##### . So designing a propeller in 3D and test with finite element produces very nice designs but is a form of empiricism costly in time and does not necessarily give good results. Prior to model the object, the method of calculating propeller must determine the speed induced by the propeller at the same time as its form, this method exists, its history is summarized on this page, but it presents the mathematical difficulties (convergence of nonlinear equations Resolved by Newton method) as the offices of mechanical studies have left to theorists of fluid mechanics. Heliciel The software has been designed to integrate this method in modern design offices mechanical studies. This does not not exclude the use of 3D CAD model because the optimum blade created using Heliciel in IGS Format may be injected into the CAD!
Evolution of methods of calculating screw propeller
The screw propeller calculations evolution, teaches us that every invention is based on observation, but also on the observations made ​​by our predecessors. If "sit on the shoulders of the giant" means to use the knowledge of our peers and parents, take a little height and time to read this summary of the evolution of methods of calculations of screw propellers, an article on the history of screw propellers is also viewable..

Evolution of modern methods of calculations of screw propellers:

The screw propeller, to the origins, was considered a screw, progressing in a fluid environment exactly as does the screw in wood or metal. For the latter, the feed per revolution is not exactly equal to the screw. It was believed that the propeller efficiency would be 100/100 if so for her, since the advance along the axis would be equal for each round, to the pitch of the screw propeller. Neglecting friction, the work required to turn the screw is exactly the work required to lift a weight. The same is true for the propeller (assuming it is equated with screws) work required to turn the propeller (work done by the engine) corresponds exactly to the work necessary to "pull" the plane, still neglecting friction.

But in fact, the screw propeller, the situation is different: the fluid flows around the propeller and the propeller "back" from the position it would occupy if the fluids behave like solids. the useful work per revolution being the product of the pulling power of the actual advance of the axis for each revolution of the propeller, the propeller efficiency is therefore less than 1. Thus we can express the first theory of the screw propeller. Rankine went further, He established in 1865, that the action of the propeller could be essentially characterized by the acceleration of the mass of fluid passing through the propeller.
• Hence it follows that the change in momentum in unit time is equal to the thrust. Rankine also states that increased speed of the air mass produced by the propeller must be low for a good performance, in other words, it seemed that there was an incentive to increase indefinitely the diameter of a propeller . Such is the theory of "momentum." It can calculate an ideal performance, since it provides the thrust, but it says nothing about the mode of transmission in which this thrust passes from air to the propeller.
• Nor does it explain the reverse process: the one by which the engine power is transferred to the air passing through the propeller. Rankine had subsequently tried to intervene in his theory the frictional resistance of the blades and the interaction produced by volumes around the propeller.
• But it is first Froude in 1889, which has enriched it. Betz then makes further progress in its calculations by introducing the rotation of the stream associated with the propeller. But even after these improvements, the theory of momentum, if it assesses with high precision and traction performance, provides no indication as to the form of corresponding blade. In 1878 Froude had glimpsed another way in the theory the propeller that of "blade element" based on knowledge of the forces exerted by the blades in their movements. A few years later, Drzewiecki elaborated in his "General Theory of the propeller," the true theory of the blade element that Froude had glimpsed: here appeared the "geometry" of the blade, it was divided into a many elements, perpendicular to the radius, each of which is considered a profile moving at a speed, which is the result of the forward speed, and the tangential velocity

Here is the foreword of "General Theory of the screw propeller" published by S.Drzewiecki
in 1920 which outlines the theory of blade elements :

##### Automatique traduction of french original text: S.Drzewiecki
After the theorie of the blade element is, in 1912, the vortex theory of screw propeller of Joukowski. In this theory, each propeller blade is considered to be a vortex attached to the blade whose circulation is variable along the blade. This variation produces a sheet of free vortices from each blade element. This theory is a combination of the above theories, momentum and blade element. It was perfected by the work of German Betz and Helmbold, Karman, Bienen, the British Wood and Glauert, the Italian Pistolesi Lanchester, Prandtl, Japanese Moriya and Kawada