Determining optimal cadence for an individual road cyclist from field data

Figures & data

Figure 1. Means for each training session for each rider. Rows correspond to power output (watts), heart-rate (bpm), cadence (rpm), and duration (minutes); columns corresponding to riders 1–4.

Figure 2. Power output (watts) vs. cadence (rpm) and heart-rate: (a,b) rider 1; (c,d) rider 2. Solid line: fitted, expected power output from the model equation (1) with heart-rate 151 bpm (rider 1), 139 bpm (rider 2); heart-rate lag 30 seconds.

Table I. Coefficient estimates (standard errors in parenthesis) and explanatory power for the power output/heart-rate model, equation (1), for each rider and for different values of heart-rate lag, l.

	l	α	β	γ	log μ	R^2	AIC
Rider 1	1	1.58 (0.01)	0.021 (0.0005)	0.91 (0.06)	−4.59 (0.29)	84.0	69,664
	2	1.56 (0.01)	0.020 (0.0005)	0.90 (0.06)	−4.51 (0.31)	84.2	70,919
	6	1.53 (0.01)	0.018 (0.0006)	0.77 (0.07)	−3.88 (0.33)	85.9	72,600
	12	1.51 (0.01)	0.017 (0.0006)	0.71 (0.07)	−3.55 (0.35)	85.8	72,727
Rider 2	1	1.66 (0.02)	0.024 (0.0008)	0.75 (0.08)	−3.71 (0.42)	74.7	50,095
	2	1.65 (0.02)	0.024 (0.0009)	0.84 (0.09)	−4.15 (0.44)	75.9	50,659
	6	1.61 (0.02)	0.023 (0.0010)	0.61 (0.10)	−2.99 (0.49)	76.5	51,362
	12	1.56 (0.02)	0.020 (0.0010)	0.28 (0.11)	−1.36 (0.51)	75.7	52,218
Rider 3	1	1.17 (0.03)	−0.0015 (0.001)	1.06 (0.14)	−5.19 (0.68)	58.9	32,595
	2	1.13 (0.03)	−0.0033 (0.001)	1.05 (0.14)	−5.14 (0.70)	61.2	33,024
	6	0.99 (0.03)	−0.0095 (0.001)	1.23 (0.15)	−5.95 (0.75)	63.5	33,228
	12	0.95 (0.04)	−0.0113 (0.002)	0.92 (0.15)	−4.45 (0.75)	63.6	33,156
Rider 4	1	0.15 (0.03)	−0.0007 (0.002)	1.47 (0.14)	−2.59 (0.69)	8.7	82,794
	2	0.09 (0.03)	−0.0055 (0.002)	0.09 (0.15)	−4.08 (0.77)	9.2	83,476
	6	0.18 (0.04)	−0.0020 (0.002)	1.47 (0.16)	−2.84 (0.78)	11.1	84,747
	12	0.20 (0.04)	−0.0012 (0.002)	1.72 (0.17)	−4.25 (0.82)	12.6	85,994

Table II Fitted, expected power output for model (equation 1) for a range of cadences above and below the statistically optimum cadence, along with the percentage reduction in power output for each sub-optimal cadence. Rider 1 (left) and rider 2 (right), for heart-rate lags of 30 seconds, at heart-rates of 151 and 139 beats per minute for riders 1 and 2 respectively.

Change in C from C*	Cadence	Expected power output	Change in power output	% change in power output	Change in C from C*	Cadence	Expected power output	Change in power output	% change in power output
−20	63.4	178.2	−9.6	−5.1	−20	50.4	174.9	−14.7	−7.7
−10	73.4	185.5	−2.2	−1.2	−10	60.4	186.2	−3.4	−1.8
−5	78.4	187.2	−0.5	−0.3	−5	65.4	188.8	−0.8	−0.4
0	83.4	187.8			0	70.4	189.6
5	88.4	187.3	−0.5	−0.3	5	75.4	188.8	−0.7	−0.4
10	93.4	185.9	−1.9	−1.0	10	80.4	186.8	−2.8	−1.5
20	103.4	180.8	−7.0	−3.7	20	90.4	179.5	−10.1	−5.3