Aerodynamic center

Aerodynamic center

Overview
The torques or moments acting on an airfoil
Airfoil
An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....

moving through a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

can be accounted for by the net 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...

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 aerodynamic center is the point at which the pitching moment
Pitching moment
In aerodynamics, the pitching moment on an airfoil is the moment produced by the 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 of the airfoil...

coefficient for the airfoil does not vary with 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...

i.e. 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...

, so this choice makes analysis simpler
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Encyclopedia
The torques or moments acting on an airfoil
Airfoil
An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....

moving through a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

can be accounted for by the net 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...

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 aerodynamic center is the point at which the pitching moment
Pitching moment
In aerodynamics, the pitching moment on an airfoil is the moment produced by the 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 of the airfoil...

coefficient for the airfoil does not vary with 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...

i.e. 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...

, so this choice makes analysis simpler
.
where is the aircraft 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...

.

The concept of the aerodynamic center (AC) is important 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...

. It is fundamental in the science of stability of aircraft in flight.

For symmetric airfoils in subsonic flight the aerodynamic center is located approximately 25% 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...

from the leading edge of the airfoil. This point is described as the quarter-chord point. This result also holds true for 'thin-airfoils'. For non-symmetric (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...

) airfoils the quarter-chord is only an approximation for the aerodynamic center.

A similar concept is that of 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...

. The location of the center of pressure varies with changes of lift coefficient and angle of attack. This makes the center of pressure unsuitable for use in analysis of 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...

. Read about movement of centre of pressure.

Role of aerodynamic center in aircraft stability

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...

:     and

For directional static stability:       and

Where:

For A Force Acting Away at the Aerodynamic Center, which is away from the reference point:

Which for Small Angles and =, , , simplifies to:

General Case: From the definition of the AC it follows that
.
.

The Static Margin can then be used to quantify the AC:

where:
= yawing moment coefficient = pitching moment
Pitching moment
In aerodynamics, the pitching moment on an airfoil is the moment produced by the 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 of the airfoil...

coefficient = rolling moment coefficient = X-force ~= Drag = Y-force ~= Side Force = Z-force ~= Lift
ref = reference point (about which moments were taken)
c = reference length
S = reference area
q = dynamic pressure = 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...

= sideslip angle

SM = Static Margin

• 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....

• 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...

• 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...

• Thin-airfoil theory
• Joukowsky transform
Joukowsky transform
In applied mathematics, the Joukowsky transform, named after Nikolai Zhukovsky, is a conformal map historically used to understand some principles of airfoil design.The transform is...