UniCopter_Stability

UniCopter ~ Trim, Stability & Control - Stability

Overview:

Theoretical notes re the effect of Absolutely Rigid Rotor disks on the stability of the Unicopter.

The rigid connection of rotor to fuselage may make the helicopter statically unstable. The UniCopter will not have the positive stability characteristics that the conventional helicopter receives from flap-back.

For general information, see:- OTHER: Dynamics - Stability

Symbol Definitions - Dynamics

Static Stability: See also:- OTHER: Dynamics - Stability - Static

Speed Stability: (Static Longitudinal Stability) [forward transition along the X-axis]

At higher forward speeds the parasitic drag of the fuselage and particularly the landing gear must be counteracted. This is of particular concern for the Absolutely Rigid Rotor because there is no flapback.

Nose Down Attitude in Forward Flight: This will not be a problem.

The rigid rotor means that the mast will be normal to the rotor disk during fast forward flight, unlike the more horizontal fuselage of a conventional helicopter with soft rotor.

The parasite drag is located below the rotor disks. Unlike a conventional helicopter, ever increasing forward speed may require ever increasing rearward longitudinal cyclic, to keep the nose up. The torque from the rotor about the lateral axis will add to the nose-down pitching, but a power failure may cause a sudden rise of the nose.

Faster forward speeds will probably not entail higher rotor torque, just higher propeller thrust

Potential Solutions:

Keep the fuselage as clean as possible.

The landing gear must be streamlined skids or be retractable.

Mount miscellaneous items, such as Pitot tube, strobe light (and ballistic parachute?), which add to the drag, in the tail, which is above the disk and thereby helps offset the fuselage's drag.

Mount the fuselage and the rotor disk as close together as possible to minimize the frontal area and moment arm.

Make sure that there is ample longitudinal cyclic so that at the highest possible forward velocity there is still enough rearward cyclic to raise the nose.

Pitch the horizontal stabilizer down and/or make it an inverted asymmetrical airfoil and/or make it a 'T' tail so that its drag is above the rotor disks. June 7, 2001 ~ It looks like a NACA 0012 'T' tail of 3 sq-ft (approx.) with an angle of attack of - 9 degrees may offset the fuselage and landing gear drag.

Consider constructing the blade tips wit some dihedral. This may;

Allow the blades when at 180º azimuth to provide some lift.

Allow the blades when at 0º azimuth to provide some downward force. Both 1/ & 2/ thereby reducing the size of the HS slightly. There may not be a need for a horizontal stabilizer. See UniCopter ~ Trim, Stability & Control - Stability - Angle of Attack Stability - Decalage.

DESIGN: UniCopter ~ Rotor - Disk - Pusher Prop Assist

Decrease the tip vortices

The Nonuniform Induced Velocity may contribute toward positive Speed Stability on an Absolutely Rigid Rotor at slow forward speeds. At higher speed in will probably not.

The Pre-cone will contribute toward positive Speed Stability on an Absolutely Rigid Rotor at faster forward speeds.

Theoretical example to support the above statement.

During forward flight, the airflow's streamline is only parallel to the chordline of blades when they are at 90º and 270º azimuth. At all other azimuths the streamline is at an angle to the chordline. Of course, the greatest angle will be at 180º and 0º azimuths.

For simplicity of description, if we assume that; the craft has forward velocity, the tip path plane is horizontal, the rotor has a 5º-coning angle, the blades have zero pitch about there pitch axis, and its two blades are STOPPED at azimuths of 180º and 0º. The streamline is now 100% spanwise, not chordwise. Therefore, (remembering that the airflow is spanwise) the blade at 180º azimuth presents a pitch angle of +5º to the airflow and the blade at 0º azimuth presents a pitch angle of -5º to the airflow.

These two STOPPED blades will be trying to pitch the nose of the craft up.

Now (forgetting that rotation is required for centrifugal force) in this hypothetical example, if the collective was lowered then the coning angle would reduce to 0º on both the blade at 180º and the blade at 0º azimuth.

These two STOPPED blades will no longer be trying to pitch the nose of the craft up.

In other words, the reduced coning angle will let the nose fall.

Of course, on a rotating rotor the angle between the streamline and the chordline will be no where near the 90º that it is in the above hypothetical example.

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"One of the natural ways of augmenting longitudinal stability is by increasing the tailplane effectiveness, normally achieved through an increase in tail area." A primary means of creating positive speed stability is with the horizontal stabilizer. See items 0912 and 0902 below.

Consider: DESIGN: UniCopter ~ Rotor - Disk - Dihedral at Blade Tip. Would this be an alternative to Pre-cone?

Rotor Torque:

The UniCopter's rotors turn outside forward.

Bad - The pitch moment [M_P & M_S] components of both rotor torques is negative. It is an additive to the parasitic drag of the fuselage.

The negative pitching moment will be suddenly lost upon loss of power. Shortly thereafter the descent of the craft should cause the HS to eliminate the positive.

A nice fact is that the obliqueness on the UniCopter is less than earlier intermeshing helicopters.

Pusher Prop:

Could the pusher propeller increase the downwash through the front of the disk and thereby work against Static Longitudinal Stability?

A lowering of the crafts nose, as its forward velocity increases, will probably result in more air being fed to the upper half of the propeller's disk. This may want to increase the nose down attitude. (I.e. negative speed stability)

Canard:

A canard at the front of the craft would assist with speed stability, as does a horizontal stabilizer. Like an airplane, the canard creates lift at the front (good) v.s. the H.S., which creates a downloading at the rear (bad). Unfortunately, the canard would have to be ahead of the rotor disk and at an elevation near to, or even above, the rotor disk. The tip dihedral, mentioned above, may help a little.

Angle of Attack Stability: [rotation about the Y-axis]

This looks like it should be OK since;

The 'absolute' rigidity of UniCopter rotors does not allow flapback.

Elimination of Horizontal Stabilizer Considerations on a Craft with 'Absolutely' Rigid Rotors: (plus its drag and cost).

Concern: "For rotors with appreciable hinge offset, or hingeless rotors, the horizontal tial size required to overcome the rotor instability tends to be quite large, lending to other control and safety issues." ~ Journal of the American Helicopter Society January 2005, page 6 & Ref. 71.

Reasons:

The reduction of drag and cost of the HS.

The elimination of any (possible) situations where the HS and the blades are producing opposing vertical aerodynamic forces. ???

Forward center of gravity:

If the lift moments are equal around the effective rotor disk then the center of lift will be at the center of the effective disk. If the center of gravity of the craft is ahead of the center of lift then an updraft should result in a stabilizing action by wanting to pitch the nose down. This will have been achieved without a horizontal stabilizer.

Decalage might be implemented.

A potential method would be to locate the thrust line of the propulsor above the center of drag. This will want to pitch the nose of the craft down during cruise. To offset this negative pitch; the angle of attack in the aft quadrant of the disk will be less than the average angle of attack, and the angle of attack in the forward quadrant of the disk will be greater than the average angle of attack.

Example: Assume that the blades' angle of attack are 2º when at the reared and are 4º when at the front. If the effective rotor disk is now subjected to an updraft that increases overall angle of attack by 2º then the lift at the rear will be increased by 100% whereas the lift at the front will be increased by only 50%. This will cause the craft to pitch nose down thereby giving angle of attack stability; without a horizontal stabilizer.

This could be considered somewhat similar to the first Sikorsky with is two horizontal fans.

In addition, any reduction or loss of power will result in the noes pitching up slightly and I think that this will be an advantage.

A forward center of gravity should assist and thereby reduce the length of the arm between the propulsor thrustline and the CG (or center of drag) and this may be advantageous.

Possible problem: Look into bunting {power push over PPO) on gyrocopters where the centerline of thrust is above the center of gravity. From an article by Greg Gremminer ~ Sorry, a slightly high prop thrustline is the reliable way to achieve positive Airspeed Static Stability, positive G-Load Static Stability, and good Power Stability - at the same time. It is true that the "high prop thrustline" must be "balanced" by a properly configured HS,

Possible problem: A change in the location of the CG may result cause the example above to be circumvented.

Possible solution: The rotor is 'absolutely' rigid not teetering therefore the above mentioned problems may not exist.???

There is a thread on PPRuNe called 'Theoretical Aerodynamics; Is an HS required on a rotorcraft with 'absolutely' rigid rotors? It discusses this subject. It is summarized here; DESIGN: UniCopter ~ Fuselage - Tail - Stabilizer - Horizontal ~ Need for HS

Directional Stability: [rotation about the Z-axis]

A large enough vertical stabilizer should handle this. Note that too large a vertical stabilizer might produce an unstable spiral dive.

Alternatively, twin booms will result in twin vertical stabilizers. They will give good directional authority in forward flight, but since they are side by side, they will give less resistance to yaw in hover. See; Twin Vertical Stabilizers. This should be advantageous. It should also have the same effect as the Variable Vertical Fin Concept

Dihedral Effect: (Static Lateral Stability) [transition along the Y-axis]

Sideslip:

During hover there is lateral symmetry of lift in each rotor, This means that the complete rotor disk should have a dihedral of 3-4º; as shown by the red lines in the following sketch.

As the forward speed increases the advancing (lower) blades will assume more of the lift than the retreating blades (because of ABC). This means that the dihedral will diminish with increasing speed and may probably become anhedral during cruise. This may not be a problem. In fact a shallow 'V' in the horizontal stabilizer may offset any potential problem.

Related to this is that the Interleaving configuration has anhedral between its two rotor. As the forward speed increases the advancing outer blades will assume more of the lift than the retreating blades (because of ABC). This means that the dihedral will increase with increasing speed.

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Synchropter Directional Stability Information: from 'Stability and Control of Rotary Wing Aircraft: Note that the UniCopter rotors are turning outside forward and this is the opposite of the SynchroLite. On the UniCopter, a side velocity as from a gust, yawed flight, or sideslip will act in a destabilizing manner. The Lambda (Λ) angle (Vee angle between masts on intermeshing helicopter) on the UniCopter is less then those of the Synchropter and other previous intermeshing helicopters. Hopefully, this will minimize the destabilizing effect on directional stability.

Sideslip to the left will reduce the torque on the left rotor and increase it on the right rotor. When view from above, the right rotor is turning CCW and this means that a CW moment is imparted to the craft. At the tail, the CW moment will be overcome by the free airflow from the left to right on the vertical stabilizer and this will yaw the craft to the left (nose into free airflow). The vertical stabilizer is above the center of drag therefore any CCW roll (when viewed from the back) caused by the free airflow against the body of the craft may be offset by free airflow against the VS.

On a conventional helicopter the flapback may overcome or minimize sideslip.

A partial solution may be to locate as much of the vertical fin as possible above the rotor disks and also have it as far forward as possible. Large side openings in the cockpit may reduce (or increase) drag in sideslip.

See: OTHER: Dynamics - Stability ~ Directional Stability

Additional Possible Solutions (if required):

The current thinking is to have a conning angle (precone) of 4º, for longitudinal static stability. This should offer some, assistance to lateral stability. DESIGN: UniCopter - Rotor - Disk - Pre-cone

Perhaps a low center of gravity and high lateral drag (center of gravity is below the aerodynamic center) will reduce this. The V's shape of the fuselage in the Y-Z plane just behind the masts may give some dihedral.

The high vertical empennage should also help.

Additional ideas:

1: Perhaps the changes of lift within the disk during roll will want to resist the roll. This is the same as the Robinson we-wa. Unfortunately, the most that could be expected from this is neutral stability, not any positive stability. What is desired is to have the fuselage/empennage to be, constantly and without any movable controlling surface, aerodynamic attempting to hold the craft in the upright position about the X (roll) axis. In forward flight the air flow will be parallel to the X-Z plane. It will also be from front to back, but its angle about the Y axis will vary depending upon forward velocity, climb or autorotation. If the HS and VS are airfoils then the act of rolling will increase the angle of attack on the correct sides of the airfoils but the corrective action is probably not going to be enough

2: If the horizontal stabilizer is coupled to the collective then it will always be experiencing a downward air force. If this stabilizer is an inverted 'V' then a roll in one direction will cause the stabilizer on the other side to receive a greater downward air force, and this force is opposed to the roll. Maybe it will not be receiving a much greater downward force since most the air that is not coming from straight ahead is coming from the rotor, which always has the same orientation to the stabilators.

3: Consider winglets extending out one to three feet from the secondary gearboxes. These winglets will have controllable angles of attack and will rotate in opposite directions to each other. They are controlled by an air driven gyro and will counter any tendencies of the craft to roll. ~OR~ This could be mounted high in the vertical stabilizer. For more information on the gyro see [Source ~ HT p. 851 - 862]

Copy of posting on PPRuNe

Lateral Stability of the V-22 and other side-by-side rotorcraft

Pictures;

Sud Est Aviation (Aerospatial) SE-3000 http://www.lasercamera.de/xml/content/OF00000000400003/1/74/462741.jpg

Focke-Achgelis Fa223 Focke-Achgelis_Fa223.jpg

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Hendrick Focke, the inventor of the FA 223, said in the Jan/1947 issue of the 'American Helicopter' magazine;

"The Fa223 is statically and dynamically completely stable around all axes other than the longitudinal one. At traveling speed of 140 to 150 km/h all controls can be released, because longitudinal instability disappears at about 120 km/h. Then this aircraft behaves just like a normal airplane and is automatically stable."

Jean Boulet, the test pilot of the SE3000, said some time later;
"Despite the first successes of the Focke aircraft, the two lateral rotors formula is not satisfactory. It shows a good longitudinal stability, because the empenage is well out of the rotor's stream, but in return the formula has defects concerning the lateral stability:

- Dynamic instability of roll while hovering in ground effect; the ground effect increases on the side toward which the aircraft is leans, tends to push the aircraft to the other side.

- Static instability of roll in translation at low speed; when a turn is engaged, at a speed lower than the climbing speed, the increase in the relative speed of the external hub produces an increase in lift which leads to increase in initial tilt.

It will be necessary to waight for the era of automatic pilots which will artificially fix these defects, to see reappear the lateral rotor's formula with the Bell XV 15."

Translated by Claude Dawson from the French publication 'History of the Helicopter' by Jean Boulet.

My thoughts;

Did Focke play down the faults because it was 'his craft'?
Did Bouet and SNCASE resent the fact that Focke and his German employees left the company as a group for England?
Would these two problems even be of concern to the interleaving and the intermeshing since they both have closer spaced rotors and in addition the short fuselage of the Intermeshing is less likely to react to the push of the increased ground effect on the low side.

Backing Up: [rearward transition along the X-axis] (This is all my thinking at the moment)

Pro: The horizontal stabilizer is sloped to give a downward thrust in forward flight. It might therefore give an upward thrust in rearward flight and result in positive stability.

Con: The horizontal stabilizer is aft and above the (leading) edge of the disk. It may therefore detract from the lift at the (leading) edge and result in negative stability.

Roll: [rotation about the X-axis]

The blades on the descending side of the disks will experience a larger angle of attack whereas the blades on the ascending side of the disks will experience a reduced angle of attack. The rigid rotor to fuselage connection will impart a righting moment (spring) or at least a slowing (dampening) of the roll.

See comments on static and dynamic instability of roll [Source ~ HOTH p.130] The craft being discussed is the Side-by-side SE 3000 and the two problems should not be as applicable, to the interleaving and the Intermeshing configurations.

Heave: [upward transition along the Z-axis]

Is there anything here to consider or do we just accept heave as an un-correctable?

Sink: [downward transition along the Z-axis]

Is there anything here to consider or do we just accept heave as an un-correctable?\

Hover:

Isn't this just the result of the above stability?

Pitch-Roll Coupling:

May not be a problem with the UniCopter because there is no flapping.

Pitch- Sideslip Coupling:

May not be a concern because of the counter rotation of the rotors.

Dynamic Stability: See also:- OTHER: Dynamics - Stability - Dynamic

Hover:

notes

Forward Flight:

The stiffer the rotor the less stability during high-speed flight. Hopefully, the gyroscopic inertia of the two counter rotating rotors may help to alleviate this problem by damping. It should be noted that the high mass of the strong 3-blade rotors will contribute toward higher stability and the slower rotational speed will contribute toward lower stability.

Short Period Mode:

Long Period Mode ~ Phugoid:

See: More on Phugoid

Dutch Roll:

Spiral Dive:

Sideslip:

The stiffer the rotor the less stability. Why?

Also, the gyroscopic inertia of the two counter rotating rotors will not alleviate this problem (If it is a problem). This is because the gyroscopic processional forces of the two rotors are self-canceling within the power-train frame. In other words, the gyroscopic effect will do nothing for damping. Perhaps, during hover, when the ABC is not in effect, the equal thrust on the higher, retreating side of the disks will provide some dihedral.

Autorotation:

Damping in Pitch and Roll

Due to Aerodynamic Resistance:

With a rigid rotor, the blades will provide some dampening due to the motion being normal to the cord-span plane of the blade:

Due to Gyroscopic Precession:

The UniCopter's rotor disks are completely rigid. They rotate in opposite directions and are close to being located on a common axis. When the ARR helicopter rotates about the X (roll) or Z (yaw) axes the craft may experience an amount of cross coupling between the two axes due to gyroscopic precessions. Perhaps not ~ reference the experiment with the bike wheels.

See: Counterrotating Gyroscopes

Working Papers:

DESIGN:

B299

MAKE:

Items:

DESIGN:

	Name	Item
	Static Stability:
	Stability - Static - Longitudinal (Speed Stability) (about Y-axis)	0902
	Stability - Speed Stability and the Horizontal Stabilizer	0912
	Stability - Static - Directional (Weathercock) (about Z-axis)
	Stability - Static - ???? (Roll Stability???) (about X-axis)
	Dynamic Stability:

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Last Revised: January 29, 2008