Mechanical models of cycling time-trial performance have indicated adverse effects of variations in external power output on overall performance times. Nevertheless, the precise influences of the magnitude and number of these variations over different distances of time trial are unclear. A hypothetical cyclist (body mass 70 kg, bicycle mass 10 kg) was studied using a mathematical model of cycling, which included the effects of acceleration. Performance times were modelled over distances of 4-40 km, mean power outputs of 200-600 W, power variation amplitudes of 5-15% and variation frequencies of 2-32 per time-trial. Effects of a "fast-start" strategy were compared with those of a constant-power strategy. Varying power improved 4-km performance at all power outputs, with the greatest improvement being 0.90 s for ± 15% power variation. For distances of 16.1, 20 and 40 km, varying power by ± 15% increased times by 3.29, 4.46 and 10.43 s respectively, suggesting that in long-duration cycling in constant environmental conditions, cyclists should strive to reduce power variation to maximise performance. The novel finding of the present study is that these effects are augmented with increasing event distance, amplitude and period of variation. These two latter factors reflect a poor adherence to a constant speed.