Hypersonic drag - spherical vs pointed nose

[technobot]

This is a hypothetical question that I am curious about..

Suppose we are trying to design a projectile that is intended to travel at high hypersonic velocities, on the order of mach 10 or 20, through air (you can assume sea-level density for argument's sake).

Would an ideally sharp round projectile, shaped like this: () , (i.e. with pointed nose and tail, somewhat like a fat version of an olympic spear), have a lower drag coefficient at such velocities than the standard tear shape (i.e. with a rounded nose and sharp tail), in theory? If not, what would be the most efficient shape for this case?

I'm thinking that if both ends of the projectile are ideally sharp (to atomic level or close to it), then this should be able to cut though the air with minimum turbulence. But at high hypersonic velocity there are probably various effects that I'm not familiar with, and even at subsonic speeds I'm not really qualified to answer this question..

EDIT: Forgot to ask - what would be the drag coefficient of such a shape (the most efficient one), more or less?

 

[mgb_phys]

I think the aerodynamics of supersonic aircraft is actaully simpler - you basically just need the sharpest shape ( a la concorde) possible because you don't have to worry about turbulence, boundary separation and all that stuff.
All you care about is trying to get the aircraft low enough drag to get to that speed + getting through the sound barrier

Of course I could be talking total crap - I'm an astronomer/optics engineer.
Hopefully FredGarvin will show up with a real answer.

 

[FredGarvin]

Most hypersonic stuff I have seen, and that aint much, usually shows that for a lot of bodies, the drag coefficient tends to flatten to a constant at high Mach numbers. So MGB is right, as far as I know, that the regime itself does not dictate the shape. Getting there does. This is why ballistic missiles have the usual pointed shapes they have.

However, one aspect to the whole "most efficient" question is that with pointed and sharp edges that leads to a lot of headaches because of the incredibly high stagnation temperatures. If you have a very sharp point and very high stagnation temperatures, you had better be using some very stout stuff, a la rhenium, niobium or some other very high temperature capable materials.

 

[Astronuc]

The tip would be something like alumina (doped) or HfC/TaC, which have high melting points and are tough at high temps. It can't be metal since the metals oxidize rapidly at those temps.

Bascially the thermal design incorporates radiative cooling. One of the biggest challenges in hypersonic aircraft is the cooling of leading edges.

 

[mgb_phys]

One of the biggest challenges in hypersonic aircraft is the cooling of leading edges.

On Concorde fuel was used to cool the wing surface and leading edges.

 

[Hyperiz]

I know this is an old thread but I just came across it and felt the need to get involved in the discussion.

As Mach number increases, the leading edge shock angle gets more and more acute which is one of the main arguments for slender, sharp-nosed hypersonic vehicles. Unfortunately, the smaller the nose radius, the higher the stagnation convective heat transfer. As mgb_phys points out, Concorde used the its fuel as a heat sink for leading edge cooling. However, Concorde only traveled at Mach 2.02. Assuming a cruise height of 18000m (close to max) this gives a stagnation temperature of 392 Kelvin (119 deg C), less than twice the local air temperature. A vehicle traveling at the same altitude at Mach 10 would have a stagnation point temperature 21 times the local air temp.

The smaller the nose radius, the greater the heat per metre squared. The advantage of the tear-drop shaped vehicle is that you get a bow shock standing away from the surface rather than two oblique shocks. In this case, a lot of kinetic energy is lost through the bow shock so that the stagnation temperature at the nose is much much lower. The pressure drag, however, is now very much higher.

There's only so much heat that can be absorbed by the fuel. This is one of the factors in favour of liquid hydrogen as a fuel for hypersonic airbreathing vehicles since as well as having a much higher specific impulse than hydrocarbon fuels, the specific heat capacity is 6-8 times higher and the LH fuel can therefore deal with a far higher heat transfer.

Unfortunately, in supersonic/hypersonic flight boundary layer separation/turbulence etc. are still incredibly important. If your boundary layer separates from the wing you still lose lift. In fact, things like shock-induced separation become a serious issue. Transition from laminar to turbulent boundary layers is also a serious consideration since turbulent boundary layers have heat transfer rates and skin friction coefficients several times higher than their laminar counterparts.

In the end, vehicle shape comes down to how fast do you want to fly, at what altitude and for how long. How much weight are you willing to use up in active cooling or what materials can you use for passive cooling? Are you willing to let your leading edge ablate? The space shuttle and Apollo re-entry capsules are highly rounded since they are designed for re-entry flight and as such want to lose as much speed as possible high up in the atmosphere where the air density is lower. Designs for NASP etc. on the other hand show slender bodies and sharp leading edges since these are aiming for accelerating hypersonic flight within the atmosphere.

 

[mgb_phys]

Welcome to PF Hyperiz, thanks for the explanantion