Is it always better to use multi stage rockets?

[Januz Johansen]

Hello all!
I was wondering if there is a scenario,
where a single stage rocket will be superior to a multi-stage rocket, and if so, why?
i'm under the impression that multi stage is always better, but i don't think that is entirely correct.

Good day to you all

 

[phinds]

Your question is very vague. The V2 (single stage) is a rocket that had more impact on England that the American space program's multi-stage rockets, so I'd guess it depends on what you want to do.

 

[Januz Johansen]

Your question is very vague. The V2 (single stage) is a rocket that had more impact on England that the American space program's multi-stage rockets, so I'd guess it depends on what you want to do.

Oh yes sorry i see what you mean. I mean is it always better to use a multi stage rocket to getting a higher velocity, lifting a bigger payload, or traveling longer. Or are there some cases where it is cheeper or in any way better to use a single stage rocket to achieve one of these things.
Thanks

 

[jbriggs444]

Oh yes sorry i see what you mean. I mean is it always better to use a multi stage rocket to getting a higher velocity, lifting a bigger payload, or traveling longer. Or are there some cases where it is cheeper or in any way better to use a single stage rocket to achieve one of these things.

That's still pretty vague.

What trade-offs can you think of between the competing approaches?

 

[rootone]

Multi stage rockets have an advantage for long range or heavy lifting because the weight of expended fuel tanks is dispensed with,
which means the rocket makes more effective use of the remaining fuel.
On the other hand multiple stages introduce engineering complications, and stage separation is often the cause of a failure.

 

[Januz Johansen]

Multi stage rockets have an advantage for long range or heavy lifting because the weight of expended fuel tanks is dispensed with,
which means the rocket makes more effective use of the remaining fuel.
On the other hand multiple stages introduce engineering complications, and stage separation is often the cause of a failure.

Thank you rootone :D

 

[sophiecentaur]

Ideally, you would have a Rocket motor with zero mass - all the mass would be in the fuel and ejects. A solid fuel rocket is nearer ideal but it is not controllable.
When reusable first stages can work reliably, you have the best of both worlds (for Earth launches, at least). That is work in progress. There is nothing fundamentally desirable about a single stage system, I think.

 

[CWatters]

If multistage was always better then there wouldn't be a limit to the number of stages. We would have rockets with 10, 20, 30... stages. So must be an optimum number of stages and I imagine that's depends on a bunch of factors.

 

[sophiecentaur]

If multistage was always better then there wouldn't be a limit to the number of stages. We would have rockets with 10, 20, 30... stages. So must be an optimum number of stages and I imagine that's depends on a bunch of factors.

This could be achieved with a solid fuel arrangement in which the structure of the combustion chamber was part of the fuel and would be eroded and ejected at the same rate as the fuel was used up. An infinite number of stages.
One limiting factor with multi stages of the conventional style is that the combustion mechanism needs to have strength to deal with the forces involved. This is an overhead with each stage.

 

[Cutter Ketch]

The advantage of a two stage rocket is that you get to drop the structure of the first stage so that the fuel of the second stage isn't being used to accelerate dead weight. The disadvantage is the extra structure and rocket motors you have to carry in order to have the staged system. Two stages cease to be advantageous at the point that the structure you get to drop weighs less than the extra structure and rocket motors you have to add in order to be able to drop the first stage.

Ok, that's oversimplifying a little in that the first stage also had to carry that extra second stage weight, but that's the basic idea.

In detail, let m1 be the mass of the first stage structure. Let f1 be the mass of the first stage fuel. Let f2 be the second stage fuel. Let m2 be the mass of the structure needed to add a second stages worth of fuel to a single stage rocket. Let me be the extra mass to make it truly a second stage. Let mp be the mass of the payload. Let ve be the exhaust velocity, and let the burn rate be constant.

For a single stage rocket:

v final = ve ln[(f1+m1+f2+m2 + mp)/(m1+m2+mp)]

For a two stage

v final = ve ln[(f1+m1+f2+m2 + mp + me)/(m1+m2+mp+me+f2)] + ve ln[(f2+m2+me + mp )/(m2+me+mp )]

Divide the two stage v by the single stage v and see when the ratio >1. Basically as long as m1 is significantly larger than me two stages are better.