From What I understand the Wright brother never had university training and although never getting a high school diploma they did attend high school. Looking at the diagrams of their original work they needed to work out pressure differentials on the surface of the propeller using mathematical formula. Their work appears to have quadratic equations and cross products in the calculations complete with torque and power. Does anyone know where they may have learned these skills ? I don't believe any high school of that day in that area of the country would have had the ready math and physics needed to these tasks. Or was it the case that they were self taught in all the needed math,experimental, managerial, drafting and tooling skills needed for such an accomplishment? The diagrams are more along the line of advanced undergraduate but way beyond high school or at least those of today. Thank you.
How or where did the Wright brothers develop the expertise to formulate quadratic equations to design their first propeller?
The Wright brothers developed no serious theory for designing propellers. Wilbur Wright, in one of his notebooks, wrote the calculations you can see in the attached picture. He applied no calculus, no quadratic equations, but used a combination of empirical formulas already in existence.
This is the propeller theory of the Wright brothers (dated March 6, 1903).
The only things the Wright brothers published before being seen flying, on August 8, 1908, in France, were a few articles containing pictures of their gliders and also they filed 5 patents (see the book below). None of these documents contain drawings or photos of powered flying machines with engine and propellers. The pictures, allegedly made in 1903, 1904 and 1905, showing their airplanes flying or on the ground, were published for the first time in September 1908.