RAD

RESEARCH AND DESIGN

Performance Modelling Case Study

THE QUESTION

A tandem team was preparing for a world championship 4 km pursuit. We built a physics model of the race to estimate the finish time for a given power, and to find which changes were worth the most time. The model was calibrated against track data from a preparation camp in October 2026.

THE MODEL

The model steps through the race and balances the power produced against aerodynamic drag, rolling resistance, and drivetrain loss. Inputs:

Air density, 1.2 kg/m3 for the venue.
System mass, 150 kg for both riders and the bike.
Drivetrain efficiency, 0.96 to 0.97.
Rolling resistance (Crr), 0.002 to 0.004.
CdA for the steady-state position, and 1.5 times that during the standing start, when the riders are out of the saddle.
1,500 W for the first 15 seconds, then a steady power for the rest of the race.
Track geometry for a 250 m velodrome, plus a line offset: how far up the track the riders hold their line. The extra distance matters, as the results show.

Assumptions: both riders have the same drivetrain efficiency, Crr is constant even though tires scrub in the corners, and CdA does not change with speed.

CALIBRATING ON THE TRACK

Early in the camp the team rode an easy 5 km at about 455 W combined. Laps of 18.5 s were measured at 48.7 km/h on the black line and 49.4 km/h on the red line, at 87 to 88 rpm. We ran the model for two parameter sets, in bibs and jerseys with no socks or shoe covers:

Case	Crr	CdA	Model speed
High rolling resistance	0.004	0.23	49.4 km/h
Low rolling resistance	0.003	0.24	49.7 km/h

Both land within 0.3 km/h of the measured speed. Speed and power alone cannot separate CdA from rolling resistance, because a change in one can be traded against the other. That is why we also record tire pressure and wheel speed, and measure CdA directly in the field. Later in the camp the team rode flying kilometres on a 61x14 gear in 1:01.99 to 1:02.3, with laps between 15.3 and 16.0 s.

RACE SCENARIOS

We then ran the model for six race situations at about 767 W steady power. The first five use Crr 0.004 and drivetrain efficiency 0.96. The last uses the improved equipment values described below.

Scenario	CdA	Distance	Finish
Low head, black line	0.21	4,000 m	4:07.0
High head, black line	0.23	4,000 m	4:13.3
Low head, midpoint line	0.21	4,040 m	4:09.6
Low head, red line	0.21	4,087 m	4:12.2
High head, red line	0.23	4,087 m	4:18.6
Race trim, optimal	0.21	4,000 m	4:00.5

WHAT THE MODEL SHOWED

Head position. A 0.02 rise in CdA from a higher head costs about 6 seconds over 4 km at the same power.
Line. Every extra 40 m ridden costs about 2.6 seconds. Holding the red line instead of the black line costs about 5 seconds.
Equipment. New tires at high pressure (Crr about 0.002) and a better chain and wax setup (efficiency 0.97) are worth about 6.5 seconds together. At 120 psi the rolling resistance is about 15% higher than at 150 psi, so we track pressure loss.
Clothing. A base-layer speed suit and shoe covers should cut CdA by 0.02 to 0.03. One test found about 0.005 from a base layer alone.
CdA under load. One rider's CdA rose from 0.165 to 0.175 at high effort, mostly from shoulder rock. A slightly easier start with a stronger finish should hold CdA lower later in the race.
Gear. At the race-trim time, a 61x14 gear works out to about 107 rpm.
Model limits. Early estimates of system mass ran 5 kg high, and a rolling resistance of 0.004 was a conservative figure for worn, patched tires. No real race covers exactly 4,000 m, so the times show size of savings rather than a prediction.

THE CHARTS

Three panels of lines showing the steady power needed for finish times from 3:50 to 4:20 across CdA from 0.18 to 0.26, for line offsets of 0, 0.325, and 0.65 metres — Steady power needed for each finish time, by CdA and line (1,500 W for the first 15 s, start CdA 1.5 times steady).

Chart of required power divided by CdA against 4 km finish time for three line offsets, with shaded bands for CdA between 0.18 and 0.26 — Required power divided by CdA against finish time for each line. Shaded bands cover CdA from 0.18 to 0.26. Read across for your own CdA.

WHAT WE ARE WORKING ON

Holding a straighter line.
Keeping the head down.
Reducing shoulder scrunch and rock, the main cause of CdA rising under power.
Choosing the race gear, 61x14 or 62x14.
Reaching top speed faster after the start.
Consistency: a more even race is a faster one.
Recording tire pressure, ambient conditions, and wheel speed for every run.

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