How Do I calculate Delta-V on more than one engine?

[Wjolcz]

That is the question. I found a delta v calculator on the internets and I'm not sure about the number of engines. So when I have 3 LV-Ns do I sum their ISP together?

Maybe I'll just toss it here:

87 tons

70 after the burn

3 engines, every single one of them has 800 ISP

and this is the calc:

http://www.strout.net/info/science/delta-v/

[El wonso]

Don't sum.

[Wjolcz]

then how do i calculate that?

BTW I want this little baby go all the way to Duna:

And no, I don't want to use any mods to do that

Edited June 5, 2013 by Veeltch

[Uberick]

I've got that at 1706 d/v. The calculator agrees.

If the engines all have the same Isp, you only put in the ISP of your engine once. If you use multiple different engines with different ISPs, you average them to get their combined ISP, and then put that in once. Extra engines count as dead weight. Adding more will get you faster acceleration, but less efficiency. You're going to have to decide which you want to have depending on the mission. Ideally, you want to use only one of the most efficient engine, that'll get you the most delta v. Still, noone is going to strap an ion engine on anything bigger than a garbage can, it just takes forever to go anywhere.

1706 is plenty to get to Duna, the transfer only costs 1050.

Happy Launchings!

[falofonos]

as krl.krl said, the ISP of your engines doesn't sum.

So with your burn of 17 units of fuel, the deltaV is 1705.67

curses, ninja'd again.

[Wjolcz]

Ah! Great info you two! Thanks!

[UmbralRaptor]

Isp can be though of as how much impulse a given mass of fuel provides. Adding more engines with the same Isp increases the thrust, but does not change how much each unit of propellant affects the craft's momentum. If all engines have the same Isp, just use that; they act like a single giant engine with extra mass and thrust.

[tavert]

If you use multiple different engines with different ISPs, you average them to get their combined ISP, and then put that in once.

Careful, it's not arithmetic average when you combine engines with different specific impulses. It's a bit more complicated than that, you have to consider thrust and fuel mass flow rate.

Let's do 2 engines to start, say an LV-N combined with an LV-909 operating in vacuum as an example. Hopefully the extension to arbitrary engines and number of engines should be intuitive enough.

Engine 1 has stats thrust_1 and isp_1. Fuel flow rate is given by thrust_1 / (9.81 m/s^2 * isp_1). The 9.81 m/s^2 is just a conversion factor since Isp is given in seconds (refer to the Scott Manley video for a longer explanation). For our example let's say engine 1 is an LV-N, giving flow_1 = 60 kN / (9.81 m/s^2 * 800 s) = 0.007645 tons / s

Now for engine 2 being an LV-909, we get flow_2 = 50 kN / (9.81 m/s^2 * 390 s) = 0.01307 tons / s.

Total thrust and total fuel flow just add, so thrust_total = thrust_1 + thrust_2 = 110 kN, and flow_total = flow_1 + flow_2 = 0.0207 tons / s

So we get effective Isp as a function of thrust_total and flow_total:

Isp_effective = thrust_total / (9.81 m/s^2 * flow_total), which for our example combination gives 541.3 s.

TLDR summary, you actually want the reciprocal of the thrust-weighted-average of the reciprocal Isp's.

Edited June 6, 2013 by tavert

[tomf]

The effective ISP of multiple engines firing at once is (Thrust_Engine1 * ISP_Engine1 + Thrust_Engine2 * ISP_Engine2 ...)/(Thrust_Engine1 + Thrust_Engine2 ...)

[tavert]

The effective ISP of multiple engines firing at once is (Thrust_Engine1 * ISP_Engine1 + Thrust_Engine2 * ISP_Engine2 ...)/(Thrust_Engine1 + Thrust_Engine2 ...)

Incorrect. For my example of one LV-N and one LV-909, that would give (60 * 800 + 50 * 390) / 110 = 613.6. Both Engineer and MechJeb agree with the number I calculated above, 541.

[Supernovy]

I believe, then, that the total Isp is the average Isp weighted by mass flow rate.

I tried the calculation this way with your numbers and arrived at 541.7s. May have been an error on my part.

EDIT: thinking about it, this seems intuitive - impulse per mass with bigger contributions from greater mass per time. But, this doesn't come cleanly out of what you derrived (unless I'm missing something) and I can't ignore that 0.4s difference.

Edited June 6, 2013 by Supernovy

[tavert]

I think that should be a valid way of looking at it, since (isp_1 * flow_1 + isp_2 * flow_2 + ...) / (flow_1 + flow_2 + ...) is proportional to (thrust_1 + thrust_2 + ...) / (flow_1 + flow_2 + ...), and the constant of proportionality is 9.81 m/s^2 like it should be. The 0.4 difference might just be a rounding error.

[Imaginer1]

Reference: http://wiki.kerbalspaceprogram.com/wiki/Tutorial:Advanced_Rocket_Design

Incorrect. For my example of one LV-N and one LV-909, that would give (60 * 800 + 50 * 390) / 110 = 613.6. Both Engineer and MechJeb agree with the number I calculated above, 541.

That's incredibly odd...

[tavert]

I'm having a hard time finding references to back myself up here (anybody have access to a spacecraft engineering textbook that covers this?), but that equation on the KSP wiki is wrong.

There's no logical reason to take a thrust-weighted average of the Isp. Isp is proportional to thrust divided by mass flow rate, so why would you square the thrust in trying to compute an average?

[Imaginer1]

http://www.grc.nasa.gov/WWW/k-12/airplane/specimp.html

Okay, there are the actual equations. Let me do some math, alright?

[Rickenbacker]

then how do i calculate that?

BTW I want this little baby go all the way to Duna:

And no, I don't want to use any mods to do that

You know, you have three engines doing nothing but add weight on that thing! Why not flip the second half, and when docking it, rotate it so that the engines are between the first half's. That way you can use all six engines to get a shorter burn!

[Imaginer1]

Here you go:

The ISP of multiple engines.

All original equations come from http://www.grc.nasa.gov/WWW/k-12/airplane/specimp.html

[tomf]

Hmm, yes I have always just used the answer from the wiki that does appear to be wrong. I'm surprised now that my rockets have always made it to orbit.

[Wjolcz]

Alright guys! I calculated stuff correctly this time and found out that that thing actually had 3500 m/s of Delta V! Went to Duna on one tank only! xD

Great thanks for help anyway!

Edited June 6, 2013 by Veeltch

[jbakes]

Is there anyway someone can simplify this in a way that I can understand it?

I'm still confused on how to calculate the ISP of different engines.

 

[Snark]

3 minutes ago, jbakes said:

Is there anyway someone can simplify this in a way that I can understand it?

I'm still confused on how to calculate the ISP of different engines.

Side note:  you just necro'd a thread that's been lying dormant for two and a half years. That's usually not a great idea-- tends to confuse the issue, folks looking at the thread may not notice the dates and realize that it's an obsolete thread, and often much of what's in the thread will be totally irrelevant due to game mechanics having changed since the original posts went out.  (By a happy chance, the particular topic discussed in this thread is still relevant and valid, so I'll go ahead and respond.)

Figuring out the net Isp of multiple engines of differing Isp working together is not just a matter of averaging the Isp.  You use the formula that Imaginer1 gives, above:

• Take the total thrust of all the engines
• Divide by the sum of "thrust / Isp" for each of the engines
• That's your net Isp.

Thus, let's say I have one engine with a thrust of 100 kN and an Isp of 350 s, plus an engine with a thrust of 200 kN and an Isp of 250 s.  What's the net Isp?

• Total thrust = 100 + 200 = 300 kN
• Thrust / Isp for engine #1 = 100 / 350 = 0.2857 kN / s
• Thrust / Isp for engine #2 = 200 / 250 = 0.8 kN / s
• Putting it all together, total Isp = 300 / (0.8 + 0.2857) = 276 s

 

[jbakes]

48 minutes ago, Snark said:

Ok got it, this clear things up, thank you.

 

 

[PnDB]

And, to add to Snark's concise answer, consider the special case similar to the original poster's where you have three identical engines burning at the same time.

 

Engine 1:  thrust of 100 kN and Isp of 350 s

Engine 2:  thrust of 100 kN and Isp of 350 s

Engine 3:  thrust of 100 kN and Isp of 350 s

Total thrust = 100 + 100 + 100 = 300 kN

 

Thrust/Isp for Engine 1 = 100 / 350 = 0.2857 kN/s

Thrust/Isp for Engine 2 = 100 / 350 = 0.2857 kN/s

Thrust/Isp for Engine 3 = 100 / 350 = 0.2857 kN/s

Putting it all together, total Isp = 300 / (0.2857+0.2857+0.2857) = 350 s

 

This can be extended to N identical engines; Isp is the same as if you had one of that engine.

Putting it all together for N identical engines, total Isp = N * (thrust of one engine) / (N * thrust of one engine/Isp of one engine) ... the Ns cancel out , the thrusts cancel out, and you end up with just the Isp remaining.

 

 

[Edax]

On 6/5/2013 at 3:56 PM, Veeltch said:

then how do i calculate that?

BTW I want this little baby go all the way to Duna:

And no, I don't want to use any mods to do that

Calculating Delta V for that is easy, it's zero.  Your front engines and rear engines will negate each other, and you will fail to move in any direction.  That's what happens when you let Sir Issac Newton design a ship.

[Wjolcz]

5 hours ago, Edax said:

Calculating Delta V for that is easy, it's zero.  Your front engines and rear engines will negate each other, and you will fail to move in any direction.  That's what happens when you let Sir Issac Newton design a ship.

No way

Those 2013 posts of mine are just as cringey as old posts on Facebook. Any mod reading this feel free to lock it.

Edited February 1, 2016 by Veeltch