Gravity drag
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191350089
2008-02-14T04:25:52Z
Wolfkeeper
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{{unreferenced|date=October 2006}}
In [[astrodynamics]], '''gravity drag''' (or '''gravity losses''') is [[inefficiency]] encountered by a [[spacecraft]] [[thrust]]ing while moving against a [[gravitational field]].
Percentage losses due to gravity drag depend on the relative sizes of the acceleration due to the thrust and due to gravity as well the direction the thrust is applied in. Percentage of gravity losses are lower when the thrust is mostly lateral, and when the acceleration is large compared to the gravity.
==Introduction==
Once a vehicle has left the ground and until it reaches a stable orbit, the acceleration due to gravity must be opposed by the vehicles engines, at the cost of some propellant. Gravity drag is the delta-v needed due to this.
As an extreme example, consider a launch from Earth. One could plan a rocket that climbs to 1000 feet above the ground and then hovers there for a minute before proceeding onward and eventually into orbit. Certainly, this rocket will burn more fuel than one which proceeds directly to orbit without a hover. The reason for this inefficiency is that the thrust is simply supporting the weight of the rocket (during the hover) and not increasing the rocket's speed. This illustrates the rule of thumb that a time-consuming launch is inefficient.
It might be supposed that given that gravity is around 9.8 m/s^2, that a loss of delta-v of 9.8 m/s would occur per second. However, this greatly overestimates the losses in many cases.
==Calculation==
If the gravitational [[acceleration]] [[vector (spatial)|vector]] is <math>g</math> and the thrust vector per unit mass (acceleration produced by the engine) is <math>a</math>, then the actual acceleration of the craft is <math>a-g</math>, while using [[delta-v]] at a time-rate of <math>a</math>; that is, the delta-v of the vehicle used is <math>|a|/|a-g|</math> 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 <math>a</math> only slightly more than <math>g</math>, the gravity drag is very large.
When applying [[delta-v]] against gravity to increase [[specific orbital energy]], it is advantageous to spend delta-v at the highest speed 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 ==
[[Image:GravityDrag.png|right|thumb|A pure rocket vehicle maintaining vertical velocity/altitude can have an effective [[Lift to drag ratio]] comparable to that of airliners.]]
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 3 [[g-force|''g'']] thrust directed upward to an acceleration of 2 ''g'', for an efficiency of 67%. However, the same 3 ''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 2.8 ''g''. Achieving 2.8 ''g'' acceleration with 3 ''g'' thrust gives an efficiency of over 94%.
As orbital speeds are approached, the efficiency climbs further as the vehicle needs less vertical acceleration to maintain altitude, as momentum (or equivalently centrifugal effects in the rotating frame of reference around the center of the Earth) cancel the gravitation of the Earth, and more of the thrust can be used to accelerate.
It's important to note that "efficiency", in this sense, is not the only objective of a launching spacecraft. Rather, the objective is achieve the position/velocity combination for the desired orbit. For instance, the way to maximize acceleration is to thrust straight downward, leading to "efficiencies" over 100% because gravity actually aids the rocket's acceleration; however, thrusting downward is clearly not a viable course of action for a rocket intending to reach orbit.
On a planet with an [[Celestial body atmosphere|atmosphere]], the objective is further complicated by the need to achieve the necessary [[altitude]] to escape the atmosphere, and to minimize the losses due to [[atmospheric drag]] during the launch itself. These facts sometimes inspire ideas to launch orbital rockets from high flying airplanes, to minimize atmospheric drag, and in a nearly vertical direction, to minimize gravitational drag like in the above calculations.
==See also==
*[[Atmospheric drag]]
*[[Delta-v budget]]
*[[Oberth effect]]
[[Category:Astrodynamics]]