OTHER:Mechanics - Definitions & Algorithms
Symbols are American National Standard Letter Symbols where possible.[See ~ MH p.115]
Note: The algorithms are in blue.
Outside Web Sites:
There is, currently, duplication on Dynamics, Aerodynamics & Mechanics.
Acceleration - Linear:[a] (m/s2)
a = F * mThe time-rate change of velocity and is expressed as velocity divided by time or as distance divided by time squared, that is, in feet per second per second or feet per second squared. The metric SI unit is the meter per second squared, where force is in Newtons and mass is in kilograms.
Acceleration - Angular: [α] [alpha] (rad/s2)
Acceleration of Gravity: [g]
The acceleration of a free falling body. 32.16 ft / sec2.
Angle of Repose:
The angle at which a body will be just able to remain stationary, the frictional resistance being very nearly overcome by the tendency of the body to slide down.
The tangent of this angle equals the coefficient of friction. Tangent = opposite / adjacent.
Angular Acceleration: [α] (rad/s2)
See above; Acceleration - Angular
Synonymous with the angle. (rad/s)
Angular Speed ~ Angular Velocity: [ω] | [ωR], [ωZ], [ωX] & [ωY]. Wr, Wx, Wy, Wz. [OmegaR], [OmegaZ], [OmegaX] & [OmegaY], (rad/s)
The change in
[Angular velocity(ω) (radians per second) = Angle of rotation (θ) (radians) / time (t) (seconds)].
Conversion;Ω = RPM * 0.1047197, RPM = Ω * 9.549304.
Angular Momentum: [L]
A measure of an object's rotation about a particular axis; more specifically, the product of its rotational inertia and rotational velocity. For an object that is small compared to the radial distance, it is the product of mass speed, and radial distance of rotation. Angular Momentum = rotational inertia x rotational velocity = JMω or mvr or Iω
Thederived SI units of angular momentum are newton·metre·seconds; N·m·s (kgm2s-1). 1 N = kilogram * meter / second2.
Thelength of a circular arc of a circle with radius r and subtending an angle θ (measured in radians)
Brake horsepower (bhp), sometimes called shaft horsepower, is the amount of power available for useful work. Bhp is less than ihp because of the various power losses which occur during engine operation.
To determine the brake or shaft horsepower that is delivered as useful work by an engine, the sum total of all mechanical losses must be deducted from the total ihp.
Center of Gravity:
The center of gravity of a body, volume, area or line is that point at which if the body, volume, area or line were suspended it would be perfectly balanced in all conditions. For symmetrical bodies of uniform material, it is at the geometric center.
Center of Mass:
The location within a body at which its entire mass is considered to be located.
Center of Oscillation:
Center of Percussion:
Baseball bat Baseball bat & Mallet The Physical Pendulum [See ~ MH p.149]
An fictitious outward force that is due to rotation. In an inertial frame of reference, it is fictitious in the sense that it doesn't act on the rotating object but on whatever supplied the centripetal force; it is the reaction to the centripetal force. In a rotating frame of reference, it does act on the rotating body and is fictitious in the sense that it is not an interaction with an agent or entity such as mass or charge but is a force in itself that is solely a product of rotation; it has no reaction-force counterpart.
Centrifugal force is "inertia" or momentum expressing itself against a centripetal force pulling a moving object toward a center of rotation.
Centripetal Force and Centrifugal Effect:
Action-reaction force pair associated with circular motion. Centripetal (center-seeking) force is the constant inward force necessary to maintain circular motion. The centripetal force is supported by a reaction force, the centrifugal (center-fleeing) force, which acts on the circling object and on the source of centripetal force, usually located at the circle's center. The two forces are equal in magnitude and opposite in direction.
Center of mass.
Centroidal Distance: [y]
The distance from the base (baseline) to the center of the mass.
Constant Velocity Joint (CV):
A Constant Velocity Joint is one that provides consistent drive shaft speeds regardless of the operating angle of the joint
Control Moment Gyroscope (CMG):
The most effective CMGs include only a single gimbal. When the gimbal of such a CMG rotates, the change in direction of the rotor's angular momentum represents a torque that reacts onto the body to which the CMG is mounted, e.g. a spacecraft. Except for effects due to the motion of the spacecraft, this torque is due to a constraint, so it does no mechanical work (i.e. requires no energy). Single-Gimbal CMGs exchange angular momentum in a way that requires very little power, with the result that they can apply very large torques for minimal electrical input.
Coriolis Effect: Should this be in Flight Dynamics?
Conservation of energy. 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 or cones in flight. This change in distance during flapping is the result of the flapping hinge being offset. A rotor with teetering hinge will experience the Coriolis effect during a change in the coning angle but not during the act of teetering.
For additional information see:Coriolis and Hooke's Joint
Explanation and algorithms relating to Coriolis Effect. For mathematical explanation see; [Source ~ RW, section 2.7]
A collective-pitch - throttle synchronization device that automatically adjusts the amount of throttle in a relationship with changes to the collective setting.
A component that if it were to fail, would result in the loss of the aircraft.
Design Load Factor:
See; DESIGN: SynchroLite ~ Rotor - Hub - Bearings - Pitch - Elastomeric
The endurance limit is the highest stress or range of stress that can be repeated indefinitely without failure of the metal. Graph
Energy:[Ek], [K] & [T]
The capability of a body to do work.
Due to translation:
EKT = (1/2) * M * V2 = (W * V2) / (2 * g); [EKT in ft-lbs], [W in pounds], [V in ft/sec.], [g in 32.16 ft/sec/sec.]
Due to rotation:
EKR = (1/2) * JMO * ω2; [EKR in ft-lbs], [JMO ~ moment of inertia of the body about a fixed axis 0, in lbs-ft-sec2]
The most common example is a body having potential energy because of its position in a field of force is that of a body elevated to some height above the earth.
EPF = W * S weight * elevation [EPF in ft -lbs.]
Equivalent Dynamic Bearing Load: [Pr]
When both dynamic radial loads and dynamic axial loads act on a bearing at the same time, the hypothetical load acting on the center of the bearing which gives the bearings the same life as if they had only a radial or only an axial load.
Equivalent Static Bearing Load: [Por]
The static equivalent load is a load which would cause the same total permanent at the most heavily stressed contact point between the rolling elements and the raceway as under actual load conditions; that is when both static radial loads and static axial loads are simultaneous applied to the bearing.
Fatigue Load Limit: [Pu] [bearing]
The SKF New Life Theory introduces the concept of a fatigue load limit Pu analogous to that used when calculating endurance for other machine components. This fatigue load limit is the load below which fatigue will not occur in the bearing under ideal conditions.
Force: [F] (newton or lbf or ozf)
A push or a pull.
The rapid corrosion that occurs at the interface between contacting, highly loaded metal surfaces when subjected to slight vibratory motions.
Splined couplings are one of the commonest methods of connecting elements in rotating machinery. Their performance is limited not only by torsional fatigue but also by fretting wear arising from angular misalignment. The wear problem is especially common in mechanical transmissions, which have lightweight and flexible casings, such as those in helicopters.
All so known as
The characteristic that causes the gyroscope to react to an applied force at a point 90-degress away from the point of application, in the direction of its rotation.
The angle between the axis of a helical gear and an imaginary line that is tangent to the gear tooth. Helix angles can vary in size from 0° to 90 degrees.
Hooke's Joint Effect:
This appears to be valid explanation for the flapping and teetering hinges. If only the teetering hinge is being considered then the explanation of a Knuckle Joint will be appropriate. (see:Coriolis and Hooke's Joint).
Not sure of proper definition. Has to do with lifetime of a part re hours of operation. There is also the phrase Design-life.
That property of matter which causes it to resist any change in its motion or state of rest.
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.
Kinetic Energy: [K]
The kinetic energy of an object is the extra energy, which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity
Linear (metric): EK = 1/2 * m * v2
Rotational (metric): K = 1/2 * I * ω2
Linear (english): KE = (m * v2)/( 2 * gc)
Rotation (english): KE = (m * v2)/( 2 * gc) This is my merging of rotational Metric and linear English.
A unit of weight equal to 1000 pounds.
I am having a problem with this; for bearings, gears, etc.For information see; http://www.dbsmfg.com/rightspec.html
For now see;Safety Factor:
Limit Load Factor:[NL]
The point where structural damage occurs (objectionable permanent deformation). Limit load factors are about 2 to 3 G for observation and utility aircraft and as high as 5 G for modern attack helicopter.
NL =Maximum normal static load / Design gross weight
SeeOTHER: Flight Dynamics - Definitions ~ Limit Load Factor and see below.
Linear Momentum: [?]
The product of the mass [
SI unit is kg·m/s, or, equivalently, N·s. ~ English units in ft-lb/s.
It should be noted that linear momentum is a vector quantity, the momentum being in the same direction asV.
Load Factors:The following are not in any specific order, yet. The comments may not be correct. The Load Factors should be put on Mechanics page or Flight Dynamics page only.
For some additional information see
For most bearing calculations life is expressed as the number of hours that 90% of a group of identical bearings will exceed under a give set of conditions, and is referred to as the L10 life.
Mass: [m] or [M] = W / g
A measurement of the inertia of a body.
Inertial mass is a measure of an object's resistance to changing its state of motion when a force is applied. An object with small inertial mass changes its motion more readily, and an object with large inertial mass does so less readily.
In theSI system of units, mass is measured in kilograms (kg).
More to come.
Mass = Weight [lb] / 32.17 [ft/sec2]
A slug has units of lbf·s²/ft. It is a mass that accelerates by 1 ft/s2 when a force of onepound-force (lbf) is exerted on it. Therefore a slug has a mass of or 32.17405 pound-mass or 14.5939 kg.
In theSI system of units, mass is measured in kilograms (kg). Many other units of mass are also employed, such as: grams (g), tonnes, pounds, ounces, long and short tons, quintals, slugs.
Mechanical Properties of Materials:
See FORM: PT - Material Properties for values.
The branch of physics that deals with the motion of material bodies and the phenomena of the action of forces on bodies.
In this web site ~ Information related to the mechanical aspects of helicopters. Mainly the power train.
The branch of mechanics dealing with bodies, masses or forces at rest or in equlibrium.
The description of movable mechanical structures consisting of joints and links including the number, location, and orientation of the joints.
Meters per second:
SI symbolic abbreviation is m·s−1, or equivalently, m/s;
Modulus of Elasticity [E]
Modulus of Rigidity[G]
Is also known as the Modulus of elasticity in Shear. It is the reatio of shear stress[τ], to shear strain [γ], in radians.
A measure of the tendency of a force to rotate the body upon which it acts about its axis.M = F * r. The SI unit is N·m.
Moment of Inertia [I]
A physical property of a member that helps define rigidity or stiffness and is expressed in inches raised to the fourth power. It is a measure of the resistance to rotation offered by a section's geometry and size.m is its mass, and r is its perpendicular distance from the axis of rotation.
Inertia = mass times square of distance from axis,I = ò r2dm
SI units kg m², Former British units slug ft2 or ft-lb-sec2 (1 slug = 1 pound second2 per foot)
Inertia can be linear as well.
The quantity of motion of a moving object, equal to the product of its mass times its velocity.
SI unit is kg·m/s, or, equivalently, N·s
See on this page: Linear Momentum and Angular Momentum.
A more sophisticated definition of "inertia" is one that includes values of mass, speed, and direction.
A newton is the amount of force required to accelerate a body with a mass of one kilogram at a rate of one meter per second squared. [Newton's 2nd law.]
1 N = kilogram * meter / second2.
Origin of Coordinates for Total Helicopter:
The SynchroLite's origin is at the intersection of the centerlines of the two mast's.
The UniCopter's origin is at the mid-point between the centers of the two rigid hubs; and the center of the hub is the point where the centerlines of the pitch axis of the three blades intersect.
The conventional method is to have the origin at the center of total helicopter mass (center of gravity). Because the CG has not been established for the SynchroLite and UniCopter, the following offset are to be added to the other offsets; on the X-axis lCG, on the Y-axis yCG, and on the Z-axis hCG.
The largest diameter of the worm gear teeth. It is equal to the diameter of the outside circle.
Polar Moment of Inertia of Plane Area [J]
See up above.
Polar Moment of Inertia of Mass [JM] or [I]
See up above.
Power: [P] [W watt]
Power Losses 
Total power losses at see level amount to 18%(plus 7% more for tail rotor). Installation losses (10%) derived from pressure drop in the intake system, back pressure from the exhaust and muffler system and from heated air recirculating from the engine cooling and exhaust into the air intake system. Engine cooling is 4% and the transmission is approximately 4%. [Source ~ HH p.5]
A change in the direction of the axis of a rotating object. See Gyroscopic Precession above.
Precessional Frequency [ωp]
The angular frequency of the axis of rotation.
Radius of Gyration[k]
Is the distance from the neutral axis of a section to an imaginary point at which the whole area of the section could be concentrated and still have the same moment of inertia. Formula: The square root of (the moment of inertia in inches^4 divided by the area of the section in inches^2) expressed in inches.
Value for circular disk w/ axis through center:k = 0.7071 r
To calculate values for standard shapes run program: Engineering Power Tools ~ Mechanical ~ Moment of Inertia.
Radius of Center of Mass: [Rcm]
Radius of Percussion: [Rcp]
Rcp = Rg2/Rcm + Rcm 'g' in this instance is acceleration due to centrifugal force. This is an assumption at this point. For best description and algorithm see [Source ~ MH p.149]
Direction of the airflow produced by an object moving through the air.
Rotational Inertia: [JM or I]
See above; Moment of Inertia ~ Polar moment of inertia of mass
Rotational Speed: [RPM or (Ω or ω)]
The safety factors that are used on the mechanical and structural components of helicopters.
A number as opposed to avector, function.
Aphysical quantity that can be completely charactirized by just one number.
The distance between one thread and its neighbor.
The distance the nut advances when the screw is rotated one complete revolution.
A unit of mass, which is equal to 1 pound second2 per foot. M = W / g in which M = mass in slugs, W = weight in pounds, and g = acceleration due to gravity commonly taken as 32.16 feet per second.
Systems of Measurement:
Metric SI: .
The diameter of the throat circle at the center line of the worm gear face (the lowest point on the tooth face). .
Torque: [τ] [tau] [Q]
τ = dL / dt
whereL is angular momentum
so ifJM is constant,
whereα is angular acceleration, a quantity usually measured in radians per second squared.
Torque rise, or torque reserve, is a measure of lugging ability (low-end power) when the going gets tough and the engine revs down
In the linked case the rated torque of the diesel engine is 477 lb.-ft. at the maximum speed of 2400 RPM and the peak torque is 657 lb.-ft. @ 1200 RPM. The torque rise is: 657 - 477 divided by 477 = 38%. The idle speed is 1000 RPM.
Torsion is a mode of loading where a shaft is subjected to a torque about its longitudinal axis, resulting in a twisting deformation.
Amplitude modulation of torque measured in degrees peak-to-peak referenced to the axis of shaft rotation.
Ultimate Load Factor:
The point where structural failure occurs. The Ultimate Load Factor equals the Limit Load Factor times the Safety Factor.
Velocity: (mps or ipm)
Constant Linear Velocity:
Constant Angular Velocity:
OTHER: Mechanics - Vibration - Engine Induced
OTHER: Flight Dynamics - Definitions & Algorithims ~ Vibration:
The distance between the throat and the base of the tooth. It is equal to the addendum plus the dedendum.
Work: [Energy] [W]
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Last Revised: June 28, 2012