SpaceX's Starship has successfully demonstrated reentry at about 7.7 km/s. On the other hand, Mach 8 at sea level is a bold proposition; how did you estimate drag at hypersonic speeds? (And please note that it is not "friction" which heats up the aircraft; it is the compression of air by the fast moving object.) (And the temperature that the aircraft would reach depends on how it is designed. For example, when Starship reenters at 27,000 km/h, the plasma surrounding it reaches 2,600 °F = 1,400 °C, but the Ship itself remains very much cooler.)

@AlexP I basically empirically adjusted for transonic and supersonic drag. However, this aircraft could spend days at speed, so conduction of heat from the skin to the interior could be an issue.

I'm pretty sure you don't calculate it for yourself without huge simplifying assumptions, unless you want to be able to quit your job and become a specialized aeronautics engineer when you're done.

It may be worth reviewing whether your rocket needs to be in atmosphere at all. If you're just doing something that requires you to go to a place on the ground, like traveling between distant cities, it'll be much easier to add 300km to your flight and just go around the atmosphere, and for short hops you'll be acceleration limited by your passengers. And if you're doing observation or fighting, you'd need to go slow enough to look at things or fight things before you're flashing over the horizon.

@gs These aircraft fly through the gyre, which is a system of air-filled distance-reduced tunnels between the stars. If you leave the tunnels, you leave the gyre. Gyre tunnels between stars can be several hundred thousand kilometres long... like flying from the earth to the moon, but through air the whole way. There is no 'avoiding the air'.

Maybe I wasn't clear. Flying at Mach 8 at sea level is not believable.

@AlexP Why is it not believable? Personally, I believe that the heat accumulated from pushing through so much air so fast would make the hull melt or the occupants roast alive (hence this question), but if there's enough propulsion power, it seems at least theoretically possible.

Propulsion power as such is useless. It needs to be converted into thrust somehow. The only reasonable way to do it would be to use some sort of rocket engine, but I'm afraid the required reaction mass would be prohibitive.

Is there a need that the air in the tunnels stands still? For practical reasons I would blow the air through a pair of one directional tunnels. Accellerating a tunnel of air is both simple and useful to decrease the drag, respectively increase the top speed. I assume the air in the tunnels can move roughly as fast as the aircraft itself can move (drag on tunnel walls equals drag on aircraft hull). Thus It could double the top speed or remove the need to let the aircraft move itself.

@AlexP The first words of the question are, "I've designed an atomic powered aircraft with reactionless propulsion". Reaction mass is not a problem.

@Thibe In my story/TTRPG, the gyre is at 0.35 ATM pressure, it has wind streams running in both directions at up to 2,000kph, and the ships fly down the gyre close to the streams to take advantage of the wind at 5000kph relative to the streams, so ~7000kph total. However, since I don't know how to calculate heat, that's just a guesstimate.

I think your upper speed limit is a bit too high. The Sprint anti-ballistic missile accelerated at 100G and after 5 seconds, the skin reached over 6000 F (in videos, the skin of the missile is brighter from heating than the rocket exhaust). The SR-71 "only" flies at Mach 3 and skin temperatures reach 750 F.

Can we presume that your ship isn't using ablative shielding? That raises the short-term temperature achievable.

Given infinite power you can afford an arbitrarily large vehicle Imagine an earth sized vehicle solely devoted to reducing atmospheric heating. Please ask a more specific question.

@sphennings I'm deliberately not providing the details of the aircraft, because I want to be taught how to fish, not just be provided with a fish.

Well how far is your craft going to go? Are we talking point to point flights? Because those would not last very long and the equilibrium temperature would be less relevant.

It could gather or suck subsonic recirculating air at trailing section, liquefy that air and pump it towards leading section or nose, and use it there as transpiration coolant.

@causative The individual gyre tunnels may be 200,000km to 400,000km long, and voyages in the millions of kilometres. The aircraft would slow down after each leg for navigation checks.

@user721108 I don't need to know about cooling, just how to calculate heating due to speed... very approximately.

Then don't ask for the max speed. Ask questions that will enable you to solve the multivariable optimization problem. You may also want to ask yourself how accurate or precise you actually need things to be. Ask as an example you could ask if there's a rule of thumb to follow for atmospheric heating you can follow for a rough speed range.