Why do we need multistage rockets

[500]

For sake of simplicity I neglect gravity and drag forces. This is a formula of rockets final speed:

I = specific impulse or exhaust gasses velocity, M - total rocket mass, M(t) - final rocket mass, Mp - mass of the propellant. Since typical exhaust gasses velocity is about 3000 m/s, we get this simplified formula:

All we need to know for our calculations is total mass of rocket (M) and mass of propellant (Mp).

Now lets take Falcon 9 rocket as example. It has two stages. Here approximate weights:

425 t - total 1st stage
400 t - propellant in 1st stage

1 t - interstage adapter (connects 1st and 2nd stages)

94 t - total 2nd stage
90 t - propellant in 2nd stage

8 t - payload with fairing

Total weight: 425+1+94+8= 528 t

Lets calculate its final speed.

1st stage: V = 3000*ln(528/528-400) = 3000*ln(528/128) = 4251 m/s

Total second stage with payload is 94+8=102 t. So here its speed contribution:

2nd stage V = 3000*ln(102/102-90) = 3000*ln(102/12)= 6420 m/s

Together they provide 4251 + 6420 = 10,671 m/s

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Now lets calculate same total mass of propellant rocket but single state.

Two stages combined have 400+90= 490 t of propellant. Since we dont need the interstate adapter and second stage engine we save up to 2 tons of weight.

So we get 526 t total mass including 490 t of propellant.

And here its speed:

V = 3000*ln(526/526-490) = 3000*ln(526/36) = 8045 m/s

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Despite saving mass on interstage and second stage engine we lose more than 2,600 m/s of speed with same mass of propellant. Thats huge.

But there is more. Lets assume we still insist on 1 stage rocket, just make it bigger to increase speed. Lets increase propellant weight 2 times!

We get 1044 t total mass rocket (with same 8 t payload) and 980 t of propellant.

V = 3000*ln(1044/1044-980) = 3000*ln(1044/64) = 8376 m/s

We increased propellant weight twice, but speed increased only by 300 m/s. More than 2000 m/s less than 2 stage rocket with half of the propellant!

 

[Nilgiri]

It basically boils down to not carrying the empty weight of the (now redundant after fuel burn) structure compared to multi-stages (that discard them at discrete moments).

A hypothetical ideal system would be like a rope/taper/match burning where there is no structure at all, just fuel that burns from start to end.

 

[AZADPAKISTAN2009]

If energy source was Nuclear fuel , we won't need multi stage Rockets the unlimited supply of fuel from Miniature Nuclear power plant would give you enough power to fly the whole rocket intact into outer space

The fuel source we use is outdated 100 year old tech being refined and reapplied

 

[krash]

It basically boils down to not carrying the empty weight of the (now redundant after fuel burn) structure compared to multi-stages (that discard them at discrete moments).

A hypothetical ideal system would be like a rope/taper/match burning where there is no structure at all, just fuel that burns from start to end.

Also, I believe the different stage rocket motors are or, at least, can be optimised (specific pulse) for the different atmospheric conditions that they are meant to operate in.

 

[timmy_area51]

israeli shavit rocket :

simplistic as hell , nothing like the miztnefet hahaha

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no one really needs to understand all that mathmatical equations . a rocket carries both fuel and engine both of which are heavy .. when it's staged the stage engine is released and it becomes more light weight

 

[Nilgiri]

Also, I believe the different stage rocket motors are or, at least, can be optimised (specific pulse) for the different atmospheric conditions that they are meant to operate in.

Yup exactly! Good point. It's much cheaper to use non-cryo for lower bulk burn stage....till you have developed the economies of scale there too (depending on final rocket throw weight) where it becomes feasible there too.

 

[Hamartia Antidote]

If energy source was Nuclear fuel , we won't need multi stage Rockets the unlimited supply of fuel from Miniature Nuclear power plant would give you enough power to fly the whole rocket intact into outer space

The fuel source we use is outdated 100 year old tech being refined and reapplied

Nuclear rocket engines were achieved in the 1960's.

 

[500]

Generally speaking we can check this formula again:

Its a logarithmic function, which looks like this:

Here we see two problems of single stage rockets:

1) Its almost impossible to increase M/M-Mp ratio more than ~15 times (if we add more fuel we need to add weight to fuel tanks and add engines).
2) The growth of logarithmic function slows down quite fast, so increasing that ratio does not make much sense anyway.

So currently the only solution is multistage rocket. Here how it works:

Second solution is increase specific impulse, but its simply not possible with chemical powered engines, while nuclear and ion engines have not enough power to lift the rocket from the ground. They are good only in space.

 

[timmy_area51]

Rocket physics was invented by Verner Von Braun , a Nazi .


https://en.wikipedia.org/wiki/Wernher_von_Braun

those are the stages if you are really interested

 

[saltyashell]

Easily the most useful post i have read on this site since joining.
The trick is to find a fuel which is dense enough to reduce size of stages(stage) while providing the specific impulse required.
Discarding single use stages is a big waste and while spacex is doing good in this aspect , its still a compromise with the stages requiring extensive checks before reuse.
The dream is something like a modern jet liner. Refuel and reuse.

 

[timmy_area51]

Easily the most useful post i have read on this site since joining.

The trick is to find a fuel which is dense enough to reduce size of stages(stage) while providing the specific impulse required.

that's Solid fuel , like in Russian TOPOL or the american Minuteman ..

Refuel and reuse.

that's of no use , only for a show off like Elon musk and SpaceX

 

[saltyashell]

that's Solid fuel , like in Russian TOPOL or the american Minuteman ..



that's of no use , only for a show off like Elon musk and SpaceX

I have to disagree. Spacex has reduced costs from 100 m usd for a 5 t payload to geo to 60 m usd and aims to lower even more.
And why is a reusable , light weight , self propelled vehicle of no use ? I dont mean like the space shuttle which had discardable 1st stage solids.

 

[timmy_area51]

space X copies (Buys) russian tech

 

[saltyashell]

space X copies (Buys) russian tech

Actually no. Not spacex .They have the complete nasa brain trust behind it.
i think delta rockets use russian cryogenic engines. Not sure.

 

[timmy_area51]

Complex nasa brains recycle the soviet ideas just like the Nazi ideas ..

the mars Rover for instance was the soviet moon Rover ... it's just that no one remembers the soviet moon rover