General Cycling Discussion - Sprocket sizes: Twist on an old debate

I've read repeatedly that a small sprocket will cause a reduction in transmission efficiency, especially at very small sizes. My question is, is it the small size of the sprocket or the limited number of teeth that matters more?

I ask because I have a unique bicycle with an expanding front sprocket. It's called the "Yankee Bicycle" and was featured in Popular Science about 20 years ago. The sprocket consists of six segments, two of which have teeth and four of which are idlers. The segments expand and retract along arms that radially extend from the bottom bracket axle. It can approximate the sizes of traditional sprockets ranging from 32 to 56 teeth, but it does so in shape of a hexagon, rather than a circle. It only touches the chain at a few points (at the points of the hexagon), unlike a traditional sprocket.

Here's a link (http://ustimes.com/Bicycle/) (not mine). In addition, here's an image: http://ustimes.com/Bicycle/geardrive.jpg

I presume that there's some transmission efficiency lost because of the design, but can't figure out whether it's to the same degree as for a traditional small sprocket.

I've read repeatedly that a small sprocket will cause a reduction in transmission efficiency, especially at very small sizes. My question is, is it the small size of the sprocket or the limited number of teeth that matters more? ....
It has to do with both.
The loss is related to the amount of angle that the links have to turn to run around the sprocket. Larger sprocket = less angle and shorter links = less angle, though it is difficult to find roller-link chain that's less than 1/4" pitch or so.

I remember seeing that gear setup in the print magazines at the time, but never saw any in real life.
I don't think I'd worry about the chainline efficiency so much as I'd wonder about the long-term reliability (especially since new parts probably aren't available now...).

By looking at the thing I would say it's destined for failure, no wonder it didn't make it very far.

By looking at the thing I would say it's destined for failure, no wonder it didn't make it very far.

Oh how can your say that? It's clearly made of "hard steel", not that soft and floppy kind.

For maximum efficiency, you need one of these:
http://i192.photobucket.com/albums/z172/stephenhazelton/MiscBike2011/DSCN1306_191.jpg

For maximum efficiency, you need one of these:
http://i192.photobucket.com/albums/z172/stephenhazelton/MiscBike2011/DSCN1306_191.jpg

That'd put some good sprocket gouges into your calf when you wreck...