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More specifically, I'd like to know if unmanned rockets need to be specially designed to withstand the heat generated from air friction and shock waves during launch. I found the diagram below on the NASA website which shows some fairly high stagnation temperatures, but the problem is that I don't know how fast a typical rocket travels on its way to, say, low earth orbit. I also don't know what the velocity profile looks like, i.e. Mach number vs. altitude.

Most of the information I've found only talks about orbital velocity and reentry temperatures, neither of which is very useful.

enter image description here

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Judging from this profile of a Delta IV launch, it doesn't appear like it gets very warm at all, since it maintains a speed of less than 3.5 km/s until it is mostly out of the "thick" atmosphere (~90 km). A few calculations show stagnation temperatures as below. Though these temperatures are very high, they are not achieved until the higher altitudes, where the density is very low, so the surface temperature will not likely equal the temperature in the shock layer (or boundary layer)

$T_{0,11km} \approx 265 K$

$T_{0,45km} \approx 2470K $ (but massive error due to perfect gas/isentropic assumption due to Mach number of ~6)

$T_{0,90km} \approx 6300K$ (again, same argument as for 45 km)

enter image description here

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  • $\begingroup$ Could you post the equations you used to calculate the temperatures? And show where the assumptions are made which lead to the huge error? $\endgroup$
    – rul30
    Oct 23 '15 at 22:09
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    $\begingroup$ I used the 1976 US Standard Atmosphere to get the speed of sound at the first few altitudes (to compute the Mach number), then fed the Mach number into the isentropic flow equations, specifically for $\frac{T}{T_0}$, where $T$ is the freestream temperature and $T_0$ is the stagnation point temperature. $\endgroup$
    – costrom
    Oct 23 '15 at 22:45
  • $\begingroup$ Some of the phenomena that arise at the high Mach numbers are chemical reactions in the shock layer (which also becomes very thin), radiation heat transfer between the flow and the body, between the flow behind the shock and away from the shock, and dissociation of the components of the air, all of which make it tough to keep using the same isentropic flow relations to estimate the stagnation point temperature accurately. During reentry, I believe I have seen flow temperatures mentioned in the 20000K region, but the body itself doesn't ever get to that, thanks to ablation and other means. $\endgroup$
    – costrom
    Oct 23 '15 at 22:48

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