Nose cone design

Conic

Conic nose cone render and profile with parameters shown.

Spherically blunted conic

Spherically blunted conic nose cone render and profile with parameters shown.

In practical applications such as re-entry vehicles, 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, using similar triangles, from:

x_{t}={\frac {L^{2}}{R}}{\sqrt {\frac {r_{n}^{2}}{R^{2}+L^{2}}}}

y_{t}={\frac {x_{t}R}{L}}

where $r n$ is the radius of the spherical nose cap.

The center of the spherical nose cap, $x o$ , can be found from:

x_{o}=x_{t}+{\sqrt {r_{n}^{2}-y_{t}^{2}}}

And the apex point, $x a$ can be found from:

x_{a}=x_{o}-r_{n}

Bi-conic

Bi-conic nose cone render and profile with parameters shown.

Tangent ogive

Tangent ogive nose cone render and profile with parameters and ogive circle shown.

Spherically blunted tangent ogive

Spherically blunted tangent ogive nose cone render and profile with parameters shown.

A tangent ogive nose is often blunted by capping it with a segment of a sphere. The tangency point where the sphere meets the tangent ogive can be found from:

{\begin{aligned}x_{o}&=L-{\sqrt {\left(\rho -r_{n}\right)^{2}-(\rho -R)^{2}}}\\y_{t}&={\frac {r_{n}(\rho -R)}{\rho -r_{n}}}\\x_{t}&=x_{o}-{\sqrt {r_{n}^{2}-y_{t}^{2}}}\end{aligned}}

where $r n$ is the radius and $x o$ is the center of the spherical nose cap.

Secant ogive

Secant ogive nose cone render and profile with parameters and ogive circle shown.

Alternate secant ogive render and profile which show a bulge due to a smaller radius.

Elliptical

Elliptical nose cone render and profile with parameters shown.

Parabolic

Half (

K' = 1/2

)

Three-quarter (

K' = 3/4

)

Full (

K' = 1

)

Renders of common parabolic nose cone shapes.

Power series

Half (

n = 1/2

)

Three-quarter (

n = 3/4

)

Haack series

LD-Haack (Von Kármán) (

C = 0

)

LV-Haack (

C = 1/3

)

Power Series

A power series nosecone is defined by $r=x^{n}$ where $(0\leq x\leq 1)$ . $n<1$ will generate a concave geometry, while $n>1$ will generate a convex (or "flared") shape^[1]

Parabolic Series

A parabolic series nosecone is defined by $r={\tfrac {2x-Kx^{2}}{2-K}}$ where $(0\leq x\leq 1)$ and $K$ is series variable. ^[1]

Haack Series

A Haack series nosecone is defined by $r(x)={\frac {1}{\sqrt {\pi }}}{\sqrt {\theta -{\frac {1}{2}}\sin(2\theta )+C\sin ^{3}\theta }}$ where $\theta =\arccos \!\left(1-{\frac {2x}{L}}\right)$ ^[1]. Parametric formulation can be obtained by solving the $\theta$ formula for $x$ .

Von Kármán Ogive

The LD-Haack ogive is a special case of the Haack series with minimal drag for a given length and diameter, and is defined as a Haack series with $C = 0$ , commonly called the Von Kármán or Von Kármán ogive. A cone with minimal drag for a given length and volume can be called a LV-Haack series, defined with $C={\tfrac {1}{3}}$ .^[1]

Aerospike

An aerospike can be used to reduce the forebody pressure acting on supersonic aircraft. The aerospike creates a detached shock ahead of the body, thus reducing the drag acting on the aircraft.

Nose cone shapes and equations