My Attempt At Re-entry Temp. Calculation

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SUMMARY

The discussion focuses on calculating the temperature (t2) of an object during re-entry based on specific heat capacity, re-entry speed, and other factors. The derived formula for t2 is t2 = (1/2pv2CDAy + mct1) / mc, which incorporates dynamic pressure and energy-temperature relationships. The accuracy of this equation is questioned, particularly regarding its neglect of skin friction effects during freefall. The user seeks to understand the implications of dynamic pressure on temperature gain during re-entry.

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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.
 

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