Chapter 1: How a Propeller Makes Thrust

The propeller as a rotating wing

A propeller blade is an aerofoil, just like a wing, but it moves along a helical path. The engine turns it; the lift it produces, tilted forward, is thrust. The drag of the blade acting in the plane of rotation is felt by the engine as propeller torque, which the engine must overcome. A propeller converts engine shaft power into thrust power, with a typical efficiency of about 80–87 %.

• The face of the blade is the flat (pressure) side, facing the pilot on a tractor propeller. The back is the cambered (suction) side, facing forward.
• The chord line runs from the leading edge to the trailing edge of a blade section.
• Thrust depends on blade angle, rpm, air density, forward speed, blade area and aerofoil shape.

Blade element theory

Blade element theory divides the blade into many narrow sections (elements) from hub to tip. Each element is treated as a small aerofoil with its own radius, chord, blade angle and local airflow. The lift and drag of each element are calculated and then summed along the blade to find total thrust and torque.

• The rotational speed of an element is 2π r n (r = radius, n = revolutions per second). The tip moves fastest, so the tip produces most thrust.
• To keep the angle of attack nearly constant (and near its best value of about 2–4°), the blade is twisted: high blade angle near the hub, low blade angle at the tip.
• Because the blade angle varies, it is quoted at a reference station: often the 75 % station (75 % of the radius from the centre of the hub), or a station given by the manufacturer.

Blade angle, angle of attack and relative airflow

• Blade angle (blade pitch angle) is the angle between the chord line and the plane of rotation. It is fixed by the hub and pitch-change mechanism, not by the airflow.
• The relative airflow (resultant wind) at an element is the vector sum of its rotational velocity and the aircraft's forward velocity. The angle between this airflow and the plane of rotation is the helix angle (angle of advance).
• Angle of attack = blade angle − helix angle. It is the angle between the chord line and the relative airflow.
• For a fixed blade angle:
  • more forward speed (same rpm) raises the helix angle and reduces the angle of attack;
  • more rpm (same forward speed) lowers the helix angle and increases the angle of attack;
  • at static run-up (no forward speed), the angle of attack equals the blade angle, and a coarse-pitch blade may be partly stalled.
• This is why a fixed-pitch propeller is efficient only at one combination of airspeed and rpm. A variable-pitch propeller changes blade angle to keep the angle of attack efficient as conditions change.

Pitch, slip and efficiency

• Geometric pitch — the distance the propeller would advance in one revolution if it moved like a screw in a solid medium. At the 75 % station: GP = 2π R × tan(blade angle).
• Effective pitch — the distance the aircraft actually advances in one revolution.
• Slip — the difference between geometric and effective pitch, often given as a percentage of geometric pitch. Slip is not wasted energy in itself; it reflects the angle of attack the blade needs to make thrust.
• Propeller efficiency = thrust power ÷ shaft power. It peaks at a small angle of attack and falls when the blade stalls (low speed, coarse pitch) or approaches zero lift (high speed, fine pitch).
• Tip speed must stay below the speed of sound. As the tips near Mach 1, shock waves form, efficiency falls sharply and noise rises. This limits diameter and rpm, which is why large engines drive propellers through reduction gears.

The range of blade angles

A windmilling propeller (blade angle too fine for the airspeed) is driven by the airflow and turns the engine, creating a large drag. Feathering prevents this on multi-engine aircraft.