# Multi-stage Vs. single stage rockets

• Januz Johansen
In summary: I am not going on a wild goose chase, i put the equations like so:and work it out for ms1 > 0 right?In summary, the two stage rocket has a greater velocity than the single stage rocket.
Januz Johansen

## Homework Statement

Hello all
I have to show why there advantageously can be employed multi-stage rockets

## Homework Equations

How do i do this best, a graph/plot?

## The Attempt at a Solution

i have done some calculations for a single stage rocket and a multistage rocket, but how can i show this more over all?

It is very difficult to follow your equations. If you would like to make a more general statement use variables rather than numbers. Also define what those variables mean.

Cutter Ketch said:
It is very difficult to follow your equations. If you would like to make a more general statement use variables rather than numbers. Also define what those variables mean.

Hello i have the equation with variables:

Should i explain this mathematicaly, and if so can you give a little hint? :)
Thanks

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Now you need to relate the two situations. What if the single stage and the two stage have the same total mass. Also say they have the same payload mass and fuel mass. The part that is missing is the mass of the structure. Say they have the same structure mass, but with the two stage rocket you get to throw away a large fraction of that for the second stage. Can you show the final v is greater in the two stage?

Ps. In your first stage you do not burn all the fuel, so some of the fuel mass should appear in the denominator in the log.

Cutter Ketch said:
Ps. In your first stage you do not burn all the fuel, so some of the fuel mass should appear in the denominator in the log.
Hello
i have done it with structure mass and so, I am not sure on how to relate the two situations, if they have the same payloat its mp =mp and same fuel mass; mf=mf1+mf2 - and the same structure mass then its ms=ms1+ms2?

and why is there fuel left in the first stage?

The fuel left after the first stage is the fuel carried in the second stage. The second stage has to have fuel!

To relate them write the single stage eqn using the same terms assuming things are equal because you want to compare similar rockets.

Same amount of structure: not ms, but ms1 + ms2,
Same amount of fuel, so not mf, but mf1+mf2

Now with both equations in the same terms can you prove algebraicly that the two stage velocity is greater than the single stage?

Cutter Ketch said:
The fuel left after the first stage is the fuel carried in the second stage. The second stage has to have fuel!

To relate them write the single stage eqn using the same terms assuming things are equal because you want to compare similar rockets.

Same amount of structure: not ms, but ms1 + ms2,
Same amount of fuel, so not mf, but mf1+mf2

Now with both equations in the same terms can you prove algebraicly that the two stage velocity is greater than the single stage?

Mann you are so great :D

but I am a bit unsure, because, in the 2. stage rocket the u, could be different in each stage, so

i have taken the part that goes out with each other, and i can see it must be larger.

Januz Johansen said:
Mann you are so great :D

but I am a bit unsure, because, in the 2. stage rocket the u, could be different in each stage, soView attachment 109531
i have taken the part that goes out with each other, and i can see it must be larger.

What you wrote in the first line in each kind of rocket is correct. I think the math leading to the second line in each case is flawed. That's ok. You only need the first line of each. Now put them on a line together with ">?" between them and do algebra until you prove it's true. You should be able to prove it's true as long as ms1 > 0. (And to be sure I'm not asking the impossible I did work it out myself)

Cutter Ketch said:
What you wrote in the first line in each kind of rocket is correct. I think the math leading to the second line in each case is flawed. That's ok. You only need the first line of each. Now put them on a line together with ">?" between them and do algebra until you prove it's true. You should be able to prove it's true as long as ms1 > 0. (And to be sure I'm not asking the impossible I did work it out myself)

ok, just so I am not going on a wild goose chase, i put the equations like so:

and work it out for ms1 > 0
right?
and ofc again thank you for helping

Just do algebra. The inequality will get simpler and simpler until all you are left with is ms1>0. So if ms1>0 then the inequality was true from the top.

Cutter Ketch said:
Just do algebra. The inequality will get simpler and simpler until all you are left with is ms1>0. So if ms1>0 then the inequality was true from the top.
okay thank you, i don't know why i think it is more difficult then it is... you know rockets... no, but really thank you for your help and your patience, i really appreciate it. i will go do some algebra :D

Hint: the u cancel. Then exponentiate both sides and remember exp(a+b) = exp(a) exp(b)

Cutter Ketch said:
Hint: the u cancel. Then exponentiate both sides and remember exp(a+b) = exp(a) exp(b)
can you give a little hint, I am having som trouble with the u, i always end up with a u, the u cancel a u on the other side, but what about the last u? because if the 2 u's are different, that could be a possibility in a multi stage rocket right?

Januz Johansen said:
can you give a little hint, I am having som trouble with the u, i always end up with a u, the u cancel a u on the other side, but what about the last u? because if the 2 u's are different, that could be a possibility in a multi stage rocket right?

Well, you have to do legal algebra. If you don't know algebra then this isn't going to be easy. All terms have a u. When you divide both sides of the equation by u you must divide all terms by u according to the distributive property. You shouldn't wind up with a second u. Please think carefully about doing proper algebra.

Cutter Ketch said:
Well, you have to do legal algebra. If you don't know algebra then this isn't going to be easy. All terms have a u. When you divide both sides of the equation by u you must divide all terms by u according to the distributive property. You shouldn't wind up with a second u. Please think carefully about doing proper algebra.
oh yes i see now :D much easier, now i get the correct solution, totaly forgot about dividing all the terms :D
Thank you so much you were a great help :D

## 1. What is the main difference between multi-stage and single stage rockets?

The main difference between multi-stage and single stage rockets is the number of stages they have. Single stage rockets have only one stage, while multi-stage rockets have multiple stages that separate and fall off as the rocket ascends.

## 2. Why do some rockets have multiple stages while others only have one?

Rockets with multiple stages are able to reach higher altitudes and achieve greater speeds than single stage rockets. This is because the weight of the empty stages is shed as the rocket ascends, making it more efficient.

## 3. How do multi-stage rockets work?

Multi-stage rockets are designed to have multiple sections, or stages, that contain their own engines and fuel tanks. As each stage runs out of fuel, it separates and falls off, reducing the weight of the rocket and allowing it to continue its ascent.

## 4. What are the advantages of using single stage rockets?

The main advantage of single stage rockets is their simplicity and lower cost. They require less engineering and fuel compared to multi-stage rockets, making them a more practical option for smaller payloads and shorter distance missions.

## 5. What are the limitations of multi-stage rockets?

One limitation of multi-stage rockets is their complexity and cost. They require more engineering and fuel compared to single stage rockets, making them more expensive to develop and launch. Additionally, the separation of stages can sometimes be unpredictable and lead to mission failure.

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