LLO velocity is about 1.6km/s.If we assume a vehicle takes off from the Moon's with an average acceleration of 16m/s, the time of the powered ascent would only be 100 seconds, assuming no gravitational losses, but even if we assume 100% possible gravitational loss during the boost, the maximum loss would only be 160m/s, so in practice the required delta v to LLO shouldn't be more than 1600m/s + 160m/s = 1760m/s
Quote from: Warren Platts on 12/20/2012 06:03 pmHow do you calculate suborbital delta v's on the Moon? It would be nice if there was a simple formula that would give the delta v as function of distance or latitudinal degree equivalents....Use the technique described in Bate, Mueller, and White (for ballistic missiles at Earth) except use the moon's gravitational parameter and rotation rate, and double the answer (since you need to slow down propulsively at the end rather than letting the atmosphere do it).
How do you calculate suborbital delta v's on the Moon? It would be nice if there was a simple formula that would give the delta v as function of distance or latitudinal degree equivalents....
Quote from: Andrew_W on 12/21/2012 05:03 amLLO velocity is about 1.6km/s.If we assume a vehicle takes off from the Moon's with an average acceleration of 16m/s, the time of the powered ascent would only be 100 seconds, assuming no gravitational losses, but even if we assume 100% possible gravitational loss during the boost, the maximum loss would only be 160m/s, so in practice the required delta v to LLO shouldn't be more than 1600m/s + 160m/s = 1760m/sySo Apollo took 430 seconds of flight time to reach LLO; you're proposing doing it in 100 seconds. Assuming the same specific impulse, doing it in 100 seconds will take 4.3 times the thrust (to expend the same total propellant mass).I could point to some side effects of that thrust requirement. But perhaps a better approach is to suggest a different sizing technique, i.e. a lift-off thrust to weight ratio of about 2. That would give the vehicle an upwards acceleration of 1.6 m/s^2, which is about what a vehicle on Earth would get with a T/W ratio of 1.15. I think it's the case (but double-check!) that the engine then doesn't have any need to throttle; constant thrust even against the reduced mass at the end of the burn still won't push the vehicle beyond what structure, cargo or crew could tolerate.
LLO velocity is about 1.6km/s.If we assume a vehicle takes off from the Moon's with an average acceleration of 16m/s, the time of the powered ascent would only be 100 seconds, assuming no gravitational losses, but even if we assume 100% possible gravitational loss during the boost, the maximum loss would only be 160m/s, so in practice the required delta v to LLO shouldn't be more than 1600m/s + 160m/s = 1760m/sy