C of E for small landsailor soft sail

I have a 5sq M landyacht I have modified, longer wheelbase and wider beam. I have had a 3sq M high aspect pinhead sail made for high winds, 20-30mph. The 4.5sq M sail is tough to handle in puffy conditions over 20, but I have never capsized the craft. The 3sq M sail is tough to handle in puffy conditions over 25 and I have had 2 violent capsizes with it, the last in wind less than 20. After the 1st, I increased the the wheelbase and tried to find where the CofE might be. I've read the Good Ol' Boat reference, James Wharram's article on stability, all the landsailer's articles I can find. On the x axis, the first 2 articles put the CofE 50% or a little more back of the mast, the landsailers use 30% back.
Even on a small craft a 20% difference can make a big difference in where and how to adjust the mast placement. At least the underwater variables are eliminated from this problem, and the sailplan is simple (the fabrics are hi-tech and the sailmakers were experienced and known in this field). I suspect there are some dynamic forces at work and there may not be a specific point on the horizontal axis that is the CofE.
Where is the CofE? Or what is the range of the CofE in this circumstance and what affects its movement while under way? If a good estimate cannot be arrived at through measuring and calculating, are there some indicators or tests that can be done to see where it is?
(CofG on landsailors is readily found through balancing the loaded craft. Pulling the loaded craft sideways on a sliding surface produced the same results on my craft and most others)
Looking forward to Tom's "Feeding and care of the boundary layer". Steve Blevins

 

I'm not sure if you're looking to find the vertical center of effort or the longitudinal center of effort, since you talk about capsizes but then refer to the X axis. I also don't know if your capsizes were while going upwind or downwind.

There's a difference between the vertical center of effort and what I'll call (since I've never heard anyone else talk about it) the vertical aerodynamic center. What I call the center of effort is the heeling moment divided by the lift. It's the height where you'd pull horizontally with a rope to produce the same heeling moment. But when you increase the lift, say when a gust hits, the change in heeling moment is centered at the aerodynamic center, not the previous center of effort. And the new center of effort will move closer to the aerodynamic center. The reason there's a difference between the aerodynamic center and the center of effort is because sail is twisted. If the sail were rigid and you reduced the total lift to zero by changing the angle of attack, the heeling moment would not be zero. In aeronautical terms, this is the difference between the basic lift distribution and the additional lift distribution. So one problem you might have is the new sail has a different relationship between the center of effort and the aerodynamic center.

Then there's the fact that the sail is not rigid. The 5-square landyachts use a very bendy rig with a nearly square-topped sail. I don't have much experience with them myself, but the 5-square pilots I've talked to say you don't dare sheet out in a gust because the rig will stand up and feed more draft in the sail, powering it up more than it sheets out. By going to a pinhead sail, you've reduced the sail's tendency to blow off at the top and you've probably also reduced the bending moment applied to the mast by the leech tension. So you've changed how the rig responds dynamically in a gust, possibly in a way that makes it less forgiving so that you have to be more on top of things to steer up or down as you get overpowered.

Finally, pulling a landyacht sideways does not indicate where the rolling center of lateral resistance is. When you're sailing, the tires are not skidding, even though they are slipping to leeward at a rate that's proportional to the sideforce applied by the rig. This leeward slipping - the same as leeway in a sailboat - is due to tire flexibility, not skidding. Imagine you replaced the tire with a whole bunch of feet, connected to the rim by springs. As each foot comes in contact with the ground, the spring deflects as the load comes onto it and the rim moves that much to leeward with the foot planted on the ground. As the foot comes off the ground it springs backinto the plane of the rim. So the wheel walks its way to leeward as each foot is planted, flexes, and springs back. The same thing is happening with flexibility in the tire sidewalls. There are lots of models for how tires behave - see http://naca.larc.nasa.gov/reports/1958/naca-tn-4110/ for some test data and relationships you might be able to adapt by measuring the vertical deflection of your tires under load at different tire pressures.

The current 5-square yachts evolved to their present design through a lot of generations - the original 5-square landyahcts were much like the Manta's! You've made some big changes and I suspect it'll take a fair amount of experimentation to get things back in balance.

 

Tom, thanks for your reply. Both capsizes were going upwind. Sorry about the x-axis error, I'm not concerned with the vertical CofE outside of keeping it low as possible. I'm trying to figure how much adjustment to put into an adjustable mast step system, or if expedient just add one more step, and where to put that. So I'm looking for a guide to the longitudinal CofE.

The observations about the sail and rig are what I have experienced. I did not sheet out in the capsizes, partially for the reasons you state.The 5sm class seems to be oriented to beach sailing in sea breezes which makes the craft overpowered in stronger desert winds and hard western desert playas.

I did come across a catamaran designer/manufacturer's statement that the CofE (y-axis) will be at the deepest draft point. This seems right to me, but everything I have learned so far about fluids has been counter-intuitive.
I hope this clarifies my question, because I really need a better quantitative idea of where the forces are that I need to balance.