Feb 18, 2010

Roll manoeuvre

The cheapest way to put something in space (satellite or shuttle) is at the equator while launching due East with an orbital inclination of zero degree (relative to the plane that cuts the earth at the equator). Why is that? Well, at the equator the rotation speed (relative to a fix point in space) is at its maximum and that is free speed that your ship will not have to generate. That would obviously put your ship in an orbit that fly strait above the equator. Logically we want to fly above more than a single strip of land and that's where the roll is used. If you need to fly over land that is half way toward the North Pole you would then have an orbital inclination of 45 degrees. By doing so you lose some of the earth initial speed and your launch would cost more money or you would have to compromise on weight to accelerate faster. The maximum orbital inclination (unless you have money to throw out the window) is then 90 degree and that would put your ship in a polar orbit, which is the most expensive one. So, unless there's a good reason, you always want to launch with as little orbital inclination as you can.

Where is the roll in all that? Normally, your ship on the launch pad is always pointing in the same direction, unless you have a fancy launch pad that can pre-orient the ship before takeoff. This means that the ship will have to rotate (roll) early in the flight to orient itself in the plane of the orbit.

Why is the shuttle rolling if the cheapest way to launch is at an orbital inclination of zero? It all depends on the location of your launch pad. Let's start by saying that the further you are launching from the equator the bigger your minimum orbital inclination will be. Like I mentioned before, at the equator the minimum orbital inclination you can achieve is 0 degree but at the poles the minimum is 90 degrees. This is because you can only achieve an orbit where the orbit plane is cutting the planet through it center of mass. In the case of the earth, since it's fairly round and the density is not uneven, orbit planes would cut the planet in half. The location and orientation of the shuttle launch pad and the target orbital inclination for each mission will, most certainly, force the shuttle to roll to set his orbital plane. The distance from the equator is also why the ISS orbital inclination is 51.6 degrees (far from zero). This is because of the Russian launch pad location is very far from the equator and the minimum orbital inclination that can be achieved from there is 51.6 degrees.