# Center of pressure

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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 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.

## Contents

### 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 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 design to represent the position on a sail 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 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 should be forward of the ship's center of mass around which it will pivot.

### 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 not only produces lift, but a moment. 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.[1][2] A similar idea is the aerodynamic center which is the point on an airfoil where the pitching moment produced by the aerodynamic forces is constant with angle of attack.[3][4][5]