Here is a tidbit I found on the net that might be useful for determining absolute top speed in an atmosphere. ( no credit to me... I'm not clever enough )

The highest temperature for a melting point so far is just over 4000C. Top speed would be limited to temperatures that the hull can remain solid.

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At lower speeds (below Mach 5-ish), stagnation temperature (TAT) is a very accurate proxy for skin temperature. But at mid/high hypersonic speeds (especially in the thin upper atmosphere where mass flow is low), thermal radiation bleeds off a significant amount of heat, especially as temperatures climb into the thousands of Kelvin.

I've come up with a very crude formula to estimate the skin temperature. It assumes that the power P

absorbedto stagnate the oncoming air [intercepted by an area equivalent to the drag area CD A

ref] is radiated away over the entire vehicle skin surface area A

radP

absorbed=P

radiated1/2 * m

flowrate v

2=A

rad σ ϵ T

41/2 * (ρ v CD A

ref)v

2=A

rad σ ϵ T

4T = ( ρ v

3 CD A

ref / 2 A

rad σ ϵ )

1/4(σ is the Stefan-Boltzmann constant, emissivity ϵ is estimated at unity, T is skin temperature)

Here are a couple examples:

# | Airframe | Mach | Speed | Altitude | Drag area | T (DATA) | T (stag) | T (rad)

----|----------|------------|-----------|----------|-----------|----------|--------------------

4. | HTV-2 | Mach 20. | 5,812 m/s | 125k ft? | 0.05 m^2 | 2,200 K | 21,000 K | 2,771 K

8. | X-43A #3 | Mach 9.6 | 3,000 m/s | 109k ft | 0.10 m^2 | 2,255 K | 4,900 K | 2,143 K

8. | X-43A #2 | Mach 6.83 | 2,123 m/s | 109k ft? | 0.10 m^2 | 1,700 K | 2,514 K | 1,650 K

3. | X-51A | Mach 5.1 | 1,500 m/s | 64k ft | 0.10 m^2 | 2,200 K | 1,355 K | 2,058 K

13. | SR-71 | Mach 3.2 | 930 m/s | 79k ft | m^2 | ,640 K | ,651 K | , K

(Data are actual temperatures, where available. Stag is stagnation temperature. Rad is predicted temp using the above formula. Drag areas are pure guesses. Surface areas were 10-12 m^2 for the X-43A, X-51A, and HTV-2. Mass flows were 20-40 kg/s/m^2), except for the X-51A, which encountered 140 kg/s/m^2).

For predicting skin temp, stagnation temperature seems more accurate at lower mach, formula temperatures at higher mach, as expected. Admittedly, I'm pleased (and surprised) that the formula even yields ballpark figures. However, it's a bit sensitive to drag area and radiating surface area, and these are the only data for which I have estimated surface area, so I can't be confident this formula works well for other aircraft.

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found at

https://physics.stackexchange.com/quest ... mperatures