Scaling plywood

scale model stresses

If we are still talking about the bending, and scale shape conforming properties here, then for a material with the same elastic modulus which is not depending on sheet thickness, the stresses in the sheet material will be exactly the same in the full size hull and the scale model hull.

This is considering only the loading on the material in bending it to the required shape, not wind and water and gravity loads on a boat hull, an entirely different matter than was posed in the original thread question.

For example, the sides of a full size hull, a steel plate for the side of a new Sharpie, 1/4 inch thick steel, 3 feet width, and 28 feet long. Say the bow section is to be bent along frames to a radius of 192 inches,

For the model, 1/4 size, we use a steel plate 1/16 inch thick x 9 inches wide x 7 ft long, and we bend it to 48 inch radius of curvature near the bow.

Fundamental Equations:

Stress = Bending Moment * Distance from neutral axis / Moment of inertia.

Moment of inertia relative to this bend problem = (1/12) Width * Thickness^3

Radius of Curvature = Elastic Modulus in Bending * Moment of Inertia / Bending Moment

For this example, the moment of inertia for the model is only 1/256 the bending moment of inertia of the full size piece. The model's bending moment is 1/64 th of the full size plate, but the maximum tensile stress, at the extreme fibers of the plates, are the same value for the full size plate or the model's plate, 19,500PSI.

This is clearly true for most metals used in boatbuilding, such as steel or aluminum. For plywood, the difference will manifest when the bending elastic modulus is variable, but for many applications the differences here are small.