A a principle
of helicopter aerodynamics
, that caused considerable headaches for the pioneers
of rotary wing aircraft
. By definition it is the difference between the amount of lift created by the left and right semicircles of the disc traced by the rotor blades as they spin; this issue relates directly to the stability
of a helicopter.
A helicopter's rotor blades create lift because they have an aerofoil cross-section, the same as the wings on a fixed-wing aircraft. An aerofoil, because of its shape, tends to force air that flows over it downwards (air and other fluid substances tend to follow the contours of curved objects they come into contact with: see Coanda Effect). In forcing the air downwards an equal and opposite force is applied to the aerofoil, forcing it to rise. At sufficient rotation speed the blades create enough lift to rise and pull the helicopter with them. The higher the pitch angle (called the angle of attack) of the blades, the more lift they create (to a point, after which they create more drag than lift).
This is all fine while the helicopter is hovering because the speed of each rotor blade (and thus the lift it generates) is constant, but if the helicopter is also moving laterally (i.e. forwards, backwards or sideways) or is hovering in wind it gets complicated. See, the relative airspeed of each rotor blade will change for every point in its rotation because the air that is flowing over them is already moving. This will inevitably vary the amount of lift that each rotor blade produces as it rotates.
To use a dumbed down analogy, imagine you throw a ball at 20mph out of the window of a car driving along at 50mph. If you throw the ball in the direction the car is travelling, the ground speed of the ball will be the sum of the speed you threw it at and the speed of the car - i.e. 70mph (ignoring drag for the sake of simplification). If you threw the ball in the opposite direction, behind the car, the ground speed of the ball would be the speed of the car, minus the speed the ball was thrown at - i.e. 30mph. However it would still be travelling in the same direction as the car because the ball was not thrown at sufficient speed to counteract the speed it was already travelling at, when inside the car. If the car were travelling at 20mph and the ball was thrown behind the car at 20mph, the ball would stop dead and fall to the ground.
It becomes clear(er?) now that if the helicopter is moving relative to the air (or vice versa), the rotor blades generate more lift when they are turning towards the approaching air because they are effectively travelling faster. This effect causes the helicopter to pitch up or down (depending which direction the rotor blades turn) because one side of the rotor disc is generating less lift than the other. This effect is exemplified in the following paragraphs, referring to the diagram below:
Flight Direction Relative Wind
(speed 100knots) (speed 100knots)
/ \ \ /
/ Rotation \
/ <---- \
Retreating Rotor Blade --> |_______\||________|
| \_______| <-- Advancing Rotor Blade
\ Rotation /
\ ----> /
In this example, a rotor blade will reach the highest airspeed at the 3 o'clock position and the lowest at the 9 o'clock position. The wind velocity means that the airflow over the rotors will be higher at certain points than at others, and we've established that the higher the velocity of the air over an aerofoil, the more lift it will generate. The rotors in this example will generate the most lift around the 3 o'clock position and the least lift around the 9 o'clock position.
Again to simplify (because details are extraneous and don't help here, frankly), let's say that the speed of the rotor blades in the example is 350 knots at the tips. When at the 3 o'clock position, the airspeed of each rotor tip will be 450 knots because the relative wind speed (100 knots) is added to the speed of the rotor tip. Conversely, when retreating at the 9 o'clock position, the airspeed of each rotor blade will be 250 knots because the relative wind speed is subtracted from the speed of the rotor tip. In fact there is a small circular area between the 8 and 9 o'clock positions that the inner portion of each rotor blade passes through, in which air actually flows backwards over them (from sharp end to blunt end). Shockingly this is called the 'Reverse Flow Area'.
Before continuing, a clarification would probably be timely:
- Advancing rotor airspeed = Rotor speed + Airspeed in direction of travel
- Retreating rotor airspeed = Rotor speed - Airspeed in direction of travel
Anyway, one can see there is a 200 knot difference between the airspeed of the advancing and retreating rotors. Since lift increases as the square of airspeed, that's quite a potential variation in lift with all rotors at equal pitch. This must be compensated for, otherwise the imbalance of lift that the rotors create will cause the helicopter to pitch indefinitely (whether it pitches up or down depends on the direction the rotors turn); although the point of greatest lift is on the left or right of the rotor disc, because of gyroscopic progression this lift will not 'take effect' until 90° of rotation later. The fact that this is hardly dignified is the least of the potential problems incurred, the largest probably being death. There are two main methods of counteracting lift dissymmetry, as seems to be a recurring theme in helicopter design (compensating for unwanted forces); these follow.
Flapping Rotor Blades
With this system, each rotor blade can pivot up or down a set amount, to compensate for differences in lift it creates at various points in its rotation. This works very well as the advancing rotor blades tend to rise (reducing their angle of attack and thus reducing the lift they create) and the retreating rotor blades tend to drop (increasing their angle of attack and thus increasing the lift they create), resulting in an overall balance of lift over the rotor disc (before any cyclic control by the pilot). This also acts as a shock absorber of sorts against turbulence, as some of the difference in wind speed is absorbed by the flapping motion of the rotor blades and is less likely to vibrate the fuselage.
The way this system is implemented depends on the number of blades in the main rotor. If the helicopter has two blades on its main rotor, both are rigidly attached to the hub, which is attached to the top of the rotor shaft by a teetering hinge. This allows the blades to pivot and rock as a unit: when one blade rises the other one drops, and vice versa. If the main rotor has more than two blades, each blade is hinged to the rotor hub individually and flaps independently of the rest of the rotor disc.
With this system, the pitch of each rotor blade is finely controlled at each point in its rotation so the overall lift generated by the rotor disc is equal. This involves increasing the angle of attack of retreating rotor blades and decreasing that of advancing rotor blades. This is often an automatic part of the cyclic system (though in less advanced helicopters the pilot must compensate for lift dissymmetry manually); it works independently of the pilot's cyclic control, but the way in which cyclic feathering is applied is directly related to any cyclic control by the pilot.
It is interesting to note here that due to the area near the root of the retreating blade that does not generate appreciable lift (the Reverse Flow Area and other overlapping areas called the Negative Lift Area and the Negative Stall Area), the length of the retreating blade that generates useful lift is notably shorter than that of the advancing blade. Yet, because of the variable angle of attack of the blade it still produces the same amount of lift as the whole length of the blade when it is advancing!
I have had to simplify the description of this because the finer points require diagrams with a detail level that ascii cannot provide. The first source contains a full diagram of the effect as well as explanation of said finer points.
Thanks to BlakJak, Hexter, The Custodian and Wiccanpiper for their comments and editing assistance.
- Dynamic Flight Inc.; "Disymmetry of Lift"; <http://www.dynamicflight.com/aerodynamics/dissymmetry/>
- National Air and Space Museum, Smithsonian Institution; "Cierva C.8W"; <http://www.nasm.edu/nasm/aero/aircraft/cierva_c8w.htm>
- Federal Aviation Administration; "Basic Helicopter Handbook; Other helicopter components and their functions"; <http://www.geocities.com/flyingmouse1/Chapter_5.html>
- Jane's Information Group Ltd; "Longbow 2 User Manual"; Printed word.