Len, yes if you do it that way, by keeping a constraint on sail area in addition to a constraint on batten balance, then you are right: the sail with a higher aspect ratio will have a centre of area which is closer to the mast centre line. You are correct in that case.
I hadn’t thought of calculating it that way – in fact I was looking at Arne’s three model sail plans (AR 1.8, 2.05 and 2.25) in which for comparison all three sails have the same chord length and their centres of area all lie on approximately the same vertical line same - but, of course, they do not each have the same area.
So, following your reasoning and keeping the sail area constant, let us scale down the AR 2.25 sail in Arne’s suite of sails, so that it has the same sail area as his AR 1.8 sail. The scale factor for that area transformation will be 35.31/46.46 which is about 0.76. Using the square root of that, for a linear scale factor, that taller sail will now have a chord of about 4.36. If both sails are now given the same batten balance (let us say 10% of chord) the centre of area of the AR1.8 sail will be 2m aft of the mast centre line, compared with the centre of area of the AR2.25 sail which will be 1.64m aft of the mast centre line.
So as a result of that drastic change of AR (from 1.8 to 2.25) we can in theory get about 36cm of “wriggle room” when it comes to mast placement – provided the batten balance is not more than 10%. As you have hinted yourself, this is not a very rational way to choose the aspect ratio of your sail, as a number other important factors are also involved.
Furthermore, I think when you were discussing aspect ratio you were doing so in the context of a split rig. A split rig really makes no sense at all unless the batten balance is at least 30% or more, so while we are in the mood to do a little arithmetic, let us also consider the same question in relation to a batten balance of 33%, which is probably the optimum for a split rig. In that case, a change of aspect ratio from 1.8 to 2.25 would lead to the centre of area being 0.85m aft of the mast centre line in the first case, compared with 0.73m in the second case – a difference of 12cm in regard to Arne’s suite of model sails. This is not an exact business, and 12cm is surely within a reasonable margin of error, that is to say: negligible on a 30’ long-keel vessel.
Summary: I think we both agree that the starting point is to have some idea of where the centre of area of the sail plan should probably lie. From there, the goal is to find a sail type which is centred there and, as far as possible, is in harmony with the requirements of the type of vessel, its internal layout, placement of berths, hatches, sheeting position etc. If there is a preferred place for the mast, then this will largely dictate batten balance of the sail, though in some cases a little bit of fine tuning with mast rake and (as you have rightly pointed out) aspect ratio might also make a small difference. If batten balance of more than 30% is dictated by the preferred mast position, then a split rig might be the answer but I would not venture to allow more balance than about 33% (35% if you want to be a pioneer) and in that case aspect ratio would not make a lot of difference in the quest for helm balance. I suppose it could be argued that every little bit helps, so your suggestion was good, and thanks for correcting me.
The important point to keep in mind, in my opinion, is that the split rig may in some cases be the perfect answer (I am very pleased with mine) – but it is probably one of the least amenable to being used as a platform for experimentation and, of all rigs, offers the least amount of opportunity for adjustment later if things don’t quite work out in regard to helm balance.
All this academic stuff is perhaps a little less crucial when it comes to the vessel which is the subject of this thread. The nice thing about this Fisher 30 is that it will have a good auxiliary engine – but more importantly in regard to this discussion, it has a long keel which ought to make it a little bit more tolerant to small variations in the position of the sail plan – and it presents the potential for a ketch rig which, as Arne has pointed out, allows the sheeting of the mizzen sail to contribute towards adjusting helm balance. Personally, I am very much in agreement with Len's sentiments, and would rather love to have a Fisher 30.