Electric Cannons and Kinetic Impactors

One staple of the science fiction armoury is the railgun. Spinal-mounted or in turrets, it has adorned spaceships from Halo to the Honorverse. However, there are strong arguments against their use in 'hard' sf, such as their relatively low muzzle velocity and large mass penalty.

Here's how you keep your guns.
To start off with, we must remember that railguns are only one sort of electric cannon.

Railguns have a conducting projectile trapped between two rails. An electric current run up one rail, across the projectile and down the other creates the Lorentz Force. This tries to push the rails apart, but if they are braced, the projectile is ejected instead. The projectile can be conducting, or held within a conducting sabot.

Coilguns have a projectile levitated inside a series of electrical coils. These coils are switched on and off one in series, creating magnetic fields that push and pull the projectile along. The projectile can be ferromagnetic, conductive or containing a magnetic coil within itself.

Railguns are better as lower velocity, lower complexity weapons. They are less efficient due to electrical resistance and friction between the projectile/sabot and the rails, leading to lower velocities, but are rather cheap to produce, and damage to the cannon in operation can usually be fixed by simply swapping out the rails. The projectile has to be heat resistant and able to maintain contact with the rails at a wide range of velocities. The rails can easily cooled by running loops of coolant against the them.

The projectile might need some magnetic shielding too.

Coilguns are more high-tech and higher velocity weapons. Since they can levitate the projectile and use magnetic fields to manipulate it, they eliminate friction losses. They also generally have lower electrical resistance and if superconducting, can be very efficient. However, they have many technical challenges. Their maximal velocity is limited by how fast the coils can be switched on and off. Cooling the coils themselves is more difficult.  Overall, they are heavier than railguns.

Each coil needs bracing against repulsive forces.

So what can electric cannons do?

Impressive amounts of damage, that's what. The main damage mechanic is kinetic. The projectile encounters no aerodynamic resistance in space, so muzzle exit velocity is equal to impact velocity.

At the projectile velocities we are used to on Earth, we get plastic deformation. This means that the forces on impact are so great, that even steel bullets bend and smush like plasticine. How far a projectile penetrates into a dense material, like steel armor, is a complex interaction between kinetic energy, projectile and target material strength, projectile shape, speed of sound within materials and so on...

Soon, we will have operational railguns on Navy warships, later, on the ground. These will enter the hypersonic regime. Even so, they are slower than Explosively Formed Projectiles found in HEAT shells and ATGMs.

Between 800m/s and 2km/s (Mach 6), we have the Newtonian model. Basically, it states that at those velocities, the kinetic energy involved dwarfs the strength of cohesion of the materials. All that matters is the length of the penetrator and the relative density of the projectile and armor.

Newton did more than mess with apples.

This one of the reasons behind the long, dense penetrators used for tank-gun APFSDS shells. They are aerodynamically sound, less likely to shatter when striking at an angle, and are guaranteed excellent penetration depths with the Newtonian approximation.

However, the velocities that will likely be involved in space combat are even greater. To cross the vast distances between two spacecraft quickly, projectiles have to be shot at speeds of 20km/s, 100km/s or even a few percentages of the speed of light in some settings.

In that case, even the Newtonian model is insufficient, since projectile is vaporized into plasma upon impact. The best model for these high-energy events is hydrodynamic or 'crater' model. Densities, shapes... nothing matters except the kinetic energy involved and the vaporization energy of the target material.

The hydrodynamic model states that at those velocities, the material strength is irrelevant and you can treat the problem as one hydrodynamic jet of fluid penetrating another stationary fluid.

The equation is: 

• Penetration depth = Projectile Length * sqrt(Density A/ Density B)

It is similar to the Newtonian model, but uses the square root of the density ratios for a more accurate penetration depth.

However, even this penetration depth can be surpassed by the crater produced by projectiles of extreme kinetic energy:  

The bottom of the crater is usually regarded as the penetration depth, but armor is deformed deeper down.

We can use simple equations to find how deep the impact crater gets.

• Kinetic energy = 0.5 * Projectile Mass * Velocity^2
• Crater Volume = Kinetic Energy / (3 * Yield strength of the armor)

The 'crater strength' of the armor is about three times the yield strength of the material. By approximating the crater as a hemisphere, we can work out the radius, therefore depth:

• Crater Depth = (0.159 * Kinetic Energy / Yield Strength of armor) ^ 0.33

Let's say we have a 50km/s coilgun projectile trying to punch through a meter of steel armor:

50 km/s coilgun
10 kg projectile
Kinetic energy = 12.5 GJ
Yield Strength of steel =250 MPa
Crater Strength of Steel = 750 MJ/m^3
Crater Volume = 16.7 m^3
Crater Depth = 1.38 m

Our coilgun digs through a minimum of 138 cm of armor per shot, and can do so at any distance. Multiple shots will overlap their craters and achieve full penetration of the armor.

The greatest benefit to kinetic weapons is their secondary damage mechanics. Impact craters create shockwaves that are supersonic within the material, shattering and fracturing armor outwards from the impact site and making further impacts penetrate further.  Furthermore, shockwaves bouncing off the rear face of the armor causes spallation which have to be dealt with using Whipple shielding.

Not a great representation of metal armor, but displays fracturing and shockwave rebound.

So we've confirmed that electric cannons are deadly effective at digging through enormous volumes of armor, and thanks to crater ejecta, shockwave fracturing, plastic deformation and spallation, are more devastating joule per joule compared to lasers.

Why are they shunned by hard scifi?

The main reason is Time to Target.

Imagine two spacecraft, one equipped with a laser and the other with a railgun. The railgun has to stay outside of the laser's effective range unless it want to be reduced to scrap.

As we've seen in the Laser Problem posts, the effective range of lasers can be tens of thousands, hundreds of thousands or even millions of kilometers. The railgun's projectiles must cross this distance.

• Time to Target = Distance / Projectile Velocity  

At 10km/s, a railgun projectile takes three hours and 46 minutes to reach its target from 100000km away. It would need more than a day to cross a million km.

We quickly see that even the fastest projectiles would take hours, or even days, to cross those distances. In that time, they can be destroyed by laser defenses, or the target craft can simply manoeuvre out of the way. 

Another problem is their acceleration per meter. Most railguns have a limit in the heat the projectile can survive and the forces the bracing can support, and coilguns are limited by how fast the switching is and how much momentum they can impact per switch. These translate into a maximal increase in projectile velocity per meter length of the cannon.

In the 50km/s railgun example above, the cannon needs to impart 12.5GJ of kinetic energy to the projectile. If it has capacitors that can discharge at a rate of 100kW/kg (super-supercapacitors by today's standards), and is expected to have about 400 kg/m length (according to DARPA's EMM project estimates) then it can have the following design:

50 km/s railgun

20 tons of 100kW/kg capacitor: 2 GW discharge rate
Total acceleration time: 6.25 seconds
Acceleration rate: 8000m/s^2 or about 815G
Railgun length: 156 km
Railgun mass: 156000*0.4 = 62,400 tons
Total mass: 62,420 tons

This mass is ridiculous, as is the length.

The solution is to massively increase the acceleration, so that the length is shortened. Let's use value typical of rifle bullets or tank guns.

50km/s railgun 100,000g acceleration

Acceleration time: 50000/(100000*9.81) =  0.051 seconds
Energy transfer rate: 245 GW
Capacitors needed: 245/0.000001 = 2,450,000 kg or 2,450 tons
Railgun length: 1.27 km
Railgun mass: 510 tons
Total mass:  2960 tons

In either case, the mass dedicated to the railgun is still very high, and the extreme length imposes design restrictions. Improving your 'technological' numbers, such as mass per meter or capacitor discharge rate, also helps competing weapon systems (supercapacitors help create pulsed lasers that are even more effective than continuous lasers).

In comparison, a laser-armed opponent using lightweight weaponry can out-range and generally out-perform railgun-equipped spaceships. 

At 1000000km, the railgun rounds will take 5.6 hours to hit their targets. 

At 100000km, it still takes over half an hour.

In the next post, we'll discuss ways to improve the usefulness of electric cannons, and even make them competitive against weapon systems such as lasers or missiles. After all, variety is what makes combat interesting!