Calculations and Principal Assumptions
Propeller Operating Conditions
The principal assumptions are that the propeller is operating at a constant speed and constant rotation rate under moderately light disc loading. This latter assumption means this code should not be used for static or very low speed operating conditions. The propeller is also assumed to be operating at a very small aircraft angle of attack. This allows a propeller design for a single operating condition. Each blade station is designed to have the same effective blade angle of attack. In this case the angle of attack with the best lift/drag ratio is chosen. No attempt is made in this version of the program to analyze off-design conditions. An illustrated discussion on prop motion and the idea or flight helix pitch is given in the page Prop Motion
The Effect of Inflow
The light loading means that inflow velocities are small relative to the aircraft velocity. This assumption is used to estimate the inflow. A constant inflow velocity is assumed over most of the propeller disc, which is close to optimum. Inflow near the tip is corrected to account for the effect of a finite number of blades. This correction is also reflected in the pitch distribution and the element efficiency.
A short discussion of inflow with example calculations taken from my web site is at Inflow .
Other distributions of inflow will have lower efficiency and slightly different pitch distribution from the one selected here. A tip correction is applied to account for the effect of the inflow and lift reduction at the propeller tip caused by non-uniform (in time) inflow. This effect is greater when fewer blades are used and causes the 'effective' propeller diameter for one or two blades to be less than 90% of the 'infinite number of blades' configuration.
The Effect of Mach Number
The effect of Mach number is accounted for by a simple Prandtl-Glauret correction to the lift curve slope. Because the blade elements are designed to operate at the best subsonic angle of attack, the rule used reduces the angle of attack at non zero Mach numbers by a factor of SQRT(1-M^2). This factor may not create enough reduction in angle of attack at Mach numbers greater than 0.8, however, it is significantly better than using the best subsonic angle of attack at all Mach numbers. The lift/drag ratio can be maintained to moderately high Mach numbers by using thin sections.
A discussion and graph of these effects of transonic Mach number as measured in a wind tunnel are on the Mach Number page
The Effect of Reynolds Number
No account is made for the effect of Reynolds number on blade section aerodynamics. One of the data elements in the output file is the chord required to produce a constant Reynolds number (Re) along the blade. The nominal value set is 200000. For Re below this value the skin friction coefficient increases roughly like the reciprocal square root of Re. In other words, reduce the Reynolds number by a factor of 4 and the skin friction coefficient goes up by a factor of 2. After Re=200000 the skin friction coefficient decreases very slowly up to Re=106 at which time the flow is predominantly turbulent. Smaller values of Re can be used, but values less than 100000 not only entail higher skin friction but also have a greater tendency to flow separation at angle of attack.
In general lower Re is bad. the value of 200,000 is chosen because the dramatic improvements in aerodynamics by increasing Re at lower Re are no longer available. The chord output by the program is a recommended minimum chord. In many cases the chord can not be made as large as this, but an attempt should be made to come close to the recommended chord. This will usually mean larger blade chord near the root of the propeller than is used in current designs. Continued discussion of this is on the page Reynolds Number
The constant Re blade shape in the output is roughly consistent with the shape that produces the best inflow distribution over the middle of the blade. Very close to the root the chord should be reduced. At the tip the chord should be reduced. A rounded tip, with a low thickness/chord ratio should be used consistent with the drop in efficiency at the very tip. The "effective diameter" produced by the output file can be used as a place at which tip rounding can commence, but not any closer to the root. Note that the chord should be kept high where the blade element efficiency is high. This procedure would produce a propeller with larger chord from, say, the inner 20% to the inner 50% of blade radius .
A discussion of some aspects of efficiency taken from my web site is at Efficiency .