How to Use a Slide Rule as a Bicycle Gear Chart

Anyone who has an old dusty slide rule lying around that they are not sure how to use may be interested to know that slide rules are great for doing gear calculations too. Seriously.

Let F be front chainwheel size, that is, number of teeth. Let R be rear sprocket size, that is, number of teeth.

Gear ratio measurement values discussed here must be those obtained by using a formula of the form W*F/R.[*] In the case of "gear inch" measurements, W is simply the wheel diameter in inches. In the case of "metres of development", W is PI multiplied by the wheel diameter in metres. Etc.

So, the method is simply to determine W, and then:

Line a given value F, a chainwheel size, on the scale CI(C inverse), with W on the D scale. Values on the D scale now correspond to sprocket sizes, which line up with their corresponding ratio measurement on the CI scale.

[*]Gear ratios can be measured using the form W*R/F. An example of this might be measuring them by determining the cadence theoretically necessary to maintain 20mph in each particular gear. This probably isn't particularly useful, not even for ==>tandems<==.

You can also use the C and D scales. Line up W on the C scale with R on the D scale. Now, each chain wheel size on the D scale lines up with its corresponding gear ratio value on the C scale.

While this has the virtue of avoiding the difficult-to-use CI scale, which necessitates using the cursor, it has the disadvantage that you cannot read off the values for eight sprockets at a time without moving the slide, as can be done by using the CI scale.

Sheldon Brown of Newtonville Massachusetts ( adds the following observations:
From!CaptBike Sun Oct 16 14:19:06 1994 From: To: Subject: Slide rules & ==>tandems<== To find sprocket combinations that will yield a desired gear value, set the desired gear (C scale) above the wheel size (D scale) Any chainwheel value on the C scale will be right over the rear sprocket value on the D scale that will yield the desired gear. On further consideration, the previous message on slide rules is correct for solos, but for ==>tandem<== applications you should use the A & B scales instead of C & D. The A & B scales have a whole cycle for the captain, plus another for the stoker! Using the C & D scales as I indicated doesn't work so well for gears over 100", a serious problem for those of us who ride twofers.