Design of a New Propeller

Until now the combined momentum-blade element theory and vortex theory have been developed more from the standpoint of analyzing a given propeller than from the standpoint of designing a new one. We now present the procedure for designing a propeller for a desired purpose.

For a free-stream propeller, that is, one for which the inflow is uniform, the optimum propeller satisfies the Betz condition, as proved in Ref. 5, which states that the trailing vortex sheet moves aft as a rigid helical sheet. In terms of the blade element velocity diagram, this means that from Fig. 4-5 the following must hold:

cor tan (ф – I – a,) = constant.

If H’o is defined as

w0 = cor tan (ф + a,) — V, af = tan-1

or in dimensionless form

Then, either from Mach number, stalling, control margin, or optimum l/d considerations, a radial distribution of C, is selected, which leads to the values of a along the blade and, if a thickness ratio is chosen, to the distribu­tion of e. With £, new values of T and Q can be calculated to include the profile drag losses and w0 adjusted accordingly.

Blade sections can now be selected to produce the desired C, values. For a propeller with a high tip speed, in which compressibility might be a problem, high-speed airfoil sections operating at the design lift coefficient, hence producing flat pressure distributions, would be selected. For marine propellers the same procedure is followed to avoid the onset of cavitation.

Again, in laying out the sections, their cambers and angles of attack should be corrected for wide-blade and thickness effects, as previously discussed.

Most propellers for V/STOL operation will, of course, be variable pitch. This means that they will be designed for some condition; for example, static performance. One will then simply “live” with whatever performance they possess at off-design conditions. It is usually better for VTOL operation to design the propeller for static thrust conditions and to accept the efficiency in cruise that the propeller delivers. In general, this efficiency is only a few percent lower than that produced by a propeller designed for cruise. On the other hand, the static performance of the latter propeller can be significantly poorer than that of the propeller designed for static conditions.

Recently, Wald [6] treated the problem of the finite hub for an infinite number of blades. Unlike McCormick [4], who considers an infinitely long hub, Wald treats a hub that is finite in length. He argues that Betz’s condition must hold in the ultimate wake in which there is no hub. Hence for the same number of blades and advance ratio the loading distribution in the ultimate wake is the same with or without a hub, and w, can be calculated as if there were no hub. Continuity can be used to find the increased radius at the plane of the propeller through which the streamline passes and which has the value of 2w, in the ultimate wake. Circulation is preserved on the streamline so that 2w, just aft of the propeller plane will be less than in the ultimate wake.