Semi-Ellipsoid Calculator

Name: Semi-Ellipsoid - Geometry Calculator
Author: Jürgen Kummer

Calculations at a semi-ellipsoid (or hemi-ellipsoid, or half ellipsoid). This is an ellipsoid, at which one axis is bisected along the other two axes. The halved axis becomes the whole axis of the semi-ellipsoid, while the other two axes or semi-axes remain unaffected.
Enter the bisected axis and the other two semi axes and choose the number of decimal places. Then click Calculate.

Formulas:

A \approx 2 π \cdot {(\frac{{(a \cdot b)}^{1.6075} + {(a \cdot c)}^{1.6075} + {(b \cdot c)}^{1.6075}}{3})}^{\frac{1}{1.6075}} + π \cdot b \cdot c

V = \frac{2}{3} \cdot π \cdot a \cdot b \cdot c

pi:

π = 3.141592653589793...

The axes 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.

As with the ellipsoid, the curved part of the surface of a semi-ellipsoid cannot be calculated algebraically and is estimated using Knud Thomsen's approximation formula. The area of the semi-ellipsoid is half the area of the ellipsoid plus the area of the ellipse at the intersection. The volume is exactly half that of the corresponding ellipsoid.
If the two semi-axes b and c are equal, then the semi-ellipsoid is a semi-spheroid. For a spheroid, an exact surface area calculation is possible. The surface area of the semi-spheroid is half the surface area of the spheroid plus the area of the circle at the intersection. If a is also the same length as b and c, then it is a hemisphere, where the calculation is much simpler.

The semi-ellipsoid is mirror-symmetric about two planes of symmetry, which run along the lines through a and b, and a and c, respectively. It is rotationally symmetric about the axis of rotation passing through a, at an angle of 180 degrees and multiples thereof. Unlike the ellipsoid, the semi-ellipsoid is not point-symmetric. A semi-spheroid has a higher level of symmetry than a semi-ellipsoid.

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