8.2 Rotor Aerodynamics: Blade Design, Thrust, Drag and Torque

The Blade as an Aerofoil

A multirotor rotor blade is a rotating aerofoil, and three design features determine how well it works.

• Aerofoil shape. The cross-sectional profile. A cambered (asymmetric) section produces lift efficiently at a modest angle of attack, which is what a rotor wants. A thicker section is stronger but draggier; a thinner one is more efficient but more fragile — which is why a cheap propeller flexes noticeably under load while a quality carbon blade does not.
• Blade twist. The blade angle decreases from root to tip. Because the tip travels much faster than the root, twist is what keeps the angle of attack roughly constant along the span, so the whole blade contributes rather than the root stalling while the tip idles.
• Blade taper. Narrowing the chord toward the tip reduces tip losses (where high- and low-pressure air spills around the tip and forms a vortex) and reduces the mass at the fastest-moving, most highly stressed part of the blade.

The Airflow Vocabulary

Schedule 4 topic 3(b) asks for six terms, and they only make sense together.

Here is the chain that ties them together. The blade is set at a fixed blade angle to the plane of rotation. Rotation gives it a horizontal airflow. The rotor's own downwash gives it a downward induced airflow. The vector sum of the two is the relative airflow, and the angle between that resultant and the blade's chord line is the angle of attack.

The consequence is important and slightly counter-intuitive: induced airflow reduces the angle of attack. As a rotor spools up and generates more downwash, the induced flow increases, tilting the relative airflow further downward and reducing the blade's angle of attack. That self-limiting effect is one reason a rotor's thrust does not rise linearly with rpm, and it is why a rotor descending into its own downwash — the vortex ring condition — behaves so badly.

Thrust and Drag Resolved

Take the total aerodynamic force produced by a blade section and resolve it perpendicular and parallel to the plane of rotation:

• The component perpendicular to the plane of rotation is rotor thrust — the useful output that holds the aircraft up.
• The component in the plane of rotation, opposing motion, is rotor drag — the cost, paid by the motor in torque and by the battery in current.

Anything that increases the blade's angle of attack increases both. The design task is to maximise the thrust component while minimising the drag component, which is what aerofoil selection, twist and taper are for.

This is also the mechanical link between aerodynamics and the electrical unit. More rotor drag means more torque required, which means more motor current, which means more heat and less endurance. When a payload is added and the rotors must produce more thrust, the extra current draw is not an accounting quirk — it is the electrical shadow of increased rotor drag.

Torque Reaction and How a Multirotor Cancels It

Newton's third law applies to rotation as well as translation. Applying torque to spin a rotor one way applies an equal and opposite torque to the airframe the other way. On a single-rotor helicopter this is what a tail rotor exists to counter.

A multirotor cancels it by pairing. Half the rotors turn clockwise and half counter-clockwise, arranged so the torques balance. On a quadcopter the two diagonally opposite rotors turn the same way; on a hexacopter the directions alternate around the frame.

Three consequences follow:

1. In a balanced hover, net torque is zero and the aircraft holds heading with no yaw input required.
2. Yaw is produced by deliberately unbalancing the torques. Speed up the clockwise group and slow the counter-clockwise group by the same amount: total thrust is unchanged, so the aircraft neither climbs nor descends, but the net torque is now non-zero and the airframe rotates in the opposite direction to the dominant torque.
3. Fitting a propeller with the wrong rotation direction destroys both the thrust and the torque balance on that arm. The blade meets the air backwards, produces a fraction of the intended thrust, and the aircraft typically flips on take-off.

Where the thrust actually goes

A rotor accelerates a mass of air downwards, and the reaction lifts the aircraft. The thrust produced is proportional to the mass flow and the velocity change imparted to it:

$\text{Thrust} \propto \dot{m} \times \Delta v$

There are two ways to produce a given thrust: move a large mass of air slowly, or a small mass of air quickly. The first is far more efficient. That is why a heavy-lift multirotor uses large-diameter, low-pitch rotors turning at modest rpm, and why the same aircraft fitted with small, fast rotors would drain its battery in minutes. The disc area — the total swept area of all rotors — is the single strongest predictor of hover efficiency for a given weight, which is the aerodynamic reason large aircraft have large rotors rather than more of them.