I read on a thread recently about optimum mast foot postion being a fairly standard distance from the transom to the back face of the mast.  On the river at the moment there is a trend to go for tall (22"6) rigs which have a higher aspect ratio.  The question is - would you expect to have to move the mast foot further forward or back (or not at all) with a taller rig?  Thanks

Find the centre of effort of each main a rough approximation is by bisecting the head, clew and tack angles where they meet is the centre off effort (approx')the lower rig for an equal jib size (main area varies with rig height?) will have a longer mainsail foot and might be expected to have a slightly further aft centre of effort thus with a higher rig, the mast a smidge further aft or more mast rake might be the thing.

Mr Smiley is right, but it can't be very far different and the sails are not triangular so it is difficult to do by theory. However you could try the old designer's trick of making small scale, flat, card cutouts of the shape of your different rigs (Main and jib),  and find where they balance horizontal on a pin. Similarly make a side view cutout of your hull with plate and rudder included and balance that This gives you a fairly good approximation of centres of effort and hull resistance and you can scale back up to where to put the various rigs on the hull to get the rig centre directly above the hull centre.
After that "Sail suck it and see" to fine adjust. Hours of fun!

A pin? I think a ruler might be easier - line up with each corner in turn, and find where the lines cross!

Don't forget the holistic nature of the boat. The effort of two sail, jib and main (and the slot between them), versus the lift from two foils, centreboard and rudder. Don't forget that moving the mast forward closes the slot between the jib and main, moving it back opens the slot. Then there is the cut of the jib and the position of the jib cars etc.

You could try and work it out on paper, but in the end you will have to do some practical experiments, and the river isn't the best place to do that - a day ticket to Queen Mary or similar is the order of the day. Ideally a 2 boat tuning excercise against a boat that is known to go well. Change one thing at a time only. The balance of centre of effort can be compensated by the position of the c/board, which can be adjusted temporarily by lifting/dropping it in the normal way to find the best balance. Sailing dead flat to find out how much weather or lee helm you have. There are multiple theories of how much weather helm is ideal, I think that was covered in another thread.

Just re-read the prior thread. I think it has everything you need to know, plus a special discussion on ho wto go fast on a river.

The simple way.
On a lightish wind day set the mast to upright, centreboard down, boat flat, and trimed, sails correctly adjusted on a beam reach,   it will go in a straight line, if you then rake the mast back it should luff, if you rake forwards or lift the centreboard it should bear away.

DV, 
Throw mast up in any old position, tie up with a couple of bits of string due to incorrect shroud lengths , borrow various sails from various relatives positioned around the boat park and off you go, a normal sunday race for you..........

...thats before the arms race escalated!

Why have you employed a decent helm ?..........