Tangent Ogive Dimension Algorithms

A tangent ogive is an arc of a circle that meets the bullet body contour smoothly, creating a smooth transition where the ogive joins the cylindrical body. The center of rotation of the arc lies in the plane of the base of the nose.

The dimensions of a Tangent Ogive may be defined by 4 dimensions:  The radius of the curve, the length of the nose, the base diameter and the tip diameter. If any three of the dimensions are known, the fourth may be calculated using the algorithms defined below.

 Let L = The length of the ogive nose from base to tip.     Let D = The diameter of the base of the ogive.     Let T = The diameter of the ogive tip.     Let R = The radius of the curve of the ogive in inches.                       SqRt {**} denotes the Square Root of a value.     Sqr [ **] denotes the Square of a value. To find the Radius of the ogive:     R = Sqr[ L ] / ( D  T ) + ( D  T ) / 4                  ~     R1 = Sqr[ L ]     R2 = R1 / ( D  T )     R   = R2 + ( D  T ) / 4     To find the Length of the ogive:     L = SqRt{ R * ( D - T ) - Sqr[ D - T ] / 4 ) }                 ~     L1 = Sqr[ D - T ]      L2 = L1 / 4     L3 = R * ( D - T ) - L2     L   = SqRt{ L3 } To find the diameter of the ogive tip:      T = D - 2 * R + SqRt{ 4 * ( Sqr[ R ]- Sqr[ L ] ) }                  ~     T1 = Sqr[ R ] - Sqr[ L ]     T2 = SqrRt{ T1 * 4}     T   = D - 2 * R + T2     To find the diameter of the ogive base      D = T + 2 * R - SqRt{ 4 * ( Sqr[ R ]- Sqr[ L ] }                  ~      D1 = Sqr[ R ]- Sqr[ L ]      D2 = SqrRt{ D1 * 4 }      D   = T + 2 * R - D2

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