Undersling and Cone Angle

donshoebridge

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If I understand correctly, if a line were drawn from the center of lift of the rotor blades, this line should pass through the teeter bolt. So rotor RPM, blade weight, etc., all have to be taken into account to determine where this line is. There are various hub bars that have features in them that set the blades in a pre-coned angle if you will.


Question...

1. If the pre-coned angle of the hub bar is removed, can/does/should the undersling distance be reduced so that the lift line passes through the teeter bolt, and not over it?

2. What would be the effects of having a reduced undersling distance?

Don
 
No, the pre-coned angle does not affect the actual coning angle. The actual angle is caused by the centrifugal force of the rotor blades compared to the weight being lifted. A pre-coned angle is only there to remove the bending force to the hub bar. The undersling would not be reduced if the pre-coned angles is there or not. The blades will still cone, just bend more (more stress) if the hub bar is not pre-coned.
 
Don,

I don't believe center-of-lift has anything to do with it. Someone will correct me if I'm wrong on this, but I believe you want to be able to draw a between the vertical centers-of-mass of the two blades while coned, and have it pass through the teeter bolt. The center of lift of each blade will be located closer to the tip than the center-of-mass, except in a case of very concentrated tip weight.
 
Ken,

You CAN reduce the coning angle from what a fully limber blade will cone by using a stiffer blade that doesn't bend as much. The Magni rotor does this somewhat - and helps to reduce the required undersling. The Magni also uses higher RRPM to reduce the coning angle and required undersling.

As Paul states, the teeter height, or undersling should match the line drawn between the CG of each rotor blade so that the CG of the entire coned rotor lies on the teeter bolt pivot. This prevents or minimizes the amount of radial offset of the rotor CG from the axis of rotation. During cyclic action or forward speeds, spindle axis and rotor disk axis are offset in angle - about 2 degrees for normal airspeeds. If the CG were not exactly on the teeter bolt, this would result in the CG of the spinning rotor being offset from the spindle, and a 2-per vibration occurs.

It is not possible for the coning angle to exactly match the teeter heigh in all cases and situations. But, the closer it is the better.

It is also better to keep the teeter height to a minimum - as Magni does with a stiffer rotor and higher RRPM. A shorter teeter height presents a smaller lever arm for any rotor vibrations to act through, and a shallower coning angle means that the normal deviations of coning angle don't amount to large CG offsets from the spindle axis. As a for instance, the Magni rotor uses an offset of 2-2.5 inches, where other rotor systems of the same gross weight gyro might have teeter heights of 6 or more inches. The shorter teeter height is a method to keep overall rotor shakes minimized.

It has been my experience that most rotor shake probably comes from mismatch of coning angle and teeter height. It is relatively easy to mass balance the rotor dynamically in span and chord - 1 per out-of-balance shakes! You can verify if the 1-per rev is gone - good dynamic balance of the rotor - by descending flat vertically, no airspeed. The lack of forward airspeed will align the spindle axis and the rotor disk axis - eliminating the 2-per rev shakes of improper teeter height. But, in a flat vertical, no airspeed descent, any out-of-balance of teh rotor will be the only shake you should see. Then, it is relatively easy to see the 2-per rev shake from teeter height mis-match by increasing forward airspeed. This causes the cyclic rotor "blow back" angle and causes the CG or the rotor disk to offset radially from the spindele axis. If there is teeter height mis-match, a 2-per rev will start showing up and get worse with more airspeed.

There are other sources of 1-per rev rotor shake, essentially an aerodynamic center that is different than the dynamic mass center. If this is the case, it is probably impossible to "balance" the blade perfectly - a change in chord balance for instance also moves the aerodynamic center. But, quality blades will have a reasonable match for the aerodynamic center and the mass center.

A span-wise mis-match of the aerodynamic center (with the dynamic mass center) can be adjusted on most blades. this is normally what is called a "tracking" adjustment - getting the tips to track over each other in flight. For quality matched rotor blades, a mis-match of tracking at the tips essentially means the cone is tilted toward one blade. This amounts to a shift of the aerodyanic center from the mass center. For a good set of blades - consistent airfoils at each section of rotor blade - a tracking adjustment re-aligns the aerodyanmic center, spanwise, with the mass center. Get them both centered on the spinning axis, and you have done a lot to eliminate 1-per rotor shake. then, work on the teeter height 2-per rev shake

Thanks, Greg Gremminger
 
The undersling in inches, Al, that locates the teeter bolt on the coned rotor CG can be found from the simple relation:

Undersling = 34,800 * { (AUW - rotor weight)/(rotor weight * RPM^2)}

Tip weights don't affect undersling except for their contribution to total weight. With tip weights, the coning angle is shallower but blade CG is proportionately farther out.

A given rotor will fly at about the same coning angle and necessary undersling whatever the AUW. As AUW increases, the rotor speed and centrifugal force increase proportionately.

In actual practice, a rotor is usually smoother if undersling is a bit less than calculated. I suppose 2/rev shake from mass force is out of phase with 2/rev aerodynamic input. I suspect optimum undersling is also affected by mast compliance, ie., the resonant frequency of the mast/rotor system.
 
Thanks all!

Then what I'm understanding here is that, YES, the teeter bolt height can be reduced, so long as other factors change to compensate, such as rotor RPM, ie. a smaller rotor disk.

The main reason I was asking the question in the first place was I have had an idea for a new rotor head design, but I don't think it would work correctly unless I reduce the teeter distance. Pictures MAY be forth coming, if there's interest.

Thanks again.
 
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