We have 3 interesting radii:  

(1) CG- all mass is considered concentrated here to calculate centripetal force.  

(2) Radius of gyration- all mass is considered concentrated here to calculate moment of inertia.  

(3) Center of percussion- all mass is considered concentrated here when the blade swings as a pendulum.

 Every time I try to look at this analytically, it seems, as Jean Fourcade said, that with flapping, if the teeter bolt is not on the CG plane, the rotor CG rotates in a 2/rev circle. 

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34800 x ([Gross Wt] - [Rotor wt]) / ([Rotor wt] x [Rotor RPM]^2)

34800 x ( (550 / 2) - 21 ) / ( 21 x 600^2 ) = 1.1692"

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With blade at the coning angle for straight and level flight, draw a line between the center of gravities of the 2 blades. This line will pass through the teeter bolt. You need to end-up with the center of gravity of the coned rotor system. This would include the blades, hub bar, and chord block. This center of gravity should always be on the center of the teeter bolt, and stay there throughout all aircraft loading weights and flight regimes with no more than 1/2" difference.

From 0735 the coning angle is 1.8706 degrees.

From 0729 the radius of the center of gravity is at 37.812".

The vertical dimension is sin(1.8706 degrees) * 37.812" = 1.234"

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Trying to eliminate 2/rev shake is often like wrestling an octopus. Get one tentacle (I once had a young lady in my employ who always confused tentacle with testicle; she now has a Ph.D. in education) pinned down and another pops loose.

As a first cut, the teeter bolt ought to be located on the CG of the coned rotor. Take a length of welding rod and put an abrupt bend in the center so as to create a shallow 'V' to simulate a coned rotor. Lay a straight welding rod on a level surface, place the bent welding rod on top and slide things around until the bent rod balances. Assuming each leg of the bent welding rod touches the straight rod at the same span wise point, the CG of the coned rod is at the center of the straight rod. This is where the teeter bolt ought to go. But life with teetering rotors is seldom that simple.

If the undersling is too little, the rotor CG rotates in a 2/rev circle with cyclic flapping in forward flight. The spatial visualization of combined rotation and flapping is very difficult for left handed people and nearly impossible for right handed people.

Too little or too much undersling produces a 2/rev fore and aft shake in forward flight The shake from too little undersling is out of phase with the aerodynamic input to the rotor and produces some cancellation. Most rotors, depending to a very large extent on mast stiffness, are smoother with undersling a bit less that a consideration of CG alone would indicate.

This is a subject not covered in any text book I've been able to locate and involves a bit of speculation on my part. I'll now wait to be shot down.

I've put together some very simple programs on Excel to calculate undersling, tail volume as a percentage of rotor volume, disc loading, blade loading and HP Vs torque. It's very easy to use and might appeal to those people who don't agree that pie are square. Email me for a copy.

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