thrust and Isp for multiple (differing) engines

[draeath]

How does one calculate the "combined" thrust and Isp when multiple (differing) engines are in play?

For example, let's say I have a 120kN engine with a 400 second Isp, and two 50kN engines at 350 second Isp. How would you work this into a single "engine" to then use in delta-V calculations?

Edited January 9, 2014 by draeath

[LORDPrometheus]

Delta V is a single calculation and multiple inputs can be simply plugged in the same way

[blizzy78]

Delta V is a single calculation and multiple inputs can be simply plugged in the same way

That is not what OP was asking.

The formula is pretty simple:

                  thrust1 + thrust2 + ...
IspTotal = -------------------------------------
           thrust1 / Isp1 + thrust2 / Isp2 + ...

So in your case, the combined result would be an Isp of 383.87.

The total thrust is simply the sum of all single thrusts, thus 170 kN in your case.

[capi3101]

http://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design#Multiple_engines

So add up your thrust - (120 + 50 + 50 = 220)

Divide the first engine's thrust by the Isp (120 / 400 = 0.3)

Divide the second engine's thrust by the Isp (50 / 350 = ~0.142857)

And solve: 220 / (0.3 + 0.142857 + .142857) = 375.60976 s

Combined thrust is just the total thrust of the engines...220 for your example case.

EDIT: Semi-ninja'd - blizzy missed the fact that you had two of the second engine type in your example...

EDITEDIT: and sciguy rounded.

[sciguyCO]

Assuming all engines are firing at once:

Thrust(total) = Thrust1 + Thrust2 + Thrust3 + ...

So this craft would have 220kN of thrust with all three firing.

Isp is a little more complicated. I found this equation from the KSP wiki:

Isp (total) = (Thrust(total) / ( Thrust1 / Isp1 + Thrust2/Isp2 + Thrust3/Isp3 + ...)

So you'd have:

220 / (120/400 + 50/350 + 50/350) = 220 / (0.3 + 0.14 + 0.14 ) = 220 / 0.58 = 379s

Again, that's assuming that they're all firing in the same stage (and probably being fed by the same fuel supply). To account for staging in delta-V calculations, you have to do each stage independently (treating all non-firing engines / fuel as "dead weight" for each) and add them up to get the craft's total delta-V.

[blizzy78]

EDIT: Semi-ninja'd - blizzy missed the fact that you had two of the second engine type in your example...

I was just checking if you pay attention.

[draeath]

Thank you, folks! I forgot all about that wiki page!!

[capi3101]

I was just checking if you pay attention.

Uh-huh. Sure. I believe you...

[mhoram]

Since there is currently no Addon available, that calculates these stats, I am developping a Plugin, that makes just that in the VAB automatically.

http://forum.kerbalspaceprogram.com/threads/58531-Finding-the-best-ascent-path-for-rockets?p=890096&viewfull=1#post890096

[draeath]

Thank you guys very much!

The fruits of my (and thus yours, by proxy): FireMarshal!