Fixed pitch propellers are operated by changing the throttle only, thereby changing thrust and RPM at the same time. Constant speed propellers are more complicated because the pitch can be set separately from the throttle and range from full fine to coarse during flight and into feather and reverse for certain operations as emergency and ground maneuvers.
A full understanding of operating propellers is required of the pilot as overspeeding the engine or setting reverse in flight or on finals would be nothing less than a disaster.
In case of an engine failure the propeller should be positioned in the low drag setting. Thus with the blades perpendicular on the airflow thus full coarse, this is called feathering the propeller.
These emergencies and special operations should be practiced with a qualified instructor and on a regular basis, as such the biannual flight review is a good moment to review these procedures.
Some types of variable pitch propellers have the option to select a feather or reverse thrust position. It is obvious that it must be impossible to select reverse thrust during flight. Doing that would create an immediate emergency with terrible results.
This position is used when an engine has failed. The drag from a windmilling propeller/engine is very high and will reduce aircraft glide performance. Feathering the propeller will stop the engine from rotating and this will reduce drag. Some motor gliders use this feature when, after climbing to altitude, they shutdown their engine and feather the propeller for much better glide performance of their aircraft.
Feathering can be done manually of automatically. Large turboprop aircraft will have the latter. On aircraft without a feather position it is important that the propeller be set in the full coarse position after engine failure and thus reducing drag and increasing the glide distance.
This is used to reduce the landing roll. The blades are first set to a negative pitch angle (20°) and then power is applied. Adding power while the pitch angle is around 0° could result in an engine overspeed due to the lack of propeller torque, mechanical devices are used to prevent this situation.
It is even possible to use this to back the aircraft out from a parking stand, although caution is required. The aid from a marshaller is recommended as the pilot usually is unable to look backwards from his position in the cockpit.
Some military transport aircraft use this feature to backup after landing to the beginning of the runway to takeoff again. But these guys are trained to do this, GA pilots should not attempt these maneuvers without proper guidance.
A constant speed propeller has two mechanical stops: they are at the full fine and the full coarse pitch. With each setting there is a maximum airspeed the aircraft can reach. If the propeller overspeed fails then the propeller blades end up at the full fine pitch setting due to aerodynamic forces and with an airspeed probably higher than is normally attainable with that setting.
With the application of power the engine will then overspeed and produces no thrust until the airspeed is reduced below the maximum indicated airspeed with the propeller at the fine pitch stops.
The FAA has issued a Special Airworthiness Information Bulletin CE-10-21 (SAIB) to alert operators, pilots, and aircraft manufacturers of concerns for an optimum response to a propeller overspeed in piston engine aircraft with variable pitch propellers. At this time, the FAA has concluded that the airworthiness concern is not an unsafe condition that would warrant airworthiness directive (AD) action.
The appropriate emergency procedures should be followed to mitigate the emergency situation in the event of a propeller overspeed; however, pilots should be aware that some reduction in airspeed may result in the ability for continued safe flight and landing. The determination of an airspeed that is more suitable than engine out best glide speed should only be conducted at a safe altitude when the pilot has time to determine an alternative course of action other than landing immediately.
Overhead of an suitable runway or airport would be a good place to test this situation.
Text partially from the SAIB.