Item 0871

DESIGN: UniCopter ~ Rotor - Disk - Lateral Dissymmetry of Lift and Drag? - (3-blades)

Review 1073.html in Obsolete folder to see if these two pages are in agreement

Overview:

Evaluation of the oscillating rolling moments with two 3-blade really rigid rotors, during forward flight, caused by dissymmetry of lift.

Conclusion:

There will be vibration, with 3-blade rotors. The side of the helicopter that has the advancing blade located at 90º azimuth will have greater lift than the other side where the advancing blades are at 30º and 150º azimuth. This is irrespective of whether the rotation is outside-forward or inside-forward.

Potential Solutions:

Evaluation of the oscillating yawing moments during forward flight, caused by the dissymmetry of H-force drag, may be later considered on a separate web page.

Drawing of Lateral Moment Arms of a Single Rotor:

Hover:

Moment on Y-Y: (100 lbs. * 1.0) = (2 * ( 100 lbs. * .5))

If all three blades are providing an equal amount of lift then the center of the lift will be at the centerline of the disk. Brilliant; I didn't need a drawing to prove this.

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Perhaps the significance of this is that if the center of lift is behind the centerline of the blade's pitch axis then the blades will be imparting a loading on the pitch arms. During hover, there should be no cyclic oscillation because the sum of the moments of the three blades should equal zero. There will be a force on the collective.

The center of lift on the VR7 blade varies from 41% of chord at Alpha = 0º to 29.3% of chord at Alpha = 12º.

This page was done to assure that the wheels in the 'swash-ring' are always in contact with the same flange of the ring and therefore not having to change their direction of rotation ( at 600 RRPM) 40 times per second. They will contact both flanges if Higher Harmonic Control is implemented. See swishring with revision for one torus with a follower on the top and a follower on the bottom.

Forward Flight: (Lateral Dissymmetry of Lift and Drag)

I think that the single advancing blade at 90º azimuth will have a greater thrust than the other rotor's two advancing blades which will be at 30º and 150º azimuth, Note the moment arm lengths and the air velocity. This will cause a rotational vibration about the longitudinal axis (roll). Higher Harmonic Control will allow the lift at 30º and 150º azimuth to be increase somewhat and the lift at 90º azimuth to be decrease somewhat.

Flight-Control Solution:

Consider adjusting HHC pitch by a spring steel 'warpable' swishring. Adjust by heat (bimetal), electrical (magnet) or mechanically.

The 1P will involve frequent changes, as the cyclic stick is moved. Changes to the HHC will be gradual and infrequent, relative to the primary control, since it is controlled by the forward velocity of the craft. The 3P control may be similar to the SynchroLite's Opposed Lateral Cyclic. For possible means of flight control, see DESIGN: UniCopter ~ Control - Flight - Swishring - Fixed Azimuth Overview

Re Drag: An airfoil that has a higher cl/cd than another should have a lower dissymmetry of drag for a given lift.

Calculations: by   FORM: Lateral Dissymmetry ~ UniCopter

Default Values:

Slope of lift chord: a = 6.0 / radian

Vertical velocity in hover: v1 = 25 fps

Density: ρ = 0.002377 slug/ft3 @ ISA

Rotor: Ω = 600 RPM

Radius: r = 0.75 * 8.33 = 6.2475 feet

Chord: c = 0.666 feet

Blade segment Δr = (8.33 / 10) = 0.833 feet

Collective = 5.5º

Inputs:

Collective: θ0

Higher harmonic 3P blade pitch: θ3P.

Forward Velocity: V

Cyclic amplitude: θ1P

Cyclic amplitude azimuth: Ψ1P

3rd harmonic amplitude: θ3P

Algorithims:

Tangential (local) Velocity: U = (Ω * r) + V * sin(Ψ * ( π / 180) [ft/sec]

Inflow Angle: φ = v1 / (U) [radians]

Cyclic amplitude at azimuth: θ1P = θ1P * sin(Ψ1P) This will have to be checked.

3rd harmonic amplitude at azimuth: θ3P = θ3P * sin(Ψ * 3) This will have to be checked.

Blade Pitch: θ = θ1P + θ3P

Angle of Attack: ά = θ - φ [radians]

Lift [L]:

An aerodynamic force caused by air flowing over an airfoil. The vertical component of thrust.

For an airplane wing: LW = (ρ / 2) * V2 * CL * S . Where S is the area of the wing.

ΔL = (ρ / 2) * (Ω * r)2 * a(θ - (v1 / (Ω * r)) * c * Δr

ΔL = (ρ / 2) * (U)2 * a(θ - (v1 / U)) * c * Δr

ΔL = (ρ / 2) * (U)2 * a(θ - φ) * c * Δr

ΔL = (0.002377 / 2) * (U)2 * a(θ - φ) * 0.666 * 0.833

ΔL = 0.001188 * (U)2 * a(θ - φ) * 0.666 * 0.833

L = (U)2 * a(θ - φ) * 0.000659

Thoughts on coding:

Base calculations on r = .75R at all azimuths, even though it will be greater on the retreating side.

FORM: Lateral Dissymmetry ~ UniCopter

The following values assume that the rotor disks have no forward pitch and all the forward thrust is coming from a pusher propeller.

The following thrust values are only for the blade segment at .75R of a helicopter weighing 750 lb GW and are probably not representative of the whole blade.

MPH: | Collective: | 3P amplitude: | Blade Segment Thrust @ .75R at Noted Azimuth and Rotor: | Moments: | Total Lift:

 MPH: θ0 θ3P 90º Port 30º Star 150º Star 270º Star 210º Port 330º Port PORT STAR Total Lift: lbs lb-ft lbs lb-ft lb lb-ft lbs lb-ft lbs lb-ft lbs lb-ft Port Star 0 5.5 0 58 427 58 246 58 246 58 -296 58 -116 58 -116 724 723 348 50 5.4 0.1 79 580 69 294 69 294 38 -195 46 -92 46 -92 772 775 347 100 5.1 0.3 95 704 80 341 80 341 22 -113 33 -67 33 -67 816 817 343 150 4.8 0.5 110 814 92 389 92 389 11 -55 23 -47 23 -47 872 869 351 200 4.3 0.6 119 877 97 414 97 414 3 -16 15 -30 15 -30 888 893 346 250 3.8 0.7 122 900 102 434 102 434 0 -1 9 -18 9 -18 904 901 344

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Port is the port rotor and Star is the starboard rotor.

Violet color represents forces and moments on port side of craft.

Red represents forces and moments on starboard side of craft.

PORT is the sum of the positive rolling moment and STAR is the sum of the negative rolling moment. They must be in balance.

The collective and the 3P-amplitude have been adjusted as the forward velocity increases so as to maintain a constant thrust, plus no rolling moment.

So far it appears that the 3rd harmonic (swashring) only needs a maximum amplitude of 0.7º.

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The following is the same as the previous table excepted that it checks the roll moment at the 150-mph conditions, when the blades are at a different azimuth.

MPH: | Collective: | 3P amplitude: | Blade Segment Thrust @ .75R at Noted Azimuth and Rotor: | Moments: | Total Lift:

 MPH: θ0 θ3P 105º Port 45º Star 165º Star 285º Star 225º Port 345º Port PORT STAR Total Lift: lbs lb-ft lbs lb-ft lb lb-ft lbs lb-ft lbs lb-ft lbs lb-ft Port Star 150 4.8 0.5 111 797 105 587 71 195 11 -55 17 -56 34 -16 854 852 349

Looks good!

None of the forgoing yet considers forward cyclic on the rotors.

Reference:

Advancing Blade Concept (ABC) Dynamics ~ Vibration, page 5 onward ~ Presentation May 1977

Advancing Blade Concept (ABC) High Speed Development ~ Vibration, page 10-12 ~ Presentation May 1980

 OTHER: Aerodynamics - Vibration - Rotor Induced - Higher Harmonic Control 0793 DESIGN: UniCopter ~ Control - Flight - Swashring - Fixes Azimuth Overview 1092

Drawing:

Consider 2P and 4P higher harmonic, as alternative.

Direction of Rotation:

Objective:

To get a comparative value of the moment about the craft's roll axis, based upon the direction of rotor rotation (i.e. outside-forward or inside-forward).

Conclusion:

The direction of rotation does not change (improve or worsen) the lateral dissymmetry of lift.

Supporting Calculations:

• The FORM: Lateral Dissymmetry ~ UniCopter was used for these calculations.
• The current default values (which will not be the final ones) were the same for every blade azimuth.
• The forward velocity of 100 mph was selected.
• A fixed collective value was used and no cyclic values were used. The assumption is that the prop is providing all forward thrust.
• The blade azimuths and approximate moment arms are as shown in the second drawing on this page.

The craft's rolling moment is positive (+) when it is CW when viewed from the rear.

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Rotors Turning Outside-Forward.

 Rotor: Azimuth: Lift: (pounds) Arm: (1) (feet) Moment; (ft-lb) Direction of Roll: (viewed from aft) Port 90º 109.5067 7.3725' (88.47") 807.3384 CW Port 210º 38.1645 2.0048' (24.06") -76.5113 CCW Port 330º 38.1645 1.9893' (23.87") -75.9194 CCW Sum of Port Moments: 654.9077 CW Starboard 30º 81.6424 4.2496' (50.99") -346.9485 CCW Starboard 150º 81.6424 4.2444' (50.93") -346.5265 CCW Starboard 270º 22.5509 5.1225' (61.47") 115.5169 CW Sum of Starboard Moments: -577.9581 CCW Resultant Moment: 76.9496 CW

(1) The Arm values are back calculated from the Access generated Lift and Moment.

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Rotors Turning Inside-Forward.

This table is the above table with values switched so as to represent the crafts moment about its X-axis if the blades were rotating inside-forward.

 Rotor: Azimuth: Lift: (pounds) Arm: (1) (feet) Moment; (ft-lb) Direction of Roll: (viewed from aft) Port 30º 81.6424 1.9893' (23.87") -162.4112 CCW Port 150º 81.6424 2.0048' (24.06") -163.6757 CCW Port 270º 22.5509 7.3725' (88.47") 166.2565 CW Sum of Port Moments: -159.8304 CCW Starboard 90º 109.5067 5.1225' (61.47") 560.9481 CW Starboard 210º 38.1645 4.2444' (50.93") -161.9854 CCW Starboard 330º 38.1645 4.2496' (50.99") -162.1838 CCW Sum of Starboard Moments: 237.7789 CW Resultant Moment: 77.9485 CW

Comparison with Coaxial

Objective:

To compare the above two intermeshing roll moments with that of an identical coaxial configuration.

Conclusion:

All three rotor configurations have the same lateral dissymmetry of lift (moment).

Rotors Crossing at 90º - 270º:

• This is the 60º index, which the Sikorsky first used.
• Upper rotor turns CCW
• This table is identical to the above tables except that the stagger is 0" .
 Rotor: Azimuth: Lift: (pounds) Arm: (1) (feet) Moment; (ft-lb) Direction of Roll: (viewed from aft) Lower 90º 109.5067 6. 25' 684.4169 CW Lower 210º 38.1645 3.125' -119.2641 CCW Lower 330º 38.1645 3.125' -191.2641 CCW Sum of Lower Moments: 301.8887 CW Upper 30º 81.6424 3.125' -255.1325 CCW Upper 150º 81.6424 3.125' -255.1325 CCW Upper 270º 22.5509 6.25' 140.9432 CW Sum of Upper Moments: -369.3219 CCW Resultant Moment: 67.4332 CW

Vibration:

Lockheed XH-51A article from the Nov 2004 issue of Stu Field's magazine Experimental Helo

The rotor head was of a "hinge-less" design. Prouty further states, the "hinge-less" design suffers from the characterization that "they all shook". Lockheed added a fourth blade and controlled the shaking to a more pilot acceptable level.