High-Wheeler Gear Calculator

Why The Penny Farthing's Wheel Got So Tall (And What It Teaches Modern Cyclists)

The arms race of the inseam: In 1878, the engineers building the first mass-produced Ordinary bicycles faced a constraint that sounds absurd today: the only way to make a direct-drive bicycle go faster was to make the front wheel bigger. There was no chain, no cassette, no derailleur — the pedals were bolted directly to the axle. One rotation of your legs equalled exactly one rotation of the wheel, so speed was purely a function of circumference. This created an extraordinary engineering feedback loop: wheel diameters climbed from 48 inches to 52, then 56, then 62, limited only by how far down a rider's legs could reach the pedals. Riders competed not just on the road but in the shop, ordering custom wheels a fraction of an inch larger than their rivals. The machine was, quite literally, designed around the proportions of the human body.

Gear inches and the gain ratio explained: The term "gear inches" survives from this era. It originally described the diameter of the Ordinary's front wheel directly — a 52-inch wheel gave you 52 gear inches, full stop. When chain-driven safety bicycles appeared in the 1880s, cyclists needed a way to compare their new geared machines to the familiar Ordinaries, so they asked: "What size wheel would give me the same distance per pedal stroke?" That hypothetical wheel diameter became the gear inch number. The gain ratio — popularised by the cycling historian Sheldon Brown — goes one step further: it divides wheel radius by crank arm length to give a dimensionless number representing true mechanical leverage. A 52-inch wheel with a 5-inch crank gives a gain ratio of 5.20, meaning your foot travels 5.2 times further than the wheel axle for each stroke. Higher ratios mean more speed for the same effort, but also more resistance when starting or climbing.

Why this matters for modern riders: The Ordinary's lessons are directly applicable to today's fixie and single-speed cycling renaissance. Track cyclists, urban fixed-gear riders, and velodrome racers all choose a single gear ratio and live with it — exactly as the Victorian wheelmen did. Understanding cadence (RPM) × gear size = speed is the foundation of all cycling fitness science. A 52-inch Ordinary at 60 RPM produces 9.3 mph. A modern fixed-gear track bike geared to 90 gear inches at 90 RPM reaches 16.1 mph. The mathematics are identical; only the hardware changed. This tool lets you explore where the Ordinary sits in that spectrum — and appreciate exactly what the Victorian racer was dealing with.

The riders who made it work: Victorian wheelmen were elite athletes by any modern standard. H.O. Duncan averaged 14.66 mph over 100 miles in 1887 on a 60-inch wheel — a sustained performance that would be respectable on a modern geared road bike. The Cyclists' Touring Club recorded members regularly covering 80–100 miles in a single day on Ordinaries over unpaved roads with no cushioning beyond a leather saddle. The constant cadence requirement (no coasting, no gear changes, no breaks from pedalling) built extraordinary cardiovascular fitness and leg strength. When the safety bicycle arrived with its chain drive, pneumatic tyres, and ability to coast, the old guard dismissed it as a machine for weaklings — and were promptly beaten in every race by riders who could, for the first time, actually rest their legs on a descent.