# Is an orbital launch more like a vertical climb or a Hohmann Transfer?

It is said that a launch to orbit requires a Delta V of 9.3–10 km/s, and this encompasses orbital speed, air drag, gravity drag, and the energy to raise altitude to low Earth orbit. But I'm troubled by vastly different estimates of the amount of Delta V that goes to the altitude term.

To demonstrate, consider the two obvious physical models and the numbers they produce. First, we have a perfectly vertical "toss" of a rocket, like a sounding rocket or a suborbital flight. Second, we can ignore Earth's atmosphere and imagine two burns to reach LEO. Assuming 200 km orbit:

1. $v\approx \sqrt{2 h a}$, for about 1.98 km/s, or use the more accurate $GM/r$ potential for 1.95 km/s
2. With the Hohmann Transfer formula, get $\Delta v_1$ and $\Delta v_2$ to be 61 m/s and 60 m/s, for a grand total of 121 m/s, or 0.121 km/s

That's a big difference there. For an actual rocket launch, what is the appropriate mental model? On the one hand, the early parts of the launch aren't very close to the horizontal. But on the other hand, the characteristic height of our atmosphere is like 8 km, which is much lower than the altitude of the orbit.

If one were to give a ballpark figure for how much of the delta v budget goes into raising the altitude, what would be a good estimate?

Furthermore, does the burn even last for half an orbit? How Hohmann-ish is the climb to orbit?

• If you're already moving 7.9 km/s, a .6 km/s burn adds quite a few joules. – HopDavid Jun 19 '14 at 22:25
• Remember that when on the surface of the Earth you are NOT orbiting the Earth. To orbit the Earth just above the surface you would need to be moving at ~8km/s over the surface. – ThePlanMan Jun 19 '14 at 23:24