Check my combined Isp formula?

[Kyrt Malthorn]

So I'm putting together a spreadsheet - in part because KER is not up to date yet, in part for learning experience.  Something I've meant to do for a while.

Need someone who knows what they're doing to check my math logic here.

What I've got going on:

I've got a table of engine data and rather than make a user type in their vessel's Isp, I have them place a quantity next to each engine type.  These quantities are 0 if none.  Might put down they have 1 skipper and 2 thumpers, though.

So from what I can tell, the way to measure combined Isp with combinations of engine types is a thrust-weighted average.  I guess because thrust and isp are both in relationship to exhaust velocity? Check me here.

The formula I've found is: thrust / (thrust 1* isp1 + thrust2*isp2 ...).

Since I'm factoring in the quantity of these engines as well, I fist multiply thrust1 by quantity1, so if quantity is 0 the thrust and isp of that engine is removed from the picture.  And if they have 2 or 3 of an engine, thrust is doubled, tripled, etc, affecting the weighting of the isp.

So where T= total vessel thrust, Tx, Qx, and Ix are thrust, quantity used, and isp of engine number x, this is my formula...

 

T/(T1*Q1/I1 + T2*Q2/I2 ...)

 

 (formula runs through every engine in the list this way so it changes as soon as engine count changes)

If I tell it I have 1 terrier or 100 terriers, it correctly tells me my Isp is 345, can someone give me test cases and answers to run through my formula? 

 

 

 

 

 

 

 

 

 

 

[Streetwind]

The final formula you have looks correct (though the initial formula you found is not).

One needs to divide the thrust of each engine by its Isp. Then take the sum of all those results, and divide the sum of all thrusts by it. Multiplying an engine number into the thrusts is a valid shortcut in this case.

(This is called the weighted harmonic mean, in case you're curious.)

Edited October 14, 2016 by Streetwind

[Dman979]

8 hours ago, Streetwind said:

(This is called the weighted harmonic mean, in case you're curious.)

I was not curious, but I'm glad I learned that!

[Kyrt Malthorn]

On Friday, October 14, 2016 at 1:48 AM, Streetwind said:

The final formula you have looks correct (though the initial formula you found is not).

One needs to divide the thrust of each engine by its Isp. Then take the sum of all those results, and divide the sum of all thrusts by it. Multiplying an engine number into the thrusts is a valid shortcut in this case.

(This is called the weighted harmonic mean, in case you're curious.)

 

 

 

@Streetwind, if I understand you correctly, the reason my final formula was right even though I got there with a faulty understanding, was because T was already the sum of all engine's thrusts? 

Thanks so much! Isp combination was not intuitive enough for me to be certain of what I was doing.

Edit: Never mind, I see i put *isp instead of /isp.  

Edited October 15, 2016 by Kyrt Malthorn
technical difficulties