Delta3, gyroscopic precession.
Lu,
I think the answers can be found in the following results
(sorry guys this is from an egg-head-pilot)
First (you never know) To the pilots : DISCLAIMER
The data is only approximative, precise enough to illustrate
the discussion points, but not to be used to plan flights.
The author declines all responsabilities.
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In the last year I have read a number of heated discussions
concerning the R-44 rotor. As I am mathematically inclined I decided
to make a detailed blade element dynamic model of the rotor
in order to investigate its behaviour. The model is pretty detailed
and even takes viscous fluid, mach, reynolds numbers etc into account.
I have 3-D animations but cannot publish this on the net.
I do want to share some curves concerning
the flapping angle of the rotor calculated for two scenarios:
1. sudden wind gust (with and without delta3)
2. sudden cyclic forward (with and without delta3)
The math shows that the rotor stays perfectly aligned thanks to delta 3
and illustrates the remarks Frank Robinson made a long time ago concerning
- right blow back because of coning (wind)
- wee-waa or zig-zag in case of cyclic transient
Image 1. Sudden 50 knts gust : R44 rotor blows back but stays aligned.
See legend to see what curves mean. The X-axis is in number of rotations.
Remark how fast rotors react to disturbances (1,5 revolutions)
Image 2. Same without delta3 : rotor blows to the right (blade at the left is higher)
Image 3. No wind but sudden 2degree forward cyclic: Rotor moves forward fully align both during and after the transient
Image 4. Same without delta3 : since there is no wind the rotor is aligned after transient, but tilts to the right during the transient (blade is higher at the left during the firs 180 degrees)
With respect to the question in this thread: the possive coning delta3 provoques no instabilities (wind,cyclic, collective inputs). It just increases coning to a design angle.
Removing this delta3 has only one effect : coning angle decreases.
SORRY ... (edited october 22)
The following paragraphs are wrong : the lift increased in the experiment because coning delta3 increased blade pitch
START OF ERROR
So I assume the following design choice were made:
1. the coning is determined by the precise lift distribution and centrifugal forces along the blade (these are fully detailed in the used model).
2. if blades have extra tip weight coning is reduced
3. a 2-3 degree coning is wished
4. the coning delta3 increases coning in this case by approx 0,5 degrees.
I could also model the R22, which I did not yet, but my guess is that the original R22 blades were lighter with less tip weight, so rotor coned enough without coning delta3.....
""(END of ERROR)
CORRECTED VERSION :
After introduction of coning delta3 the collective needs to be lowered to achieve the same trust level. So I guess this delta3 primarily acts as a simple linear (quasi non dynamic) amplifier on the collective handle. I still maintain the conclusions about the stability
END OF CORRECTION
Delta3
A very hypothetical case
Suddenly introduce the coning delta3 to a rotor.
It would in practice take a very advanced servo to achieve this,
but this mathematical scenario can help clarify a stability
question : suddenly introduce the control law in the
system and look what happens:
not oscillations, just an increase in coning angle
Delta3