The traditional or secant ogive is a surface of revolution of the same curve that forms a Gothic arch; that is, a circular arc, of greater radius than the cylindrical section ("shank"), is drawn from the edge of the shank until it intercepts the axis.
If this arc is drawn so that it meets the shank at zero angle (that is, the distance of the centre of the arc from the axis, plus the radius of the shank, equals the radius of the arc), then it is called a tangential or spitzer ogive. This is a very common ogive for high velocity (supersonic) rifle bullets.
A secant ogive of sharpness |
The sharpness of this ogive is expressed by the ratio of its radius to the diameter of the cylinder; a value of one half being a hemispherical dome, and larger values being progressively pointier. Values of 4 to 10 are commonly used in rifles, with 6 being the most common.
Another common ogive for bullets is the elliptical ogive. This is a curve very similar to the spitzer ogive, except that the circular arc is replaced by an ellipse defined in such a way that it meets the axis at exactly 90°. This gives a somewhat rounded nose regardless of the sharpness ratio. An elliptical ogive is normally described in terms of the ratio of the length of the ogive to the diameter of the shank. A ratio of one half would be, once again, a hemisphere. Values close to 1 are common in practice. Elliptical ogives are mainly used in pistol bullets.
Missiles and aircraft generally have much more complex ogives, such as the von Karman ogive.
In rocketry "ogive" has become a synonym of nose cone.
In later Gothic styles, an ogival arch is a decorative arch delineatng a void with a pointed head, formed of two ogee, or S-shaped curves.