How to Understand the Delta V Formula?

[Sam1235]

Hi All.

So I know the Delta V Formula is ÃŽâ€v = Isp *ln(Total Mass/Dry Mass) But I always seem to come up with Incorrect answers, and I think that is related to not understanding to "ln" or logarithm. I have tried to read the Wiki on it, it is way too complicated for me, and I am not sure what to do with it in the calculation. Can Anyone simply explain what I have to do with it when Calculating Delta V?

Edited January 7, 2014 by Sam1235

[Guest]

ln stands for Natural Log, which is not the same as hitting "log" on your calculator.

http://en.m.wikipedia.org/wiki/Natural_logarithm

[Sam1235]

I thought It was the "ln" button on the windows scientific Calculator?

[Specialist290]

Welcome to the forums!

When you're just starting out, you really don't have to know so much what "ln" is exactly as what to do with it when you get to that step. Basically, for now, just remember "Divide total mass by dry mass, then push the 'ln' key on your calculator and multiply that by exhaust velocity."

When I was first starting out with figuring out how delta-v calculations work myself, I came across this page on Atomic Rockets that I think does a good job on explaining how the rocket equation works in layman's terms, as well as its companion page on applying those principles to multi-stage rockets. Another set of pages you might find helpful regarding the subject might be the "Orbital Mechanics - Basics" articles over at MyKSPCareer.com, which discuss the concepts specifically from a KSP perspective.

Hope this helps!

[I_Killed_Jeb]

I thought It was the "ln" button on the windows scientific Calculator?

make sure you're putting the numbers in with the correct order. with the windows calculator you'll have to do the mass ratio first, then hit ln, then multiply ISP. also note that if you're doing the calculation for atmospheric dv it's tough due to changing isp with thinning air

[Sam1235]

Thank you very much! I was confused by the timing of pushing the button (Do I add it, multiply it or just press it?) but now I understand. Thank you very Much!

[capi3101]

OP: You're missing standard gravity in the equation you wrote down in the original post - it should read:

ÃŽâ€v = ln(Total Mass/Dry Mass) * I_sp * g_o

That might explain some of the problems you've been having with getting correct values.

And you usually just press the ln button once you've got the mass ratio calculated.

For example: lessay you've got a Mk16 Chute, Mk1 Command Pod, LV-T30 and 9 FL-T200 fuel tanks in your rocket.

The chute weighs 0.1 tonnes, the command pod is 0.8, the LV-T30 is 1.25, and each tank is 1.125 tonnes full and 0.125 empty.

The total mass of the rocket full is therefore 12.275 tonnes, empty it's 3.275 tonnes. The launch I_sp of the LV-T30 is 320

So you just plug all that in:

ÃŽâ€v = ln(Total Mass/Dry Mass) * I_sp * g_o

ÃŽâ€v = ln(12.275/3.275) * 320 * 9.81

ÃŽâ€v = ln(3.74809) * 320 * 9.81

ÃŽâ€v = ln(3.74809) * 320 * 9.81

ÃŽâ€v = 1.32125* 320 * 9.81

ÃŽâ€v = 420.79898 * 9.81

ÃŽâ€v = 4,147.658 m/s

And there you go.

Incidentally, you'll wind up with slightly higher delta-V than this in practice, and that's because your Isp is in fact going up as you ascend. The design I described actually has the delta-V necessary to obtain a stable orbit with enough leftover to de-orbit afterwards. Take that rocket, aim it poleward, do EVA reports as it passes over various biomes and you've got yourself a Tier 0 single-stage rocket...not quite reusable as you will crunch the engines and a few tanks on landing, but......

Edited January 7, 2014 by capi3101

[blizzy78]

I was confused by the timing of pushing the button (Do I add it, multiply it or just press it?)

The natural logarithm is a function. So in general for using a function, you usually enter the argument for the function into your calculator, then press the function button. For example, to calculate ln(123), you would need to push 1, 2, 3, ln.