# Design of a Propeller

The computer program is based on the formulas presented in [10] (comparison Adkins vs. Larrabee). Based on the theory of the optimum propeller (as developed by Betz, Prandtl, Glauert), only a small number of design parameters must be specified. These are

• the number of blades B,
• the axial velocity v of the flow (flight speed or boat speed),
• the diameter D of the propeller,
• the selected distribution of airfoil lift and drag coefficients Cl and Cd along the radius,
• the desired thrust T or the available shaft power P,
• the density rho of the medium (air: ~1.22 kg/m³, water: ~1000 kg/m³).

The number of blades has a small effect on the efficiency only. Usually a propeller with more blades will perform slightly better, as it distributes its power and thrust more evenly in its wake. But for a given power or thrust, more blades also mean more narrow blades with reduced chord length, so practical limits have to be considered here. The chord length can be increased while decreasing the diameter to keep the power consumption constant, but a diameter reduction is usually a bad idea in terms of efficiency, as long as the tip mach number or tip cavitation is not an issue.

### The Velocity

The velocity of the incoming fluid together with the velocity of rotation (r.p.m.) determines the pitch distribution of the propeller. Large pitch propellers may have a good efficiency in their design point, but may run into trouble when the have to operate at axial velocity. In this case, the blades tend to stall. usually the best overall propellers will have a pitch to diameter ratio in the order of 1.

### The Diameter

The propeller diameter has a big impact on performance. Usually a larger propeller will have a higher efficiency, as it catches more incoming fluid and distributes its power and thrust on a larger fluid volume. The same effect can be shown for lifting surfaces, which results in sailplanes having large span but slender wings.

### Lift and Drag Distributions

Instead of the lift and drag coefficients, it usually convenient to specify an airfoil with a prescribed polar and the design angle of attack at each radius. In JavaProp, definition sections are spread along the radius where airfoil and the design angle of attack can be prescribed. The distribution of Cl and Cd along the radius can be examined later by performing an analysis for the design point. For maximum performance, the airfoils must operate at maximum L/D. But if the propeller should also work reasonable well under off-design conditions, it is usually necessary to use a lower angle of attack for the design. Again, you can check the Cl and Cd distributions for off-design cases by performing several single off-design analysis for different settings of the flow velocity v. Stall should occur gently when the velocity is reduced. The analysis code will probably give unreliable results for very small velocities.

### The Fluid Density

The density of the fluid has no influence on the efficiency of a propeller, but strongly affects its size and shape. As the forces and the power are directly proportional to the fluid density, a hydro-propeller will have much smaller dimensions than a propeller working in air. Also, lifting surface under water tend to develop cavitation when the local pressure of the flow field falls below the vapor pressure. Therefore it is not possible to use high lift coefficients in hydro-props, usually they have to stay below Cl = 0.5. The same is true for high speed tips of aircraft propellers, where not cavitation, but supersonic regions may occur if the pressure gets too low. Therefore the tip sections of propellers operating at Mach numbers above 0.7 should be designed to operate at small lift coefficients below 0.5 too. The analysis module of JavaProp uses the fluid density to calculate thrust and power during the multipoint analysis. The dimensionless coefficients Ct and Cp are not affected by a variation of density, but the values for thrust and power are. Thus a propeller engine combination will find different operating points depending on the fluid density. This makes a difference for aircraft propellers, where the performance of propeller and engine depends on the altitude.

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