Optimal shape for hypervelocity kinetic projectiles from space

Question

In my universe, coilguns/railguns are popular weapon in ship-to-ship combat. But, they also have a place in orbital bombardment, as a ship on low orbit can hit a ground target in few seconds using relatively cheap weapon.

The question is, what is the optimal shape for a projectile in magnetic cannons, that would make them survive atmospheric reentry, with much of their former velocity?

As for the weapon specifications, projectile velocity is 25 km/s to 40 km/s.

As a side question, does shape of projectile affect how "good" will it hit even with such great velocities involved?

Answer 1

The equations point the way

The question states two use cases, projectiles in a vacuum and projectiles in an atmosphere. As the shape of a projectile in a vacuum is simple, ie. whatever shape fits the barrel, the rest of the answer will concern itself with the more complicated atmospheric case.

The drag equation will have a lot to do with the shape of the projectile. It is..

$$D = Cd \cdot \frac{\rho \cdot V^2}{2} \cdot A$$

where $D$ is drag, $Cd$ is the drag coeffiient, $\rho$ is the density of the air, $V$ is velocity, and $A$ is the area.

Also, the kinetic energy equation will mean a lot too. It is...

$$E_k = \frac{1}{2} mv^2$$

...where $E_k$ is the energy of the object, $m$ is mass and $v$ is velocity. Remember kids, it's kinetic energy that kills.

Natural Shapes for Projectiles

From these equations we can see that we want to get our projectile's velocity and mass as high as possible, while also keeping the frontal area and drag as low as possible. Both deorbiting objects and railgun projectiles provide spectacular initial velocity to work with. Hooray!

Let's go step by step then...

1. A plate has a huge frontal area so we want something more narrow.
2. A sphere has the least surface area to most volume of any geometric shape. However, spheres aren't especially aerodynamic and are notoriously difficult to aim.
3. We observe that the longer an object is, the more likely it is to self-correct its trajectory. We want to hit what we aim for. (Aerodynamics, of course, play no part in space battles but we don't want to carry more ammo types than we have to.)
4. A rod is long, so it's easier to aim, plus it has minimal frontal area which keeps the value of $A$ low. Rods also provide lots of volume to put all that lovely mass that we need to make our $E_k$ values really terrifying.

What the equations don't say

Hypervelocity projectile noses are not intuitively shaped. While the projectiles are generally rod shaped, the nose of the rod may not be pointy. The front of the projectile shot out of the US Navy's rail gun is blunt. There's a YouTube Channel run by a guy named Taofledermaus who does lots of experimental shotgun loads. So very often, he'll take a slug that looks aerodynamic but just tumbles on the way to the target. It's not easy.

Aerodynamics is also an extremely complicated field. Trans-sonic aerodynamics is notoriously difficult within an already difficult field. Above the speed of sound, air behaves like a solid. Below the speed of sound, it behaves like a fluid. Around the speed of sound, it behaves like something else.

Also, aiming from orbit is really difficult as demonstrated by this WB answer. Without terminal guidance to track and adjust trajectory to hit a smaller target, this hypervelocity projectiles probably won't be accurate enough to be really dangerous. You'll be able to hit static targets without too much trouble but moving targets are too difficult, especially when you have to lead by a few minutes.

Even lead times of 30 seconds or so can be defeated with relative ease. WW2 bomber pilots received extensive training on how to avoid flak. Even a few seconds lead time is enough to make a shot miss, as this AC-130 gunship (WARNING: Graphic)demonstrates. Even changing direction a little bit will make a shot miss by enough to be ineffective. Throw in trying to hit targets in a 3D space, it gets very difficult, very quickly.

Answer 2

Project Thor - Using Titanium (heat resistance) rods (closer to a needle) that would drop from orbit and hit with the force of a small nuke without the fallout.

Now if said projectile was launched from a railgun, the damage should increase dramatically, as well as penetration power.

So long, needle-like projectiles made out of heat resistant metals for space-to-land combat and more cheap steel/scrap/ect for ship-to-ship, where penetration is usually not as important unless fighting large capital ships or stations.

Answer 3

Set and Spike

Here is a more outré take on dropping things from space. Consider air resistance. The more dense the air is, the higher the resistance. One way to lower the density of air is to heat it up. You can heat it up with a projectile dropped from space.

Thus: the first projectile is sacrificial. The job of the Set is frictional, heating a path through the atmosphere without itself breaking up. Probably it is some super ceramic with a blunt front, spinning fast (possibly on the inside only, to prevent yaw) for gyroscopic stability. From the ground the Set would look like a column of fire coming down from the sky.

Immediately on its heels comes the Spike. The superheated air in the path of the Set is much less dense and offers much less resistance. The Spike would come down the column of fire, blowing it apart. The Spike would catch up to the much slowed Set, bursting through it shortly before impact.

I like this idea most for the sweet wrath of god CGI I envision. Note also - lightning from clouds and ground would strike the pillar of fire as it formed, because the frictional heating of the atmosphere would also impart charge to the molecules heated.

Answer 4

Maybe i'm missing something here...

Are you wanting to destroy say an airfield or an entire city, because the design of you projectile would need to be far far more complex by firing it out of a railgun then simply dropping something out of orbit, which would provide enough speed to make a kinetic warhead obliterate a small area and do extensive damage to a city.

The real issue is orbital mechanics, anyone who works for NASA would tell you the difficulties in dropping something accurately out of orbit, but if you want real professionals at it then you'll need to speak to those that have played Kerbal Space Program.

If you fire something down at the planet from orbit, (We're not talking railgun speeds here) it wouldn't de orbit, just have an altered highly elliptical orbit. the way to de orbit the projectile is to fire it behind you, this would slow the projectile down and therefore make it speed up in relation to the ship that fired it. this will then de-orbit the projectile and allow you to hit the surface

Realistically it would need to have a spherical ceramic front with some form of stabilization fins trailing behind, this should withstand re-entry speed and heat while not losing all the speed it pickup up while re-entering.

Highly recommend you try out Kerbal Space Program as it would give the chance to actually test some of your designs pretty accurately, and you'll see the issues with orbital maneuvers