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Phil Dalencour
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Phil Dalencour

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this was fantastic. the read I mean. 
 
Here's a video of a ping pong paddle being hit by a ball, flying at supersonic speeds, filmed at 30,000fps. You can watch the ball punch a hole through it, Wile E. Coyote style - which might surprise you if you think about it, since if you throw a rock at a window, the window shatters, it doesn't punch a hole. What's the difference?

The magic is in the speed of sound.

The question that first inspired me to look at this was one which Bob Laughlin (a mad scientist whom I used to TA for, and who later won the Nobel Prize) once set as an exam question: to design our new strategic missile defense system, Brilliant Pot Roast. It worked by putting lumps of pot roast with rocket engines in orbit, and firing them at ICBM's; students had to calculate pretty much everything required for this, including answering the key physical question of what happens when a pot roast strikes a nuclear missile.

It turns out that the most important factor in this is actually not about the structural integrity of the materials, since at high enough impact speed nearly anything will break. The most important factor turns out to be the speed of sound in the objects which are colliding, and how this compares to the speed of impact.

To see why this is, imagine throwing a baseball at a sheet of metal. When the baseball hits the metal, it will start to transfer its energy into the metal, and this energy might cause the metal to shake, bend, tear, or shatter, depending on just how much energy the ball had. 

Now, let's consider how the energy gets from the ball into the metal. Start by thinking about ordinary baseball speeds. When the ball first touches the metal, it's going to literally push the metal some. The metal will then try to bounce back (because metal has a tensile strength and tries to keep its shape; which is to say, metal is a solid, and not a liquid or a gas) and you'll see a wave of motion go out from the impact point. 

This makes sense: energy from the ball's impact will be radiated out through the metal in the form of a big vibration of the metal, which travels out in a wave, just like it would if you dropped a rock into a pond. (There, the restoration force comes from gravity rather than the tensile strength of water) But there's a name for a vibration wave travelling through a material: sound. Waves flowing through the material will therefore (by definition) travel at the speed of sound in that material, which can be computed from the physical properties of that material or simply looked up. (If you're interested, the formula for a solid is v = √K/ρ, where K is the bulk modulus of the material -- a measure of its stiffness -- and ρ is its density) Some typical values are:

The speed of sound in dry air at sea level: 330 meters per second.
The speed of sound in Uranium: 3,100 meters per second. (Very dense)
The speed of sound in ice: 3,100 meters per second. (Less dense than Uranium, but low strength)
The speed of sound in glass: 3,960 meters per second. 
The speed of sound in steel: 6,100 meters per second. (Much higher tensile strength than glass)
The speed of sound in aluminum: 6,420 meters per second. (About the same tensile strength as steel, but less dense)

So if we imagine our baseball striking the metal, the ball will transfer its energy to the "primary impact area" -- that is, the area under the ball -- by directly pushing on the metal, and then that energy will flow out to the rest of the metal. Since the ball is travelling much slower than sound, what's really going to happen is that the ball starts to touch the metal, and sound waves start to travel out instantly; by the time all of the ball's energy has been transferred to the metal sheet, the energy will already have been carried far and wide by the sound waves. This means that the ball's energy will be spread widely across the whole metal sheet.

The exact consequences will then depend on things like the tensile strength of the metal, how brittle it is, and so on. For example, if the metal is brittle for some reason (perhaps it was improperly forged), or if it was a sheet of glass instead of metal, then cracks will start to appear in it. These cracks will spread out at the speed of sound, and by the time the ball has finished striking the glass, all of the glass will be cracked. The window will shatter into many pieces. If, on the other hand, the material is sturdy enough to withstand the impact, say a sheet of decent aluminum, then the vibration will go through all of the metal (making a loud "thump"), and if there's bending of the metal, it will bend the metal all over the place, into a big dome.

(And what happens to the baseball? The exact reverse! The baseball hits the metal, but the metal hits the baseball, too, so vibrations travel through it at the speed of sound in baseballs)

Now let's imagine what happens if it's a supersonic impact -- that is, if the impact speed is higher than the speed of sound in the target material. This time, the baseball will start to transfer its energy into the primary impact area, and it will keep doing so faster than energy can escape from there. This doesn't just mean that all the energy will be deposited into a small area: this also means that, if the material is going to be able to stop the baseball, it has to do so using only the strength of the material under the baseball, since the rest of the material "hasn't yet gotten the news" that the baseball has hit it; it's still at rest. 

This means that if the energy transferred by the baseball is greater than the structural strength of the metal directly under it, the metal won't be able to stop it, and the baseball will keep going, and in fact the baseball will be gone before the message reaches beyond the primary impact area. That means that the baseball will basically leave a baseball-shaped hole in the metal, with only some minor tearing and unevenness around the edges. (That small area which did get the message from the very last bits of the baseball, just as it passed)

At this point, it turns out that the faster the ball went, the cleaner the hole will be. If it's fast enough, it will simply punch out the hole and disconnect it before almost any of the sound waves from the impact can get beyond the hole; that means that very little energy will reach the rest of the metal at all. On the other hand, if it isn't that much faster than sound, then the energy from the outer bits of the baseball might have gotten past the rim of the hole before the hole got fully punched, and that energy will escape into the rest of the metal and damage it.

So now, let's test the hypothesis: in the experiment below, a ping-pong ball is fired supersonically at a paddle. We would therefore predict a few things.

(1) The ball will punch a ball-shaped hole in the paddle.

(2) Because the ball isn't going that much faster than sound, some energy will escape, and push the paddle in the direction that the ball was moving. If the paddle is trying to be anchored in place by its handle, then that handle is going to be having a bad day.

(3) We can also look at the reverse problem: what happens to the ping-pong ball? Energy is transferred into it from the paddle, which should cause vibrations, and ping-pong balls, not being very robust, are likely to break. (In particular, if you imagine a giant wave flowing over the surface of the ball, the surface will tear) However, by the time the vibrations hit the ball, it will already have punched a hole through the paddle. So we expect the ball to be ripped to shreds, but this ripping will happen after the hole is punched.

I leave the video as an illustration that the laws of physics do, indeed, work.

(Oh, and what about Brilliant Pot Roast? Well, it depends on what the pot roast hits. A pot roast in space is basically ice, so its speed of sound is roughly 3,100m/s. If it hits the aluminum of the missile, that has a speed of sound of 6,100m/s; if it hits the actual core, that has a much lower speed of sound, 3,100m/s. The impact velocities could range widely, but they'll be on the scale of orbital velocities around the Earth. Apogee for a Minuteman III ICBM is 1,600km, travelling at roughly 6,600m/s. Orbital speed for a pot roast orbiting at that altitude is about 16,000m/s, which means that even if the pot roast hits the missile at a maximally unfortunate angle -- coming up on it from behind -- the relative speed at impact will be over 9,000m/s, well over the speed of sound in all of the materials concerned. This means that the pot roast will punch a fairly clean hole through the missile. At its minimum impact speed, that hole may be less clean, whereas at maximum speed (26,600m/s) it's going to be quite clean indeed. This may cause problems for the missile as it reenters the atmosphere, since it has an unexpected pot roast-sized hole in it, but it won't destroy the missile outright. The pot roast will therefore need to decelerate prior to impact, or alternately carry explosives with it.)
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Phil Dalencour

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Phil Dalencour

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Summer/Fall to do list:

Edge of Tomorrow - June 6
Guardians of the Galaxy - 8/1/14
Lucy - August
Let's Be Cops - August
Kingsmen - Oct 24
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hahahaha... hilarious. was mentioning something not far off to +Kaloma Smith after I watched it. Think that First Class was a better movie, where in comparison, if First Class was a 10, this one was a 6.5-7.5 depending. 
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In which I'm actually interested... Surprisingly I think?
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Looks great!
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+Yauri-Sabrinthia Kelly-Dalencour as seen on Room #9 :( but also :)
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Today was a good day.
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Michael going hard over the remix. #throwbackanydays

Still... Can't get #blackdynamite visual of young Michael out of my head though...
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Work
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  • Google Inc.
    Global Product Operations Manager, present
  • Time Inc
    Manager, Advertising Product Technology
  • MTV Networks
    Online Ad Product Technology Manager
  • BrandSphere Partners
    Associate
  • Bender/Helper Impact
  • United States Marine Corps
    Lance Corporal, Nuclear Biological Chemical Defense Reconnaissance
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Husband, enraptured father of two princesses, media technologist & studious web + print designer
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