Item 1160
DESIGN: Dragonfly ~ Rotor -
Disk - Blade to Blade Clearance (3 blades)Going to use dissimilar lateral cyclic to negate contact. ~ See note on 1176.html
Parameters:
Specification - Dragonfly ~ Rotor; 8'-0" [R]adius, [VR] of 22º, 24" stagger [ds] between hub centers, 13.5" offset [e] and a 2.0º coning angle [β0]. Horizontal plane of reference (0,0) is the XY-plane passing through the center of the virtual teetering hinges of both rotor hubs. Positive dimensions are up.
Drawing:
Design:
Intersection Azimuths of Blade & Angular Distance Between these Azimuths:
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Azimuth: |
Distance: |
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37.0º |
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53.0º |
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90.0º |
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53.0º |
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143.0º |
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60.0º |
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203.0º |
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67.0º |
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270.0º |
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67.0º |
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337.0º |
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60.0º |
Blade to Blade Vertical Clearance:
The following calculations are based on a 25" stagger and 2º coning angle but the results will be so close to the exact values, why change.
Coordinate Azimuth Dimensions:
At azimuths of 0 and 180 degrees
At azimuths of 90 degrees the blade tip is (sin(11+2)*96) = +21.50" above the horizontal plane (0,0) and it is (cos(11+2)*96) = 93.54" horizontally from its hub center.
At azimuth of 270 degrees the lower blade tip is (sin(-11+2)*96) = -15.02" below the horizontal plane (0,0) and it is (cos(-11+2)*96) = 94.82" horizontally from its hub center.
The upper blade tip will be located directly above the
((93.54 - 25)/94.82) = 0.72R of the lower blade therefore the elevation of the lower blade at this location will be (0.72 * -15.02) = -10.81".. The vertical clearance at azimuths 90/270 degrees, between the upper blade tip and the .716R point of the lower blade is (21.50 + 10.81) = 32.31"Critical Azimuth Dimensions:
At azimuths of 53/67 The upper blade tip and the lower blade are closest when the upper blade is at azimuths of 53 +/- 90 degrees and the lower blade is at azimuths of 67 +/- 270 degrees.
At azimuths of 90 +/- 53 the upper blade elevation will be
At azimuths of 270 +/- 53 The upper blade tip will be located roughly (from measuring plan view of drg 1160) above the .86R of the lower blade. At this location the lower blade elevation will be ((((-10.81 - 2.74)*((90-67)/90))+2.74)*0.86) = -0.62".
The vertical clearance between the upper blade tip and the 82.87"R of the lower blade is (10.45 + 0.62) = 11.07"
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 22º to each other. The application of longitudinal and/or lateral cyclic should not change this angle between the two disks. When yaw is applied (opposed longitudinal cyclic) one disk will tip forward and the other will tip back. Therefore at two of the four quarterly opposed intersection points the low blade will be at its highest allowable position and the high blade will be at its lowest allowable position.
A second potential for blade clash is when the RRPM is very low on start-up or shut-down, should a gust of wind cause the lower passing blade to sail up just before closure of the two blades. See;
DESIGN: Dragonfly - Rotor - Hub - Droop & Rise StopIt should be noted that the critical intersection points will probably be in the rear quadrants, since this is where the blades are closing on each other.
Calculations - Based on Opposed Longitudinal Cy
clic: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.
The following uses the 1:30 o'clock as a working example;
The blade of the port disk will be at an azimuth of 143º. It is the higher blade but will be tipped down by the yaw. The danger point will be at the 8.0-ft. (96") radius on this blade.
The blade of the starboard disk will be at an azimuth of 204º. It is the lower blade but will be tipped up by the yaw. The danger point will be at the 6.9-ft (82.87") radius
The sin of 53 degrees is .80. Therefore, the port blade at azimuth of 143 degrees moves down .80 as much as it does at azimuth of 180 degrees.
The sin of 66 degrees is .91. Therefore, the starboard blade at azimuth of 204 degrees moves up .91 as much as it does at azimuth of 180 degrees.
Where did the 14.98" below come from?
Why is it not 11.07" like the first line?
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Longitudinal Flap Angle |
Drop of LH blade |
Rise of RH blade |
Clearance |
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0 |
0.0" |
0.0" |
11.07" |
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1 |
sin 1 * 96 * .80 = 1.34" |
sin 1 * 83 * .92 = 1.33" |
14.98 - (1.34 + 1.33) = 12.31" |
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2 |
sin |
sin |
14.98 - () = " |
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3 |
sin |
sin |
14.98 - () = " |
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4 |
sin 4 * 96 * .80 = 5.36" |
sin 4 * 83 * .92 = 5.33" |
14.98 - (5.36 + 5.33) = 4.29" |
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5 |
sin 5 * 96 * .80 = 6.69" |
sin 5 * 83 * .92 = 6.66" |
14.98 - (6.69 + 6.66) = 1.63" |
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6 |
sin 6 * 96 * .80 = 8.03" |
sin 6 * 83 * .92 = 7.98" |
14.98 - (8.03 + 7.98) = -1.03" |
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Note
: The above does not take into account any unusual activity at the blades (gust etc.). For yaw, it will be necessary to use differential collect; but yaw causes problems. This is because of the blade clearances, particularly when there are external forces such as gusts.See
MAKE: SynchroLite ~ Control - Flight - Directional for means of determining yaw torque.
Blade - Blade Clearance re Longitudinal Cyclic
Longitudinal cyclic will not make any significant difference on clearances, therefore it can be ignored.
(I think) But, on forward cyclic, at the rear, the lower blade will rise faster than the upper blade, because it is closer to azimuth 0 (where the most tipping is).
The following data in light gray is
DESIGN: SynchroLite ~ Rotor - Disk - Blade to Blade Clearance data that has not been changed to Dragonfly. It must be changed to Dragonfly, at some time, but it looks like the clearances will not be a problem.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.
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Degree |
Drop of lower blade |
Drop of upper blade |
Clearance |
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0 |
(sin(-12.5+3)*104)*0.72 = -12.30" |
(sin(12.5+3)*104) = 27.79" |
40.09" |
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2 |
(sin(-10.5+3)*104)*0.72 = -9.72" |
(sin(10.5+3)*104) = 24.28" |
34.00" |
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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 =/- 66.5 degrees on the lower blade and at 90 +/- 52.5 degrees on the upper blade.
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Degree |
Drop of lower blade |
Drop of upper blade |
Clearance |
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0 |
0.0 |
0.0 |
20.36" |
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2 |
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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 SynchroLite's 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 - InteractionFebruary 12, 2003 ~ This form was used to look only at the elevation of the upper blade's tip above the lower blade plane and no coning angle was considered. The results show that the vertical gap increases approximately 3/4's of an inch for every one degree increase in the 'V' angle and the vertical gap decreases very slightly for every one inch increase in the stagger.
This would indicate that the stagger should be 24" (ie. SynchroLite's 27" but with lower rotor hubs), and the 'V' should be 24 or 25 degrees. A 'V' angle of 22 degrees might be considered if the blades had reduced out-of-plane flex and the 'hub-spring' resisted the extreme longitudinal cyclic angles.
Same Page ~ Different Craft:
~ SynchroLite ~ UniCopter
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Last Revised: November 22, 2003