Math / Physics
Stits Playboy Proj
The best size and speed of a propeller is a trade off of many factors. The most important factors include weight, efficiency, ground clearance, rpm vs hp, and aerodynamics.
The recommended fastest tip speed for cruising is about 85% of the speed of sound (Mach) for metal props, or 80% for wood and composite. Additional design information is provided below the input form.
Ideal Tip Speed
The theoretical best propeller would provide all the needed thrust with one blade, 1 rpm, be a mile long, 1 inch wide, and have no weight. With all the factors listed below, the best compremise is the longest diamter that does not exceed about 85% of Mach at cruise RPM. This speed is a compromise of engine speed, horse power, propeller weight, and drag.
The smaller the propeller the lighter it will be. Weight favors a minimum diameter size.
The longer and thinner the blade, as well as the fewer the blades, the better the efficiency. Efficiency favors large diameter propellers.
Nearly all installations favor shorter blades for ground or fuselage clearance. The shorter the blades, the shorter the landing gear, thus saving weight. Even high wing multi-engine planes with plenty of ground clearance prefer short propellers that place the engine as close to the fuselage as possible so that asymmetric thrust is minimized if an engine fails.
RPM VS HP
Slower RPM is more efficient. However, more thrust for lighter engine weight is achieved through higher engine RPM. Engine weight and HP favors faster propellers.
Long thin blades have the least aerodynamic drag. Fewer blades means less tip vortex drag. The fastest portions of the slipstream begins to break the sound barrier when an object approaches 90% of Mach. When air travels at Mach speed, drag dramatically increases and cavitation causes efficiency to drop. Aerodynamics favor long thin slow moving propellers.
The original auto (1961-1965) 1200cc VW engine was red lined at
3600rpm ALL OTHER models had a 4000rpm red line. The most critical aviation
related rpm limitation is prop tip speed - it is best to keep the tip speed
below 80% mach. The formula for tip speed is...
Common prop sizes for VW engines is 50-60 inches. If we use a 54 inch prop for our example, we find that a 54" prop at 4000rpm is travelling approximately 85% of the speed of sound - a reasonable value during takeoff. A target of 4000rpm also gives maximum rated hp for the VW engine.
mph = 4.5 * 3.14 * rpm * 60 / 5280 = 642 mph
Static RPM for fixed pitch props is about 80% of red line so...
A climb prop will be about 10% more and a cruise prop about 10% less...
v = d * r / 229.9