OTHER: Aerodynamics - Definitions & Algorithms


Flight Dynamics:




CNC Workstation:

Definitions & Algorithms

Definitions & Algorithms

Definitions & Algorithms

Definitions & Algorithms

Definitions & Algorithms

Definitions & Algorithms







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.

Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: C:\Helicopter\Web_Page\Group_B\GreenAndBlackStripe.gif

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

Active Blade Twist: (ABT) [θ1A] [blade & flight control]

In-flight changing of the twist on the blades, to increase thrust, plus reduce vibration and noise.

    1. A pitch control of the root of the blade and twist control along the span of the blade. The pitch at the tip of the blade is the result of these two controls.
    2. A pitch control of the root of the blade and separate pitch control of the tip of the blade.

Advance Ratio: [rotor]

See: Tip Speed Ratio

Advancing Blade Concept (ABC): [rotor]

A coaxial rotor configuration built by Sikorsky where the advancing blades developed more thrust than the retreating blades.

Aerodynamic Center: [blade] [rotor] [craft]

The point about which the resultant lift force acts when the incidence is changed.

Will vary depending on application of cyclic.

The one special point on an airfoil for which it is found that the section moment coefficient [Cm ] is constant (note ~ constant, not zero) and independent of the angle of attack. [Source ~ PHA p.267]

The point along the chord of the airfoil where all the changes in lift effectively take place. If the point about which the moment is taken is properly chosen (the aerodynamic center), the moment coefficient is essentially constant up to maximum lift. The aerodynamic center varies with airfoil thickness, with the exception of the NACA 00xx series. See graphs for various airfoils. [Source ~ TWS p.182] It is not affected by the camber nor angle of attack. It is located between the 23% and 27% of chord length.

It has been estimated that moving the aerodynamic center back 2% on the chord can result in a 10% saving in total blade weight. [Source ~ RWP1 p.421]



AC position: %chordwise x/c

AC position: %spanwise y/c

AC position: %thickness z/c


NACA 0009





NACA 0012



0 Assumed











Aerodynamic Forces:

Aerodynamic Precession: [rotor]

The act of the rotor disk flying to position.

The characteristic that causes the rotor disk to react to an aerodynamically applied force at a location that is approximately 90-degress away from the location of application, in the direction of its rotation.

Aerodynamically Variable Disk Area:

The <= 50% reduction in the effective aerodynamic disk area during forward flight from that during hovering flight. This is achieved by combining of two rotors, which are aerodynamically independent during vertical flight (side-by-side or fore-aft configurations), into a counterrotating propeller set during forward flight.


The dynamics of bodies moving relative to gases, especially the interaction of moving objects with the atmosphere.

Angle of Attack: [α]

Relative Angle of Attack (geometric angle of attack):

Aligned with the chord line of the blade.

Absolute Angle of Attack:

The zero angle of attack corresponds to zero coefficient of lift. According to the standard terminology, the angle measured in this way is called the absolute angle of attack.

See Angle of Incidence, below.

Angle of Incidence: [α]

Angle of incidence is the angle between the blade chord line and the plane of rotation of the rotor system. See: Angle of Incidence ~ by Paul Cantrell. On an airplane it is the acute angle formed between the chord line of the airfoil and the longitudinal axis of the craft on which it is mounted.

Other applications of incidence;

The angle formed by the mast centerline and a line that is perpendicular to the helicopter's body X-axis. iM The body axis system is used on this web site therefore there is no angle of incidence for the mast.

The angle formed by the blade's chord line and the tip path plane. iM

The angle between the horizontal stabilizer's chord line and the and the helicopter's body X-axis. iH

Angle of Zero lift: [αL=0] [airfoil]

........depends on the camber of the airfoil.

See Theory of Wing Sections, p 128

Angular Momentum:

See: Mechanical - Definitions & Algorithms


A downward slope or bending of the rotor blade, or blade tip. Opposite to dihedral.

More: DESIGN: UniCopter ~ Rotor - Disk - Anhedral along Blade Span

More: DESIGN: SynchroLite ~ Rotor - Blade - Composite - VR-7b - Anhedral (drooped tip)

Aspect Ratio: [AR]

The ratio of the blades length to its chord. Aspect ratio = R/c


Descent of a helicopter without engine power applied to its rotor. An aerodynamic force causes the rotor to spin.

See: OTHER: Aerodynamic - General - Autorotation

See: DESIGN: Electrotor-SloMo ~ Rotor Disk

See: DESIGN: UniCopter ~ Rotor Disk - Autorotation

See: DESIGN: SynchroLite ~ Rotor Disk - Autorotation

Blade Angle: [propeller]

The angle formed between the propeller's plane of rotation and the chord line of its airfoil section. It is expressed in degrees. Measured at 75% of the blade's radius.

Blade Area: [Ab] [blade]

The sum of the area of all the blades on the helicopter.

Blade Element Theory:

It involves breaking a blade down into several small parts then determining the forces on each of these small blade elements. These forces are then integrated along the entire blade and over one rotor revolution in order to obtain the forces and moments produced by the entire propeller or rotor.

Blade Loading: [BL] [craft]

Blade Loading Coefficient: [CT] [rotor]

The coefficient of thrust divided by the solidity.

Blade Vortex Interaction:

The perturbation on a blade caused by its passage through the vortices of a previous blade.

Blended Wing Body:

An alternative airframe design, which incorporates design features from both a traditional fuselage and wing design and the flying wing design. The purported advantages of the BWB approach are efficient high-lift wings and a wide airfoil-shaped body. This enables the entire craft to contribute to lift generation with the result of potentially increased fuel economy.

Camber: [airfoil]

Camberline (mean camber line): [airfoil]

A line drawn through a series of points, each of which is located midway between the upper and the lower camber.

Center of ....

Blade: [airfoil]

See: Center of Pressure below.

See DESIGN: SynchroLite ~ Rotor - Blade - Composite - VR-7b - Centers, Radii & Moments

Disk: [rotor]

See DESIGN: SynchroLite ~ Rotor - Disk - Center, Radii & Moments

Helicopter: [craft]

Aerodynamic Center: Center of Parasitic 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 .

Center of Pressure: [xcp] [airfoil]

The chordwise distance between the point of application of the normal force and the ac. xcp being positive when measured ahead of the ac and negative, aft.

The center of pressure moves to different locations on the chord with changes in the angle of attack.

Also see Aerodynamic Center (AC) above on this page.

Related Notes:

·        Helicopter Theory ~ Wayne Johnson (1980) ~ ‘Aerodynamic Center’ is mentioned to 19 times. ‘Center of Pressure’ mentioned once; at the top of page 920 and it appears to be limited to the subject of ‘noise’.

·        Rotary-Wing Aerodynamics, in Chapter VI, Airfoils for Rotary-Wing Aircraft ~ Stepniewski and Keys (1984) ~ ‘Aerodynamic Center’ is not mentioned. ‘Center of Pressure’ is discussed at length.

·        Helicopter Performance, Stability, and Control ~ Prouty (1995) ~ ‘Aerodynamic Center’ has a small section on page 420. ‘Center of Pressure’ is not mentioned.

·        Principles of Helicopter Aerodynamics ~ Leishman (2000) ~ ‘Aerodynamic Center’ is section 7.7.1. ‘Center of Pressure’ is section 7,7,2.  


Addition information: Center of Pressure or Aerodynamic Center? ~ by Prouty, Vertiflite2002 Directory p.28.

Centrifugal Force: [rotor]

See: Mechanical - Definitions & Algorithms

Centripetal Force: [rotor]

See: Mechanical - Definitions & Algorithms

Chord (chordline): [c] [airfoil]

An imaginary straight line drawn through an airfoil from its leading edge to its trailing edge. It connects the extremities of the leading and trailing edges.

Chord-axes System:










Center of hub


Positive toward tip




Leading edge


Positive toward trailing edge






Positive upward

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] This appears to differ from Theory of Wing Sections.

Circulation: [blade]

The strength of the bound and trailing vortices. Its value is proportional to the lift of the blade divided by the forward speed. This and more; [Source ~ RWP4 p.33]

Circulation Control: [blade]

Schemes to improve the lift of a blade.

See: OTHER: Aerodynamics - General

Centripetal Force and Centrifugal Force:

See: Mechanical - Definitions & Algorithms

Chord: [c] [airfoil]

An imaginary line drawn through an airfoil from its leading edge to its trailing edge.

Coaxial Rotors: [rotor]

Coaxial rotors of a helicopter are mounted on concentric shafts in such a way so that they may turn in opposite directions to cancel torque.

Coefficient of Drag: [cd] [airfoil]

A dimensionless number used in the formula for finding the induced drag of an airfoil as it relates to the angle of attack.

Drag coefficients are almost always determined experimentally using a wind tunnel.

Coefficient of Lift: [cl] [airfoil]

A dimensionless number relating the amount of aerodynamic lift produced by an airfoil to its angle of attack.

Coefficient of Moment: [cm] [airfoil]

Pitching Moment Coefficient. 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.

Coefficient of Rotor Lift: [cT']

[Source ~ RWA II p.104]

See: OTHER: Dynamics - General - Rotor Coefficients

What should be used to determine the intermeshing rotor's solidity ratio?


Coefficient Equations:

'The following 6 are valid equations for fixed wing aircraft. Some of these

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 coefficient.

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


Coefficient of Thrust [CT] & [Ct]; [rotor]

Coefficient of thrust is nondimensional. It is the thrust (equal to weight at low speed) divided by the rotor disk area, the air density, and the square of the tip speed.

See: OTHER: Dynamics - General - Rotor Coefficients

Coefficient of Torque [CQ] & [Cq]; [rotor]

See: OTHER: Dynamics - General - Rotor Coefficients

Coefficient of Power [CP] & [Cp]; [rotor]

See: OTHER: Dynamics - General - Rotor Coefficients

Compound Configuration:

A compound helicopter includes all of the elements of a helicopter, plus a wing.


Rotor configurations: Single, Coaxial, Intermeshing, Interleaving, Side-by-side, Tandem, Compound etc.

See: OTHER: Aerodynamic - Rotor Disk - Dual Configuration

The single, the compound, the tandem and the coaxial soon to become relegated to history as lateral twin main rotors reclaim the preeminent position that they once held. Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: C:\Helicopter\Web_Page\Group_B\Wink.gif

Constant of Proportionality: [k]

The constant of proportionality varies with blade twist, for varying the twist shifts the loading inboard or outboard on the blade. From a series of power-required calculations the constant k is given by; k = 3.17 - 2.70 * θT , where θT = total twist [in radians], usually negative.

Critical Mach Number: [Mcr] [rotor]


Cutout Ratio: [rotor]

The distance from the center of the mast to the blade root divided by the rotor radius. xo / R

Damping: [c]

The resisting moment per unit angular velocity of the helicopter.

Density of air: [ρ] [rho]

At sea-level standard conditions ρ = 0.002377 slugs per cubic foot

Differential Collective:

The means of providing yaw on coaxial and most intermeshing helicopters. Yaw is achieved by increasing the thrust and drag on one rotor while decreasing the thrust and drag on the other. The net thrust will not change but the torque of the two rotors will no longer be equal. The higher torque of one rotor will rotate the craft in the opposite direction.

Dihedral: [ ]

The positive angle formed between the lateral axis of a helicopter and the blades which are flapping up on the side which is leading the sideslip. Dihedral is used to increase the lateral stability of an aircraft. The opposite is anhedral.

Re: Horizontal Stabilizer: Sweeping a wing back also gives a dihedral effect, with about 5 degrees of sweep being equivalent to 1 degree of dihedral.

Calculation of Equivalent Dihedral Angle: http://www.rc-soar.com/tech/spiral_eda.htm

More: DESIGN: UniCopter ~ Rotor - Disk - Dihedral at Blade Tip ~ Bladelet Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: C:\Helicopter\Web_Page\Group_B\smile.gif

Disk Area: [A] ~ Single rotor [AONE], Multiple rotors [ASYS]; [rotor]

Disk Loading: [DL] [w] [rotor]

  1. The ratio of the gross weight to the system (effective) disk area.. DL = GW/ASYS
  2. The ratio of the rotor thrust to the system (effective) disk area. DL = T/ASYS

The simple concept of disk loading has served as a quick tool to evaluate aerodynamically independent rotors. However, this concept has two major flaws. One is that it assumes that the disk loading is equitably distributed about the disk. The other is that it does not take into account aerodynamic interactions with other items such as another rotor or the fuselage etc.

The up-and-coming rotorcraft will have multiple main-rotors. These rotors will aerodynamically interact. In addition, they will incorporate features such as; Slowed Rotors, Advancing Blade Concept, Reverse Velocity Utilization and Higher Harmonic Control. When all of the above is considered during hover flight, and then totally reconsidered during cruise flight, the concept of disk loading is no longer 'simple'.

Consideration regarding ABC (the 'unloading' of the retreating blades) and slow speed rotor. See; DESIGN: UniCopter ~ Rotor - Disk - Large Chord & Low Tip Speed ~ Disk Loading

Dissymmetry of Lift: [rotor]

The unequal lift across the rotor disc resulting from the difference in the velocity of air over the advancing blade half and retreating blade half of the rotor disc area.

Downdraft: [rotor]

In an intermeshing configuration, the upper blades will pass through the downdrafts created by the lower blades.

Downwash: [rotor]

Air forced down by aerodynamic action below and behind the rotor of a helicopter. The body of the craft may be subjected to this downwash. In an intermeshing configuration, the lower blades will pass through the downwashes created by the upper blades. . The body of the intermeshing configuration may be subjected to the downwashes from both rotors.

Downwash Angle: [ε]

The angle formed between the direction of air movement as it approaches an airfoil and its direction as it leaves.

Drag: [D] [blade][rotor] [craft]

Drag Divergence Mach Number: [Mdd]

The value of the free stream Mack number at which the drag coefficient increases significantly. [Source ~ PHA p.284]

For helicopters ~ The Mach number at which the drag coefficient is twice its incompressible value. [Source ~ PRW1 p.409]

Dutch Roll:

See: More on Dutch Roll

Dynamic Inflow:

Induced velocity delay [Source ~ RWP4 ch. 27]

Dynamic Pressure: [q]

The pressure a moving fluid would have if it were stopped [pounds / square foot] q = (ρ / 2) * V2 [density divided by two, then times the square of the velocity].

Dynamic Pressure Ratio:

In rotor wake: q/ DL. This will be radically more complex for intermeshing rotors.

Dynamic Stall:

Retreating blade stall.

Efflux: [E]

The discharge of exhaust and cooling gases.

Element: [blade]

The span of the blade is divided into approximately 10 to 15 segments for aerodynamic computations and an element is one of these segments. See Station:

Equivalent Chord: [ce] [airfoil]

The singe average chord, which would yield the thrust of the actual planform. [Ref. ~ AH p.86]

For a linear tapered blade, it is the chord at 0.75 Radius.

Equivalent Drag: [De]

De = D + SHP * 550 / V [D in lbs, V in fps]

Equivalent Flat Plate Area: [f] [craft]

The area of a hypothetical flat surface perpendicular to the direction of motion of the body that produces the same opposition to the airflow as the streamlined body. f = D / q [ft2]. f = Σ CD * frontal area [ft2]. This hypothetical flat surface has a drag coefficient of 1 and this should not be confused with Flat Plate Area.

Equivalent Lift to Drag Ratio: [L / De]

A means of evaluating the overall efficiency of a vehicle in horizontal translation. [Source ~ RWA, Book I, p.135]

W/De = (W * V) / (550 * SHP) [D in lbs, V in fps]

Equivalent Solidity: [σe]

Accounts for the major effects in varying the chord.

F-force: [F]

The sideward-pointing component of rotor force, perpendicular to the control axis. [Source ~ AH p.183] Is this the same as Y-force?


The action which changes the pitch angle of helicopter rotor blades by rotating them about their feathering axis.

Fineness Ratio:

The ratio of length to breadth of a streamlined shape , is called the fineness ratio of a streamlined body. For best results it should be about 4 to 1 (NACA 0025}, but it really depends on the air speed; the higher the speed, the greater should be the fineness ratio, but experiments show that there is not much variation in the drag for quite a large range of fineness ratios.

Flapback, Blow Back, Back Flap: [rotor]

In forward flight, the rotor disk has a natural tendency to tilt back (longitudinally) because of the dissymmetry of lift that would be produced if the advancing blade was not allowed to reduce its angle of attack and the retreating blade increase its angle of attack.

OTHER: Aerodynamic - General - Flapback

Flapping: [rotor]

The vertical movement of a rotor blade about its delta, or flapping, hinge.

Longitudinal: See Flapback.

Lateral: This effect arises because of coning. Note that in a hypothetical case with no coning (UniCopter - Absolutely Rigid Rotor), the blade sees the same increase in angle of attack at ψ = 0º and 180º and there will be no lateral tilt.

Flapping to Equality:

The flapping or teetering of the rotor's blades so as to overcome any dissymitry of lift between two sides of a disk.

Flat Plate Area: [A]

The area of a flat plat placed normal to the air stream.

Flying Wing:

A flying wing is a fixed-wing aircraft, which has no definite fuselage, with most of the crew, payload and equipment being housed inside the main wing structure.

Fountain Effect:

Geometric Pitch: (Propeller Pitch)

The distance that a propeller will move forward in one revolution. This is based on the propeller blade angle at 75% blade station. It is theoretical in that it does not take into account any losses due to inefficiency.

Gimbaled (Gimballed) Rotor:

Basically the gimbaled rotor is the multi-blade counterpart of the teetering rotor.

Ground Effect: (Ground Cushion)

"The [ground] effect has long been recognized but the aerodynamics are still not fully understood." ~ Leishman

  1. An increase in the lift of a helicopter flying very near the ground. This additional lift is caused by an effective increase in the angle of attack without an accompanying increase in induced drag.
  2. The ground reduces the vortices coming off the rotor blade tips, reducing induced drag.
  3. A ground effect cushion that provides a significant up-load on the airframe.
  4. It is the result of the resistance of the mass of air, located between the rotor disk and the ground, having to change its momentum from vertical to horizontal. It is not due to the compression of the air, since the velocity of the air is not supersonic.

For additional information see; [Source ~ RWA Book II, p.44]. Outside web page: Ground Effect

Gurney Flap:

An aerodynamic 'dam' on the trailing edges of helicopter stabilizing surfaces

Part 1 by Prouty: http://www.avtoday.com/reports/rotorwing/previous/0200/02rwaero.htm

Part 2 by Prouty: http://www.avtoday.com/reports/rotorwing/previous/0300/03rwaero.htm

Gust: (wind)

A temporary increase in the speed of the wind. A gust lasts for a very short period of time, and it is usually followed by a wing whose speed is lower than normal.

H-force: [H]

The rearward-pointing component of rotor force, perpendicular to the control axis. [Source ~ AH p.183]

Higher Harmonic Control: (HHC)

An oscillatory modulation is superimposed on the basic pitch control of the swashplate. (The swashplate is comprised of two parallel plates, providing the means by which collective and cyclic pitch of the blades is achieved [Seddon, 1990].) Thus, all the blades are affected equally despite inherent differences in (the time dependent inputs to) each blade. This is unrelated to Active Blade Twist.


A lot of hot air. It's good for giving lift to balloons but not for helicopters. Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: C:\Helicopter\Web_Page\Group_B\Bullshit.gif

Ideal (hyperbolic) Twist:

·        Will theoretically give uniform inflow distribution along the span of the blade, with constant chord blades. θ = θTIP (R /r): [Source ~ AH p.57].  This is probably fairly accurate for a propeller because all locations on disk area of the propeller are experiencing a fast and equal free stream air velocity.

·        The expression for the coefficient for power, for an ideally twisted rotor turns out to be identical to that for a linearly twisted rotor. Georgia Tech. This may be more appropriate for rotors, particularly when they are in Climb.


Angle of attack. See: Angle_of_Incidence

Independent Root & Tip: (IRAT) [blade & flight control]

A project to improve the L/D ratio and Figure of Merit of rotors; by providing a much greater rate and amplitude of pitch change than that of current active blade twist methods;

Individual Blade Control: (IBC) [rotor]

A method by which the pitch of each blade is controlled individually. This is unrelated to Active Blade Twist.

Induced Power: [Hpind]

·        The power required overcoming the drag produced by an airfoil when it is producing lift. I assume that the drag is only Induced drag and does not include the Profile drag.

·        http://www.math.usu.edu/powell/ornlab-html/node7.html

·        http://www.pprune.org/rotorheads/19951-rotor-profile-power-induced-power.html

·        Helicopter Rotor Lift Distributions for Minimum Induced Power Loss

·        See section 2.9 in the 1st version of ‘Principles of Helicopter Aerodynamics’ ~ Lleishman.

Induced Power Factor: Power Correction Factor, see below. [Κ]

·        An increase in the required power above that of 1 for the actuator disk. .

Induced Velocity: [v]

The downward air velocity generated in the process of developing rotor thrust.

NACA Report ~ 1954 ~ #1184 Have hard copy.

Inflow Angle [φ] [rotor]

Defined by the two mutually perpendicular velocities. φ=v1/Ωr

Inflow Ratio: [λ] [rotor]

Dimensionless velocity normal to the reference plane; λ = (V * sin(α) + v) / ΩR = μ * tan(α) + λi

For small disk inclination; λ = μ * α + λi

Interference-induced Power Factor: [κint] [rotor]

For Coaxial Rotors. [See ~ PHA p.69]

For coaxial rotors in close proximity, the value is 2 = 1.41

For coaxial rotors with the lower one in far-field wake, the value is 1.28. Note ~ My calculations, using Prouty's blade element theory, of a two 2-blade rotors vs. one 4-blade rotor gave a 28% increase in power for the 4-blade rotor. Is this coincidental? ~~~ See Figure 3.14 in RWA. ~ Then see Figure 26 in Stepnieski's ABC Synchropter. ~ Then see notes in HT, middle of p. 119. ~ re source of 0.56 value.

See; Required Power Comparison. Also a coaxial helicopter will have a total of six blades. [See ~ PHA p.71]

I think that this is similar to the Overlap Interference Factor: [kOV] (Induced Power Overlap Correction Factor) for tandem and side-by-side rotors.

Interleaving Rotors: [rotor]

Two rotor disks which are located in the same horizontal plane and where the stagger is greater than the radius of the disk, but less the diameter of the disk. Examples; Landgraf H-4 and Mil Mi-12 (Homer). Active Blade Twist is an essential prerequisite for this configuration.

Intermeshing Rotors: [rotor]

Two rotor disks which are located in different planes and where the stagger is less than the radius of the disk.

International Standard Atmosphere [ISA]:

Sea level: Temperature 59 deg F or 15 deg. C; Pressure 2116.7 lb/ft^2, Density 0.002378 slug/ft^3

Laminar Flow:


Lateral Displacement: [B1's ] or [B'1s ] [rotor] (Sikorsky ABC)

Leading Edge: [airfoil]

The edge of a blade that reaches a point in space ahead of the rest of the blade. An exception to this is root end of a retreating blade, which is in the reverse velocity region.

Lift [L]: [airfoil]

An aerodynamic force caused by air flowing over a blade element. Normal to the resultant velocity at this element.


The vertical component of a rotor's thrust vector. The horizontal component being Propulsive Force.

For an airplane wing: LW = (ρ / 2) * V2 * S * CL . Where S is the area of the wing in ft2 and V is the forward velocity in fps, knots, mph, furlongs/eon????

Lift Overshoot:

See; Vertiflite, Winter 2001 ~ 'Dynamic Lift', p. 30, by Prouty.

Adaptive Airfoil Dynamic Stall Control

Lift-Curve Slope: [a] [airfoil]

The ratio of change in lift coefficient to change in angle of attack.

Lift-to-Drag Ratio ~ Airfoil: [cl/cd] [airfoil]

"To obtain the best hover performance, the airfoil should be flown at the angle of attack that gives the highest lift-to-drag ratio." [Source ~ RWP5 p.23]

"... suggests that the emphasis in airfoil design should be for good L/D, while the maximum lift coefficient performance is less important" ~ Airfoil Design and Rotorcraft Performance Excellent paper. Have hard copy.

Outside web page on Lift and Drag Curves

Lift / Drag Ratio ~ Airfoil ???: [cl3/2/cd] [airfoil]. What is the proper name for this one and where did I see this mathematical expression?

A measurement of the efficiency of an airfoil section. [Source ~ XXX p.xx]

Lift-to-Drag Ratio ~ Rotor: [cL/cD] [rotor]

For proposed methods of improving L/D click on title.

Lifting Body:

Mean Aerodynamic Chord: [MAC] [airfoil]

The imaginary straight line joining the trailing edge and the center of curvature of the leading edge of the cross-section of an airfoil.

Mean Camber (Mean-line): [airfoil]

A line that is drawn between the upper and lower camber of an airfoil section.

Mean-line Form:

The form of the mean line determines almost independently some of the most important aerodynamic properties of the airfoil section. E.g. the angle of zero lift and the pitch moment characteristics.

Mean Thrust (Mean Rotor Loading):

The amount of rotor thrust that the undersling in a teetering rotor is optimized for. Will it be above or below the GW?

Momentum Theory: [rotor]

Allow one to derive a first-order prediction of the rotor thrust and power.

Non-uniform Inflow: [rotor]

See; [HT, section 13-2]

Operational Flight Envelope (OFE):

The limits to the operational capability. The combination of airspeed, altitude, rate of climb/descent, sideslip, turn rate load factor and other limiting parameters that bound the vehicle dynamics, required to fulfill the user's function.

Opposed (Differential) Lateral Cyclic: (Lateral Displacement ~ Sikorsky ABC)

The application of left cyclic to the CCW rotating rotor and right cyclic to the CW rotating rotor in a helicopter with two laterally disposed main rotor, during horizontal flight. For additional information see; DESIGN: SynchroLite ~ Rotor - Disk - Opposed (Differential) Lateral Cyclic Same as above ~ Lateral Displacement

Oswald's Efficiency Factor: [e]

Derived from: Tip speed ratio [μ], Blade twist [θ1], Angle of attack in tip path plane [αTPP] and Coefficient of thrust over Solidity of rotor (CT/σ). ~~ Maybe e = L^2 /Sum {A^2}

Overlap: [ov] [rotor]

A value between 0 (no overlap and 1 (total overlap). It is a linear consideration and does not equate with the 2-dimentional change in disk area.

Overlap Interference Factor: [κOV] [rotor]

A multi-rotor interference factor. This factor is calculated as the ratio of the induced power required for a multi-rotor system relative to the induced power of a system of an equal number of isolated single rotors, when operating at the same disk loading. See the appendix of Dual Rotor Interference, [PHA, p.71] and [RWA Book 2, p.188]

I think that this is similar to the Interference-induced Power Factor: [κint] for coaxial rotors.

Overlap Ratio: [m']

The percentage of the overlapped area to that of the total area of the two rotor disks. See the appendix of Dual Rotor Interference.


[rotor] The term P-factor is defined to mean ``asymmetric disk loading''. It is an extremely significant effect for helicopters. When the helicopter is in forward flight, the blade on one side has a much higher airspeed than the other. If you tried to fly the blades at constant angle of attack, the advancing blade would produce quite a bit more lift than the retreating blade.

[propeller] Asymmetric loading is caused by the resultant velocity of the propeller in its plane of rotation and the velocity of the air through the propeller disc. With the airplane at positive angles of attack the right, or down swinging blade has a higher velocity than the left, or up swinging blade. Since the propeller blades are in themselves airfoils increased velocity results in increased lift, and the increased lift on the right blade tends to yaw the airplane to the left. | Asymetric propeller loading, P factor (Animation)


See: More on Phugoid

Pitch: [θ] [blade (rotor)]

Pitch angle [θ] = Angle of attack [α] + Inflow angle [φ].

Pitch: [propeller]

The forward distance theoretically traveled by a propeller in one revolution. Measured at 75% of the blade's radius.

Geometric Pitch is the theoretical distance a propeller would advance in one revolution.

Effective Pitch is the actual distance a propeller advances in one revolution in the air.

Absolute Pitch: ??

Pitch-Diameter Ratio: [propeller]

The relation between the propeller pitch and diameter expressed as a mathematical proportion, as 1.5 to 1, and so on.

Pitch Distribution: [propeller]

The twist in a propeller blade along its length.


A pitching motion is a periodic variation of the angle of attack.

Pitching Moment:

See; Coefficient of Moment:


A plunging oscillation is a periodic translation of the airfoil in a direction normal to the free stream.

Power Correction Factor:

·        The ratio of the actual induced power to the ideal induced power.

·        Two correction factors are particularly important because they are commonly used to correct test day data and provide the basis for estimates of climb and descent performance. These are KP (power correction factor) and KW (weight correction factor). The determination of these factors requires considerable planning and dedicated flight time. Power correction factor flights require the aircraft be flown through altitude bands (as in the paragraphs above) with incrementally higher and lower power settings above and below that required for level flight. Gross weight should be held nearly constant and therefore frequent ballasting is required. A range of altitudes are flown and the recommended climb airspeed for each altitude is maintained. After this array of data are plotted, normally a family of curves (or if you are lucky, straight lines) will result, thus providing the relationship between power increments and change in rate of climb. A typical power correction factor relationship is shown in Figure 8.15

o   See: Power Correction Factor – Section and Figure 8.15

·        Also see ‘Induced Power Factor' above.

Profile Power [HPOH]

The power required overcoming the air friction drag of the individual blade elements.

PropRotor (tilt rotor): [rotor]

Propulsive Force:

The horizontal component of a rotor's thrust vector. ~&~ The horizontal component of a propeller's thrust. Lift being the vertical component of both thrusts.

Pull: [rotor]

The horizontal component of a rotor's thrust vector. It is opposed by profile drag; and perhaps the H-force drag.

Push: [thruster]

The horizontal force of a pusher device, such as a propeller. It is opposed by profile drag; and perhaps the H-force drag.

Radial Flow Effect:

See Swirl

Reverse Velocity (Flow) Region: [rotor]

The area on the retreating side of a rotor disk abutting the center of rotation where the speed of flight exceed the velocity of the blade. The diameter of this region = μ * R

Reverse Velocity Rotor:

A rotor that is designed to operate at high cruise velocities where a portion or all of the retreating blade near azimuth 270º is immersed in reverse airflow.

Reverse Velocity Utilization: (RVU) (Reverse Velocity Rotor), [rotor]

To causes the portion of a retreating blade, which at high forward velocities is experiencing an airflow from the so called 'trailing edge' to the 'leading edge', to have a negative pitch, so that this reverse airflow will create lift.

Reynolds Number: [Re] [RN] [airfoil]

Reynolds number = chord (ft) x speed (mph) x 9360. Re = c x MPH x 9360

Root Cutout: [x0]

The blade root cutout. Expressed as a fraction of the disk's radius.

See also; DESIGN: UniCopter ~ Rotor - Blade - General - Root Cutout

Rotor Axes:


Rotor Coefficients:

See: OTHER: Dynamics - General - Rotor Coefficients

Rotor Configurations - Twin Rotors:

See: OTHER: Aerodynamic - Rotor Disk - Dual Configuration

Side-by-Side Rotors:

Two rotor disks which are located in the same horizontal plane and where the stagger is greater than the diameter of the disk.

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.

Slant-line Distance: [dR]

The diagonal distance between rotors. (dR = root(g^2 + ds^2) )


The strong flow of air moved rearward by a propeller.

Slope of Lift Curve: [a] [blade]

See Lift-Curve Slope above

Solidity Ratio: [σ] [sigma]

The solidity represents the ratio of the lifting area of the blades to the area of the rotor(s).

Solidity is the total area of the blades divided by the area of the rotor disk(s).

Span Efficiency Factor: [δ] [delta] Oswald Efficiency Factor??

See [Source ~ RWP1 figure 8.17]

The span efficiency factor, e, does not include the viscous drag terms. It is the ratio of the induced drag of an elliptically-loaded wing of span, bref, to the induced drag of the lifting system under consideration when both have the same total lift.


A single piece horizontal tail surface, which serves the purpose of both horizontal stabilizer and elevator.


Fixed horizontal tail surface.

Stall: [airfoil]

Stall Development Time: ?? [c/V]

The approximate time it takes for a particle of air to travel from the leading edge to the trailing edge of the airfoil. [Source ~ RWA II p.108]

Station: [blade]

A point on the span of the blade. See Element:

States of Flow:

Five States of Flow through Rotor

Streamline Flow:

The flow of a fluid in which there is no turbulence. All particles of the fluid move in continuous smooth lines.

Sub-Wing Tip: [Rotor]

A small secondary airfoil attached to the tip of the rotor blade. The sub-wing generates a secondary vortex, slightly offset from the primary one. Interference between the two vortices tends to defuse both very rapidly,mitigating the outcome of blade-vortex interaction.

Supercritical Airfoil:

An airfoil designed to delay the onset of wave drag in the transonic speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered (curved) aft section, and greater leading edge radius as compared to traditional airfoil shapes. The Supercritical airfoil shape is incorporated into the design of a supercritical wing.

Sweep Angle: [Λ]

The sweep angle is the angle at which the aircraft's wings are angled back from the position of perpendicular to the fuselage. A sweep angle of zero corresponds to wings oriented straight out from the fuselage. Actually, the sweep angle is (usually) measured along a theoretical line at 25% of the chord of the wing.

Swirl: (Wake swirl) (Slipstream rotation) (Radial Flow Effect) [rotor][propeller]

A small swirl component of the velocity in the rotor wake, induced by the spinning rotor and propeller.

OTHER: Aerodynamics - General - Swirl (slipstream rotation)


A tab can be used on portions of the trailing edge of an airfoil to help negate pitching moment. [See ~ PHA p.272]

Tandem Rotors:

Two rotor disks which are separated by both stagger and gap.

Taper Ratio: [blade]

The ratio of the blade's root chord to the tip chord.

For more see: DESIGN: UniCopter ~ Rotor - Blade - General - Taper

Teetering Hinge:

Used at the center of a semi-rigid, 2-bladed, articulated rotors. This hub operates on the principle of a universal joint. The teetering hinge constitutes one of the axes of the universal's X-yoke and the feathering hinges constitutes the other axis. I think.

See: OTHER: Aerodynamic - General - Semi-Rigid

Thickness Form:

The thickness form is of particular importance from a structural standpoint.

Thickness Noise:

Blade slap, which occurs at high advancing tip speeds.

Thickness Noise of Helicopter Rotors At High Tip Speeds Have hard copy.

Thrust: [T] [rotor]

Aerodynamic force created by a rotor disk. The thrust line (thrust vector) is usually normal to the rotor disk (tip path plane).

T = 2 * ρ * V2 * A, [in pounds]. Thrust can be resolved into 'Lift' and 'Pull'.

Thrust Weighted Solidity: [σT]

Equivalent Thrust Weighted Solidity: [σe]

The aerodynamic biasing toward the tip, if the blade is tapered. [Ref. ~ AH p.86; PHA p.110: RWP1 p.17]

For a linearly tapered blade, the effective chord [ce] is the chord at 0.75 of radius [0.75*R]: σT = (b * ce ) / (π * R)

Ref: FORM: Blade Taper & Function tapered_blade ()

See also: OTHER: Aerodynamics - General - Coefficient of Blade Loading [CT/σ]

Tip Brake: [rotor]

Control in yaw achieved by means of rotor blade tip-mounted air (drag) brakes. Movable tip brakes are located at the tips of all blades on both rotors. They provide, by their deflection, positive directional control in all conditions of flight by creating an unequal torque distribution in the rotor system. A left turning moment results from starboard rotor tip brake deflection while a right turning moment results from starboard rotor tip brake deflection. In the neutral condition, both sets of tip brakes are undeflected. For more information and pictures see; Gyrodyne

Tip Loss Factor: [B] [rotor]

·        Used to take into account that the blade has drag but no lift at its tip. From about 0.95 to 0.98.

·        An increased number of blades results in a lower tip loss factor.

·        B=1-(ct/2R); B=1-√(2CT)/b; B=0.97 ~ Is this 0.97 for the SynchroLite?

Tip Speed: [ΩR] [OmegaR] [blade]

The speed of the blade tip [ft/sec]. Rotational speed of rotor [Ω] [rads/sec] times Rotor radius [R] [ft].

Tip Speed Ratio (Advance Ratio): [μ] [mu] [rotor]

The relationship between forward speed and rotor's tip speed. Ref: FORM: Tangential Velocity

Dimensionless velocity parallel to the reference plane; μ = (Vfwd * cos(α)) / ΩR.

For small disk inclination; μ = Vfwd / ΩR

Tip Weight: [blade]

The weight that is located in the tip of each main rotor blade. Increasing the weight will delay the rotor decay at the start of autorotation, provide more energy for the autorotative flare and cause responses to cyclic input to be a little 'softer'. In addition, it will also reduce overall vibration slightly because the coning angle will be smaller. It increases the centrifugal loading on the rotor components.

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'.

Trailing Edge Angle: [τ] [airfoil]

Included angle between the tangents to the upper and lower surfaces at the trailing edge of the airfoil.

Transverse Flow Effect: (Inflow Roll) (Rotor Upwash) [rotor]

See; http://www.copters.com/aero/transverse.html , [See ~ RWP3 p.28] , [See ~ RWP4 p.34]


In forward flight, air passing through the rear portion of the rotor disc has a higher downwash velocity than air passing through the forward portion (nonuniform induced velocity). This is because the air passing through the rear portion has been accelerated for a longer period of time than the air passing through the forward portion. This increased downwash velocity at the rear of the disc decreases the angle of attack and blade lift, hence in combination with gyroscopic aerodynamic precession, causes the rotor disc to tilt to the right (the advancing side). The lift on the forward part of the rotor disc is greater than on the rearward part. According to the principle of gyroscopic aerodynamic precession, maximum deflection of the rotor blades occurs 90° later in the direction of rotation. This means that the rotor blades will reach maximum upward deflection on the left side and maximum downward deflection on the right side. This transverse flow effect is responsible for the major portion of the lateral cyclic stick control required to trim the helicopter at low speed.

More: http://www.dynamicflight.com/aerodynamics/transverse_flow_eff/

Transverse flow effect is greatest between 10 and 20 knots thus greatest vibration due to unequal drag in the fore and aft portion of rotor disk. Rotor Upwash appears to be another way of explaining Transverse Flow Effect [Source ~ RWP4 ch 9]. The Transverse Flow Effect diminishes at higher forward speeds. See; [Source ~ RWP4 Fig. 9-4]

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


Roll during forward flight is also the result of the coning angle presenting a greater angle of attack at the front of the disk then at the rear of the disk. This effect from the coning angle increases as the speed of forward flight increases. See also; DESIGN: SynchroLite ~ Rotor - Disk - Opposed (Differential) Lateral Cyclic


My thoughts re the UniCopter with its Absolutely Rigid Rotor; The helicopter will be probably subjected to Rotor Upwash but it will not manifest itself as Transverse Flow effect or Inflow Roll. This is because, unlike the above, the aerodynamic precession will be close to 0º not 90º. I think that forward cyclic will be required, not left lateral cyclic. It appears that the lack of sufficient cyclic on Sikorsky's ABC was a lack of forward cyclic. [Source ~ RWP4 p. 35] Later, move this paragraph to a UniCopter page and link from here?

Twist: [θ1] (Washout) [blade]

Blade twist is the difference in a blade's pitch between its root and tip. The tip has less pitch and the amount is referred to as a negative value, in degrees. For more see: DESIGN: UniCopter ~ Rotor - Blade - General - Twist

The blades on a gyrocopter have a small amount of positive twist, because they operate full-time in autorotation.

See also; Ideal Twist:


Upwash - Rotor: [rotor]

See Transverse Flow Effect above, specifically as related to an Absolutely Rigid Rotor. [Source ~ RWP4 p.33]

Variable Geometry Airfoil: [blade]

The use of trailing edge flaps, tabs or adjustable contour, and/or leading edge slats, pivoted nose droop or adjustable contour, the position(s) of which can be controlled in flight.


OTHER: Aerodynamics - Vibration - Rotor Induced

OTHER: Flight Dynamics - Definitions & Algorithims ~ Vibration:


The reference to the following page may be from a different location; later OTHER: Aerodynamics - Vibration - Rotor Induced - Blade Vortex Interaction (BVI)

Vortex Generators:

Small low aspect ratio airfoils mounted on the upper surface of wings. The air spilling over their upper ends forms swirl or vortices. Vortex generators prevent the air separating from the surface of the wing.

Vortex Ring State: [rotor]

VRS is strictly defined by the ratio of the descent rate to the downwash velocity of the specific helicopter. VRS is unlikely at vertical speed ratios of less than .5 and greater than 1.5

For more information see; Vortex Ring State Discussion by Nick Lappos

Wake Contraction Ratio: [rotor]

The ratio of the radius of the far wake to the radius of the rotor. Momentum theory calculates it at 1/√2 = 07.07, but experimentally it has been found to be only about 0.78.

Washout: (Twist) [blade]

A twist in the blade between the rotor's center of rotation and the blade's tip.

Winglet: (tip fin)

An out-of-plane surface extending from a lifting surface.

Y-force: [?]

The sideward-pointing component of rotor force, perpendicular to the control axis. [Source ~ AH p.183]

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