That’s good, do all the reading you can: Arne’s notes and Hasler McLeod. Then you will see that placement of the mast is not a simple question which is decided in isolation. Its not a difficult question, though. I’ve only ever done one conversion so not an expert, but I do understand the slightly over-whelming prospect of having to think it all through for the first time. Be reassured, you’ll get plenty of good expert help once you get started on the design.
If that sail plan I posted matches the one on your boat – and if you are happy with the helm balance of the vessel as it is, then some of the work in calculating mast placement has already been done for you, and you need not worry too much about calculating the so-called centre of lateral resistance of the hull. You can simply calculate the centre of area of the existing bermudan rig and use that as a guide to the placement of your proposed junk sail. So, you first step might be to superimpose a proposed junk sail onto your drawing, with its centre of area where you deem it should be.
(In the case of a split junk rig, vis-a-vis the original bermudan rig, the two centres of area can actually coincide. For other types of junk rig, get advice from those who have designed them, as the best placement of centre of area may not quite coincide with the centre of area of the original Bermudan sail plan, though probably not too far away).
Now, your proposed junk sail will have a percentage of balance, which determines where the mast will go. (The “balance” of the sail being the proportion of the sail outline which lies ahead of the mast centre line). If you have a fixed figure in mind for balance (it might be anywhere between, say, 5% and 35%) then your mast position is determined.
However, if you are open as to the geometric shape of the sail and how much balance you are happy to have, then you will have a certain amount of choice as to where the mast can go. The position of the centre of area of the sail can’t be changed much, but the position of the mast can vary. In simple terms, if your proposed junk sail is one with a low amount of balance (and the concomitant high yard angle) then the mast will be at the forward end of the range of possible positions. If the sail you propose is the type with a high amount of balance (and correspondingly a low yard angle), then the mast will necessarily go towards the aft end of the range.
You can reverse this reasoning to some extent: if the internal accommodation arrangements and/or structural considerations make it desirable to place the mast in a particular position (within the range of possible positions) – then you don’t move the centre of area of the sail, but you can re-consider the shape of the sail, ie the different amount of balance which this mast position makes necessary. That in turn decides on the type of junk sail which fits your choice of mast position– in simple terms, the mast position can determine the shape of the sail: a high yard-angle/low balance sail, or a low yard-angle/high balance sail, or something in between.
In practice, the boat, the type/geometric shape of junk sail and the placement of the mast will all be considered together to find the most harmonious solution.
A further variation on mast position is also to consider the rake of the mast. A forward rake means the bottom part of the mast can be placed aft a little, if other requirements dictate. Or, to reverse the reasoning, a little bit of tweaking of the rake might allow movement of the centre of area of the sail if that is found to be necessary later. Some people prefer a certain amount of forward rake. Aft rake is not considered so desirable on a free-standing rig.
There are people reading this thread who are considerably more qualified to comment further, and my guess is, as David Th has suggested, if you have a go, and put forward a scale drawing of your proposed sail plan superimposed on the underwater hull drawing (or better still, superimposed on the hull drawing with the original Bermudan rig) you will get plenty of help and guidance from those people, some of whom have designed many junk sail conversions. (Also needed to be considered: span clearances, sheeting arrangements, structure, accommodation requirements – they will all fall into place).