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 with 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 too. 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 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. If a launched craft followed a purely vertical flight path, then it would fight gravity throughout its entire burn, putting the least possible percentage of thrust towards acceleration which greatly decreases the net Delta-V. 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, 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 small 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.
On bodies with atmospheres, 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 two things: the gravitational pull of the body it is on and the density of any atmosphere, though the thrust-to-weight ratio (TWR) of the craft also comes into play.
The least efficient gravity turn, regardless of the body the craft starts on, is to launch the craft and maintain a vertical heading, and then once the craft is both outside of any atmosphere and above nearby surface obstructions, turn to face horizontally and burn to circularize the orbit. In such a gravity turn, all of the fuel in the initial burn is spent resisting gravity and none is spent gaining horizontal speed.
On bodies with no atmospheres, a craft need not worry about any drag generated, and thus should turn to face near horizontal as early as possible in the launch 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 it escapes the atmosphere, then the craft will have to spend more delta-V to regain altitude, if the TWR of the current stage allows it. If not, then it will result in an inevitable surface collision. For example, the most efficient gravity turn on Kerbin begins at 10 kilometers, with the ship and vector marker facing at 30 to 40 degrees above the artificial horizon.
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 fuel is consumed, losing stages also affecting TWR, the Weight in the TWR changing with altitude, 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.
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
