My Attempt At Re-entry Temp. Calculation

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Vodkacannon
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I wanted to figure out the temperature(t2) of any object based on things such as its specific heat capacity, re-entry speed, etc.

Work: W = Fy

Force by Air: FD = 1/2pv2CDA

Energy-temperature relationship: Q = mc(t2 - t1)

Setting things equal & solving for t2 gives:

t2 = (1/2pv2CDAy+mct1) / mc

(I'm sorry I could not get latex to format all of the formulas correctly so I formatted none of them...)

So, how accurate is this equation in describing temperature gain through freefall back down to earth?
 
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I'm going to take a guess and say you get an estimate by finding the dynamic pressure (q = 0.5 * density * velocity^2) and solving for the adiabatic heating due to the pressure rise. This doesn't take any skin friction into account however.