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For a project, I need to calculate how much thrust and how much fuel I need for getting into LEO.

What I know:

  • Delta-V necessary ($\approx 9.4$ km/s)
  • Dry (empty spacecraft mass)

What I don't know:

  • How much fuel I'm bringing
  • How much thrust I need

Are there any good ways of calculating this?

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  • $\begingroup$ What's the extra 1.3km/s for? $\endgroup$ – Russell Borogove May 17 '18 at 18:07
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    $\begingroup$ "Atmospheric and gravity drag associated with launch typically adds 1.3–1.8 km/s to the launch vehicle delta-v" -- Wikipedia $\endgroup$ – JSCoder says Reinstate Monica May 17 '18 at 18:08
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    $\begingroup$ That's included in the normally quoted 9400m/s. Orbital velocity is ~7800m/s. $\endgroup$ – Russell Borogove May 17 '18 at 18:10
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    $\begingroup$ Hint: your thrust needs to be greater than the vehicle weight at liftoff. $\endgroup$ – Organic Marble May 17 '18 at 18:12
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The Tsiolkovsky rocket equation tells you how much delta-V you get for a given exhaust velocity and full/empty mass ratio per stage. Typically you'll want to divide the total 9400m/s requirement into two (or more) stages and work backward from the uppermost stage. Select an appropriate engine for the stage, decide how much dry tankage/structural mass you need per mass of fuel, solve.

As Organic Marble notes, the first-stage thrust needs to exceed the weight of the fully loaded rocket, or it won't lift off. Typically the thrust to weight ratio starts at somewhere between 1.15:1 and 1.5:1. (Upper stages can relax that limit a little bit but will usually start close to 1:1 to maximize the amount of fuel they bring.) Pick an engine and add multiples of them until your thrust is sufficient!

The devil is in the details, of course. I suggest running the numbers from an existing rocket to make sure you understand the principles before trying your own.

Here's part of a spreadsheet that I use for quick-and-dirty feasibility tests. Making it useful to you is left as an exercise.

  • Stage mass: total mass of an individual stage, fully loaded with propellant.
  • Prop fraction: fraction of stage mass which is propellant.
  • Structure: structural (non-propellant) mass of stage.
  • Propellant: propellant mass of fully loaded stage.
  • Upper: total mass of all stages above this one, fully loaded.
  • Ballast: inert payload mass attached to the stage.
  • M0: total mass of the rocket at ignition of the stage.
  • M1: total mass of the rocket at burnout of the stage.
  • ISP: specific impulse of the stage's engines.
  • Thrust: total thrust of the stage's engines.
  • Delta-v: single stage delta-V contribution, summing to total delta V below.
  • G0: acceleration at stage ignition, in g (equivalent to TWR).
  • G1: acceleration at stage burnout.

Masses in metric tons, ISP in seconds, thrust in kN, delta-V in m/s. I use the sea level specific impulse of the first stage engine, which yields a slight underestimate for delta-v because ISP will increase over the course of the burn.

Value view: enter image description here

Formula view: enter image description here

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  • $\begingroup$ +1, nice link, but do you have an example of the equation being used on an existing rocket? $\endgroup$ – Magic Octopus Urn May 17 '18 at 18:28
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    $\begingroup$ Ooooo the spreadsheets are a very nice touch $\endgroup$ – kim holder May 17 '18 at 18:44
  • $\begingroup$ Dang this is a good answer. I’ll wait 24hr and accept unless there are other better answers $\endgroup$ – JSCoder says Reinstate Monica May 17 '18 at 19:48
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    $\begingroup$ oh my god, I didn't know that Formula View could be done. That's real good. $\endgroup$ – Erin Anne May 17 '18 at 20:29
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    $\begingroup$ @ErinAnne CTRL+` will turn it on and off. $\endgroup$ – BruceWayne May 18 '18 at 2:29

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