Re: The physics of a mooring ball...
Not exactly your question, but possibly of interest?
Cruising off the grid (uncharted atoll interiors) we found we could not use traditional anchoring techniques when anchored in sand with large coral heads rising to near the surface (10 feet down in 30 to 50 feet of water) around the sandy spot. As the tide changed we would wrap the chain around one or more heads in a day and end up with zero scope.
I switched to a short chain of 30 feet and line from there. After setting the anchor I would use a large fender to float the chain as high as possible and place smaller floats on the line at intervals of about 10 feet.
It worked like a charm, never dragging and no more wrapping around the coral heads.
"Any idiot can make a boat go; it takes a sailor to stop one." Spike Africa aboard the schooner Wanderer in Sausalito, Ca. 1964.