Rocket Efficiency: Why Use Multistage Rockets?

[Januz Johansen]

Homework Statement

Show why it is advantageous to use multistage rockets

Homework Equations

- 3. The Attempt at a Solution [/B]
Hello there
I have to show why using multi stage rockets are an advantage, i have done som calculations for a 2. stage rocket and a singel stage, with the same payload mass, and the same total fuel, i took 80% of the stage
was fuel, and in total 800, i think this is right, (plis correct me if I'm wrong, the math is shown in the pic) - so to my question, can i make a plot like a graph, to show the multistage rocket is superior, i have tryed to plot v as a funktion to t v(t), but i can't seem to get a t into the equation.
sorry if it sounds a bit silly, but hope someone can help, rocket physics is difficult :/ - thanks

 

[haruspex]

i have tryed to plot v as a funktion to t

Typically you do not care how long the rocket takes, so time is not that interesting. What you care about is how much fuel it needs to lift a given payload into a given orbit. Relate that to the velocity achieved.

 

[Januz Johansen]

Typically you do not care how long the rocket takes, so time is not that interesting. What you care about is how much fuel it needs to lift a given payload into a given orbit. Relate that to the velocity achieved.

Okay, yes i see your point - can you give me a hint to what equations i can use for this. I am a bit unsure on how to calculate, how much fuel there are used at a specific velocity.
But Thanks :)

 

[haruspex]

Okay, yes i see your point - can you give me a hint to what equations i can use for this. I am a bit unsure on how to calculate, how much fuel there are used at a specific velocity.
But Thanks :)

You did not define all your mass variables, but I assume some of them refer to fuel masses in the stages. You ended up with an equation for velocity achieved. So you could just plot velocity achieved in the two cases (1 v. 2 stages) against total fuel.
Before you do that, it would be handy to figure out the optimal distribution of fuel between two stages for a given total.

 

[Januz Johansen]

You did not define all your mass variables, but I assume some of them refer to fuel masses in the stages. You ended up with an equation for velocity achieved. So you could just plot velocity achieved in the two cases (1 v. 2 stages) against total fuel.
Before you do that, it would be handy to figure out the optimal distribution of fuel between two stages for a given total.

Hello thank you for your help, i will try that. I have read that a 2. stage rocket with the same exhaust velocity, should be ½ and ½. Sorry for being a bit slow - if i take the single stage again, i take u*ln( total mass / total mass - fuel)

so how can i plot velocity achieved against total fuel?

again thank you for helping

 

[haruspex]

Hello thank you for your help, i will try that. I have read that a 2. stage rocket with the same exhaust velocity, should be ½ and ½. Sorry for being a bit slow - if i take the single stage again, i take u*ln( total mass / total mass - fuel) View attachment 109449
so how can i plot velocity achieved against total fuel?

again thank you for helping

Rewrite the equation in terms of payload and fuel mass, instead of using total mass. Vary the fuel mass an plot the result.

 

[Januz Johansen]

Okay i understand now :) thanks