
At what distance from earth would you have to drop a steak for it to be cooked medium rare by reentry into the atmosphere?

>>5209670
And then use this
http://en.wikipedia.org/wiki/Atmospheric_reentry#Shock_layer_gas_physics
Not sure what temp you need the meat at to get it medium-rare though
>>5209670
if the steak is a ball, then one can't assume that it's isothermal, if it's nice and thin then we can assume it to be isothermal
Though I guess we need to treat it as a ball for aerodynamic purposes
Things are going to get pretty weird though if the meat's going hypersonic, there's a good chance the meat will ablate taking heat with it, so the only way we'll be able to figure this out is with some testing.

>medium rare
sorry, I'm not a wolf
>>5209695
found properties of steak and apparently the isothermal assumption holds:
www.et.byu.edu/~vps/ME340/PROJECTSF11/009.ppt
now if there was only a way to figure out how the air speed and air temperature of our steak change with time.
Though I'm willing to bet that even if we manage to cook our steak, by the time it hits the ground it will be cold
>>5209669
Yeah, I realize that... the joke is that you're technically supposed to flip a steak once (if you know what you're doing), and flipping it at the correct time is an important part of cooking a steak properly (which is essentially an impossibility for a single flip to occur naturally in free fall). Also >implying if it began rotating from a great height it wouldn't quickly attain such a high angular velocity that the centrifugal force would rip it apart.
>>5209652
>>5209698
Using these, and a terminal velocity of 125 mph,
assuming the steak is at a refrigerator temperature of 40 degrees. We would have to raise the steak 86 degrees Fahrenheit. This is 47.77 degrees Kelvin/Celsius.
Since steak is 1.59KJ/kg*C, it means we have to get 47.77*1.59KJ/kg=76KJ/kg.
Energy/kg it would get from Earth's gravity is G*M(1/R-1/x) where M is mass of earth, and R is radius of earth. x is what we are solving for.
since terminal velocity is 56 meters/sec, this leads to our final equation of 76,000+.5*56^2=G*M(1/R-1/(x+R))
Solve for everything, http://www.wolframalpha.com/input/?i=%286*10%5E24%29*%286.67*10%5E-11%29%281%2F%286.35*10%5E6%29-1%2
F%28%28x%29%2B6.35*10%5E6%29%29%3D76000%2B.5*56%5E2
And you get that you would have to drop the steak from at least 7825 meters. Or about 4.9 miles. Of course this is assumes all of the energy went into the steak, so the actual figure would be a bit higher.
>>5209751
You assumed a 1kg steak. Seems like a lot of meat but I'll roll with it.
>All the energy going into the steak
Under the assumption that the equation for gravity didn't already, you could factor out the kinetic energy
KE=(1/2)m*v^2
=.5*1*(56)^2
=1566J
>>5209751
But this is very wrong.
You're supposed to determine how far from the earth that the steak needs to drop from in order to accelerate to a speed so significantly higher than terminal velocity that, upon entry into the atmosphere, the friction between the steak and air would be great enough to generate the heat required to cook the steak.
>>5209810
We don't care about the energy of the steak, rather the friction between the steak and the atmosphere to generate the heat necessary to cook the steak. Simply dropping it from 5 miles up will lead to a rather cold steak when it hits the ground...
>>5209814
>>5209819
The calculation assumes all the energy from air friction goes into heating the steak. To put it simply, △Gravitational Energy=△Kinetic Energy+△Thermal Energy. The only reason the calculation is a bit under is because it doesn't account for the change in thermal and kinetic energy of the air.
>>5209810
It would have to be extremely high altitude (far above a point where air resistance would be a factor) so that it could accelerate to a speed much higher than terminal velocity. Upon entering the atmosphere, the massive amount of friction (due to the speed much higher than terminal velocity) would cook the steak. There's no way that it could be cooked from falling at a point within the atmosphere.
>>5209832
I'm assuming we are only caring about the heating due to the atmosphere. Although we certainly could calculate what it's heat will be when it comes to rest and set velocity equal to 0. Although △kinetic energy is rather small compared to the △thermal energy, so the answer wouldn't change by much.
>>5209826
You math looks good, but that energy from gravity is going to go into more than kinetic energy and thermal energy of the steak, most of the heat is going to be going into displacing and heating the air that the steak is bumping into :( sorry.

Steak from 100km, top speed Mach 3.2, pulling 5g
The time of day would have a huge impact here. The steak being exposed to sunlight in the vacuum of space could have an impact here couldn't it? Also wouldn't the atmosphere in sunlight expand and therefore expand further out.
Also OPs question could be that the steak has to be cooked before reentry.
This question requires the knowledge of the suns intensity around earth and the energy required to cook a steak and then you work out the time required for it to cook and finally work make that time match the time it would take for the steak to reenter the atmosphere from x height.
I know it is possible to cook eggs and things on rocks exposed to the sun in some places, it would probably be easy enough to do this in space...

A steak from the ISS, assuming zero initial velocity.

You need to accelerate above the steak's terminal velocity before it hits the atmosphere so that the friction heats it up.
When in the atmosphere you have to start slowing it down to where it stops cooking and also to keep it from burning up.
Then you need to make sure it lands on your plate for you to eat.
Encapsulating the steak is probably the only option, that way we can control the heat and also have a way to stop it's acceleration with a parachute.
In short: how fast does it have to go to produce the heat necessary to cook it?
How long does it have to stay at this temperature to cook?
How do we stop it from burning up? That means slowing it down.
How do we catch it for consumption?
>>5209912
No init velocity in the vertical or horizontal?
The ISS moving with horizontal velocity around the Earth, how would one factor in the air resistance/drag when its coming into the atmosphere at an angle and not straight down?
>>5209873
Packaging would prevent air friction from directly affecting the steak, and most packaging would not heat as well as a steak would.
The best thing to do would probably be to aerate the steak.
Or you could "package" it in an oven.
Rough estimate...
According to the ideal gas law
the velocity of one nitrogen molecule (28 atomic masses or 3.32*10^-27 kilograms) at 160 degrees celsius (433 kelvin) is
v^2 = 3* boltzmann constant *433/(3.32*10^-27)
v^2 = 5.4*10^6
v = 2320 m/s or 5230 miles per hour
v^2 = 2as = 19.6s, 5.4*10^6/19.6 = s = 276000 meters
You would have to plug in more factors to get a more accurate result. I'm sure being low density though that the piece of meat will not re-enter like a space craft, might want to cook at a lower temperature though, slow cook medium-rare.
Might need an RFID chip so you can find it after it lands.

The heat gained from air friction would be negligible, it wouldn't cook at all.
Why the hell are people equating gravitational potential energy to heat? Do you even heat and mass transfer?

Thank you, based OP!
Funniest, most original thread I've seen a while on any board.
Known (Can easily be found on the internet):
Initial Temperature
Final Temperature
mass
specific heat
Terminal Velocity
Drag force =1/2pv^2CdA
Cd you can find online I assume (coefficient of drag)
p=density of air
A=Area of steak
∆U+∆KE+∆PE = Q - W
(U2-U1) + (K2-K1) + (PE2 -PE1) = Q - Work from friction of reentry
U2-U1 will the rise in internal energy of the steak.
U1=(Specific Heat)(mass)(temperature Initial)
U2=(specific Heat)(mass)(temperature final)
Assuming the steak starts from rest
K2=1/2m(velocity)^2
Placing the datum at the place where the steak reaches medium rare temperature reduces ∆PE to
PE1=mgh (for simplicity we can assume g doesn't vary at all)
For major simplicity, if we assume velocity remains constant and the density of the air doesn't vary with height (which it does, but w/e), we can pull out all the constants and find work.
W = int(F*x)dx from h1 to h2 gives us
W = -1/2pv^2CdAh1
mCTf - mCTi + 1/2mv^2 - mgh = Q(f) - W(f)
m( CTf - CTi + 1/2v^2 -gh1 ) = Q(f) - W(f)
m( CTf - CTi + 1/2v^2 - gh1) = Q + 1/2pv^2CdA(h1)
Don't feel like finishing the rest, I'm probably approaching the problem completely wrong, would be a waste of time if it was, however, someone else is welcome to finish ;) ;) ;)
>>5210580
Omg imagine if you could space order pizza, so they drop/shoot it to you from orbit at your house, so it cooks on the way down then when its done a parachute or something is released letting it drift to your doorstep
>>5209751
Everything about this is so wrong. I can't believe I actually have to explain this, but he specifically asked about heat from re-entry, which is when an object that is travelling faster than terminal velocity enters the atmosphere, and undergoes heating from the friction.
Calculating the potential gravitational energy to heat? Are you retarded?
Try work against friction next time.
>>5209751
HAHAHA oh my lawd, is someone taking year 8 physics? Do you even know what terminal velocity is? It's when the drag force on an object equals the force of gravity you fucknut.
Something heats up from re-entry because it's initially travelling faster than terminal velocity, and friction converts the object's kinetic energy into thermal energy as it decelerates to terminal velocity.
You don't get anything beyond negligible thermal energy from something travelling under or at terminal velocity.
My fucking god is this board full of twelve year old faggots who can't into basic physics.
>>5210898
>>5210916
Did you morons even read all the way to the end of >>5209751 ? It's a simple conservation of energy argument and totally valid. Condition 1: steak stationary at altitude. Condition 2: steak about to hit ground. Difference in energy of those states is the maximum possible heat that could be transferred to the steak through friction.
It neglects the heat that's transferred to the atmosphere (both from the steak, and via aerodynamic heating) but it provides an absolute lower bound.
>>5210916
You seem to have some misconceptions about this, namely.
>You don't get anything beyond negligible thermal energy from something travelling under or at terminal velocity.
Terminal velocity is a function of atmospheric thickness, mass of the object, and cross section of the object. A human in low atmosphere caps out at 250km/h or so terminal velocity, a bomb-shaped solid lead weight? Several times the speed of sound, and such an object would heat significantly.
As you move higher in the atmosphere the dynamics change also, while I don't actually know if this is valid my gut feeling says that air resistance in a thin atmosphere at terminal velocity in said atmosphere would generate more heat than terminal velocity in a very thick atmosphere.( gut feeling influenced by the extreme points; a syrup atmosphere where you move 1cm/hour, or a near-vacuum where you move with a significant fraction of c, striking some hydrogen atoms every now and then.)

we would have to calculate a lot of factors and we need to use calculus to look at how the various factors change continuously as the meat descends
the height
gravity, gravity is weaker as height increases
air resistance's effect on velocity
the amount of energy converted into heat
the aerodynamic properties of the meat which strongly affects both air resistance and the amount of energy converted into heat, complicated things might happen like we might start to get a meatspin
for this reason I propose we make meatballs
air pressure's effect on heat generated
the heat released by the meat due to radiation
the heat released by the meat due to conduction, which depends on air pressure and velocity
the effect of the heat on the cooking of the meat, if the meat is scorched for a few seconds before quickly slowing down to terminal velocity it won't cook properly
what other major factors have I missed?
>>5211208
>for this reason I propose we make meatballs
Already proposed
>air pressure's effect on heat generated
We are going to assume pressure wont have any effct if we have it in some metal shield. Density of air, however will have an effect if not assumed to be constant
>the heat released by the meat due to radiation
wut
>the heat released by the meat due to conduction, which depends on air pressure and velocity
This is going to be cancelled out when we find the velocity at which the meat is going to heat up
>the effect of the heat on the cooking of the meat, if the meat is scorched for a few seconds before quickly slowing down to terminal velocity it won't cook properly
This is our largest problem. I think we need to wrap the meat in something, as proposed already
>>5211223
> if we have it in some metal shield
Well that changes the game. We could just create a re-entry vehicle that absorbs heat and slowly transfers it to the meat.
>the heat released by the meat due to radiation
http://en.wikipedia.org/wiki/Thermal_radiation
Heat energy can be converted into radiation which has a cooling effect.
>This is going to be cancelled out
Heat loss due to conduction increases as heat increases.
>I think we need to wrap the meat in something, as proposed already
The thing is we don't even know whether it will be scorched or cook slowly, we haven't calculated anything yet.

I'm curious what sort of impact the Yarkovsky and YORP effects would have on the steak's trajectory and spin rate as it descends from orbit before reentering the atmosphere, given its comparatively low mass, unusual shape, and its decreasing albedo as it cooks.
Of course it's possible these effects may not come into play over the relatively short timescale of the steak's reentry.
>>5211318
Sample 1 - A bare steak dropped from orbit
Sample 2 - A steal wrapped in foil dropped from orbit
Sample 3 - a steak grilled on a George Foreman Grill on the ground
Sample 4 - a steak grilled on a George Foreman Grill... in space
Sample 5 - a steak placed out in the Sun
Control - a steak grilled on a charcoal grill... the way God intended.
>>5211324
Now we're getting somewhere.
I believe sample 2 should effectively minimize heat radiation and improve heat transfer?
The reflective surface would also reduce the effect of heating from the sun I imagine... Calculations may become tricky...



Assuming you drop the steak at a height that causes it to cook to medium rare upon re entry ... wouldn't it cool down to ambient temperature afterwards during its travel to the ground?
Wow /sci/ really is retarded
Some people are massively overcomplicating it to look clever, and others are just plain missing the point.
The heat from re-entry doesn't come from Gravitational Potential Energy, it comes from Kinetic energy. Felix didn't burst into flames but if we hurled him down from that height at the speed of a meteorite he would.
Take the terminal velocity as negligible compared to the speed you'd need to chuck it out of the spaceship at and do a back of the envelope calculation assuming all the KE is converted to heat to get a rough ballpark figure.
>>5211692
red bull guy's top speed was 0.37 km/s
deorbiting space craft have speed of 8 km/s
return from the moon is 11 km/s
meteorites are in 15-70 km/s range
apparently many km/s is enough to burn you, unless you have an ablative shield.
>>5211688
You can't just say KE=Q, if you are using energy equations, you need some type of boundary. If the boundary is your entire steak, there is going to be work done on the system from the drag force, Heat transfer to the steak from conduction(could be convection? Not quite sure actually) from the surrounding air that is heated up from friction. Certainly the internal energy of the steak is increasing, otherwise the temperature of the steak wouldn't increase. Gravitational Potentinal Energy could be neglected, but it is needed to answer OP's original question, the distance needed to drop the steak.
>>5211716
>You can't just say KE=Q
Sure we can this is just an order of magnitude thing for fun.
If you're looking for an exact answer that's hardly the biggest source of error. The steak would probably immediately break up for a start.`
>>5211759
I'm not talking about Gravitational Potential Energy. Obviously that's wrong.
I'm talking about getting it up to speed before it hits the atmosphere by throwing it which is the only real way you could do this.
Just put in some numbers and it would need to be in the order of 1000's of metres per second (so some 1-10 km/s let's say).
I assumed it would heat up by 200 degrees and remain at that temperature for freefall at terminal velocity for however long it takes steaks to cook.
E = mcT = 1/2mv^2
v = sqrt(2cT) = sqrt(6.4e5) is gonna be somewhere in the range of hundreds to thousands of metres per second. The real value will obviously be higher for various reasons. I used c = 1.6 kJ/kgK from earlier in the thread.

>>5209751
>Of course this is assumes all of the energy went into the steak, so the actual figure would be a bit higher.
>the actual figure would be a bit higher
>a bit higher
>a bit
Look at this faggot.
Allow me to throw out a few of the many concepts that would relate to this problem:
>Forced convection
>Variation in atmospheric density and temperature with altitude
>Stagnation conditions
>Thermal conductivity of the meat itself (MIGHT be negligible, but probably won't be)
>Actual average drag coefficient of the meat (remember, it will change depending on the meat's orientation), including wave drag (which will also vary once you go transonic)
Even that will only get you a first approximation.
>>5211774
How about setting the steak at a distance from the earth where it could enter an extremely weak orbit and, after gaining a significant amount of speed, reenter earth's atmosphere and cook? If that were possible, which it likely isn't, then the steak would not have to be shot at the earth.
>>5211785
This isn't computational fluid dynamics it's a back of the envelope calculation.
Also I don't see how things like the drag coefficient and varying atmospheric density are really relevant. I'm not trying to model it's descent, just considering the beginning and end conditions.

Thank you based /sci/, this has been one of the most entertaining threads I've read in a while.
>>5211680
yeah, how might we go about slowing down an object descending rapidly through earth's atmosphere. if only some sort of simple device capable of increasing drag had been invented, it would be able to save our steak, and may have even saved that poor red bull man from slamming into a mountain at the speed of sound.
>>5211680
Well, depending on its angle of descent it will probably aerobrake part of the way down. Then we can bring it the rest of the way using chutes, thrusters, or a combination of both.
Maybe have one of those big airbag things blow up around it as it nears the ground.

>>5212712
Steak skycrane!!
Once the steak reaches the lower atmosphere and hits terminal velocity, a 'harness' of sorts rendezvous with and captures the steak before engaging the thrusters.
The thrusters slow the steak to descent speed and maneuver it to the landing site.
20 meters above the ground, the skycrane lowers the steak ever so gently onto a waiting plate which already contains a baked potato, corn, and a dinner roll.
Bon apetit

>>5212738
>20 meters above the ground, the skycrane lowers the steak ever so gently onto a waiting plate which already contains a baked potato, corn, and a dinner roll.
MAKE IT HAPPEN /sci/!!!

>>5212642
If we do it correctly, it will hit terminal velocity right after it is cooked to it's maximum temperature. We could easily catch it in a net then. If we have it in an apparatus, then we can just design a parachute to come out of the apparatus.
Best thing to come out of /sci/ for a while
http://what-if.xkcd.com/28/
What if we caught the stack while on a plane to prevent cooling...
The solution to bad airplane food? Perhaps.
^^ Embarrassing to see 4chan act like the usual gaggle of retards it is with plenty of idiots who sincerely think they know what they are talking about argue over this stuff all for it to be drawn to a conclusion by someone with some actual intelligence
drop it from 2 inches above the grill and you should be good.
yfw a /sci/ thread made it on xkcd
inb4 4,000 more visitors
>plenty of idiots who sincerely think they know what they are talking about argue over this stuff all for it to be drawn to a conclusion by someone with some actual intelligence
Oh dear here we go.
Answer:
http://what-if.xkcd.com/
>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. There was no clear conclusion.
>poorly-informed physics tirades intermixed with homophobic slurs
Yeah, after reading through this entire thread I think I can safely place into question both the above commenter's claim of "actual intelligence" on the part of the author of that article, and whether or not he read the thread at all instead of just scrolling down and then going "well seeing as it's 4chan I'm guessing they're all idiots".
I guess that >>5212189 got what he wanted.
>http://what-if.xkcd.com/
Looks like a pretty solid analysis until he gets to this:
>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.
That's just absurd. Thermal soak does not suddenly stop in its tracks when ablation begins to occur. In fact, for ablation to occur, the surface of the steak will NECESSARILY have to be at the temperature at which it pyrolyzes, much like it would be on, say, a hot grill.
Now, a steak is incapable of making a gradual, drawn-out lifting reentry like Soyuz and the Shuttle do, so any reentry it makes will necessarily be approximately ballistic. Mercury capsules following such trajectories from low Earth orbit took anywhere from seven to ten minutes to go from reentry interface to drogue deployment at ~mach 1.2. Assuming about half of this is spent heating within the ablation zone, the steak will be cooking for 3:30-5 minutes, on "high," so to speak. The resulting steak WOULD be cooked - if slightly rare (for MY tastes, anyways) and HEAVILY seared - by the end of the ablation phase. And it would, of course, be cold by the time it reached the ground, but it would NOT be raw.
To be fair to the xkcd guy there are 2 people called faggot in this thread, and I'm pretty sure at least half of these assumptions in physics are wrong.
pwned by xkcd
wow