What If? (18 page)

Steak Drop

Q.
From what height would you need to drop a steak for it to be cooked when it hit the ground?
—Alex Lahey

A.
I hope you like
your steaks Pittsburgh Rare. And you may need to defrost it after you pick it up.

Th
ings get really hot when they come back from space. As they enter the atmosphere, the air can’t move out of the way fast enough, and gets squished in front
of the object
—
and compressing air heats it up. As a rule of thumb, you start to notice compressive heating above about Mach
2
(which is why the Concorde had heat-resistant material on the leading edge of its wings).

When skydiver Felix Baumgartner jumped from 39 kilometers, he hit Mach
1
at around 30 kilometers.
Th
is was enough to heat the air by a few degrees, but the air was so far below
freezing that it didn’t make a difference. (Early in his jump, it was about minus 40 degrees, which is that magical point where you don’t have to clarify whether you mean Fahrenheit or Celsius
—
it’s the same in both.)

As far as I know, this steak question originally came up in a lengthy 4chan thread, which quickly disintegrated into poorly informed physics tirades intermixed with homophobic
slurs.
Th
ere was no clear conclusion.

To try to get a better answer, I decided to run a series of simulations of a steak falling from various heights.

An 8-ounce steak is about the size and shape of a hockey puck, so I based my steak’s drag coefficients on those given on page 74 of
Th
e Physics of Hockey
(which author Alain Haché actually measured personally using some lab equipment). A
steak isn’t a hockey puck, but the precise drag coefficient turned out not to make a big difference in the result.

Since answering these questions often includes analyzing unusual objects in extreme physical circumstances, often the only relevant research I can find is US military studies from the Cold War era. (Apparently, the US government was shoveling tons of money at anything even loosely
related to weapons research.) To get an idea of how the air would heat the steak, I looked at research papers on the heating of ICBM nose cones as they reenter the atmosphere. Two of the most useful were “Predictions of Aerodynamic Heating on Tactical Missile Domes” and “Calculation of Reentry-Vehicle Temperature History.”

Lastly, I had to figure out exactly how quickly heat spreads through
a steak. I started by looking at some papers from industrial food production that simulated heat flow through various pieces of meat. It took me a while to realize there was a much easier way to learn what combinations of time and temperature will effectively heat the various layers of a steak: Check a cookbook.

Jeff Potter’s excellent book
Cooking for Geeks
provides a great introduction to
the science of cooking meat, and explains what ranges of heat produce what effects in steak and why. Cook’s
Th
e Science of Good Cooking
was also helpful.

Putting it all together, I found that the steak will accelerate quickly until it reaches an altitude of about 30–50 kilometers, at which point the air gets thick enough to start slowing it back down.

Th
e falling steak’s speed would steadily
drop as the air gets thicker. No matter how fast it was going when it reached the lower layers of the atmosphere, it would quickly slow down to terminal velocity. No matter the starting height, it always takes six or seven minutes to drop from 25 kilometers to the ground.

For much of those 25 kilometers, the air temperature is below freezing
—
which means the steak will spend six or seven minutes
subjected to a relentless blast of subzero, hurricane-force winds. Even if it’s cooked by the fall, you’ll probably have to defrost it when it lands.

When the steak does finally hit the ground, it will be traveling at terminal velocity
—
about 30 meters per second. To get an idea of what this means, imagine a steak flung at the ground by a major-league pitcher. If the steak is even partially
frozen, it could easily shatter. However, if it lands in the water, mud, or leaves, it will probably be fine.
1

A steak dropped from 39 kilometers will, unlike Felix, probably stay below the sound barrier. It also won’t be appreciably heated.
Th
is makes sense
—
after all, Felix’s suit wasn’t scorched when he landed.

Steaks can probably survive breaking the sound barrier. In addition to Felix, pilots have ejected at supersonic speeds and lived to tell about it.

To break the sound barrier, you’ll need to drop the steak from about 50 kilometers. But this still isn’t enough to cook it.

We need to go higher.

If dropped from 70 kilometers, the steak will go fast enough to be briefly
blasted by 350°F air. Unfortunately, this blast of thin, wispy air barely lasts a minute
—
and anyone with some basic kitchen experience can tell you that a steak placed in the oven at 350 for 60 seconds isn’t going to be cooked.

From 100 kilometers
—
the formally defined edge of space
—
the picture’s not much better.
Th
e steak spends a minute and a half over Mach
2
, and the outer surface will likely
be singed, but the heat is too quickly replaced by the icy stratospheric blast for it to actually be cooked.

At supersonic and hypersonic speeds, a shockwave forms around the steak that helps protect it from the faster and faster winds.
Th
e exact characteristics of this shock front
—
and thus the mechanical stress on the steak
—
depend on how an uncooked 8-ounce filet tumbles at hypersonic speeds.
I searched the literature, but was unable to find any research on this.

For the sake of this simulation, I assume that at lower speeds some type of vortex shedding creates a flipping tumble, while at hypersonic speeds it’s squished into a semi-stable spheroid shape. However, this is little more than a wild guess. If anyone puts a steak in a hypersonic wind tunnel to get better data on this,
please,
send me the video.

If you drop the steak from 250 kilometers, things start to heat up; 250 kilometers puts us in the range of low Earth orbit. However, the steak, since it’s dropped from a standstill, isn’t moving nearly as fast as an object reentering from orbit.

In this scenario, the steak reaches a top speed of Mach 6, and the outer surface may even get pleasantly seared.
Th
e inside, unfortunately, is still uncooked. Unless, that is, it goes into a hypersonic tumble and explodes into chunks.

From higher altitudes, the heat starts to get really substantial.
Th
e shockwave in front of the steak reaches thousands of degrees (Fahrenheit or Celsius; it’s true in both).
Th
e problem with this level of heat is that it burns the surface layer completely, converting it to
little more than carbon.
Th
at is, it becomes charred.

Charring is a normal consequence of dropping meat in a fire.
Th
e problem with charring meat at hypersonic speeds is that the charred layer doesn’t have much structural integrity, and is blasted off by the wind
—
exposing a new layer to be charred. (If the heat is high enough, it will simply blast the surface layer off as it flash-cooks it.
Th
is is referred to in the ICBM papers as
the “ablation zone.”)

Even from those heights, the steak
still
doesn’t spend enough time in the heat to get cooked all the way through.
2
We can try higher and higher speeds, and we might lengthen the exposure time via dropping it at an angle, from orbit.

But if the temperature is high enough or the burn time long enough, the steak will slowly disintegrate as the outer layer is repeatedly
charred and blasted off. If most of the steak makes it to the ground, the inside will still be raw.

Which is why we should drop the steak over Pittsburgh.

As the probably apocryphal story goes, steelworkers in Pittsburgh would cook steaks by slapping them on the glowing metal surfaces coming out of the foundry, searing the outside while leaving the inside raw.
Th
is is, supposedly, the
origin of the term “Pittsburgh Rare.”

So drop your steak from a suborbital rocket, send out a collection team to recover it, brush it off, reheat it, cut away any badly charred sections, and dig in.

Just watch out for salmonella. And the Andromeda Strain.

Hockey Puck

Q.
How hard would a puck have to be shot to be able to knock the goalie himself backward into the net?
—Tom

A.
Th
is can’t really happen.

It’s not just a problem of hitting the puck hard enough.
Th
is book isn’t concerned with that kind of limitation. Humans with sticks can’t make a puck go much faster than about 50 meters per second, but we can assume this puck is
launched by a hockey robot or an electric sled or a hypersonic light gas gun.

Th
e problem, in a nutshell, is that hockey players are heavy and pucks are not. A goalie in full gear outweighs a puck by a factor of about 600. Even the fastest slap shot has less momentum than a ten-year-old skating along at a mile per hour.

Hockey players can also brace pretty hard against the ice. A player
skating at full speed can stop in the space of a few meters, which means the force they’re exerting on the ice is pretty substantial. (It also suggests that if you started to slowly rotate a hockey rink, it could tilt up to 50 degrees before the players would all slide to one end. Clearly, experiments are needed to confirm this.)

From estimates of collision speeds in hockey videos, and some
guidance from a hockey player, I estimated that the 165-gram puck would have to be moving somewhere between Mach 2 and Mach 8 to knock the goalie backward into the goal
—
faster if the goalie is bracing against the hit, and slower if the puck hits at an upward angle.

Firing an object at Mach 8 is not, in itself, very hard. One of the best methods for doing so is the aforementioned hypersonic
gas gun, which is
—
at its core
—
the same mechanism a BB gun uses to fire BBs.
1

But a hockey puck moving at Mach 8 would have a lot of problems, starting with the fact that the air ahead of the puck would be compressed and heated very rapidly. It wouldn’t be going fast enough to ionize the air and leave a glowing trail like a meteor, but the surface of the puck would (given a long enough flight)
start to melt or char.

Th
e air resistance, however, would slow the puck down very quickly, so a puck going at Mach 8 when it leaves the launcher might be going a fraction of that when it arrives at the goal. And even at Mach 8, the puck probably wouldn’t pass through the goalie’s body. Instead, it would burst apart on impact with the power of a large firecracker or small stick of dynamite.

If you’re like me, when you first saw this question, you might’ve imagined the puck leaving a cartoon-style hockey-puck-shaped hole. But that’s because our intuitions are shaky about how materials react at very high speeds.

Instead, a different mental picture might be more accurate: Imagine throwing a ripe tomato
—
as hard as you can
—
at a cake.

Th
at’s about what would happen.