To: Helisphere
You have finally discovered the secret. Helicopter aerodynamics is taught in the following way.
1) They discuss Bernoulli’s theorem and then address how a venturi works.
2) They apply this to the operation of an airfoil of a fixed wing aircraft and explain how it generates lift
3) They in turn apply this theory to a rotating airfoil and they use the autogyro as an example
4) Without shifting gears they start talking about helicopters and apply the logic of the autogyro to the helicopter and that is where flapping to equality comes from.
I brought this subject up in the Robinson certification thread.
Thanks for bringing it up on this thread.
To: Crab
It looks like we are about the rekindle the war of 1812. If I remember my history the United States defeated the British. Just a bit of humor to get us started.
If I read you correctly you are stating that the lead angle of the pitch horn in your illustration is zero. If I do understand this premise it would appear that everything you say after that point is contrived to fit the basic premise. Also your diagram of the circle and the horizontal line with the vertical lines establishing the angular distance traveled (or in other words the amount of pitch change) is also flawed. If everything in the system is rotating about a fixed point then the angular displacements must be referenced to the point of rotation. That way, you can divide the circle into equal parts and the distance between each two points is equal to the distance between any other two points.
I have in front of me the Sikorsky Blue book. This book is issued to anyone that attends a technical school at Sikorsky whether they are a pilot or a mechanic. On page thirty of the blue book there is an illustration of blade pitch change as the blades rotate 360-degrtees. Although the figures are different from those quoted in my post the angular change of the blade is consistent for each degree of travel around the circular path.
I don’t know if you are familiar with a constant pressure variable delivery hydraulic pump but it too has a swashplate. As the internal mechanism rotates the swashplate action causes pistons to move in and out of a cylinder that resembles the cylinder in a Webley (spelling) revolver. The movement is constant and can be diagrammed just like a sine wave. If the pistons moved in the way you diagrammed the movement by drawing vertical lines from a base line the pump would tear itself apart and if it didn’t your hydraulic system would have to incorporate a pulse damper or, an accumulator. The pump described does not require an accumulator because of the smoothness of the output. Using this same analogy on the rotorhead, if the angular pitch change were not consistent with the degrees of rotation then you would have a constant medium to high frequency vertical beat in your rotor system.
Also, in your illustration of the 0-degree pitch horn the blade would have to be directly over the lowest part of the swashplate (down over the nose) in order to get the maximum pitch change which would place the blade at its’ lowest pitch relative to collective. Assuming it is possible to do this if using gyroscopic theory the disc would tilt to the left when you pushed the cyclic forward. Which way would it tilt using your theory?
The rules are the same for a bell with a 90-degree pitch horn and a Sikorsky using a 45-degree pitch horn and a 45-degree offset of the swashplate. In either case the lead relative to the selected direction of flight is 90-degrees. You stated in a past posting that the Lynx was like the Robinson in that in rigging the helicopter the blades were offset by 15-degrees on the Lynx and I stated that the Robinson blades were offset by 18-degrees. The result of this offset is that the blade will have maximum response 90-degrees later in rotation. My theory about the Robinson is yet to be proved but you had indicated in a previous post that the Lynx without the Auto Control System would roll to the left or 90-degrees later in rotation from the offset position.
In every case, the figure 90-degrees keeps popping up. Why does this figure keep coming up when discussing rotary wing flight? The answer is simple if you are on this side of the pond. It pertains to gyroscopic precession.
Regarding phase lag, it is 90-degrees whether you are addressing a Bell or a Sikorsky. As stated above the Bell pitch horn leads the blade by 90-degrees and on the Sikorsky it leads by 45-degrees and the swashplate tips down 45-degrees ahead of the selected direction of flight. Most helicopters excepting Boeing CH-47s and CH-46s follow this method of cyclic control input. But even on the Boeing helicopters the rotor placement is governed by gyroscopic precession.
Regarding your illustration about the only time that precession would play a part in the displacement of the rotorhead would be in a vacuum. I don't think that would work as the only thing you would do is change the angular setting of the blades but since there is no atmosphere you cant generate the lifting forces that would cause the disc to tilt due to precession.
In your last paragraph you asked me to look at a rotorhead and swashplate and see the tilting of the swashplate relative to where the blade pitch horns are. Assuming a Bell rotor and it is disposed across the lateral axis and the cyclic stick were displaced forward on the center of the rigged axis then the swash plate would move down forward and up aft. (Not on all Bell two blade systems as on some the swash plate moves opposite but the pitch horn is on the rear of the blades so the angular displacement related to blade position would be the same. On a Sikorsky as described above when the cyclic is pushed forward the swashplate will tip down 45-degrees ahead of the longitudinal axis and up 45-degrees ahead of the lateral axis. The blades if disposed over the lateral axis will have minimum pitch on 3:00 and maximum pitch at 9:00 relative to the basic collective pitch setting.
Over.
------------------
The Cat
[This message has been edited by Lu Zuckerman (edited 22 January 2001).]