R22 Corner

[delta3]

90 or 72, its 90 even in a robby

To Lu

I have read and re-read your comments on the rotor system
and I do not understand why you keep coming back to so-called rigging
offset of the R22/R44. Forgive me for trying...
A rotor is a very complex system. Most Rotorheads appear
to understand flapping and gyroscopic precession.
This is however only a first approximation and as Frank Robinson
pointed out in november 2000 there is more to it.
I assume that most Ppruners are not interested in heavy math, but
allow me to say that the mathematical equations do exist, that I think I understand them (took me a while) and that they confirm to phenomena described.
(Helicopters by Prof Dick, Von Karman institute for instance, 1991)
Allow me to rephrase Frank words (and of course I hope Frank allows me).

The first phenomenon described by Frank is a transient behaviour, that is when changing the cyclic to a new position, say from neutral to forward.
Before the rotor disk takes on its new position parallel with the requested swashplate position, the transient provokes a phase shift making a rotor tilt not fully aligned with the requested forward position, but provoking a temporary lateral effect to the right. A delta-3 coupling, that is creating a feedback system between the angle of attack and the flapping of the blades when swashplate and rotor disk are not parallel can reduce this effect. Delta-3 is achieved by tilted hinges, by elastomeric deformation or by displacing the pitch control link with respect to the flapping hinge center line. The delta-3 angle has nothing the see with the swashplate angle rigging. It provoques the upward flapping blade to reduce its angle of attack by pivoting and vice versa, so counteracting the flapping (for the mathematical inclined readers, the equation is: pitch angle change = - tg(delta-3) times flap angle change, for 18° this is -0.32, so 1 degree of extra flap changes pitch angle by -0.32 degrees). This first transient phenomenon is similar to gyroscopic precession, and happens also for instance with the B206. Try to tilt a fly-wheel forward and it will want to tilt at 90 degrees. To summarize: there can be a temporary/transient deviation between the way the cyclic is moved and the rotor disk moves. The designer may want to be compensated that as Robinson did.

The second phenomenon described by Frank happens in the case of an articulated rotor with a positive coning in steady forward flight. Important here is positive coning. The equations show that flapping is not maximal in the forward (or backward) position but is shifted by a small angle (the cone tilts again to the right as Frank stated). Simply stated this is due to the fact that the fully forward blade -because of its upward coning- still has extra lift (the wind hits it from below increasing the angle of attack, whereas the backward blade is hit from above) The aerodynamic forces on the forward blade decrease a little later (past fully forward) than would be derived from a flat disk model, creating the phase shift in the blow-back. This has nothing to see with gyroscopic precession (which again is 90°) but with coning geometry (I suggest you make a drawing of this). It is also not transient but permanent. The equations show that again a delta-3 feedback can offset the effects of this coning phase shift. Vice a versa, given a delta-3 setup, there exists a coning angle that best balances phases shift provoqued by the delta-3.

In the case of the R22 apparantly nearly full compensation of both phenomena was achieved (at +- 1°) according to Frank Robinson. In both cases this setup increases 'controllability' as you define it Lu.

I happen to own an R44 and can of course confirm that the theory works as all pilots did, forward means cyclic forward and not 18 degrees... (in the end it is as simple as that). Furthermore I checked with my own eyes and hands the following : push the cyclic forward, the swashplate goes forward (and exactly forward with no deltas). At standstill this creates a non alignment between rotor (who did not move) and swashplate : You notice a pitch change (differentially). This is because the pitch link is positioned behind the flap hinge axis (by 18°). Remark that the Delta-3 angle does not add or substract from the fixed 90° rigging, the action of this fasing is only temporary when the rotor disc is not parallel to the swashplate. Visually of course this creates an 18° angle in the rotor head, but this does not mean that the rigging is at 72°. If you don't like math go and look at the real stuff. It also may be instructive to look at the very large delta-3 angle in opposite direction of the R44 tailrotor which is not achieved by displacing rigging in the head but plainly by tilting the flap axis by I would say more then 45°. You also will remark that the R44 tail rotor has a negative coning.