### Let Them Taste the Triple Gun

Navy test fires electromagnetic cannon

The story tells you it was a 33 MegaJoule shot, and it traveled (or would travel) 200 km. What it doesn’t say is how big the projectile is. The maximum range for a projectile is going to be v^2/g, in the limit of no air resistance (and also assuming a flat surface, but we’ll ignore that because that’s probably a small effect here). If we pop in the equation for kinetic energy and solve for the mass of the particle, we get m = 2E/dg. The amount of recoil energy given to the ship will be negligible; momentum is conserved and KE = p^2/2m, so the amount of energy scales with the mass ratio, which will be some number measured in kg compared to a kilo-metric-ton or so, which gives us a part in a million. So yeah, we can ignore that.

So 33 MJ gives us a mass of about 33 kg. But that’s assuming the energy of the pulse is the same as the energy of the projectile, i.e. the system is 100% efficient, and still ignores the pesky air resistance. This article mentions an earlier test, and puts the weight of the projectile at 7 pounds, or about 3.3 kg, meaning the system is at least 10% efficient.

The article also mentions the launch happening at five times the speed of sound, which is about 5*340 = 1700 m/s, which for a 3.3 kg projectile, is just under 5 MJ. All of those estimations seem to agree reasonably well. It also predicts the ideal maximum range of about 290 km, so we see just how much loss we have due to the air. Engadget says Mach 7, which is 10 MJ. Still ballpark; I wonder if one is launch speed and the other is impact speed, since the maximum range formula assumes a 45ยบ launch, and in reality this isn’t the case.

The time it takes the shell to travel this path is at least four minutes. I’m guessing that the final version would not be “dumb;” you would attach a gps guidance system to it and have some better control of where it would land.

## 1 Comment so far

1. rob on December 13th, 2010

mach 7 impact?

ouch!