There are problems with the traditional ground based compass swinging:
should be done at cruise power but cruise RPM often can't be achieved on the ground
hard to line up the plane accurately
a hassle to do in bad weather, or at grass locations when the grass is soft
compasses can be heavily affected by electrics e.g. alternator load, which lights are on, etc. Wingtip-mounted fluxgate magnetometers tend to be a lot better but all these things are affected by e.g. a steel hangar 50-100m away.
one cannot be sure there is no metal in the ground, especially on concrete
As a result most compasses are way off, notwithstanding the deviation card carrying impressive figures like 1 degree max error.
It is intuitively obvious one could use the highly accurate GPS track for this. Suprisingly, I did not find much on google... there is the usual "TAS from GPS" stuff like this, which is commonly used for calibrating one's ASI.
In zero wind, track=heading. But how can you be sure there is no wind aloft? Fly two reciprocal headings, and if this yields reciprocal tracks, then either wind=0 or you are flying in line with the wind, and in both cases track=heading.
If there is wind, it will usually be unknown, but if one flies reciprocal headings and increases them (say 15 degree increments) until one is seeing reciprocal tracks, then you have nailed the above case.
Unfortunately, a compass has one screw for N-S adjustment and another screw for E-W adjustment, so one really wants a method which yields more or less direct N-S and E-W headings.
It is hard to explain without a diagram, but it is fairly obvious that if you fly N-S reciprocal headings, and (assuming there is wind) you get non-reciprocal tracks, then your compass error will be determined from the assymetry between the non-reciprocity of the tracks and the headings being flown, and you can set this error directly on the compass. Then repeat this for E-W.
Example:
Fly 360 and 180.
If the track is 360 and 180, you have no (relevant) wind so set the compass to 360/180 (the easy case).
If the track is 010 and 170 (obviously a westerly wind from 270) then the non-reciprocity is symmetrical about the heading, so set the compass to 360/180 as before.
If the track is 008 and 168 (obviously a slight southerly component in the above wind) then your actual heading is 358.
I hope I got that right...
The above works to a first order accuracy i.e. the wind effect is small relative to your TAS. If you fly at 50kt and the wind is 50kt, the geometry becomes quite complex, and possibly needs and iterative solution.
Has anybody come across a directly usable formula for calculating the mag heading from the mag (GPS) track?
Obviously it would require several tracks to be flown, and the GS measured on each one.
The other thing is that if one has an EHSI (I have the Sandel SN3500) then the adjustment on that is much simpler: you just align the aircraft on the four cardinal headings, and set each one up in the config. The software then works out the conversion for the whole "compass rose". Then one ends up with an accurate EHSI, and it is then trivial to calibrate the liquid compass from the EHSI (not the prescribed method, sure, but a lot more accurate).
Not an answer, but there used to be purpose-built facilities for compass adjustment. The remains of one are still visible at EBGB Grimbergen, or so I am told: it was a wooden platform, onto which a plane could be rolled, and that could pivot on glass balls like a crude ball bearing.
PS if you are concerned about magnetic variation, come over here for your exercise, we are close to 0 degrees right now. Can't guarantee zero wind, though. But does it matter? I was told compasses have an accuracy of 5 degrees at the very best of times...
PPSS I have a very vague memory of an EMEA phrase that gives magvar information, but have never tried to get it. Nor can I imagine how the poor bit of electronics can be expected to determine magvar for a given location, as the value changes over time.
The mag variation should be taken care of by the IFR GPS, which has a lookup table for the variation, given the lat/long. There is also a formula for it (a long polynomial) which works well enough over most of the earth's surface.
Incidentally, how does an IFR GPS update its mag variation table? Does it come fresh with each database?
hard to line up the plane accurately
You don't need to you measure its alignment with a Datum compass
compasses can be heavily affected by electrics e.g. alternator load, which lights are on, etc. Wingtip-mounted fluxgate magnetometers tend to be a lot better but all these things are affected by e.g. a steel hangar 50-100m away.
one cannot be sure there is no metal in the ground, especially on concrete
That's why you use a surveyed compass base
As a result most compasses are way off, notwithstanding the deviation card carrying impressive figures like 1 degree max error.
I think that has far more to do with the system than the calibration. I have seen aircraft compasses that are good to half a degree and others that are not.
Unfortunately all the facilities I have are a piece of grass.
It would be much easier if one could do it in flight.
I did a search of some previous discussion of this topic elsewhere and one poster suggested that the answer would be in a book called
Performance of Light Aircraft (Library of Flight) by John Lowry
(Amazon)
Unfortunately the only copy showing is £173 
Does anybody have this book?
I don't think it is possible to solve this problem, (although I may have got the wrong end of the stick about how compass errors arise).
Assuming the compass error is due to a magnetic field which is fixed with respect to the aircraft, (e.g. something that behaves like a magnet on the right wing) then what happens when you fly North by the compass?
The 'N' of the compass needle is pulled ahead by the North pole, and to the right by the magnet. You turn right slightly (a little to the East), until the 'N' of the compass needle points straight ahead.
If the earth's magnetic field has strength '1', and the magnet's field has a strength 'm' in the same units, let's say 0.17 as an example, then you will turn till
sin(heading) = m, e.g. sin(10) = 0.17
Now if you fly South by the compass, what happens?
The 'N' of the compass needle is pulled backwards by the North pole, and to the right by the magnet. So the "S" of the compass needle is pulled to the left, and you turn to the left (which is once again a little to the East), until the 'S' of the compass needle points straight ahead.
Once again
sin(heading) = m, e.g. sin(170) = 0.17
The problem is that we had a drift to the East on both legs. Unfortunately a westerly component of the unknown wind would also give a drift to the East on both legs.
The GPS enables us to measure our drift, but one measurement cannot give us two numbers. We cannot tell how much is wind drift, and how much is 'compass error drift'.
There is a similar issue with a magnet stuck to the tail, and flying East/West.
Your North/South technique is perfect for a compass error which is always to the right (or left), but I don't think real life errors are like that. Sorry not to be more helpful!
I have a copy of John Lowry's book "performance of light aircraft" (and know John personally, very nice chap universally enthusiastic about aviation, and helpful to anybody who asks). It's currently at the bottom of a box in the middle of an office move, but I should have it back in a fortnight.
It does contain a method for compass calibration in flight against GPS - I've never tried it but it would be interesting to have a go. Shout if you fancy a play Peter - might be an interesting exercise, and I've a lot of practice in that sort of testing that I wouldn't mind brushing off.
G
Update!
Looking at the wind vector diagram, the North/South technique does actually allow an compass-error estimate, but it is horribly 'ill-conditioned', i.e. prone to error.
If you look at the Northerly components of the velocities, you can glean something from the differing ground speeds. If 'e' is the compass error, 'Gn' and 'Gs' the two ground speeds, and 'Tn' and 'Ts' the two tracks, then:
2 x TAS x cos(e) = Gn x cos(Tn) + Gs x cos(Ts-180)
You know everything on the right hand side, and you more or less know TAS, so you can solve this equation. The equation itself is general and exact, but it is ill-conditioned. Specifically, if you are 1% out in the TAS estimate, you will be 8 degrees out in the 'e' estimate!
I have a copy of John Lowry's book "performance of light aircraft"
I looked that up but Amazon shows just one used copy for £170.
The maths is a bit beyond me but I would have thought that given the magnetic track, and given reasonably light winds aloft, one is looking at second order effects due to the wind or the TAS.
After all, as the wind reduces to zero, so does the error. It's the same with DR - it works pretty well at higher speeds and light winds.
Shout if you fancy a play Peter - might be an interesting exercise, and I've a lot of practice in that sort of testing that I wouldn't mind brushing off.
Definitely up for that :)
