Dual propulsion efficiency

[Guest]

Say I have a craft powered by both an LFO engine with 350 Isp and a monoprop engine with 300, would I get more delta-v out of burning the more or the less efficient propellant first? Or both at the same time?

Would the answer be different if I had vastly different impulses and/or propellant densities (eg. hydrolox+xenon)?

Edited November 23, 2016 by Guest

[James Kerman]

Yes, you will get more dv burning your less efficient fuel first - this means your more efficient fuel pushes less mass.

[Streetwind]

Also, it does not change if the difference between impulses is larger. Finally, it is independent from propellant densities. Only raw mass is important, and using the lowest impulse fuel first is always more efficient.

Keep in mind though that there are situations were you deviate from this rule. For example, I'm sure as heck not going to start my Jool transfer burn with my RCS thrusters, even if I have lots of monoprop. Also, a ship with both chemical engines and ion drives is likely going to conserve the chemical engines until the end of the trip... because the ion engines aren't strong enough to land on Moho, for example.

Edited November 23, 2016 by Streetwind

[FancyMouse]

Or if you want a more mathematical proof - suppose I have two types of fuel of mass m1, m2 resp., and engines at Isp1, Isp2, resp., assume a unit system of empty mass m0=1 and g=1 (just for formula simplicity). Also assume Isp1 > Isp2

Burning m1 first gives dV=Isp1*ln((1+m1+m2)/(1+m2)) + Isp2*ln(1+m2).

Burning m2 first gives dV'=Isp2*ln((1+m1+m2)/(1+m1)) + Isp1*ln(1+m1).

dV-dV'=(Isp1-Isp2)*ln((1+m1+m2)/(1+m1)(1+m2))

Since m1,m2>0, the stuff inside ln is <1, so ln(...)<0. So if Isp1>Isp2, then dV-dV'<0, meaning burning m2 first (less efficient one) gives more delta V.

 

Personally I've never found any convincing intuitive argument until I sit down and write a math proof.

Edited November 23, 2016 by FancyMouse

[Snark]

@James Kerman nailed it, and @FancyMouse proved it mathematically.     The simple answer is:

To maximize dV, always burn your lowest-Isp fuel first.

This is why (at least, in terms of raw dV efficiency) SRBs are a great idea on the launch pad, but not so much for upper stages:  they have significantly lower Isp than LFO engines.  (Nothing wrong with using SRB in an upper stage for other reasons, of course-- as a challenge, or role-playing, or running realism mods that add certain disadvantages for liquid-fuel engines, or what-have you.  I'm just talking about dV efficiency here.)

 

[MaxL_1023]

I have this problem in RSS/RO - I would LOVE to use hydrolox for my Mars/Jupiter/Venus orbit injection stage, but it all boils off on me. I have to use hypergolics, which are less effective, making my rockets much, much larger on the pad for the same total impulse. 

[Maxsimal]

On 11/23/2016 at 0:01 PM, MaxL_1023 said:

I have this problem in RSS/RO - I would LOVE to use hydrolox for my Mars/Jupiter/Venus orbit injection stage, but it all boils off on me. I have to use hypergolics, which are less effective, making my rockets much, much larger on the pad for the same total impulse. 

You know you can also use cryogenic tanks?  AFAIK they prevent all boiloff at the cost of some EC.

Btw, to answer the OP's question with a little more nuance:

Impulse doesn't matter UNLESS you're dealing with the oberth effect.  If you have a high efficienty, low impulse engine, you can't get as much out of the oberth effect as you can with a higher impulse engine - though you can split up burns to still get the oberth effect boost before you've reached escape velocity.  

Propellant density doesn't matter - but different tankage dry mass penalties do.  For instance, if your high density propellant has a tank dry mass fraction is 3% while your low density propellant tank dry mass fraction is 10%, it has an impact on your ISP.   Once you're in space already with a particular ship, though, that's locked in, so you should burn the low-ISP engine first.

 

[Starman4308]

18 minutes ago, Maxsimal said:

You know you can also use cryogenic tanks?  AFAIK they prevent all boiloff at the cost of some EC.

Btw, to answer the OP's question with a little more nuance:

Impulse doesn't matter UNLESS you're dealing with the oberth effect.  If you have a high efficienty, low impulse engine, you can't get as much out of the oberth effect as you can with a higher impulse engine - though you can split up burns to still get the oberth effect boost before you've reached escape velocity.  

Propellant density doesn't matter - but different tankage dry mass penalties do.  For instance, if your high density propellant has a tank dry mass fraction is 3% while your low density propellant tank dry mass fraction is 10%, it has an impact on your ISP.   Once you're in space already with a particular ship, though, that's locked in, so you should burn the low-ISP engine first.

 

On high vs. low-thrust engines: that's a big part of why people are looking into VASIMR engines, as you can trade specific impulse for thrust for the same electrical consumption.

I'm not 100% sure what you're saying about propellant density is correct. Tankage dry mass is wholly independent of specific impulse; it comes out inside the logarithmic instead of the multiplicative part of the rocket equation. It does lead to some interesting math, though: dV = Isp * g0 * ln(payload + fuel + tankage / payload + tankage).

The equations I'll use when explicitly including dry tank masses:

dV = g0 * Isp * ln(payload + fuel + tankage / payload + tankage)

fuel# = fuel + tankage (as I'm usually looking to add a total tank mass to some fixed payload + engine)
tank ratio = full tank / dry tank
I'll use alternating ({({ })}), because multiply nested parentheses get confusing.

dV = g0 * Isp * ln (payload + fuel# / payload + (fuel# / tank ratio))

fuel# = payload * ({e^(dV/{g0 * Isp})} - 1) / (1 - {e^(dV/{g0 * isp}) / tank ratio)

Because it makes the math a lot cleaner:
expDV = e^(dV / {g0 * Isp})

fuel# = payload * (expDV - 1) / (1 - {expDV / tank ratio})

 

Edited December 12, 2016 by Starman4308

[Maxsimal]

2 minutes ago, Starman4308 said:

On high vs. low-thrust engines: that's a big part of why people are looking into VASIMR engines, as you can trade specific impulse for thrust for the same electrical consumption.

I'm not 100% sure what you're saying about propellant density is correct. Tankage dry mass is wholly independent of specific impulse; it comes out inside the logarithmic instead of the multiplicative part of the rocket equation. It does lead to some interesting math, though: dV = Isp * g0 * ln(payload + fuel + tankage / payload + tankage).

The equations I'll use when explicitly including dry tank masses:

dV = g0 * Isp * ln(payload + fuel + tankage / payload + tankage)

fuel# = fuel + tankage (as I'm usually looking to add a total tank mass to some fixed payload + engine)
tank ratio = full tank / dry tank
I'll use alternating ({({ })}), because multiply nested parentheses get confusing.

dV = g0 * Isp * ln (payload + fuel# / payload + (fuel# / tank ratio))

fuel# = payload * ({e^(dV/{g0 * Isp})} - 1) / (1 - {e^(dV/{g0 * isp}) / tank ratio)

Because it makes the math a lot cleaner:
expDV = e^(dV / {g0 * Isp})

fuel# = payload * (expDV - 1) / (1 - {expDV / tank ratio})

 

I'm sorry I wasn't being precise in my terminology.  Rather than saying 'impacts your ISP' I should have said something more like "affects your effective fuel efficiency,"  The latter is what the OP is really asking about when discussing when to burn what, and because this KSP, ISP is often used as a shorthand for fuel efficiency, rather than its precise technical meaning.  

[Starman4308]

1 minute ago, Maxsimal said:

I'm sorry I wasn't being precise in my terminology.  Rather than saying 'impacts your ISP' I should have said something more like "affects your effective fuel efficiency,"  The latter is what the OP is really asking about when discussing when to burn what, and because this KSP, ISP is often used as a shorthand for fuel efficiency, rather than its precise technical meaning.  

It's alright.

As you can probably tell from me having that equation (in a quick-and-dirty Java program I use for off-the-cuff stuff to boot), I tend to be very precise about things. I'm the sort to immediately hit timewarp after a maneuver node completes so there is the least possible error caused by the non-rails physics engine.

[foamyesque]

FWIW, propellant density can matter because compact propellants can be much easier to fit into fairings or otherwise put on stacks. It doesn't impact the performance once you're up there (mostly -- you can still get floppy craft) but it can have a very important effect on the rocket that gets you up there.