§1. Finishing stainless steels: sensitization and AOD [00:02]
Stainless steels — they're, I talked about active and passive and how they have better corrosion resistance. Regular carbon and alloy steels, their Achilles heel is their corrosion resistance. They've estimated that this country loses $200 billion a year to corrosion, and probably eighty percent of that cost is due to corrosion of steels, because steels are the structural materials we use most commonly. Even in concrete, the rebar is steel and it corrodes in a chloride environment.
You tend to use stainless steels in two types of environments. One is an aqueous system where you need water corrosion resistance. The second is high-temperature oxidation. These are actually similar, because it's the chrome oxide on the surface that forms the passive layer. In the high-temperature case there's no water around — you're above the melting temperature of water — but it's still the stability of the chrome oxide on the surface that protects you from diffusing oxygen into the steel and forming a big thick layer of rust.
The Achilles heel for stainless steels in aqueous corrosion is chlorides. You can add molybdenum, but at a price. Something here might be $4,000 a ton nowadays — depends on what the current prices of chrome and nickel are. Probably around $4,000 today; ten years ago it was probably $2,000. 316 might add $10,000 a ton to that, and 317 might add $20,000 a ton. That gives you better chloride resistance. Up at the nickel-chrome-iron alloys, where you add lots of nickel and you're essentially sixty percent nickel, these are $50,000 to $100,000 a ton. That's sort of what you build nuclear reactors out of — although we build nuclear reactors out of 304, because it's much cheaper. You don't want to build a nuclear reactor out of something that costs this much. Pressurized water reactors — they do make them out of this type of stuff.
The low-carbon versions of stainless steel — the process for making low-carbon stainless steel was essentially invented here at MIT, and that's argon-oxygen decarburization. What happens is, in a particular temperature range, you can precipitate chrome carbides at the grain boundaries. Because carbon diffuses faster than chrome, when you precipitate the chrome carbides you end up with a region that's depleted. The carbon comes from lots of distances, you form lots of chrome carbides, and you end up with a low-chromium region. This might be eighteen percent chrome out here, but in the depleted region it can be ten percent. I've measured eight percent chrome in some of what we call sensitized stainless steels. Eight percent chrome is not enough to be corrosion resistant.
If you put this in a corrosive environment, you can eat away right around the carbide. The carbide doesn't dissolve, but the steel around it does, because it's low-chromium. And so if you weld these steels — this is a weld temperature plot — you have some peak temperature, but you'll have some adjacent temperature that's between 800 and 1000 degrees roughly, and that will precipitate these chrome carbides. If you take one of these stainless steels and put it in something like nitric acid, you'll end up with a region that just dissolves away, because nitric acid won't touch greater than ten or twelve percent chromium stainless. But if I've got eight percent stainless steel here, it's just going to eat it away. It's called weld sensitization. It created a real problem for trying to weld stainless steels in the 1940s.
People developed other steels that had low carbon, but they had double and triple the price, until AOD came along. Now you can make almost everything low carbon. If you look at temperature versus time, you can look at the precipitation kinetics for different amounts of carbon. If you're below the specification for the L grade — 0.03 carbon or less, that's 300 parts per million or less — at around 0.019 carbon it'll take 100 hours of heating in that range to precipitate the chrome carbides, because there's so little carbon to diffuse. But up at 0.08, which is the specification for the maximum carbon in 304 steel — not 304L, but 304 — it takes less than a minute. You could be welding stainless steels and get the low-chromium heat-affected zone, which will just be eaten away in a lot of acids.
Student: [question about the precipitation plot]
No, this is just to start the reaction. If you put the finishing reaction on top of this, everything would just look like a mess. If you go to a thousand hours at that temperature, it's going to be down around six percent chromium in that region, so it'll be even worse. Above 900 C, you can resolutionize those carbides — you can heal the process. But above 900 C the whole structural part could turn into a pretzel in the annealing furnace. You have to quench it through this region within less than a minute, and so it's not very practical. You have to be careful how you heat-treat stainless steels, unless you're 304L. You've got 10 hours there — you can weld it all day long. But you can't operate them between 800 and 1200 degrees Fahrenheit, or 500 to 700 C. You can dissolve the chrome carbides at lower temperatures if you have lower carbon — it's easier to dissolve it if there's less carbon in the matrix.
Is this a problem? Yes. General Electric built nuclear reactors in the 1970s, and what happened to them — they were surprised — they're using the world's cleanest water. If you take absolutely pure hydrogen and absolutely pure oxygen gas, react them to make water, and measure the electrical resistance, it will be 18 megohms. Whenever you put any mineral in there, some sulfate or chloride, the resistance goes down because the ions conduct electricity. When we talk about nuclear-reactor-grade water, the goal is 18 megohms — that's absolutely pure water with no ions in it. Distilled water — you don't even talk about resistance; it has lots of conductivity because there are still enough ions in distilled water. But when you're down to parts per trillion or less of salt in the water, you can start measuring water purity in megohms.
I've got a failure of some stainless steel baskets that were filters in a gas-fired plant in Georgia. They had 14-megohm water — 14-megohm water is very clean. Someone said, oh, it's the chlorides in the water. There aren't a lot of chlorides in that water, believe me. I said, I don't think this is a corrosion problem. It turns out it's not — it's a design problem, a thermal problem for the way they designed what was going through this filter. But General Electric ran into a two-billion-dollar worldwide problem, because they had stress corrosion cracking in water that had a tenth of a ppm chlorine and one ppm oxygen. It's the combination of oxidizing chloride environment that kills stainless steels. No one in the world thought you could get stress corrosion cracking in 304 stainless steel at those extremely low levels of oxygen and chlorine. Except in a nuclear reactor environment, where you have high residual stresses, you don't — but they did. And it costs a fortune, once the whole plant is radioactive, to go in there and fix it, because people have to go in there in radioactive suits, and they can't stay in the radioactive environment very long before they get their yearly dose.
They fixed the problem, and they did a lot of things to improve the stainless steels, such that now you can get 304L. It's basically an ultra-low carbon, not much more than 0.01. But when they got the carbon down that low, they didn't have enough tensile strength, because carbon adds strength to steel, so they had to add nitrogen back. 304LN is an extra-low version of carbon with some nitrogen put back. Nitrogen doesn't form chrome carbides — it forms chrome nitrides, but they're not as stable.
Back in the 1940s they created other grades — they added titanium to the stainless steel rather than going to extra-low carbon. The titanium would tie up the carbon as titanium carbide. That's what this picture is all about. It shows two steels welded together. This one is regular old 304, this one is 321, stabilized with titanium — it's like 0.02 percent titanium — to tie up the chrome carbide. They also came up with 347. They added niobium and tantalum, which are strong carbide formers and do the same thing as titanium. All of this down here is basically ways to get around the welding problems of chrome carbide precipitation. We call it sensitization, and it's a problem for aqueous corrosion resistance of stainless steel.
Down here there's a little aside. If you go to 317, which has lots of molybdenum, you can add even more molybdenum, up to six percent. Now you're talking sixty-thousand-dollar-a-ton steel. Add more nickel, nitrogen, get some higher strength, and you get what they call the super austenitic stainless steels. The US Navy about 10 years ago was interested in building submarines out of this material. Why? Because they're not magnetic. The problem with magnetic submarines is, if you've got a superconducting quantum interference device up there in a satellite, you can see 100 feet down, and you can see this long magnetic hot dog in the ocean. But they finally gave up — our navy has more capital ships than all the rest of the world's navies combined. Except the Chinese are starting to try to catch up with us, sort of like what happened to Germany and France and Britain after World War One. So maybe we're heading for something else.
Then they took the nickel out — this is another grade — and they form 430, which is a ferritic stainless steel. If you add some extra chrome and molybdenum, you can get a superferritic. These have very good corrosion resistance, particularly in wet chloride environments, better than the austenitics. If you're adding chrome and nickel for strength and oxidation resistance, this is the second application of stainless steels — oxidation resistance at high temperatures. You go to things that are thirty percent chrome and twenty percent nickel, so it's only fifty percent iron. You hardly call it a steel anymore — it's basically just a high alloy. Sometimes they call them heat-resisting materials rather than steels, because you get to the point where they're not steels. If you get to the Inconel alloys, where you might be sixty percent nickel and only twenty percent iron, they aren't steels anymore — they're nickel-based alloys. But they all grew out of this 304. Now you're talking about alloys that can cost $30,000 to $100,000 a ton. Not cheap.
§2. The Inconel griddles [16:53]
Now, we used to have steak fries in the department. Back in the early 1990s I had some leftover Inconel sheet, left over from some surplus, and I had four griddles, four grills, made out of this. I'd designed them, and over in Building 13 we used to have steak fries on registration day when I was department head. I used to call these my thirty-thousand-dollar griddles, because the four of them weighed about a thousand pounds. If you think of Inconel sheet as back then about thirty dollars a pound fabricated, if you'd gone out to purchase these you would have probably paid thirty thousand dollars for them. I paid about fifteen hundred dollars to have them fabricated, but the metal in them is great. They will last forever.
Since then, Professor Suresh killed the steak fries. One of them got stolen, another I gave to the guy who used to run the forge, another I gave to a charitable organization, and the last one's in my garage. They were two feet by four feet, and you can cook a lot of steaks on a griddle that size. But anyway, I made Inconel grills once upon a time. That's another story.
Any questions? I had some other stories on stainless steel. I told you about the aquarium. Can't think of another one — anybody have questions on stainless steel? I had another one I was thinking of this morning, but that's okay — we might as well start on aluminum.
§3. Aluminum: introduction and MMPDS handbook [18:42]
Aluminum is the second most widely used metal in the world. It's come a long way since 1850, when it was more valuable than gold. It's not the second most widely used structural material — the second most widely used structural material is concrete. Number one is stone, number two is concrete, number three is steels, and number four is aluminum. But of metals, it's second most widely used. It was more precious than gold; now it's about five times the price of steel on a weight basis, but on a volume basis only about two and a half times. So aluminum can substitute for steel when you need lightweight, particularly in something like spacecraft or aircraft. Everything I've told you about how wonderful steel is — now let me take it back and prove to you that it's not so valuable if lightweight is important. That's another Achilles heel of steel.
You might want to take a pen and pencil out, because you can get this for free from the US government. It used to be called MIL-Handbook-5. It's a nine-volume set. If you want a hard copy, you have to pay $110 for all this. It's Metallic Materials Properties Development and Standardization. It's now called MMPDS, dash 05. For 40 years it was called MIL-Handbook-5. This Chapter One is an introduction. In spring of 2004 MIL-Handbook-5 was classified as non-current, and they switched it to this. This is a joint publication by the Federal Aviation Administration and the Department of Defense. If you want to build an aircraft or spacecraft, this has the properties for a wide range of aerospace materials, and you must use this as the minimum standard. If you want a higher standard for your material, you can, but your material must meet these qualities. It has several different qualities — one for spacecraft and one for aircraft. It has statistics, built up over 50 years.
Here's the volume on steel. Here are the three volumes on aluminum. So which one's more important than steel? Aluminum happens to be more important than steel in aerospace applications. It will give you for the A and B grades — one is aerospace, one is aircraft. Aerospace might be something they require for a military jet, as opposed to a commercial jet. It's got the mechanical properties — longitudinal, transverse — for this particular material, which is clad 2024 and 2014 aluminum sheet and plate, what the outside surface of old Boeing or McDonnell Douglas aircraft used to be made out of. It'll go on for about 20 pages, give you graphs of the minimum properties. These are the design properties. If you're going to design an aircraft for military or civilian applications and you want government certification, you must certify that everything you put in your aircraft meets these minimum standards. You can have higher standards, but these are the minimums, built up over 50 years from Boeing, McDonnell Douglas, government laboratories — all kinds of places.
They have nine volumes. Chapter Four is magnesium alloys, not very thick — I'll talk about magnesium later and why we don't use it very much. Chapter Five is titanium alloys, obviously used a lot, and almost as thick as steels, because we use more titanium than steels in aircraft. Heat-resistant alloys — this is sort of what might go in your jet engine. Hey, you're building a nuclear reactor and want to know the properties of heat-resistant alloys — this is a good place to start. Miscellaneous alloys and hybrid materials, not very thick — some resin composites, fasteners, lots of different things. And then the last thing you want in an aircraft is joints, so they have a fairly thick section on structural joints that tells you the strength capabilities, mostly of aluminum alloys, when you start to weld them — because a lot of your high-strength aluminum alloys lose their strength. It also has data on rivets, riveted joints, and other things. That's a free resource — just download it.
§4. Aluminum alloy series and end-use markets [26:14]
Aluminum is also great because it's relatively low-melting — about 660 degrees centigrade, as opposed to 1500 for steel, 1600 for titanium, or 1400 for nickel alloys. Aluminum is much lower-melting, and therefore you can extrude it, you can make fancy shapes, you can do all kinds of things with it that you can't do with steel.
Here's where the market for aluminum is. Beverage containers is the largest single use for aluminum — thirty to forty percent of the aluminum market. Exports don't really count for a product; it's actually just shipping aluminum overseas. Containers and packaging — that could also include aluminum foil. Transportation, which is all your aerospace, but also includes railroad cars. A lot of railroad cars are made of aluminum because it's lightweight. They have limits of weight on the railroad, just like on the highway. More and more we're using aluminum in heavy trucks.
I remember as an assistant professor, Professor Flemings arranged — one of his classmates whose last name was Walter, who graduated from MIT in the early 50s — needed some welding help because they were trying to weld aluminum tire rims. Dayton Walther Corporation was the world's largest manufacturer of tire rims at the time. In the late 70s everything was steel rims, because aluminum rims couldn't meet the half-million- or million-mile fatigue limits you had to have for truck wheels. Cars, yeah — we had aluminum wheels on cars, because they only went 100,000 miles before the steel rusted out anyway. But trucks get a lot of miles on them. I went out to Dayton Walther and met with him, and they were trying to put aluminum into the rims of truck wheels. We now do that. At Alcoa's Cleveland plant, they forge these great big — they don't weld, good reason to stay away from welding — they forge aluminum rims, and they're getting the weight out, and it saves I don't know how many thousands of gallons of diesel fuel over the life of the vehicle. They get a million miles on these things.
Building and construction — aluminum-frame windows, aluminum siding. Electrical — aluminum is second to copper in large-volume electrical conductors. Silver, for example, is a better electrical conductor than copper, but it's a little pricey. Consumer durables, machinery and equipment. So that's where aluminum is used — lots of different markets, but the big one is beverage containers. And by the way, these cans are getting thinner and thinner over time, and at different pressures. Soda cans have to hold a little more pressure than beer cans, because they develop higher pressures.
There are actually three different aluminum alloys in a can, which leads me to aluminum alloys. For the Aluminum Association, 1000 series aluminum is 99% aluminum, essentially pure. 1060 alloy is 99.6% aluminum, or 99.4 — I can't remember. You can get up to four-nines aluminum commercially. The problem is, these thousand-series alloys don't have strengths better than about six or eight ksi. If you look at this MIL-Handbook, it has the 2000 series alloys through the 5000 series, and then the 6000 to 7000 series alloys. It doesn't have a thousand-series alloys, because no one's going to make an aircraft out of something that's only got six to eight ksi strength — too heavy for the loads imposed on it.
Copper — the 2000 series — was the original heat-treatable aluminum alloys. The Wright Brothers' engine block on Flyer One, the one they flew at Kitty Hawk, was an aluminum-copper alloy. That engine block is in the Smithsonian. A few years ago they took a little piece out of it and looked at it in the transmission electron microscope, to see how big the aluminum-copper precipitates had grown after a hundred years since they'd been heat-treated. They're coarsening over time. One of the problems with aluminum alloys: they melt at low temperatures, but they will also soften. You can heat-treat them and get 10 to 12 times the strength of pure aluminum, but they can degrade over time at relatively low temperatures.
§5. The Concorde flight [32:42]
Did I tell you the story that the SST, the Concorde that the French and British built, flew not on speed but on temperature? The skin temperature was limiting their speed. They had sensors to measure the temperature of the outside skin, so if it was really cold out, it could go faster. I flew the Concorde once. This was back in the 90s, and I'd never flown a supersonic transport — most people hadn't. I had to go to Europe for something, and MIT had to pay my business-class airfare, and I said, okay, I will spend the $2,400 for the upgrade coming back out of my own pocket just to see what it's like to fly on an SST.
Well, it was an interesting experience. First, you do not get jet lag flying on the SST. The only thing I can figure is the flight is shortened so much. We took off from London at five o'clock London time, we arrived at JFK at 4:45 New York time — 15 minutes earlier, of course with a few time zones in between. It's a relatively short flight. The next day at four o'clock I'm working in the garden, and I realized I don't have jet lag. You're also flying super first class. Everybody who has a ticket is in super first class, and everybody wants to board first. It's a very small fuselage — sort of like being on a small commuter jet in terms of the size of the seats. They also had limited aircraft, so they never had time to do maintenance. It was the filthiest commercial airplane I've ever been on. The food was terrible. The maintenance was terrible.
The guy sitting next to me was the number-one flyer on British Airways, and they saved his ticket. I was in seat 1B because I'd made my reservation six weeks before. Most people who flew the Concorde were these super-wealthy people who would make their reservations a couple of days ahead. They saved 1A for this guy every Friday afternoon until noon — if he called before noon on Friday he would get that seat. He was 23 years old, his father was a Greek shipping tycoon, and his typical week was to fly around the world. He would decide on a Friday to go from London to New York, work Saturday and Sunday morning in the New York City office, then take the two o'clock flight back from JFK to London on Sunday. Then Monday morning he was flying to somewhere in the Middle East, then somewhere in India, then somewhere in Japan. He would go around the world once a week, which is why he had the most frequent flyer miles. But his tray table was broken — he had to eat one-handed, holding the table with the other, because the tray table was broken. They didn't have time to maintain the equipment. Which gives you a lot of confidence to know your aircraft hasn't been maintained.
§6. Aluminum alloy designations and aluminum-lithium [36:11]
Other alloy designations. 3000 series are manganese — they're basically like the 1000 series, but with about one percent manganese, which gives them some strength. So the can stock, the body of the can, is typically 3003 or 3004 alloy. The top, I think, is a 5000 series alloy, because they have to stamp it — it has to have a certain strength. And the pull tab is a third alloy. Recycling these gets to be a bit of a problem, because you've got aluminum-manganese alloys, aluminum-magnesium alloys, and another 5000 series. If you mix them all together and melt them all at once, you've got a problem, because you don't want manganese in your 5000 series. What are you going to use this for? And this is forty percent of your recycling stream, maybe more. People chop the cans up into little pieces and try to separate them.
Magnesium-silicon, 6000 series alloy. 6061 is a workhorse alloy. You want an aluminum structure and you want to order it from some local place, you can get anything you want in 6061-T6. It's the workhorse heat-treatable alloy. The 7000 series, zinc-based, are the ones they used to use for aircraft for the first 50 years. Now they tend to use some of the 8000 series alloys, which are special alloys with other elements. 9000 series is unused. The 8000-series other elements are basically things like aluminum-lithium. Aluminum-lithium was a big deal when I was an assistant professor.
Student: [question about why 7000-series was replaced]
Corrosion resistance — stress corrosion cracking. They've come up with 79-something to replace 7075. If you were circa 1960, 7075 and 2024 were the two workhorse alloys. In the 70s they started getting better fatigue resistance. There's more fatigue data on aluminum than on steels — there's a reason for that, which I'm not going to go into. But one reason is, we use them for aircraft, and aircraft are nothing more than flying fatigue machines. They vibrate, and that tends to be life-limiting.
This was out of a 1998 book — it might have been the substance of what they ended up using in a 777. The aluminum-lithium alloys were developed in the former Soviet Union, and they have like five to ten percent lithium. Lithium is very light, which gives you a lower density — ten percent lower. But it also increases the modulus, which is interesting. Usually alloying at that level doesn't change the modulus of the material, but it actually increases the modulus by 10 or 15 percent. If you look at structural beams in bending, the modulus divided by the density, E over rho, is the relevant parameter. If you get 10 to 15 percent higher modulus and 10 percent lower density, you suddenly get a 20 to 25 percent improvement in stiffness. You can eliminate 25 percent of your weight.
So all through the late 70s and early 80s, there was a huge amount of research on aluminum-lithium alloys. The military started using them in the mid-80s, commercially in the 90s. There are all kinds of alloys — 8090-T81, the T is a heat treatment and temper. This is probably a concept vehicle for what's now the F-22 or Joint Strike Fighter or something early on, using 8090 where they can. A lot of the skins end up being titanium because of the supersonic speeds and temperatures — you need something much better.
The aluminum-lithium alloys give you tremendous strength. If you look at the alloys, you can get 90,000 to 94,000 tensile strength ksi. The yield strength would be 60 to 88 in these aluminum-lithium alloys. In the 7000 series you can get those types of strengths too, but you don't have the good E-over-rho that you get from aluminum-lithium. So what supplanted the 7000 series — first it was better 7000 series, and now it's better 8000 series — is mostly that aluminum-lithium E-over-rho.
But they had to develop forming, and first they had to develop casting techniques to get homogeneous melts, ingots, and then they had to worry about forming, they had to worry about joining. It takes 20 years to bring one of these things on and get it qualified. I don't even think this 2010 edition of the MIL-Handbook really has the 8000 series in there. You probably have to certify to the FAA — this is what we got, and eventually it will probably find its way in. But it takes time to get into codes and standards.
§7. The aluminum baseball bat and Little League injuries [43:08]
The aluminum-lithium alloys have up to 90, 95 ksi strength. But your homework problem was: what product uses the highest-strength aluminum alloys? And I told you it was aerospace. Anybody figured it out? If you look here, you'll find it. That's right — 100 ksi.
[Tom produces an aluminum baseball bat.] So it's about the right time to tell you a story. I paid $130 on Amazon for this. Typically you might pay $300 for a bat. This has a THT-100 alloy, a scandium alloy. This is the world's largest use for scandium. We only make two tons of scandium a year. The Soviets discovered that scandium is a tremendous grain refiner. When they make these metal bats, they extrude them, and they have a relatively thin wall — this may have a 28-thousandths wall. It has 100 ksi strength, and when you hit it with the ball, it'll go farther than with a wooden bat. It's lighter than a wooden bat. It has to weigh a certain amount. This is a minus-10 bat — see the minus 10? That means it's 29 inches long and weighs 19 ounces. You take 19 ounces and subtract 29 inches, and you get minus 10. They were making minus-13 bats a few years ago, but they would almost crack the first time you hit a ball with them.
These are great business, because you can sell anything to a sports fan. The best sports fans are golfers, because they're past middle age and they've got disposable income. You can sell anything to a golfer if he thinks it'll allow him to snub his business acquaintance at the 19th hole. He will pay for it, and pay a lot. They basically extrude a tube, and after they extrude it they put it in what we call a swaging machine, which is rotary hammers that thicken up this region. There's a lot of technology in this. Most of it comes out of southern California, because a lot of the people who worked on this were the aerospace engineers who used to work on the high-strength alloys for aircraft.
As they're extruding it, they control the extrusion ratio so it comes out at the temperature where it's solutionized, and they quench it as it's shooting out of the extrusion machine. It's got scandium as a grain refiner, which is better than titanium or zirconium or the other things we typically use on the bigger alloys. You can get extremely fine grain, extremely high strength that will hopefully last long enough that you won't get too upset. If you go on the web and find people's comments about the bats — broke the first time we hit it, dented the first time because it's so thin. Others say, this lasted for a while. The product insert that came with this basically said on the warranty card: rotate bat one-quarter turn at each at-bat. You don't have to worry about hitting it with the grain — you've got to worry about distributing the dents, or not building up residual stress. I haven't studied that in detail.
But I did study bats and injuries for another application. A kid was playing little league down in New Jersey, and it was a minus-12 bat that Little League approved. The pitcher got hit in the chest and his heart stopped. Now he's on a ventilator for the rest of his life. There have been people who've died — this was a little worse, because it's easier to die when you're 14 or 16 years old than to live the rest of your life on a ventilator. Although most of those people on ventilators don't live that long. I was asked several times if I would take an aluminum bat case, because most people didn't want to. I tried to pass them on to Professor Lagace [Lagacé] over in Aero and Astro. He's a big Red Sox fan — he's a consultant to the Red Sox. He did a model of Fenway Park and put it in the MIT wind tunnel, to show that when they put the press boxes up there, they actually did hit more home runs because of the change in the wind pattern coming over the press boxes.
Paul is a baseball nut, and I tried to pass him on. Paul thought about doing it for a while and decided he didn't want to. They finally came back to me — won't you do it for us? I said, yeah, I'll look at it. They called me up — this was the Friday afternoon right around Thanksgiving — and said, we need you, you said you'd do this. I said, yeah, but they hadn't sent me anything, so I didn't know anything about the problem. They said, we need the report by next Thursday. Less than one week. The problem was I was leaving on Monday for a trip. I said, you realize I have to write this tonight. I went home that Friday night and said, what am I going to write? I don't have any data. They sent me one report from the time some people had done some high-speed movies at the Naval Surface Weapons Lab in China Lake, California, of a ball hitting a bat.
I looked at the high-speed movie, and it showed the dent in the bat on impact and the dent in the ball on impact. I thought, well, I learned in freshman physics — even though I almost flunked it, I did learn something. The maximum momentum and energy transfer is when the two parts weigh the same. I'd ordered some ping-pong balls to show you the coefficient of restitution. I can drop the bat on a hard surface, and it bounces up 20 or 30 percent. It doesn't have very good coefficient of restitution. If it bounced up 100 percent it would be all elastic, 100% elastic energy, no energy losses. If I took a bean bag and dropped it, it goes splat — no bounce, 100% plastic. Coefficient of restitution is just the ratio between 0, 100% energy loss, and 100% elastic rebound.
I had Feynman — here's a section on momentum and energy conservation. You write one-half mv squared, conservation of energy. You write mv, conservation of momentum. You solve those two equations simultaneously. This was a homework problem I never could figure out as a freshman. But I remembered it, because I did so poorly on it. He describes conservation of momentum and energy. I wrote about three or four pages about the fundamental principles: you want the same stiffness. I changed momentum and energy to elastic stiffness, like springs. Same formulas — one-half kx squared, and the force is kx. I wrote it all in words about how you want to match the stiffness of the ball to the stiffness of the bat. And from this high-speed video photograph, by going to 28-thousandths thick they had matched the stiffness of the bat to the stiffness of the ball.
I wrote this report. The next week I got some balls and put them in a compression machine and measured their relative stiffness. The ball has a lot of hysteresis, which complicates things, but nonetheless. We took one of our bats and pushed on the bat, measured its stiffness, and lo and behold, they were the same within 30 or 40 percent. Billiard balls are great — equal-mass objects, you can prove, have the best combination of momentum and energy transfer from one object to the next. So you want equal stiffness. I started looking — eventually I got 10,000 or 50,000 pages of discovery of all the tests they've done on these things. Sure enough, they make them for maximum performance. In fact, it says right here on the little insert: "This is a high-performance product designed to deliver maximum performance within the limits of the association rules."
Many of the associations — the Japanese started in their colleges, and they said you can't have more than, I think, a minus-eight bat in Japan in college. The NCAA has been talking about restrictions. Little League said our kids aren't strong enough to do anything. People may have gotten to the point now where minus 10 is about the most anybody can make. But they're still going to the best aluminum alloys. Get on the web — it will give you the history of the last 30 years of how Alcoa has been developing the highest-strength aluminum alloys for bats, not for aircraft. Because, let's face it: 19 ounces, 130 bucks — that's $100 a pound, folks. Someone's making a profit off this. Pretty good markup. So now you know what the highest-tech aluminum product is.