How is rocket energy (or fuel consumption) is distributed between
- gaining orbital velocity
- gaining orbital height
- fight aerodynamic drag
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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.