Principles of Flight

Torque to Thrust: Propeller Aerodynamics

Propellers · Lesson 1 of 2•10 min read

The engine delivers torque: a twisting effort about the propeller shaft. The aircraft needs thrust: a force along the flight path. The propeller is the converter, and it converts the way every device in this course generates force: with an aerofoil at an angle of attack. This lesson builds the blade element, the small slice of blade on which the whole subject stands, and follows it through pitch, twist, propeller types, the four operating regimes, efficiency and ice.

The blade element and its velocity triangle

Cut the blade at a reference section and look at the slice. Its chord line is an aerofoil chord like any other. But the air it meets comes from two motions at once: the blade's rotation (velocity ω·r, in the plane of rotation, growing with radius) and the aircraft's forward flight (the TAS, along the flight path). Their resultant is the element's relative airflow, arriving at the advance angle (helix angle) φ above the plane of rotation. The chord sits at the blade angle (pitch angle) θ to the plane of rotation, and the difference is what the aerofoil actually feels: the blade angle of attack, α = θ − φ. Everything a propeller does follows from this triangle.

Check you understood

Three questions from this lesson — one straightforward, one that applies it, one that pushes a little further. Nothing is recorded, and you can draw a new set as often as you like.

1. Warm-up
A constant-speed propeller holds its rpm by:
2. Applying it
As airspeed increases at constant rpm, the blade angle of attack of a fixed-pitch and a constant-speed propeller respectively:
3. Pushing it
The blade element's total aerodynamic force can be resolved into:

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Three pitch definitions attach to the triangle:

Geometric pitch — the theoretical distance the propeller would advance in one revolution at zero blade angle of attack, the advance at which the blade would slice the air without working (this is the definition the examination uses).
Effective pitch — the distance it actually advances per revolution in flight.
Propeller slip — the difference between the two, and it is no defect: slip is what gives the blade its working angle of attack, exactly as a wing flies at an angle to its path.

Fine pitch and coarse pitch are the working vocabulary for the blade angle:

fine = a small θ (the blade nearly in the plane of rotation).
coarse = a large θ (the blade turned toward the flight direction).

Blade twist

One blade angle cannot serve the whole blade. The rotational velocity ω·r grows from almost nothing at the root to its greatest value at the tip, while the TAS is the same for every station, so the advance angle φ is large at the root and small at the tip. A blade with constant θ would therefore fly its root at a huge α and its tip at almost none. The cure is blade twist: the blade angle decreases from root to tip, following the changing φ so that every station works at a similar, efficient angle of attack. Twist is to the propeller what washout is to the wing: a built-in variation of angle that makes every station do useful work.

Resolving the force: thrust and torque

At its working α the element generates a total aerodynamic force, and there are two useful ways to cut it. Cut it against the relative airflow and you get the aerofoil pair: lift perpendicular to the airflow, drag along it. Cut it against the aircraft's axes and you get the propeller pair: thrust, the component along the flight direction, and the torque component, the part lying in the plane of rotation, opposing the blade's motion — the part the engine's torque must continuously overcome. Both resolutions describe the same force; the second is the one the aircraft feels.

How the pair varies with IAS (at fixed rpm and blade angle): accelerate, and the growing TAS steepens the advance angle φ, so α falls: the element's force shrinks, and with it both the thrust and the aerodynamic torque decrease. Propeller thrust is greatest at the start of the take-off roll and falls steadily with forward speed (the propeller aircraft's defining performance signature), and the falling torque is why an unattended fixed-pitch engine overspeeds as the aircraft accelerates: less air resistance on the blades, same engine effort, rising rpm.

Propeller types

The syllabus lists the family by how the blade angle is managed:

Fixed pitch — the blade angle is built in and never moves. Simple, light, cheap, nothing to fail; but α is correct at only one combination of speed and rpm, and everywhere else the propeller works below its best.
Adjustable pitch — the blade angle can be reset, but only on the ground: a compromise chosen per operation rather than per flight phase. (Exam questions often treat 'adjustable pitch' and 'variable pitch (non-governing)' as one category; EASA lists them together.)
Variable pitch (non-governing) — the pilot changes the blade angle in flight by hand, choosing fine or coarse as the phase demands, with no automation watching the rpm.
Constant speed (variable pitch, governing) — a governor adjusts the blade angle continuously to hold the rpm the pilot selects: speed up and the governor coarsens the blades to keep the rpm from rising; slow down and it fines them off. The blade α stays near its efficient value across the whole speed range.

The trade between the extremes (the syllabus asks it directly): the fixed-pitch propeller is light, simple and maintenance-free, but perfect at one speed only, which forces the climb-versus-cruise choice:

Climb propeller — fine-pitched: at low TAS its α is right, the engine reaches full rpm and power, take-off and climb are strong, but in cruise it turns too fast and pulls too little.
Cruise propeller — coarse: efficient at cruise TAS, but at take-off its α is so large that the engine cannot reach full rpm; power and acceleration suffer exactly when the runway is finite.

The constant-speed propeller dissolves the choice: near-best α everywhere, the engine at whatever rpm suits the phase — at the cost of weight, complexity, expense and a governor that can fail.

Two relationships tie the types together. For a fixed-pitch propeller, θ is constant, so α is at the mercy of airspeed: high at low TAS, shrinking as speed builds. For a constant-speed propeller, the governor moves θ with the airspeed so that α and the rpm hold steady. And at constant IAS, changing pitch works the other way around: coarsen the blades and α rises, the aerodynamic torque rises, and the rpm falls (the engine cannot overcome the larger torque at the same speed); fine off and the rpm rises. Pitch coarse = rpm down, pitch fine = rpm up: the lever the governor works continuously.

Normal, windmilling, feathered, reverse

The blade element explains all four operating regimes by where its force points:

Normal operation — positive α, force tilted forward: thrust ahead, torque opposing rotation, the engine paying the torque.
Windmilling — the engine fails with the blades at fine pitch; the oncoming airflow now strikes the forward-facing side of the blade (in propeller terminology, confusingly, the blade's 'back', the cambered side; the flat rear side is the 'face'). The force reverses in both respects: its axial component points rearward (drag), and its in-plane component points with the rotation, driving the propeller like a windmill, spinning the dead engine.
Feathered — the blades are turned to roughly 90° of blade angle, edge-on to the airflow: almost no force in either direction, the rotation stops, and the drag falls to its minimum.
Reverse — the blades are driven to a negative blade angle, the force points rearward by design, and the propeller brakes the aircraft on the runway.