How to calculate the perfect gearing for individual pursuit on a 250 m velodrome

Choosing chainring and cog for individual pursuit on a 250 m velodrome is not intuition or copying last year's winner. It is a calculation of four coupled variables: target final speed, sustainable cadence, roll-out in metres per stroke, and gear ratio. When they line up, the athlete rides at their natural cadence for four minutes. When one fails, the dead spot shows up at minute three.

Starting point: target final speed

Before touching the chainring you must decide what time you are chasing. In a sub-4:15 men's IP the average speed is 56.47 km/h. Sub-4:10 demands 57.60 km/h. Sub-4:05 requires 58.78 km/h. For women's sub-3:20 over 3 km, the average is 54.00 km/h. These are not abstract numbers: they are the only valid input to calculate the correct gearing.

Average speed is a useful simplification, but a pursuit is not run at constant speed. There is a 10-15 s start above 60 km/h, a stabilisation phase at average speed, and a fatigue drift of 0.5-1.2% in the last kilometre. Gearing is chosen for cruise speed, not for the start.

The basic equation: metres per stroke and cadence

A gearing is expressed in metres advanced per pedal stroke:

With a 700c wheel and 23 mm tubular the effective diameter is 0.668 m. A 51-tooth chainring with a 14-tooth cog gives:

Target cadence closes the equation:

At 110 rpm with 7.64 m/stroke: 7.64 × 110 ÷ 60 = 14.01 m/s = 50.43 km/h. Not enough for men's IP. Move the chainring to 54, keep the 14: 8.09 m/stroke, 53.40 km/h. Still short. The 54×13 combination gives 8.71 m/stroke, 57.50 km/h at 110 rpm: right on the sub-4:10 target.

The sustainable cadence window

Cadence is not an aesthetic preference. It is bounded above by neuromuscular efficiency (past 120 rpm economy drops) and below by sustainable muscular torque (below 100 rpm on track the rider is pushing 400+ W of parasitic load). At world-class level the effective window is 105-115 rpm. Gearing that demands 118 rpm to reach target speed usually explodes at kilometre three.

Reference table: common gearings in 250 m IP

UCI roll-out and why measuring it matters

UCI regulations require the gearing ratio to allow the crank to turn without lockup. In specific events (kilo and 500 m) the minimum roll-out declared by the team before the race must be respected. Measurement is by roll-out: mark the floor, do a full pedal revolution with the bike straight and measure the displacement. If the declared roll-out is 7.85 m and the actual measurement is 7.79 m, the commissaire disqualifies. Picking up the gearing for the first time on race day is not an option.

The tubular's effect on real roll-out

Effective diameter changes with the tubular mounted. A Dugast Pista Cotton 22 mm at 10 bar deforms less than a Vittoria Pista 23 mm at 9 bar. Differences of 3-5 mm in effective diameter translate to 6-10 cm per stroke. Over 200 strokes of a 4 km pursuit that is 12-20 m. With times decided in tenths, this variation is not marginal: measure with a real roll-out of your race bike, not the catalogue's.

Start cadence vs cruise cadence

In the first 250 m the rider goes from 0 to cruise speed. Cadence starts at 60-70 rpm and climbs in 15 seconds to the target window. Too-long gearing extends the start phase, burns anaerobic W' and arrives late at cruise. Too-short gearing forces spinning above 120 rpm at cruise. Rule of thumb: pick the longest gearing you can start cleanly in under 15 seconds.

References: Corbett J. (2009), IJSPP. Underwood & Jermy (2010), Procedia Eng.. UCI Cycling Regulations, Part 3, Track Racing, art. 3.2.024.