Item 0717

DESIGN: SynchroLite ~ Rotor - Disk - Opposed (Differential) Lateral Cyclic 

Reasons for Opposed Lateral Cyclic on Helicopters w/ Two Laterally Located Main Rotors:

In a conventional counter-rotating single rotor-disk helicopter a small non-linear amount of increasing left lateral cyclic must be applied as the forward velocity increases. The SynchroLite has two rotor-disks with the port one is rotating CCW and the starboard one is rotating CW. This means that in forward flight, some left lateral cyclic should be applied to the port disk and some right lateral cyclic applied to the starboard disk. In other words, they should receive some opposing lateral cyclic.

There is a second reason for being able to apply opposed lateral cyclic. The desired amount of yaw force may not be available from the maximum amount of opposite longitudinal pitch. By tipping the two disks outward 2 or 3 degrees more the obliqueness of 12.5 degrees will give more blade to blade clearance between rotors and thereby allow a couple of more degrees of opposite longitudinal pitch.

Note that on the UniCopter, the rotors turn in the opposite direction and thus the lateral cyclic will be the opposite direction to that of the SynchroLite.

1. For Forward velocity:

See lateral cyclic to forward speed plot in Figure 9-4 in Prouty's Even More Helicopter Aerodynamics

My thought;~ The conventional intermeshing helicopter, SynchroLite and Dragonfly, may not require as much opposed lateral cyclic as a coaxial helicopter does. This is because during hover the pitch of the advancing (inside) blade must take into account the downdraft caused by the inner portion of the retreating blade. But, during forward flight the downdraft from the inner portion of the retreating blade is reduced which should mean that the advancing blade's relational angle of attack is automatically increased.

Re the coaxial: How is opposed lateral cyclic applied to a coaxial (if the two swashplates are interlocked by the 3 or 4 connecting rods), or is it, or does it need to be?

2. For Higher Yaw Rate in Hover:

DESIGN: Rotor - Disk - Blade to Blade Clearance [ 0199] shows the maximum allowable opposite longitudinal cyclic for yaw as 6 degrees. This page also shows that the blade gap decreases approximatly 2.25" for every additional opposite longitudinal degree of yaw. Therefore, to be able to get to the maximum of 9 degrees there must be 4 degrees of opposed lateral cyclic.

3. For Wee-wa:???

Wee-wa is when the blade in the front half is seeing a greater angle of attack because the front of the disk is IN THE PROCESS of tipping (pushing) down. This is of a very short duration. It is called an 'Acceleration Cross-coupling' because the front of the disk is accelerating downward. I wonder about this. The only other reference I have found to "the so-called washed-out coupling effects" is [Source ~ HFD p.419] It references two reports. It appears to occur in helicopters with feedback control systems (augmented rotorcraft). Perhaps Frank Robinson considers the delta-3 to be a feedback control system.

See 'Wee-wa', below and at R-22 Rotor

Another reason might be flapback caused by a gust from the rear while the helicopter's rotors are turning with the controls in neutral on the ground. This gust may cause the retreating lower blades to climb and the advancing upper blades to drop. The blades may strike each other; unless the Forward Velocity Adjustment also adjusts the cyclic for reverse remote airflow.

Drawing:

 

Design:

Clearance without Opposed Lateral Cyclic

The following dimensions are calculated on blades having a 3 degree coning angle.

The following dimensions are centerline to centerline and do not take blade thickness into account.

Elevation of upper blade

The tip is 5.4429" above horizontal at azimuths of 0 & 180 degrees.

The tip is 27.7928" above horizontal at azimuths of 90 degrees.

The tip is above the horizontal at azimuths of 39.0731 + 90 and at 39.0731 - 90 degrees is;

27.7928 - ((27.7928 - 5.4429) * (39.0731 / 90)) = 18.0897"

Elevation of lower blade

The tip is 5.4429" above horizontal at azimuths of 0 & 180 degrees.

The tip is 17.1649" below horizontal at azimuths of 270 degrees.

The tip is above the horizontal at azimuths of 50.9521 + 270 and at of 50.9521 - 270 degrees is;

-17.1649 + ((17.1649 + 5.4429) * (50.9521 / 90)) = -4.3658"

-4.3658 * (82.5177 / 103.3691) = 3.4852"

The clearance between blade is 18.0897" + 3.4852" = 21.5749". This checks out with calculation on Document 0199. The above calculation should be more accurate.

The blade tip of the upper blade is directly over the lower blade at azimuths of +&- 39.2210 degrees.

At this location the lower blade is at azimuth of 180 +&- 50.7982 degrees.

With both blades having a cone of 3 degrees, the clearance between these 2 points is 21.5749".

Additional Clearance for 1-degree Opposed Lateral Cyclic

Upper blade movement

(29.6857 - 27.7928) * ((90 - 39.0731) / 90)) = 1.0711"

Lower blade movement

(19.0109 - 17.1649) * ((90 - 50.9521) / 90)) = 0.8009"

-0.8009 * (82.5177 / 103.3691) = 0.6394"

Increase in gap

1.0711" + 0.6394" = 1.7105"

Giving both rotors 1 degree of outward (opposed) lateral cyclic the above clearance becomes 23.2854". The clearance therefore increases 1.7105" for every degree of opposed lateral cyclic.

Unchecked notes removed from another .doc.

Forward Velocity Adjustment

 

Consider hanging a light clear plastic flap from a horizontal axle. The axle will span the distance between the upper bearing points on the 2 masts. The flap will have a cutout for the pilots head and it will be clear so that the pilot can turn and look through it if need be. As the horizontal velocity increases this flap will swing back from its vertical home position. This backward movement will, by control linkage, cause the lateral cyclic of both rotors to move outward (increase pitch at 90 degree azimuth) slightly. It will also deflect the air down toward the engines, slightly. The pilot's head, which is a little ahead of the flap will help divert more horizontal flowing air onto the flap and there by increase the force on the flap, slightly.

If the fuel tank projects horizontally back for 2-4" below the flap and does not slope down too quickly then the air pressure may give more force for a larger amount of rotation before the air moves down behind the seat.

The following is from Internet news.

"Para 6-12 b. Compensating for Transverse Flow Effect

A left cyclic input decreases the pitch angle and angle of attack of the blade

over the nose while increasing the pitch angle and angle of attack of the blade

over the tail. These changes to blade angles of attack cause changes to lift.

As the pilot senses the right tilt of the rotor, he must apply left cyclic to

prevent the right tilt of the rotor as a result of transverse flow effect. At

higher airspeeds, lift differential between the fore and aft portions of the

disk begins to decrease. The cyclic stick must be moved back to the right at

higher cruise speeds."

Wee-wa:

Mr. Frank Robinson, in his posting in Pprune.org on Nov. 29, 2000, states that there are two reasons for incorporating delta3 into the R-22 rotor. They are;
    1. "The rotor disc will have some lateral tilt while the rotor disc is tilting forward, sometimes referred to as 'wee-wa.'."
    2. "The other undesirable characteristic in rotor systems having 90-degree pitch links is the lateral stick travel required with airspeed changes during forward flight at higher airspeeds."

Reason number 2. has been discussed further up this web page and the reasoning is relatively straight forward.

Reason number 1. Re Wee-wa. Mr. Frank Robinson states;

"For instance, feathering occurs while the rotor disc is being tilted, because an aerodynamic moment on the rotor disc is required to overcome the gyroscopic inertia of the rotor. But once the rotor disc stops tilting, the rotor disc and swashplate again become parallel and the delta-three has no effect on the phasing."

"In a steady no-wind hover, when forward cyclic pitch is applied, the 90-degree rotor disc will end up tilted in the forward direction, but if no lateral cyclic is applied, the rotor disc will have some lateral tilt while the rotor disc is tilting forward, sometimes referred to as "wee-wa." This occurs because while the rotor disc is tilting, the forward blade has a downward velocity and the aft blade has an upward velocity. This increases the angle-of-attack of the forward blade causing it to climb, and reduces the angle-of-attack of the aft blade causing it to dive. If no lateral cyclic was applied, this would result in a rotor disc tilt to the right while the rotor plane was tilting forward. Pilots subconsciously learn to compensate for this by applying some lateral cyclic as the cyclic is being moved forward. The amount of delta-three required to eliminate "wee-wa" in the R22 rotor system was calculated to be 19 degrees."

My thinking on this subject is;

Assuming that the pilot takes 1 second to apply a 20 degree forward tilt to the disk. Assuming also that a desired incremental forward tilt of the rotor disc takes place within a single revolution of the disk. Then at 500 RRPM the rotor has rotated 8.3 times in the 1 second interval. This means approximately 2 degrees of forward tilt per revolution. It is assumed that the lateral tilt will be merely a fraction of this forward tilt. Perhaps the 19 degrees fully removes the lateral tilt. This maybe BS. Mr. Robinson mentions "In a steady no-wind hover". In this situation, with a conventional teetering hinge, there should not be any cross-coupling.

Possible solutions:

Have forward motion of the cyclic stick put the opposed lateral cyclic into the rotors. There may be vibrations initially as the helicopter accelerates, but this vibration should disappear at cruise speed.

Opposed lateral cyclic is required because of lateral flapping. This lateral flapping is caused by asymmetrical airloads on the blades over the nose and tail, caused by conning. If the coning was eliminated by the use of a Absolutely Rigid Rotor [0815], then there is no opposed lateral cyclic. Problem solved.

Relevant Patents:

 

Control for helicopter having dual rigid rotors

4,008,979

February 22, 1977

 

 

Analog mixer to vary helicopter rotor phase angle in flight

4,027,999

 June 7,1977

 Have hard copy

Excerpt from the above patent 4,008,979;

"It is interesting to note that when the famed aviation pioneer, Igor I. Sikorsky, built his first helicopter early in the twentieth century, it included a dual, coaxial, counterrotating, rigid motor. Glauert suggested in his book "Aerodynamic Theory" that rotor roll moment might be overcome by using two, counterrotating, rigid rotors. Bergquist, Michel and Fradenburg advanced the art in their U.S. Pat. No. 3,409,248 when they suggested that differential lateral cyclic pitch be varied selectively as a function of aircraft forward speed to both cancel or reduce the roll moments and to optimally position the lift vector of each rotor so as to produce optimum lift-to-drag ratio performance. The mechanism taught in the Bergquist et al patent to accomplish this function was a simple linkage to provide an input directly to the control rods of each rotor either manually or through an air speed sensor which used a computer to derive correct gains. Lewis, in his U.S. Pat. No. 3,570,786, suggested the coupling of collective stick to the differential lateral cyclic inputs of the control system so as to produce differential lateral cyclic pitch as a function of collective stick input. Lewis felt that at high speed flight where the collective stick position is constant, that a constant differential lateral cyclic input would provide adequate efficiency."

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Last Revised: March 18, 2007