Aerohed, the red and green templates are both based exactly on the clock face template you described. I made a circle, found its exact center, then projected a line from the center at 25°. I then traced that shape. This yields the templates I made.
I just analyzed these further and found some stuff out.
If I make a teardrop out of your "4 Seconds" diagram, I get a 2.75:1 shape using a semi circle as the front. The circular section on top travels through 25°. (Red)
If I make a teardrop that is 2.5:1 using a semi circle front, it yields a top circular section that travels 28° or 4.5 seconds after midnight. (Blue)
More questions & graphics later, I would like to nail this down pat as I'm sure many who are looking in on this would.