Orbital Rendezvous With The FlightGear Space Shuttle

Flying a spacecraft to rendezvous with a space station is an experience completely different from nearly any situation in an aircraft. It involves a complicated choreography of bringing the orbits of two objects moving at around Mach 27 to an intersection point where relative velocity is nulled, followed by proximity operations where the spacecraft is gradually nudged to the docking port.

In fact, the whole choreography already starts at launch, when the spacecraft has to be inserted into the same orbital plane as the space station. During the next few hours to days, under guidance from mission control, the spacecraft then manoeuvres into a near-circular orbit that is slightly lower than that of the target, and in a location slightly behind. Since lower orbits are characterized by faster orbital speeds, from that position the spacecraft gradually catches up with the target from below and behind.

Much work is currently being done in FlightGear to allow a realistic rendezvous experience flying the Space Shuttle to ISS, with all the sensors (like the ranging radar or the star tracker camera) providing the right data to the on-board computers and the avionics helping the crew with the task. Here is a preview to the last hours of a rendezvous, and how it will look in FlightGear when the next version of the Shuttle is released (anyone brave enough to try right now can always download the latest version from the development repository).

Lambert Targeting

We start about 65 nm behind and 5.5 nm below the ISS, from a so-called 'phasing orbit' on which we gradually move closer to the ISS. In principle we could wait till we are just at the right position such that if we ignite the thrusters to raise the orbit by 5.5 miles, we will meet the ISS. However, there are other concerns for doing a rendezvous - primarily it is highly desirable to have daylight in which to get a visual on the target early on, and to fly proximity ops and docking while being able to see the target properly.

Thus, from the current position (at dusk over central Africa, with a thunderstorm visible in the background), we need to compute a transfer orbit to the ISS which brings us there a bit after sunrise. Computing such transfer orbits with specified departure and arrival times is known as a 'Lambert Problem', and aboard the Shuttle, the final transfer to the ISS is not guided from the ground but computed with the on-board avionics - here the SPEC 34 (orbital targeting) page.

Once the times are inserted, the Lambert solver computes a two burn sequence that will transfer the Shuttle to the ISS. In the event, to get to the ISS faster the solution is to push the Shuttle down to a temporarily lower orbit on which the catch-up rate will be accelerated, and then, when the Shuttle comes up again due to the increased centrifugal force, make a deceleration burn.

The Nile delta in the bright light of a full moon just becomes visible as the spacecraft pitches down into burn attitude for the first manoeuver.

   

The Correction Burn

Two things to consider: the position of the ISS isn't exactly known to the Shuttle's avionics, nor can a manoeuvring burn be executed perfectly. Thus about two-thirds into the transfer, it's reasonable to run the targeting routines again with the actual position of the Shuttle, so as to get better accuracy on arrival.

As expected, the required velocity corrections are fairly small. To get better accuracy of the burn time, in this situation, it is reasonable to utilize only one of the two Orbital Maneuvering System (OMS) engines. Basically this doubles the time the burn will take and hence cuts relative errors in burn duration in half.

After the correction burn is done, as expected, a new dawn greets the Shuttle. Sunrise is quick when going eastward at Mach 27 - it's just a few minutes from darkness to bright morning light.