Delta-V question in relation to thrust

[SlinkyBlue]

So, I've got a question for you all. Maybe there's a set answer or maybe there's a debate going on about it, either way I'm curious as to what you guys think.

I've been designing a large ship, with two orange fuel tanks, to go to Jool. Along with spots to hold many probes, I included 5 docking hardpoints for nuclear engines to be attached on-orbit. Hey, it looked cool.

While I was pondering this at work today, I came across a thought; Adding engines increases fuel consumption right along with the added thrust, of course, so therefore the ship won't "go any farther" (delta-V) with 5 engines as opposed to like 2 or 3. When you factor in the mass of the added engines, I thought that it might even *decrease* my delta-v by adding more engines onto the same chassis.

Then I thought: does this same logic go all the way down to one engine?

My question for you: Is ONE and ONLY ONE engine always the best way to get the most delta-V out of my ship? Do the added engines and thrust reduce the delta-V from the weight that is added?

Thanks for any help, I'm sure this concept is well understood by most of you, but it's not something I could figure out for myself.

-Slinky

[Dynamo]

Ah, a math question. I've actually just come to grips with this one - i've been doing the math for a Jool system mission to seed every body with probes. To put it in the short way, the Delta-V does not change based on the number of engines you add on (seems strange, however),only TWR. Stop reading now if you don't like a little math, but here's why:

This is our standard formula for Delta-v (straight from the wiki which has awesome guides for all the math), the net gain in energy we can exert on our spacecraft.

Our variables here are as follows: Mstart = "Wet mass", all fuel tanks full, Mend= "Dry mass", all tanks empty, Isp is the specific impulse or efficency of your engine (this is listed for every engine, plug it in), and the last number is the acceleration of gravity. The "ln" stands for the natural log, it's just an operation on the sci calc (don't need to explain that here). Plug all that in for delta-v!

Notice one thing from all that garbage, however: The formula doesn't care about the total mass of the spacecraft, only the fuel mass (which is the difference between Mstart and Mend). Therefore, you are right: since the engine mass is added to both Mstart and Mend, the number will not affect delta-v! What it does change, however, is TWR (thrust-to-weight ratio). This is how fast the craft accelerates with the thrust of its engines, or how fast it dispenses the Delta-V it has. You will find it impossible to use a large interplanetary ship with a low TWR, as they take forever to make transfer burns, and cannot deliver the Delta-V when it counts to save a mission in emergencies.

So, the rule is with engines: Add as many as you like as long as you can haul them into orbit and onto the ship, and watch that TWR. Cheers!

P.S. Be warned! The NERVA's have a very poor TWR to balance for high ISP. You may need to add 10 of them to get anywhere with those two oranges! Don't be afraid to use other engines.

[SlinkyBlue]

Ah, a math question. I've actually just come to grips with this one - i've been doing the math for a Jool system mission to seed every body with probes. To put it in the short way, the Delta-V does not change based on the number of engines you add on (seems strange, however),only TWR. Stop reading now if you don't like a little math, but here's why:

This is our standard formula for Delta-v (straight from the wiki which has awesome guides for all the math), the net gain in energy we can exert on our spacecraft.

Our variables here are as follows: Mstart = "Wet mass", all fuel tanks full, Mend= "Dry mass", all tanks empty, Isp is the specific impulse or efficency of your engine (this is listed for every engine, plug it in), and the last number is the acceleration of gravity. The "ln" stands for the natural log, it's just an operation on the sci calc (don't need to explain that here). Plug all that in for delta-v!

Notice one thing from all that garbage, however: The formula doesn't care about the total mass of the spacecraft, only the fuel mass (which is the difference between Mstart and Mend). Therefore, you are right: since the engine mass is added to both Mstart and Mend, the number will not affect delta-v! What it does change, however, is TWR (thrust-to-weight ratio). This is how fast the craft accelerates with the thrust of its engines, or how fast it dispenses the Delta-V it has. You will find it impossible to use a large interplanetary ship with a low TWR, as they take forever to make transfer burns, and cannot deliver the Delta-V when it counts to save a mission in emergencies.

So, the rule is with engines: Add as many as you like as long as you can haul them into orbit and onto the ship, and watch that TWR. Cheers!

P.S. Be warned! The NERVA's have a very poor TWR to balance for high ISP. You may need to add 10 of them to get anywhere with those two oranges! Don't be afraid to use other engines.

Thank you for the reply. The math is a bit over my head, but the TWR seems to be the thing I was not quite accounting for. So, obviously if we're discussing an alternative engine to throw onto the ship, the 909 is out of the question. Would some 45's make more logical sense to you?

[GoDores]

Notice one thing from all that garbage, however: The formula doesn't care about the total mass of the spacecraft, only the fuel mass (which is the difference between Mstart and Mend). Therefore, you are right: since the engine mass is added to both Mstart and Mend, the number will not affect delta-v!

This isn't right. Adding the same number to the numerator and denominator of a fraction changes the fraction.

Example: Ship with 10t fuel and a single 1t engine (no other payload). Mstart=11 and Mend=1. Mstart/Mend = 11/1 = 11. Adding a second 1t engine gives Mstart=12 and Mend=2. Mstart/Mend = 12/2 = 6.

Adding engines will increase the mass of your ship and therefore reduce the total dV, so one engine will always give you the most total dV with all else being equal. But a single engine might give you such a poor TWR that you can't make an efficient transfer burn, so there are times when you might need (or just prefer) additional engines for shorter burns.

[metaphor]

Notice one thing from all that garbage, however: The formula doesn't care about the total mass of the spacecraft, only the fuel mass (which is the difference between Mstart and Mend). Therefore, you are right: since the engine mass is added to both Mstart and Mend, the number will not affect delta-v!

That is not true. The formula doesn't care about the difference between Mstart and Mend, it cares about the ratio between them. A ship that is 110 tons full and 10 tons empty is going to have a lot more delta-v than a ship that is 200 tons full and 100 tons empty. The mass ratio is what matters.

So yes, adding more engines of the same type to your ship will always decrease your delta-v since they contribute to the empty mass.

But, delta-v might not be all that matters here unless you want to be super efficient. TWR is a problem with large ships. If you only put a single nuclear engine on a big ship, you're going to be looking at ion-engine-long burn times and needing to do more than one pass to get out of Kerbin orbit. The extra engines might not weigh too much compared to the rest of your ship. If you have 2 orange fuel tanks, that's already 8 tons of empty mass, so adding 4 more nuclear engines is not going to make a huge difference.

So, if you want to be super efficient with your fuel, use only one engine. If you want shorter burn times, use more than one engine.

[mcirish3]

My question for you: Is ONE and ONLY ONE engine always the best way to get the most delta-V out of my ship? Do the added engines and thrust reduce the delta-V from the weight that is added?

-Slinky

Short answer is what you said above and GoDores said below.

THe formula is correct but as GoDores pointed out below the added mass of the engines will reduce delta-v.

This isn't right. Adding the same number to the numerator and denominator of a fraction changes the fraction.

Example: Ship with 10t fuel and a single 1t engine (no other payload). Mstart=11 and Mend=1. Mstart/Mend = 11/1 = 11. Adding a second 1t engine gives Mstart=12 and Mend=2. Mstart/Mend = 12/2 = 6.

Adding engines will increase the mass of your ship and therefore reduce the total dV, so one engine will always give you the most total dV with all else being equal. But a single engine might give you such a poor TWR that you can't make an efficient transfer burn, so there are times when you might need (or just prefer) additional engines for shorter burns.

Of course if your design is robust enough you could have it set up to use some onion or better yet asparagus staging (even if the main ship is in orbit, takes some work with manually decoupling or rearranging your staging or a combination of the two and some innovative fuel transfers.) Doing this will get you more delta-V but you will have to shed parts as you go along. Good luck

Edited July 29, 2013 by mcirish3

[Frederf]

Highest mass fraction and specific impulse always result in highest dV (per configuration). The optimization comes from the fact that different performance rockets need different amounts of dV to do the same mission. A TWR of 1.01 means that it'll take more dV to lift off from Kerbin than a TWR of 2 or so. The TWR 1.01 might have 500 more dV but it might take 1000 more dV to get into orbit in that configuration. Even orbital maneuvers suffer at very low TWRs because you can't give your impulse at the better points in the path due to Oberth.

[Wesreidau]

The TL;DR is this; rocket engines tend to be either efficient (ion, nerva) or powerful (mainsail, SRB). You are correct in assuming less engines are more efficient. However, more engines will allow you to make more radical maneuvers, such as braking into an orbit, with much less time. If you go with a single engine be prepared to carefully plot your course and burn early and often. If you want a better margin of error, take a second NERVA to approximately double your TWR. Don't toggle one off; it would be a waste to carry all those tons into Kerbin escape and not use them. Personally though, I would take a single NERVA.

[Bacterius]

Yes, basically dV is orthogonal to thrust, so you can maximize your dV by minimizing your thrust (i.e. less engine mass, more fuel mass) but you still care about thrust because:

A) you actually need to be able to lift off from whatever celestial body you are on, that is, you require a TWR greater than 1

with a very low thrust you will spend forever in the atmosphere, bleeding away dV which could have been spent on orbital maneuvers instead had you actually gotten in orbit quickly

C) you need to complete your burns in reasonable time, else you will be way off and will spend a lot of time thrusting, correcting, thrusting, correcting, and so on (unless you use an autopilot and can accurately compensate)

D) as Frederf said above, an extremely low thrust can't take advantage of things like the Oberth effect in any appreciable way

So using a single engine does not always result in the best possible craft. Or, in other words, it depends.

Edited July 29, 2013 by Bacterius