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 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.

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 lift, 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 radians 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 V_NE, 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 V_NE 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.