Dissymmetry of lift
Encyclopedia
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 helicopter
s in lateral flight, whether the direction of flight be forwards, sideways or in reverse.
The dissymmetry is caused by differences in relative airspeed between the advancing blade and the retreating blade. The relative airflow parallel with the plane of the rotor disc (caused by the combination of forward flight and wind) determines the average relative speed of air passing over the rotor blades. When a blade is moving into the relative wind, it is called the advancing blade. The advancing blade experiences faster than normal airflow, and therefore greater lift. The blade moving with the wind (away from the direction of flight) is called the retreating blade. The retreating blade experiences airflow that is slower than normal, thereby creating less than normal lift. Unless countered, dissymmetry causes the helicopter to roll to the retreating side.
Dissymmetry is countered by "blade flapping": rotor blades are designed to flap – lift and twist in such a way that the advancing blade flaps up and develops a smaller angle of attack, thus producing less lift than a rigid blade would. Conversely, the retreating blade flaps down, develops a higher angle of attack, and generates more lift.
When dissymmetry causes the retreating blade to experience less airflow than required to maintain lift, a condition called retreating blade stall
occurs. This causes the helicopter to roll to the retreating side and pitch up (due to gyroscopic precession). Once this dangerous condition arises, control may be lost, resulting in loss of the aircraft.
, which is a phenomenon analysed while the helicopter is in the hover condition (see the appropriate article for discussion of that phenomenon).
Let a single-rotor helicopter be in forward flight, and let the helicopter be analysed from a point some distance above the rotor hub. Let the angular speed of the rotor disc (in radian
s per second) be ω, and let the forward linear speed (in metres per second) of the helicopter be v. The diagram below illustrates this. Furthermore, let the radius of the rotor disc (the distance from the centre of the rotor hub to the tip of any rotor blade) be r.
Now, in the diagram, let the state of the rotor tip be considered at points A and B, given the conditions stated in the diagram with respect to speed and direction of rotation of the rotor disc. When a rotor tip reaches the point A in the diagram, the linear speed through the air will be a combination of the linear speed imparted to the rotor tip due to its rotation about the rotor hub, and the forward speed of the helicopter. Since the quantities being added are properly velocities rather than speeds, the addition will be a vector addition, in which direction is important. At point A in the rotation cycle of the rotor blade, the linear speed of the tip through the air will be equal to rω+v. When the rotor blade has rotated further in the cycle, so that the rotor tip is at position B, the rotor speed will be equal to rω-v.
Since the lift generated by an aerofoil is proportional to its linear speed through the air, the rotor tip at position A in the diagram will be producing a lift proportional to rω+v, while the rotor tip at position B in the diagram will be producing a lift proportional to rω-v, a linear speed of lower magnitude. Therefore, the rotor disc will be, in the case of the hypothetical helicopter illustrated, producing more lift on the right hand side than on the left hand side, all other conditions being equal.
To reduce dissymetry of lift, modern helicopter rotor blades are mounted in such a manner that the angle of attack
varies with the position in the rotor cycle, the angle of attack being reduced on the side corresponding to position A in the diagram, and the angle of attack being increased on the side corresponding to position B in the diagram. However, there exists a limit to the degree by which dissymetry of lift can be diminished by this means, and therefore, since the forward speed v is important in the phenomenon, this imposes an upper speed limit upon the helicopter. This upper speed limit is known as VNE, the never-exceed speed. This speed is the speed beyond which the aerodynamic conditions at the rotor tips would enter unstable régimes - if v was sufficiently fast, the rotor tip at position A would be travelling fast enough through the air for the airflow to change radically as the rotor tip became supersonic
, while the rotor tip at position B might have insufficient net linear speed through the air to generate meaningful lift (the stall
condition - known as retreating blade stall
. Needless to say, entry of the rotor tip into either of these aerodynamic régimes is catastrophic from the point of view of the pilot, and the maintenance of stable forward flight.
The situation becomes more complex when helicopters with two sets of rotor blades are considered, since in theory at least, the dissymetry of lift of one rotor disc is cancelled by the increased lift of the other rotor disc: the two rotor discs of twin-rotor helicopters rotate in opposite senses, thus reversing the relevant directions of vector addition. However, as entry of the rotor tip into the supersonic aerodynamic realm is one of the unstable conditions that affects forward flight, even helicopters with two rotor discs rotating in opposite senses will be subject to a never-exceed speed. In the case of tandem-rotor helicopters such as the CH-47 Chinook
, additional factors such as the aerodynamic drag of the entire design, and the available engine power, may conspire to ensure that the helicopter is incapable of achieving the VNE imposed upon it by dissymetry of lift. In the case of the Kamov Ka-50 Werewolf, which is a coaxial
design, it is possible for the helicopter to enter this aerodynamic régime as it has sufficient engine power, and pilots of this machine need to take this into consideration during the operation of the helicopter.
Rotorcraft
A rotorcraft or rotary wing aircraft is a heavier-than-air flying machine that uses lift generated by wings, called rotor blades, that revolve around a mast. Several rotor blades mounted to a single mast are referred to as a rotor. The International Civil Aviation Organization defines a rotorcraft...
aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...
refers to an uneven amount of lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...
on opposite sides of the rotor
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...
disc. It is a phenomenon that affects single-rotor 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...
s in lateral flight, whether the direction of flight be forwards, sideways or in reverse.
The dissymmetry is caused by differences in relative airspeed between the advancing blade and the retreating blade. The relative airflow parallel with the plane of the rotor disc (caused by the combination of forward flight and wind) determines the average relative speed of air passing over the rotor blades. When a blade is moving into the relative wind, it is called the advancing blade. The advancing blade experiences faster than normal airflow, and therefore greater lift. The blade moving with the wind (away from the direction of flight) is called the retreating blade. The retreating blade experiences airflow that is slower than normal, thereby creating less than normal lift. Unless countered, dissymmetry causes the helicopter to roll to the retreating side.
Dissymmetry is countered by "blade flapping": rotor blades are designed to flap – lift and twist in such a way that the advancing blade flaps up and develops a smaller angle of attack, thus producing less lift than a rigid blade would. Conversely, the retreating blade flaps down, develops a higher angle of attack, and generates more lift.
When dissymmetry causes the retreating blade to experience less airflow than required to maintain lift, a condition called retreating blade stall
Retreating blade stall
Retreating blade stall is a hazardous flight condition in helicopters and other rotary wing aircraft, where the rotor blade rotating away from the direction of flight stalls. The stall is due to low relative airspeed and/or excessive angle of attack...
occurs. This causes the helicopter to roll to the retreating side and pitch up (due to gyroscopic precession). Once this dangerous condition arises, control may be lost, resulting in loss of the aircraft.
Analysis
To simplify the analysis, forward flight will be considered here, but the analysis applies regardless of the direction of flight because circular geometric symmetry applies. This is to be contrasted with asymmetry of liftAsymmetry of lift
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...
, which is a phenomenon analysed while the helicopter is in the hover condition (see the appropriate article for discussion of that phenomenon).
Let a single-rotor helicopter be in forward flight, and let the helicopter be analysed from a point some distance above the rotor hub. Let the angular speed of the rotor disc (in 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) be ω, and let the forward linear speed (in metres per second) of the helicopter be v. The diagram below illustrates this. Furthermore, let the radius of the rotor disc (the distance from the centre of the rotor hub to the tip of any rotor blade) be r.
Now, in the diagram, let the state of the rotor tip be considered at points A and B, given the conditions stated in the diagram with respect to speed and direction of rotation of the rotor disc. When a rotor tip reaches the point A in the diagram, the linear speed through the air will be a combination of the linear speed imparted to the rotor tip due to its rotation about the rotor hub, and the forward speed of the helicopter. Since the quantities being added are properly velocities rather than speeds, the addition will be a vector addition, in which direction is important. At point A in the rotation cycle of the rotor blade, the linear speed of the tip through the air will be equal to rω+v. When the rotor blade has rotated further in the cycle, so that the rotor tip is at position B, the rotor speed will be equal to rω-v.
Since the lift generated by an aerofoil is proportional to its linear speed through the air, the rotor tip at position A in the diagram will be producing a lift proportional to rω+v, while the rotor tip at position B in the diagram will be producing a lift proportional to rω-v, a linear speed of lower magnitude. Therefore, the rotor disc will be, in the case of the hypothetical helicopter illustrated, producing more lift on the right hand side than on the left hand side, all other conditions being equal.
To reduce dissymetry of lift, modern helicopter rotor blades are mounted in such a manner that the angle of attack
Angle of attack
Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...
varies with the position in the rotor cycle, the angle of attack being reduced on the side corresponding to position A in the diagram, and the angle of attack being increased on the side corresponding to position B in the diagram. However, there exists a limit to the degree by which dissymetry of lift can be diminished by this means, and therefore, since the forward speed v is important in the phenomenon, this imposes an upper speed limit upon the helicopter. This upper speed limit is known as VNE, the never-exceed speed. This speed is the speed beyond which the aerodynamic conditions at the rotor tips would enter unstable régimes - if v was sufficiently fast, the rotor tip at position A would be travelling fast enough through the air for the airflow to change radically as the rotor tip became supersonic
Supersonic
Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
, while the rotor tip at position B might have insufficient net linear speed through the air to generate meaningful lift (the stall
Stall (flight)
In fluid dynamics, a stall is a reduction in the lift coefficient generated by a foil as angle of attack increases. This occurs when the critical angle of attack of the foil is exceeded...
condition - known as retreating blade stall
Retreating blade stall
Retreating blade stall is a hazardous flight condition in helicopters and other rotary wing aircraft, where the rotor blade rotating away from the direction of flight stalls. The stall is due to low relative airspeed and/or excessive angle of attack...
. Needless to say, entry of the rotor tip into either of these aerodynamic régimes is catastrophic from the point of view of the pilot, and the maintenance of stable forward flight.
The situation becomes more complex when helicopters with two sets of rotor blades are considered, since in theory at least, the dissymetry of lift of one rotor disc is cancelled by the increased lift of the other rotor disc: the two rotor discs of twin-rotor helicopters rotate in opposite senses, thus reversing the relevant directions of vector addition. However, as entry of the rotor tip into the supersonic aerodynamic realm is one of the unstable conditions that affects forward flight, even helicopters with two rotor discs rotating in opposite senses will be subject to a never-exceed speed. In the case of tandem-rotor helicopters such as the CH-47 Chinook
CH-47 Chinook
The Boeing CH-47 Chinook is an American twin-engine, tandem rotor heavy-lift helicopter. Its top speed of 170 knots is faster than contemporary utility and attack helicopters of the 1960s...
, additional factors such as the aerodynamic drag of the entire design, and the available engine power, may conspire to ensure that the helicopter is incapable of achieving the VNE imposed upon it by dissymetry of lift. In the case of the Kamov Ka-50 Werewolf, which is a coaxial
Coaxial rotor
Coaxial rotors are a pair of helicopter rotors mounted one above the other on concentric shafts, with the same axis of rotation, but that turn in opposite directions...
design, it is possible for the helicopter to enter this aerodynamic régime as it has sufficient engine power, and pilots of this machine need to take this into consideration during the operation of the helicopter.