Isp calculation of mixed engines stage

[VoidFoo]

Looking for some help. I'm getting a different result for my Isp calculation than KSP / KER, and I can't figure out why.

My dummy test rocket has a single stage:
- 1 Reliant engine and two FL-T800 tanks
- 3 Hammer SRBs
- Dummy 20.6t payload
- Atmosphere, not vacuum

My calculation is giving me and Isp of 187s (and therefore 924 m/s DV), KER is saying 224s (and therefore 1109 m/s DV).

Wiki says sum of thrust of each engine, divided by sum of (thrust / Isp). ( https://wiki.kerbalspaceprogram.com/wiki/Specific_impulse#Multiple_engines )

            3 * 197.9 + 205.161
Isp = ----------------------------------- = 187.23
      (3 * 197.9 / 170) + (205.161 / 265)

What am I doing wrong?

Forum won't let me insert image, but here is the screenshot: https://imgur.com/a/IGwdTuW

[king of nowhere]

perhaps the problem is that the hammers will run out much sooner than the reliant. so you won't have 1 stage, you have 2 stages where first you have reliant and 3 hammer, for Isp 187, and then you have reliant alone, for Isp 265, and the 224 given is an average of those two weighted for their burn times.

[OhioBob]

@VoidFoo, your calculation is correct, it looks like KER is wrong.

I built the same rocket as you and I'm seeing the same numbers in KER.  However, if you look at the built-in KSP dV indicator, it shows the Isp as 187 s, which agrees with you.

I also confirmed the correctness of your calculation by performing an in-game test.  I sent the rocket to the launchpad, ignited the engines, and ran it until the SRBs burned out.  This took about 24 seconds, during which we burned 1125 units of solid fuel, 210 units of oxidizer, and 172 units of liquid fuel.  That's a total mass of 10.3475 metric tons of propellant, which gives us a propellant flow rate of 10.3475 / 24 = 0.43115 t/s.  Thus, the specific impulse is,

Isp = thrust / (flow rate * go) = 798.85 / (0.43115 * 9.80665) = 189 s

I'm off a little bit from your calculation because of error in my measurements.

But as far as computing the delta-v is concerned, @king of nowhere is correct, you have to consider it a 2-stage rocket.  You must compute the dV for the first 24 seconds when all engines are running, and then compute separately the dV for the period of time when just the Reliant is running and burning what propellant remains.

You might want to report your findings in the KER thread so perhaps the dev can fix the error.
 

Edited September 23, 2021 by OhioBob

[OhioBob]

I've been trying to figure out how KER comes up with that 224.6 s number but I can't reproduce it.  Computing the average Isp over the entire burn (as king of nowhere suggests), I come up with a number of 216.2 s.

[VoidFoo]

Both you guys' explanations help out a bunch. Thanks!

I switched the calculation to two stages:
- SRBs running: mass 41.53 -> 31.23, Isp 187.24 --> 522.95 m/s DV
- SRBs empty: mass 31.23 -> 25.1, Isp 265 --> 567.97 m/s DV
-------
1090.92 m/s DV

Used the fuel consumption rate on the wiki, which matches your in-game fuel consumption test. Working backwards that would give a total average Isp of 220.84 s I suppose? Yet another value for the Isp collection

Inspired by your in-game test I put a probe core on it, hyperedited it into Kerbol orbit and burned prograde. Payload now 20.92t and the rest now using vacuum values, the calculated DV matched the orbital velocity increase exactly (1255.2 m/s DV). So it all seems good!

Did not know about that built-in KSP indicator btw, TIL...

[OhioBob]

2 hours ago, VoidFoo said:

Working backwards that would give a total average Isp of 220.84 s I suppose?

I computed that number too, using the same method.

The 216.2 s number I got this way...  Specific impulse is typically computed as thrust/(fuel flow rate*go), but I figure we could also take (thrust*time)/((fuel flow rate*time)*go).  Of course thrust*time is the total impulse of the rocket, and fuel flow rate*time is just the total amount of fuel. I compute the burn time of the SRBs to be 23.69 s and that of the Reliant to be 101.34 s at full thrust.  Therefore,

((197.897 * 3 + 205.161) * 23.69 + 205.161 * (101.34 - 23.69)) / (16.4375 * 9.80665) = 216.23 s

The same number can be arrived at more simply this way, Σ(fuel mass*Isp)/Σ(fuel mass).

(8.4375*170 + 8*265) / (8.4375 + 8) = 216.24 s

The 220.84 s number is probably more correct, but I doubt KER would compute it that way.  I was attempting to find a method that I though KER might use to compute the combined Isp.  Of course neither method nor any other method I tried would reproduce KER's 224.6 s number.  I don't know where that comes from.