## Wednesday, February 10, 2016

### Gravity turn

When you watch a rocket launch, you see that it gently tips over as it climbs.  This is because to stay in orbit, a vehicle must travel sideways, very fast.  However, it must also climb above the atmosphere.  Obviously, going straight up until you reach space, then turning 90 degrees and going into orbit is inefficient, and going sideways immediately after launch is also inefficient.  So what do rockets do?
First, there are three terms we must familiarize ourselves with: gravity losses, drag losses, and steering losses.
These term refer to things which require delta-v aside from expending delta-v just to increase your total speed in a vacuum.  So your total speed after expending all propellant would be total potential delta-v (if your rocket was going in one direction in a vacuum with no gravitational losses) minus gravity losses, drag losses, and steering losses.

Gravity losses are the delta-v expended that is just fighting against gravity, instead of speeding up the vehicle.  To imagine this, think of a rocket with a thrust to weight ratio of exactly 1, that is hovering just above the launchpad.  This rocket, in free space, could accelerate to 1,000 m/s, but, because gravity losses take up all of the potential delta-v, it's end speed is zero.

Drag losses: if your rocket expends 1,000 m/s of delta-v in a gravity-less vacuum, you end up travelling at 1,000 m/s.  However, if you put an atmosphere in that vacuum which your rocket must travel through, then drag will slow the rocket down, even as it continues to accelerate.  The difference between the total potential delta-v and your end speed is the drag losses.

Steering losses: you have a total potential delta-v of 1,000 m/s, and you expend 500 m/s going in one direction in a gravity-less vacuum, then you turn around 180 degrees and expend the remaining 500 m/s.  Your end speed is zero, because your steering losses are 1,000 m/s.

Back to gravity turns.  A gravity turn is the optimized curve from vertical to horizontal of a rocket traveling to orbit.  Because a rocket "balances" on its engines, gravity slowly pulls the front of the rocket down, which works efficiently, because less delta-v is needed for steering the rocket, and because the angle of attack (angle of the rocket to the air it's passing through) in almost zero throughout the entire ascent.  An ideal one will have a minimum of drag, gravity, and steering losses.  Turning too sharply to early will result in high steering losses, and turning too late will result in high steering losses.

Ideally there should only need to be one steering event, at the very start of the gravity turn, pitching over 5-10 degrees while the rocket is still fairly low in the atmosphere.  Then gravity should take over.