Don -
your question starts to take us towards the “physics” involved in boat design - along with a myrid of other “sciences”.
One must go back to drawings, to determine “where” to place a mast, and that is dependant on sail area and how it is distributed between jib and main. (very basic here guys - don’t want to get too technical.)
When you view the hull, keel and rudder from the side, “somewhere” there is a point of lateral resistance - what keeps boat from sliding sideways. Called the CLR, it is a mathematical point where all the sideways (resistance) forces are located. The designer/architect will then draw a sail plan, and both the jib and main will have a point called center of effort (CE). This is a “point” calculated mathematically, where all the effort is concentrated on the sail plan.
Usually, the designer/architect will locate this CE (center of effort) point slightly to the rear (aft) the center of lateral resistance. (CLR) When the CE is behind the CLR, the boat will tend to exhibit weather helm - meaning it will turn into the wind if no pressure is applied to the tiller/rudder. If the CE is forward of the CLR, the boat will exhibit a tendencey to fall away from the wind (lee helm).
Depending on the CE distance forward or aft of the CLR, determines HOW MUCH weather or lee helm one has.
With current computers, and designs that are known to work, a lot of these calculations are now removed, because after seeing boats for a while, one’s eye can almost tell by experience where the mast should be located. But, remember, if you change the shape or sail area of jib or main (or both) there will be a new CE and the process starts all over again. If you use a known boat, and simply measure back from the bow, you will be reasonably close. Being able to move mast forward or backwards still might be required. If you look at the US1M construction guide, there is a great illustrative mast step made out of multiple tubes in a line that can be attached to the top of your keel. It allows the mast step to be moved forward or back. Looks like a multi-barrel cannon! [:D]
Anyway, as the boat goes through the water, the pitching (hobby-horsing) as bows goes up over waves, or down in a gust also impacts boat handling so keeping weight near center and reducing the pitching also is important.
Finally, if you want to do your own experiments, remove a lot of the variables - use the same sail plan, and transfer the outline to paper. If you make it into a (general) pyramid shape, you can draw lines perpendicular to each of the three sides (where one side is the jib luff, the other side is main leech, and the third side is the combined foot of both main and jib). Where these cross is the approximate (note: APPROXIMATE) Center of Effort (CE) and you can use that to move the rig location and locate from side view of the hull. Granted, in reality, it is a little more complicated, and does involve math and is made easier with computer programs, but this kind of gives you an idea of where and how to locate a mast if it is completely new sail area.
Best to stick with known designs/locations, and only have to tune the rig a minimal amount. But, still a fun thing to do and see how close you are for the first sail.
