Propeller Aerodynamics, II
A propeller is an airfoil and like a wing it will generate an aerodynamic force much the same way. It has a leading and trailing edge, camber and a chord line. The cambered side is called blade back and the flatter side the blade face. The angle which the chord makes to the plane of rotation is the blade angle. The propeller is rotated by the engine and this creates thrust and moves the aircraft forward.
Previous page discussed the propeller blade twist and performance, in this section we will discuss blade twisting forces and length and tip speeds.
Having a understanding of these principles will really help you with learning to fly and keep your aircraft under control during take-off when these effects are most prevalent.
Propeller Twisting Forces
Large stresses are involved when the propeller rotates. Think of centrifugal force and twisting and aerodynamic twisting forces acting on the blades, hub and pitch changing mechanism. Centrifugal force is opposed by centripetal force acting toward the hub (if this was not the case the blade would be thrown away), this force is proportional to the mass of the blade times the square of the rotational velocity.
During rotation centrifugal force acts from the hub span wise along the blades outward (pulling on the blade) and also on the leading and trailing edges along the blade. As the blade has a twist (blade angle) compared to the plane of rotation, the centrifugal force will try to fine the propeller along the pitch change axis toward the plane of rotation.
This twisting force places a great demand on the pitch mechanism, counterweights are used to balance out this twisting toward the fine pitch. The force will be greater on wide bladed propellers compared to narrow blade types.
This force develops when the total reaction force acts on a point ahead of the pitch axis of the blade. It tries to increase the blade angle, coarsen the propeller. This will only partially offsets the centrifugal twisting force.
With a windmilling propeller the total reaction force is opposite and acts in the same direction as the centrifugal twisting force both trying to move the propeller to the fine position. During a steep dive these forces might become stronger than the pitch changing mechanism, effectively locking the propeller into fine pitch and possibly overspeeding the engine. Despite the fact of having a constant speed propeller.
As the propeller rotates in a circle it becomes clear that with increasing engine/propeller RPM the propeller tip speed rises too. When the tips come close to or reach the sound barrier (Mach 1.0) they will then become very noisy and propeller effectiveness is much reduced. Less thrust is the result.
But reducing the tip speed by reducing the RPM has one big disadvantage, propeller thrust will reduce also. Some propellers solve this noise problem by curving leading edges to the rear near the tips. The trick is to keep the RPM high enough to generate useful thrust but low enough to keep the propeller quiet for the neighbors.
This maximum tip speed is between Mach .88 and .92 and the RPM where that is reached depends on the propeller diameter and atmospheric conditions.
Speed of sound
In the International Standard Atmosphere (ISA 15 °C) the speed of sound is 340,3 m/s (1225 km/h or 661,4 kts) and it varies with temperature also, as that influences density too.
The formula to calculate this is: 331,3 √ (1 + T / 273,15), where T is the outside air temperature in Celsius.
Calculating tip speed
The formula VTIP = π d n, were π is a constant (3,14159), d is diameter in meters and n is angular velocity (RPM) in revolutions per minute. VTIP then results in meters/minute.
For example: a propeller of 72" diameter (1,83 m) with angular velocity of 2600 RPM gives a tip speed of: π * 1,83 * 2600 = 14947,7 meters/minute or 896,9 km/h.
Propeller tip Mach speed
Divide the propeller tip speed by the actual speed of sound at standard ISA (15 °C) and our 72" propeller at 2600 RPM will then have a tip Mach number of 896,9 / 1225 = .73 Mach. Which is below Mach .88 so we can increase RPM a bit or use longer blades to increase thrust without generating a lot of extra noise.
Increasing thrust by using larger blades (more effective thrust area) has the advantage over increasing RPM.