New World Man

Today I learned how to use a slide rule. I didn't build a bridge, it was for something much less complicated. I was thinking about gear ratios on my bike.

For Saturday's ride my bike was equipped with a 46 and 30 tooth double chainrings and a 14-28 six speed freewheel. One of my fellow riders commented that I would have trouble on the hills without triple chainrings. My thinking when I built my bike was a 30/28 low gear, which is about a 29 gear inch, is plenty low. Probably lower than many of the triple chainring roadbikes out there today. For example, take a look at a current Dura Ace or Ultegra triple crank. The "granny" gear is a 30, and coupled with a 25 in the back, you get a about a 32 gear inch, so my little gear is easier.

And I was right, I picked a good range for me. Saturday I could climb all the hills with no more difficulty than I expected. I'm no Michael Rasmussen and don't expect to be. But I thought about optimizing my gear choices, and how to maximize available gears as much as possible minimize overlap. Here's where the slide rule came into action.

A slide rule allows you to compare ratios of numbers. For basic math, most of us know that 1/2, 5/10 and 10/20 all represent the same number. But if you have 52 and 39 tooth chainrings, do you know which gears on the 52 are the same as those on the 39? With the slide rule, we can calculate 52/21 is the same as 39/16, 52/19 the same as 39/14, 52/17 the same as 39/13. So you see that with a typical road bike set up you don't get the promised 20 gears. You get something more like 13 different gears. I can't push a 52/12, so for me I'd have even fewer. And with a short chainstay bike you have even fewer gears because as the chain moves from the inside cog to the outside cog (or vice versa) while not changing to the other chainring, the chain noise gets louder and louder. That's because the chain is no longer parallel to the chainring and cogs. Much of what I've read on the web that includes science and/or engineering indicates that this does not increase friction but it is annoying.

So what did I calculate with my slide rule? With my current freewheel I can have 46 and 24 tooth chainrings and have fewer overlaps. If I went up to a 50 chainring I could have no overlap, but a) I don't have a derailer that can handle that difference and 2) a fifty is too big for me on this bike anyway. So I'll stick with my gearing on this bike, but I may break out the slide rule again when I find a 14-32 freewheel on eBay.