatever the atmospheric pressure is.
00:17:13.770 -- OK. Right, what do you see on
00:17:17.368 -- this top surface right up here?
00:17:21.580 -- Well, big shockwave.
00:17:22.555 -- The flow is turning into itself.
00:17:24.510 -- Changes 10 degrees,
00:17:25.740 -- so in oblique shock.
00:17:27.380 -- Forms right there and what's
00:17:29.240 -- the direction of the flow?
00:17:31.100 -- Flow follows the wall.
00:17:34.730 -- So it goes up this way.
00:17:36.790 -- OK, so here's where the here's
00:17:38.680 -- where the messed up part happens.
00:17:40.830 -- What occurs around the turn here?
00:17:44.510 -- Expansion wave.
00:17:46.340 -- OK, here's the question.
00:17:47.572 -- What is the turning angle
00:17:49.112 -- across the top there?
00:17:53.090 -- For me. 20 degrees.
00:17:59.000 -- Everybody see why that is.
00:18:01.140 -- If not, let's talk about it.
00:18:03.400 -- OK, if this is where the mistake comes in.
00:18:06.970 -- If it were 10 degrees.
00:18:09.810 -- Then what would be the direction
00:18:11.904 -- of the flow coming out here?
00:18:13.990 -- It would be horizontal.
00:18:16.970 -- If that turning angle 10 degrees
00:18:18.938 -- 'cause it goes down this way goes up
00:18:21.458 -- 10 degrees and so it's going to turn
00:18:23.919 -- another 10 degrees just to go horizontal.
00:18:26.330 -- OK, however the flow is not
00:18:28.772 -- horizontal on that side.
00:18:30.400 -- It goes down this way another 10 degrees.
00:18:34.230 -- OK, so this turning angle.
00:18:37.910 -- Right there. 20 degrees.
00:18:42.960 -- OK. Alright.
00:18:46.690 -- OK, you can calculate the
00:18:48.475 -- pressure in this region.
00:18:49.910 -- You can calculate the pressure
00:18:51.700 -- on this plate right here?
00:18:53.490 -- Can you calculate the pressure
00:18:55.280 -- in this region right here?
00:18:57.070 -- Absolutely OK with those three pressures.
00:18:59.910 -- Determine what the force is.
00:19:02.860 -- And then some of the forces.
00:19:05.930 -- In the vertical.
00:19:08.090 -- And the horizontal directions
00:19:09.534 -- get the lift in the draft.
00:19:11.700 -- OK.
00:19:12.160 -- Good.
00:19:12.620 -- OK, this is not so critical in
00:19:15.840 -- your calculations of lift and drag,
00:19:19.470 -- but an actually an oblique
00:19:22.250 -- shockwave forms here.
00:19:23.920 -- And the reason that is is because
00:19:26.188 -- the flow now comes down this way
00:19:28.809 -- and it's going to turn horizontally.
00:19:31.180 -- Across here.
00:19:31.922 -- So the float turns into itself,
00:19:34.150 -- and so there's going to be
00:19:35.890 -- an oblique shockwave,
00:19:36.760 -- but you don't have to worry about that
00:19:38.864 -- for to calculate the lift and drag.
00:19:41.090 -- OK, so it's this turning angle right there.
00:19:44.010 -- That causes problems.
00:19:45.102 -- I wanna make sure you got that down OK?
00:19:48.280 -- Excellent.
00:19:50.460 -- OK.
00:19:52.370 -- Overhead,
00:19:52.728 -- alright,
00:19:53.086 -- so actually all this is just a
00:19:55.592 -- review of what we talked about here
00:19:57.736 -- that the lift is equal to the sum
00:20:00.230 -- of the vertical components of all
00:20:02.150 -- the forces that act on the plate.
00:20:06.740 -- Very good. The lift coefficient
00:20:08.890 -- often used in the in determining
00:20:11.560 -- what kind of airfoil you want to
00:20:14.570 -- use and over what flight regimes.
00:20:17.590 -- OK is just the lift lift force.
00:20:21.340 -- Divided by 1/2 rho V squared,
00:20:23.660 -- this is the dynamic pressure.
00:20:26.230 -- Multiplied by the.
00:20:28.420 -- Multiplied by S here,
00:20:31.340 -- that is the area of the wing.
00:20:35.170 -- That's what S is there.
00:20:36.980 -- OK, and we showed in class in
00:20:39.101 -- the past that 1/2 rho V squared
00:20:41.245 -- is the same as one half P Mach
00:20:43.857 -- number squared right there.
00:20:47.600 -- OK.
00:20:50.040 -- So let's look at some.
00:20:51.890 -- Let's look at some things.
00:20:53.730 -- Let's let's just solve for L for
00:20:56.999 -- this relationship right here.
00:20:58.910 -- L and let's see what we can
00:21:01.101 -- do to generate lift here. OK.
00:21:03.381 -- We could have a better lift coefficient.
00:21:06.960 -- OK, so that's going to depend.
00:21:08.720 -- That's going to depend on
00:21:10.190 -- the shape of the airfoil.
00:21:11.660 -- OK, we could get better lift if you
00:21:14.212 -- have a higher freestream pressure.
00:21:16.990 -- OK, are you higher in the atmosphere,
00:21:19.430 -- lower in atmosphere that governs that?
00:21:22.880 -- But look at this right here. The lift.
00:21:26.392 -- Goes like the Mach number squared.
00:21:30.870 -- So what does that say about how fast you fly?
00:21:33.580 -- What is that going to generate?
00:21:36.120 -- More. Lift.
00:21:39.910 -- OK, so that means you can have
00:21:42.570 -- some very poorly shaped airfoils.
00:21:45.090 -- OK, so this Isabelle.
00:21:46.890 -- This lift coefficient might be bad.
00:21:49.590 -- But if your Mach number is high enough.
00:21:52.050 -- You can generate a lot of lift.
00:21:54.650 -- My number squared.
00:21:56.045 -- Also says that the that the wing
00:21:59.398 -- area S the larger the wing area,
00:22:02.320 -- the greater the lift you have.
00:22:05.290 -- OK, now this actually works well.
00:22:07.580 -- Not this relationship right here,
00:22:09.480 -- but this relationship.
00:22:10.953 -- If we wrote this is 1/2 Rho
00:22:14.496 -- v ^2 s think about a glider.
00:22:17.250 -- Moves very slow, right?
00:22:19.790 -- V is pretty small.
00:22:21.042 -- How does a glider make up for the
00:22:23.660 -- lift that it has to generate?
00:22:25.640 -- Was it have?
00:22:28.740 -- Lots of wing area.
00:22:30.344 -- Wings are very, very long,
00:22:32.350 -- so as if we wrote this as rho V squared.
00:22:36.080 -- Just substituting this right here.
00:22:37.940 -- If V is small then you could have
00:22:40.428 -- a large wing area right here to
00:22:43.223 -- generate whatever list you have nice.
00:22:45.770 -- OK, so that's the balance.
00:22:47.640 -- In aerodynamic design there OK?
00:22:50.770 -- We we've seen this diagram a few times and
00:22:53.920 -- showing the difference between a subsonic
00:22:56.374 -- airfoil you seem kind of nice rounded,
00:22:59.390 -- symmetric airfoil right there.
00:23:00.958 -- This is subsonic.
00:23:02.140 -- Speeds is getting close to transonic
00:23:04.408 -- here at the transonic regime.
00:23:06.450 -- Remember we said that now all the shockwaves
00:23:10.146 -- start to form right up there in the top.
00:23:13.870 -- And then that subsonic airfoil
00:23:15.900 -- has a bow shock here when it's
00:23:19.414 -- traveling supersonically,
00:23:20.810 -- whereas whereas a supersonic airfoil
00:23:23.765 -- like we see right here very thin.
00:23:27.830 -- OK, here you can see the shaded area right
00:23:30.827 -- here is going to give you it's roughly
00:23:33.616 -- related to the amount of drag that you see.
00:23:36.700 -- OK, so this shaded area right here
00:23:39.129 -- is smaller compared to its companion
00:23:41.223 -- there at the top same Mach number,
00:23:43.520 -- but different airfoil has
00:23:45.388 -- a nice rounded shape.
00:23:47.260 -- And then Supersonically right here,
00:23:48.920 -- you see, an oblique shockwave that forms.
00:23:51.870 -- Across that very thin airfoil,
00:23:53.290 -- whereas whereas you would have a bow shock
00:23:55.714 -- if you have a subsonic airfoil there.
00:23:58.250 -- OK, so again subsonic airfoils are great.
00:24:01.640 -- Flying subsonic Lee, they're awful.
00:24:04.060 -- Supersonically supersonic airfoils
00:24:05.512 -- are awful subsonic Lee,
00:24:07.450 -- but very good supersonically OK.
00:24:09.870 -- And then we talked a little bit
00:24:12.894 -- last time about these airfoils.
00:24:15.670 -- Here you see,
00:24:17.764 -- it's very thin.
00:24:19.860 -- K very thin right across here.
00:24:21.620 -- It's got a little curve there at the
00:24:23.764 -- bottom gives a little camber little
00:24:25.599 -- curvature so that you can generate lift.
00:24:27.800 -- Subsonic Lee.
00:24:28.722 -- This is the Russian.
00:24:30.570 -- This is the Russian aircraft that didn't
00:24:33.125 -- have that crashed really bad.
00:24:35.550 -- That's our 71 and then we talked about this
00:24:39.042 -- plane and F15 that flew with only one wing.
00:24:42.450 -- OK, Why was able to fly with one wing?
00:24:45.890 -- Well,
00:24:46.273 -- if we went back to our CISA Bell right?
00:24:49.720 -- He already went over it.
00:24:53.180 -- Right here, so it loses a wing.
00:24:55.880 -- So that means this area S decreases.
00:24:58.240 -- But as you increase the
00:24:59.920 -- Mach number right there,
00:25:01.270 -- you can generate the lift that you
00:25:03.552 -- need in order to fly in order to
00:25:06.088 -- in order to stay straight and level
00:25:08.430 -- roughly straight and level OK.
00:25:13.130 -- So actually before we get to that, here is.
00:25:19.100 -- So Mr Castle, sorry it's a Navy plane.
00:25:21.560 -- You OK with that? OK good.
00:25:24.310 -- So this is an F18 Hornet right here.
00:25:28.120 -- I want you to look. At the wings.
00:25:34.040 -- Can you get an idea for what that
00:25:36.152 -- for those wings look like right?
00:25:38.100 -- There? You see how thin those are?
00:25:40.870 -- It's got a very sharp leading edge.
00:25:44.130 -- OK, very thin all the way across there.
00:25:47.850 -- OK, now this actually has a really,
00:25:51.100 -- really cool design to fly.
00:25:53.430 -- Subsonic Lee. We saw F-14.
00:25:55.750 -- Tomcat had the swing wings.
00:25:58.080 -- Variable variable, swept wings.
00:25:59.860 -- If you look closely on
00:26:02.085 -- this airplane right here.
00:26:06.620 -- There is a hinge there and
00:26:09.608 -- the hinge right there. OK.
00:26:11.979 -- So what this plane does this is this
00:26:15.011 -- is awesome engineering as well.
00:26:17.960 -- OK, what this plane does with
00:26:20.234 -- this hinge here and the ailerons
00:26:22.601 -- here in the back. What it does?
00:26:28.420 -- OK, so as you say,
00:26:30.290 -- unhinged is probably a little bit unhinged,
00:26:32.900 -- so OK, so there's a hinge right there.
00:26:36.530 -- Flat plate for the surface of the wing
00:26:39.210 -- and then the other runs here in the back.
00:26:42.240 -- OK, so there's a kind of a classic
00:26:44.456 -- real thin supersonic airfoil.
00:26:46.270 -- What this leading edge hinge
00:26:47.965 -- does when it flies subsonic Lee.
00:26:49.970 -- Is that this actually bends down a little
00:26:52.906 -- bit and I'm just going to exaggerate
00:26:55.447 -- it so you can see what's going on.
00:26:58.450 -- So look like this.
00:27:01.320 -- Then the wing comes across here.
00:27:04.430 -- And then either on comes
00:27:05.855 -- back down there a little bit.
00:27:07.580 -- You see what that does to the wing?
00:27:11.290 -- Provides a little bit of curvature
00:27:14.170 -- little camber to the wing there so
00:27:17.438 -- that subsonic Lee you can take off and
00:27:21.124 -- land relatively relatively safely.
00:27:23.780 -- OK, that's that's pretty cool
00:27:25.880 -- design right there.
00:27:27.140 -- OK, will show some pictures a little
00:27:29.975 -- bit later on in the semester,
00:27:32.600 -- but one of the one of the research areas
00:27:35.750 -- that Aerodynamicists are working on now.
00:27:38.900 -- So let's say you're in the class,
00:27:41.840 -- which you really like materials.
00:27:43.940 -- OK, your control systems,
00:27:45.620 -- and not necessarily interested in that.
00:27:48.140 -- Fluids in the aero part they're
00:27:50.660 -- working water called smartwings.
00:27:52.340 -- OK, so smart wing.
00:27:55.400 -- So it has a surface like this cake
00:27:57.480 -- kind of a classic subsonic airfoil,
00:27:59.740 -- but this airport is actually
00:28:01.770 -- made up of a bunch of sections.
00:28:04.930 -- Right here. OK, on the wing.
00:28:08.774 -- So kind of looks like this,
00:28:11.390 -- and so those sections and
00:28:13.010 -- I'm just putting a squares.
00:28:14.630 -- I think they're hexagons.
00:28:15.926 -- I don't recall right off hand,
00:28:17.870 -- but you get the idea.
00:28:19.490 -- OK,
00:28:19.804 -- each of these little sections and
00:28:21.688 -- what they what they do depending on
00:28:24.008 -- the flight regime that you're in,
00:28:25.970 -- flying really fast or really slow,
00:28:27.920 -- it actually changes the shape
00:28:29.535 -- of the wing or your fly.
00:28:33.950 -- OK, so there are little.
00:28:37.460 -- Their little devices, little little motors,
00:28:39.530 -- little servos here on the inside that can
00:28:42.322 -- move up and down and change the shape of
00:28:45.297 -- the wing to make it the most aerodynamic
00:28:48.091 -- and the most the most efficient wing
00:28:51.070 -- for that particular flight regime.
00:28:54.050 -- That school engineering. OK.
00:28:59.040 -- Good, here's a here's another
00:29:01.895 -- little bit of supersonic design.
00:29:04.750 -- OK, I don't mean to.
00:29:06.570 -- I don't mean to brag on
00:29:08.682 -- this little guy right here.
00:29:10.570 -- Here's the X one.
00:29:11.966 -- We mentioned that it did break.
00:29:14.580 -- The sound barrier didn't have swept wings.
00:29:17.130 -- Not not the best compressible flow design.
00:29:19.670 -- Here's another part that Aerodynamicists
00:29:21.884 -- didn't understand at the time,
00:29:23.680 -- but is not a good design here is
00:29:27.192 -- that if you look at the tail.
00:29:30.490 -- OK, if you look at the tail right there,
00:29:33.700 -- notice it's got cut.
00:29:35.256 -- Classic tail design tail here and you see
00:29:38.286 -- you see here these tabs here in the back.
00:29:41.200 -- In the back there so that when this
00:29:43.816 -- is flying this remains flat and
00:29:45.979 -- then those back parts go up and
00:29:48.565 -- down again so that can maneuver
00:29:50.791 -- the plane going like this.
00:29:52.696 -- Turns out that Supersonically that is
00:29:55.054 -- not a very good way to maneuver in aircraft.
00:29:58.680 -- OK, so let's see why.
00:30:00.390 -- If this is flying super fast or if it's
00:30:03.261 -- flying this in the in the supersonic regime,
00:30:06.220 -- there were going to form there at the front.
00:30:12.230 -- Oblique shockwaves OK,
00:30:13.565 -- so an oblique shockwave forms there and
00:30:16.755 -- then these fins go up and down like this,
00:30:19.700 -- and so another shockwave is
00:30:21.665 -- going to format that side.
00:30:23.630 -- So you get 2 shocks that would form
00:30:26.014 -- and what aerodynamics is found is that
00:30:28.404 -- you could get a shock interaction
00:30:30.724 -- between those two shockwaves that
00:30:33.329 -- form their supersonic aircraft.
00:30:35.420 -- Nowadays will go back to
00:30:37.385 -- our F18 Hornet right here,
00:30:39.350 -- and you look at the tail.
00:30:42.720 -- Right here, OK, notice that there's no.
00:30:45.740 -- There's no part in the back there
00:30:49.408 -- that the whole tail moves up and down.
00:30:53.600 -- Like this or like this OK?
00:30:56.020 -- And it turns out that aerodynamically
00:30:58.438 -- again when this, when this turns,
00:31:01.363 -- say down like that.
00:31:03.650 -- Shockwave's going to form there at the
00:31:06.037 -- top and then you get smooth flow all
00:31:08.703 -- the way across the rest of the elevator.
00:31:11.420 -- OK, so that's another sign that you
00:31:13.583 -- could tell of what a supersonic
00:31:15.632 -- aircraft looks like if that whole
00:31:17.750 -- tail moves as opposed to just the
00:31:20.057 -- just the back portion of the tail.
00:31:24.300 -- Alright.
00:31:26.960 -- Aren't you gonna glad
00:31:27.896 -- you came to class today?
00:31:29.070 -- I'm glad that you came in class. OK.
00:31:33.690 -- Alaskan, so one of the things that now
00:31:36.554 -- that we've got this here, so let's see.
00:31:39.450 -- Did you send this to me?
00:31:41.610 -- Yes, so I got an email from Samantha.
00:31:44.490 -- He ran. She said that you should check
00:31:46.826 -- out this particular design and it's
00:31:49.187 -- called a coleopter Anna Coleoptile.
00:31:51.330 -- If you notice there that it has a,
00:31:54.210 -- it has a rounded wing on it.
00:31:57.880 -- That's that's kind of cool
00:31:59.755 -- right across there.
00:32:00.880 -- So here's the rounded wing.
00:32:02.760 -- Now it turns out that when
00:32:05.268 -- you have a finite wing.
00:32:07.520 -- Like you have here,
00:32:08.820 -- the pressure on the bottom of the
00:32:11.148 -- wing is higher than the pressure
00:32:13.014 -- on the top of the wing does.
00:32:15.150 -- That's how you generate lift.
00:32:16.740 -- But what happens is you have
00:32:18.504 -- what are called end effects.
00:32:20.240 -- So in end effect occurs when
00:32:22.052 -- the air on the bottom of the
00:32:24.311 -- wing kind of leaks out here,
00:32:26.280 -- and so you have high pressure air on the
00:32:29.133 -- bottom and low pressure air on the top.
00:32:31.690 -- And what that does is generate
00:32:33.826 -- these vertical structures go like
00:32:35.582 -- this and that causes a lot of drag.
00:32:37.730 -- It's a parasitic drag problem.
00:32:39.590 -- End effect drag problem OK in in
00:32:43.545 -- aerodynamics class you'd learn about how
00:32:46.926 -- wings can be shaped to minimize that.
00:32:50.610 -- The Spitfire that flew in World War
00:32:53.263 -- Two has elliptical shaped wings.
00:32:55.390 -- Beautiful beautiful aircraft but those
00:32:57.545 -- elliptical shapes right there minimized
00:32:59.759 -- the formation of those tip foresees.
00:33:01.750 -- OK so menace and minimizes
00:33:03.740 -- the drag flights faster.
00:33:05.340 -- OK so one of the nice things
00:33:08.028 -- about this design over here of
00:33:10.389 -- the coleopter is that it's got a
00:33:13.105 -- rounded wing so that there are no
00:33:16.024 -- tip effects that go across there.
00:33:18.489 -- Alright so you might think well.
00:33:20.910 -- How the heck does that generate
00:33:23.046 -- any kind of lift?
00:33:24.470 -- OK,
00:33:24.817 -- well it turns out that the angle
00:33:27.246 -- of attack is also related to the
00:33:29.756 -- amount of lift that you have,
00:33:31.950 -- so the higher angle of attack that you get,
00:33:35.150 -- the more lift you can generate.
00:33:37.290 -- Now for those that are paper airplane.
00:33:40.370 -- Enthusia STS
00:33:44.170 -- is it cold after I hear? Ever seen this?
00:33:48.130 -- And you can fly it. We'll see,
00:33:50.858 -- maybe we can catch this in slo-mo
00:33:53.266 -- from our from our from the cameras
00:33:55.583 -- here so you can fly this like this.
00:34:00.800 -- Not very good. Not very good.
00:34:04.260 -- But the idea is that you can generate lift.
00:34:07.500 -- Now you might think how can you
00:34:09.803 -- generate lift from something like that.
00:34:12.180 -- And again notice that in the picture
00:34:14.812 -- here it's flying at an angle of attack.
00:34:17.580 -- OK, so an airplane like this right here.
00:34:21.240 -- OK, actually has a slight angle of attack
00:34:24.008 -- built into it so that when it takes off.
00:34:26.710 -- In fact, if you if you look at it
00:34:29.374 -- straight and level right here, that Wing
00:34:31.812 -- has a little bit of an angle of attack.
00:34:34.760 -- OK, so that angle of attack is going to
00:34:37.460 -- create a small shockwave on the bottom.
00:34:39.920 -- Slight expansion wave on the top
00:34:41.852 -- so it generates lift.
00:34:43.140 -- OK, now it also answers the age old question
00:34:46.632 -- of how can a plane like this fly inverted?
00:34:50.330 -- OK, again, if this plane and you'll
00:34:52.283 -- notice it notice any aircraft when it
00:34:54.374 -- flies upside down screen level like
00:34:56.233 -- the Blue Angels and the Thunderbirds
00:34:57.871 -- when they do a flight show like that,
00:35:00.422 -- there's always a little bit of an
00:35:02.957 -- angle of attack as it goes down so
00:35:05.253 -- that it generates lift. OK, good.
00:35:10.130 -- That's your area lesson for today.
00:35:12.980 -- Alright. Got any questions?
00:35:14.924 -- Any questions? Anything we've seen so far?
00:35:18.570 -- OK.
00:35:21.500 -- So let's see here what we'd like to do now is
00:35:24.903 -- to figure out what we know for turning angle,
00:35:27.980 -- you can accelerate the flow.
00:35:29.600 -- What is the maximum turning angle?
00:35:31.540 -- How much can you turn?
00:35:33.810 -- And then what is the associated
00:35:35.670 -- Mach number associated with that?
00:35:37.230 -- OK, so here's our parental Meyer angle.
00:35:39.410 -- Theta of M is equal to this relationship,
00:35:41.900 -- right here it's got an arctangent of
00:35:43.972 -- the Mach number there and arctangent
00:35:45.881 -- of the Mach number right over here, OK.
00:35:48.439 -- So this is this will harken
00:35:50.353 -- back to your calculus days.
00:35:52.400 -- I know that was three or four years ago,
00:35:54.870 -- right so?
00:35:57.110 -- We're going to take a limit.
00:35:59.800 -- And what we're going to do is we're going
00:36:02.500 -- to take the limit as this angle as Phi.
00:36:05.330 -- We want to know what that
00:36:07.988 -- maximum turning angle is.
00:36:09.760 -- Of of our flow here.
00:36:11.500 -- So notice that in these arc
00:36:13.480 -- tangents right here we have gammas.
00:36:15.660 -- Cagamas are going to be constant for the air.
00:36:18.780 -- The only variable that we
00:36:20.515 -- have is the Mach number.
00:36:22.250 -- So we want to say if this
00:36:25.029 -- Mach number goes to Infinity.
00:36:27.460 -- What's the turning angle going to be?
00:36:30.510 -- OK, so just from mathematics right here.
00:36:33.560 -- The arctangent of Infinity is π / 2.
00:36:40.720 -- So we figure that one out.
00:36:43.170 -- Arctangent of Infinity is π / 2.
00:36:45.917 -- Let's go to the overhead here.
00:36:49.080 -- So have a triangle.
00:36:52.060 -- OK, and this is fi right here.
00:36:56.910 -- What's the tangent of Phi?
00:37:01.070 -- Say X. Why? Z what's tangent feet?
00:37:10.090 -- Tangent of Phi. The rise over the run. Y / X.
00:37:16.840 -- OK, alright, so let's let's
00:37:19.200 -- expand fi a little bit here.
00:37:26.040 -- Here is why an X.
00:37:30.280 -- 10s if he's going to get bigger
00:37:32.555 -- there right? 'cause your eyes.
00:37:34.314 -- Why is large and X is small here?
00:37:37.390 -- What happens when you have
00:37:38.560 -- a triangle look like this?
00:37:46.200 -- Look at this rise divided by
00:37:48.858 -- that teeny tiny run right there.
00:37:51.840 -- And then eventually.
00:37:53.553 -- You just have a straight line.
00:37:56.980 -- This is 90 degrees right here.
00:37:59.530 -- Which is the same. Is π / 2?
00:38:05.520 -- So the arctangent.
00:38:07.371 -- A fee from our little trigonometry
00:38:11.073 -- bit right there is π / 2.
00:38:14.287 -- That's why the limit as
00:38:16.972 -- fee tends to Infinity. OK.
00:38:21.280 -- Net fee is just the rise over the run.
00:38:23.900 -- That's why are y / X here is equal to π / 2.
00:38:27.653 -- OK, so if we take that limit then
00:38:29.757 -- Theta taking the limit here as
00:38:31.596 -- N goes to Infinity here an as N
00:38:34.053 -- goes to Infinity here substituting
00:38:35.528 -- in π / 2 to both of those terms,
00:38:38.160 -- we get that Theta is equal to π /
00:38:40.780 -- 2 times the square root of gamma
00:38:42.803 -- plus one divided by gamma minus one.
00:38:44.850 -- All this minus one right here.
00:38:47.720 -- So you can actually get a turning
00:38:51.066 -- angle of 130 degrees.
00:38:53.440 -- If you could turn that flow 130 degrees,
00:38:55.910 -- you would accelerate it to Infinity.
00:38:59.920 -- Obviously that's not going to happen OK,
00:39:02.030 -- Anna 130 degrees.
00:39:02.930 -- I mean, if you think about it,
00:39:05.040 -- it's got not just 90 degrees,
00:39:06.840 -- but now it's coming back
00:39:09.105 -- in the opposite direction.
00:39:10.920 -- Not an actual physical limit,
00:39:12.320 -- but a theoretical limit on what
00:39:14.474 -- the term could be in your flow.
00:39:16.940 -- OK, little bit of mathematical
00:39:20.750 -- gymnastics there OK?
00:39:23.040 -- This is the problem that was
00:39:24.912 -- cancelled in your homework assignment,
00:39:26.850 -- but I want you to make sure that
00:39:29.258 -- we've got shock tubes down so that you
00:39:32.133 -- understand how a shock tube works.
00:39:34.460 -- OK, so again,
00:39:35.264 -- this is 1/2 of it as a rehash from
00:39:38.039 -- when we did normal shocks and moving
00:39:40.909 -- normal shocks in a shock tube.
00:39:43.110 -- You have a driver section.
00:39:44.840 -- OK, high pressure gas right?
00:39:46.570 -- Over here there's a membrane that
00:39:48.856 -- separates this high pressure region
00:39:50.786 -- from a low pressure region right over here.
00:39:53.520 -- And this is what the pressure
00:39:55.986 -- profile looks like.
00:39:57.220 -- So you have a high pressure
00:39:59.542 -- region in the driver region.
00:40:01.740 -- A low pressure area right
00:40:03.795 -- here in the DRIVIN region.
00:40:05.850 -- OK then we break the membrane
00:40:08.406 -- and what that membrane does is
00:40:10.967 -- that it creates a normal shock
00:40:13.277 -- and that normal shockwave then
00:40:15.692 -- propagates down from left to right.
00:40:18.810 -- OK,
00:40:19.214 -- and so this stuff that we talked
00:40:22.042 -- about in class when we did
00:40:24.901 -- normal shops right across here.
00:40:27.350 -- Right across here,
00:40:28.307 -- we figured out what the pressure
00:40:30.602 -- profiles the Mach number is.
00:40:32.200 -- The Mach number of the wave, and so on.
00:40:35.225 -- We figured all this stuff out and we
00:40:38.262 -- ignored the things on the left hand side OK.
00:40:41.780 -- Kate, now that we know about expansion waves.
00:40:44.930 -- What's going on here between 3:00 and
00:40:47.450 -- 1:00 is an expansion wave problem.
00:40:50.330 -- Just like we talked about before.
00:40:53.610 -- OK,
00:40:54.067 -- so what's happening here is that again
00:40:57.266 -- you have a high pressure region here.
00:41:00.780 -- There is a lower pressure region
00:41:02.898 -- right across here in Region 3.
00:41:04.980 -- In fact,
00:41:05.714 -- if you look at the pressure
00:41:07.916 -- profile here it is.
00:41:09.180 -- This is the driven section
00:41:10.930 -- has a low pressure,
00:41:12.330 -- goes across the shock.
00:41:13.610 -- That's what this region is right
00:41:15.597 -- across here and then that pressure
00:41:17.727 -- remains constant to what's called
00:41:19.582 -- the contact surface right here.
00:41:21.430 -- And that's where Region 3 contacts Region 4.
00:41:24.230 -- And then there is a gradual
00:41:26.606 -- increase in the pressure right up
00:41:29.075 -- here and then the driver section.
00:41:31.480 -- OK,
00:41:32.021 -- so this gas this high pressure gas
00:41:35.808 -- begins to expand. As it goes across.
00:41:40.872 -- OK.
00:41:41.640 -- Draw that out, drawn out process out here,
00:41:44.900 -- OK?
00:41:46.430 -- So.
00:41:52.870 -- So here's the membrane.
00:41:54.442 -- Here's the high pressure section.
00:41:56.410 -- Here is the low pressure section here.
00:41:59.160 -- OK, when the membrane breaks.
00:42:03.680 -- Creates a shockwave.
00:42:06.900 -- Propagates down this direction here,
00:42:09.680 -- and an expansion wave
00:42:12.464 -- forms as this gas expands.
00:42:15.950 -- Into this region right over
00:42:18.695 -- here so that wave propagates.
00:42:21.440 -- Starts out small here,
00:42:23.416 -- gets a little bit larger.
00:42:25.890 -- And then that distance increases
00:42:27.525 -- right across there as this high
00:42:29.536 -- pressure gas region expands
00:42:30.820 -- and goes across this way.
00:42:35.040 -- As a as my kids say, you know fun
00:42:39.299 -- fact fun fact about expansion waves.
00:42:42.140 -- OK, this behaves exactly like.
00:42:46.240 -- A traffic jam or traffic
00:42:49.620 -- flow at a red light. OK.
00:42:54.940 -- But how could that be OK?
00:42:57.100 -- Think about this.
00:42:58.180 -- You have a red light right here.
00:43:04.440 -- We want to make this authentic,
00:43:06.310 -- so there's a red light right there.
00:43:08.480 -- OK? And there are cars lined up.
00:43:11.840 -- And it's all bumper to bumper, right?
00:43:13.897 -- I'm sure all of you keep a safe
00:43:16.593 -- distance right when you break.
00:43:18.520 -- In traffic, especially,
00:43:19.669 -- the traffic jams here in Moscow ID OK,
00:43:22.620 -- so looks like this and you can have a line
00:43:26.893 -- of cars that go all the way back here.
00:43:30.670 -- OK, so the red light then turns green.
00:43:35.490 -- Green light right here.
00:43:40.130 -- There's a green light OK,
00:43:42.170 -- and now the cars go do all seven of
00:43:45.050 -- these cars move at the same speed and
00:43:48.453 -- propagate through their drive-thru light?
00:43:51.150 -- No, what happens?
00:43:52.809 -- First car goes it's here.
00:43:55.580 -- And there's a larger distance
00:43:57.390 -- between that one and the next one,
00:43:59.880 -- and then that distance gets a
00:44:01.890 -- little bit smaller and smaller,
00:44:03.810 -- and the way in the back here is that,
00:44:07.040 -- and I've had this happen to me before.
00:44:09.900 -- Is that you see the green light here,
00:44:12.760 -- but the distance when I'm parked
00:44:14.710 -- way back here the distance between
00:44:16.863 -- me and that car hasn't changed.
00:44:19.210 -- Heckuva lot for 1015 seconds,
00:44:21.000 -- however long it takes to
00:44:22.790 -- propagate that through these cars.
00:44:24.580 -- Driving through here.
00:44:26.062 -- It turns out have the same
00:44:29.026 -- mathematical modeling associated
00:44:30.809 -- with expansion ways right there.
00:44:33.820 -- Same modeling process here.
00:44:35.308 -- This membrane breaks the gases expand.
00:44:37.540 -- This wave goes faster than this one,
00:44:40.140 -- which goes faster than this one and so on.
00:44:43.490 -- So as this as this pressure wave
00:44:46.381 -- propagates there through the back
00:44:48.431 -- has the same properties as cars
00:44:50.645 -- parked not part but in a in a
00:44:53.369 -- traffic line right across there.
00:44:57.160 -- There you can tell your folks
00:44:58.984 -- over the break that you learned
00:45:01.030 -- something here in gas dynamics.
00:45:02.940 -- OK, like I said, fun fact.
00:45:05.720 -- OK, shock tubes in let's go and here is
00:45:09.374 -- what happens after the membrane breaks.
00:45:13.010 -- OK, so let's look at the
00:45:15.920 -- expansion wave process.
00:45:17.380 -- OK, so here again these waves
00:45:19.840 -- propagate back and as they propagate
00:45:22.606 -- back eventually this high pressure
00:45:25.216 -- region is going to completely expand.
00:45:28.560 -- OK, so the initial state of our
00:45:32.179 -- of our shock tube right here.
00:45:35.730 -- Of this pressure difference
00:45:36.918 -- across here from one to two,
00:45:38.700 -- we have a high pressure region
00:45:40.380 -- in a low pressure region,
00:45:41.970 -- right across here,
00:45:42.858 -- that's called the diaphragm pressure ratio.
00:45:46.930 -- OK, right across there after that
00:45:49.348 -- diaphragm or the membrane breaks,
00:45:51.510 -- then the pressure in Region 3 is the
00:45:55.190 -- same as the pressure in region 4.
00:45:58.840 -- And the speed in Region 3 is the
00:46:01.216 -- same as the speed in region 4.
00:46:03.520 -- So if we go back to our
00:46:05.627 -- little drawing right here,
00:46:06.950 -- these two pressures are the same.
00:46:08.820 -- Cross this contact surface and the speed
00:46:11.004 -- of the air or the gases between those
00:46:13.570 -- two regions are the same as well. What?
00:46:16.176 -- What do you think would be different?
00:46:19.580 -- Speeds the same pressures the same.
00:46:21.010 -- What do you think would be
00:46:23.380 -- different across there?
00:46:24.570 -- What happens to the temperature
00:46:27.760 -- across a shockwave?
00:46:29.680 -- It goes up what happens to the
00:46:32.214 -- pressure downstream of this expansion
00:46:34.112 -- wave as it starts to expand.
00:46:36.320 -- Goes down. OK, so there's a.
00:46:38.530 -- There's a temperature difference between
00:46:40.365 -- 3:00 and 4:00, right across there.
00:46:42.586 -- OK, T4 is going to be higher than T2,
00:46:45.890 -- and T3 is going to be higher than T1.
00:46:49.830 -- That's really what defines that difference
00:46:51.882 -- right across there is that temperature OK,
00:46:54.380 -- but the pressures in those
00:46:56.130 -- two regions are the same.
00:46:57.880 -- The speed in those two regions of the same.
00:47:01.030 -- OK, so again, across an expansion wave,
00:47:03.480 -- the flow is isentropic.
00:47:04.764 -- So we can use our isentropic relations here.
00:47:07.680 -- P3 or P1 is equal to T3 over T1 to
00:47:10.572 -- the gamma over gamma minus one power.
00:47:13.630 -- Or we could write that in terms
00:47:16.843 -- of the densities as well.
00:47:19.090 -- You know this is nice because
00:47:20.590 -- once we get it in this form,
00:47:22.390 -- we can write this in terms
00:47:24.412 -- of the speed of sound.
00:47:26.330 -- So now P3 over P11 minus gamma one.
00:47:30.120 -- Over 2 times V 2 /, 81 squared.
00:47:33.334 -- So this is the Mach number.
00:47:36.680 -- OK, in the expansion region right there to
00:47:39.272 -- the two gamma sub one over gamma minus one,
00:47:42.260 -- right across there.
00:47:43.769 -- OK if we solve for V then.
00:47:47.290 -- We can solve for V2.
00:47:48.760 -- We can solve for the speed and region 2.
00:47:52.260 -- Right across there and it is just
00:47:54.808 -- a function of the speed of sound.
00:47:57.450 -- He said one and this pressure ratio,
00:48:00.050 -- the diaphragm pressure ratio P2 over P1 OK.
00:48:04.450 -- What it gives us here is that since gamma
00:48:07.105 -- minus one this power right over here,
00:48:09.410 -- gamma minus 1 / 2 gamma is less
00:48:11.658 -- than one as PP1 tends to Infinity.
00:48:14.060 -- This term is going to go to zero,
00:48:16.540 -- and So what this does is you
00:48:18.990 -- can generate a maximum.
00:48:20.780 -- Speed in region 2.
00:48:22.528 -- From this term right there twice,
00:48:25.150 -- the speed of sound divided
00:48:26.930 -- by gamma minus one.
00:48:28.360 -- OK, enough gammas for air,
00:48:29.850 -- that's one point 4 -- 1 or that's two
00:48:32.588 -- times the speed of sound divided by .4.
00:48:34.920 -- What it tells you can do is you
00:48:37.608 -- can generate pretty high speeds.
00:48:39.820 -- With the shock tube.
00:48:42.040 -- OK, they don't last for very long.
00:48:44.230 -- OK,
00:48:44.522 -- but you can get hypersonic flows from a
00:48:46.858 -- shock tube that comes right across here,
00:48:49.240 -- OK?
00:48:51.270 -- Good,
00:48:51.614 -- so that was the problem
00:48:53.334 -- that was cancelled is
00:48:54.781 -- to figure out the expansion portions
00:48:56.983 -- of the flow. OK, any questions? Yes.
00:49:04.810 -- OK, I'm getting to that,
00:49:06.520 -- so I answer part one.
00:49:08.220 -- No shock tube questions,
00:49:09.572 -- no moving shock problems on the exam.
00:49:14.180 -- What's that? And an airfoil
00:49:18.041 -- is not a shock tube, so yes,
00:49:20.052 -- so there is an airfoil problem.
00:49:21.770 -- There is not a shock to problem.
00:49:23.780 -- OK, I just want to make sure that
00:49:26.068 -- you understood kind of the basic
00:49:27.825 -- workings of what a shock tube are.
00:49:29.810 -- OK, not answer your question here.
00:49:31.530 -- Exams are open book.
00:49:33.690 -- Open notes OK.
00:49:37.600 -- And it's also open laptops if you
00:49:40.414 -- choose that you've got a laptop to use
00:49:43.203 -- com prop that is OK to use as well,
00:49:45.950 -- but there are no communications
00:49:48.122 -- with the outside world or the
00:49:50.278 -- inside world on your laptop.
00:49:51.870 -- So if you have a phone 'cause you
00:49:54.558 -- want to use your app, that's OK too.
00:49:59.430 -- OK, so open book, open notes, open com,
00:50:02.910 -- prop, or if you've got some other,
00:50:05.960 -- you know if you use some other device
00:50:08.848 -- for your compressible flow tables,
00:50:11.610 -- that's OK as well, yes?
00:50:17.110 -- Open Book open notes.
00:50:24.070 -- There are five problems on the exam,
00:50:25.450 -- so if you spend all your time looking
00:50:26.946 -- at your notes, you're not going to
00:50:28.408 -- have time to solve the problems.
00:50:32.510 -- OK, so be sure that your
00:50:34.682 -- your laptops are charged.
00:50:36.130 -- We don't have a whole lot of.
00:50:38.660 -- Let's see. Do you have?
00:50:40.470 -- Do you have plugs underneath?
00:50:44.200 -- Not sure what you got there. OK.
00:50:48.770 -- And you will have the hour and 15
00:50:51.746 -- minutes to solve the exam as well.
00:50:54.520 -- OK, I will talk to the greater today and we
00:50:57.548 -- will try and get this graded by tomorrow.
00:51:00.370 -- So if you want to pick him up
00:51:02.818 -- tomorrow you could come by my
00:51:04.854 -- office and pick up the exams.
00:51:06.870 -- That's fine.
00:51:07.616 -- The solutions are also will
00:51:09.481 -- be available this afternoon.
00:51:11.310 -- So even though even if you don't
00:51:12.689 -- have your homework assignment,
00:51:13.750 -- if the greater can't get it back in time.
00:51:17.120 -- Can you can always look online on TV learn?
00:51:21.160 -- OK. Good, so let's see here.
00:51:24.980 -- I would say that the exam problems
00:51:26.807 -- are going to be very similar to what
00:51:28.959 -- you see in the homework problems.
00:51:30.830 -- Let's just let's just review.
00:51:33.610 -- Write reviews 'cause then you
00:51:35.720 -- can see how intelligent you have
00:51:38.277 -- become over the last one week.
00:51:40.500 -- Six now, let's see what we've discussed here,
00:51:43.740 -- OK?
00:51:45.680 -- Just going through just going through the
00:51:49.460 -- going through the table of contents here.
00:51:53.280 -- OK, let's see here.
00:51:54.708 -- You probably won't have any problem that
00:51:57.396 -- just discusses the continuity equation.
00:51:59.780 -- You probably won't have a problem
00:52:02.222 -- that just has the ideal gas law,
00:52:05.050 -- but you could certainly use it.
00:52:08.650 -- OK,
00:52:09.065 -- some fundamental aspects
00:52:10.310 -- of compressible flow.
00:52:11.560 -- You know how to calculate the speed of sound?
00:52:16.350 -- OK, and you know how to calculate
00:52:18.380 -- Mach numbers and Mach waves.
00:52:19.950 -- I would say that's going to
00:52:21.840 -- be something to study up on.
00:52:23.550 -- Make sure that you understand what
00:52:25.224 -- a Mach wave is and how different
00:52:27.348 -- it is from an oblique shockwave.
00:52:29.250 -- What is the difference?
00:52:32.300 -- What's the difference between an
00:52:33.910 -- oblique shockwave animac wave?
00:52:37.280 -- A Mach wave is an infinitesimally
00:52:40.880 -- weak oblique shockwave.
00:52:42.680 -- OK. Good. Uh, now?
00:52:49.560 -- You probably won't have a problem.
00:52:50.820 -- It says, just calculate the speed of sound,
00:52:52.500 -- but you will likely have a problem.
00:52:53.970 -- You'll have to calculate the speed of sound.
00:52:56.440 -- OK, so this is all fundamental
00:52:59.068 -- stuff right here.
00:53:00.390 -- OK, in chapter four we learned about
00:53:02.938 -- isentropic flows and the difference
00:53:05.251 -- between stagnation conditions,
00:53:06.980 -- static conditions and critical
00:53:08.732 -- conditions right there, OK?
00:53:12.020 -- You probably won't have a problem
00:53:14.138 -- that says what is the stagnation
00:53:16.500 -- temperature of such and such.
00:53:18.680 -- You might OK, but you'll be able to.
00:53:21.820 -- You'll need to calculate what stagnation
00:53:25.144 -- temperatures are and pressures.
00:53:27.360 -- Pretty straightforward using
00:53:28.542 -- the tables using comp.
00:53:30.120 -- However you want to do it OK.
00:53:32.880 -- We learned about shockwaves.
00:53:35.072 -- OK, and you'll probably see some problems
00:53:38.584 -- that have a normal shocks in him.
00:53:41.890 -- OK, that's very important in gas dynamics.
00:53:46.210 -- OK, pitot tubes. Are also important,
00:53:51.190 -- so make sure you got those down.
00:53:54.150 -- Don't worry bout moving normal shocks.
00:53:58.200 -- OK.
00:54:00.360 -- Are oblique shock waves are important?
00:54:02.620 -- Make sure that you've got those down
00:54:05.147 -- and expansion waves are also important.
00:54:07.520 -- Make sure that you've got that down.
00:54:12.350 -- And make sure that you've got
00:54:14.702 -- the reflection part of oblique
00:54:16.895 -- shockwaves down pretty well. OK.
00:54:21.310 -- Again, as you learn in your problems,
00:54:23.570 -- a lot of it's just the geometry.
00:54:25.830 -- Make sure you've got the
00:54:27.890 -- direction of the flow right. OK.
00:54:32.670 -- Just to re clarify. We're going to
00:54:36.557 -- go back to our normal shocks here.
00:54:42.040 -- Region 1. Region 2 flow goes
00:54:44.950 -- this way comes out this way.
00:54:47.930 -- This is the region that is upstream.
00:54:53.590 -- It is also ahead. Of the shock.
00:54:59.930 -- OK, this is the supersonic flow.
00:55:03.280 -- Regime this is the subsonic flow.
00:55:07.240 -- Regime this is. Downstream.
00:55:12.700 -- Of the shock, this is also behind.
00:55:17.250 -- The shock there means the same thing.
00:55:21.530 -- OK, sometimes a problem will ask
00:55:23.396 -- what's the temperature and
00:55:25.004 -- pressure just downstream of the shock?
00:55:26.870 -- Where does that where you where?
00:55:28.750 -- Are you looking to calculate that?
00:55:31.280 -- Right there.
00:55:34.070 -- Just downstream so you don't have to
00:55:35.876 -- worry about any of the flow anywhere else.
00:55:38.000 -- What's the temperature and pressure?
00:55:39.310 -- The Mach number just downstream of the
00:55:41.564 -- shock just in that region right there?
00:55:44.080 -- OK. Excellent. Any questions?
00:55:52.850 -- OK, have a wonderful day study
00:55:55.724 -- up for the exam and we'll see
00:55:59.529 -- Thursday bright and early.
STAT 422 SU 23 SESSION 4
Back to, well, our beginning review stuff, but that's okay, all right.
So we finished up last time in Chapter 2 and Chapter 2 basically was just kind of talking through about some errors in surveys that can happen looking at the types of sampling.
So we do probability sampling now and not quota sampling and that kind of stuff.
So just a little bit of basics.
Make sure you do read through this chapter though, because it will actually go over the nitty gritties of some questions and what have you and some examples of say like open versus closed questions, good versus bad questions, those kinds of situations.
So make sure you definitely read through Chapter 2.
So chapter three starts us.
If I can get to chapter 3, here we go.
One more page, some basic concepts, and then we'll move into chapter 4, which talks about basically the starting of our first actual design, the simple random sample.
So for right now, we got to review some basic concepts.
So some more notes today.
I promise we won't always be doing handwritten notes, but it does slow me down because I talk too fast.
So it helps you and me.
All right, so let's go here and talk about starting some basic concepts.
So one of the first things we need to do is to be able to follow.
We're talking about objectives.
So one of the main objectives is to find a way to phrase an inference about a population, or equivalently, to describe a set of measurements.
Equivalently to described just to describe a set of measurements.
All right, so that's one of the first thing.
One of the second one is to consider how inferences can be made about the population from information contained in a sample.
And then we'll actually have two things we want to consider on one.
So how inferences can be made about the population from our information contained in a sample contained in a sample?
There we go.
So for those we need to consider two things.
We need to consider the probability distributions of sample quantities or sampling distributions, probability distributions of sample quantities, or sampling distributions, which we will discuss to remind you of sampling distributions.
Usually in your intro class the sampling distributions are introduced about probably about the halfway point of the semester, and it's usually what precedes the inferential statistics when you first start alerting confidence intervals and hypothesis testing.
So that was what preceded that because we carry the sampling distributions through the process in our confidence intervals and our hypothesis testing.
So for this, the reason why we want to do this is this allows us to choose proper inference procedures because we don't want to choose an improper one.
And I'm not trying to be cute or funny about that.
I mean it and then I laugh.
But no, I'm serious.
I mean it now in a lot of situations and especially business and social sciences, our main method of inference and business and social sciences is estimation.
Now a lot of times in inference your goal wasn't necessarily for estimation, but in specific applications of business and social sciences.
We are not going after say, answering a question about a whole population in terms of you know, is the mean equal to 5 or whatever number is K We want to actually look at the estimator.
We are interested in estimation.
So estimators and bounds, All right, Now we're going to look at summarizing information in populations and samples.
Populations and samples.
Now the ones we learned in intra class, unless yours went into a little bit more concepts of outside of it.
But for the most part in your interclass we learned procedures and about summarizing information and populations and samples by using our summary statistics and what have you.
And we are talking about that.
But what we were doing before with the populations is we were looking at infinite populations and that's all of the methods you mostly learned in intraclass were based on infinite populations.
That being said, the caveat for that is it if your intro class went into a little bit more for sampling design like more detailed, you might have actually seen finite populations.
But for the most part, our introductory course talks about infinite populations.
And well, you don't mean infinite as in truly infinite, but you know, relatively large, so infinite populations.
That's kind of where we're starting.
No, we have problems now think about populations sometimes, not all measurements in a population are generally available for study.
OK, so even though all measurements in a population for a study are generally not available, we can still do something we can still get.
Actually, I screwed up my language here.
We may still, there we go, be able to assume some reasonable graphic shape graphical shape for our relative frequency distribution of our of our probability distribution of the population.
So we were still able to assume some reasonable graphical shape, so we can still get an idea of the distribution for the relative frequency distribution of the population.
So we can still get an idea.
Even if we can't get all the information from the population, like every single measurement, we can still get an idea to assume some reasonable graphic graphical shape for their relative frequency distribution of the population.
So what we're going to be doing is looking at being able to calculate some summary calculate in summarizing numerical measurements and quantities like the mean, variance, standard deviation, etcetera.
So I'll just say we can calculate summarizing numerical measurements like the mean variance.
There's an E on the end, sorry, standard deviation.
Our book likes to abbreviate standard deviation with like literally just a capital SD, but that's OK.
However you want to do that, we can also use S if we're talking about the sample standard deviation or Sigma.
There we go.
So let's assume a population.
Let's do a little, let's do a little, a little experiment here, a little, some calculations.
So we're going to go over and look at a population that consists, I'll say, of a large number of integers.
You could think about them like a random number generator.
A large number, sorry, of integers between zero and nine.
OK, and these are all going to be in equal proportions, all right.
And our relative frequency histogram With this, if each of our numbers zero through 9 have an equal proportion, equal probability of happening.
Pardon my drawings, I am not an artist.
Then their probability would look some their distribution, their histogram.
Let me make sure I have 9 bars here, 12345, yes.
So there's zero and there's nine.
And these are all going to have .1 chance.
So this down here we denote as Y and up here we denote as the probability or relative frequency.
There we go.
So this is what it look like.
I'll put a little label there of integers 01 tonight.
There we go.
So it look like this.
Yay, this is what our distribution looks like.
Not very exciting, but it's okay.
It still works.
So let's talk about a procedure we like to do.
We say, let's pick a number at random, Okay.
So one number, select it at random.
Then the probability there's a T in there Ty there we go.
That the selected number the randomly selected number out of our group of integers from zero to 9.
The probability that that selected that the selection that we there we go.
Sorry I should just start a new piece of paper but I won't.
So the probability that we selected the number will be a four.
Actually let me write out the actual #4 is 110th.
So in other words the probability of say 4.
I don't have enough bars, do I?
I screwed it up.
There we go.
Pardon my, pardon my screw up here.
And this is #8.
This is #9.
I should have made 10 bars.
There we go.
So the probability that was a four, if they're all equal probabilities, it's just 110th because there are 10 total numbers, 123-4569 ten.
There we go.
OK, now what we usually end up doing is we select.
Suppose one number is to be selected at random, and its value will be denoted as Y or by Y.
However you want to say that.
Now for the most part we're just going to be using lowercase Y, but if you see my y's for me, lower case will look like this.
I'll try and always put a little curve in there, almost like a U and then a a little tail for the Y upper case, I usually make it more straight so it's more more angled.
I don't know in case that comes up later on.
I just wanted you to see the differences between my Y's because sometimes they don't look that much different if you're not really saying it Nexus or worse.
All right, So the possible values for Y we have them are 01 all the way up to 9, OK.
And the probabilities that are associated with those associated with those values, which in this case is going to be 110th for all values of Y constitute what we call the probability distribution for the random variable Y.
You may have used X in your intro class.
I know my intro textbook uses X but XY Pick a letter, it doesn't really matter.
Let's see here.
So, and the probability associated with those values constitute what we call the probability distribution of Y.
Well, let me say that again, probability distribution for the random variable Y.
And if you remember what a random variable is, it's basically just a valued function and it works similar to a function hey, where we look at the values of Y and their probabilities.
So notation wise, probability y = 0 in this case is also equal to all the other probabilities for us Equals...
Equals probability y = 9, and they're all equal to 110th.
We'll put it in a little table here in just a moment too, because I like to put it in an actual physical table.
Tables are nice, all right.
Now for shorthand notation, not because it's so difficult to write P y = 0 or P y = 1.
You can actually write it in a little bit slightly more shorthand notation.
You can just put P of 0 or P of 1.
In this case, they're all I did it.
I was bad, naughty.
There we go, there we go.
I was trying to go back to this Y notation.
So if you see this, especially in the book, likes to use this, it just means the same thing.
It's like talking about a random variable.
In this case equals zero or one or nine.
Just different notations.
No big deal.
All right, let's put it in a table though.
Table is awesome.
Tables are great.
So let's look at our actual probability distribution.
So when you see probability distribution, it just spells out what the distribution looks like.
It either gives you a function, if we're looking at something that, say, continuous, or we have a table for what, in this case, discrete distributions.
So now I got to figure out how many I need.
Well, I need 100123456789100.
There's No 10.
Sorry, I just wanted 10 numbers, No .1.
Or you can use fractions.
I don't care.
Whatever makes your brain happy.
OK, so there's our probability distribution of this scenario we're looking at.
Now, this is nice because it nicely organizes all your information.
So you can go, Oh well, if Y is 4, what is my probability?
Oh, there it is right there.
Now in this case, all of our probabilities are identical, just through this little example.
They won't necessarily always be, but it looks much better and a lot more organized in a little table like that.
Kind of funny how something small like that makes a huge difference.
Now at this point it's great so that you can see the distribution and all the values everything takes on.
There are some other things that we'd want to do, of course there are.
So we want to look at numerical measures that are used to summarize.
So numerical summaries, so numerical measures or measure, yeah, that are used to summarize what we call the characteristics of the population.
TICS, there we go of the population are defined.
As expected values.
Probably a word you've heard before.
I'm going to kind of underline these because this is kind of a new concept.
Well, it's not really super new.
You've heard it before, but these are defined as expected values of Y or like a function of Y.
By definition, the expected value of Y, which we don't have to always write out as the actual word expected value.
We have a nice nice pretty notation of Y, so we do E of Y.
Kind of like function notation.
If you remember, function notation was like F of X, so it kind of looks the same.
It's not exactly because this was implying that we have something continuous.
This isn't necessarily all right.
So is expected value of Y.
Take the sum of each Y times the probability of that Y and you add them all up, and then we talk about for which P of Y has to be greater than 0.
Now we know probabilities to be valid can be equal to 0, but in terms of the using this, when we want to look at the variance, we need to have probabilities that aren't necessarily zero.
It's really not the probabilities we're has worried about.
But anyways, so for which P of Y is greater than 0?
So then our expected value of Y.
When I expand this, we take zero times the probability of 0 + 1 times the probability of 1.
Oh so on and so forth.
I put one too many dots, pardon my ellipse, it was wrong.
And then we go out to the last one.
So to do that for us, for our little example here, we take zero times the probability of 0, which is .1 or 110th.
I'm going to put in fractions.
I like fractions plus one times 110th because that is the probability of 1 all the way out to 9 * 1/10.
So 0 summed all the way through nine gives us 45 and we multiply that by 110th and we get 4 1/2, so that is our average for this thing.
And so this EY expected value of Y is equal to the mean, the mean value.
So this is what we're going to be looking at in terms of calculating some of these summaries.
OK, let's do the variance.
Because we want to look at the variation.
Variation is very, very, very important to look at because it actually tells us a lot more of what's happening, say with our mean if we know the variation around it.
So we always want to look at variation.
It's the big one variance.
We do this V of Y.
The other thing we want to say is that more often than not, before I move on to the variance real quick, when we do this, this is what we call an unbiased procedure.
So then the expected value of Y should equal mu OK.
Mu should equal this value.
The sample mean.
The expected value should be equal to the population mean.
OK, and that actually comes from intro class.
That X bar or Y bar estimates our mu, whatever it is.
The mean, whatever that mean is.
All right, so variance.
All right, this one's not too bad.
So what we want to do then is take.
It really is the expected value of Y minus mu quantity squared, and we calculate this by taking the sum of each value of Y minus the mean.
We square the difference, and then we multiply it by the corresponding probability of Y.
Let's do it.
So we're going to still use our distribution.
So to do this, we're going to take each value of Y and subtract the mean from it.
And our mean is 4 1/2.
That's what we calculated.
So we're saying mu is 4 1/2.
So now we take each value of Y.
So we're going to start with 0 minus the mean squared times the probability of 0.
Could you put in a .1 and said yes, you don't have to use fractions.
Evidently I'm on a fraction kick.
I like fractions.
So there is the second value of Y and we go on to the next one and I'll actually do the whole thing.
Ooh, ( 2 -, 4 1/2, ^2, Quantity squared times probability of two.
And then we go on to three.
I did it over again, 3 -, 4, 1/2.
Sorry, ignore that little whatever that is.
Times the probability of three 4 -, 4, 1/2.
Oh, almost got a 0.
Not close enough for us to have a zero.
And then we have going to five times probability of five, and then six, 7-8 and nine, and we'll be done.
But we still need to subtract each value from the mean, square that difference, and then multiply it by the probability of the Y value we're on squared times probability of.
There we go.
We're almost done.
No, of course I couldn't squeeze that last one in there on that road.
That's okay, yay.
So we do all that.
So that's really.
You could actually factor out a 110th from each single one, so it'd be 110th times the sum of all these squared differences.
You'll get the same way either way you go.
So when we saw we can, we take all these values and we subtract them from their mean and we square them and we add them all up.
After we factored out the 10th, 110th, we get 82.5, so 82.5 * 1/10 gives us 8.25.
And this would have squared units of measurement, the expected value, the mean that has normal units of measurement.
In this case, they're arbitrary, so we're just saying units, whatever they are, variance has squared units.
Now commonly you may see variance of Y be denoted by Sigma squared.
It can also be denoted by s ^2 that usually that usually infers that we're dealing with a sample versus a population.
OK, now the standard deviation.
Ah, it's a lovely thing.
I like standard deviations.
You've already done all the hard work and the variance.
So standard deviation you can denote it as Sigma or you can actually do.
I use this notation in my class.
Standard deviation of Y works the same.
This is fine too.
And now keep remembering that Sigma is the square root of Sigma squared.
So that means that the standard deviation of Y is equal to the square root of the variance of YOK.
So it's the same relationship.
So for our little example, we'll take sqrt 8.25.
I don't know what that is.
That's why I brought calculator.
I don't know.
Do we need to?
You guys can watch it.
It's not that exciting.
I don't know how how good it's going to show up, and it has nothing to do with the cameras here.
It's just trying to get this thing on a camera is pain.
You can kind of see it maybe a little bit.
Yeah, sqrt 8.252 point 87, do we need to round it out to your take it out to like 16 decimal places?
No, 2.87228 and we'll round that to probably 2.87 or even 2.9 is fine.
And this would be back down to singular units of measurement, not squared units of measurement.
Things we've seen before, you know, may have been a little while since you've seen some of them, but you know we've have.
You have had exposure to this before, or at least you should have.
And if you haven't had much exposure to it before, please don't hesitate to contact me and I'll give you some extra things so that you can work through it and maybe kind of help grasp it a little better.
If you're having issues.
All right now in our statistical studies, studies, our population of interest contains unknown quantities or unknown measurements.
Contains or consists of.
There we go, unknown measurements, because you can't contact everybody.
You know everything or every person in the population.
Most of the time especially.
Well, you can't in the infinite population.
So it's just what we're dealing with.
So in infinite populations, we're going to have a chunk of the, you know, the population of interest is going to have consist of unknown measurements.
OK, so we can only speculate about the nature of our relative frequency histogram, about the graphical shape, because we can get an idea from a sample.
It doesn't necessarily mean that the entire population looks exactly like that.
OK, but we can still gain some, you know, get some nature, glean some idea of what this is supposed to be about.
The graphical shape or the size of our mean and standard deviation.
So mu and Sigma.
So remember, these are population values, They represent the actual true mean and true standard deviation.
OK, so for samples we calculate the sample mean Y bar, which is the sum of all of our Y's divided by N, or you can see it 1 / n times the sum of Yi.
So we take all of our observations, add them up, multiply by 1 / n or divided by N However you want to look at that, I'll get you the same direction.
So this is our sample mean.
OK, S ^2 then would be our sample variance.
So we take the sum of each value minus its mean quantity squared.
We divide by n -, 1, and then S is just sqrt s ^2 and it's always the positive square root.
So because you know when you take square roots you can actually get a negative or a positive answer.
But our variances and standard deviations always need to be greater than 0.
Well, greater than or equal to 0.
So yeah, we only get the positive sqrt s ^2.
Sample standard deviation s ^2 needs to be greater or equal to 0, and so does S Important.
All right, so we're going to go back to our examples.
This is our population.
Y can go from zero all the way up to 9..., 9, and the probabilities of all.
I'll just say Yi equals 110th.
So I'm just saying any of these is going to be 110th.
What if we just sample out of here?
Oh God, no, not a sample.
We're going to take a sample out of our population.
Let's do it.
Take a sample.
It's a random sample, so I'll say random of n = 10 measurements from this population.
All right, so to do that, let's pretend it was already done.
OK, because it was already done.
We'll talk about how we actually draw samples in a little bit, too.
But so each of the 10 measurements was selected at random.
You can think about drawing, you know, 10 pieces of slips of paper out of a box or out of a hat, you know, whatever.
Picking 10 playing cards.
Well, if that was what we're doing, playing cards aren't very exciting because they won't do us.
They won't give us the zero through nine thing.
But think about, you know, just drawing numbers out of a out of a hat.
OK, so our sample measurements, here's the sample we got a 693817884 and a zero.
No twos, no, no fives.
It was this random sample.
It could happen.
So for this sample we'll calculate our sample statistics.
So Y bar is the sum of all of our Y's divided by how many.
We have sample size, so 6 + 9 plus 38178840 divided by 10 and we get 54 tenths or 5.4.
So there's our mean.
We know that the true mean of the whole population.
We've already figured that one out.
That's what we were doing before.
The true mean of our whole population should be 4 1/2 out of our sample.
We got 5.4.
OK, it's not perfect, but it happens.
Let's do s ^2.
So we want to take the.
This is just another derivation of this formula.
So we take 1 / n -, 1 times the sum of HY minus the mean quantity squared.
So for us that's going to be, well, 1 / n -.
1 is going to be 1 ninth times.
And then we get to do all these fun things.
So we take our first value, which was a six minus the new mean, and then we go on to the next one, 9 -, 5.4 ^2, all the way to the last one.
And yes, we still have to do the zero.
So when we get all this we get 1/9 * 92.4 or 92.4 / 9.
Same thing 10.27.
Remember we're dealing with squared units now.
What was our true variance of our population?
Our true variance was 8.25.
This one's 10.27.
Not too horrible, but notice it's not exactly the same.
So square root for this 1 sqrt 10.27 gives us our standard deviation of 3.20468, but we'll just round it.
Now if we didn't know mu.
If we actually didn't know what the true mean was, and we didn't know it was in fact 4 1/2, this is actually a reasonable estimation or approximation for mu.
If we didn't know mu, so Y bar is a reasonable approximation to mu.
If mu were actually unknown, no, Since we know it, we know that this Y bar is a little off, and that happens with samples.
I could take another sample of 10 measurements out of that population and we'd end up with a different mean, but eventually all those little means should actually converge or average out to the true mean.
OK, but we're not quite there yet.
But right now, if we didn't know mu why bar is actually still a reasonable approximation.
Now, yes, there is a difference between 5.4 and 4.50 K by .9, but really, that's not too bad considering.
OK, considering we didn't know the whole population and this was just a random sample, this is pretty good.
I'm not going to say it's perfect because it's not, but if mu were unknown, this would be a reasonable approximation.
Same thing with the variance if S square.
If Sigma squared, our actual true variance was not known.
OK, the one we got was is considered to be reasonable reasonable approximation.
So s ^2 might be again a reasonable approximation for Sigma squared if Sigma squared is truly unknown.
And then of course the same thing goes with S The sample standard deviation S is a reasonable approximation for S if S is true.
If the true S is unknown, so S the way the book words it might form a reasonable approximation to Sigma.
So Y bar estimates.
Mu Sigma square s ^2, sorry, estimate Sigma squared and S estimates S Sigma trying to do too many, too many on the same thing.
So the other thing is we want to look at and think about is that for randomly selected samples from infinite populations are mathematical properties of of expected values can be used to derive some facts.
Mathematical properties of expected value can be used to derive the that our expected value of Y bar the sample mean.
Notice we were doing expected value of Y before, but we're doing that.
We're now saying expected value of Y bar is equal to mu.
The variance of Y bar is equal to Sigma squared divided by N And the standard deviation.
Well, we don't actually talk about the standard deviation, which is weird.
That equals Sigma divided by square root of N because we take the square root of this whole thing right here.
So Sigma over square root of N You can also see that the estimated variance of Y bar can be used when we were using sample information.
So notice that these two are basically the same.
This V hat means that it's an estimated variance of Y bar versus an actual variance of Y bar.
So this is an estimate.
But this estimate using S ^2 should give us pretty close to what Sigma squared is over N So these should be.
This should estimate the variance of Y bar.
Now we need to talk about sampling distribution, so that is going to be the first thing we hit.
Next time is sampling distributions because that is important.
And we will also have hopefully a simulation so that we can look and see how a specific sampling distribution theorem works.
And as a reminder, like most of us should have seen this theorem that's coming up in our neutral class.
And if you haven't, that's OK.
I'm still going to reintroduce it.
So, all right.
So I'm going to wrap this up and next time we are going to continue on from here, but we're going to be specifically talking about sampling distributions and then we'll go on from there.
Have a great day.
00:00:21.060 -- Audi so this is the 7th lecture and
00:00:25.486 -- we're going to continue on with work
00:00:28.634 -- related musculoskeletal diseases.
00:00:30.250 -- So when I talked about anthropometry
00:00:33.778 -- couple lectures ago I talked a little bit
00:00:37.595 -- about this one commercial where Shaquille
00:00:40.120 -- O'Neal is trying to get into a small car.
00:00:43.670 -- And I have found that video and I'm waiting.
00:00:46.270 -- I'm trying to find another video that I
00:00:48.310 -- want to show from anthropometry as well,
00:00:50.610 -- and I haven't located it yet,
00:00:52.340 -- but I want to show this video really quick,
00:00:54.940 -- and again it's throwback to
00:00:56.380 -- a previous lecture,
00:00:57.250 -- but it's pretty interesting
00:00:58.430 -- how they how they set it up.
00:01:12.700 -- I may have retired from the game.
00:01:14.870 -- But not from being big. Good thing.
00:01:17.104 -- One car gives me full size luxury and
00:01:19.916 -- 36 MPG which is nice because I've got
00:01:22.596 -- shoes that are bigger than most hybrids.
00:01:25.370 -- And more stylish too.
00:01:27.990 -- If you don't know the luxurious yet fuel
00:01:30.542 -- efficient across you, don't know Buick.
00:01:32.433 -- Get two years of premium services
00:01:34.359 -- with nothing to at least signing on.
00:01:36.520 -- The EPA estimated 36 Hwy MPG
00:01:38.416 -- lacrosse with the assist.
00:01:39.680 -- Consider it if you don't know the looks.
00:01:43.570 -- If you don't know the luxurious.
00:01:46.810 -- And more.
00:01:49.340 -- So I don't know if you see this self.
00:01:52.570 -- You along with me along with
00:01:55.096 -- this commercial but you can see
00:01:57.888 -- Shaquille O'Neal sitting here.
00:01:59.940 -- They've obviously put the seat way back
00:02:02.495 -- so he could actually sit in the car.
00:02:05.390 -- You can see where his knees are
00:02:07.693 -- in relationship to the dashboard
00:02:09.563 -- and the steering wheel.
00:02:11.190 -- It's obvious that he doesn't
00:02:13.235 -- fit into this car very well.
00:02:15.770 -- He is a a big person.
00:02:18.660 -- And it's just almost ridiculous
00:02:20.525 -- that they have him trying to look
00:02:23.146 -- comfortable in this car because he
00:02:25.192 -- could not drive this car comfortably.
00:02:27.710 -- It be like me trying to fit in
00:02:30.998 -- my daughter's Honda Fit which is
00:02:33.748 -- about the same as Shaq sitting
00:02:36.590 -- in this Buick Lacrosse.
00:02:38.740 -- So again from anthropometric standpoint,
00:02:40.570 -- it's a mismatch.
00:02:41.830 -- He would be very uncomfortable
00:02:43.930 -- and probably sore at the end
00:02:46.020 -- of a very short drive.
00:02:51.800 -- So. We're going to talk about work related
00:02:57.095 -- musculoskeletal diseases of the spine.
00:03:01.300 -- And.
00:03:06.060 -- Paratroopers, helicopter pilots,
00:03:07.296 -- other people in the Military,
00:03:09.360 -- Navy Seals that have to ride in
00:03:12.314 -- the Zodiac boats quite a bit,
00:03:14.730 -- all experience a high degree of back
00:03:17.376 -- injuries associated with their professions.
00:03:19.690 -- Now these are militaries standpoint.
00:03:23.300 -- People of all professions.
00:03:25.460 -- Office workers,
00:03:26.540 -- people that are working on shop floors.
00:03:32.000 -- All experienced back problems
00:03:33.784 -- at various times depending on
00:03:36.014 -- the type of tests are doing.
00:03:38.230 -- There's some genetic components to it.
00:03:40.720 -- The fact that sometimes are not moving
00:03:43.583 -- around and so they can experience problems.
00:03:47.170 -- So what we're going to talk
00:03:49.606 -- about in this today's lecture,
00:03:51.980 -- our spine anatomy and then spinal work
00:03:55.452 -- related musculoskeletal diseases?
00:03:56.940 -- I do have several videos,
00:03:58.890 -- again talking about very aspects
00:04:01.200 -- of various aspects of.
00:04:03.050 -- Dumb.
00:04:04.900 -- No musculoskeletal diseases of
00:04:06.440 -- this particular one talks about
00:04:08.365 -- the anatomy of the spine.
00:04:10.040 -- This is when I found it's truly it.
00:04:12.970 -- More educational and in nature,
00:04:14.810 -- and then we'll go through it in
00:04:17.134 -- detail as we go through the lecture.
00:04:23.150 -- Hi there, I'm doctor Gary Simmons
00:04:25.412 -- of Curling Clinic neurosurgery
00:04:26.980 -- and we're going to talk a little
00:04:28.877 -- bit about the human spine today.
00:04:30.810 -- We talked in the past about
00:04:32.712 -- the anatomy of the spine,
00:04:34.470 -- but what I want to talk about
00:04:36.661 -- today is what goes into the spine,
00:04:39.130 -- because really,
00:04:39.902 -- that's the most important thing
00:04:41.832 -- about your spinal column and that
00:04:43.874 -- is what's on the inside of it.
00:04:45.790 -- Well, what's on the inside of it are nerves,
00:04:48.790 -- and they are the main wiring of your body.
00:04:51.790 -- When your brain tells you to move your hand.
00:04:55.140 -- That has to go through a network
00:04:57.317 -- of wires if you will.
00:04:58.960 -- That eventually goes from the part
00:05:00.904 -- of the brain giving the command out
00:05:03.178 -- to the muscles that move your hand,
00:05:05.320 -- and the same thing goes for if you
00:05:07.688 -- touch a hot stove that the message
00:05:10.054 -- of wow that's hot has to go through a
00:05:13.033 -- series of wires all the way back up
00:05:15.496 -- to your parts of your brain that say,
00:05:18.040 -- you're you're putting your hand
00:05:19.770 -- on a stove that's incredibly high
00:05:21.847 -- and that all goes through the main
00:05:23.828 -- wiring of your body, which is housed.
00:05:26.233 -- Within your spine. Now the main wiring.
00:05:29.610 -- The principle wiring is in what
00:05:32.172 -- we call the spinal cord.
00:05:34.400 -- The spinal cord is a whole bunch of
00:05:37.360 -- wires bundled together basically,
00:05:39.620 -- and those wires run all the way from
00:05:42.996 -- the brain coming out of the head and
00:05:46.639 -- into the spinal column and run all
00:05:49.773 -- the way down through the canal of the
00:05:53.115 -- spine until it reaches somewhere in your.
00:05:56.230 -- Upper low back or your upper
00:05:58.834 -- lumbar region of your back there.
00:06:01.620 -- The bundling of the wires kind of
00:06:04.588 -- breaks up an each wires hanging down
00:06:07.724 -- from the end of the main wiring or
00:06:11.399 -- the spinal cord and almost looked
00:06:14.165 -- like a horses tail in the end part
00:06:17.784 -- of the spinal column.
00:06:19.580 -- In other words,
00:06:20.993 -- a whole bunch of wires just hanging
00:06:24.387 -- there off the end of your spinal cord.
00:06:27.900 -- Looking like a horses tail.
00:06:29.790 -- So in medicine we often use Latin
00:06:32.303 -- terms and that area of your spine
00:06:34.920 -- is called the cauda aquina and
00:06:37.196 -- that means horses tail in Latin,
00:06:39.590 -- and that's what that part of the
00:06:42.243 -- anatomy is now for all that main wiring
00:06:45.363 -- to connect out to your legs and arms
00:06:48.410 -- and lungs and all that sort of thing,
00:06:51.326 -- they have to get out of your spine somehow
00:06:55.255 -- and the way they do it is each time.
00:06:58.390 -- Two vertebrae,
00:06:59.404 -- 2 bones of your spine come together.
00:07:02.960 -- There's a little hole on the side.
00:07:08.980 -- We give that yet another fancy term
00:07:11.528 -- we call that the nuro foramen,
00:07:13.990 -- but it's basically the nerve whole,
00:07:16.300 -- and that's all neural foramen means.
00:07:18.610 -- It's a nerve, whole.
00:07:20.158 -- It's a hole through which a nerve
00:07:22.963 -- jumps out of the spinal column and
00:07:25.728 -- goes off to where it needs to go
00:07:28.736 -- off to an everywhere two vertebrae
00:07:30.928 -- come together from your neck,
00:07:32.850 -- and your thoracic region or the
00:07:35.064 -- chest region to lumbar region,
00:07:37.090 -- which is your lower back region.
00:07:39.510 -- Nerves pop out of these little
00:07:41.928 -- holes now once they get out of
00:07:44.621 -- the holes they tend to go into the
00:07:47.558 -- little Los Angeles freeway exchange.
00:07:50.250 -- In other words,
00:07:51.456 -- several nerves will come out
00:07:53.466 -- of several holes,
00:07:54.790 -- and then they'll go and interchange
00:07:57.112 -- for awhile and then spring
00:07:59.186 -- out is totally different.
00:08:00.990 -- Nerves and those nerves are
00:08:03.050 -- are called peripheral nerves.
00:08:04.700 -- The nerves inside the holes.
00:08:07.920 -- Are called nerve roots,
00:08:09.440 -- so will often talk about nerve
00:08:11.792 -- roots in my business,
00:08:13.270 -- and that's what they're talking about.
00:08:15.560 -- It's the nerve after it comes off
00:08:18.045 -- the spinal cord and comes out the
00:08:20.635 -- little holes before they go into the
00:08:23.299 -- Los Angeles freeway exchanges and
00:08:25.364 -- become what we call peripheral nerves.
00:08:27.776 -- So if you talk about some people
00:08:30.422 -- might talk about the median
00:08:32.271 -- nerve which gets caught in your
00:08:34.448 -- wrist in carpal tunnel syndrome.
00:08:36.570 -- That's what's called a peripheral nerve.
00:08:38.860 -- It's well far away.
00:08:40.700 -- From the spinal nerves that are
00:08:43.558 -- coming out of your spinal column.
00:08:46.540 -- Now again, this is important stuff.
00:08:49.550 -- This spine is designed to give
00:08:52.772 -- you stability and mobility and
00:08:55.440 -- all that sort of thing,
00:08:57.560 -- but really it's designed to protect your
00:09:01.039 -- spinal nerves and your spinal cord,
00:09:04.080 -- and it's obviously made up of tough
00:09:07.545 -- bone and surrounds that, nor the.
00:09:10.262 -- Spinal cord,
00:09:10.934 -- as much as it can to give it protection.
00:09:14.550 -- You might even argue that some of
00:09:16.769 -- the stuff on the backside here
00:09:18.870 -- was to protect you and Saber.
00:09:21.030 -- Tooth tigers were trying to bite
00:09:22.920 -- you in the old days or something.
00:09:25.460 -- But All in all,
00:09:26.920 -- the spinal column is a protective
00:09:29.185 -- element for these very delicate
00:09:31.335 -- wiring of your body.
00:09:33.060 -- We'll talk more about this later
00:09:34.860 -- and further episodes.
00:09:35.760 -- Thank you very much for listening today.
00:09:37.860 -- Bye bye now.
00:09:48.370 -- I don't need a school to just promise me
00:09:51.016 -- the tools for change. I need to school.
00:09:58.340 -- That's the problem about using.
00:10:00.020 -- YouTube is then all the sudden.
00:10:02.030 -- All these advertisements pop up or
00:10:04.208 -- or other videos start to pop up.
00:10:06.380 -- You can't download the videos where
00:10:08.252 -- you can and keep them yourself,
00:10:10.400 -- but it's not the easiest thing to do as well.
00:10:15.470 -- So when we look at the general
00:10:18.228 -- population for every five people in
00:10:20.754 -- a classroom or an office building,
00:10:23.280 -- 80% will experience significant back
00:10:25.925 -- pain at some point in their lives.
00:10:29.760 -- So four out of five people in a room
00:10:33.234 -- will experience some sort of back pain.
00:10:36.930 -- So when I was 20 years old,
00:10:39.290 -- I was working at a marine warehouse.
00:10:42.870 -- Truck driver pulled up.
00:10:44.686 -- Add 2/5 gallon buckets on the
00:10:47.498 -- back of the truck.
00:10:49.040 -- I assume that they were typical 5 gallon
00:10:52.176 -- buckets containing 5 gallons of paint,
00:10:54.290 -- so I grabbed both of them and pulled
00:10:57.794 -- him off the back of the truck.
00:11:00.970 -- And they turned out to be 100 pounds
00:11:03.666 -- of chain and each 5 gallon bucket.
00:11:06.300 -- And so I went straight down to the
00:11:08.836 -- ground and pulled my back muscles.
00:11:11.160 -- So do I tell anybody?
00:11:12.890 -- No, I was 20 years old.
00:11:14.980 -- This was a different era.
00:11:16.710 -- You didn't report every accident
00:11:18.445 -- that you had.
00:11:19.490 -- It was a small company.
00:11:21.220 -- I knew the owner well so you know,
00:11:24.000 -- I didn't report anything.
00:11:25.476 -- I didn't want anyone to
00:11:27.321 -- know that I had done this,
00:11:29.200 -- but that pain lasted for a couple
00:11:31.629 -- weeks and I still remember to
00:11:33.940 -- this day how painful it was.
00:11:36.310 -- And how long it took me to
00:11:38.907 -- overcome that pain?
00:11:40.020 -- At that time,
00:11:40.986 -- you really didn't even have things
00:11:42.918 -- like mottron readily available.
00:11:44.880 -- Ibuprofen there was Tylenol.
00:11:46.376 -- There was aspirin,
00:11:47.500 -- so I didn't really even have things to
00:11:50.588 -- help alleviate the pain at that point.
00:11:55.340 -- I'm lucky that I haven't had persistent
00:11:58.273 -- back pain since that point in time.
00:12:01.060 -- Other people have persistent
00:12:03.408 -- back pain their whole lives.
00:12:06.350 -- I've talked about my colleagues, husband.
00:12:08.581 -- You saw this.
00:12:09.694 -- The hardware that's in his back.
00:12:11.920 -- I have another colleague.
00:12:14.950 -- Who also her husband has significant
00:12:18.172 -- amount of hardware in his neck
00:12:21.375 -- and has constant back pain.
00:12:23.760 -- So back pain is second only to
00:12:26.350 -- the common cold for keeping
00:12:28.574 -- American workers from their jobs,
00:12:31.160 -- and this is from nine 2003 at.
00:12:34.200 -- The statistics still applies today.
00:12:36.380 -- Back pain is very significant amongst people.
00:12:40.040 -- As people get older generally
00:12:42.470 -- there they experience more back
00:12:44.980 -- pain for one reason or another.
00:12:47.450 -- Spinal stenosis is one of those things
00:12:49.823 -- that seems to crop up as people get older,
00:12:52.730 -- and that's where there's a narrowing in the
00:12:55.930 -- opening for the spinal cord to get through.
00:12:59.060 -- This final bones. So.
00:13:04.240 -- When we look at the spine.
00:13:07.240 -- Here's a couple.
00:13:09.490 -- Diagrams of it.
00:13:12.570 -- The diagram at the left.
00:13:14.710 -- Shows the various sections of the spine.
00:13:17.810 -- We have seven vertebrae
00:13:19.162 -- and the cervical spine.
00:13:20.520 -- The skull rests on top of the
00:13:22.550 -- top of the cervical spine.
00:13:24.590 -- They said, I think,
00:13:25.946 -- in the first day of lecture,
00:13:27.980 -- if you reach back and touch.
00:13:30.960 -- I'm going to stop sharing for a second.
00:13:35.720 -- If you reach back and fill that
00:13:37.869 -- lump on the back of your neck
00:13:40.246 -- right here, that's your C6.
00:13:41.915 -- Your cervical 6 vertebrae.
00:13:43.220 -- It's a really easy reference to find,
00:13:45.500 -- so you have one more cervical vertebrae.
00:13:47.780 -- Be a below that, and then it
00:13:49.971 -- starts the thoracic spine.
00:13:57.250 -- So the thoracic spine is the
00:13:59.950 -- least movable part of the spine.
00:14:02.740 -- There are 12 thoracic vertebrae
00:14:04.640 -- T1 to T12 as compared with seven
00:14:07.392 -- for this sort of cervical spine.
00:14:09.710 -- They provide some motion,
00:14:11.254 -- but they're more immobile.
00:14:12.800 -- The discs are not as thick in that region.
00:14:16.290 -- The cervical spine discs are fairly movable.
00:14:18.990 -- That's why we can move our
00:14:21.150 -- heads all the way around.
00:14:25.810 -- But the thoracic spine
00:14:27.710 -- is not as more moveable.
00:14:30.090 -- And then we have the lumbar spine.
00:14:33.090 -- Which is 5 vertebrae, L1 to L5,
00:14:35.860 -- and that's bears most of
00:14:37.835 -- the weight of our body,
00:14:39.810 -- and any load that we pick up.
00:14:43.340 -- So when we're talking about lifting tasks,
00:14:46.110 -- will talk about biomechanics
00:14:48.058 -- during the next couple lectures.
00:14:50.500 -- The server the lumbar spine is what
00:14:53.860 -- actually supports the load of our
00:14:56.602 -- bodies and anything we pick up.
00:14:59.020 -- And then the below the lumbar spine.
00:15:02.100 -- We have the sacrum,
00:15:03.632 -- and it consists of five fused
00:15:06.018 -- and modified vertebrae,
00:15:07.820 -- and with two ilium bones,
00:15:10.020 -- which completes the pelvic ring.
00:15:12.820 -- And then at the very end is the coccyx.
00:15:16.020 -- I know I've talked about a lot
00:15:18.533 -- of different injuries I've had.
00:15:20.300 -- I fell ice skating.
00:15:21.692 -- One time this we were skating on Hayden Lake,
00:15:24.920 -- outside Corda Lane which is in North
00:15:27.594 -- Idaho and all of a sudden we heard
00:15:30.387 -- a large crack of the ice through
00:15:32.750 -- the lake and we both took off.
00:15:35.250 -- A friend of mine and I both took
00:15:37.746 -- off on our skates skating as hard
00:15:40.410 -- as we could because of this crack.
00:15:43.330 -- And I fell and broke my coccyx
00:15:45.374 -- and that took several months to
00:15:47.435 -- to feel better again.
00:15:48.920 -- It's a really easy bone to break
00:15:51.839 -- if you fall on it. It doesn't it.
00:15:54.648 -- It heals by itself and less it gets
00:15:57.140 -- displaced and so it's it's just
00:15:59.234 -- something that a lot of people have
00:16:01.744 -- experienced in the course of their lives.
00:16:04.287 -- So in general we have this large
00:16:07.416 -- structure of bone and are back and in
00:16:10.671 -- between each of the vertebrae there's a disk,
00:16:14.430 -- except in the sacrum,
00:16:16.034 -- because again, they are fused bone.
00:16:22.630 -- So, interesting enough.
00:16:26.160 -- When we look at this final column.
00:16:29.270 -- And we just saw in that one video.
00:16:33.710 -- How the processes work?
00:16:38.600 -- On the back of the spinal
00:16:41.456 -- column and again if he filled
00:16:43.983 -- at C6 vertebrae in the back,
00:16:46.410 -- those Bony processes project out.
00:16:49.860 -- And they protect ingeneral the spinal cord.
00:16:55.020 -- But the discs and the bulk of the bone.
00:16:58.710 -- Are medial to the body versus the
00:17:01.538 -- spinal cord, which is more distal?
00:17:03.966 -- So when you think about it,
00:17:06.390 -- the spinal cord is out away from the
00:17:09.894 -- body compared with where the discs and
00:17:13.229 -- the majority of the vertebral bone is.
00:17:16.390 -- So in this diagram on this slide,
00:17:19.360 -- you can see we have the intervertebral
00:17:22.720 -- disc where the spinal cord is.
00:17:25.620 -- That's right here.
00:17:28.550 -- The cursor is being able to be seen.
00:17:31.260 -- We have these processes that come
00:17:33.342 -- out and the processes have a lot
00:17:35.838 -- of different small muscle groups
00:17:37.573 -- attached to him and they provide us
00:17:39.880 -- the movement that we have back and
00:17:42.106 -- forth that control our body moves.
00:17:44.140 -- There's a lot of these little
00:17:46.780 -- muscles that help us move our
00:17:49.472 -- bodies in a whole variety of ways.
00:17:52.420 -- So vertebrae are similar to
00:17:54.005 -- STACK children's building blocks.
00:17:55.280 -- Best way to sit.
00:17:58.460 -- They physically are not connected
00:18:00.715 -- to each other.
00:18:02.070 -- By bone other than in the sacrum,
00:18:04.840 -- but they are test, of course,
00:18:07.210 -- via the discs in the back.
00:18:10.140 -- And then have a course.
00:18:11.300 -- The spinal cord that goes through.
00:18:14.430 -- If you look at the bottom diagram
00:18:16.775 -- you can see the vertebrae.
00:18:19.200 -- You can see the disc in between,
00:18:21.770 -- which is that light blue color.
00:18:23.970 -- You can see how the nerves come
00:18:26.903 -- out in between the vertebral discs.
00:18:30.080 -- And they, as a video talked about.
00:18:32.580 -- They go out and they innervate
00:18:34.740 -- your whole body so that you can.
00:18:37.220 -- Your brain can talk to your arms or legs.
00:18:41.610 -- Body your skin,
00:18:43.176 -- your fingers,
00:18:44.220 -- everything within your body
00:18:46.760 -- has a connection to the brain.
00:18:50.570 -- So in an injury and will go back up.
00:19:00.620 -- Certain injury we've all heard about
00:19:02.804 -- people who broken their backs,
00:19:04.690 -- which is like crack in the vertebral
00:19:07.210 -- discs or severing the booty galore,
00:19:09.500 -- totally smashing a vertebral disc.
00:19:11.950 -- And then cutting the.
00:19:15.420 -- Spinal cord so dependent on where the
00:19:17.702 -- spinal cord is cut in an accident and
00:19:20.567 -- hopefully nobody ever watching this
00:19:22.451 -- video has not, but it does happen.
00:19:25.170 -- Determines where the body
00:19:27.010 -- is paralyzed or now.
00:19:28.570 -- You don't have that transmission of
00:19:30.820 -- the brain to the rest of the body,
00:19:33.630 -- or vice versa, because it's a two way St.
00:19:36.890 -- It's not just that the brain
00:19:39.260 -- sends signals out and also
00:19:41.425 -- collects signals coming back out.
00:19:43.930 -- So if the vertebrae or the spinal column.
00:19:47.960 -- Is broken twords the neck.
00:19:49.830 -- You may be a person will become
00:19:52.980 -- a quadriplegic versus if it's
00:19:55.272 -- lower down in the back and again
00:19:58.247 -- depending on where the break is.
00:20:00.630 -- Determines what level of paralysis
00:20:03.240 -- somebody might experience.
00:20:08.860 -- So again, we have the small bones
00:20:11.548 -- and project from each of the
00:20:13.998 -- corners of the vertebral disc,
00:20:16.020 -- and these processes, actors,
00:20:17.612 -- attachment points for muscles and ligaments.
00:20:23.960 -- So one of the interesting things is
00:20:26.508 -- this slide talks about in the morning.
00:20:29.150 -- You're about half an inch taller than you
00:20:31.862 -- are in the afternoon, and the reason is,
00:20:35.094 -- is why we're standing or sitting.
00:20:37.320 -- We compress those discs and
00:20:39.175 -- they tend to lose fluid.
00:20:41.030 -- If we're dehydrating,
00:20:42.488 -- we can lose fluid out of those discs.
00:20:46.550 -- People that are on the space station
00:20:49.399 -- astronauts actually become taller during
00:20:51.444 -- the period of time because their disks
00:20:54.069 -- along gate because there's no gravity
00:20:56.259 -- acting on the body and so they are.
00:21:01.570 -- They are a living thing.
00:21:02.960 -- I don't know how is this drive it.
00:21:05.170 -- Bone is a living thing also,
00:21:06.830 -- but disks actually change
00:21:08.250 -- during the course of a day.
00:21:10.380 -- So there are cushions of
00:21:13.445 -- tissue between most vertebrae.
00:21:15.900 -- Which absorbs shock and
00:21:17.744 -- protect the spine from impact.
00:21:20.050 -- So if you're going to be in a hard fall,
00:21:23.120 -- it's better to break a disc than
00:21:25.024 -- it is to break a vertebrae.
00:21:29.170 -- So they are an interesting
00:21:31.405 -- structure because they. The.
00:21:35.370 -- Connective tissue that they're
00:21:37.098 -- made up of are an annular rings,
00:21:40.230 -- and within each of these rings there's
00:21:43.457 -- a gelatinous substance we heard last.
00:21:45.980 -- Unless lecture people talked about something
00:21:48.746 -- similar to like crab meat consistency.
00:21:51.870 -- And that's basically what they're like.
00:21:54.400 -- They're not a solid thing.
00:21:56.500 -- They're not like a gummy bear,
00:21:59.030 -- though they probably are
00:22:00.938 -- closer to a gummy bear than.
00:22:03.800 -- Then a piece of steak.
00:22:06.030 -- But they are squishing,
00:22:07.726 -- but not like you could squish
00:22:10.350 -- him every different way.
00:22:12.270 -- They are hydrophilic,
00:22:13.728 -- meaning that water is attracted into
00:22:16.644 -- the disk versus going out of it,
00:22:19.410 -- and the whole idea is we want to
00:22:22.874 -- have water flowing into the disks
00:22:25.902 -- to keep the spine mobile and to
00:22:29.636 -- keep the spinal cord protected.
00:22:32.920 -- And the endplates of the.
00:22:36.750 -- Discs are covered in cartilage, so it
00:22:39.854 -- makes it a very strong stuff structure.
00:22:46.440 -- Interesting enough.
00:22:49.440 -- When you look at those the way the stone
00:22:52.887 -- spine is built and the vertebral discs,
00:22:56.110 -- you can see that generally the
00:22:58.456 -- posterior side or the structured
00:23:00.563 -- towards your back distal from the
00:23:03.317 -- body is compared with medial is less
00:23:06.313 -- strong than the frontal part of it.
00:23:09.132 -- And for whatever reason,
00:23:11.180 -- I think it adds more mobility so
00:23:13.805 -- that you can bend forward better.
00:23:16.690 -- But if you're going to rupture disc,
00:23:18.730 -- more than likely you're going
00:23:20.635 -- to rupture it towards the back.
00:23:22.960 -- So herniated or ruptured
00:23:24.784 -- disc basically are similar.
00:23:26.610 -- The walls, the disk have broken
00:23:30.096 -- down and the fluid bulges out.
00:23:33.820 -- So in this diagram you can see on the
00:23:36.835 -- right side there's a ball in there.
00:23:39.520 -- Basically,
00:23:39.875 -- that's not really a ball,
00:23:41.650 -- it's just demonstrating the way
00:23:43.430 -- that the disk works,
00:23:44.860 -- that the posterior side is weaker
00:23:46.996 -- than the anterior side.
00:23:51.780 -- So the nerves emerge from the spinal
00:23:54.468 -- canal through openings in each
00:23:56.539 -- vertebrae and potential problems of
00:23:58.654 -- nerves become trapped or compressed.
00:24:00.910 -- So I want to show this diagram
00:24:03.066 -- for a couple of reasons.
00:24:04.850 -- We see the spinal nerves,
00:24:06.490 -- how they come out and you'll notice
00:24:08.765 -- how they kind of wrap around the body.
00:24:11.410 -- So on the on the anterior view or
00:24:13.826 -- the front of the body you can see
00:24:16.315 -- again how they kind of wrap around
00:24:18.690 -- the legs and the nerves innervate
00:24:20.880 -- the body and in various locations
00:24:22.890 -- as the physician talked about.
00:24:24.530 -- In that short video that we
00:24:26.498 -- just saw the spine,
00:24:27.810 -- the nerves come out from the vertebrae
00:24:30.309 -- and they branch into much smaller.
00:24:32.640 -- Nerves,
00:24:33.171 -- and then there's secondary nerves
00:24:35.826 -- that are the peripheral nerves that
00:24:39.104 -- interact with these spinal nerves.
00:24:41.790 -- So if a nerve becomes trapped
00:24:44.196 -- because of a compressed disk.
00:24:48.810 -- Then the person feels the pain.
00:24:51.920 -- Sometimes in the whole length of
00:24:54.002 -- the nerve for the nerve innervates.
00:24:56.640 -- So if we see that towards the lumbar
00:24:59.313 -- part of the body lower part of the body
00:25:01.900 -- can see here this is the spinal
00:25:04.593 -- column and these nerves that come out.
00:25:07.062 -- If this if the nerve is compressed in
00:25:10.107 -- this location, the person could feel that
00:25:12.670 -- compression all the way down to their toes,
00:25:15.330 -- for instance, or part of their foot.
00:25:19.590 -- If somebody is developing sciatica because
00:25:21.972 -- the sciatic nerve is compressed either from
00:25:24.737 -- the spinal column or from sitting in a chair,
00:25:27.910 -- that's not designed well.
00:25:30.490 -- People develop problems from sitting
00:25:31.905 -- at trucks for a long period of time.
00:25:34.120 -- Truck drivers.
00:25:35.186 -- Then that whole length of that nerve.
00:25:38.920 -- Can become irritated and people wish
00:25:41.416 -- filled out shooting pain all the way down.
00:25:44.310 -- I talked in the first class about my
00:25:47.150 -- problem with compressing nerves in my legs.
00:25:50.110 -- And this is a good diagram that shows if
00:25:53.386 -- I'm have my wallet in my front pocket.
00:25:56.660 -- And I can press that nerve that
00:26:00.132 -- nerve wraps around my leg.
00:26:02.420 -- I fill it in my heel.
00:26:04.420 -- And until you look at a diagram
00:26:06.835 -- like this and realize.
00:26:08.570 -- That depending on where
00:26:10.250 -- the nerve is compressed,
00:26:11.930 -- where you might actually feel the sensation
00:26:15.017 -- of that compression of that nerve.
00:26:17.390 -- Nerves are sensitive.
00:26:18.590 -- Some people's nerves are closer to the
00:26:21.466 -- surface than other peoples, obviously.
00:26:23.789 -- Mine I am sensitive to pressure on
00:26:27.422 -- my nerves in my arms go to sleep.
00:26:30.730 -- Without much pressure on him, for instance.
00:26:34.730 -- And so again,
00:26:35.963 -- you want to protect the spinal column.
00:26:38.840 -- Make sure people are sitting
00:26:40.895 -- in the proper chairs,
00:26:42.540 -- not doing activities that can injure
00:26:45.630 -- the spinal cord or the discs so that we
00:26:49.849 -- we don't have this pain in the future.
00:26:53.320 -- The majority of back pain comes
00:26:56.002 -- from just muscular issues and then
00:26:58.896 -- secondarily it's nerve issues.
00:27:06.030 -- So within the body.
00:27:08.386 -- We have these antagonistic muscle
00:27:11.331 -- pairs so one muscle will contract
00:27:14.521 -- while the other one is relaxed
00:27:17.651 -- and depending on how we move,
00:27:20.820 -- determines whether or not we have a
00:27:24.131 -- a muscle that's that's compressing
00:27:26.922 -- or contracting versus one that's at.
00:27:30.750 -- A relaxed state, so the diagrams
00:27:33.414 -- on this side shows some of this.
00:27:36.410 -- We see the in diagram.
00:27:38.580 -- A healthy muscle is balanced,
00:27:40.760 -- it's normal and either both of them are.
00:27:45.870 -- Not being flexed at that time.
00:27:48.620 -- Sometimes if there's an imbalance,
00:27:50.230 -- the stronger muscle pull to
00:27:52.540 -- one side or another.
00:27:54.390 -- In some cases where people's
00:27:56.550 -- muscles are flexed a lot,
00:27:58.710 -- they develop that pain in their back.
00:28:03.480 -- The 10s machine sometimes is
00:28:05.605 -- used to help relax the muscles.
00:28:08.490 -- They'll give a pulse of electric electrical
00:28:12.564 -- energy so that the back will relax.
00:28:16.420 -- In the abdominal muscles,
00:28:17.720 -- one idea is that to keep your core
00:28:20.475 -- muscles strong because of the spine
00:28:22.695 -- movement as well as back muscles,
00:28:24.870 -- thousands of muscles of rack
00:28:26.570 -- participate in every move you
00:28:28.331 -- make and keeping muscle strong.
00:28:30.150 -- The abdominal muscles and the back muscles.
00:28:33.650 -- An imbalance is a key to help prevent.
00:28:38.360 -- Pain and injury to the back.
00:28:40.450 -- With weak muscles,
00:28:41.428 -- there's little back support and
00:28:43.058 -- when muscles are imbalanced the
00:28:44.609 -- entire spine can be out of balance.
00:28:46.570 -- If we see somebody sitting
00:28:48.735 -- in an awkward posture.
00:28:50.470 -- This is sometimes how people can get to
00:28:53.262 -- where one muscles stronger than another.
00:28:56.170 -- Muscle or muscles are used adequately.
00:28:58.610 -- They'll atrophy,
00:28:59.422 -- meaning they get smaller,
00:29:01.050 -- and then there's more of a
00:29:03.546 -- potential for back injury as well.
00:29:12.080 -- So at the end of the lecture,
00:29:13.410 -- what we're going to do is we're
00:29:15.013 -- going to look at a couple of
00:29:16.709 -- videos we looked at before.
00:29:17.900 -- But when we see something like this,
00:29:20.510 -- you know what are the potential work
00:29:23.856 -- related musculoskeletal disorders?
00:29:25.290 -- So the diagram on the left
00:29:27.654 -- you see a person welding.
00:29:30.060 -- They're bending over at the waist.
00:29:32.900 -- Their head actually is at about a
00:29:35.406 -- 90 degree angle with their torso,
00:29:37.800 -- but the torso is bent over
00:29:39.978 -- totally into 90 degree angle.
00:29:41.950 -- I mean the head is at a.
00:29:45.930 -- Correct angle to the torso,
00:29:47.490 -- but the back is bent at a 90 degree angle.
00:29:50.610 -- This is a very unhealthy posture and can put
00:29:53.418 -- a tremendous amount of pressure on the back.
00:29:56.660 -- On the right side we see that this
00:29:59.156 -- dental hygienist or dentist is
00:30:00.876 -- working on this person's teeth.
00:30:02.600 -- They're not only sitting cross.
00:30:05.960 -- Asymmetrically.
00:30:06.446 -- So there are twisted at the trunk.
00:30:09.850 -- His head is twisted and it's also bent.
00:30:13.330 -- When we talk about bio mechanics and
00:30:15.500 -- we get into these couple ergonomic
00:30:17.640 -- tools that are called Rula and Reba,
00:30:20.310 -- we'll talk about what the level of
00:30:23.145 -- stress that's actually putting on the body.
00:30:25.860 -- But in both diagrams,
00:30:27.668 -- the person could experience
00:30:29.476 -- Backcountry overtime on the right side.
00:30:31.610 -- The person could experience
00:30:33.254 -- neck injury on the left side,
00:30:35.720 -- not so much with neck injury because
00:30:38.597 -- the head is in a relatively
00:30:41.840 -- good posture according to.
00:30:43.770 -- The persons torso.
00:30:48.760 -- Not sure. This little video
00:30:52.412 -- talks about back pain.
00:31:00.170 -- Sometimes I want to pinch myself
00:31:01.796 -- 'cause I think I'm dreaming.
00:31:03.420 -- I've just been able to enjoy my life again.
00:31:06.070 -- It's a miracle I'm a miracle.
00:31:20.420 -- I had severe sciatica.
00:31:21.636 -- It was to the point where I couldn't
00:31:24.117 -- even get out of bed in the mornings.
00:31:26.500 -- I couldn't stand very long.
00:31:28.020 -- I couldn't sit very long.
00:31:30.760 -- Thing for a long period of time,
00:31:32.850 -- I mean more than five or 10 minutes
00:31:35.066 -- it had gotten to be that severe.
00:31:37.340 -- How's your pain today?
00:31:38.532 -- Zero pain.
00:31:39.130 -- That sounds very good.
00:31:52.290 -- She also had an unstable
00:31:53.815 -- condition or lumbar spine.
00:31:55.040 -- She had a condition called
00:31:56.830 -- spondylolisthesis where one
00:31:57.904 -- bone is slipped forward on top
00:31:59.829 -- of the other and that tends to
00:32:01.881 -- slowly get worse over the years
00:32:03.435 -- and it can cause a lot of pain.
00:32:05.750 -- It can even cause paralysis.
00:32:18.750 -- Of that operation, however,
00:32:20.042 -- is that in order to treat the problem,
00:32:22.780 -- we have to also cause a fair
00:32:25.076 -- amount of injury and damage
00:32:26.807 -- to the spine to the bones.
00:32:28.830 -- The muscles to the tendons,
00:32:30.510 -- which are all structures that are
00:32:32.484 -- very important in these patients
00:32:34.202 -- when it comes to recovery.
00:32:49.320 -- It's a 3 dimensional GPS system that
00:32:51.308 -- allows us to navigate very accurately
00:32:53.400 -- and very precisely within the spine.
00:32:55.760 -- Even though we're operating through
00:32:57.450 -- very small incisions, we equip the
00:32:59.487 -- tools that we use with little sensor.
00:33:01.860 -- You're operating on the patient,
00:33:03.560 -- but on the screen you see
00:33:05.636 -- exactly where you are.
00:33:07.020 -- Within the Spine 5 and then 14 millimeters
00:33:09.564 -- we're really at the forefront of
00:33:11.881 -- minimally invasive spinal surgery
00:33:13.501 -- patients benefit from this because
00:33:15.358 -- they recover now much faster from
00:33:17.332 -- these operations then they would have.
00:33:19.450 -- Maybe not a few years ago when I woke
00:33:22.186 -- up five hours after the surgery,
00:33:24.770 -- I had no more sciatica pain is scared.
00:33:28.290 -- 'cause I haven't been paying
00:33:30.110 -- free for over a decade.
00:33:31.930 -- Yeah, life is real good.
00:33:33.750 -- It's extremely good.
00:33:34.842 -- You know.
00:33:35.570 -- I'm blessed.
00:33:45.120 -- So grateful for this new technology
00:33:46.962 -- that the Doctor performed on man,
00:33:48.600 -- you know I got my life back and there's not
00:33:51.941 -- enough time in hours in the day. For me,
00:33:54.912 -- 'cause there's so much I want to do now.
00:34:20.230 -- So there's been quite a few advertisements.
00:34:22.620 -- It's usually around Christmas for teeters.
00:34:24.660 -- Hang up, teeter hang ups,
00:34:26.370 -- which basically you lock your feet in and
00:34:29.090 -- then you lean back and get to posture.
00:34:31.820 -- That feels comfortable for a person.
00:34:33.870 -- And that idea is the same thing.
00:34:36.260 -- It decompresses the spine,
00:34:37.624 -- takes the pressure off the nerves,
00:34:39.670 -- and people experience less back pain.
00:34:41.710 -- OK, so a couple of issues with
00:34:44.069 -- that before anybody ever uses
00:34:45.825 -- one of those types of devices,
00:34:47.850 -- they need to consult with their physician.
00:34:50.700 -- Because if you think about it,
00:34:53.570 -- you're upside down the pressure
00:34:56.610 -- and your pressure in your.
00:34:59.650 -- Brain increases because you're
00:35:00.958 -- in that inverted posture,
00:35:02.270 -- so you need to be checked out before
00:35:05.454 -- anybody uses it to make sure that
00:35:08.285 -- they're not a candidate for a stroke.
00:35:11.050 -- So no problems are commonly associated
00:35:13.024 -- with prolonged exposure to static postures,
00:35:15.210 -- typically as a consequence of
00:35:16.945 -- visual requirements of a task.
00:35:18.680 -- So we saw the dental hygienist,
00:35:20.770 -- and that one diagram a couple minutes ago,
00:35:23.540 -- and that person is at a higher.
00:35:26.980 -- Potential for.
00:35:29.494 -- Neck injuries and there is evidence
00:35:33.210 -- of flexion beyond 30 degrees.
00:35:36.780 -- Leads to more rapid onset of fatigue.
00:35:39.970 -- So if you're sitting in a posture again,
00:35:42.700 -- your natural posture for your neck is
00:35:44.702 -- about a three degree inclination forward.
00:35:47.130 -- If you're at a 30 degree inclination forward,
00:35:49.860 -- the idea is it puts pressure on the
00:35:52.612 -- nerves and blood vessels of the neck and
00:35:55.945 -- can increase your potential for fatigue.
00:35:58.630 -- People who use microscopes
00:36:00.498 -- for long periods of time,
00:36:02.840 -- like pathologists do experience potential
00:36:05.430 -- problems with fatigue and also the
00:36:08.496 -- potential for disc problems in the neck.
00:36:13.420 -- So disc generation.
00:36:15.121 -- Can happen and an older individuals
00:36:18.523 -- as well as younger individuals.
00:36:21.930 -- So we see here on this diagram
00:36:24.002 -- and this is pretty exaggerated.
00:36:26.300 -- On the left side we see a normal disc.
00:36:29.570 -- It's equal, it's not bulging out,
00:36:31.760 -- so it's not putting excess
00:36:33.580 -- pressure on the spinal cord.
00:36:37.520 -- The next diagram down is a herniated
00:36:40.586 -- disk and this is on the left side
00:36:43.786 -- and you can see where the walls.
00:36:46.550 -- Of the disc are starting to breakdown
00:36:49.154 -- and you see a bulging out and
00:36:51.988 -- putting pressure on the spinal cord.
00:36:54.450 -- So minor pressure is not a big
00:36:56.963 -- deal as it gets worse and worse.
00:36:59.970 -- It puts more pressure on and people
00:37:03.358 -- experience a higher degree of pain or
00:37:06.415 -- start to fill lack of use of a limb.
00:37:09.660 -- Or both legs, for instance,
00:37:11.530 -- both arms dependent on where
00:37:14.480 -- the disc is herniated.
00:37:16.840 -- A bulging disc is a little bit
00:37:19.073 -- different than a herniated disc.
00:37:21.120 -- It's the same idea.
00:37:22.488 -- Only in this case it's much worse,
00:37:25.050 -- and in this case the annulus outer layer
00:37:28.498 -- of the disc bulges into the spinal cord.
00:37:32.490 -- And then we have thinning discs and
00:37:35.535 -- this is on the right side as the disc
00:37:39.484 -- thins out that the spinal cord tends to.
00:37:43.270 -- Spinal column tends to compress more,
00:37:45.250 -- putting more pressure on those nerves that
00:37:47.966 -- are coming out of the various openings.
00:37:50.840 -- And then finally we have discussed
00:37:52.856 -- the generation and it's something
00:37:54.680 -- similar to osteoporosis where calcium
00:37:56.765 -- and phosphate or leaving the bone
00:37:59.079 -- making it much weaker and the bone
00:38:01.109 -- starts to get smaller and smaller.
00:38:03.160 -- So when you see somebody an older
00:38:05.575 -- person that maybe you haven't seen
00:38:07.715 -- for three or four years and before
00:38:10.200 -- they were your height and now you're
00:38:12.664 -- 4 inches taller and taller than them.
00:38:15.128 -- But two things could have happened.
00:38:17.240 -- Either you grew or the disks in this
00:38:20.320 -- person's back. Hands for table.
00:38:24.660 -- Vertebrae have started to degrade
00:38:26.760 -- and the person is actually getting
00:38:29.513 -- shorter overtime.
00:38:33.670 -- So here's a diagram. An X ray of
00:38:36.158 -- a herniated disk on the left side.
00:38:38.410 -- You can see where it's actually bulging
00:38:40.629 -- out and pressing on the spinal column.
00:38:45.040 -- And you can see.
00:38:46.208 -- So this is on the right side.
00:38:48.400 -- Is the posterior view and the
00:38:50.056 -- left side is the anterior view.
00:38:52.060 -- You can also see at the
00:38:54.778 -- bottom of the Lombard.
00:38:56.590 -- Vertebrae these are the lumbar
00:38:58.415 -- vertebrae right here, and these.
00:39:00.560 -- This is the sacrum.
00:39:02.660 -- How that curve is and you
00:39:04.436 -- can see here at the bottom.
00:39:06.490 -- This disk also appears to
00:39:08.080 -- start to have problems,
00:39:09.360 -- and usually if you have problems
00:39:11.154 -- in one disc it can lead to
00:39:13.432 -- problems and other disks.
00:39:17.960 -- So on the right side.
00:39:20.260 -- You see a ruptured disc.
00:39:21.970 -- This is what the actual
00:39:23.670 -- disc material looks like.
00:39:25.030 -- As they said in the one deal
00:39:27.354 -- about looking like crab meat.
00:39:29.130 -- That's kind of what it looks like.
00:39:32.830 -- They see the tear through the.
00:39:35.330 -- The cartilage area.
00:39:39.440 -- And the concentric rings of
00:39:41.010 -- the disk material itself.
00:39:42.270 -- And if you look closely,
00:39:43.840 -- you can see a tear in this area
00:39:45.992 -- that tare allows the fluid to flow
00:39:48.210 -- through from one area to another area.
00:39:50.740 -- Generally again it's hydrophilic,
00:39:52.000 -- meaning it's water loving.
00:39:53.260 -- But still,
00:39:53.886 -- when you start to break those rings,
00:39:56.080 -- it starts to release fluid out and
00:39:58.250 -- this is where the disk and bulge.
00:40:00.480 -- I don't think in this particular
00:40:02.208 -- case this person is going to notice
00:40:04.433 -- because obviously it's a cadaver,
00:40:06.130 -- but that's beside the point.
00:40:11.050 -- So we're going to show this video.
00:40:13.140 -- I don't think I keyed it up. Oh, here it is.
00:40:22.130 -- Hi there, I'm doctor Gary Simmons
00:40:24.260 -- of Curling Clinic neurosurgery and
00:40:25.969 -- I'm going to talk to you a little
00:40:27.785 -- bit about lumbar disc surgery.
00:40:29.520 -- You may remember from previous
00:40:32.800 -- discussions that there are times
00:40:36.189 -- where a cushion or lumbar disc.
00:40:39.420 -- Has problems.
00:40:40.410 -- The disc is tough on the outside,
00:40:43.880 -- squishy on the inside.
00:40:45.308 -- The inside looks like crab meat
00:40:47.522 -- and sometimes a chunk of crabmeat
00:40:49.508 -- will rip out and push backwards and
00:40:51.953 -- to the side exactly where nerve is
00:40:54.410 -- trying to get out of your spine,
00:40:56.860 -- and when it pushes up against the
00:40:59.212 -- nerve the nerve gets irritable and
00:41:01.377 -- you may feel pain, numbness, tingling,
00:41:03.542 -- have some weakness all the way down your leg.
00:41:06.690 -- Usually it's just one leg,
00:41:08.450 -- but it can be miserable now.
00:41:10.550 -- Luckily most get better.
00:41:12.154 -- All by themselves,
00:41:13.360 -- but sometimes they don't,
00:41:15.092 -- and when they don't,
00:41:16.830 -- and that nerve is continuously
00:41:19.005 -- being pushed on,
00:41:20.310 -- it can be absolutely miserable and people
00:41:23.621 -- can be totally laid up by the pain.
00:41:26.820 -- And if the pain doesn't go away,
00:41:29.850 -- we sometimes will resort to surgery.
00:41:32.460 -- Now sometimes we can get by with
00:41:35.071 -- shots in the back where a numbing
00:41:38.274 -- medicine is used initially.
00:41:40.270 -- But really,
00:41:41.190 -- a steroid medicine is put on the nerve.
00:41:44.870 -- Now, this isn't an athlete steroid.
00:41:46.830 -- This is an anti inflammatory steroid
00:41:48.810 -- and the idea is to calm the nerves down.
00:41:51.720 -- But it doesn't do anything for the
00:41:53.925 -- crab meat that's sitting there on the nerve.
00:41:56.610 -- So if the nerve wants to stay
00:41:58.647 -- irritable it will stay irritable.
00:42:00.520 -- So sometimes we have to resort
00:42:02.398 -- to literally going in there and
00:42:04.396 -- removing the disk,
00:42:05.410 -- removing the crab meat that's
00:42:07.035 -- pushing on the nerve.
00:42:08.340 -- Now one of the misconceptions is
00:42:10.080 -- that we take the entire discount.
00:42:12.250 -- That's not the case at all really.
00:42:14.540 -- What we're going after.
00:42:16.040 -- Is that chunk of crab meat that
00:42:18.788 -- ripped out created out?
00:42:20.470 -- Herniated discs slip.
00:42:21.469 -- This ruptured disc.
00:42:22.470 -- They all mean the same thing.
00:42:24.470 -- In fact, we've got another name,
00:42:26.460 -- herniated nucleus pulposus
00:42:27.795 -- all mean the same thing.
00:42:30.020 -- We go in there surgically and
00:42:32.786 -- sometimes take the chunk off the nerve.
00:42:35.920 -- The way we do it is usually through
00:42:38.464 -- a small incision in the back.
00:42:40.740 -- This can be done through little
00:42:42.804 -- tubes with TV scopes,
00:42:44.180 -- or could be done with a microscope,
00:42:46.580 -- but usually it's a relatively small incision.
00:42:48.990 -- There are gaps between the vertebrae
00:42:51.096 -- here and we sneak in through the gap.
00:42:53.810 -- Sometimes we make the gap a little larger,
00:42:56.560 -- but we sneak in through the gap.
00:42:58.970 -- Find the nerve that's being pinched.
00:43:01.030 -- Find the crab meat that's pinching it,
00:43:03.440 -- grab the crab meat and we throw it away.
00:43:06.650 -- Literally throw it away.
00:43:08.498 -- We give it to the pathologists,
00:43:11.270 -- the.
00:43:12.810 -- All for all intents and purposes,
00:43:15.320 -- that surgery is now done.
00:43:18.910 -- Our goal is to get that nerve
00:43:21.024 -- swinging in the breeze.
00:43:22.470 -- Have nothing pushing on it.
00:43:24.090 -- I can't fix the nerve.
00:43:25.710 -- I can't make the nerve feel better
00:43:27.992 -- I can't make it less irritated
00:43:29.898 -- but I can get it out of
00:43:31.964 -- trouble. I can get the pressure off
00:43:34.518 -- of it and if I get the pressure off
00:43:37.452 -- of it 9 * 99 times out of 1095 times
00:43:40.296 -- at 100 it will feel much, much better
00:43:42.927 -- off and it feels better instantly.
00:43:45.150 -- Patients can be wheeled out of the
00:43:47.285 -- operating room where they're going.
00:43:49.040 -- Oh my goodness, my leg is better already.
00:43:52.120 -- But it doesn't always happen that quick.
00:43:54.440 -- Sometimes it can take weeks for the nerve
00:43:57.032 -- to settle down while we're in there,
00:43:59.400 -- we usually will go into the disc itself
00:44:01.656 -- and try to grab any other loose pieces
00:44:04.152 -- so that another piece doesn't just
00:44:06.282 -- immediately follow the first piece,
00:44:08.340 -- but we don't take the whole disk out.
00:44:10.990 -- That's a misnomer,
00:44:11.980 -- is not what happens.
00:44:13.300 -- We don't take the whole disk app we leave,
00:44:16.280 -- we put everything back together and we leave
00:44:19.192 -- just trying to keep that nerve nice and calm.
00:44:22.140 -- But it often feels better
00:44:24.380 -- real quick afterwards.
00:44:25.730 -- Can you re herniated disc?
00:44:27.360 -- Can you have another chunk
00:44:28.985 -- of crabmeat come out?
00:44:30.290 -- Unfortunately yes,
00:44:30.942 -- 10 to 15% of people who have had one
00:44:34.002 -- herniated disc will go on and do it again,
00:44:36.810 -- either at the same place or there
00:44:39.092 -- slightly more prone to having it occur
00:44:41.408 -- somewhere else in the lower back.
00:44:43.330 -- So it's not a cure all.
00:44:45.290 -- But boy,
00:44:45.890 -- if you're in that desperate shape where
00:44:47.990 -- it's been going on for weeks and weeks
00:44:50.214 -- and weeks and you're feeling absolutely
00:44:52.328 -- miserable and nothing is helping,
00:44:54.420 -- it really can feel like a miracle within.
00:44:57.250 -- Within often a matter of hours or
00:44:59.574 -- days if it's not getting better.
00:45:02.020 -- If that nerve decides not to settle down,
00:45:04.960 -- well, there's other tricks up our sleeves,
00:45:07.530 -- but the majority of the time getting
00:45:10.064 -- that hunk of crabmeat out of there and
00:45:13.042 -- off the nerve will make you feel much,
00:45:15.970 -- much better.
00:45:16.656 -- Why don't we do it the first day
00:45:19.477 -- that you have a herniated disc?
00:45:21.840 -- Because 80 plus percent of people
00:45:24.102 -- who have a herniated disc will
00:45:26.400 -- feel better within a few weeks.
00:45:28.550 -- So you can be saved from having to
00:45:31.262 -- have surgery if you just take it
00:45:33.676 -- easy and let things settle down,
00:45:35.770 -- but when it's not selling down,
00:45:37.840 -- it really is a wonderful operation in
00:45:40.171 -- that it helps a lot of people will
00:45:42.742 -- talk about other types of operations
00:45:44.718 -- in the spine in future sessions.
00:45:47.130 -- Bye bye now.
00:46:10.790 -- So if you want to watch the rest of
00:46:13.814 -- the series, it's pretty interesting
00:46:15.899 -- this guys are a good speaker and does
00:46:18.834 -- a good job about explaining these
00:46:21.180 -- various operations that they do.
00:46:22.930 -- Obviously we saw two videos today and you
00:46:26.386 -- could see how well he explained things.
00:46:30.130 -- So there are other types of injuries,
00:46:33.160 -- and some of these you may have
00:46:36.044 -- experienced if you go into the workplace.
00:46:39.220 -- Many times you'll see these injuries
00:46:41.848 -- or these conditions of the spine.
00:46:44.420 -- Sometimes they're not injuries,
00:46:46.148 -- but they're just how people have
00:46:48.814 -- how their spines are basically,
00:46:50.910 -- so ideally we see that we have
00:46:54.529 -- our person on the left.
00:46:57.260 -- Who has his ears over shoulders,
00:46:59.260 -- shoulders over his hips,
00:47:00.588 -- hips over his knees,
00:47:01.920 -- knees over his ankles,
00:47:03.852 -- and the neutral posture?
00:47:05.790 -- The person that's diagram to the right of
00:47:09.334 -- him or her more likely him in this case.
00:47:13.360 -- You see that he's got extreme lordosis.
00:47:17.310 -- Meaning the upper part of the
00:47:19.842 -- spine is protruding out.
00:47:23.640 -- When we get into biomechanics two
00:47:25.578 -- and a couple of photos that I have,
00:47:28.200 -- this one person you can see has a
00:47:32.120 -- pronounced lordosis. Basically.
00:47:37.870 -- From working or kyphosis from working,
00:47:40.380 -- doing these laundry tasks
00:47:42.932 -- over a period of time.
00:47:46.130 -- So and somebody can experience a
00:47:48.446 -- couple of these conditions together,
00:47:50.650 -- kyphosis and lordosis and also
00:47:52.705 -- scoliosis at the same point.
00:47:57.620 -- If you've ever seen the movie Molly's game.
00:48:01.730 -- It talks about the star of the show,
00:48:04.170 -- so to speak, or what the story centers
00:48:07.018 -- around the person it centers around.
00:48:09.630 -- But she grew up and all the
00:48:11.933 -- sudden she developed scoliosis.
00:48:13.680 -- Severe case of scoliosis for spying
00:48:15.780 -- twisted and she had to undergo
00:48:18.007 -- surgery to straighten your spine out.
00:48:20.300 -- Scoliosis is,
00:48:21.401 -- I don't wanna say real common,
00:48:23.610 -- but it is relatively common.
00:48:25.450 -- And when somebody experiences at a young age,
00:48:28.400 -- what they normally do is put
00:48:30.320 -- the person in a back brace to
00:48:32.928 -- help the spine straightened out.
00:48:35.020 -- In very severe cases,
00:48:36.652 -- they do have to do operations.
00:48:39.100 -- And they have to pin the spine so
00:48:42.228 -- that it is more straight in nature.
00:48:45.690 -- And you see,
00:48:46.761 -- water kyphosis is for this
00:48:48.546 -- bulges out at the top,
00:48:50.120 -- a lordosis where the lumbar area bulges in
00:48:53.168 -- and then scoliosis for the spine is crooked.
00:48:56.630 -- So with the ideal posture,
00:48:58.350 -- the forces are evenly distributed
00:49:00.080 -- through the body and all the joints are
00:49:02.818 -- in their neutral zone and this results
00:49:05.091 -- in minimal wear and good muscle and
00:49:07.590 -- stable stabilizer muscle recruitment.
00:49:09.150 -- When they talk about the fact that.
00:49:12.510 -- Oh you know, just.
00:49:15.852 -- When you're growing up and they
00:49:17.676 -- say you know have a good posture,
00:49:19.780 -- keep your head up.
00:49:20.888 -- Keep your shoulders back.
00:49:22.000 -- That helps put you in that neutral posture
00:49:24.296 -- and helps prevent some of these conditions.
00:49:26.760 -- Poor posture,
00:49:27.402 -- the joints are out of alignment,
00:49:29.330 -- their type,
00:49:30.320 -- the muscles are shortened or weak.
00:49:33.290 -- Jason muscles are weak and important.
00:49:36.010 -- Stabilizers are inefficient.
00:49:42.450 -- So we do have disk congenic and neurological
00:49:45.418 -- types for conditions where the disc
00:49:48.338 -- prolapses there's nerve irritation,
00:49:50.440 -- nerve entrapment.
00:49:52.360 -- We have muscular ligament and tendon
00:49:54.952 -- problems which are caused by trauma,
00:49:57.450 -- strain, sprain and tear.
00:49:59.186 -- And then we have muscle weaknesses
00:50:01.867 -- which cause imbalances.
00:50:03.560 -- And then we have structural
00:50:05.970 -- and genetic type problems.
00:50:07.900 -- Real common and thank God knock knock.
00:50:11.100 -- I don't experience this,
00:50:12.852 -- but my family has a history of stenosis,
00:50:16.580 -- meaning and narrowing of the.
00:50:20.470 -- Vertebral vertebrae,
00:50:21.326 -- where the spine goes through,
00:50:23.470 -- and this put can put pressure
00:50:26.416 -- on the spinal column.
00:50:28.380 -- There's cartilage damage,
00:50:30.063 -- bone where osteoarthritis and osteoporosis.
00:50:36.420 -- So why do people get back pain or
00:50:38.748 -- New Years starting up a new activity?
00:50:41.240 -- If you've never shoveled dirt before
00:50:43.262 -- and today you're out shoveling dirt or
00:50:45.518 -- like what we've had to do this winter,
00:50:47.980 -- is shovel a lot of snow,
00:50:49.900 -- and this is the first time you do it.
00:50:52.790 -- People can experience back pain.
00:50:55.070 -- There's misuse cumulative effect of bad
00:50:57.494 -- body use over a long period of time.
00:51:00.660 -- So poor postural alignment or
00:51:02.545 -- pushing their body too far too often?
00:51:05.170 -- There's overuse repetitive use of one
00:51:07.276 -- group of muscles causing an imbalance,
00:51:09.480 -- and then diseuse lack of exercise
00:51:11.484 -- may cause a back problem,
00:51:13.430 -- but one can result when we attempt an
00:51:16.158 -- activity requiring a certain degree
00:51:18.023 -- of strength or fact flexibility.
00:51:19.890 -- So if you don't do something for a
00:51:22.530 -- long period of time and then you try
00:51:25.245 -- doing it with without proper training,
00:51:27.790 -- so to speak, to get into the shape,
00:51:30.660 -- to do that activity, you can cause an injury.
00:51:36.150 -- So again, I've shown this picture before.
00:51:39.010 -- This is hardware and a colleague
00:51:41.428 -- of mine's husband's spine
00:51:43.113 -- that keeps his back together.
00:51:45.130 -- You can see in this X ray how
00:51:47.730 -- those two vertebrae aren't
00:51:49.466 -- really lined up as well either,
00:51:52.470 -- but without this he would have tremendous
00:51:55.333 -- pain with this hardware in his back.
00:51:58.180 -- What he does is he lacks flexibility.
00:52:02.740 -- But you can do stuff.
00:52:06.240 -- So from an economic perspective,
00:52:08.360 -- what can we do? We can rest.
00:52:11.330 -- We can change the risk factors.
00:52:13.870 -- We can get physical therapy.
00:52:15.990 -- We can do hold your holistic,
00:52:18.540 -- natural path type things.
00:52:22.020 -- If we have pain,
00:52:23.228 -- we can use over the counter
00:52:25.115 -- medication or prescribed medications.
00:52:27.660 -- One of the things that many
00:52:29.148 -- physicians talk about now and again.
00:52:30.660 -- I'm not a physician.
00:52:32.464 -- But again, using topical type pain relief
00:52:36.220 -- rather than consuming Mot ran or Tylenol,
00:52:40.220 -- but putting on like asper
00:52:43.075 -- cream or Salon pass patch.
00:52:45.930 -- One of those things that are
00:52:49.842 -- a topical type pain reliever.
00:52:53.810 -- Steroidal injections basically what
00:52:56.062 -- they do is they reduce inflammation.
00:52:59.440 -- Of course they have to be done by
00:53:02.496 -- a physician cauterizing nerves.
00:53:04.960 -- So when you cauterize the nerve,
00:53:06.330 -- what do you do?
00:53:08.480 -- You basically are killing the nerve.
00:53:10.980 -- But in some cases.
00:53:12.920 -- If there is an irritated
00:53:15.345 -- nerve that can't be called,
00:53:18.020 -- they will cauterize it to prevent it
00:53:22.521 -- from rapidly firing or firing at.
00:53:26.060 -- Overtime.
00:53:27.740 -- And then disc fusion or disc replacement.
00:53:29.930 -- And really it's not disc replacement.
00:53:31.810 -- They are getting to the point
00:53:33.688 -- of replacing disks.
00:53:34.630 -- You can look it up and you can
00:53:36.654 -- see the material they use diagrams
00:53:38.611 -- on the right here in this slide
00:53:41.083 -- shows some of those things that
00:53:43.039 -- are used as disc replacements.
00:53:44.908 -- Again,
00:53:45.352 -- this is really radical surgery
00:53:47.572 -- and rather risky,
00:53:48.930 -- but in cases where a person
00:53:51.150 -- is in constant pain,
00:53:52.630 -- it may be what is required
00:53:55.132 -- to help alleviate that pain.
00:53:57.320 -- And then from an ergonomic perspective,
00:53:59.350 -- that's why we're here.
00:54:00.710 -- Prevention is the best solution.
00:54:02.410 -- Not getting to the point of pain.
00:54:07.630 -- So this video and I'm not
00:54:09.322 -- going to show it here.
00:54:10.860 -- Because it's quite long and
00:54:12.440 -- also it's more like goes over
00:54:14.562 -- preventing various types of work
00:54:16.957 -- related musculoskeletal diseases,
00:54:18.400 -- music, orgonomic solutions,
00:54:19.591 -- but wanted to provide it.
00:54:21.580 -- Here is a link that you can
00:54:23.932 -- watch at your own convenience,
00:54:26.340 -- again on the GBU learn website.
00:54:28.730 -- All these video links will be
00:54:31.526 -- there along with the original
00:54:34.063 -- videos that I'll be showing.
00:54:36.940 -- So what I want to do?
00:54:40.710 -- Just go back to some of these videos
00:54:42.494 -- that we've watched in the past.
00:54:55.880 -- And have you think about what
00:54:58.118 -- types of injuries somebody could
00:55:00.120 -- develop from doing this activity?
00:55:02.290 -- Some of these you haven't seen before.
00:55:05.150 -- Show these first.
00:55:06.452 -- No, I had some students several
00:55:09.056 -- years ago and do a project at a
00:55:12.007 -- lamb Weston potato processing
00:55:13.736 -- facility in American Falls.
00:55:16.140 -- And some of these videos
00:55:17.785 -- we took when we were there,
00:55:19.950 -- and it's a potato processor in handling.
00:55:24.190 -- This first one.
00:55:35.240 -- Is a logging operation.
00:55:36.768 -- You can tell that it's loud also.
00:55:39.510 -- But when their one machine breaks down,
00:55:41.690 -- they have to stack boxes manually.
00:55:45.110 -- I'd like you to watch it and
00:55:46.601 -- just think about the types of
00:55:48.140 -- injuries this person could develop.
01:00:03.570 -- So I went back a couple of steps.
01:00:07.670 -- And this is a good place to
01:00:09.336 -- stop for a couple of minutes.
01:00:11.240 -- So you can see that he's picking
01:00:13.102 -- the boxes off a conveyor line.
01:00:14.890 -- You can see that how he's twisted.
01:00:17.720 -- His back is twisted.
01:00:18.884 -- He's got 1 foot planted.
01:00:20.340 -- He's got the other foot
01:00:22.390 -- slightly off the floor.
01:00:24.030 -- He's reaching for the box.
01:00:25.610 -- This is a posture he always uses to take the
01:00:29.372 -- boxes off the conveyor belt to stack him.
01:00:32.800 -- So of course, when he's on the 1st
01:00:34.936 -- tear down at the bottom of the pallet,
01:00:37.230 -- he asked to lower the box down.
01:00:39.790 -- When he's at the top of the pallet,
01:00:41.650 -- he has to raise the box all the way up.
01:00:44.730 -- So if you think about this posture and
01:00:46.794 -- the other postures that he develops
01:00:48.592 -- during the course of doing this task,
01:00:50.760 -- what types of entries could he
01:00:52.938 -- experience in the long run?
01:00:54.740 -- So you can see that at the end of
01:00:56.900 -- the time that he's left in his boxes,
01:00:59.360 -- so move forward just a little bit.
01:01:11.440 -- So watch here and see how fatigued he is
01:01:15.067 -- lifting this last box up to that top tier.
01:01:26.200 -- So just standing there you can see
01:01:29.007 -- that he's getting very fatigued.
01:01:31.370 -- That he's tired of moving these boxes
01:01:33.477 -- now I don't remember exactly weight,
01:01:35.930 -- but I think it's either 40 pounds,
01:01:38.390 -- 35 pounds, forty pounds,
01:01:39.794 -- something like that.
01:01:40.850 -- It's not like a box of
01:01:43.292 -- potatoes that weighs £50.
01:01:44.920 -- But you can see the this posture that he has.
01:01:49.060 -- He's always twisting the same way.
01:01:51.500 -- You could develop the differential
01:01:53.885 -- muscle strength in his back.
01:01:56.270 -- With the muscles aren't pulling evenly
01:01:58.808 -- and he could develop a problem like
01:02:01.628 -- that doing this task all day long.
01:02:04.090 -- And again they this is.
01:02:06.050 -- This task is required when the stacking
01:02:09.291 -- machine breaks down the automatic stacker
01:02:12.112 -- so he has to stack things manually.
01:02:15.250 -- But it in this particular facility,
01:02:17.130 -- even though they had two of
01:02:19.386 -- these stacking machines.
01:02:20.520 -- They were breaking down quite frequently,
01:02:22.650 -- so one of the things we're looking
01:02:24.960 -- at is not only the ergonomics of it,
01:02:27.980 -- but also you know what was the
01:02:30.024 -- economical tradeoff of purchasing
01:02:31.459 -- another stacking machine,
01:02:32.950 -- or trying to find one that's more reliable.
01:02:37.280 -- OK.
01:02:47.310 -- This is not stocking
01:02:49.294 -- machine I'm talking about.
01:02:51.280 -- The two stocking machines.
01:02:53.920 -- So when they're working, they work great.
01:02:55.970 -- When they don't work,
01:02:57.782 -- they have to stack the boxes by hand.
01:03:01.320 -- So like I said, there's two of am.
01:03:03.110 -- You see the one on the left.
01:03:04.680 -- There's also one on the right
01:03:06.060 -- that's kind of out of you.
01:03:10.290 -- But they automatically palletized the boxes.
01:03:12.630 -- They stack a man.
01:03:14.242 -- Then they put shrink wrap or stretch
01:03:17.294 -- plastic around the outside of the pallet.
01:03:21.060 -- First four, then using a forklift
01:03:23.088 -- and then for putting in the back
01:03:25.428 -- of a truck so manually stacking.
01:03:27.270 -- They can't put the same number
01:03:29.094 -- of boxes on a pallet that they
01:03:31.415 -- can with a stack of machine.
01:04:30.810 -- And the third video is kind of interesting.
01:04:37.070 -- So these are £500 totes.
01:04:41.290 -- So when the one packaging
01:04:44.990 -- machine breaks down.
01:04:47.210 -- They would have to put the French fries
01:04:50.050 -- or tater tots in these 500 pound toes.
01:04:52.990 -- And so again, we were looking at.
01:04:56.730 -- What are the efficiencies or what's the
01:04:59.817 -- cost trade off on putting in another
01:05:03.287 -- packaging line versus storing these
01:05:05.862 -- spuds in these 500 pound totes?
01:05:08.750 -- So what happens with these 500 pound toads
01:05:11.342 -- is they are stacked up on top of each other.
01:05:14.400 -- You know, they're fairly rigid boxes.
01:05:17.450 -- And they actually the stuff inside
01:05:20.534 -- the product inside helps provide
01:05:23.321 -- structural stability as well.
01:05:25.900 -- But they lose about 10% of the French
01:05:30.418 -- fries when they use these 500 pound totes.
01:05:35.870 -- So also when you see the person doing it,
01:05:38.530 -- the motions that they have to
01:05:40.324 -- have while they're putting the.
01:05:44.030 -- Product into those 500 pound toads.
01:05:53.390 -- Then once they get the toe down,
01:05:55.670 -- when they start to fill the packaging again,
01:05:58.270 -- there's some activities that they
01:06:00.685 -- have to do for that as well.
01:06:03.930 -- It's one of those things whether it's
01:06:06.359 -- a cost tradeoff to lose in a £500 to
01:06:08.999 -- losing 10% of the product which is.
01:06:11.700 -- £50 of French fries that
01:06:14.490 -- are ground to a pulp.
01:06:17.280 -- Or do they get another packaging
01:06:19.134 -- line which is several $100,000?
01:06:20.950 -- So that's another one of
01:06:22.620 -- those things we looked at.
01:06:24.290 -- And of course you see the worker here
01:06:27.410 -- wondering why in the world we're videotaping.
01:06:30.650 -- But we're we're doing that look
01:06:32.696 -- at efficiency of the operation.
01:06:38.900 -- So there is a lot of operations
01:06:41.112 -- associated with this.
01:06:42.060 -- It's not real simple. Again,
01:06:45.095 -- once the tow gets to certain level,
01:06:47.790 -- they've gotta move the product
01:06:50.130 -- around inside there manually.
01:06:52.010 -- So that the product is evenly spaced
01:06:55.167 -- and doesn't collapse the box when
01:06:57.738 -- it's stacked up on each other.
01:07:57.730 -- So we're going to go back and watch
01:08:00.074 -- the life raft one again and then
01:08:02.371 -- it'll be time to complete this.
01:08:04.410 -- But think about this operation.
01:08:06.270 -- Now that you know more about work
01:08:08.965 -- related musculoskeletal diseases and
01:08:10.506 -- think about the types of injuries
01:08:12.432 -- that these people could experience.
01:11:14.040 -- So if this were alive class we talked
01:11:17.088 -- about this as a goat, do this task.
01:11:19.813 -- But just think of this stress again.
01:11:22.340 -- What they're putting on their
01:11:23.920 -- bodies and the type of injuries
01:11:26.006 -- that they could experience.
01:11:27.760 -- 'cause these aren't little
01:11:29.076 -- forces that they're using to
01:11:31.108 -- put these clamshells together.
01:11:32.810 -- They're using a lot of force to
01:11:35.323 -- try to get that thing compressed.
01:11:38.370 -- And where it's not crimping the.
01:11:42.010 -- The raft inside.
01:13:52.170 -- So also think about what other tools they
01:13:54.874 -- might use to if this task weren't changed,
01:13:57.740 -- which we know that it was changed.
01:14:00.170 -- The pods are bigger now and
01:14:02.606 -- the equipment is different.
01:14:04.230 -- But think about the tools that
01:14:06.120 -- would help this. Then do this job.
01:14:09.570 -- Better than like a rubber mallet
01:14:12.120 -- and a handle that they push in.
01:14:15.020 -- 5 minutes. Pushing for the raft.
01:16:01.150 -- So that's it today.
01:16:06.520 -- We'll talk a little bit about injuries,
01:16:08.760 -- the next lecture, and then
01:16:10.950 -- started in biomechanics. Thanks.
Good evening everybody.
I think we can start now. So basically what we're going to do today, we'll go through the lecture file that I posted last time but didn't finish because of the.
Early class release.
But today is not the case like that. So we are going to go up to what is the time 9.
That's dreadful. OK, we'll see what happens. Because when I feel like tired, that means it's time. It's time to go. Not you guys feel tired. Not that that time is not. Yeah, it's always advantage the instructor.
Correct. So anyway, of course if you have to go somewhere, you can always tell me that you have to go for some reason.
Extraordinary circumstances then you can, but otherwise, you know, just stick with me and see how far we can go. All right? So last time.
What we did was just going through chit chatting basically, and everybody got the syllabus.
Let me see. I was having few left with me. Do you need one?
Like commercial power reactors, are all thermal reactors OK? Fast reactors are generally the ones that we had before.
Like BR1BR2 then FF.
Fast, fast flux.
Or in that area where the Pacific Northwest National lab.
Is near that area.
But they are not operating anymore.
But other countries are doing that progressing now. If we don't have a fast reactor, we cannot do lot of irradiation work.
Faster, you know, we would like to have that and also we would like to know what happens with fast neutrons, right? So we would like to have that past reactor and that's where the versatile test reactor can help PTR.
Can anybody tell me some?
Overseas fast reactors.
That are operating. There are also mainly research reactors.
Russia has bore 16.
I don't know they whether they have a more advanced one now.
But that is 1 reactor. I can think of France as Phoenix.
Japan has jail.
Right something like that. So everybody has this fast reactors but the but we don't have so that's very important that we have we have DTR.
And recently I gave an interview.
To Idaho Statesman, it's a local Idaho paper.
Right. So they came up with a new system there, OK.
And the reported took like almost 30 minutes interview, OK. And they also told me that they are going to talk to final people.
So I said yeah, because you should talk to IRL people more because they know more than that, right? I don't know much. So when the item came out, I just got one sentence that Doctor Cherith, chair of the Nuclear Engineering Industrial management department, said.
That nuclear is great for baseload, the continuous electricity.
Not like solar range, that's my contribution to that news item. OK, that's good for me because it's OK. So what I said like I had little bit of contribution to that, OK, so.
Now basically you can see however it is important.
Important to have a break.
But I don't give a break like for long like 15 minutes. Actually, they want me to give you.
How many minutes you want break?
It will be very late, like 945, you'll go home.
How about you go home 9:30?
That's better. So I'll give you 5 minutes break. OK then. Right now it is 818. So if you add five minutes here, it becomes 823.
OK. You can come back 823, you have to take, you know, refresh yourself and then we'll continue.