Item 0199

DESIGN: SynchroLite ~ Rotor - Disk - Blade to Blade Clearance (2-blades)

Drawing:

 

Design:

Blade to Blade Vertical Clearance:

Parameters: 8.66-ft (R)adius, V of 25-degrees, 2.25-ft between hub centers and a 3-degree coning angle. Horizontal plane of reference (0,0) is the XY-plane passing through the center of both rotor hubs. Positive dimensions are up.

May want to check the * below plus the following calculations to see if the hub center dimension is taken from the teetering hinge or the intersection of the blade centerlines

Primary Azimuth Dimensions:

At azimuths of 0 and 180 degrees the 3-degree coning angle will cause the blade tips of both rotors to be ((sin(3)*104*")*cos(25/2)) = +5.31" above the horizontal plane (0,0) and they are (cos(3)*104") = 103.85" horizontally from their hub centers.

At azimuths of 90 degrees the blade tip is (sin(12.5+3)*104) = +27.79" above the horizontal plane (0,0) and it is (cos(12.5+3)*104) = 100.22" horizontally from its hub center.

At azimuth of 270 degrees the lower blade tip is (sin(-12.5+3)*104) = -17.16" below the horizontal plane (0,0) and it is (cos(-12.5+3)*104) = 102.57" horizontally from its hub center.

The upper blade tip will be located directly above the ((100.2176. - 27)/102.2176) = .716R of the lower blade therefore the elevation of the lower blade at this location will be (0.7163 * -17.16) = -12.30". This is irrelivent though because the blades are not crossing at this location. The vertical clearance at azimuths 90/270 degrees, between the upper blade tip and the .716R point of the lower blade is (27.79 + 12.30) = 40.09"

Critical Azimuth Dimensions:

At azimuths of 39/51 The upper blade tip and the lower blade are closest when the upper blade is at azimuths of 39 +/- 90 degrees and the lower blade is at azimuths of 51 +/- 270 degrees.

At azimuths of 90 +/- 39 the upper blade elevation will be (((27.79 - 5.31)*((90-39)/90))+5.31) = 18.05".

At azimuths of 270 +/- 39 The upper blade tip will be located roughly (from measuring plan view of drg 0199) above the .82R of the lower blade. At this location the lower blade elevation will be ((((-12.30 - 5.31)*((90-51)/90))+5.31)*0.82) = -2.25". The vertical clearance between the upper blade tip and the lower 71.63R point is (18.05 + 2.25) = 20.36"

The following table summarizes the above elevations and radiuses.

Azimuth

0

51

90

129

180

141

270

309

Tip Elevation

+5.31

 +18.08

 +27.79

 +18.08

+5.31

 -??

 -17.16

 -??

** Radius

----

  ----

  ----

  ----

----

 .82R

 .716R

 .82R

** Elevation

----

  ----

  ----

  ----

----

 -2.25

 -12.30

 -2.25

Tip Radius

103.85

 

100.22

 

103.85

 

 102.57

 

** Location on lower blade directly below tip of upper blade; as a fraction of disk (R)adius.

Blade - Blade Clearance re Yaw

It appears that the greatest potential for blade clash between the two rotor hubs will be when applying yaw. The planes of the two rotor disks are at 155 degrees to each other. The application of longitudinal and/or lateral cyclic should not change this angle between the 2 disks. When yaw is applied one disk will tip forward and the other will tip back. Therefore at two of the four diametrically opposed intersection points the low blade will be at its highest allowable position and the high blade will be at its lowest allowable position.

Calculations

Assume a yaw to the right.

The front of the port disk will be down and the front of the starboard disk will be up.

The two danger points will be at 1:30 o'clock and 7:30 o'clock.

 Using the 1:30 o'clock as a working example;

The blade of the port disk will be at an azimuth of 129 degrees. It is the higher blade but will be tipped down by the yaw. The danger point will be at the 8.66-ft. (104") radius.

The blade of the starboard disk will be at an azimuth of 219 degrees. It is the lower blade but will be tipped up by the yaw. The danger point will be at the 6.75-ft (81") radius

 The sin of 39 degrees is .63. Therefore left-hand blade at azimuth of 130 degrees moves down .63 as much as it does at azimuth of 180 degrees.

The sin of 51 degrees is .78. Therefore right-hand blade at azimuth of 220 degrees moves up .78 as much as it does at azimuth of 180 degrees.

Yaw degree

Drop of LH blade

Rise of RH blade

Clearance

0

0.0"

0.0"

20.3"

1

sin 1 * 104 * .63 = 1.14"

sin 1 * 81 * .78 = 1.10"

20.36 - (1.14 + 1.10) = 18.12"

2

sin

sin

20.36 - () = "

3

sin

sin

20.36 - () = "

4

sin 4 * 104 * .63 = 4.57"

sin 4 * 81 * .78 = 4.41"

20.36 - (4.57 + 4.41) = 11.38"

5

sin 5 * 104 * .63 = "

sin 5 * 81 * .78 = "

20.36 - () = "

6

sin 6 * 104 * .63 = 6.85"

sin 6 * 81 * .78 = 6.6"

20.36 - (6.85 + 6.6) = 6.91"

7

sin 7 * 104 * .63 = 7.98"

sin 7 * 81 * .78 = 7.70"

20.36 - (7.98 + 7.70) = 4.68"

8

sin 8 * 104 * .63 = "

sin 8 * 81 * .78 = "

20.36 - () = "

9

sin 9 * 104 * .63 = 10.25"

sin 9 * 81 * .78 = 9.88"

20.36 - (10.25 + 9.88) = .23"

10

sin 10 * 104 * .63 = 11.38"

sin 10 * 81 * .78 = 10.97"

20.36 - (11.38 + 10.97) = -2.29"

11

sin 11 * 104 * .63 = 12.50"  

sin 11 * 81 * .78 = 12.05"

20.36 - (12.50 + 12.05) = -4.19"

 

 

 

 

Note: For yaw, it may be necessary to use differential collect in lieu of or in addition to differential longitudinal cyclic. This is because of the blade clearances, particularly when there are external forces such as gusts.

Blade - Blade Clearance re Longitudinal Cyclic

Longitudinal cyclic will not make any significant difference on clearances, therefore it can be ignored. (I think)

Blade - Blade Clearance re Lateral Cyclic

The following table is at azimuths of 270 degrees on the lower blade and at 90 degrees on the upper blade.

Degree

Drop of lower blade

Drop of upper blade

Clearance

0

(sin(-12.5+3)*104)*0.72 = -12.30"

(sin(12.5+3)*104) = 27.79"

40.09"

2

(sin(-10.5+3)*104)*0.72 = -9.72"

(sin(10.5+3)*104) = 24.28"

34.00"

9

(sin(-3.5+3)*104)*0.72 = -0.65"

(sin(3.5+3)*104) = 11.77"

12.49"

The following table is at azimuths of 270 =/- 51 degrees on the lower blade and at 90 +/- 39 degrees on the upper blade.

Degree

Drop of lower blade

Drop of upper blade

Clearance

0

0.0

0.0

20.36"

2

 

 

 

9

sin 9 * 81 * .63 = 7.98"

sin 9 * 104 * .78 = 12.69"

20.36 + 7.98 - 12.69 = 15.65"

 See drawing 0720 for side view of critical azimuths.

Question & Reply by Nick Lappos on rec.aviation.rotorcraft:

The type of rotor (articulated, rigid, teetering) is important in assuring that adequate control power is available during the critical entry maneuver into autorotarion, where low rpm will tax the control of the helicopter. Really, the most important index here is the hinge offset. Teetering rotors are notorious in having problems during rapid down collective movements during auto entry, due to both low G and large flapping excursions that may cause self mid-airs.

FORM: Rotor - Disk - Interaction

Same Page ~ Different Craft: ~ Dragonfly ~ UniCopter

Back to top | SynchroLite Home Page

Last Revised: December 14, 2004