Elliptical sprocket

This is Greg Kolodziejzyk setting a 24hr distance record with his home built boat Critical Power 2. I found one of Greg's earlier record setting vehicles when I was researching human powered vehicles. His efforts & his story were inspiring to me so I offered to machine him anything he needed on any future projects, this sprocket is what he asked for.

To see the full story of the water distance record: click here.

The concept behind an elliptically shaped sprocket is it gets bigger & harder to push (because it's transferring more power) when your leg is in its strongest part of the stroke.

At the point in your pedal stroke where you are the weakest you want the sprocket mounted so that the smallest diameter is engaging the chain. All those small holes around the center are so you can adjust the orientation of the sprocket relative to the pedals & "dial-in" your power position. The big sprocket was for the race boat, the little one was for the training bike.
This project shows the value of doing fun & interesting work, not just the stuff that makes you money - how do you calculate the circumference of an ellipse?
Calculating a circle is easy, but what about an oval? The circumference needed to be exact to fit the correct number of teeth, the spacing between adjacent teeth has to match the pitch of the chain, any mis-spacing between teeth or between the first & last tooth would ruin the smooth operation of the chain. This project provided the opportunity to solve that problem.