We all know the Wright brothers built the first successful airplane. But their advances in propeller design are less known. They realized a propeller is really just a rotating airfoil (wing). By applying knowledge gained from their wind tunnel testing on wings, they greatly improved propeller design. Incredibly, their first hand carved propellers were 95% as efficient as the best designs we have today!
Propellers produce thrust in precisely the same way a wing produces lift. A cross section of a propeller is indistinguishable from a wing. They often have a slightly longer upper surface known as camber but this is not essential.
Bernoulli's principle describes an increase in speed as a fluid (air) passes through a constriction in a tube. With this acceleration comes a drop in pressure. Propellers and wings make use of this pressure differential to generate thrust and lift. As air accelerates over the top of the propeller blade it's pressure becomes lower than the airflow beneath. The shape and camber of the blade is not as important as commonly believed.
The angle of attack of the propeller blades is the prime influence to thrust generation, much more than shape does. This is where Newton's laws come into play. The propeller blades act on the mass, air, which is accelerated rearward. The equal and opposite reaction generates thrust to pull the aircraft forward. Small aircraft must strike the best compromise between low and high angles. Where weight and complexity are less critical, variable pitch propellers are used. Multiple engined aircraft can "feather" the blades when an engine fails. This decreases the angle of attack to reduce drag as much as possible. Complex aircraft can reverse the pitch to produce reverse thrust and shorten landing runs. They can also vary thrust to aid in steering, especially handy for float planes.
The second influencing factor is speed. As engine rpm increases, the higher propeller speed generates more thrust. Some aircraft have a gearbox, which can adjust propeller speed. Float plane pilots must be careful of blade speed on the water. A blade damaged by excessive speed on the water looks like it was damaged by coarse sand blasting. Blade speed increases with the distance from the hub. The "twist" in the blades are required so the amount of thrust generation will be the same all the way out to the tip. Because the speed nearest the hub is much slower, the angle of attack can be much higher. The higher angles provide more "bite" in the air.
Aircraft speed and blade speed are the limiting factors in propeller designs. A propeller is at maximum speed when the blade tips approach the speed of sound. Although propellers are more efficient than turbojets, drag, inefficiency and noise increase dramatically if the tips go supersonic. For this reason, propeller aircraft are limited to speeds below Mach 0.7
Propellers are vulnerable to icing just as wings are. To combat icing, blades have heated leading edges. They also share a similar system that sprays glycol antifreeze onto the blades.
The spinning action of propellers impart asymmetrical torque onto the aircraft. Some aircraft use two contra rotating propellers per engine. This zeroes out the torque and is more efficient as the blade tip vortexes cancel each other out. Cost and complexity limit these to military aircraft.
Jet engines seemed destined to replace the propeller driven aircraft. The economy of piston engines and the advantages of gas turbine engines guarantee propellers are not a thing of the past. The trend to replace them with jets has actually reversed. Increased efficiency and decreased noise have allowed aircraft such as the Bombardier Q400 to compete head on with similar jet powered aircraft.