Item 0729
DESIGN: SynchroLite ~
Rotor - Disk - Centers, Radii & MomentsThe data on this page is incomplete and erroneous; to say the least.
Overview:
Centers, forces, moments, vectors, etc. related to the rotor disk. Based upon the blade below.
For information related to the individual airfoil [VR-7 & VR-7b] see:
OTHER: Aerodynamics - Airfoil - VR-7 & VR-7bFor information related to the specific blade [VR-7b] for the SynchroLite see:
DESIGN: SynchroLite ~ Rotor - Blade - Composite - VR-7b - Centers, Radii & Moments
Axes of Reference for Individual Disk: -
Polar Coordinate System:|
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Axis: |
Orientation: |
Origin: |
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r |
radius |
Centerline of hub |
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ψ |
Azimuth |
Centerline of hub |
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Z |
Elevation |
Centerline of hub |
Disk is viewed in tip path plane
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Centers, Radii and Moments:
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Center of mass (gravity)(weight) |
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Center of lift (aerodynamic center) |
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Center of thrust (aerodynamic center) |
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Center of drag (aerodynamic center) |
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Radius of Lead/Lag Hinge (offset) |
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Radius of Flapping Hinge (offset) |
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Polar moment of inertia |
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Center of torsional twisting (this is re the blade only ?) |
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Center of Gyration - Centrifugal (centripetal) Force |
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Center of Percussion (this is re the blade only ?) |
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Geometric Center |
Moments at the flapping hinge produced by the following Forces must equal zero:
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Aerodynamic |
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Centrifugal (centripetal) |
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Weight |
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Inertia |
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Gyroscopic |
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Degrees of Freedom:
The disk
(or perhaps it's the fuselage) has 6 degrees of freedom3 translations expressed as
3 rotations expressed as
θ theta, φ phi, and ψ psi.A rotor adds at least 3 more; coning, longitudinal flapping and lateral flapping. Is lead-lag another?
See:
B263 - Axes.
Disk
My
rough initial guess at what are possible centers, axes and planes:Just a thought:-
If all the following centers were concentric at all times then it would appear that there could never be any rotor induced vibrations.|
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3 Axes |
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Center of Lift |
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Center of Drag |
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Center of Mass (includes yoke & grip etc.) |
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Center of Gyration (centrifugal (centripetal) force?) |
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Center of Lift:
This will vary depending on the helicopter's horizontal motion. During hover, and considering only 1 rotor disk and half the gross weight, the mid-point of lift on the span of the blade should be about 75% of the disk radius.
L
ook at blade element data. I suspect that the center of lift will shift slightly span-wise at different angles of attack just as it shifts chord-wise. In forward flight it will probably vary span-wise depending on the azimuth of the blade.
Center of Drag:
A hypothesis.
Assume that sufficient cyclic has been applied to eliminate flapping. The two blades must be producing identical lift. To do this the pitch of the retreating blade must obviously be greater that of the advancing blade. A blade's coefficient of drag is not in a direct correlation with its coefficient of lift. The blade elements on both blades have differing angles of attack and are subjected to different air velocities.
The implication is that, when the two blades are producing identical lift, they are not subjected to identical drag. Therefor vibration. This may have been the reason for the rotor gimbal on the Bell 47 and comments about the mast absorbing incidental force in later designs of teetering rotors, which do not have provision for lead-lag.
This is only theoretical speculation on my part.
Center of Mass:
Located at the teetering pin when the rotor disk is subjected to its 'normal loading'.
This is probably not going to be perfectly true since other factors may reposition the teetering hinge. This 'normal loading' may be the determiner of the pre-coning angle.
Center of Gyration:
Radius of gyration is the distance such that if all the mass were that far from the center of mass, the center of mass would be the same.
This may be wrong since I think it encompasses gravity.
re: Centrifugal (centripetal) Force:
See [Rotor - Disk - Coning Angle] 0735
Pre-coning of Hub:
The form [Rotor - Hub] calculates the coning angle as 1.8706 degrees (0.0327 radian); at hover, using VR-7 composite blades, option 2 and with .75 pound tip weights. The blade is 104" long therefore the rise at the blade tip is sin(1.8706)*104 = 3.395". The Lock number
[γ] is 6.526The following is very rough:
Half the moment is 5.759/2 = 2.879 slug-ft^2. Element 10 is 3.033. This would put the center of gyration at about 91% of disk radius.
The center of gyration appears to be too close to the tip of the blade and the Lock number is quite high. Perhaps the "heavy tip weight is the reason. Good for autorotation!
With no tip weight the center of gyration is about 82% of disk radius. It should also be remembered that, using option 2, a large portion of the leading edge weight is located in the outer 50% of the blade only.It appears that increasing the tip weigh will reduce the coning angle and the teetering height, but it will also move the center of gyration out (and up) which will increase the coning height. In other words changing the tip weight may possible have little or no affect on the teetering height??
Center of Gyration: The sum of the coning angles to 90% of R is .3267 - .0723 = .2544 radians. . The average of the coning angles is .2544 / 9 = .0283 radians. The radius at the point is 104" * 90% = 93.6" Therefore the rise at the 90% location sin(.0283 radians) * 93.6 = 2.649".
Using the center of gyration as the coning height seems too high considering that the coning angle is only 1.87 degrees!The hub's yoke and grip etc. are part of the teetering mass. They therefore must be included when calculating any of the centers. The hub's effect will be considerable when considering the center of gravity. The hub's effect will be quite minimal when considering the center of gyration. When the blades tip the center of gyration changes slightly because the mass of the hub has now swung, like a pendulum, out to the high blade side and this will move the center of gyration to this side also. By lowering the teetering height slightly the moment of inertial of the hub moving to the high blade side will be offset by the moment of inertial of the blades moving toward the low blade side.
Should the center of gyration be inside or outside the center of lift, or does it matter?
Radii:
~ Author: CA BEATY ~ Date: February 09, 1999We have 3 interesting radii:
(1) CG- all mass is considered concentrated here to calculate centripetal force.
(2) Radius of gyration- all mass is considered concentrated here to calculate moment of inertia.
(3) Center of percussion- all mass is considered concentrated here when the blade swings as a pendulum.
Every time I try to look at this analytically, it seems, as Jean Fourcade said, that with flapping, if the teeter bolt is not on the CG plane, the rotor CG rotates in a 2/rev circle.
Outside information:
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Last Revised: December 13, 2007