Asymmetry of lift

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Asymmetry of lift is the term used to describe the nature of aerodynamic lift generation by the rotor blades of a helicopter.

The phenomenon is best analysed when a helicopter is in the hover condition (i.e., maintaining a fixed altitude above ground level, with no lateral movement in any direction relative to the ground). This simplifies the analysis enormously, though the phenomenon is always present regardless of the state of motion of the helicopter.

In an elementary analysis, the lift generated by an aerofoil (all other factors being constant) is proportional to the speed with which the aerofoil travels through the air. In the case of a fixed-wing aircraft, the principal lift generators are the wings, and these travel through the air at a speed dictated by the forward speed of the entire aircraft. In the case of helicopter rotor blades, the determination of 'speed through the air' is more complex. Here, it is necessary to distinguish between angular speed (more correctly angular velocity and linear speed - the former (measured in SI units of radians per second) is a measure of the rate of change of angular orientation of a given rotor blade with respect to a fixed direction, while the latter is a measure of the rate of change of distance moved. There exists a simple mathematical relationship between the two: taking the case of a rotor blade in motion, if the rotors are spinning about the rotor axis with an angular speed of ω radians per second, and a point on the rotor blade is r metres distant from the axis of rotation, then the linear speed of that point on the rotor blade is equal to the product rω, measured in metres per second. Thus it becomes apparent that the linear speed of a given part of a rotor blade depends, once the rotor blades are all driven at a fixed angular speed, upon the distance from the axis of rotation. The rotor tips will thus be travelling through the air at the fastest linear speed, and the outermost sections of the rotor blades will, as a corollary of lift being proportional to linear speed, be generating more lift than those parts of the rotor blades that are closer to the rotor hub.

Because different parts of the rotor blade generate different amounts of lift, a rotor blade is said to be an aysmmetric generator of lift, in contrast to an aeroplane wing, which is a symmetric generator of lift because all parts of the aeroplane wing are travelling through the air at the same linear speed, and presumably generating the same amount of lift over the entire extent of the wing (ignoring factors requiring a more advanced analysis).

Of course, the above is an elementary analysis, and fails to take into account a range of complicating factors such as variation in cross-sectional aerofoil geometry of an advanced rotor blade design, factors arising from the viscosity of the air, and other phenomena that are best described by intricate systems of differential equations, and therefore in general not amenable to analytic solution. The typical example of such a system of differential equations used to describe fluid flow when viscosity is taken into account is the Navier-Stokes system of equations, whose behaviour for a given system requires numerical approximation techniques and the use of the tools of computational fluid dynamics. In practice, even such advanced analysis does not detract from the fact that rotary-wing flight is characterised by asymmetry of lift, it merely changes the fine detail of the shape of the asymmetry curve relating lift to distance from the rotor hub.

Asymmetry of lift, being an intrinsic phenomenon associated with helicopter flight regardless of the state of motion of the helicopter, should not be confused with dissymmetry of lift, which is a different phenomenon dependent upon the lateral motion of the helicopter.

Helicopter manufacturers reduce this phenomenon by adding a principal called Wash-out. Wash-out is either achieved by tapering the blades toward the tips so that the tip surface area is reduced and hence produces less lift, or by twisting the blades (commonly called geometric twist) so that the blade root presents a higher angle-of-attack than the tip.