Because of 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, shell 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.
Nose cone shapes and equations
General dimensions 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, aerodynamic, or thermodynamic reasons.
Conic
y = x R L = x tan ( ϕ ) ϕ = arctan ( R L ) {\displaystyle {\begin{aligned}y&={\frac {xR}{L}}=x\tan(\phi )\\\phi &=\arctan \left({\frac {R}{L}}\right)\\\end{aligned}}}
Spherically blunted conic
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