Pitching moment

# Pitching moment

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Encyclopedia

In aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

, the pitching moment on an airfoil
Airfoil
An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....

is the moment
Moment (physics)
In physics, the term moment can refer to many different concepts:*Moment of force is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. A moment is valued mathematically as the product of the...

(or torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

) produced by the aerodynamic force on the airfoil if that aerodynamic force is considered to be applied, not at the center of pressure
Center of pressure
The center of pressure is the point on a body where the total sum of a pressure field acts, causing a force and no moment about that point. The total force vector acting at the center of pressure is the value of the integrated vectorial pressure field. The resultant force and center of pressure...

, but at the aerodynamic center
Aerodynamic center
The torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift applied at some point on the foil, and a separate net pitching moment about that point whose magnitude varies with the choice of where the lift is chosen to be applied...

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.

The lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

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
Angle of attack
Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...

changes on a cambered
Camber (aerodynamics)
Camber, in aeronautics and aeronautical engineering, is the asymmetry between the top and the bottom surfaces of an aerofoil. An aerofoil that is not cambered is called a symmetric aerofoil...

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
Camber (aerodynamics)
Camber, in aeronautics and aeronautical engineering, is the asymmetry between the top and the bottom surfaces of an aerofoil. An aerofoil that is not cambered is called a symmetric aerofoil...

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 aerodynamic center
Aerodynamic center
The torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift applied at some point on the foil, and a separate net pitching moment about that point whose magnitude varies with the choice of where the lift is chosen to be applied...

the moment of the lift force changes in proportion to the square of the airspeed. If the moment is divided by the dynamic pressure, the area and chord
Chord (aircraft)
In aeronautics, chord refers to the imaginary straight line joining the trailing edge and the center of curvature of the leading edge of the cross-section of an airfoil...

of the airfoil, to compute a pitching moment coefficient, this coefficient changes only a little over the operating range of angle of attack of the airfoil. 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 aerodynamic center
Aerodynamic center
The torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift applied at some point on the foil, and a separate net pitching moment about that point whose magnitude varies with the choice of where the lift is chosen to be applied...

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, is given by
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
Longitudinal static stability
Longitudinal static stability is the stability of an aircraft in the longitudinal, or pitching, plane during static conditions. This characteristic is important in determining whether an aircraft will be able to fly as intended...

of aircraft and missiles.

The pitching moment coefficient is defined as follows
where M is the pitching moment, q is the dynamic pressure, S is the planform area, and c is the length of the chord
Chord (aircraft)
In aeronautics, chord refers to the imaginary straight line joining the trailing edge and the center of curvature of the leading edge of the cross-section of an airfoil...

of the airfoil.
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 aerodynamic center
Aerodynamic center
The torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift applied at some point on the foil, and a separate net pitching moment about that point whose magnitude varies with the choice of where the lift is chosen to be applied...

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
Camber (aerodynamics)
Camber, in aeronautics and aeronautical engineering, is the asymmetry between the top and the bottom surfaces of an aerofoil. An aerofoil that is not cambered is called a symmetric aerofoil...

airfoil. Consequently the pitching moment coefficient for a symmetric airfoil is zero.

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.

• Aircraft flight mechanics
Aircraft flight mechanics
In aeronautics, aircraft flight mechanics is the study of the forces that act on an aircraft in flight, and the way the aircraft responds to those forces.Aircraft flight mechanics are relevant to gliders, helicopters and aeroplanes....

• Flight dynamics
Flight dynamics
Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw .Aerospace engineers develop control systems for...

• Longitudinal static stability
Longitudinal static stability
Longitudinal static stability is the stability of an aircraft in the longitudinal, or pitching, plane during static conditions. This characteristic is important in determining whether an aircraft will be able to fly as intended...

• Neutral point
Longitudinal static stability
Longitudinal static stability is the stability of an aircraft in the longitudinal, or pitching, plane during static conditions. This characteristic is important in determining whether an aircraft will be able to fly as intended...

• Lift coefficient
Lift coefficient
The lift coefficient is a dimensionless coefficient that relates the lift generated by a lifting body, the dynamic pressure of the fluid flow around the body, and a reference area associated with the body...

• Drag coefficient
Drag coefficient
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...