Item 0994
OTHER:
Aerodynamics - General - Dissymmetry of Lift
Dissymmetry of Lift is defined as the unequal lift across the rotor disc resulting from the difference in the velocity of air over the advancing blade half and retreating blade half of the rotor disc area. The implication is that flapping will negate this dissymmetry of lift and that feathering will negate this flapping.
I would, arguably, say that there is no such thing as symmetry of lift, when discussing forward flight. In other words, during undisturbed forward flight, the lift on the advancing blade never equals the lift on the retreating blade. A more accurate expression for 'Dissymmetry of Lift' might be 'Dissymmetry of
Moment', since it is the CW and CCW moments that are brought into equilibrium.The following three sketches show;
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The average distribution of lift acting on a rotor blade. This depiction of lift will exist during hover. The center of this lift is indicated by the heavy vector, which is at 2/3 of radius. |
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The distribution of lift acting on the advancing side of the rotor. The center of this lift is inside the 2/3 of radius. |
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The distribution of lift acting on the retreating side of the rotor. The center of this lift is outside the 2/3 of radius |
A moment is the tendency to cause rotation about an axis. It is measured as [
moment = force x distance]. In each of the above sketches, the force is concentrated at the center of lift. The distance is the length between the teetering axis and this force.It can be seen from the sketches that the
distance is different between the advancing side and the retreating side. To stop the rotor disk from tipping laterally there must not be any moment, therefore the lift on the advancing side must be greater than the lift on the retreating side.In other words, in forward flight there will be Symmetry of Moment, but not Symmetry of Lift.
Symmetry of Moment, as applied the Bell and Robinson rotors:
The following two sketches are forward facing views of the Bell and Robinson rotors in forward flight. The advancing blade is on the right and the retreating blade is on the left. For the sake of clarity and simplicity, the values of the lift and the distances to the centers of lift have been grossly misrepresented.
In both of the above sketches, the total lift is 1000 pounds.
In the Bell example, the blade-to-hub rigidity and the equal moments
(100# x 9') = (900# x 1') mean that there is no cause for rotation of the disk about the teetering hinge in a lateral direction.The Robinson has coning/flapping hinges and therefore there is less blade-to-hub rigidity. These additional two hinges negate the equality of moments about the teetering hinge. The teetering hinge will therefore experience lateral oscillate at once per rotor revolution. This oscillation will interface with the longitudinal oscillation resulting from the normal forward longitudinal cyclic of forward flight. Both oscillations, or to be more accurate - the combined oscillation, will increase as the crafts forward velocity increases. It might be noted that the oscillation(s) will affect the blade pitch because of the delta-3.
The above is not intended to show a preference for the operation of one rotor hub over the other. It is only presented for consideration and discussion.
Related Information:
DESIGN: SynchroLite ~ Rotor - Disk - Opposed (Differential) Lateral Cyclic
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Last Revised: February 4, 2007
