# How much fuel is necessary to cause delta-v?

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?

• What's the extra 1.3km/s for? – Russell Borogove May 17 '18 at 18:07
• "Atmospheric and gravity drag associated with launch typically adds 1.3–1.8 km/s to the launch vehicle delta-v" -- Wikipedia – JSCoder says Reinstate Monica May 17 '18 at 18:08
• That's included in the normally quoted 9400m/s. Orbital velocity is ~7800m/s. – Russell Borogove May 17 '18 at 18:10
• Hint: your thrust needs to be greater than the vehicle weight at liftoff. – Organic Marble May 17 '18 at 18:12

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:

Formula view:

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