Asymmetry of lift
Encyclopedia
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 wing
s, 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 radian
s 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 equation
s, 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.
Helicopter rotor
A helicopter main rotor or rotor system is a type of fan that is used to generate both the aerodynamic lift force that supports the weight of the helicopter, and thrust which counteracts aerodynamic drag in forward flight...
of a helicopter
Helicopter
A helicopter is a type of rotorcraft in which lift and thrust are supplied by one or more engine-driven rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forwards, backwards, and laterally...
.
The phenomenon is best analysed when a helicopter is in the hover
Hover
Hover may refer to:*Hovering , the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contactIn transport* Hover , nearly stationary flight in a helicopter...
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
Elementary algebra
Elementary algebra is a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic. It is typically taught in secondary school under the term algebra. The major difference between algebra and...
analysis, the lift generated by an aerofoil
Airfoil
An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....
(all other factors being constant) is proportional to the speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
with which the aerofoil travels through the air. In the case of a fixed-wing aircraft, the principal lift generators are the wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...
s, 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
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...
and linear speed - the former (measured in SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units of radian
Radian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...
s 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 equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, 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
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
techniques and the use of the tools of computational fluid dynamics
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
. 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
Dissymmetry of lift
Dissymmetry of lift in rotorcraft aerodynamics refers to an uneven amount of lift on opposite sides of the rotor disc. It is a phenomenon that affects single-rotor helicopters in lateral flight, whether the direction of flight be forwards, sideways or in reverse.The dissymmetry is caused by...
, 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.