Gravity drag

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In astrodynamics, gravity drag (or gravity losses) is inefficiency encountered by a spacecraft thrusting while moving against a gravitational field.

If the gravitational acceleration vector is [g] and the thrust vector per unit mass (acceleration produced by the engine) is [a], then the actual acceleration of the craft is [a-g], while using delta-v at a time-rate of [a]; that is, the delta-v of the vehicle used is [|a|/|a-g|] times the actual increase in speed. In the case of a very large thrust during a very short time, a desired speed increase can be reached with little gravity drag, while for [a] only slightly more than [g], the gravity drag is very large.

For example, at the beginning of launch from Earth, a rocket does not have significant horizontal speed yet (which provides a centrifugal force away from the center of the Earth), so just staying aloft costs delta-v every second. Therefore a time consuming launch would be highly inefficient.

When applying delta-v against gravity to increase specific orbital energy, it is advantageous to spend delta-v at as high speed as possible, rather than spending some, being decelerated by gravity, then spending some more, or spending it at less than full capacity. 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:

The specific energy gained per unit delta-v is equal to the speed, so spend the delta-v when the rocket is going fast; in the case of being decelerated by gravity this means as soon as possible.
It is wasteful to lift fuel unnecessarily: use it right away, and then the rocket does not have to lift it.

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.

Vector considerations

It is important to note that acceleration is a vector quantity, and the direction of the acceleration has a large impact on the overall efficiency. For instance, gravity drag would reduce a 2.6 G thrust directed upward to an acceleration of 1.6 G, for an efficiency of less than 62%. However, the same 2.6 G thrust could be directed at such an angle that it had a 1 G upward component, completely cancelled by gravity drag, and a horizontal component of 2.4 G, unaffected by gravity drag. Achieving 2.4 G acceleration with 2.6 G thrust gives an efficiency of over 92%.

Note, however, that the objective of the craft is not only to maximize acceleration, or else it would direct its 2.6 G thrust downward, achieving 138% efficiency but never reaching orbit. Rather, the objective is to achieve the necessary specific orbital energy to sustain the desired orbit. On a planet with an atmosphere, the objective is further complicated by the need and to achieve the necessary altitude to escape the atmosphere, and to minimize the losses due to atmospheric drag during the launch itself.

Gravity drag

Vector considerations

See also