> at 1 mile you’re looking at ~300g acceleration, 150g at 2 mile.
Could you explain? Centripetal acceleration is v^2/r, so naively I'd think something moving at LEO orbital velocity in a radius of 1 mile requires ~4,000g because LEO has a radius ~4k miles under 1g.
That is only about 1/4 of the velocity needed for low earth orbit [1]. The goal here seems to be to replace the first stage of a rocket by flinging it above most of the atmosphere.
Yes — rocket is still needed for circularizing burn (i.e, achieving orbital velocity).
(Which makes sense — if you managed to accelerate something to orbital velocity at sea level, it would (1) shed much of that speed before it actually reached a near-zero-atmosphere altitude and (2) burn up.)
25% the velocity but 1-.75^2 = 43.75% of the energy.
Further the rocket equation is a bitch so your saving even more fuel. The problem is you also end up with a lot of atmospheric drag and heat so the final savings are not as huge.
I don't think you did that right. The energy to get to (1/4)V is (V2)/16. The energy to get to V is (V2)/1. So your payload is only 1/16th of the way there or 6.25%.
Agreed about the rocket equation though - that first 6.25% of payload energy is much harder than the rest
If it makes you feel better picture the same energy accelerating the space shuttle it's solid rocket boosters and that huge fuel tank to some velocity vs just the shuttle to a much higher velocity. Or say to yourself it's all relative. Like tossing a ball between you and your friend on a train does not take more or less energy from you as the train is moving at higher or lower speeds, but it does take different amounts of energy from the train.
Rockets get energy from their fuel directly from burning it, but also from the kinetic energy of their fuel. So in space a rocket that can add 100km per hour of delta V from fuel before running out can do that at 0MPH , 1000 MPH, or -10,000MPH all the way up until relativity becomes an issue.
So, first find out how much speed/energy you need as a baseline it's velocity squared (100% velocity)^2 = (1v)^2 = 1e = 100% energy. Now instead of that we need to go from V1 to V2 you need (V2 - V1)^2 energy. That's (100%v - 25%v)^2 = (1v-0.25v)^2 = (0.75v)^2 = 0.5625e so we still need 56.25% as much energy, and we gained 100%e - 56.25%e = 43.75% energy.
PS: Unfortunately, these things don't start in space so we need to consider air resistance.
Could you explain? Centripetal acceleration is v^2/r, so naively I'd think something moving at LEO orbital velocity in a radius of 1 mile requires ~4,000g because LEO has a radius ~4k miles under 1g.