Delta V to get TO an altitude

[Mister Dilsby]

After unsucceeding with a few 150t Eve return landers I am trying to go the other way: an ultralight ion-powered ship. No, this is not an SSTO attempt, I know that's impossible! But I am pretty sure that I can use the ion engines to bring the final stage (rocket-powered lawn chair) high enough to carry Jeb the rest of the way.

However I do not want to try to fly on xenon and sunlight alone all the way from sea level to 32km; I would like to punch through the mashed potato lower atmosphere with a liquid-fueled booster section, and start ion power a few km up.

So here's the question at last: has anyone worked out the delta V required to get to certain altitude? That is, if it takes 12000 dV to get from sea level to orbit, how high will each 1000 dV bring me? If I know that, I can design the booster to lift the ion plane that far.

If folks are interested I'll post progress of the ion ship. This would be a three-stage to orbit concept. (booster, ion plane, rocket lawn chair) Thank you!

Edited November 18, 2014 by Kuzzter

[Taki117]

For that particular situation I would just divide atmospheric height by 12 to get how high each 1km/s would get you. This will probably be very inaccurate though.

[Mister Dilsby]

Right. A closer approximation I've considered is to look at the chart of dV FROM various altitudes to orbit, and assume it works in reverse direction. The table (on the Eve wiki page) says that the dV required from sea level is 11282, and the dV required from 5000m is 8888. So one could assume that it costs 2394 m/s to get from sea level to 5000m... I dunno.

[Redshift OTF]

I think that is close enough. I have seen landers with 8500 DeltaV get from the highest peaks of Eve to orbit which are around 5000m high. I don't think you will have enough TWR for ions until you got very high in the atmosphere and even that might not be enough. Not something I have tried. The only Eve landers I have seen that use ions are ones that use the ions to return the capsule, (or seat), back to Kerbin.

[Mister Dilsby]

Ok, I did a little experiment with the help of Hyperedit. I put various single stage ships with different dV and takeoff TWR(eve) of around 2 at a launch site 452m high, and sent them straight up.

The results:

dV || max altitude

_____________________

1483 || 3210m

2457 || 5283m

4051 || 9277m

4976 || 12929m

...so, looks like the deltaV savings for launching at altitude is pretty close the deltaV cost to get to that altitude. For example the wiki says you save about 2400dV if you launch at 5000m, and it my test it cost about 2400dV to go about 5000m. And I guess i answered my own question: I need about 4200dV to lift my ion ship to 10km from sea level.