Gravity turn
A gravity turn is a maneuver used to launch a craft into, or descend from, orbit around a celestial body while using minimal fuel. In order to escape the surface, a craft must rise faster than gravity pulls it down. In order to maintain a stable orbit, the craft must have enough sideways momentum at a high enough altitude to avoid colliding with any surface features or getting slowed down by the atmosphere, if any. A gravity turn combines these two steps into one maneuver, saving fuel in the process. As a craft starts ascending vertically, it slowly turns to the side until by the end of the turn it points sideways.
For an analogy, imagine getting to orbit without a gravity turn: it would be a straight up flight, then a 90 degree turn once high enough to orbit. Think of a gravity turn as "cutting the corner", so to speak. It's a shorter path, so it saves more fuel.
This efficiency also applies to landing from orbit. Instead of killing all horizontal speed and then beginning a slow descent to the surface, it's actually more efficient to slow both your horizontal and vertical speed at the same time.
Mechanics
Gravity turns work by fighting gravity the least amount possible to gain enough altitude and horizontal speed for the desired maneuver. Since the gravity of the local celestial body is always pulling on the craft, it will always accelerate most slowly when pointing directly away from that body and would accelerate faster in any other direction than straight vertical. If a launched craft followed a purely vertical flight path, then it would spend all of its thrust accelerating in the slowest direction, effectively spending the most Delta-V to gain the least speed without gaining any lateral speed necessary to orbit. In other words, a straight vertical launch is the least efficient launch.
The gravity turn maneuver is accomplished as follows. Assuming a perfectly flat launch site, the maneuver begins as a vertical launch, and follows with the verical climb. Then once a certain altitude is reached, a slight turn is made, called pitchover maneuver. By turning away from vertical slightly, gravity will pull the velocity vector of the craft down towards that direction and the craft will tilt to follow it. As this happens, the craft will gain more speed sooner since it is travelling in a vector that is not directly opposed to gravity - the centrifugal force starts to decrease the effect the gravity, effectively saving fuel and time. The farther the vector tilts to the side, the percentage of thrust spent fighting gravity becomes smaller and the percentage of thrust spent gaining speed becomes larger. Since the majority of this vector change is done by gravity and not by the flight controls, another tiny amount of fuel is saved. By the end of the gravity turn, no fuel is wasted fighting gravity. If the craft has gained enough lateral speed at an altitude above any mountains or atmosphere, it then begins a stable orbit.
The altitude to start a gravity turn with a pitchover maneuver at depends on several factors. On bodies with atmospheres, atmospheric pressure and drag also comes into determining the most efficient gravity turn.
Timing
When to begin and the amount of tilt in a gravity turn are based mainly on three things:
- any possible obstructions in your flight path
- the density of any atmosphere, drag, and the maximal dynamic pressure
- the gravity of the local body and by extension the craft's thrust-to-weight ratio (TWR)
Any hill or mountain in your flight path should obviously be avoided. While changing the height of the turn to clear an obstacle may not be the most efficient flight path for a gravity turn, it will avoid a collision.
On bodies with no atmospheres, a launched craft need not worry about any drag generated, and thus should turn to face near horizontal as early as possible given its TWR and the height of nearby surface features. Doing this minimizes the percentage of thrust spent resisting gravity, while maximizing the percentage of thrust spent gaining enough horizontal speed to achieve orbit.
On planets with an atmosphere however, timing and amount of tilt are crucial to the success and efficiency of a gravity turn. If a craft turns too late or too little in its flight, it will waste more fuel fighting gravity than would be used resisting drag. If a craft turns too early or too far, it will travel a longer distance through the atmosphere, losing more speed to drag, requiring more fuel to regain that lost speed. If such a turn results in the craft pointing horizontal before arriving at an altitude above the atmosphere, then the craft will have to spend more delta-V to gain the necessary altitude, if the TWR of the current stage allows it. If not, then it will result in an inevitable surface collision. Worth to know, differing to a steeper trajectory from the ideal means less risk than a too shallow trajectory. In case of ascending in dense atmosphere the dynamic pressure becomes a important factor as at too high speed can damage the craft, and the increased drag increases the fuel consumption more, than the saving against the gravity. The terminal velocity indicates the optimal ascending speed.
The gravity strength of the local body also comes into effect. On bodies with very strong gravity wells, a larger portion of thrust must be spent fighting gravity, leaving a smaller portion of thrust to spend gaining altitude and lateral speed. On such a body, that means a high turn at a narrow angle. Conversely, on a body with very light gravity, the turn can be low at a sharper angle. The craft's TWR also affects when to begin a turn. Crafts with very high TWRs will have plenty of thrust to spare, so they can spend a smaller percentage of their thrust fighting gravity and a larger percentage gaining lateral speed. This means that such a craft can make their gravity turns lower and sharper than a craft with a low TWR, and also means a faster, more efficient ascending with lower Δv cost.
Gravity turns are not always perfect. The most efficient gravity turn will have a continuous burn right up to completing circularization. Factors like TWR changing as the craft flies and human reaction time keep them from being perfect. In such a scenario, the craft may need to pause its burn once any atmosphere is escaped, coast to apoapsis and then do a circularization burn.
For an example of the "simple" advices for proper turn timing and amount: "the most "efficient" gravity turn on Kerbin begins around 10 kilometers, with the ship and vector marker facing 30 to 40 degrees above the artificial horizon." This is not the most efficient method, but far easier to learn than learn at least 10 points of altitude, angle and speed for each craft (and celestial body). The ideal trajectory is calm, and follows the prograde (
) direction after the pitchover maneuver, or sometimes differs from it to correct the trajectory.
Thrust-to-Weight Ratio
The TWR of a craft can greatly influence the gravity turn of a craft. Burning fuel will keep raising the TWR of the craft over time. The TWR will also change as staging progresses, rising as empty fuel tanks are lost but falling as engines are lost. If the craft is following too sharp a gravity turn, it could completely exhaust its more powerful beginning stages before escaping the atmosphere and advance to a stage meant for a higher altitude but now has a TWR too low to fight gravity, eventually leading to a surface collision. If the craft follows too narrow a gravity turn, it could spend its more powerful beginning stages reaching an altitude above the atmosphere, but then advancing to a stage with a TWR not powerful enough to properly circularize and orbit, eventually re-entering the atmosphere and colliding with the ground.
See also
- Gravity turn on Wikipedia
