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DESIGN: SynchroLite ~ Rotor - Blade - Composite - VR-7b - Centers, Radii & Moments

The data on this page is incomplete and erroneous; to say the least.

Overview:

Disk radius is 8' - 8".

Centers, forces, moments, vectors, etc. related to a specific VR-7b blade for the SynchroLite.

For general information related to the airfoil [VR-7 & VR-7b] see: OTHER: Aerodynamics - Airfoil - VR-7 & VR-7b

For information related to the rotor disk see: DESIGN: Rotor - Disk - Centers, Radii & Moments

Axes of Reference for Blade - Cartesian Coordinate System:

See: Axes of Blade

Drawing:

 

Profile Sectional (x & z - axes)

Centers, Axes, and Moments etc; of Possible Interest:

Many of the following will differ at each blade element.

 

 

Symbol

Horizontal (chord) (X)

Vertical (thickness) (Z)

 

Aerodynamic Center

a.c.

X

 

 

Center of Pressure

cp

 

 

 

Center of Drag ??

 

 

Z

 

Center of Gravity (g)

 

X

Z

 

Moment of Inertia

I or J

X

Z

 

Radius of Gyration

r

X

Z

 

Pitch axis

 

X

Z

 

Center of torsional twisting

 

X

Z

 

Plane of vertical structural deflection (bending)

 

X

Z

 

Plane of leteral structural deflection (bending)

 

X

Z

 

Center and Radius of Oscillation

 

 

Z

 

Center of Percussion ??

 

 

 

 

Center of Pitch axis

 

X

Z

 Center of Pressure

The center of pressure will vary depending on the tab and the angle of attack [alpha]. See: DESIGN [Rotor - Airfoil Section - VR-7 & VR-7b] Item 0733. The calculations on this page are based on the center of pressure being located at 27% of chord.

Center of Gyration (Center of Gravity?) (Mass?)

Weight & Center of Gyration For 1 complete blade. The intention is to locate this at 25% of chord. Note; On option 2 this center will be different on the outer half of the blade to the

Option 2 is currently the preferred. Consider making the tip cap out of titanium and it becomes the tip weight. It will weight about 1/3 of a pound.

Option 1:

Item

Part Nbr

Weight

Arm @25%

Moment

lb.

- is forward

lb-in.

Core Rohacell 71

0672

0.2044

0

0

Carbon upper (1)

 

0.7448

0

0

Carbon lower (2)

 

0.6915

0

0

 Skin (3)

0676

1.4263

0.85

1.2124

Fixed L.E. Wt (4)

0658

 0.2252

 -1.2571

-0.2831 

Adj. L.E. Wt (5)

0730

 0.4014

 -1.1224

 -0.5820 (6)

Carbon tube for 0730

-1.1224

Tip

0679

Trailing E. Wedge 

0684

 

 3.2

 

Total

 

 3.6936

 

 0.3473

Notes:

(1) 0.0855" x 2.375" x 97" x .66 = 13.1313 cu-in x 0.0567198 lb/cu-in 

(2) 0.0794" x 2.375" x 97" x .66 = 12.1921 cu-in x 0.0567198 lb/cu-in

(3) 0.02"? x 11" x 97" = 21.34 cu-in x 0.0668355 lb/cu-in

(3) Resin weight is about the same weight as the fabric (ie. 50/50)

(4) 0.0662" dia. tungsten 96" long

(5) 0.098" dia tungsten 96" long

Tip weight not included

(6) Carbon tube goes full length but weight is outer 50% of blade only. Buy extending weight 2 feet more the moment arm will be 0.

Spar uni-directional carbon may decrease towards tip.

.66 is for decrease of carbon toward tip.

Option 2:

Item

Part Nbr

Weight

Arm @25%

Moment

lb.

- is forward

lb-in.

Core Rohacell 71

0672

0.2044

0

0

Carbon upper (1)

 

0.7448

0

0

Carbon lower (2)

 

0.6915

0

0

 Skin (3)

0676

1.4263

0.85

1.2124

Fixed L.E. Wt (4)

0658

 0.2252

 -1.2571

-0.2831 

Fixed L.E. Wt (4)

0658 

 0.2252

 -1.2174

 -0.2741

Fixed L.E. Wt (4)

0658

 0.2252

 -1.1950

 -0.2691

Adj. L.E. Wt (5)

 0730

 0.6252

 -1.0541

 -0.6590 (6)

Carbon tube for 0730

-1.0541

Tip

0679

Trailing E. Wedge 

 

 

 3.2

 

Total

 

 4.3678

 

 -0.2729

Notes:

(1) 0.0855" x 2.375" x 97" x .66 = 13.1313 cu-in x 0.0567198 lb/cu-in 

(2) 0.0794" x 2.375" x 97" x .66 = 12.1921 cu-in x 0.0567198 lb/cu-in

(3) 0.02"? x 11" x 97" = 21.34 cu-in x 0.0668355 lb/cu-in

(3) Resin weight is about the same weight as the fabric (ie. 50/50)

(4) 0.0662" dia. tungsten 96" long

(5) 0.156" dia tungsten 48" long. Note Because this leading edge weight is only in the outer 50% of the blade it means that the root half and the tip half of the blade will have different center of gyration, in the chordwise direction,

Tip weight not included

(6) Carbon tube goes full length but weight is outer 50% of blade only. But decreasing the weight by 2 feet the moment arm will be 0.

Spar uni-directional carbon may decrease towards tip.

.66 is for decrease of carbon toward tip.

 

Span (y-axis)

Centers, Axes, and Moments etc; of Possible Interest:

 

 

Span (Y)

Value

 

 

Center of Mass

m

37.812

"

 

Center of Lift (pressure)

?

75% approx.

 

 

Center of Drag

?

75% approx.

 

 

Radius of Gyration

ko

 

 

 

Center of Centrifugal (centripetal) force

?

 

 

 

Center of Percussion

q

 

 

Center of Mass:

The following weights are based on; using option 2, a tip weight of 0.75 pounds and including the hub.

Element

Weight (lbs)

Arm (in)

Moment

1

4.12426

5.2

21.446

2

.374426

15.6

5.841

3

.374426

26.0

9.735

4

.374426

36.4

13.629

5

.374426

46.8

17.523

6

0.4993

57.2

28.560

7

0.4993

67.6

33.753

8

0.4993

78.0

38.945

9

0.4993

88.4

44.138

10

1.2993

98.8

128.371

Total

9.0433

 

341.941

Center of Gravity

 

37.812

 

When viewed from the side the coning on the blade at each element is not a straight line but is bowed where the coning angle increases as one moves out on the blade. In reality, if the correct precone is put into the hub then the blade will be a straight line at a single constant angle.

Center of Lift:

Note

Center of Drag:

Note

Radius of Gyration:

Note

Center of Centrifugal (centripetal) Force:

Note

Center of Percussion: [See ~ MH p.149]

May be an obsolete concept.

Related Web Sites. Baseball bat Baseball bat & Mallet The Physical Pendulum

The center of percussion distance, a.k.a. the distance to the sweet spot, the spot on the bat where the batter in baseball wants to make contact with the ball. It turns out that the center of percussion is the same as the center of oscillation. The distance to the center of oscillation is the length of a simple pendulum that has the same frequency as the physical pendulum.

The phrase 'Center of Percussion' is mentioned in a 1954 article entitled "Stability and Control of a Rotary Wing Aircraft'. Have hard copy.

PRA Author: CA BEATY Date: July 30, 2000 ~ It is necessary to know the center of percussion to calculate the dynamic response of a rotor blade. For example, if dampening and the offset of the flap hinge are known, a universal resonance curve can be consulted to determine swash plate phasing.

Email from SW. ~ In the text by Simon Neuman (Foundations of Helicopter Aerodynamics) there is a plot of phase angle timing of the swash plate with respect to the rotor control horn line vs. the effective rotor root offset distance. See preceding paragraph for reference to swash plate phase angle timing.

Me ~ It would appear that the center of percusion in a blade might move out and away from the center of mass as the angular speed of the blade increases. [ rcp = rg2/rcm + rcm ]. I guess that since the rotor turns at a fixed rpm this distance does not vary, at least in respect to this limited consideration. It would also appear that if the aerodynamic center and the center of percussion were to be concentric then percussion might not be a source of vibration.

See More Helicopter Aerodynamics Chapter 24 by R.W. Prouty for what appears to be more information related to this subject.

Email from SW. Aug 8, 2000 ~ Looking at the numerous texts in the field of helicopter aerodynamics and aeroelasticity, I have so far seen no reference to the center of percussion, which should probably be more accurately called the center of angular impulse. The center of percussion assumes for its model a perfectly rigid body, pivoting of that body about a point in space, and delivery of a finite impulse (an integral of force with respect to time.) I suppose one could replace a distribution of forces over a finite time period by an equivalent summation in the form of an integral of distributed forces with respect to time, and if this integration resulted in the equivalent of a replacement "force" which acted effectively at the center of percussion due to the fact that the designer of the rotor blade had designed it so, that one could nullify many of the hub shears acting at the equivalent rotor offset hinge in the vertical and drag directions. It may well be that aeroelastic tailoring of the properties of the rotor blade achieves this effect but approaches it in a different manner.

______________

q = ko2 / r

 

q

Distance from the axis of rotation to the center of percussion.

 

ko

The radius of gyration of the body, with respect to the axis of rotation.

 

r

The distance from the axis of rotation to the center of gravity of the body

Miscellaneous: ??

Blade Flexing:

Vertical bending (flapping/teetering)

Horizontal bending (for/aft; lead-lag)

Stretching (along span axis)(centrifugal & centripetal forces)

Torsion (about WHICH? of the span axis)(pitch)

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Last Revised: February 13, 2003