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May. 26th, 2016 01:16 amFrom the thread [Physics question, sort of] Heat shields if you drop straight down from orbit, a reply from poster Tirunedeth:

Well, I made a lot of simplifying assumptions, and threw together a quick numerical integrator (fourth-order Runge-Kutta, if anyone's curious) to investigate this problem. To summarize these assumptions,

One dimension, so no effects due to the rotation of the Earth

Gravity is a constant (9.81 m/s straight downward)

Atmospheric density is a simple exponential function of altitude, with a scale height of 7.64 km (i.e. the density decreases by 1/e for every 7.64 km upwards you travel)

The drag coefficient is constant

The object in question is about 50 kg, has a drag coefficient of 1, an area of 0.5 m2 (rough guesstimates for a human), and starts at an altitude of 300 km

Under these assumptions, things seem to be pretty nice for about the first three-and-a-half minutes or so of your descent (aside from being in vacuum). From 210 seconds in, things start getting unpleasant. You're just above 80 km from the surface, and drag is contributing 0.05 gees to your net acceleration. Ten seconds later, this has increased to 0.75 gees, and you very shortly start to decelerate. Rapidly. At 234 seconds, you are experiencing 12.3 gees, which is probably enough acceleration to be lethal on its own, regardless of any heating that occurs. In the past 24 seconds, you've traveled nearly fifty kilometers, and lost about 600 m/s of your peak speed of 2.1 km/s. Things get progressively better from here, assuming you've survived. You're back down to 1 gee at 257 seconds, and you don't have to worry about hitting the ground (at around 41 m/s, or 90 mph) until 532 seconds.

I suspect that things won't generally be incinerated by this process. While the total energy dissipated during the above process is on the order of 700 kcal/kg, only a small portion of that will go into the falling object, and most of that will probably go towards burning off the top layers. I think the previously-linked xkcd describes this stuff a bit more, since that was the primary point of that what-if.