Fraso / nomograms

Cycling

Gear inches

Chainring and sprocket against the gear they make.

A gear inches nomogram: three vertical scales, C (28 to 60) on the left, G (20.53 to 176) in the middle and S (9 to 36) on the right. A straight line laid across any two scales cuts the third at the value that satisfies G = 26.4 · C ÷ S.6058565452504846444240383634333231302928Cteeth9101112131415161718.22022242628303236Steeth176160140120100908070605045403630272420.53Gin

Readings

teeth
teeth
in

Drag the red line, or type into any two boxes — the third is solved. The marked box is the one being solved for.

Print at 100% scale, then check the 100 mm bar with a rule before trusting a reading.

Why this one is an instrument

Choosing gears is not a calculation, it is a comparison. You are never asking "what is 50 over 17" — you are asking whether the jump from 17 to 19 costs you more than the jump from 15 to 17, and whether a smaller chainring can be paid for at the back. On paper the whole cassette is one fan of lines and the gaps between gears are visible as gaps.

Equation
G = 26.4 · C ÷ S
Constants
Wheel Ø 26.4 in (700 × 25c)
Ranges
C 28–60 teeth · S 9–36 teeth
Reading
Any two values fix the third. Outside the printed ranges the instrument stops being valid — that is what the end marks are for.

These are drawn from the stated equation and nothing else. Where an equation is itself an approximation — hyperfocal distance and tap drill sizes both are — the instrument inherits that approximation exactly, no better and no worse.