While normally I'd agree with you that aeroheating doesn't happen for very long in amateur rocketry, the N5800 is somewhat of a special case. It's such a fast, efficient, high mass fraction motor that it will tend to push minimum diameter rockets up to speeds in the neighborhood of mach 3.8 to mach 4 at an altitude of around 12k MSL (assuming a launch from BALLS). Assuming the tip is basically like a cone with a 15 degree half angle (which should be fairly close), and assuming the tip is perfectly sharp (best-case scenario), and that there is no viscosity (again, best case scenario here), the flow will travel along the surface of the cone at mach 3.1, with a pressure of around 30 PSI, and a temperature of around 265F. Adding in a rough boundary layer estimate, temperatures climb quite a bit higher - even with an extremely conservative set of assumptions, the temperature goes up to around 550F, and odds are it would be even higher than this (any surface imperfections will cause it to go up quite a bit as well - possibly as high as a worst case value of 1700F or so, which is also what the temperature will be at the tip - interestingly, this is even high enough to damage aluminum, though I doubt that's what happened). In addition, the shear at the surface is extremely high, which will tend to cause the heat transfer to occur extremely efficiently, so the cone's surface will heat up extremely quickly.Originally Posted by edwinshap1
Also, as the heat damages the surface, it will become less smooth, which will exacerbate the heating - this cycle is probably what killed the cone (assuming the cone is what failed). Also, the time the rocket spends at high speeds and low altitudes is actually fairly long - several seconds over mach 3, and more like 10 seconds at mach 2+, based on some rough RASAero estimates (though the details depend very heavily on the sleekness of the rocket). This is an extremely demanding flight, so some of the normal assumptions have to be questioned and revisited to make it successful.
(Also, I'm not sure what you mean by "mach shadow" - the whole front surface of the cone is exposed to the freestream, and just the fact that the air passes through the shock wave doesn't do a whole lot to protect the cone)
(The math for the conical flow is here, if you're interested - the boundary layer stuff is just based on numerical code)
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