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Okay, Lisa's the brakes to the airline, and so it's a great symbiotic relationship. Honeywell has an incentive to develop brakes that last longer because Honeywell has to replace the brakes. If a mechanic comes to Honeywell, says we need to replace the brakes, Honeywell has to pay for the new brakes on the airline. But the airline has fixed costs. They know exactly how much they spend on brakes for every landing, okay. So Honeywell has fixed costs, their accountants are happy, they can calculate what the profit should be — not Honeywell, but American Airlines, whoever the airline is. And then Honeywell has an incentive to make a longer-lasting brake. And the mechanics don't care about the cost of replacing the brakes because it doesn't cost their employer anything for them to decide I need to replace the brakes, okay. Just takes time. Okay, but the cost of the brakes is borne by the manufacturer.

The airlines also do that. They do, for example — airlines now lease the engines on the aircraft. They call it power by the hour. And the airline knows that for every hour that engine is operating — and you have to keep a log of every minute the engine is operating — they have to pay so much money to the owner of the engines. And the owner of the engines could be General Electric, it could be CRO Malloy [Rolls-Royce?] gas turbines, it could be a number of people. They're responsible for maintaining that engine, repairing that engine, and they lease it back to the airlines. Well, the same thing — most of the aircraft you're flying on are owned by some big investment company. American Airlines typically doesn't own that aircraft. They're leasing it. They pay a certain amount per month or per hour or whatever for the engines to one company, for the airframe to another company, for the brakes to another company. And it actually is not a bad system. It's sort of like Zipcar, right, you're renting the car.

So anyway, that wasn't what today's lecture is going to be about. I appreciate the digression. And what's your name — right, Jordan. Charles. Yeah okay, so Jordan's going to give a talk on why everything I said about two dollars a pound savings is wrong for the BMW, right, electric — for electric vehicles, and how they change the rules because of different constraints, okay. And I'm just glad that I talked about collateral weight savings, because that's — his story is basically that collateral weight savings on batteries, okay. So I just stole your thunder, okay, but it's a great presentation. I thought that — I was going to tell you how to think about writing a paper on it, seriously. You know, I thought about exactly where you publish it. But it's an interesting story and you certainly have quantified it more than the Wall Street Journal would quantify it, okay. There's nothing wrong with having assumptions as long as you state what your assumptions are in a paper. Many people don't bother to state their assumptions, and then you run into problems, okay.

Anybody have any questions before we begin? So the last time — and I couldn't really think of a summary of last time, a sort of recitation on competition among materials for water transport and then gas transport. And I actually showed this but it was the end of the hour and I didn't pass it around. [Tom holds up a piece of corrugated stainless steel tubing.] This is a piece of corrugated stainless steel tubing. There's about six billion feet of this in the United States, through most people's homes — many people's homes in the newer homes and as replacement in older homes. It's got polyethylene — this particular product has polyethylene yellow plastic. It's not really — not supposed to be for insulation. The yellow is supposed to identify it for gas piping. There's another company makes little connectors like this for forty or fifty years and they paint it yellow, okay.

This actually has a tube around — a tube of plastic around it, and the plastic has low coefficient of friction. You can pull this through the walls, okay, and the corrugations don't get stuck on the corners as you drill a hole through a two-by-four through a steel I-beam or something. So it does have a function other than just provide color. It does also provide electrical insulation, so you know hopefully it won't short out to it and arc to it from your household wiring. But in fact if you have a small manufacturing flaw that you could never even see even under microscope, if you have a very high voltage discharge — in this particular one we actually probably put a little copper wire through here, but there's a very small hole, and the electricity went through that small hole and you can't see it. Here, I'll pass it around. Created a hole about ten times the diameter in the steel underneath. The electricity doesn't attack the coating of the plastic, but it doesn't take a very big hole for all those electrons to get through the plastic. But once it hits the steel it melts it, okay.

This also occurs on aircraft wings. If you paint an aircraft and lightning hits the aircraft, the paint can actually focus the lightning energy, and it can take one ten percent of the energy of lightning stroke to perforate the wing on an aircraft. What's the problem of perforating the wing on an aircraft? Fuel. Your aircraft wing is actually your fuel container, okay. It's your structural wing for support, but it also contains fuel. So they do lots of tests at Boeing and other places. In fact I had a student do an internship at Boeing and she was working on lightning strikes to aircraft wings, although she was doing composites there. I know a lot about what happens when you hit an aluminum wing that's bare or a painted aluminum wing — if it's painted. And the two things are different. Just putting a coat of paint on it makes a big difference in how the lightning attacks it. But Chu was working on composites because Boeing wants to use more and more composites to make lighter and lighter weight vehicles, okay.

So you know, we were talking about some of the competition among materials for different things, and I'm going to change course a little bit and get more into structural material design. And I already pointed out, Ashby wrote this number of books. One is Material Selection of [in] Mechanical Design, and I've showed you the little pamphlet. And in that he has a lot of these — or now known as Ashby plots, because he was the first person to kind of do these. And what did I do? Be able to — I hit something wrong and I'll never be able to find out how to get to — now I hate to do this. I think the only way to do this — to turn this off and turn it back on to give me back to the home page that allows me to expand and contract things.

In any case, Ashby has a whole series of these plots that basically plot two material properties against one another. In this case he's plotting — someday I'll read the controls on this again, figure out how it works. I did it actually twice, but nothing's very simple anymore. I like the days when I just had little mechanical switches I could figure out. Anyway, he's plotting Young's modulus versus density. And it turns out E over rho — Young's modulus divided by the density — shows up in a lot of mechanical property formulas. And in fact if you look at the page before this in his book under material selection: Young's modulus E versus density rho, E over rho equal to some constant will be minimum weight design for stiff ties — a stiff tie being something like — if I — he might know what the hammer throw is in sports, where you have this steel ball and it's connected to a rope or something, and you lace it — a hammer throw, I guess they call it, the hammer throw. And the guy picks it up and he swings it around and he sees — he lets it go and centrifugal force sees he'll throw — how far he can throw the steel ball, which is a 16-pound ball or something.

In any case, that tie has a certain tension in it. And the strength of that, for stiff ties — the string that's holding the ball to the handle that he's got holding on with his hand — minimum deflection in centrifugal loading as an example. E to the one-half, which you can't quite see, E to the one-half over rho is minimum weight for stiff beams. So if I was looking at — I have two rulers here, I had in my office, actually in my briefcase. [Tom produces two rulers.] This is a very thin plastic beam. This is also a thin beam, actually same size ruler, but this one's got a magnetic stripe on it. It's a lot heavier and you can see this one sinks under its own weight, okay, like a diving board. This one's stiffer even though it's thinner. It's a different plastic. This one is heavier basically.

And so you can have stiffness — you can get stiffness from two different properties of a material. One is Young's modulus, which is a property of the material. It's related to that Lennard-Jones potential and the bonding between the atoms and how strong that bonding is. The Young's modulus is the second derivative of that energy potential minimum, okay. So the steeper that is — and the highest Young's modulus for any material is carbon. Tungsten is not far behind that — steepness of the Lennard-Jones potential. This is energy of bonding versus distance, radius between the two atoms, and the steeper it is, the sharper this curvature, the higher the melting point. The melting point is basically related to the depth of that energy potential well, and the stiffness, the Young's modulus, is proportional to the curvature, sharpness of the curvature. Tungsten and carbon, being diamond, are two of the stiffest materials we have. There are limits to that.

But in fact you can either get stiffness from a material property, and there's one other way to get stiffness. What's that? All right, design, thickness, design cross-section, you name it, geometry, okay. It turns out for equal areas, what would be stiffer, a solid rod or a tube of equal area? Well, this one's stiffer, okay. A tubular section is stiffer than equal weight, equal material of a solid rod. So you can get stiffness from two things, okay. And so what this plot shows you — Ashby plot will give you — is E over rho for tension, tensile stiffness, so you don't get the — if you swing the rubber band or the ball around on a steel rope, you will get less stretch than if it's on a rubber rope, okay, because Young's modulus is larger. E to the one-half is minimum design for beams, like I talked about. There. E to the one-third over rho is for plates, okay. You talked about a piece of paper — how stiff is that sheet compared to some other sheet of some other material? These are not same thickness. This one actually is flimsier. The rubber is flimsier than the paper. Actually has a higher stiffness.

So if you go to this Ashby will have all of these on one plot. The advantage of an Ashby plot, as you can see all kinds of properties on one plot for two properties. Part of the — gets another Young's modulus, and you see here guidelines for minimum weight design: E over rho — either E over rho to the first power, E over rho to the one-half, E over rho to the one-third — and they have different slopes, and you can compare those slopes. And the slopes he's put in here are E over rho to the first power, and that's ten to the fourth, okay. And that actually has units of meters per second. Does anyone know what E over rho being meters per second — what type of test in the mechanical behavior laboratory that's used for? You've heard of stress-strain curves, right? And you've got a stress-strain curve and they tell you that Young's modulus is the slope of the elastic region, and then you have the plastic region. And if you took a class — how many people took a class in high school or as a sophomore in mechanical behavior or whatever, and they told you to calculate Young's modulus from the stress-strain curve, right? It's not the way you do it in the real world.

You actually measure — you put a vibrational frequency in a rod and you measure the speed of sound in meters per second, and from that you get a much more accurate Young's modulus. This Young's modulus, when you just try to do a tensile test — it's easy to show the students a principle of measuring Young's modulus by the slope. You try to do that on a piece of aluminum, and you have 15 students do it, you'll get numbers between seven and 15 million pounds per square inch, and the real number is 10 million, okay. Because of slippage in the grips and things like that, okay. So it's not that easy to measure Young's modulus unless you do it by frequency, okay.

In fact they — in steel mills they have little machines you take a little strip of steel if you cut out and you slip it into this machine and it measures the speed of sound in that steel in a particular direction. So you have a sheet, a great big sheet of steel, and you cut out a specimen longitudinally, you've got a specimen transverse, and you cut out a specimen at 45 degrees, and you measure the speed of sound — each three of those numbers. And that modulus will be different in each three directions because of the texture of the crystals in the steel, and that steel will draw differently when you try to make a suit can [Coke can?] or something like that out of it, okay. You can predict the drawability of an automobile body based on the speed of sound, which is related to the Young's modulus and the stiffness of that. It's called a Modul-R machine, and we — you taking my deformation, Modul-R, I'll go through it, okay.

But in any case, so here's a plot. And the stiffest material is diamond, 60 million. And down here are the metals, and steel is of the stiffest metals, although tungsten alloys are higher than steels. But the highest is diamond at about 60 million. Here's a composite, tungsten carbide plus cobalt. It's really the tungsten carbide. We like to use tungsten carbide as a structural material. It's stiff for lots of things. But the problem is — anybody know the problem with tungsten carbide and why we don't use it more often? Cost. Ten thousand dollars a pound, okay. To form tungsten carbide you have to have furnaces that go to 25 — well above 2,000 C, 2,600 degrees C in some cases. So this happens to be a tool bit that we cut apart. It would have looked like this. [Tom holds up a tool bit.] And this is a tool — you would have several hundreds of these on a machine.

You ever been driving on the highway late at night on an interstate highway and they're reclaiming the asphalt? They have a great big machine. This is the tool that's on that wheel that's beating up the asphalt and throwing it back into a trailer to be recycled. And you can wear out these tools in three or four hours, in which case you have to stop that machine. The mechanic has to go in — you're doing all this in the middle of the night, you're paying people double time to work in the middle of the night on the highway, cause you don't want to disrupt the traffic. You'd like to have something that lasts for a good eight hour shift, okay. Lot of wear on that.

And it turns out if you look at the details — this one's been polished better than the other one — who pass this around a second — but if you look at the tip of this particular one — so there's some — it was a company, see if we — okay, there was a company out — it was out Uthoff [Utah?] anyway. There's a lot of people out in Utah who would like to work on diamond, because there was a guy, General Electric, Tracy Hall, in the 1950s, who developed the ways to make man-made diamond when he was at General Electric Research. But this actually is the tungsten carbide tip from here all the way up here is tungsten carbide. Looks sort of copper colored, but I'll tell you the reason for that. This is actually sintered diamond. Ordinarily the tip of this thing would just be tungsten carbide, and it would wear out in three or four hours. If you may, if you could make sintered diamond tips on these things, they'll last more than eight hours, okay, because you've got more wear because of the stronger material. So I'll pass around, and I won't get into — they did step brazing and other things. I was asked to help evaluate it because one company wanted to know if they wanted to buy this company, and we — I think they finally decided it was a great product, technologically superior, but it costs too much, so they didn't buy the company, at least that's what I heard the last. Anyway.

But so diamond is right at the top, and that's what they were able to put in there as a wear-resistant hard structural material, because tungsten carbide, which was almost as good, would have half — or one-fifth — the life of the diamond, okay. So small differences can make big differences when you get to things. This is for stiff materials. Now, well, I had something else here for stiff materials. Oh yeah, that's Ron's yours [rongeur]. So once upon a time, back in the 1980s — so this is 30 years ago — I used to do a lot of consulting for a firm down south of Boston, been around since the 1830s. It's now a division of Johnson & Johnson, makes medical instruments. Does anyone know what a Ron's your [rongeur] is? I never knew what it was. It's a French word. A Ron's your [rongeur] is basically a pair of pliers that an orthopedic surgeon would use to chew up bone, to break up bone. So this is — a Ron's your is just a pair of pliers, and it has a little cup in, so you can go in there and just bite away the bone. So they're going to do — they're going to fuse someone's spine or something, they go in there and he chips away at the bone, removes the bone that he wants to remove.

Well, when people were doing — and it's not just bone — when they want to do arthroscopic knee surgery, which was somewhat new — I have torn cartilages in both my knees now, but I had one of them since the 1960s when I got injured in a football game. And that's a — my left knee is the torn cartilage. Well, they can go in at that time, in the 1960s, to remove that torn cartilage — they would have to lay open your whole knee and you would be in a cast and on crutches for up to six months. Nowadays you can go in and you can walk out of the hospital that day. You might have crutches for a week or something, but basically they go in with microsurgery. Just put a little — rather opening up your whole knee, they can go in with microtools, they put a little slit in there, and with a little fiber optic so the surgeon can see what all blood and guts looks like in there and try to see what he wants to cut up. He can go in there and he can use a little Ron's your to eat away and pull out the cartilage and remove the cartilage that way. Minimally invasive surgery. This is one of the first big applications.

The Ron's your for that application looked like this. [Tom holds up a rongeur.] And it's basically a pair of pliers by this guy. It's a sliding mechanism, and the cutting end is down here. So you have a little post sticking up and this — slide, the slides above, and you go in there and just eat away the bone or the cartilage, okay. That's a Ron's your. Well, they try to get smaller and smaller in their tools, and you can see I got a stiffness problem here, right? And they were making them out of steel. Steel's 30 million. And they came to me and said, well what can we make it out of that would be stiffer? Well, you can go to geometry, you can go to a tubular section, except they were trying to get them smaller, and tubular sections are larger.

So I suggested — they never liked my suggestion. I loved my suggestion that they consider — what else? Their — first of all, there are not a lot of choices. I didn't have an Ashby plot back in nineteen eighty-two whenever they asked me this question or whatever. But I knew the properties of materials and I knew my choices were diamond, and I didn't know where I could get a nice long slender diamond like that, okay, but it would be a great tool, okay. Might be pricey, but this is medical instrument, so you can charge a lot for it. Silicon carbide — I didn't know how I could get any reasonable cost silicon carbide. But if you look in this area at the top there's alumina. What's another name for aluminum oxide? Sapphire. Here's a piece of sapphire, I'll pass it around. [Tom passes a sapphire boule fragment.] We can grow sapphire. This type of piece of sapphire was not single crystal. It's grown in a boule that was about the size of a great big beach ball. It took about a month to grow it in the furnace. You put the aluminum oxide powder, furnace, you take it up to the melting point which is above 2,000 degrees centigrade — about somewhere between 2000, 2100 centigrade for pure alumina — and you would cool it down very slowly over about three weeks to cool it back down to a low temperature like a thousand degrees centigrade before you'd open up the chamber and everything.

It's a ceramic. It's aluminum oxide. Sapphire is another name for it. We grow sapphire boules like this now. A sapphire boule like that cost about a hundred thousand dollars. That was just a chunk. You can saw it into little substrates, and the reason they were making these — because every LED has an aluminum oxide sapphire substrate. Just like a silicon chip on a computer, you have an aluminum oxide sapphire substrate. Doesn't have to be single crystal because it just has to match the coefficient of thermal expansion closely of the gallium arsenide that's making the LED, okay. So it's a big business now to make all these LEDs, and that's what this company was making all this stuff for. They were up here in New Hampshire. They were selling this technology — who were they selling it to? China gave them like a I-lo — three hundred million dollar order for a bunch of these furnaces. And now guess who owns the LED manufacturing market, because they own the business of making the sapphire substrates? China.

And they would slice them up on diamond saws, because what's the only thing that's going to cut that? On the hardness scale, the old Mohs scale, which is a kind of — what material would scratch another material — diamond was number 10 on the Mohs scale. What's number 9? These are empirical numbers, these are just — is sapphire, okay. Sapphire would scratch anything but diamond. Now silicon carbide will actually scratch sapphire, but silicon carbide is not a natural mineral. But on the Mohs scale — Mohs, M-O-H-S — of natural minerals, and at the bottom is talc, okay. Talc is nice and soft, a thing is number two or something like that, and gypsum might be number four or something. But the mineralogists for a hundred and fifty years have had this hardness scale. Diamond was at the top. Sapphire was number two — number nine, sorry — and I can't remember what number three was. We've come up with other things like silicon nitride and silicon carbide and boron nitride and stuff. Some of the silicon aluminum oxide we call Sialon — silicon aluminum oxygen nitrogen, okay. They're fairly strong.

So in any case I wanted to make it out of single-crystal sapphire. Now you have to understand part of the business here of medical instruments. [Tom holds up a pair of surgical scissors.] This is just a pair of scissors that a surgeon might use to go in there and snip some part of the body — your soul or cut suture or something. This back in the 80s was a $300 pair of scissors, okay. They're probably six or seven hundred now. It's brazed on the surface with a cobalt alloy for excellent wear resistance and strength and maintains sharpness. This is the type of thing once you buy this pair of scissors you can send it back whenever it's dull and they will sharpen it for free and ship it back to you and clean it up. Gold-plated handles, so that you know this is one of the premium grades of stainless steel scissors, right. But I used to help make stainless steel instruments like this. Every one of them's got a hardness indentation on it because they do a hundred percent check on the heat treatment of the hardness, okay. So it's better than your Fiskars scissors. I mean to knock Fiskars, okay, we could take someone else, but this is a better scissor.

But physicians will pay a fortune for these things. And it turns out some physicians like — I can't remember what the instrument was — Dr. DeBakey, the famous heart surgeon, he liked a particular color, and so they would color the instruments the color he liked because it was just his favorite color of instrument. And there are some — if you go to a dentist's office, you'll sometimes see some of the dental tools will be color-coded. Just — you can go to Sears and buy tools that are color-coded for different sized ratchets and, you know, wrenches and stuff nowadays. But color coding would have been great with sapphire. You could have added a little chromium to the melt, and if you added chromium to the melt you would have made ruby. So you could sell ruby instruments to the surgeon, and I mean you could charge a fortune for these things. I mean, well, I was using ruby instruments when I touch your leg open. Anyway.

So the Ron's your, I wanted to make a Ron's your at a sapphire, and I was confident that you could buy — you can buy — either his company actually is the predecessor company — is making that stuff. But it was a company that started here in Cambridge and they could grow single crystal sapphire tubes or rods or sheets. They take this 2000 degree melt and they just slowly pull the stuff out, okay, of the melt, and grow things of different size. I actually have some silicon like that in my office that Professor [Sachs] — who did one of — the inventors of the name 3D printing and stuff — he invented a company that since went bankrupt. But they used some carbon wires, carbon fiber wires, and they would lift a sheet of silica — a more polycrystalline silicon for solar cells. I got something there, they're about three or four inches wide and you just grow the silicon right of the melt as a thin sheet. You didn't have to cut it with diamond or anything else. It's going to take over the solar cell market 25 years ago.

Problem is, if you look at it cross-eyed it will fracture, okay. Silicon is extremely brittle material. To show you a brittle piece of silicon — [Tom holds up a silicon crystal.] this is a chunk of silicon, single crystal, grown by a Czochralski process. And it's completely brittle. Fracture just like that piece of sapphire. The easiest way to break it is just whack it with the hammer, okay, and it breaks. Takes a big hammer to whack the sapphire because it's pretty hard. Silicon is pretty hard. But as I pass this around, this is the — those surfaces darker, it's got some — so it's grown in a vacuum system. That steel — Parker is oxidized a little bit on this surface. You actually see some fracture patterns, which if you knew anything about fracture surfaces, or if you do already know something, you might think that's a fatigue crack, sure, because it has little what we call beach marks. In a brittle material like glass we call those hackle marks, and they're not from fatigue cyclical loading. It's just the way some material — some brittle materials, very brittle materials — fracture.

Anyway, I wanted to use, for Young's modulus reasons, sapphire. And they never would believe me that you could buy this stuff. You can buy sapphire rod for fifteen dollars. You can buy sapphire tube probably for thirty dollars for a foot long tube, and it's twice as stiff as steel, okay. And I knew I could put a solid rod and use the diamond to make a cutting tip on one end, and I could do something to put a tip on the other end, and I could basically make a Ron's your of a tube slide — or a rod sliding through a tube. No, they didn't like it, okay. Hey, what do you hire a consultant for if you don't listen, okay? So there's other things that you can look at in the Ashby type plots. This is — anybody have a question about — yep, no.

Then — they didn't like my idea. They thought sapphire would be too expensive. I thought selling sapphire and ruby instruments would have great marketing appeal, and for simple instruments, simple cutting tools, you wouldn't find a better material. It's right behind diamond on hardness, so the wear resistance of the cutting edge is fantastic, right. And the toughness is better than a lot of these ceramics tools that they use for cutting edges and stuff, okay. Anyway, they didn't like the idea. They never would try it, and I didn't think — I mean, I know that if you're actually machining with diamond tools, the stuff on that hard to machines, okay, sapphire with diamond — you can make some very intricate shapes. Got to be fairly simple. You can't do 3D printing, you got to do subtractive manufacturing. But no, you know, they didn't like the idea, so it never went anyway. And they never would tell me a reason why they didn't like it, okay. But what they said is, we want something that's stiffer, and I said there's only — if you've only got a handful of choices, look at the Ashby plot. We didn't have Ashby plots back then, but I said there's only a few materials.

It's just like for the National Aerospace Plane in the mid-80s, they wanted to develop the surface of the airplane coming back into the atmosphere. This was a — National Aerospace Plane was supposed to be a supersonic transport. They would actually get up into space and then come back down, and it could be like two and a half hours between any two cities on the globe, okay, because you'd be going at Mach 17 up there in space, okay. So all you had to do is make the boost into space, do your travel with no air around, come back through the air, land, and it would be two and a half hours anywhere in the globe. And this was actually partly — they never said it — but it was also part of Reagan's Star Wars initiative, because if you could do that and put civilians up in space, you could put hardware up in space and weapons in space, right.

But turns out if you look at that Mach 17 coming back into the atmosphere, the frictional heating will give you surface temperatures of 3,000 degrees kelvin. So they had a great idea, well we'll make it out of copper, and we'll — liquid hydrogen will be our fuel and we'll just cool the inside with liquid hydrogen. So this is a great idea, okay. I don't know where they get these people in the Air Force to come up with these ideas, but, or some of the aerospace companies. So this was going to be copper skin, this was going to be 3,000 degrees centigrade air, and this was going to be liquid hydrogen, okay. Anybody see a problem? The thickness of the copper was going to be about eighth of an inch, three millimeters. Anybody see a problem? You don't have to worry about lightning strikes because you have a better chance of just blowing yourself up. Anyway, here's the space shuttle Challenger all set to go, right? But this was — hey, you know, how many billions of dollars the US government spent researching how to make this work?

Well you might think it's sort of funny — I thought it was sort of funny until in 2002 — 2004, so I was on another National Research Council committee on aircraft propulsion for the US Air Force. This is a committee, and we were supposed to help advise the Air Force on what materials to use and designs to use for their three hundred million dollars a year the US Air Force had over the next 20 years to develop better motors. And they told us — they came in and gave us a non-classified presentation — the Air Force wanted a Mach 17 warhead to fly through the air, not through space but through the air, at Mach 17. And the reason was — this is before they killed Osama bin Laden, somewhere amid, you know, 2004-2005 — they actually had located Osama bin Laden and they had 15 minutes to get the ordinance on site, okay. But he was gone from that region, you know, within 15 minutes. But if they had the right weapon on one of the aircraft carriers in the Persian Gulf, they could have — if it went Mach 17, they could have had it on site and got — blown him up if they had a Mach 17 weapon.

Well, what's the fastest aircraft we have right now? It's like Mach two — Mach two and a half, you know. It's an F-15, F-16 or something like that. They, you know, burn all this fuel and their skin is getting hot, okay. We had Mach six or seven, the X — our 71 Blackbird or whatever, you know, this titanium-skinned aircraft that flew at a hundred thousand feet to take pictures of Cuba and stuff, or the U-2 spy plane that Gary Powers in '62 — you guys wouldn't remember that. Anyway, we built special aircraft, but we've never built anything close to Mach 17. So I knew, and I said, well this isn't going to be man-rated. No, it was going to be unmanned — it's sort of like a Mach 17 cruise missile. Great, okay. But they also had another goal. Their other goal is, they wanted to fly — they wanted to be able to fly 25,000 miles without refueling. I said, why do you need that? They said, we've determined we will not be able to have bases anywhere except in the continental United States.

Well, I'm not sure I realized — I said, actually, I said, why do you need to fly 25,000 miles, why can't you just fly 13,000 miles and get halfway, right? And they said no, we want to be able to take off, do whatever we want to do, and come back 25,000 miles, get anywhere in the earth and take off and land from same, you know, from the continental United States. And the fuel efficiency and the lightweight requirements and the Mach 17 — the temperature requirements — they're just as ridiculous as the National Aerospace Plane, okay. And I actually brought in some plots and stuff and kind of showed them that. And then they gave us plots that showed 6,000 degree temperatures, okay, from the frictional heating near the surface. And I use those to calculate just the radiation heat transfer to the surface. So we're not even talking boundary layers. You couldn't even, you know, leak out a little bit of nitrogen or something on the surface as a bounty — as an insulating boundary layer — because just by straight radiation, which goes through any gas boundary layer, you would be above the melting point of copper or anything else. It made no sense.

And then they didn't worry about — they hadn't even started to — the fact that if the top surface of the copper was at 900 degrees centigrade — it melted 1107 centigrade — and the bottom was at liquid nitrogen, there would actually be some thermal expansion differences and distortion and things like that. Somehow they were going to just design those away, okay. Mmm. Okay, and we pay people to come up with these ideas, okay. Anyway, there are other parameters. This is Ashby strength, not modulus, but fracture strength or yield strength he has here, versus density. Because if you have a minimum weight design for strong ties — remember before it was stiffness of strong ties or beams or plates — now it's minimum weight design, minimum, maximum strength from minimum weight. And here's the plot, and it doesn't change all that much, but it is slightly different if you were to compare these. Enough, you'll get these on stellar.

Oops. And you still got diamond at the top. You've just shifted these things a little bit. And at the bottom, or over here on the side, interestingly, in terms of lightweight, some of the lightest weight to strength ratio materials are something called wood, okay. Anyone heard of the Spruce Goose? Okay. What was the Spruce Goose? World's largest airplane. Howard Hughes decided to build the world's largest airplane. He built one of them. It was on display for years in Los Angeles somewhere, but it's still there, okay. It's in Oregon, okay. Is it at that space — aviation museum in Oregon? I've been there but it wasn't there when I was there, but must have been moved there in the last 10 years for something. Anyway, so I've never seen the Spruce Goose, but it's called the Spruce Goose 'cause he built it out of spruce. And if you look on here, how they have screws but — ash, the strongest wood, is ash. Where does ash grow? A lot of ash grows in Kentucky. And what do we build in Louisville, Kentucky? Baseball bats. Louisville Sluggers. And what are they made out of? Ash. Why? 'Cause it's the strongest wood. Yeah, yep.

What is — what's the advantage of maple? The answer is, I don't know, okay. And it's not tangential, it's a key question. That would be a good topic — of baseball bats. Now there's also metal baseball bats, which is a whole 'nother topic. I do know something about that, but I won't talk about that right now. But ash is actually — if you look, well here it is, it's the strongest. Then we got oak and pine. Then he didn't put maple on here, but I guarantee you maple's up here near the top too. So I suspect it might be an availability thing. In New England, if you were making bats, you might make them out of maple. In Kentucky there's all kinds of ash trees in Kentucky, which is one of the reasons Louisville Slugger is in Louisville, okay. I have toured Louisville Slugger plant. At the end they give you a little one footlong baseball bat, okay. It's very interesting and just in terms of how they rapidly machine bats and how they customize bats for certain players and stuff.

Then there's fracture toughness against density. Fracture toughness is this thing that Griffith came up with in the 1920s when he was researching the fracture of glass. And I talked about how brittle glass is, and this is where Griffith found out that things can be tough as well as strong. The original strength person to measure strength was a guy named Galileo. And here's a picture of Galileo's test apparatus, okay. There it is. If you had a beam and you put a weight on it — this was out of one of his notebooks, okay. And so he started studying the strength of beams. And this is out of a book called The History of the Strength of Materials by Timoshenko. Anybody ever heard of Timoshenko? Well — you know about Timoshenko? Yeah. Well, you've heard the name because he was a professor at Stanford University. I think — if you look on the inside, I think he lived from eighteen seventy-eight to nineteen seventy-two, but he basically — I mean, he was almost 100, he was 94 years old when he passed away, that's down here in the bottom. But Timoshenko was kind of Mr. Mechanics of Materials in the whole country. He wrote books all over the place. If you studied — if your grandfather studied mechanical engineering or materials in the first half of the 20th century, he would have been studying out of the Timoshenko books. So Stephen Timoshenko wrote this book on history of strength of materials, and well, I'll go through some of that tomorrow or another day.

But in any case, Galileo was interested in strength of materials, and I can't remember where I was — I was talking about fracture toughness. So we learned in the 1870s — actually even earlier, I'll give some more history tomorrow or — wait, no, Monday is the next day. Election Saturday — you can have off Sunday to take them both off. Anyway, I'll talk to you some more about that stuff. But fracture toughness is the energy of fracture. Galileo was looking at the strength of fracture, and Timoshenko knew about the strength of fracture. Timoshenko lived through the era from 1925 to the nineteen fifty — in 1975 — where we really learned about the toughness of fracture, which actually is a much more interesting story than just the strength of fracture to me, because we still continue to learn about the toughness — the need for toughness — in materials.

But to give you an example — well yeah, I got a minute — if you take a brittle material, you'll see me doing this on the History Channel, okay, I talked about the Titanic — but you can pull on the edge of this material, paper, with pounds of force. [Tom demonstrates with a piece of paper.] If I put a flaw in the material, which is what Griffith was looking at, flaws in glass, it takes — else's — I can lose eighty to ninety percent of my strength because of a flaw in a brittle material. Whereas if I have a ductile material, like a rubber — [Tom demonstrates with a rubber band.] that is toughness. I can pull on that piece of rubber and all I do — I don't have a sharp notch, I blunt the notch, and so I get lots of deformation without fracture. And there's a tremendous difference in ductility of fracture versus brittle fracture, and we're going to talk about that stuff on Monday. Have a good weekend.