I'll jump in here to just lay out the basics in a way that I figured out to help me understand why this occurs. That was actually for race car performance simulation stuff, but physics are of course the same for everything. Power = Energy / time Energy = Force * distance velocity = distance / time Force = mass * acceleration (now some of those variables represent physically measurable entities, and some are purely imaginary mathematical values, but that's not important here) So: P=E/t, and E=F*s, so: P=F*s/t, but v=s/t, so: P=Fv, but F=ma, so: P=mav Power = mass * acceleration * velocity So, if you produce some acceleration on some mass, then the faster that mass is going, the more power is used/produced/converted. It doesn't matter if it's a rocket, a volleyball, a race car, a proton in a particle accelerator, or a bullet. It doesn't matter if this acceleration is produced by throwing some mass in some direction, by a magnetic force, by gravity, or whatever. Rockets conveniently work by pushing on mass that is initially traveling at the same speed as the engine, so the acceleration is constant (for a given force and mass), regardless of v. So the end result is; if you burn at double the velocity, your engine produces twice as much power! (with the same amount of fuel used, with the same Isp, naturally)