# What is the distribution of ∆V amongst different stages of rocket flight?

How is rocket energy (or fuel consumption) is distributed between

1. gaining orbital velocity
2. gaining orbital height
3. fight aerodynamic drag
• take a spacecraft to LEO and gain orbital velocity are more or less the same. Maybe you mean gravity drag instead of take a spacecraft to LEO – Antzi Dec 13 '17 at 9:46
• You may distinguish between gaining orbital height, gaining orbital velocity and fighting atmospherical drag. – Uwe Dec 13 '17 at 10:08
• Yes, I mean gravity drag – Pavel Bernshtam Dec 13 '17 at 10:36
• Calculating the kinetic and potential energy for 1. and 2. is very easy, but to calculate the energy to fight drag is very difficult. Formulas for the kinetic and potential energy are found on this page. But the text is in german only. – Uwe Dec 13 '17 at 10:44
• I'm asking just about order of magnitude - like 10%/70%/20% – Pavel Bernshtam Dec 13 '17 at 11:01

## 1 Answer

Considering fuel consumption or energy expenditure may be misleading, because of the huge change in mass over the flight as fuel is expended. 2/3 of the fuel is expended by the first stage, which only produces 1/3 of the total velocity, for example.

Another way to look at the question is through delta-v expenditure; according to Bob Braeunig's simulation of the Apollo 11 launch (now offline but available on archive.org), the Saturn V produced 9,194 m/s of ∆v; Earth's rotation contributed 390 m/s of ∆v, for a total budget of 9584 m/s.

Gravity losses account for 1743 m/s; drag losses 48 m/s, and the velocity on orbital insertion is 7793 m/s. If you treat gravity loss as the cost of reaching orbital height, the breakdown is thus 18.2% gravity loss, 0.5% drag loss, 81.3% orbital velocity.