Cone ratio

Sketch of the cone ratio

The technical description of a cone shape is called the cone ratio . The cone taper can be specified either as a cone ratio or by the included cone angle . It is calculated from the difference between two diameters and divided at the cone by the distance between these diameters: ${\displaystyle C}$ ${\displaystyle 1:x}$ ${\displaystyle \alpha }$ ${\displaystyle D}$ ${\displaystyle d}$ ${\displaystyle L}$

${\displaystyle C={\frac {D-d}{L}}.}$

Common cone ratios are, for example, 1:50 in mechanical engineering or 1:20 for brass instruments (mouthpiece shaft).

The cone ratio also includes the cone angle α, which describes the opening angle of the cone. In the drawing on which is the opposite side to the half angle equal to the toned right triangle , the adjacent side equal . The mathematical relationship between the tangent (= opposite side through adjacent side) of half the opening angle and the taper ratio is therefore: ${\displaystyle \alpha /2}$ ${\displaystyle (D-d)/2}$ ${\displaystyle L}$

${\displaystyle \tan \left({\frac {\alpha }{2}}\right)={\frac {D-d}{2\cdot L}}={\frac {C}{2}}.}$

Individual evidence

• Hans Hoischen, Wilfried Hesser: Technical drawing . 30th edition. Cornelsen Verlag, Berlin 2005, ISBN 3-589-24110-1 , pp. 134 f .