##### . 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 propeller

## know the methods Evolution of propeller calculations:

The 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 propellers, an article on the history of propellers is also viewable..

Evolution of modern methods of calculations of propellers:

The 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 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 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 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 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 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

##### Here is the introduction of "the MODERN DEVELOPMENT THEORY OF propeller" Raymond Siestrunck published in 1947 : The theory of the propeller is constantly renewed and developed since the onset of theoretical essays Rankine (1865), as knowledge about the operation of the propeller aerodynamics and bearing surfaces in general were extensive, and the first proposed methods deal with the problem in a similar way to that of turbines: the helix is formed by a series of elements corresponding to the different sections of the blade and that can be considered without any interaction between them, the fluid reaches this blade member with a speed equal to the resultant of the speed of advancement and rotation of the element, whose action is a deflection of the fluid flow being evaluated by kinematic considerations deduced 0n by applying theorems of momentum and angular momentum, the basic thrust and torque provided by the member, and the total forces are obtained by integration along the blade. Other methods penetrate a little further into the aerodynamic mechanism, applying to each element of the theoretical or experimental laws of fluid resistance, determined, of course, elements of uniform translation, integration then gives the total expressions traction and torque, here is the place names of Redtenbacher (1875) and W. Froude (1878), a complete description can be found in the General Theory of the helix, Gauthier-Villars, 1920. of Drzewiecki. On a quite different basis then places the known theory H.-E. Froude (1889), which directly connects the pressure and engine power of the propeller wake created by the latter, the analysis of this trail is incomplete since admitted that the propeller communicates the fluid flowing through a certain wind speed uniformly distributed over the disk it scans, or, equivalently, that the effect of the propeller is equivalent to a discontinuity in pressure on either side of this disque.Il not until 1912 and the first memories Zhukovsky for the connection is made between previous theories and the importance of vortex emission energy exchange is already proven, and knowledge of the path of the propeller has greatly increased since the experiences Flamm (1909), which is what allows Joukowski the foundations of the current theory, in which still applies to each blade element, the experimental results of the bearing surfaces, but due to the interaction of other elements, including the vortex emission "induced" on any additional blade speeds. The connection between these induced velocities and operation of an item is made using the "traffic" that characterizes the lift of each item, the theorem that now bears the name of the Russian scientist. Joukowski work related only propellers constant traffic distribution along the blade, but not least the work ahead of the Göttingen school on airfoils and propellers (Prandtl and Betz), and since then, numerous studies have been published on the problem of the propeller, which, at the death of Joukowski, I-92 I was completely set. The further development of the vortex theory of the propeller on a similar Prandtl model for the airfoil, has faced much larger than it was in difficulties, and its development was, therefore, less brilliant and less complete. This is for the most part to the fact that the assessment of additional gear in the wake produced by the turbulent exhaust can be made in simple terms in the case of the propeller, and that, except in a few special cases, the difficulties mathematical order paralyze the development of the theory. It has, however, developed modes approached different problems regarding propellers solution, or that focuses on determining the shape characteristics of the propellants for performance imposed or that addresses the inverse problem , determining the performance of a particular family and that deduced by continuously variable pitch propeller, the first point of view resulted mainly work known Goldstein (I929 ~, which provides, in the field validity of the theory, a rigorous solution of the problem of adaptation, the second point of view leads to calculations that are a degree of complication necessarily at least one of the methods used for the wings (Glauert, Lotz) but we see that they can be made quite manageable to allow interesting comparisons between theory and wind tunnel measurements. We will briefly review the assumptions that are the basis of the current theory of the helix, and report the main difficulties they rise or remain after ....

automatique traduction from french text:

Raymond Siestrunck 1947

Among these methods of calculations propellers, Heliciel software uses the most successful (the vortex theory of the propeller) with corrections of Glauert and Goldstein