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OTHER: ~ Flight Dynamics - Definitions & Algorithms

• Definitions and Algorithms basically not related to the air medium or the power train.
 Aerodynamics: Flight Dynamics: Mechanics: Electrical: Composites: Definitions & Algorithms Definitions & Algorithms Definitions & Algorithms Definitions & Algorithms Definitions & Algorithms Definitions & Algorithms Symbols Symbols Symbols Symbols

Note: The algorithms are in blue

Ref. Symbols are in Times New Roman 2 sizes up from smallest. Subscripts are increased one size.

See: Access database for procedures running the algorithms and for additional information.

Outside Web Sites:

 Physics Glossary Glossary

There is, currently, duplication on Dynamics, Aerodynamics & Mechanics.

• A rotor whose hub, bearings and blades are structurally strong enough to support the craft without the need for the assistance of centrifugal force.
• A rotor, which because of its extreme rigidity, does not exhibit any significant flapping or lead-lag. The only two motions that it experiences are blade feathering and rotation about the mast. A crude analogy is that of a variable pitch propeller.
• The expression "Absolutely Rigid Rotor" is used in the context that 'absolute' is the optimal, albeit impossible, objective.

Acceleration:

Translational:

 Prouty Padfield x{..} ? Along the x-axis. y{..} ? Along the y-axis. Sideslip z{..} ? Aong the z-axis. Heave?

Angular:

Aeroelasticity:

The coupled field of structures and aerodynamics. Helicopter blades can be deformed by flapping (vertical), drag (horizontal) and torsion loading.

A course description of the subject: Introduction to Aeroelasticity . Studies phenomena involving interactions among aerodynamic, inertial and elastic forces. Explores influence of these interactions on aircraft design. Includes such specific cases as divergence, control effectiveness, control reversal, flutter, buffeting, dynamic response to rapidly applied periodic forces, aeroelastic effects on load distribution and static and dynamic stability.

Ailavator: (Elevon)

·        A control surface acting as both an aileron and an elevator.

When the helicopter is subjected to an angle-of-attack change in forward flight, for constant rotational speed the advancing blades are subjected to a greater upward acceleration force then the retreating blades because the product of angle-of-attack change and velocity squared is greater on the advancing side than on the retreating side. the resulting flapping motion will then tilt the disk in the direction of the initial change and an unstable moment will result. This effect is a function of tip-speed ratio and becomes more pronounce at higher speeds.

Angular Momentum:

Axes Systems of Helicopter: [craft]

• Wind
• Stability
• Body ~ This is the preferred one, and the one that is used with the SynchroLite and the UniCopter.

Axes Systems of Rotor: [rotor]

• Tip-Path-Plane Axis or axis of no flapping. Tip Path Plane (TPP).
• No Feathering Axis (root pitch axis) or the axis of no variation in cyclic pitch. Blade root pitch axis. No Feathering Plane (NFP) (root pitch plane). This is the same as the Control Axis, except for when the rotor has a Stability Augmentation System, such as delta-3. In this situation, when cyclic is applied the planes will differ until the no feathering plane reorients itself with the control plane.
• Control Axis or axis of the swashplate. The commanded cyclic pitch plane. Control Plane (CP).
• Hub (mast, shaft) Axis. Hub (mast, shaft) Plane (HP).

The above planes are arraigned in their physical top to bottom order as on the helicopter. The sequential arraignment from a commanded input is from bottom to top.

When a rotor is eventually developed that has Independent Root and Tip Control there will be the need for two separate Control Axes.

On an 'Absolutely' Rigid Rotors (ARR) the Tip-Path-Plane axis and the Hub axis will, essentially, be the same. In addition, the No-Feathering axis will, essentially, be the same, but the Control axis (axes) will be different. I think.

Azimuth: [ψ] [psi] [rotor] [craft]

Angular measurement made in the horizontal plane and in the same direction as the rotor. 0 degrees is at the back, 180 degrees is at the front and 90 degree is to the side with the advancing blade. Port rotor is CCW and starboard rotor is CW.

Bandwidth: [ωbw]

The frequency beyond which closed-loop stability is threatened.

Beat Frequency: [Ab]?

Given oscillations at 2 frequencies f1 and f2, their beat frequency is fb=|f1-f2|

See below

 Axis Orientation Location: Origin Direction: x Chord The 25% of chord line. Leading edge ?? Positive toward y Span Centerline of hub Positive toward trailing edge z Thickness Chord line ?? Positive downward

The blade axes system has the positive x direction along the blades quarter chord line. The positive y and z directions are such that the blade and hub sub systems align when the flapping is zero and the azimuth angle is 180º. [Source ~ HFD p.179]

• A self-exciting vibration. It involves the coupling of blade flexing and twist with air forces.
• Blade flutter is an oscillation condition of the rotor blades that generally occurs at a higher frequency than the rotor's RPM. Blade flutter frequency is a function of blade mass and the torsional stiffness of the blade.
• It appears that blade flapping may be the primary source. Therefor see the comments on flutter in

A self-exciting vibration, sometimes encountered in the operation of two-blades rotors.

Body Axes System: [craft]

The Body Axis System is the preferred one. The X-axis lines up with the body in the side and top views. Its main disadvantage is that the waterlines are perpendicular to the mast and therefor may not be parallel to the cabin floor. In a light one or two-seat helicopter, the floor is not significant. The Body Axis System is used on this web site.

The Z-axis is vertical, and positive downward [Waterline]. The X-axis is positive forward [Station], and the Y-axis is positive to starboard [Buttline].

For additional information see: Euler Angles, Origin, Forces and Moments

Center of ....

Disk: [rotor]

Helicopter: [craft]

Aerodynamic Center: Center of Parasite Drag is probably the same.

Center of Gravity [CG]; Center of Mass; The point in the helicopter at which all of the weight is considered to be concentrated. The sum of the moments about the center of gravity is zero. This location is established by the SynchroLite Weight and Balance Calculations and the UniCopter Weight and Balance Calculations .

Centrifugal Force: [rotor]

It is always parallel to the hub plane.

Centrifugal-Pitch Coupling: (Tennis Racket Effect) [rotor]

A type of dynamic blade twist about its feathering axis and it is caused by a centrifugal flattening moment. It is reduced by Chinese weights located perpendicular to the blade chord.

Centripetal Force: [rotor]

Centripetal Force and Centrifugal Force: [rotor]

Coefficient of Moment [cm]

A dimensionless number used to express the aerodynamic moment in respect to 1/4 of the chord. The Cm is considered positive when pulling up.

________________________

'The following 6 are valid equations, but are for fixed wing and not used in Access.

cl = L / ((ρ * A * Vfwd ^ 2) / 2)

cd = D / ((ρ * A * Vfwd ^ 2) / 2)

cy = Y / ((ρ * A * Vfwd ^ 2) / 2) Lateral force coefficient.

Cl = l / ((ρ * A * Vfwd ^ 2) / 2) Rolling moment coefficient.

Cm = m / ((ρ * A * Vfwd ^ 2) / 2) Pitching moment cofficient.

Cn = n / ((ρ * A * Vfwd ^ 2) / 2) Yawing moment coefficient.

_____________________

Coning: [rotor]

The degree of the coning angle is determined by the relationship between the centrifugal effect acting on the blades and the aerodynamic lift produced by the blades.

Coning causes an upward flapping on the forward side which results in an elevated tip on the retreating side.

For additional information see; DESIGN: SynchroLite ~ Rotor - Disk - Coning Angle

Reference:- FUNCTION angle_of_cone()

The ability to apply forces and moments to the aircraft to maintain it in a steady flight condition in gusty air or to perform a desired flight maneuver.

This plane represents the commanded cyclic pitch plane and is sometimes known as the swashplate plane.

Control Power:

1. The measure of the total moment or force available to the pilot for maneuvering from a steady trimmed flight condition, or for compensating for large gust disturbances. The rolling or pitching moment per unit stick deflection.
2. Aircraft moment per degree of tip-path-plane tilt.

Control Sensitivity:

The maximum rate of roll or pitch achieved by a unit displacement of the controls. [Source ~ AH p.277]

The measure of either aircraft acceleration or steady velocity produced by a unit of control motion. [angular velocity / stick displacement]

Coriolis Effect: [rotor]

The change in rotor blade velocity to compensate for a change in the distance between the center of mass of the rotor blade and the axis of rotation of the blade as the blade flaps in flight. I.e. conservation of angular momentum. For more see: Cyclical Coriolis and Hooke's Joint

Critical Damping: [ccrit]

The value of damping that lies on the boundary between oscillatory and non-oscillatory motion.

Cross-coupling: [rotor]

The off-axis cross-coupled response to an on-axis action.

• Acceleration (Control)
• Rate
• Washed-out

Damping: [c]

The resisting moment per unit angular velocity of the helicopter. For more on damping in pitch or roll see; [See ~ AH p.275]

Damping ratio: [c/ccrit]

c/ccrit = (γ/16) * (1 - (e/R)4) * ((1+(0.33 * (e/R))/(1-(e/R))) * (1 / (ωn/Ω))

Decalage:

A situation where two airfoils have different angles of incidence.

Decone: ,(βd) [rotor]

A removal of a portion of the precone. Done at some distance outboard of the precone.

• Precone below.

Delta-1: [δ1] [rotor]

Flap-Pitch coupling.

Delta-2: [δ2] [rotor]

Lag-Pitch coupling. Aerodynamic rotor head. See delta-4 below ??

Coefficients in a power series. [See ~ AH p.324]

Delta-3: [δ3] [rotor]

Teeter-Pitch coupling. δ3 = -Kp * β

Delta-4: [δ4] [rotor]

Lag-Pitch coupling. See delta-2 above ??

Derivatives:

There are 36 stability derivatives, says Padfield. (6 * 6) = 36 ?

There are 24 control derivatives, says Padfield. This includes tail rotor

Gimbaled gyrocopter style of hub in that the blade pitch is changed by tilting the head and not by pitching the blades with a pitch link and pitch bearings

Displacement:

Translational:

 Prouty Padfield x Along the x-axis. y Along the y-axis. z Aong the z-axis.

Angular:

 Prouty Padfield Φ Helicopter roll angle. Θ Helicopter pitch angle. Ψ Helicopter yaw angle.

A quasi-static condition where the blade twists in response to increasing load in a direction that further increases the load.

Divergence stability is assured regardless of pitch spring if the blade is mass balanced in such a way that the center of gravity is ahead of the aerodynamic center.

The characteristics of a helicopter that cause it to try to return toward its trim flight condition following an external disturbance is static stability. The correction will overshoot. The dynamic stability relates to the rate of dampening of this oscillation.

Dynamics (Kinetics):

The branch of mechanics dealing with the motions of material bodies under the actions of given forces; kinetics.

Dynamic Twist:

3 types or causes;

• Pitching moment
• Aerodynamic center and flexural axis
• Centrifugal-Pitch Coupling (Centrifugal Flattening Moment) (tennis racket effect)

Effective Hinge Offset: [(e/R)eff]

The ratio of the hinge offset divided by the radius of the rotor.

Electrotor:

An electrically drive helicopter rotor.

Elevon: (Ailavator)

·        Aircraft control surfaces that combine the functions of the elevator (used for pitch control) and the aileron (used for roll control), hence the name.

The time that the stored energy in a main rotor could supply the power to hover before stalling..

Euler Angles: [craft]

Defines the orientation of the helicopter's body axis relative to the earth.

• Θ The helicopter pitch angle
• Φ The helicopter roll angle
• Ψ The helicopter yaw angle

Figure of Merit: [FM]

A measure of the efficiency of a hovering Helicopter.

FM = Ideal power required to hover / Actual power required to hover. [Source ~ PHA p.46]

Flap Frequency Ratio: [λβ] [Ω / ωN undampened] [rotor]

The value is 1 for all blades without hinge offset. The addition of a hinge offset changes the characteristics of the rotor from being a system in resonance to one whose natural frequency is higher than the rotational frequency. With the offset, the frequency will be less than unity and the phase angle will be less than 90º. For the inverse of first flapping frequency, a close approximation is is: λβ ≈ 1 / (1 + (3/4) * (e/R) )

Flapping Hinge Offset: [e] [rotor]

The distance from the center of the mast to the flapping hinge.

Changes the characteristics of the rotor from being a system in resonance to one whose natural frequency is higher than the rotational frequency. This results in a Phase Angle that is less than 900.

The dynamics of helicopters; derivation of equations of motion; small perturbation methods; stability derivative estimation; longitudinal and lateral static stability and dynamic stability; response to control input(open-loop control); and closed-loop flight control system design.

Flutter:

Flying Qualities: [Source ~ HFD p.3]

• "at the moment of pure quality, subject and object are identical." ~ Pirsig
• "flying qualities are what you get when you've done all the other things." ~ flight dynamic engineer

• Aerodynamic
• Centrifugal
• Inertial
• Gravity
• Hub Spring

Forces on Craft: [craft]

The three pairs of forces related to the helicopter are:

• Vertical [Z]. Lift acting up and weight acting down. Positive is downward.
• Longitudinal [X]. Propulsive force acting forward and drag acting aft. Positive is forward.
• Lateral [Y]. Side forces acting to the left and right. Positive is to starboard.

Gamma: [Γ] [rotor]

The angle between input azimuth and the result's azimuth. See Phase Lag on this page.

Gap: [g]

The vertical distance between 2 rotor disks. Applicable to coaxial and tandem helicopters.

Gross Weight: [GW] [craft]

Ground Resonance: [craft]

A self-exciting vibration.

Helicopter Axes: [craft]

 X-axis Longitudinal axis + is forward θ theta Roll + rotation is CW when looking forward. Y-axis Lateral axis + is starboard φ phi Pitch + rotation is CW when looking to starboard. ?? Z-axis Vertical axis + is down ψ psi Yaw + rotation is CW when looking down

Hinge Offset: [e] [rotor]

See Flapping Hinge Offset above.

See Teetering Hinge Offset below.

Hub Spring: [rotor]

A device located in the hub of a teetering rotor that attempts to return the rotor disk to its mean position (normal to the mast) when the disk is tipped. Functionally, it will offer advantages similar to that of centrifugal effect and offset on an articulated rotor.

Ideal Power:

• ER/sec = (Force)(Velocity) = T v1 ft-lb/sec.

Ideal Rotor:

• A rotor with constant chord and an Ideal Twist distribution. In other words a uniform induced distribution over the rotor disk and hence a minimum induced power loss. With ideal twist, the blade loading is triangular.
• [Source ~ HT p.64]
• Do the above three 'Ideals' take the tail rotor loss, or swirl recovery, into account?

Igornemesis:

A rotorcraft with an Interleaving configuration; for use where the requirement is the transportation of large payloads at high speeds.

Inertial Force:

A force which must be added to the equations of motion when Newton's laws are used in a rotating or otherwise accelerating frame of reference. Some call it a "fictional force" because when the same motion is solved in the frame of the "outside world," these forces do not appear.

The branch of mechanics that deals with motion in the abstract, without reference to force or mass.

Equations of Motion and Problem-Solving

Integrating equations of motion

The following three quantities, each a vector. Additional information

• Displacement
• Velocity
• Acceleration

The point where structural damage occurs.

Limit load Rating - (the working load for airframe bearings) can be defined as the maximum radial load which can be applied to a bearing without imparting the subsequent functioning of the bearing in airframe applications. ~ Torrington

• LLF for rotor thrust loads = 4.0.
• LLF for centrifugal loads = 4.0.
• LLF for rotor torque loads = 2.0. For the UniCopter and SynchroLite (CVJ w/ HS), which have large inplane rigidity, I have increased it to 6.0.
• LLF for Intermeshing inter-rotor inplane loading = 4.0. This is my guestimate.
• LLF for inplane rigidity = 6.0. For the UniCopter and SynchroLite (CVJ w/ HS). This is my guestimate.
• LLF for tie-bars = 4.0. MDD says 1.5 for damper loads but I have increased it to 4.0 for the tie-bars. Considering that the tie-bars are carbon composite the LLF might have to be 10.0, but if the unidirectional pultruded thread is wrapped around both ends 4.0 might do.
• LLF for brake torque = 2.0.
• LLF for inverted loads = 2.0. Most of the parts will have already been designed for higher up-loads.

Note that the force is multiplied by the appropriate LLF and the Safety Factor.

Load Factors: The Load Factors should be put on Mechanics page or Flight Dynamics page only.

Lock Number: [γ] [gamma]

A non-dimensional parameter that represents the ratio of the aerodynamic to centrifugal forces on a blade. It varies from 10 for lightly built blades to 2 for tip driven blades. γ = (ρ * a * c * R^4) / Ib.

Reference:- Access FORM: Rotor - Disk & Function: blade_Lock_number()

Mission/Piloting Ratio:

The ratio of the helicopter operator's time devoted to performing the mission compared to the time devoted to flying the craft. Only relates to missions where the purpose of the flight is performed during the actual flying time, such as air filming, not transportation. Does Padfield say anything about this?

Moments:

A force that causes or tries to cause an object to rotate. Moment = Force * Distance

The three moments related to the helicopter are:

• Rolling moment [R] (Padfield uses [L]), about the X-axis. Positive is CW when viewed looking forward (down to right).
• Pitching moment [M], about the Y-axis. Positive is CW when viewing from port to starboard (nose moving up).
• Yawing moment [N], about the Z-axis. Positive is CW when viewed looking down (nose to right).

Mode Shape: [η]

The resultant deflected shape of a rotor at a specific rotational speed to an applied forcing function. A three dimensional presentation of rotor lateral deflection along the shaft axis.

Motions:

Pitch, roll and yaw. Heave, surge and sway

The number of cycles per second ao a system after being struck with a sharp blow.

A means of defining rotor characteristics in a form that are independent of rotor size.

Obliquity: (oblique angle, slant)

The lateral angle (in degrees) between the mast of an intermeshing helicopter and the vertical.

• The Flettner Fl 282 is 12º. The distance between the centers of the hubs is 22.44" (570 mm). The vertical distance between the center of the hubs and the center of gravity is 45.47" (1155 mm)."
• The Kaman Huskie is 12.5º or 13º. I've also seen 26 degrees. Teetering rotors. Horizontal distance between hub centers = 3.667 ft.
• The Kaman K-Max is 12.5º. Teetering rotors.
• The Kellett XR-8 was 12.5º.
• DeGraw - Hummingbird is 26 degrees.
• The SynchroLite is designed at 11º, with CVJ w/ Hub Spring. Distance between hub centers = 25"
• The UniCopter is designed at 9º. Horizontal distance between hub centers = 28.35"

Offset Hinge:

See Flapping Hinge Offset above.

The point at which the axes intersect. Normally the crafts center of gravity.

The origin of the SynchroLite is --- .

The origin of the UniCopter is the mid-point between the centers of the rotor disks. There is an offset from here to the center of gravity.

Parasite Power [HPp]

The power required overcoming the drag of all non-rotor components.

Phase Angle [φ]

The angle between input azimuth and the result's (moment) azimuth.

The phase shift between the control plane and the no-feathering plane.

Phase Lag: (Change in Azimuth) [Γ][Δψ]

The angle between the applied control input and the rotor response. It is 90º for most teetering rotors.

Phase Angle - Inter-Rotor [Δ φ????]

The inter-rotor phase angle is the azimuth angle of the reference rotor when the corresponding reference blade of the other rotor is at 0º azimuth. (i.e. pointing aft). The 2-blade SynchroLite is 90º, the 3-blade Dragonfly is approximately 60º and the 4-blade ARR Unicopter is close to 0º.

A flight control device that is functionally similar to the swashplate and spider, except it is for use with a 3 or 4-blade offset teetering rotor.

Causes the pitch to decrease as the blade cones upward. The preceding sentence is only correct if the rotor has coning hinges, the pitch link is located on the trailing side of the blade and the pitch horn to link connection is located inboard from the coning hinge.

Causes the pitch to automatically decrease as the blade flaps up. Positive for flap up, flap down. Kp = tan(δ3)

There are two basic delta-3 configurations.

• By flap hinge geometry. This method has an in-plane component as well.
• By control system geometry

Pitch-flap coupling introduces a aerodynamic spring that increases the effective natural frequency of the flap motion and terefore the need for a change in phase angle.

Another source of pitch-flap coupling is the mean lag angle [ζ0]due to the rotor torque. [Source ~ HT p.239]

For 2-blade teetering rotor disks, should this be referred to as Pitch-Teeter Coupling? The mean lag angle is not applicable to teetering rotors.

Planes:

See; Axes Systems of Rotor, above.

Polar Moment of Inertia [J]

Port:

The left-hand side when looking forward.

• Power loading is the ratio of thrust produced to the power required to hover. [PLH] Power loading at hover = Rotor thrust / Disk area. PL = T/P ~ Leishman
• [PLM] The ratio found by dividing the maximum weight [GW] of the helicopter by the brake (maximum available) horsepower [P] produced by the engine(s). It appears that for [P], Prouty uses 85% of an engine's rated horsepower. Also it should be noted that this rated horsepower is the derated value from maximum horsepower, as done by the helicopter manufacture.

Power - Ideal: [Pideal]

• The inescapable induced power loss.

Precone: (βideal) (βp) [rotor]

A fixed coning angle that is physically incorporated in the rotor hub. Conventionally, it is a function of the rotor loading and therefore the precone can be selected for a particular design operating condition only.

The drive train, rotor hubs and flight controls are one compact and completely assembled unit. This 'single package' is conceptually similar to the Flettner drive train, rotor hubs and flight controls. The blades, particularly if they have Active Blade Twist, should be considered as part of the principal assembly.

Propulsor:

Device for propelling a craft. The propeller or turbofan that is proposed for future Intermeshing and Interleaving rotorcraft.

• A 'shim' used to thicken the root of the blade so that it fits the rotorhead's grip.

Rotor:

• A mechanical device that provides controlled thrust in an environment of air. Anything else that it 'provides', such as weight and vibration, are in conflict with its sole purpose.
• Includes all associated components; such as the head, blades and flight controls?

Rotor Axes:

xx

Rotor Coefficients:

See: 1099

The complete rotor assembly, excluding the blades. Are associated flight controls included?

Rotor Hub:

The central fabricated component of the rotor head.

Rotor Inertia:

See: 1013

Rotor Rigidity:

The ratio Control Power (def. #2) to the Control Power (def. #2) of a teetering rotor. ~ This is the usage in document [The ABC Helicopter]

Safe Flight Envelope: [SFE]

Manufacture-defined that set the limits to safe flight, normally in terms of the same parameters as the OFE, but representing the physical limits of structural, aerodynamic, powerplant, transmission or flight control capabilities. Sensitivity:

The rate of roll (and pitch?) per inch of stick displacement. See: Control Sensitivity

Safety Factor: [SF]

For rotor thrust loads and centrifugal loads it is * 1.5. MDD has the safety factor for rotor torque loads at * 2.25. Due to the intermeshing configuration, I am taking the SF for the intermeshing configuration up to 3.0, which is on top of if the LLF increase for intermeshing. See also Limit Load Factor above. See also; OTHER: Mechanical - Safety Factor

Sideslip angle: [ß]

The angle that the fuselage makes with the air in the plan view.

Sidewash angle: [η]

The angle of lateral air flow induced by the main rotors and by the fuselage in sideslip.

Slip:

The difference between geometric pitch and effective pitch.

Slowed Rotor:

A slowing of the rotor's rpm during fast forward flight, thereby reducing the compression on the advancing tip and reducing the stalling on the retreating tip.

Smart Materials:

An overview of smart materials

Speed Stability: [B1/V] Longitudinal cyclic pitch [in degrees] / Velocity [in knots]

For a helicopter to be stable with speed, it is required that, with fixed pitch and throttle, the stick be moved farther forward for trim with increased speed.

Value to meet MIL-H-8501 B1/V > 0

Spiral Instability:

Too much area in the fin/rudder, and there is turn without skidding. Centripetal force from the turn negates all the self-righting effects, and we fly in balanced flight, but in an ever-increasing nose-down spiral.

Stabilator: (stabilizer-elevator, also all moving tailplane or all flying tail)

·        An aircraft control surface that combines the functions of an elevator and a horizontal stabilizer.

The tendency of an object to return to its original conditions following a disturbance.

A system of dampening (minimizing) externally induced control movements. Normally, SAS systems use potentiometers that quickly detect the externally induced movement, allowing the system to apply opposite countermovements. This produces a noticeable increase in stability and therefore smoothness.

Stagger: [ds]

The horizontal center-to-center distance between 2 rotor disks. It is applicable to intermeshing, interleaving, side-by-side, tandem and quad helicopters. On the SynchroLite, it is the distance between the teetering hinges. On the Dragonfly, it is the distance between the virtual teetering hinges. On the UniCopter, it is the distance between the centers of each rotor's 'non-coned' feathering axes.

Starboard:

The right-hand side when looking forward.

Static Margin:

The distance between the aerodynamic center and the center of gravity is static margin,. It is the major factor affecting the longitudinal static stability of the aircraft

The characteristics of a helicopter that cause it to try to return toward its trim flight condition following an external disturbance.

Stiffness Number: [Sβ]

The non-dimensional parameter that provides a measure of the ratio of hub stiffness to aerodynamic moment.

Sβ = 8(λβ2 - 1)/ γ | λβ2 is the flap frequency ratio. See also: Phase Lag

The ability to stop the rotation of the rotor(s) on a rotorcraft so that they may function as stationary wings, or hypothetically remove themselves from the aerodynamic activities of the craft. Good description Stopped Rotor Aircraft

Swashplate Phase Angle:

The angular difference between the azimuth of the blade's pitch axis and the azimuth of the control link.

A mechanism functionally similar to the swashplate except that it imparts a higher harmonic control into the cyclic activity.

Definitions: swash ~ to make violent noisy movements, to move about very rapidly; dash to and fro.; swish ~ to (cause to) move quickly through the air making a soft sound.

Alternate definition: Swishring ~ A device used to control the behavior of gay blades.

SynchroLite:

A very lightweight helicopter that utilizes laterally located twin main rotors. The fuselage of the SynchroLite is designed to accept a number of different; rotor configurations, types of rotor-hubs, and powertrain arrangements.

 Tail Rotor: The tail rotor is an impediment to technological advancements in rotorcraft.
• For decades, Western aerodynamic texts have mathematically shown that the tail rotor wastes 8 - 10% of the power. Kamov has stated in an article entitled Aerodynamic Features of Coaxial Configuration Helicopter that "the single-rotor helicopter's tail rotor power consumption accounts for 10-12% of total power."
• Stepniewski in 'A comparative study of Soviet vs. Western Helicopters' says that the tail rotor consumes approximately 11% of the power, during hover.
• The aerodynamic text (year 2000), by Leishman (University of Maryland) supports Kamov's position.
• Therefore, if a craft's gross weight to empty weight is 2:1, a loss of 11% will result in a difference in payload of to 22%.
• Prouty says, "... tail rotor absorbing 10 to 20 percent of the engine power". ~

Tennis Racket Effect (Centrifugal Twisting Moment):

• There is a centrifugal-pitching-couple from the rotation of the rotor tending to force everything into flat pitch.
• This is offset to some degree by 'Chinese weights'.
• (The following is my unqualified statement}- This might impart twist to the blade because the 'Chinese weights' are operating on the blade root whereas the centrifugal force is operating mostly on the blade tip.
• For more see; Aeroelastic Behavior of Twist-coupled HAWT Blades Have hard copy.

The distance from the center of the mast to the teetering hinge.

Changes the characteristics of the rotor from being a system in resonance to one whose natural frequency is higher than the rotational frequency. This results in a Phase Angle that is less than 900. Ref. More on Flapping Hinge Offset

A rotor with two or more blades where the blades and the teetering hinge of their individual yokes are offset from the center of the mast. All the yokes have undersling. Their upper portions are hinged to the rotor head. Their lower portions are interconnected so that all blades teeter in a coordinated fashion.

Thickness: [t] [airfoil]

Maximum airfoil thickness.

Thickness Ratio: [Airfoil]

The ratio of the root thickness of a blade over the tip thickness of the blade. For more information see; the ABC report Forward Flight Performance of a Coaxial Rigid Rotor by V. M. Paglino, May 1971, page 8

Thickness to Chord Ratio: [t/c] [Airfoil]

xxx

Torque: [Q] [rotor]

Torque moment on the rotor. Positive for a rotor absorbing power.

Torque Offset:

Blade/Hub Geometry. To allow the blade centrifugal force to compensate for part of the rotor torque. See 'Even More Helicopter aerodynamics; chapter 32'.

Torsional Flutter:

A self-sustaining torsional vibration of the blade in which the blade pitch varies above and below the acceptable limits at relatively high frequency and in such a way as to decrease the aerodynamic performance of the blade and impose high structural loads on the blade.

The change in the lift of a rotorcraft as it changes between rotor lift to X-wing (stopped rotor) lift.

The additional lift produced by a helicopter rotor as a helicopter changes from hovering to forward flight.

A rotor concept for providing a rotorcraft with forward speeds that are considerable faster than those of current rotorcraft. The proposed means is by deriving lift from the so-called reverse velocity region. However, the blade in this region has rotated approximately 180º about the feathering axis and the airflow passes over the airfoil in a conventional direction.

The ability to maintain flight equilibrium with controls fixed.

Undersling: (teeter hinge height) [Rotor]

• Applies to a teetering rotor head. The intent is to keep the mass of the two blades equidistant from the centerline of the mast as the disk teeters, to reduce the vibration due to the cyclical Coriolis effect.
• The amount of undersling is the vertical dimension between the teetering hinge and the intersection point of this vertical line with the centerline of the feathering axes of the blades.
• On the Offset Teetering Rotor Concept the undersling dimension is the vertical distance between the flapping axis of the blade and the axis of the tie-bar.

A rotorcraft that unifies the attributes of helicopters with those of gyrocopters; and then enhances the craft with advanced features.

Vee Angle: [Λ]

The angle between the two masts on an intermeshing helicopter. Flettner ~ 24º, Kaman Husky ~ 26º, Kaman K-Max ~ 25º, SynchroLite ~ 25º, Dragonfly ~ 22º, UniCopter ~ 18º.

Velocity:

Translational: The speed of an object in a given direction. Velocity is a vector quantity

 Prouty Padfield x{.} u Along the x-axis. y{.} v Along the y-axis. Sideslip z{.} w Aong the z-axis. Heave?

Angular:

A theoretical point that is located inline and midway between the multiple teetering hinges on a teetering rotor head w/ offset.

Vibration:

Vibration is classified into three types:

• Linear Vibration
• Bending Vibration

In order to treat such vibrations quantitatively, the following three parameters are used:

• Displacement (unit: inches)
• Velocity (unit: inches/second)
• Acceleration (unit: inches/second2)

Forced Vibration: The oscillation of a system under the action of a forcing function. Typically, forced vibration occurs at the frequency of the exciting force.

Free Vibration: Vibration of a mechanical system following an initial force-typically at one or more natural frequencies.

Wee-wa: (small washout?)

A term used by Frank Robinson. The following is an assumption of what it means:~ An incident of acceleration cross-coupling. An off-axis tilt that is experienced by the rotor disk as the disk is in the process of on-axis tilting. I.e. during a downward motion of the front of the disk, the angle-of-attack at the front of the disk is increased. This causes the disk on the retreating side to be higher than the height of the advancing side. For more information see R-22 Rotor. Also see 'Rotor Pitch-Roll Decoupling Requirements from a Roll Tracking Maneuver' ~ AHS 50th Annual Forum. Have hard copy.

The pilot moves his body and the frame, which are hanging from a gimbal, side-to-side and forward and back to move the center of gravity in respect to the center of lift. This causes the craft to roll and pitch.

A method developed by Sikorsky to include the 'radial flow effect' when calculating the rotor's lift, drag and torque etc during cruise. It takes into account the fact that the airflow passing the blade has angle that is not parallel to the chord at most azimuths.

Last Revised: January 29, 2013