Center of pressure
Encyclopedia
The center of pressure is the point on a body where the total sum of a pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

field acts, causing a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

and no 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...

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 location produce equivalent force and moment on the body as the original pressure field. Pressure fields occur in both static (hydrostatic) and dynamic (aerodynamic) fluid mechanics. Specification of the center of pressure, the reference point from which the center of pressure is referenced, and the associated force vector allows the moment generated about any point to be computed by a translation from the reference point to the desired new point.

Hydrostatic Example (Dam)

Since the forces of water on a dam are hydrostatic forces, they vary linearly with depth. The total force on the dam is then the integral of the pressure multiplied by the width of the dam as a function of the depth. The center of pressure is located at the centroid
Centroid
In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" of all points of X...

of the triangular shaped pressure field 2/3 from the top of the water line. The hydrostatic force and tipping moment on the dam about some point can be computed from the total force and center of pressure location relative to the point of interest.

Historical usage

Center of pressure is used in sailboat
Sailboat
A sailboat or sailing boat is a boat propelled partly or entirely by sails. The term covers a variety of boats, larger than small vessels such as sailboards and smaller than sailing ships, but distinctions in the size are not strictly defined and what constitutes a sailing ship, sailboat, or a...

design to represent the position on a sail
Sail
A sail is any type of surface intended to move a vessel, vehicle or rotor by being placed in a wind—in essence a propulsion wing. Sails are used in sailing.-History of sails:...

where the aerodynamic force is concentrated.

It is desirable that a sailboat be stable in the sense that the wind should naturally push the bow
Bow (ship)
The bow is a nautical term that refers to the forward part of the hull of a ship or boat, the point that is most forward when the vessel is underway. Both of the adjectives fore and forward mean towards the bow...

of the ship away from the wind rather than facing the wind such that the boat would be blown backward. To accomplish this, the center of pressure due to aerodynamic forces including the hull and the sails should be forward of the ship's center of mass
Center of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...

around which it will pivot.
The hydrodynamic center of pressure on the hull will be at a different location typically behind the center of mass of the boat.

Aircraft aerodynamics

A stable configuration is not only desirable in sailing, but in aircraft design as well. Aircraft design therefore borrowed the term center of pressure. But unlike a sail, a rigid non-symmetrical airfoil
Airfoil
An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....

not only produces lift, but a 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...

.
The center of pressure of an aircraft is the point where all of the aerodynamic pressure field may be represented by a single force vector with no moment. A similar idea is 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...

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

where 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...

produced by the aerodynamic forces is constant with 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...

.

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...

plays an important role in analysis 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 other flying vehicles. It is desirable that when the pitch angle and angle of attack of an aircraft are disturbed (by, for example turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...

) that the aircraft returns to its original trimmed pitch angle and 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...

without a pilot or autopilot
Autopilot
An autopilot is a mechanical, electrical, or hydraulic system used to guide a vehicle without assistance from a human being. An autopilot can refer specifically to aircraft, self-steering gear for boats, or auto guidance of space craft and missiles...

changing the control surface deflection. For an aircraft to return towards its trimmed attitude, without input from a pilot or autopilot, it must have positive 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...

.

Missile aerodynamics

Missiles typically do not have a preferred plane or direction of maneuver and thus have symmetric airfoils. Since the center of pressure for symmetric airfoils is relatively constant for small angle of attack, missile engineers typically speak of the complete center of pressure of the entire vehicle for stability and control analysis. In missile analysis, the center of pressure is typically defined as the center of the additional pressure field due to a change in the angle of attack off of the trim angle of attack. For unguided rockets the trim position is typically zero angle of attack and the center of pressure is defined to be the center of pressure of the resultant flow field on the entire vehicle resulting from a very small angle of attack (that is, the center of pressure in the limit as angle of attack goes to zero). For positive stability in missiles, the total vehicle center of pressure defined as given above must be further from the nose of the vehicle than the center of gravity
Center of gravity
In physics, a center of gravity of a material body is a point that may be used for a summary description of gravitational interactions. In a uniform gravitational field, the center of mass serves as the center of gravity...

. In missiles at lower angles of attack, the contributions to the center of pressure are dominated by the nose, wings, and fins. The normalized normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

coefficient derivative with respect to the angle of attack of each component multiplied by the location of the center of pressure can be used to compute a centroid representing the total center of pressure. This center of pressure of the added flow field is behind the center of gravity and the additional force "points" in the direction of the added angle of attack, this produces a moment that pushes the vehicle back to the trim position. In guided missiles where the fins can be moved to trim the vehicles in different angles of attack, the center of pressure is the center of pressure of the flow field at that angle of attack for the undeflected fin position. This is the center of pressure of any small change in the angle of attack (as defined above). Once again for positive static stability, this definition of center of pressure requires that the center of pressure be further from the nose than the center of gravity. This ensures that any increased forces resulting from increased angle of attack results in increased restoring moment to drive the missile back to the trimmed position. In missile analysis, positive static margin implies that the complete vehicle makes a restoring moment for any angle of attack from the trim position.

Movement of center of pressure for aerodynamic fields

The center of pressure on a symmetric airfoil
Airfoil
An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....

typically lies close to 25% of the chord length behind the leading edge of the airfoil. (This is called the "quarter-chord point".) For a symmetric airfoil, 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...

and 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...

change, the center of pressure does not move. It remains around the quarter-chord point for all angles of attack and lift coefficients. The role of center of pressure in the control characterization of aircraft takes a different form than in missiles.

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 the center of pressure does not occupy a fixed location. For a conventionally cambered airfoil, the center of pressure lies a little behind the quarter-chord point at maximum 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...

(large 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...

), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves toward the rear. When the lift coefficient is zero an airfoil is generating no lift but a conventionally cambered airfoil generates a nose-down pitching moment, so the location of the center of pressure is an infinite distance behind the airfoil. This direction of movement of the center of pressure on a conventionally cambered airfoil is de-stabilising, necessitating a horizontal stabiliser to provide the aircraft with 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...

. Aircraft tend to use cambered wings because they have relatively benign flights with preferred flight orientations as compared to missiles.

For a reflex-cambered airfoil, the center of pressure lies a little ahead of the quarter-chord point at maximum 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...

(large 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...

), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves forward. When the lift coefficient is zero an airfoil is generating no lift but a reflex-cambered airfoil generates a nose-up pitching moment, so the location of the center of pressure is an infinite distance ahead of the airfoil. This direction of movement of the center of pressure on a reflex-cambered airfoil is stabilising, and a horizontal stabiliser is not necessary. A tailless aircraft
Tailless aircraft
A tailless aircraft traditionally has all its horizontal control surfaces on its main wing surface. It has no horizontal stabilizer - either tailplane or canard foreplane . A 'tailless' type usually still has a vertical stabilising fin and control surface...

with a straight wing can be designed to have positive 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...

if the wing has reflex camber.

The way the center of pressure moves as lift coefficient changes makes it difficult to use the center of pressure in the mathematical 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...

of an aircraft. For this reason, it is much simpler to use 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...

when carrying out a mathematical analysis. The aerodynamic center occupies a fixed location on an airfoil, typically close to the quarter-chord point.

The aerodynamic center is the conceptual starting point for longitudinal stability. Providing the center of gravity of an aircraft lies forward of the aerodynamic center the aircraft will have positive longitudinal stability. The horizontal stabilizer
Stabilizer (aircraft)
In aviation, a stabilizer provides stability when the aircraft is flying straight, and the airfoil of the horizontal stabilizer balances the forces acting on the aircraft....

contributes extra stability and this allows the center of gravity to be a small distance aft of the aerodynamic center without the aircraft reaching neutral stability. The position of the center of gravity at which the aircraft has neutral stability is called the 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...

.

• 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...

• Aerodynamic force
• 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...

• Aeroprediction
Aeroprediction
The Aeroprediction Code is a semi-empirical computer program that estimates the aerodynamics of weapons over the Mach number range 0 to 20, angle of attack range 0 to 90 degrees and for configurations that have various cross sectional body shapes. Weapons considered include projectiles, missiles,...

• Zero Moment Point
Zero Moment Point
Zero Moment Point is a concept related with dynamics and control of legged locomotion, e.g., for humanoid robots. It specifies the point with respect to which dynamic reaction force at the contact of the foot with the ground does not produce any moment in the horizontal direction, i.e. the point...