The steaks are high
August 4, 2009 5:34 PM   Subscribe

From what height would you need to drop a steak for it to be cooked (a) rare (b) medium-rare (c) well done by the heat of its passage through the atmosphere?

We're assuming that the steak starts off frozen. Obviously.
posted by Hogshead to Food & Drink (15 answers total) 31 users marked this as a favorite
Not so much a matter of height (potential energy) as orbital velocity (kinetic energy) . . . the balloon guy jumper from the 1960s who spent minutes in free-fall didn't burn up.
posted by @troy at 5:43 PM on August 4, 2009

A steak would have a pretty slow terminal velocity. Certainly not fast enough to get any significant frictional heating.

The reason spacecraft heat up on re-entry is because they're going really, really fast. They have to be going fast to achieve orbit (the necessary speed is called escape velocity).
posted by mr_roboto at 5:46 PM on August 4, 2009 [2 favorites]

Falling from a specific height won't cook anything, terminal velocity is way slower than the speed that would generate enough atmospheric friction to create enough heat. Realistically even if you did get a steak going fast enough to heat up on re-entry it would disintegrate during that re-entry.

Try again next week bub.
posted by iamabot at 5:52 PM on August 4, 2009

Mod note: Insofar as the question is answerable, it's been pretty much answered already. If you have something constructive to add, great; keep the snark and the jokes out of it.
posted by cortex (staff) at 5:59 PM on August 4, 2009

If you assume it starts in space, this is pretty answerable, even without being stoned. If it starts out in orbit, it's going very fast (laterally) already. And it would most certainly burn up on re-entry despite being very small.

Tiny rocks do it every day, after all, and they weigh less than a nice fat steak.

But that also means that the answer is "it will always be very, very well done. It will turn into crumbled, disintegrated charcoal just like that time Dad forgot the last steak on the grill overnight."
posted by rokusan at 6:07 PM on August 4, 2009

If it starts out in orbit

well, the question was height. If we recast to throwing it off a space elevator (once one exists) there might be a definite answer, since the item will have a zero groundtrack speed yet freefall to achieve a variable amount of entry energy before hitting a terminal velocity in the atmosphere.

This is of course a tricky calculation to figure out. Kittinger jumped from 31,333m and hit a speed of over 600mph while falling. The question becomes how fast do you have to be falling at Kittinger's 31,000m starting altitude to achieve various levels of ablation. At 0 starting falling velocity there should be no significant atmospheric heating, but that is the only speed I can calculate :)
posted by @troy at 6:20 PM on August 4, 2009

The question's been pretty well answered above. Depending on your initial assumptions, either

a) you drop it straight down, and the air slows it down to terminal velocity, which prevents it from cooking.

b) it falls out of orbit, going at an incredible rate of speed, in which case it's toast.

You could make the question a bit more interesting by assuming that you're firing a steak out of a cannon, and ask

at what speed would the steak need to be fired to unthaw/cook it

Make some basic assumptions about size, air pressure, and coefficients of friction for air. Then you could calculate how much friction it would experience, how much heat would be produced, and how fast and far the steak would have to fly. Bonus points if you calculate a trajectory solution that allows it to be slow-cooked at a reasonable temperature.

I suspect the answer is going to be "really damn fast" and would require way more kinetic energy than the backyard trebuchet you're thinking of building with your buddies.

Which is all just a longer way of saying that this is improbable and leans really strongly towards chatfilter.
posted by chrisamiller at 6:27 PM on August 4, 2009

I disagree with those who say the question is unanswerable. If one extreme has the steak starting with a velocity of 0 relative to the Earth's surface and leaves it falling through atmosphere raw at terminal velocity, and the other has it entering at something like escape velocity and burning to a cinder, can't we assume that it starts out at some stable orbital velocity, which is reduced when our chef applies reverse thrusters so that the steak streaks to Earth at just the precise level of doneness?
posted by contraption at 6:41 PM on August 4, 2009

This would be impossible for other reasons than sheer height. In order for a fully frozen steak to even thaw, let alone cook, there is a certain amount of heat conduction which must happen. This is how you can get a steak which is seared on the outside, yet has that cool, pink center which leads to a litany of medical illnesses which are promptly ignored in favor of tasty meat.

I will freely admit, I am no math geek. I will leave it to curious academics or a particularly ambitious XKCD strip to hash out the exact formulae for this. Suffice it to say that we would need to determine the terminal velocity of the steak as it falls through the atmosphere, the heat produced by friction from this fall, and using Fourier's law to find out just how hot the steak will get and whether it will be enough to cook the steak without turning it into charcoal, while also reaching a sufficient temperature for long enough to leave the center thawed. Mathy stuff like that.

I will pre-empt this. First, the changing speed of the steak as it falls through the atmosphere through acceleration, friction deceleration, and irregularities within the atmosphere present the possibility of a thoroughly uneven cooking temperature, not good for a steak.

However, what is most important to remember is that the steak will not be rotating evenly as it falls. In fact, it is most likely that it will fall with the same side facing the ground most of the time. This would result in most of the atmospheric resistance being on one side of the steak with minimal flipping. At best, this will result in a steak which is overcooked on one flat end, undercooked on the other. Far more likely is the result of a steak which falls with a narrow edge pointing down. This would have the thoroughly awful effect of trying to cook a steak on its side, using conduction, with the outside temperature being below or near freezing for the majority of the journey.

Even if you can get somewhere between "Still frozen" and "burned to charcoal", it will more likely be a portion of each, rather than a happy medium-rare. If you wish to cook your steak through friction, you're going to need some sort of highly conductive metal cover to serve as an atmospheric friction oven. At that point, you would simply need to define at what height you can sustain a viable temperature for an appropriate amount of time. The design of the cover, conductivity, weight, shape, and air space left inside with the steak would need to be defined along with the previous issues of height, drag, friction, gravity, and heat needed to cook the steak.

I apologize for my inability (and to a greater extent, lack of willingness to put forth the effort) to solve your problem in detail. I hypothesize that if you are willing to permit some form of even conductive cover as an oven, a real math geek could design one and tell you from exactly what height you must drop it, or drop it and cheat with artificial acceleration for a period of time.

However, without this aid, I believe that it is impossible to produce a steak which could honestly be called edible, simply due to the number of unpredictable variables. Sorry Hogshead. You aren't going to be seeing any delicious accidental meat-eors from a NASA disaster unless your chef is Laplace's Demon.
posted by Saydur at 7:21 PM on August 4, 2009 [3 favorites]

And, also from Cornell, Why don't skydivers burn up like meteors?
posted by gimonca at 7:30 PM on August 4, 2009

um, wouldn't it be possible for the steak to cook before it entered the atmosphere? this article indicates that the outside temp in the space station is around 250 degrees f, when exposed to direct sunlight.

personally, i'd not cook a steak at that temp. a nice chuck roast might be delicately roasted before it enters the atmosphere for a calm descent.
posted by lester at 7:35 PM on August 4, 2009

Best answer: My answer's very rough and not complete, but you should be able to work it out yourself numerically at the very least. Nuts! to those above me who have avoided math!

So let's make some wild assumptions. Let's assume that the atmosphere is consistent throughout the steak's journey. Let's also assume that the steak is just a giant ball of meat. You're making a pot roast instead of a pan steak.

We're going to basically assume that we're creating an air-oven for the steak as is travels through the atmosphere slowing down. Wikipedia says "An approximate rule-of-thumb used by heat shield designers for estimating peak shock layer temperature is to assume the air temperature in kelvins to be equal to the entry speed in meters per second - a mathematical coincidence." Fantastic. This means that we have T = v. Now we can only adjust the beginning velocity vi, and the time, tf, that it reaches terminal velocity vf is determined from the equations that follow.

Now we know that is this idealized setting that the drag on the steak will be Fd = v2 * C, where C here is assumed to be a constant. This number should be p*C_d*A/2, which takes into account the mass density of the atmosphere (p ~1.2), the drag coefficient (C_d ~0.7), and the cross section of the steak (A ~ 0.3m2).

Ok, lets move on to the total work that the drag force will do. It will slow the steak down from vi to vf. So the total work done is W = m ( vf2-vi2) / 2. This will also be equal to the value of the integral of the force over the course of the steak. ... Not sure how to do this in html... W = C * \int_0^(x_f) v2 dx.

So, given vi and vf, you should be able to numerically work out the path and speed of the steak. You now take that speed v over time, and switch it directly to T, and you know what temperature you're cooking your steak.
posted by FuManchu at 8:06 PM on August 4, 2009 [6 favorites]

Best answer: Okay... took some numerical trickery, and I wouldn't bet my life on this. But using this as the standard for core temp, for a 12 inch diameter roast, I get:

Center meat           Initial Velocity
Medium rare (~57°)         650 m/s
Medium (~63°)              680 m/s
Medium well (~67°)         710 m/s
Well done (~72°)           740 m/s

posted by FuManchu at 9:39 PM on August 4, 2009 [15 favorites]

Response by poster: Awesome responses, thank you all. I shall start work on my very, very tall restaurant immediately.
posted by Hogshead at 6:10 AM on August 5, 2009

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