Calculations at a spindle torus. This is a torus, where the distance from the tube center to the torus center is smaller than the radius of the rotating circle, therefore R<r. It looks like a sphere with two opposite notches.
Enter distance and radius and choose the number of decimal places. Then click Calculate.
Distance, radius, breadth and height have the same unit (e.g. meter), the volume has this unit to the power of three (e.g. cubic meter).
A torus is the solid of revolution generated by a circle. However, the term typically refers to a ring torus, one in which the radius of rotation exceeds the radius of the circle itself, thereby creating a hole in the center. In contrast, with a spindle torus, the rotating circle overlaps itself. Consequently, no hole is formed, but rather a closed shape featuring central indentations at the top and bottom. The spindle torus can also be conceptualized as a rotating circular segment, specifically one whose height exceeds the radius of the circle, revolving around its central axis. Conversely, a rotating circular segment with a height smaller than its radius yields a shape referred to here as a spindle.
The spindle torus is, of course, rotationally symmetric and thus also mirror-symmetric with respect to any plane containing its axis of rotation. Furthermore, it is point-symmetric with respect to its center.
In contrast to the ring torus, the outer hull of the spindle torus is often not a stable form in nature. Rather, it typically undergoes rapid transformation shortly after its formation. Such a shape may appear momentarily, for instance, during the collision of bubbles or droplets. Surface tension and pressure subsequently drive a rapid reshaping, into a ring torus, a sphere-like form, or resulting in the disintegration of the structure. The underlying cause is the unfavorable distribution of surface curvature, which renders the structure energetically unstable.
