17.1 Propeller fundamentals — blade element theory, pitch, slip and forces

Scope and exam

Module 17A is taken by A1, A2, B1.1 and B1.2 (EASA: 20 questions for A, 32 for B1). 17.1 is A level 1, B1 level 2: blade element theory; high/low blade angle, reverse angle, angle of attack, rotational speed; propeller slip; aerodynamic, centrifugal and thrust forces; torque; relative airflow on blade angle of attack; vibration and resonance.

Blade element theory

A propeller blade is a rotating wing. Blade element theory divides the blade into many small sections (elements) along its length; each element is treated as an aerofoil with its own chord, blade angle, local velocity and angle of attack. Summing the lift (thrust) and drag (torque) of all elements gives the thrust and torque of the whole propeller.

Each element moves along a helical path: its velocity is the combination of

• rotational velocity = 2π × r × n (increases with radius r), and
• forward (axial) velocity of the aircraft (same for all elements).

The resultant relative airflow meets the element at an angle; the difference between the blade angle and this helix angle is the angle of attack.

Key angles

Term	Definition
Blade angle (pitch angle)	Angle between the blade chord line and the plane of rotation
Helix angle (angle of advance)	Angle between the resultant relative airflow and the plane of rotation
Angle of attack	Blade angle − helix angle: angle between chord line and relative airflow
Fine (low) pitch	Small blade angle — high rpm, take-off and climb (like low gear)
Coarse (high) pitch	Large blade angle — lower rpm, cruise at high speed
Feathered	About 90° — blade edge-on to the airflow, minimum drag, propeller stops
Reverse	Negative blade angle — thrust acts rearwards for braking
Beta range	Range below flight idle where blade angle is controlled directly (turboprops)

Blade twist (pitch distribution): because rotational speed increases towards the tip, the blade angle is made larger at the root and smaller at the tip, so the angle of attack is nearly constant along the blade. Blade angle is normally quoted at a reference station (often 75 % of radius, or a station specified by the manufacturer).

Effect of forward speed and rpm on angle of attack

• For a fixed-pitch propeller, increasing forward speed (rpm constant) increases the helix angle → angle of attack decreases → thrust and torque fall → rpm tends to rise (windmilling in a dive).
• Increasing rpm (forward speed constant) → helix angle decreases → angle of attack increases.
• At take-off (low speed) a fixed coarse-pitch propeller works at a high angle of attack and may partly stall; a fine-pitch propeller is better for take-off but over-speeds in cruise — hence variable pitch.

Geometric pitch, effective pitch and slip

• Geometric pitch — theoretical distance the propeller would advance in one revolution if it moved like a screw in a solid (no slip). FAA formula:

GP = 2 × π × R × tan(blade angle at the 75 % station), R = radius at the 75 % station.

• Effective pitch — the distance the aircraft actually moves forward in one revolution.
• Slip = geometric pitch − effective pitch (often expressed as a percentage of geometric pitch).

Worked example 1: Propeller with blade angle 20° at the 75 % station; radius at that station = 0.75 m. GP = 2 × π × 0.75 × tan 20° = 4.712 × 0.364 = 1.715 m. Aircraft speed 50 m/s at 2,400 rpm (40 rev/s): effective pitch = 50 ÷ 40 = 1.25 m. Slip = 1.715 − 1.25 = 0.465 m → 0.465 ÷ 1.715 ≈ 27 %.

Worked example 2 — tip speed: Diameter 2.0 m at 2,700 rpm: tip rotational speed = π × D × n = π × 2.0 × (2,700 ÷ 60) = π × 2 × 45 ≈ 283 m/s. Adding forward speed vectorially gives the helical tip speed; tips approaching the speed of sound (about 340 m/s at sea level) lose efficiency and become very noisy — the reason for reduction gearing on high-rpm engines.

Propeller efficiency

η = thrust power ÷ shaft (brake) power. The FAA quotes typical propeller efficiencies of about 50 % to 87 %, depending on slip. Efficiency is zero at zero forward speed (no thrust power) and falls at high speed as tips approach Mach 1.

Forces acting on a rotating propeller

Force	Effect
Centrifugal force	The largest force — tries to pull the blades out of the hub (tension in the blade and retention)
Thrust bending force	Bends blade tips forward (in the direction of flight)
Torque bending force	Air resistance bends the blades opposite to the direction of rotation
Aerodynamic twisting moment (ATM)	The centre of pressure is ahead of the blade's axis of rotation → tends to increase blade angle (towards coarse pitch)
Centrifugal twisting moment (CTM)	Mass of the blade tries to align with the plane of rotation → tends to decrease blade angle (towards fine pitch); greater than ATM

Designers use these: some propellers use CTM (plus oil pressure) to move to low pitch, and counterweights (which produce a twisting moment opposite to CTM) or springs to move to high pitch/feather.

Torque and asymmetric effects

• Torque reaction — the aircraft tends to roll opposite to propeller rotation.
• Slipstream (spiral) effect — the rotating slipstream strikes the fin, yawing the aircraft.
• Gyroscopic precession — pitching changes the plane of the propeller, producing a yaw (90° later in rotation).
• P-factor (asymmetric blade effect) — at high angle of attack the down-going blade has a larger angle of attack and produces more thrust than the up-going blade, yawing the aircraft (left yaw for a clockwise-rotating propeller seen from behind).

Vibration and resonance

• Every propeller blade has natural frequencies. Engine power impulses (piston engines) and aerodynamic disturbances can excite them.
• If an exciting frequency coincides with a natural frequency (resonance), stresses rise dramatically and can cause fatigue failure.
• Manufacturers therefore specify restricted rpm ranges (marked by a red arc or band on the tachometer) where continuous operation is prohibited.
• Other vibration sources: imbalance (static/dynamic), blade track errors, blade angle mismatch, loose spinners, damaged blades. Shortening blades during repair changes natural frequencies — only within approved limits.

Exam traps

• Blade angle is measured from the plane of rotation, not the relative airflow.
• Slip = geometric pitch − effective pitch.
• Forward speed up (fixed pitch, same rpm) → angle of attack down.
• CTM → fine pitch; ATM → coarse pitch; CTM is larger.
• Centrifugal force is the largest force on a propeller.