Nose cone design

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. 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 two-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. While 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. More optimal, streamlined shapes (described below) are often much more difficult to create. The sides of a conic profile are straight lines, so the diameter equation is simply: Cones are sometimes defined by their half angle, φ: In practical applications, a conical nose is often blunted by capping it with a segment of a sphere. The tangency point where the sphere meets the cone can be found from: where rn is the radius of the spherical nose cap. The center of the spherical nose cap, xo, can be found from: And the apex point, xa can be found from: A bi-conic nose cone shape is simply a cone with length L1 stacked on top of a frustum of a cone (commonly known as a conical transition section shape) with length L2, where the base of the upper cone is equal in radius R1 to the top radius of the smaller frustum with base radius R2.