Orbital Rendezvous With The FlightGear Space Shuttle

Flying a spacecraft to rendezvous witha space station is an experience completely different from nearly anysituation in an aircraft. It involves a complicated choreography ofbringing the orbits of two objects moving at around Mach 27 to anintersection point where relative velocity is nulled, followed byproximity operations where the spacecraft is gradually nudged to thedocking port.

In fact, the whole choreography already starts at launch, when thespacecraft has to be inserted into the same orbital plane as the spacestation. During the next few hours to days, under guidance frommission control, the spacecraft then manoeuvres into a near-circularorbit that is slightly lower than that of the target, and in alocation slightly behind. Since lower orbits are characterized byfaster orbital speeds, from that position the spacecraft graduallycatches up with the target from below and behind.

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

Lambert Targeting

We start about 65 nm behind and 5.5 nm below the ISS, from aso-called 'phasing orbit' on which we gradually move closer to theISS. In principle we could wait till we are just at the right positionsuch 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 arendezvous - primarily it is highly desirable to have daylight inwhich to get a visual on the target early on, and to fly proximity opsand docking while being able to see the target properly.

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

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

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

The Correction Burn

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

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

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

Arrival At The ISS

As already mentioned above, a Lambert solver provides a sequence oftwo burns, of which the first brings the Shuttle to a specifiedlocation, and the second nulls the relative velocity with the targetonce there. It is now time to do the second burn in the sequence, andthe blue marble of Earth is seen through the flightdeck windows as thespacecraft moves into burn attitude.

With the ISS already visible in the distance, the braking burn isexecuted with the left OMS engine firing - the burn attitudeautomatically computed to put the thrust vector through the Shuttle'scenter of gravity.

Rotating the spacecraft, we can now see the ISS through theoverhead windows some 1.6 miles away, pretty much at the samealtitude. This is the so-called 'vbar' - we are located along thevelocity vector of the ISS, which in fact means we are in the sameorbit, just a tad behind the station. The vbar is the only stableposition relative to ISS - if we were, say, above the station (alongthe radius vector or 'rbar'), our orbit would have a lower orbitalvelocity, and we'd gradually lag behind, so regular thruster firingsfor 'station-keeping' would be required.

On the vbar, we could stay for a long time, but daylight won't lastfor more than 45 minutes in this orbit, so if we want to dock soon, weneed to get moving.

The Vbar Approach

The first task is to get an accurate range to the station. So fareverything has been computed based on what the navigation system ofthe Shuttle has computed for the position of the ISS relative to theShuttle (the position of which is based on inertial navigation). Thatmight easily be off a hundred feet or more - clearly it is notaccurate enough for docking. Thus first the Shuttle is rotated suchthat the payload bay faces the ISS, then the Ku-band antenna isreassigned from keeping ground communications via the TDRS satellitenetwork, to acting as a radar ranging device.

Making the payload bay face the station will be the attitude atwhich the whole set of maneuvers (or proximity operations) is nowflown. This has a couple of advantages: First, this is the attitudeinto which the docking collar actually points, so ultimately we needto approach the ISS that way to dock. Second, from this attitude theradar ranging antenna has a clear and unobstructed view at alltimes. And finally, it is the only attitude in which the Shuttle canfire thrusters to brake close to the target without pointing thrusterexhausts directly at the station and damaging it.

The reason for the latter is the so-called 'low-Z' mode in whichforward and backward pointed thrusters fire together. Since they'remounted at an angle, the net force is downward (i.e. reducing motionalong the up direction out of the payload bay), although thiscombination of thrusters is not exactly fuel-efficient. As we'll seelater, there is an even better way to brake.

For the time being, we fire thrusters to move towards the ISS andaim slightly below the station - this is a vbar approach.

Now, orbital mechanics being orbital mechanics, we can't 'just' flyover this way. By thrusting towards the station, we increase orbitalspeed, so the Shuttle gradually starts to go higher and then getslower - which means we have to actively prevent that, so as weapproach along the vbar, we need to fire thrusters regularly to staylevel with the station (or in fact slightly lower) - till we finallyarrive about 300 feet below the ISS in the rbar position.

Docking Along The Rbar

Once in the rbar, we rotate the Shuttle again such that the ISSbecomes visible in the overhead windows and put the spacecraft intolocal horizon attitude holding mode (the ISS is stabilized withrespect to the local horizon as well).

Now we need to go 'up' till we reach the docking port. Well, itdoesn't actually feel like up, because looking out of the overheadwindows it feels more like forward. But then, rolling the Shuttlefeels like yaw, and yawing like roll. If you imagine having to flyyour favorite airplane that way, it could make your head spin! Butthis is the Space Shuttle - there's a 'control sense' switch which canbe flicked, and the avionics makes it easy - every control input willbe interpreted as if we're really flying forward toward ISS ratherthan upward.

As we've said before, the spacecraft isn't stable on the rbar, sosimply holding it there will ultimately mean the Shuttle moves down,towards Earth and away from the ISS. But this in fact is good -because if we use thrusters to move upward, there'll be a brakingforce provided by orbital mechanics that reduces upward speed - wenever need to use any thrusters to slow down with an rbar approach ifwe do it right!

Thus, the last remaining task is to gradually nudge the Shuttle up(or forward as it looks from the overhead windows) towards the dockingport while nulling the position and velocity errors on the otheraxes. That is not as easy as it might seem, because the Shuttle'sReaction Control System (RCS) thrusters are never clean translationsor rotations - any firing to hold attitude will also give a smalltranslation force, any forward firing will require subsequentattitude-hold firings --- there is plenty of mode-mixing. Slow andcareful does the trick, and in fact a full 45 minutes later, just asanother dusk begins over the Atlantic ocean, the task is done and thedocking is made.

Now the crew can take a much needed breather and enjoy the displayof the Northern Lights around the pole. Later when crossing overcentral Asia, the connection will be prepared so as to enter theinterior of ISS.

Which is not simulated... yet.

More information:

• FG Space Shuttle Wiki page
• Project overview and Flight Manual
• Development repository
• FlightGear Flight Simulator