Math check - ISP

[Alshain]

Need a quick sanity check here. It occurred to me while talking in another thread. If I have 2 identical engines on a stage, is the Isp additive, absolute, or a loss?

I don't think it is additive (could be wrong I guess), but would the Isp for the stage be the same as the Isp for one of the engines, or would it lose efficiency?

Edited September 25, 2015 by Alshain

[GoSlash27]

Alshain,

The Isp would be a constant for identical engines. You're doubling the thrust and flow rate, but exhaust velocity remains constant.

Best,

-Slashy

[ghpstage]

Two identical engines would have the same ISP as one, with a larger dry mass and more thrust.

[Alshain]

Thanks!

[GoSlash27]

Alshain,

You're very welcome.

Give 'em Hell!,

-Slashy

[pincushionman]

And if you have different engines, it will be a weighted average. Weighted by what, I don't know off the top of my head. Probably mass flow rate.

[Red Iron Crown]

And if you have different engines, it will be a weighted average. Weighted by what, I don't know off the top of my head. Probably mass flow rate.

Thrust weighted. Like so (F is thrust):

[GoSlash27]

Thrust weighted. Like so (F is thrust):

http://wiki.kerbalspaceprogram.com/images/math/5/6/4/5649bb43490708471f734294d36eb565.png

At the risk of getting too far into the weeds, either approach would technically work since the mass flow rate is proportional to thrust.

Thrust is a much more convenient value for the calculation though.

Best,

-Slashy

[Red Iron Crown]

At the risk of getting too far into the weeds, either approach would technically work since the mass flow rate is proportional to thrust.

Thrust is a much more convenient value for the calculation though.

Doesn't work out that way for me. I tried it with a 4xLV-909 + 1xLV-N cluster, thrust weighting gives ~389s while mass flow weighting gives ~365s.

[Gaarst]

At the risk of getting too far into the weeds, either approach would technically work since the mass flow rate is proportional to thrust.

Thrust is a much more convenient value for the calculation though.

Best,

-Slashy

Doesn't work out that way for me. I tried it with a 4xLV-909 + 1xLV-N cluster, thrust weighting gives ~389s while mass flow weighting gives ~365s.

Averaging by mass flow rate would work if using the same propellants with the same proportions on the different engines. Averaging by mass flow for 909s and nukes doesn't work as 909 use LFO but nukes only LF.

If you tried with a stage using solely LFO or LF or monoprop or whatever fuel your want, then I'm pretty sure averaging by mass flow rate would work.

[Red Iron Crown]

Mass flow rates don't care if it's LFO or LF, just that it's mass.

[GoSlash27]

RIC,

The process to weight them would be different, so you couldn't just plug in Rf in place of T.

When you invoke "F/Isp" in the denominator you are talking about mass flow rate at that point.

Likewise, when you invoke F in the numerator that's really the same thing as "RfIsp"*.

I would expect a proper weighting based on mass flow rate to look something like (Rf1Isp1+Rf2Isp2+...+ RfnIspn)/(Rf1+Rf2+...+Rfn) although I haven't actually verified that

tl/dr: Aside from it's use in the rocket equation, Isp can be readily converted to exhaust velocity by multiplying by 9.81. This exhaust velocity is convertible to thrust when the mass flow rate is given or mass flow rate when the thrust is given.

*not exactly, but it's proportional and that's what matters

Best,

-Slashy

Edited September 26, 2015 by GoSlash27

[Red Iron Crown]

I certainly agree that it can be calculated from mass flow rates, but it is incorrect to call it a mass flow rate-weighted average of the Isps.

We're pretty far into the weeds now.

[GoSlash27]

I certainly agree that it can be calculated from mass flow rates, but it is incorrect to call it a mass flow rate-weighted average of the Isps.

We're pretty far into the weeds now.

RIC,

Oh, sure it would be. Engine A consumes yada percentage of the fuel at such-and-such an Isp. Engine b consumes yada percentage of the fuel at such-and-such an Isp. Therefore the combined Isp is weighted proportionally.

This is actually what you're doing when you weight by F/Isp.

And yeah... definitely in the weeds. My point was just that either description would be technically correct, so Pincushion's speculation is accurate although we think of it as weighting by thrust. And of course reconstituting mass flow rate by Isp and thrust is convenient because those figures are more readily available.

Best,

-Slashy

[Padishar]

Doesn't work out that way for me. I tried it with a 4xLV-909 + 1xLV-N cluster, thrust weighting gives ~389s while mass flow weighting gives ~365s.

Indeed, this is the cause of KER showing wrong ISP values for multi-engine setups, it uses mass flow rates and gets the wrong answers. The trouble is that the mass flow rate for each engine is also inversely proportional to the Isp of the individual engine which alters the weighting. I'm currently fixing this in KER but it's also complicated by the need to account for the individual thrust vectors of the engines. E.g. if you have an LV-N pointing up and 4 909s pointing sideways (so they balance out and are just wasting fuel) then the effective Isp is much lower than if they were all pointing in the same direction.

[OhioBob]

And if you have different engines, it will be a weighted average. Weighted by what, I don't know off the top of my head. Probably mass flow rate.

Thrust weighted. Like so (F is thrust):

I think it is more correct to say it is mass flow rate weighted. That is,

I_sp = (á¹Â₁∙I_sp1 + á¹Â₂∙I_sp2 + ...) / (á¹Â₁ + á¹Â₂ + ...)

Note that Ṡ= F/(g_o∙I_sp). Therefore, by substituting F/(g_o∙I_sp) for Ṡand multiplying through by g_o, we get

- - - Updated - - -

I certainly agree that it can be calculated from mass flow rates, but it is incorrect to call it a mass flow rate-weighted average of the Isps.

A thrust weighted average would be,

I_sp = (F₁∙I_sp1 + F₂∙I_sp2 + ...) / (F₁ + F₂ + ...)

which is incorrect. I think "mass flow rate-weighted average" is the correct way to say it.

Edited September 26, 2015 by OhioBob

[Red Iron Crown]

I realized my mistake while thinking about it on the drive home today. It was the substitution of á¹Â*Isp for F that was throwing me, as well as the omission of g (though since that is applied to all terms on both top and bottom of the fraction it can be factored out).

Apologies Slashy and thanks for the correction (and your well-illustrated one, too, OhioBob).

[GoSlash27]

RIC,

Certainly no apology needed. I was the one who wandered off into the weeds and I think this gave me some food for thought on a problem I've been wrestling with.

Best,

-Slashy

[OhioBob]

It's easy to make mistakes when working with these kinds of problems. I've often seen people incorrectly compute Isp using a thrust-weighted average (I think I made the same mistake the first time I did it). A similar mistake often occurs when computing average densities. For example, what is the density of a solution containing of 1 kg water (specific gravity = 1) and 1 kg of ethanol (specific gravity = 0.789)? How about 1 liter of water and 1 liter of ethanol?

[Padishar]

Indeed, this is the cause of KER showing wrong ISP values for multi-engine setups, it uses mass flow rates and gets the wrong answers. The trouble is that the mass flow rate for each engine is also inversely proportional to the Isp of the individual engine which alters the weighting. I'm currently fixing this in KER but it's also complicated by the need to account for the individual thrust vectors of the engines. E.g. if you have an LV-N pointing up and 4 909s pointing sideways (so they balance out and are just wasting fuel) then the effective Isp is much lower than if they were all pointing in the same direction.

Actually KER uses the correct mass flow rate weighting and is generating the correct values. I believe the reports of this problem are seeing the effects of the engines with different ISPs burning out a different times during the stage which results in a different effective Isp for the stage as a whole. E.g. in the case of the LV-N and 4 909s, if the 909s burn out before the LV-N then the effective Isp will be higher than the 389s given by the weighting.