Thanks Rod....very interesting. I am seriously considering "stretching the envelope". I found following from John Elwell interview of particular interest. Sage advice.....especially the last sentence.
14. In an e-mail you mentioned that Simmons did not make bellyboards himself. So, the question that begs asking is: What would a "Simmons-design paipo board" look like? For purposes of discussion let’s assume the paipo board would be 46 to 50 inches long. How wide would the board be (i.e., what aspect ratio would be used)? How thick would the board be? What would the board template look like? How much belly would there be in the nose section and where would the concave begin? What would the rail template look like from the nose through the tail (sample rail drawings for the forward, middle, aft and tail sections)? How much thinness would there be in the rails? And for the benefit of the novice paipo designer, what is meant by the "turn-up in the nose with camber?"
One of Simmons friends told me that took some broken Simmons boards and used the forward several feet of the nose and they turned out to be excellent body boards. To my knowledge Simmons did not make any body boards, but he could have.
Keep in mind the maximum width allowable is what fits between your shoulder pits. That would mean it would be different for every individual, especially for women and kids.
Remember also that displacement is calculated with Archimedes equation for the exact load.... so dimensions would vary on
thickness and actual size of the plate. Rule of thumb "generalization" and "guestimates" would not be what engineers and naval architects would be doing. Having said that, aspect ratio can be calculated by dividing the length into the width. It should be close to .5 for the ideal. Width and length will vary to load (weight of the rider) combined with buoyancy or displacement (Archimedes calculation).
It is the roundness of the rail which is not identified clearly. Old stuff written says it has to do with "roundness." Simmons use what is called soft rails for stock boards, but not for his personal boards! His personal board had harder and more down rails, to thinner, and some 60/40 percent. This is an open area for more exact research and experimentation. It is very tough to measure the results. Maybe the new strain gauges can do it with engineers in a test tank.
So what you are asking is impossible to do unless you know the load (which is what the board will carry in weight). One also needs to consider the flotation characteristics of the board. I understand that foam can calculated by the number of bubbles and density for displacement. (My son is a chemical engineer at Dow, a pioneer, and still leader in many different types of foams that surfers don't ever know about!)
How would I make a paipo/belly board? I would copy key characteristics of a planing hull which would include a
high aspect ratio (wide and parallel: divide the length into the width -- it should be close to .5 for the ideal),
smooth uplift in the nose with "camber" (some roundness to try and capture how the water spreads it to the rail for quicker and faster lift for take offs),
shallow concave to break suction, and
foiled and rounded rail (and with more down rail).
Length is open to what you want and where you surf. Keep in mind "resurgence," an important part for speed in different situations. And also what Lord said, "A good planing hull will adjust to speed." For example, a rider will automatically adjust the attack angle (tail squat) -- more that 20 degrees is stall and as the plate moves it comes up and the rider gets his weight forward to get over the "hump."
My personal feeling is the paipo creation is like the surfboard... an accident and came about from rule of thumb. The people of Oceania had no mathematics or written language or milled flat pieces of wood until the early western explorers arrived. When plywood veneers came out, especially marine type, things changed. It was once guessed by Ben Finney that the first things used by children were coconuts for buoyancy in the shore break. I would imagine ship wreck wreckage was used. Cutting out flat pieces with a stone adz seems awfully difficult but apparently done. No one knows for sure because historians guess. Wood does not last long in the elements.
One more thing that Pat Curren said and Simmons referred to, “You will know when you have a perfect board.... then you should keep it!”