Item 1239

OTHER: Flight Dynamics - General - Lead/Lag [ζ]

Lag Motion:

The in-plane forces acting on a blade section are:

    1. an inertial force. (opposing the lag motion) Is cyclical Coriolis the only contributor to changes in the inertial force, or are there others?
    2. a centrifugal force
    3. an aerodynamic force (profile and induced drag). In forward flight, induced drag may be constant at all azimuths. However profile drag will probably be greater on the advancing side due to the greater velocity of the airflow.
    4. a Coriolis force. Is cyclical Coriolis the only source of Coriolis or could a sudden vertical motion of the craft impart a short term Coriolis effect collectively on all three blades? I thing that cyclical Coriolis will result in the greatest amount of lead being 45º after the azimuth of greatest flap. See OTHER: Flight Dynamics - General - Lead-Flap Coupling, for Intermeshing Rotors (kpβ) & Pitch-Lead Coupling (δ4)

For more information see;

[Source ~ HT, page 251] ~ Section 5-19 - Lag Motion and diagram

[Source ~ HT, page 393] ~ Section 9-3 - In-plane Motion

[Source ~ HT, page 653] ~ Section 12-3 - Flap-Lag Dynamics

Teetering Rotor: Review this section, since SynchroLite was move to a new section below..

The teetering rotor is subject to a small amount of lead-lag. Current rotors take care of this lead-lag by the mast flexing and possibly some torsional twisting of the mast. The position that teetering rotors are subject to lead-lag is supported by the following:
  1. Each of the blade elements of the two blades is subject to different amounts of lift yet the combined lift moment in one blade equals the combined lift moment in the other blade. A airfoil's coefficients of drag and its coefficients of lift are not in a direct correlation with each other. Therefor the combined drag moment of one blade cannot equal the combined drag moment of the other, when one of the blades is advancing and the other is retreating.
  2. Lu Zuckerman refers to "the lead lag action is reacted by the cone hinges which will wear in an elliptical pattern" in the Robinson. E.B. in Campbell River say that they have never replaced a cone/flap bearing, in 60 machines. Another mentioned that they showed a rotor hub with in-plane wear in the coning hinges at the Robinson training school.
  3. Gyrocopter affeceadoes refer to the fact that the stationary mast should not be too inflexible. I think that this has to do with profile and induced drag.
  4. The Kaman synchropters give the two blades in a rotor the ability to lead-lag in respect to each other. This lead-lag will be in addition to the additional lead-lag that must take place between the two rotors.

Constant Velocity Joint & Hub Spring Rotor: (SynchroLite)

See: SynchroLite ~ Rotor - Hub - 3-blade - CVJ+HS (Concentric Double Universal Joint & Hub Spring)

Offset Tri-teetering Rotor: (Dragonfly)

See: Dragonfly and OTHER: Rotor Concept - Offset Teetering Rotor

My initial thinking;

If the actual coning angle (average of flapping angles) equals the pre-cone angle [ζ0 = ζp] then during forward flight the Coriolis forces on each blade will be be trigomerically in balance, due to the virtual undersling. The flapping of the blades will be both sides of the pre-cone and therefor the radius of the blade masses in the hub plane will move inward based upon the blades azimuth and the azimuth of the tip-path-plane's tilt.

The inertial forces and the centrifugal forces on each blade should therefor also be trigomerically in balance.

The aerodynamic forces (drag) on each blade will not be in balance. But, they may not be too far out of balance since the total lift (or total lift moment) on the advancing side must equal the total lift (or total lift moment) on the retreating side.

When the actual coning angle (average of flapping angles) differs from the pre-cone angle[ζ0 ≠ ζp], then there will definitely be independent blade lead/lag about the rotor's disk. But, is this independent lead/lag able to be absorbed by in-plane flexure of all three blades? Also, would any in-plane flexing create an unwanted lag-pitch coupling? Also, consider making the tie-rods from fiberglass thread and let the stretching of the glass thread absorb the temporary lead lag while the pair of tie-bar assemblies still maintain an overall control over the lead-lag.

Which is optimal for an offset teetering rotor? ~ One central tie-bar or two (to control lead/lag relationship between the three blades)?

'Absolutely' Rigid Rotor: (UniCopter)

See: 'Absolutely' Rigid Rotor

The individual blades and the complete rotor are incapable of accepting any lead-lag. This may not be a concern since when considering the causes of lead-lag notes as noted in the first section above;
    1. should be prevented arising in the first place, due to the Absolutely Rigid Rotor,
    2. should have no effect since it will be constant,
    3. should be easily resisted, due to the Absolutely Rigid Rotor,
    4. should not arise because the Absolutely Rigid Rotor presents an extremely high resistance to flapping.

Related Information:

OTHER: Flight Dynamics ~ Rotor - Hub - Offset Teetering Hinge Concept

DESIGN: SynchroLite ~ Rotor - Disk - Lead-Lag for Intermeshing Helicopter

OTHER: Mechanical - General ~ Cyclical Coriolis Effect & Hooke's Joint Effect

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Last Revised: March 15, 2009