Why are multistage rockets more efficient than single-stage rockets?

[Januz Johansen]

Homework Statement

Assess why there can advantageously be used multistage rockets, with a calculation example.

Homework Equations

-

The Attempt at a Solution

[/B]
Hello all,
i need to show why it is an advantage to use multistage rockets, with some mathematical proof, and I am a bit lost. I have done calculations on single-stage rockets, but I am not sure where to start with multistage rockets.
So it would be great if somebody could suggest some formulas to use to proof this.

(sorry for my english)
thanks

 

[BvU]

Hi,

PF culture insists you make the first move by proposing something. But to get you under way: Suppose you have a backpack full of bottles of water. Would you get further if you carried the empty ones with you on your trip through the desert ? Or would it be better to make use of the many recycle points they have on the way to the next oasis ?

And your english is just fine (said the dutchman)

 

[Januz Johansen]

Homework Statement

Assess why there can advantageously be used multistage rockets, with a calculation example.

Homework Equations

-

The Attempt at a Solution

[/B]

Hello all,
i need to show why it is an advantage to use multistage rockets, with some mathematical proof, and I am a bit lost. I have done calculations on single-stage rockets, but I am not sure where to start with multistage rockets.
So it would be great if somebody could suggest some formulas to use to proof this.

I don't know if this is right but:

If i have tried to do some calculations on multi-stage rocket with the rocket equation,
dv=u*ln(m0/mf)+u*ln(m0-dm/mf-mr-dm) where dm is the propellant used, mr is the stage there are droped off, m0 is total mass, including propellant, i find the sum of the total delta V, in the first step i use the tsiolkovsky rocket equation, and i add it with again the tsiolkovsky rocket equation just with the new mass for the next stage.
i have tryed looking at det difference in delta V, ( the maximum change of velocity of the vehicle) but when i
comparer the numbers, the dV is a lot smaller with a 2-stage-rocket - can that be true?

thanks @BvU

(sorry for my english)
thanks

 

[haruspex]

Homework Statement

Assess why there can advantageously be used multistage rockets, with a calculation example.

Homework Equations

-

The Attempt at a Solution

[/B]

Hello all,
i need to show why it is an advantage to use multistage rockets, with some mathematical proof, and I am a bit lost. I have done calculations on single-stage rockets, but I am not sure where to start with multistage rockets.
So it would be great if somebody could suggest some formulas to use to proof this.

I don't know if this is right but:

If i have tried to do some calculations on multi-stage rocket with the rocket equation,
dv=u*ln(m0/mf)+u*ln(m0-dm/mf-mr-dm) where dm is the propellant used, mr is the stage there are droped off, m0 is total mass, including propellant, i find the sum of the total delta V, in the first step i use the tsiolkovsky rocket equation, and i add it with again the tsiolkovsky rocket equation just with the new mass for the next stage.
i have tryed looking at det difference in delta V, ( the maximum change of velocity of the vehicle) but when i
comparer the numbers, the dV is a lot smaller with a 2-stage-rocket - can that be true?

thanks @BvU

(sorry for my english)
thanks

I've not gone through what you wrote in detail, but it sounds like you have not done the right comparison. You need to compare a two stage rocket and a one stage rocket with the same payload and same total fuel.

 

[Januz Johansen]

I've not gone through what you wrote in detail, but it sounds like you have not done the right comparison. You need to compare a two stage rocket and a one stage rocket with the same payload and same total fuel.

Thanks- i see my mistake now, in my calculations for the masse i accidently changed the size of the payload's mass