Given the problem of the aerodynamic design

Design

Design as a noun informally refers to a plan or convention for the construction of an object or a system while “to design” refers to making this plan...

 of the nose cone

Nose cone

The term nose cone is used to refer to the forwardmost section of a rocket, guided missile or aircraft. The cone is shaped to offer minimum aerodynamic resistance...

 section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket

Rocket

A rocket is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction...

 or aircraft

Aircraft

An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

, missile

Missile

Though a missile may be any thrown or launched object, it colloquially almost always refers to a self-propelled guided weapon system.-Etymology:The word missile comes from the Latin verb mittere, meaning "to send"...

 or bullet

Bullet

A bullet is a projectile propelled by a firearm, sling, or air gun. Bullets do not normally contain explosives, but damage the intended target by impact and penetration...

), an important problem is the determination of the nose cone

Nose cone

The term nose cone is used to refer to the forwardmost section of a rocket, guided missile or aircraft. The cone is shaped to offer minimum aerodynamic resistance...

 geometrical shape for optimum performance. For many applications, such a task requires the definition of a solid of revolution

Solid of revolution

In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane....

 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.