Am I screwing up the Rocket Equation?

[Rodyle]

Hello there guys,

I've been working on SSTO planes/other things for a while now, and was quite disapointed when I found out that my latest creation (according to the math) wasn't able to reach the moon. I got to orbit, refueled and tried to go there anyway, because why not, and found that I was able to get there. That means that the thing had at least 1K ish delta-V, while according to the Rocket equation, it should barely have 180, since the craft weights 21.41 full, 13.41 empty and uses aerospikes for space-propulsion. Then I did some calculations and found that my tugger vehicle, capable of taking large fuel tanks to the moon, get them to the space station and then go to the moon and back again also shouldn't be able to do so.

So, does anyone have an idea of what's going on? Am I just an idiot and doing something wrong with the rocket equation? Is the Oberth effect much more powerful than I think it is?

Thanks in advance!

Edited February 11, 2014 by Rodyle

[UmbralRaptor]

Can you show us your calculations?

For a craft that masses 21.41 tonnes full, 13.41 tonnes empty, and has a 390 s Isp, I get:

ÃŽâ€V == 390 * 9.82 * ln(21.41/13.41) == 3829.8 * ln(1.597) == 1791.8 m/s

[PlonioFludrasco]

I bet you forgot that in the rocket equation you need Isp in m/s while is reported in-game in seconds.

I suppose that because it happened to me very very often!!

[Rodyle]

Oh lord... I should've been suspect when I was off by a factor of around 10. I forgot the g in the formula. Thanks guys, problem solved, I guess. XD

[Streetwind]

Yeah, the commonly given form uses effective exhaust velocity, v(e), instead of I(sp). Conversion factor is the gravity constant g(0) (not the actual gravity g). People keep disagreeing about what that constant is set at for KSP, with some claiming 9.82 and some claiming 9.81. I use the latter, because it gives me the "worst case scenario".

dV = v(e) * ln(mass ratio) = I(sp) * g(0) * ln(mass ratio)

[Rusty6899]

I think it is 9.82. The mass flow rates are given now in the VAB so g0 is calculated as...

g0=Thrust/(mass flow rate * specific impulse)

I calculated it before as being 9.82.

[capi3101]

It probably is 9.82; I think what's happening is that people are using Kerbin's surface gravity for g_o, which is listed in the wiki as 9.81 m/s[sp]2. Old debate; does not need to be rehashed on this thread

Earth surface gravity (i.e. RL standard gravity), incidentally, is 9.80665 m/s[sp]2...