Half Capsule Calculator

Name: Half Capsule - Geometry Calculator
Author: Jürgen Kummer

Calculations at a half capsule, a lengthwise halved capsule. This consists of two quarter spheres of equal size with a matching half cylinder in between.
Enter radius of the sphere and height of the cylinder and choose the number of decimal places. Then click Calculate.

Formulas:

l = h + 2 r

A = π r \cdot (2 r + h) + 2 r h

V = \frac{π}{2} r^{2} \cdot (\frac{4}{3} r + h)

pi:

π = 3.141592653589793 ...

Radius, height and length have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The half capsule is the result of one of two methods for dividing a capsule into two equal parts. In this method, the division occurs horizontally, bisecting the capsule lengthwise. The other method, a vertical division, produces an elongated hemisphere.

Such a half capsule has two surfaces. A flat surface in the geometric shape of a stadium, and a curved surface. The curved surface, in turn, consists of the lateral surface of a half cylinder and the calotte of a hemisphere, which merge into one another without any edges. The volume is the sum of the volumes of these two solids. A longitudinal central cross-section through the half capsule yields a half stadium. A cross-section taken widthwise yields a semicircle, no matter where it is taken.
The half capsule is axially symmetric with respect to this longitudinal cross-sectional plane. There exists a second plane of symmetry, perpendicular to this cross-sectional plane, located at the midpoint of the half capsule. Furthermore, this shape exhibits rotational symmetry upon a rotation of 180 degrees, or any multiple thereof, about the line formed by the intersection of these two planes of symmetry.

A half-capsule possesses moderately favorable aerodynamic properties. However, it rarely appears in this specific form as a vehicle shell, as such shells are subject to additional requirements. Certain components where aerodynamics play a role are designed in a similar manner, for instance, the cockpits of combat aircraft, though in those cases, the shape is flatter and asymmetrical.

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