Secant ogive

Given the problem of the aerodynamic design of the nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket or aircraft, missile or bullet), an important problem is the determination of the nose cone geometrical shape for optimum performance. For many applications, such a task requires the definition of a solid of revolution shape that experiences minimal resistance to rapid motion through such a fluid medium, which consists of elastic particles.

In all of the following nose cone shape equations, L is the overall length of the nose cone and R is the radius of the base of the nose cone. y is the radius at any point x, as x varies from 0, at the tip of the nose cone, to L. The equations define the 2-dimensional profile of the nose shape. The full body of revolution of the nose cone is formed by rotating the profile around the centerline (C/L). Note that the equations describe the 'perfect' shape; practical nose cones are often blunted or truncated for manufacturing or aerodynamic reasons.

A very common nose-cone shape is a simple cone. This shape is often chosen for its ease of manufacture, and is also often (mis)chosen for its drag characteristics. The sides of a conical profile are straight lines, so the diameter equation is simply

Cones are sometimes defined by their half angle, ${\displaystyle \phi \;}$ :

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