Does anyone know the formulas that the "Float Design Program" is using to determine float width and height?

I having trouble understanding how it's able to determine these measurements without any flying weight input.

Height of the float is almost a direct function of the length. If you come off the step at 4 degrees, you'll tend to have a certain amout of height of the float just by the amount the line rises before it gets to the required length. Same in the rear.

Width of the float has a lot to do with the weight they have to support, but over the years floats have gravitated to a given fineness ratio(length/width).They're probably wider than they have to be, but fit a range of weights expected for their length. So the program probably just assumes a typical value. Floats with tapered sides have wide bottoms for good planing and narrow tops to reduce frontal area where it does no good. But it's hard to call a tapered float "4" wide" unles you specify where the width is measured and the taper angle.

The Chuck Cunningham article in Randy Linderman's website has a width table vs weight, but it is for flat-bottom floats with a rectangular cross-section.

If you want to analyze it, calculate the volume of the float (tedious, but not impossible to get close.) Water weighs 62.4 pounds per cubic foot. 0.58 ounces per cubic inch. Each float should support at least the entire weight of the airplane.

As with most things, float design is not all that critical. Some people have floats that are poorly matched to their planes and they fly anyway. It's about like wheel diameter or propeller selection. There are advantages and disadvantages to every selection, not just one "Magic" configuration that will fly while something slightly different will be a disaster. Oversize floats will ride higher on the water, pop up on step more easily, and will generally provide easier takeoffs. They will add more drag to the plane, and more weight, so airborne performace will be lost. Undersize floats may fly better but may be harder to get airborne. You may get a lot more water in the prop while taxiing. Long, squirelly takeoff runs frequently result in something other than a graceful liftoff.

>As with most things, float design is not all that critical.<

I imagine that for most float design applications, "TLAR"* design principles work well enough.

*= "That Looks About Right"