Oblique Cylindrical Shell Calculator

Name: Oblique Cylindrical Shell - Geometry Calculator
Author: Jürgen Kummer

Calculations at an oblique cylindrical shell (or oblique hollow cylinder). This is an oblique cylinder, of which another oblique cylinder with the same slope and height, but smaller radius is centrically removed.
Enter both radiuses, the angle and side length or height. Choose the number of decimal places, then click Calculate. Please enter angles in degrees, here you can convert angle units.

Formulas:

h = a \cdot \sin (α)

A = 2 π \cdot [(R + r) \cdot a + (R^{2} - r^{2})]

V = π \cdot (R^{2} - r^{2}) \cdot h

pi:

π = 3.141592653589793 ...

Radiuses, length and height have the same unit (e.g. meter), the areas have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter).

Such a shape is not produced by making an oblique cut across a straight pipe, that is a straight cylindrical shell. In that case, the cut surfaces would be elliptical rings rather than circular rings (annulus), resulting in an elliptical cylindrical shell. For a shape with an oblique cut through a straight cylindrical shell, see cut cylindrical shell. If the two oblique cuts are parallel, the resulting elliptical cylindrical shell can be viewed as being composed of two equal cut cylindrical shells.

The oblique cylindrical shell has the same symmetry properties as the oblique cylinder, so it lacks axial symmetry. It also lacks rotational symmetry, thus it is not a solid of revolution. However, the oblique cylindrical shell possesses point symmetry about its center point. This center point lies at half-height, in the middle of the two circles forming the cross-section parallel to the two bases.

This shape is rarely encountered in engineering and construction, though it is used intentionally when it does appear. Often, straight pipes are simply cut at an angle. Pipes shaped as oblique cylindrical shells are custom-made for specific purposes, such as connecting elements between parallel, inclined surfaces, or as inclined pipes linking such surfaces where the inlet and outlet must be circular.

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