Gravity drag

In astrodynamics and rocketry, gravity drag (or gravity losses) is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field. In other words, it is the cost of having to hold the rocket up in a gravity field.

It is the difference between the delta-v expended and the theoretical delta-v for the actual change in speed and altitude, plus the delta-v for other losses such as air drag, that are experienced by a thrusting spacecraft.

Gravity losses depend on the time over which thrust is applied as well the direction the thrust is applied in. Gravity losses as a proportion of delta-v are minimised if maximum thrust is applied for a short time, or if thrust is applied in a direction perpendicular to the local gravitational field. During the launch and ascent phase, however, thrust must be applied over a long period with a major component of thrust in the opposite direction to gravity, so gravity losses become significant. For example, to reach a speed of 7.8 km/s in low Earth orbit requires a delta-v of between 9 and 10 km/s. The additional 1.5 to 2 km/s delta-v is due to gravity losses and atmospheric drag.

Consider the simplified case of a vehicle with constant mass accelerating vertically with a constant thrust per unit mass a in a gravitational field of strength g. The actual acceleration of the craft is a-g and it is using delta-v at a rate of a per unit time.

Over a time t the change in speed of the spacecraft is (a-g)t, whereas the delta-v expended is at. The gravity drag is the difference between these figures, which is gt. As a proportion of delta-v, the gravity drag is g/a.

A very large thrust over a very short time will achieve a desired speed increase with little gravity drag. On the other hand, if a is only slightly greater than g, the gravity drag is a large proportion of delta-v. Gravity drag can be described as the extra delta-v needed because of not being able to spend all the needed delta-v instantaneously.

This effect can be explained in two equivalent ways:

These effects apply whenever climbing to an orbit with higher specific orbital energy, such as during launch to low Earth orbit (LEO) or from LEO to an escape orbit. This is a worst case calculation - in practice, gravity drag during launch and ascent is less than the maximum value of gt because the launch trajectory does not remain vertical and the vehicle's mass is not constant, due to consumption of propellant and staging.

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