On an aircraft, the propeller is an airfoil, much like the wing of an aircraft, except that the shape of the airfoil varies along the length of the blade, however any point on the blade describes a helix as it moves through the air. The motion of the propeller blade, when placed at a positive angle of attack, produces forward thrust and tangential resistance. The resistance produces a turning moment about the propeller axis, called resistance torque, which it is necessary for the engine to overcome.
An propeller's efficiency is determined by (thrust x axial speed)/(resistance torque x rotational speed). Changes to a propeller's efficiency are produced by a number of factors, notably adjustments to the helix angle, the angle between the resultant relative velocity and the blade rotation direction, and to blade pitch. Very small pitch and helix angles give a good performance against resistance but provide little thrust, while larger angles have the opposite effect. The best helix angle is as if the blade was a wing producing much more lift than drag, roughly 45° in practice. However due to the shape of the propeller only part of the blade can actually be operating at peak efficiency, the outer part of the blade produces the most thrust and so the blade is positioned at a pitch that gives optimum angle to that portion. Since a large portion of the blade is therefore at a inefficient angle the inboard ends of the blade are subsumed into a streamlined spinner to reduce the resistance torque that would otherwise be created.
Very high efficiency propellers are similar in aerofoil section to a low drag wing and as such are poor in operation when at other than their optimum angle of attack. It required advanced control systems and better section profiling to counter the need for accurate matching of pitch to flight speed and engine speed to power so as to make these type of propellers usable.
However with a propeller at a pitch angle of 45° at low flight speeds the angle of attack will be high, possibly high enough to stall the aircraft. The obvious need to avoid this means that most propellers are fitted with mechanisms to allow variable pitch - Coarse pitch for high speed flight and fine pitch for climbing or accelerating at lower speeds. Early pitch control settings were pilot operated and so limited to only three or so settings, later systems were automatic. Variable pitch was replaced with the constant-speed mechanism.
Constant-speed propellers automatically adjust the blade pitch angle to alter resistance torque in response to sensed changes in speed. Initially in a rather crude fashion with the pilot altering the setting, but in more advanced aircraft the mechanism is linked into the entire engine management system for very fine control. The system is termed constant-speed because aeroengines produce maximum power at high revolutions and changing engine speed increases fuel consumption. It is, therefore, beneficial to run a engine at an optimum constant independent of flight speed, setting separate requirements for high power situations and cruising and controlling speed within these bands without changing engine speed.
A further consideration is the number and the shape of the blades used. Increasing the aspect ratio of the blades reduces drag but the amount of thrust produced depends on blade area, so using high aspect blades can lead to the need for a propeller diameter which is unusable. A further balance is that a smaller number of blades reduces interference effects between the blades, but to have sufficient blade area to transmit the available power within a set diameter means a compromise is needed. Increasing the number of blades also decreases the amount of work each blade is required to perform, limiting the local Mach number - a significant performance limit on propellers.
Contra-rotating propellers involves placing a second propeller rotating in the opposite direction immediately 'downstream' of the main propeller so as to recover energy lost in the swirling motion of the air in the propeller slipstream. Contra-rotation also increases power without increasing propeller diameter and provides a counter to the torque of high-power piston engines and the gyroscopic precession effects of the slipstream swirl. However on small aircraft the added cost, complexity, weight and noise of the system rarely make it worthwhile.