# High velocity mushrooms?

So y’all know meteoroites burn up in our atmosphere I’m looking for an equation or something that will allow me to calculate how fast a substance can move before it starts to burn up. Specifically I’m asking because I want to calculate the maximum velocity a mushroom can reach before it becomes a roasted mushroom.

• Aerogels might be better. – Keith McClary Jun 6 at 5:32
• Mushrooms aren't very good projectile materials. Are we assuming this is a "magic" mushroom that wont disintegrate under the aerodynamic forces? – Cort Ammon Jun 6 at 5:33
• Mushrooms have a parachute shape, so my guess is that they have a fairly low terminal velocity. – PM 2Ring Jun 6 at 5:38
• Obligatory XKCD: what-if.xkcd.com/28 – John Dvorak Jun 6 at 16:02

If we use the simpler ideal formula $$T_{stagnation}= T_{static} \left[1 + M^2 \frac{\gamma-1}{2}\right]$$ (where $$T_{static}$$ is the temperature at that level of the atmosphere, $$M$$ the Mach number $$v/c_s$$ where $$C_s$$ is the speed of sound, and $$\gamma=1.4$$ for a perfect gas), then for a burning temperature $$T_{burn}$$ we can just invert it and get that $$v_{burn} = c_s \sqrt{\frac{2}{\gamma-1}\left(\frac{T_{burn}}{T_{static}}-1\right)}.$$ For at atmosphere at 300 K with $$c_s=343$$ m/s and $$T_{burn}=477$$ K (this corresponds to oven roasting of vegetables) I get 589.1218 m/s.