Thursday, February 25, 2010
Here’s how it works: imagine the yellow arrows poking into the entire surface of the toroid—not just the outside spherical portion but from the within the funnel areas, too. Now visualize the surface of the toroid in motion, flowing out the bottom of the funnel, around the outside, and back through the middle (as depicted by the white arrows in the drawing below). Keep in mind that, despite the cross-sectional views we see here, the flow is actually taking place along the entire outside spherical surface, flowing up and over the rounded hemispheric region and down into the increasingly constrained funnel, passing through the point at the center. As the inward-poking arrows slide over the lip of the funnel and begin flowing down into the funnel, the inward-from-rim-toward-center direction flips over to become the center-pointing-outward direction.
Not only does the cohesive, inward force now appear to be a repulsive, outward force, the force itself is compressed from that generated over the entire spherical surface to a tremendously concentrated, singular point exploding outward in all possible directions into the interior of the toroid.