Modelling the start phase in individual pursuit: Gaussian power profile and anaerobic cost according to Boillet (2024)

Start01 Jun 20267 min readDr. Borja Alfaraz

Abstract. The Gaussian power model proposed by Boillet et al. (2024) for the start phase in individual pursuit on a velodrome is presented. The three parameters characterising the temporal profile —Pmax, time to peak and decay constant— are quantified across a sample of 34 world-class cyclists. The associated cost on the W' reservoir is derived, and implications for cruise phase pacing are analysed. Characteristic values by discipline are documented.

The chronometric contribution of the start phase in individual pursuit systematically exceeds the temporal fraction represented by this phase within the complete event. Although the first 250 metres constitute approximately 5% of total duration, the phenotypic manifestation of performance in the final phase remains conditioned by more than 40% by the technical and bioenergetic execution of the start (Boillet et al., 2024). The present article formalises the quantitative model applicable to pacing programming.

Characteristic start profile in world elite

The study by Boillet et al. (2024) analysed the instantaneous power profile registered during the start phase of 34 male world-class cyclists in individual pursuit. The mean curve identifies three reference points with biomechanical and bioenergetic significance:

Pmax: absolute maximum value of instantaneous power, ranging between 1,400 and 1,900 W as a function of the athlete's peak neuromuscular power.
t_peak: time elapsed between the start of pedalling and manifestation of Pmax, ranging between 5 and 7 seconds.
Decay phase: interval from Pmax to convergence with cruise power (400-480 W), of characteristic duration 8-10 seconds.

The complete profile describes an asymmetric bell: rapid ascent and progressive descent. Faithful reproduction of this pattern in simulation is essential. A start model assuming constant power from the initial instant overestimates W' consumption by approximately 15%, with consequent distortion of the budget available for the cruise phase.

Mathematical formulation of Boillet's Gaussian model

P(t) = P_cruise + (P_max − P_cruise) · exp(−((t − t_peak) / τ)²)

With τ = 4-5 s. Fitting the Gaussian model to individual empirical profiles reaches a coefficient of determination R² > 0.94 across 90% of the studied sample. The above expression constitutes the basis of the calculation implemented in AthletePro for start simulation: power is not assumed to stabilise instantaneously but is explicitly modelled as a temporally localised Gaussian bell.

Figure 1. Gaussian power profile during the first 30 seconds of an individual pursuit (Boillet 2024 model). Peak power manifests at 6 seconds and decays, over an additional 15 seconds, to cruise power.

Cost on the W' reservoir during the start phase

Integration of the function (P(t) − CP) during the first 15 seconds of exercise for a cyclist with CP = 400 W, Pmax = 1,600 W and t_peak = 6 s yields the following values:

0-6 s interval (ascending phase): 5,400 J above CP.
6-15 s interval (descending phase): 2,800 J above CP.
Total start cost: 8,200 J, equivalent to 36% of total available W'.

This expenditure does not admit operational discussion: it constitutes the inevitable bioenergetic cost of accelerating a 78 kg mechanical system (bicycle plus rider) from rest to 16 m·s⁻¹. Systematic omission of the start in W' budgeting leads to over-allocation of reserve for the cruise phase and underestimation of collapse risk in the final phase.

Critical analysis of the "conservative start" heuristic

The strategy of reducing Pmax to values close to 1,200 W with t_peak of 8 seconds —justified under the argument of "reserving W'"— presents lower W' consumption (approximately 5,500 J in 15 s), but incurs a quantifiable opportunity cost: time required to converge on cruise velocity is prolonged by 3-4 additional seconds. In events whose resolution occurs in tenths of a second, this delay constitutes an immediate net chronometric loss. Additionally, saved W' does not compensate for the penalty, given that real cruise power exceeds programmed value. The operational rule is stated as follows: execute the start with the Pmax sustainable with clean technique.

Technique of the first pedal strokes

An elite cyclist initiating execution from the starting gate applies the first two pedal strokes at cadences between 55 and 70 rpm on a gearing that at cruise velocity demands 110 rpm. This low-cadence and maximum-torque start is bioenergetically sustained by the phosphagen system (phosphocreatine), not by the W' reservoir. It therefore constitutes an energy source independent of the anaerobic lactic metabolic pool.

The operational implication is direct: cyclists who incorporate short sprint (series of 10 repetitions of 8 seconds maximum on track) into their training microcycle improve start execution without affecting sustainable aerobic power. Adaptation occurs at the level of the phosphagen system, not at W' level.

Characteristic values by discipline

Discipline	Characteristic Pmax	t_peak	Start W' expenditure
Male IP 4 km	1,600 W	6 s	8,000 J
Female IP 3 km	1,200 W	5 s	6,200 J
Male kilometre time trial	2,100 W	7 s	14,000 J
Female 500 m time trial	1,500 W	6 s	10,500 J
Team pursuit initial leader	1,550 W	7 s	8,800 J

Start simulation with the Boillet 2024 model

AthletePro Velometrics implements the Boillet Gaussian profile with configurable Pmax and t_peak parameters. Simulation quantifies exact W' expenditure at the start and the remainder for the cruise phase.

Start free trial

References: Boillet, A., Foissac, M., & Dorel, S. (2024). Modelling the pursuit start. Scientific Reports, 14, 12482. Corbett, J. (2009). An analysis of the pacing strategies adopted by elite athletes during track cycling. International Journal of Sports Physiology and Performance, 4(2), 195-205. Craig, N. P., & Norton, K. I. (2001). Characteristics of track cycling. Sports Medicine, 31(7), 457-468. Broker, J. P., Kyle, C. R., & Burke, E. R. (1999). Racing cyclist power requirements in the 4000-m individual and team pursuits. Medicine and Science in Sports and Exercise, 31(11), 1677-1685.