aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...

, the pitching moment on an

airfoil An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine. ...

is the moment (or

torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...

) produced by the

aerodynamic force In fluid mechanics, an aerodynamic force is a force exerted on a body by the air (or other gas) in which the body is immersed, and is due to the relative motion between the body and the gas. Force There are two causes of aerodynamic force: ...

on the airfoil if that aerodynamic force is considered to be applied, not at the center of pressure, but at the

aerodynamic center In aerodynamics, the torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift and net drag applied at some point on the airfoil, and a separate net pitching moment about that point whose magnit ...

of the airfoil. The pitching moment on the wing of an airplane is part of the total moment that must be balanced using the lift on the

horizontal stabilizer A tailplane, also known as a horizontal stabiliser, is a small lifting surface located on the tail (empennage) behind the main lifting surfaces of a fixed-wing aircraft as well as other non-fixed-wing aircraft such as helicopters and gyroplan ...

. More generally, a pitching moment is any moment acting on the pitch axis of a moving body. The

lift Lift or LIFT may refer to: Physical devices * Elevator, or lift, a device used for raising and lowering people or goods ** Paternoster lift, a type of lift using a continuous chain of cars which do not stop ** Patient lift, or Hoyer lift, mobil ...

on an airfoil is a distributed force that can be said to act at a point called the center of pressure. However, as

angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...

changes on a cambered airfoil, there is movement of the center of pressure forward and aft. This makes analysis difficult when attempting to use the concept of the center of pressure. One of the remarkable properties of a cambered airfoil is that, even though the center of pressure moves forward and aft, if the lift is imagined to act at a point called the

, the moment of the lift force changes in proportion to the square of the airspeed. If the moment is divided by the

dynamic pressure In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5 :q = \frac\rho\, u^2 where (in SI units): * is the dynamic pressure in pascals ( ...

, the area and chord of the airfoil, the result is known as the pitching moment coefficient. This coefficient changes only a little over the operating range of angle of attack of the airfoil but the change in moment slope against the AOA shown in figure below seems very steep so this should be of change in pitching moment of wing about CG rather than about AC. The combination of the two concepts of ''aerodynamic center'' and ''pitching moment coefficient'' make it relatively simple to analyse some of the flight characteristics of an aircraft.

Measurement

The

of an airfoil is usually close to 25% of the chord behind the leading edge of the airfoil. When making tests on a model airfoil, such as in a wind-tunnel, if the force sensor is not aligned with the quarter-chord of the airfoil, but offset by a distance x, the pitching moment about the quarter-chord point,

M_

is given by :

M_ = M_\text + \mathbf\times (D_\text, L_\text)

where the indicated values of ''D'' and ''L'' are the drag and lift on the model, as measured by the force sensor.

Coefficient

The pitching moment coefficient is important in the study of the longitudinal static stability of aircraft and missiles. The ''pitching moment coefficient''

C_m

is defined as follows :

C_m=\frac

where ''M'' is the pitching moment, ''q'' is the

, ''S'' is the

wing area A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is expres ...

, and ''c'' is the length of the chord of the airfoil.

C_m

is a dimensionless coefficient so consistent units must be used for ''M'', ''q'', ''S'' and ''c''. Pitching moment coefficient is fundamental to the definition of

of an airfoil. The ''aerodynamic center'' is defined to be the point on the chord line of the airfoil at which the ''pitching moment coefficient'' does not vary with angle of attack, or at least does not vary significantly over the operating range of angle of attack of the airfoil. In the case of a symmetric airfoil, the lift force acts through one point for all angles of attack, and the ''center of pressure'' does not move as it does in a cambered airfoil. Consequently, the ''pitching moment coefficient'' about this point for a symmetric airfoil is zero. The pitching moment is, by convention, considered to be positive when it acts to pitch the airfoil in the nose-up direction. Conventional cambered airfoils supported at the aerodynamic center pitch nose-down so the ''pitching moment coefficient'' of these airfoils is negative.Ira H. Abbott, and Albert E. Von Doenhoff (1959), ''Theory of Wing Sections'', Dover Publications Inc., New York SBN 486-60586-8

References

Bibliography

L. J. Clancy Laurence Joseph Clancy (15 March 1929 - 16 October 2014) was an Education Officer in aerodynamics at Royal Air Force College Cranwell whose textbook ''Aerodynamics'' became standard. He was born in Egypt to Alfred Joseph Clancy and Agnes Hunter. I ...

(1975), ''Aerodynamics'', Pitman Publishing Limited, London, {{ISBN, 0-273-01120-0 * Piercy, N.A.V (1943) ''Aerodynamics'', pages 384–386, English Universities Press. London
Low-Speed Stability
Retrieved on 2008-07-18 Aerodynamics Aerospace engineering Gliding technology

Measurement

Coefficient

See also

References

Bibliography