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# Delta V calculation help

## Question

Alright. Let me make on thing clear. I know how to calculate delta v. I have the math done and burned into my head. But I cam across a problem, how do I get the ISP, for different engines on the same stage? So say if I have a "MainSail" and a "Thud" sharing the same fuel on the same stage, how to I get the ISP to put into my formula?

Edited by Fri3s3N

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Another way to compute without having to look up of the propellant flow rates,

Σ(T) / Σ(T/Isp)

11 minutes ago, Dman979 said:

Pretty close.

If you have 3 mainsails, 2 Skippers, and a thud, then multiply the Mailsail's Isp by 3, multiply the Skipper's Isp by 2, and then

3*Isp(mainsail)+2*Isp(Skipper)+Isp(Thud)

6 (for six engines)

No, that's not correct.  It is not a simple average of the Isp.  Nor is it a thrust-weighted average as many people mistakenly do.  It's a mass flow rate weighted average.

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As long as they use the same fuel source (all engines burning from the exact same tanks) then you just take the average of all the different Isp's.

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9 minutes ago, FullMetalMachinist said:

As long as they use the same fuel source (all engines burning from the exact same tanks) then you just take the average of all the different Isp's.

If they all have the same fuel source, I believe what you have to do is weight the contribution of each engine to the average ISP based on its fuel consumption per unit time. For example, if you have an engine that consumes 4 units/sec and one that consumes one, you would add the ISP of the lower-consuming engine to four times the ISP of the higher-consuming ne, then divide by 5. If they have totally separate fuel sources, then things get a  bit more complicated, because you have to calculate the dry mass of each stack based on where the other ones' fuel supply will be at flameout. If you have asparagus engines, it gets a bit easier, because you can add the dV of each asparagus stage sequentially, since the other stages will all remain full while the current one is burning.

Edited by herbal space program
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ISP = Total thurst / (Total propellant flow rate * go)

Just add up the thrusts and the propellant flow rates of the different engines.

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6 minutes ago, OhioBob said:

ISP = Total thurst / (Total propellant flow rate * go)

Just add up the thrusts and the propellant flow rates of the different engines.

Pretty close.

If you have 3 mainsails, 2 Skippers, and a thud, then multiply the Mailsail's Isp by 3, multiply the Skipper's Isp by 2, and then

3*Isp(mainsail)+2*Isp(Skipper)+Isp(Thud)

6 (for six engines)

Edited by Dman979
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8 minutes ago, OhioBob said:

Another way to compute without having to look up of the propellant flow rates,

Σ(T) / Σ(T/Isp)

^ This.  OhioBob's response is correct, everyone else who has posted thus far is mathematically incorrect, so don't use their formulas.  For anyone who's not up on their mathematical notation,

• Add up the total thrust of all engines.  Call this number A.
• For each engine, take its thrust divided by its Isp, and add all those numbers together.  Call this B.
• The overall Isp is A / B.

This stands to reason.  If you have, for example, a Mainsail and a couple of Ants... it doesn't really matter what the Ants' Isp is, since they're so tiny that the overwhelming majority of fuel expended is flowing through the Mainsail, so the net Isp will be very very very close to the Mainsail's.

Moving to Gameplay Questions.

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2 hours ago, Snark said:

^ This.  OhioBob's response is correct, everyone else who has posted thus far is mathematically incorrect, so don't use their formulas.  For anyone who's not up on their mathematical notation,

• Add up the total thrust of all engines.  Call this number A.
• For each engine, take its thrust divided by its Isp, and add all those numbers together.  Call this B.
• The overall Isp is A / B.

This stands to reason.  If you have, for example, a Mainsail and a couple of Ants... it doesn't really matter what the Ants' Isp is, since they're so tiny that the overwhelming majority of fuel expended is flowing through the Mainsail, so the net Isp will be very very very close to the Mainsail's.

Moving to Gameplay Questions.

Actually I'm pretty sure that what I said for OP's scenario works out to exactly the same thing as what you and Ohio Bob said, and that nothing else I said was wrong.  You can make your weighted average using either thrust or fuel consumption/time as a factor, because of course what  ISP represents is the proportional relationship between the two. IANARS, so maybe I came at it from the wrong side, but it's still the same answer.

And of course that formula still doesn't address the issue of what to do when you have multiple separate stages burning at the same time (like side SRBs, for example), because unless they run out of fuel at exactly the same instant you have to calculate the dV in  distinct segments, divided at the moment the first of the two stages runs out of fuel and you jettison the empty boosters. So this will require you to determine the time at which the shorter stage will run out and how much fuel will be in the longer stage at that moment, to calculate the dry mass of the first segment. You then have to subtract the dry mass of the side boosters to determine the wet mass of the next segment, which you'll then calculate based on the ISP of the remaining engine(s). For each separate non-identical concurrent stage, you need to calculate another segment. No?

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If you're not keen on doing all the math out by hand, also note that mods like KER and MechJeb can figure these out for you; either while building in the VAB?SPH, or in-flight.

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10 hours ago, herbal space program said:

For example, if you have an engine that consumes 4 units/sec and one that consumes one, you would add the ISP of the lower-consuming engine to four times the ISP of the higher-consuming ne, then divide by 5.

That's correct.  What you are describing is a mass flow rate weighted average.  It can be expressed mathematically as,

Σ(ṁ*Isp) / Σ()

where Σ(ṁ*Isp) is the summation of the product of mass flow rate and specific impulse, and Σ() is the summation of the mass flow rate.

We know that specific impulse is equal to,

Isp = T/(*go)

where T is thrust and go is the standard acceleration of gravity.  We can rearrange the equation to also give,

ṁ = T/(Isp*go)

So if we substitute T/(*go) for Isp in Σ(ṁ*Isp) and substitute T/(Isp*go) for ṁ in Σ(), we get

Σ(ṁ*T/(*go)) / Σ(T/(Isp*go))

Note that ṁ and go cancel out, so we end up with

Σ(T) / Σ(T/Isp)

which is the same equation that I posted.  Generally my equation is a bit easy to work with because the thrusts are more commonly known and easier to remember than the mass flow rates.

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When I started playing KSP, when I looked at such formulas, I was terrified... because I didn't understand them

Now, when I look at such formulas, I'm still terrified... because I understand them... ##### Share on other sites

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8 hours ago, OhioBob said:

That's correct.  What you are describing is a mass flow rate weighted average.  It can be expressed mathematically as,

Σ(ṁ*Isp) / Σ()

where Σ(ṁ*Isp) is the summation of the product of mass flow rate and specific impulse, and Σ() is the summation of the mass flow rate

Thank you for taking the time to confirm that these different ways of making weighted averages work out to the same answer, OhioBob.

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