0852

Item 0852

DESIGN: SynchroLite ~ Rotor - Disk - Disk - Semi-Rigid Teetering

Overview:

To calculate the amount of lead-lag in the mast because of rotor teetering. From the perspective of the mast plane, this activity could be called 'oscillating Coriolis' or 'knuckle joint effect'.

Notes:

The following is a view of the rotor disk from the mast plane.

Note: Angular momentum must be maintained.

Polar Moment of Inertia of Mass for a cylinder J_{M =}¹/₂Mr²

Angular Momentum = rotational inertia x rotational velocity = J_Mω , or

for an object that is small compared to the radial distance, angular momentum is the product of mass, speed, and radial distance of rotation mvr

Determination of Relationship between Teetering Angle and Change in RRPM:

This proof is based on the principal of Coriolis. I.e. Conservation of angular momentum.

Tip path plane at angle β to mast plane		Tip path plane parallel to mast plane
mass * speedA * radiusA	=	mass * speedB * radiusB
m * vA * rA	=	m * vB * rB
vA * rA	=	vB * rB
vA/ vB	=	rB / rA
vA / vB	=	sec(β)
The multiplier to obtain the new RRPM	=	The secant of the angle of teeter

Example: If the maximum change in RRPM in a quadrant is 1% of RRPM then the average change in a quadrant is 0.5%. I think. There for after 90 degrees of rotation the blade in-plane lead will be 0.5% * 90° = .45°. I think

It looks like a delta3 of 38 degrees is required to offset the above. This 38 degrees removes 78% of the pitch that was put in. Not too good.

For the above coding see: Function change_in_RRPM ( )

The value for the radius of gyration of a rotor blade which has uniform mass along its span is: 0.7071 * R [R is blade radius]. A tip weight will increase this value. Additional weight at the root, such as grip etc. will reduce this value.

For delta3 effects see: DESIGN: Rotor - Disk - Lead-Lag for Intermeshing Helicopter

To run calculations see: FORM: Rotor - Disk - Delta3

Last Revised: October 19, 2001