Evaluating pedaling strategy using a principal component analysis-based analysis of crank force vectors collected during outdoor cycling

2.1. Participants

Participants who cycled regularly and had available pedaling force vector data were randomly selected from data registered in SHIMANO CONNECT Lab. Participants with the Professional (Pro) attribute were recruited separately. Of the total 91 participants, 16 possessed Pro attributes. Data were extracted from participants’ outdoor activity records by Shimano Inc. in accordance with a joint research agreement between Kansai Medical University and Shimano Inc. The data were anonymized and provided to Kansai Medical University, where the analysis was conducted. Comprehensive consent was obtained from participants at the time of registration in the SHIMANO CONNECT Lab, and the study was approved by the Medical Ethics Review Committee of Kansai Medical University (Reference Number 2024287).

As participant background factors such as height, weight, age, and sex were anonymized, functional threshold power per body weight (FTP/BW; W/kg) and ride frequency (rides/week) are shown in Table 1 to provide an overview of individual fitness levels. Ride frequency is shown only for participants who do not have the Pro attribute.

2.2. Analysis methods

The overall analysis method was as follows.

2.2.1. Data extraction for analysis

Pedal force vectors were measured at 30° crank angle intervals using a pedaling monitoring system such as crank-based power meters (Shimano Inc., FC-R9200-P, FC-R8100-P) [5] or pedaling monitor system (Pioneer, SGY-PM900 and SGY-PM910 series). Sensor accuracy was ensured through zero-offset calibration performed prior to use, as well as through factory calibration using known loads conducted by the manufacturer.

As shown in Figure 1, analysis data (219 cases, including 42 from participants with Pro attributes) were extracted from participants’ outdoor activity records by excluding inappropriate records, removing identical left-right data, and dividing the remaining data into multiple datasets according to the conditions for each left and right measurement. Specifically, the following data were excluded: (1) the first and last 15% of the entire activity, corresponding to warm-up/cool-down, (2) out-of-saddle pedaling sections (the so-called dancing state), (3) noise and outliers (data outliers). Furthermore, when groups of data with differing variances were identified within the same record, the data were divided into multiple datasets according to the conditions.

Figure 1

2.2.2. Slope calculation

For each participant, the instantaneous pedal force at each angle with respect to the workload variation was expressed using a regression equation based on the least-squares method.

(1)

$$F_i(\theta )=a_i(\theta )\overline{F_i}+b_i(\theta )+e$$

Here, F _i (θ) represents the instantaneous pedal force at angle θ for the ith dataset. The angle-specific slope a _i (θ) and intercept b _i (θ) are expressed with respect to changes in the mean pedal force represented by $\overline{F_i}$. The term e represents the residual error. For each crank angle $\theta$, the instantaneous pedal force F _i (θ) was regressed against the mean pedal force $\overline{F_i}$ and the coefficients a _i (θ) and b _i (θ) were determined by minimizing the sum of squared residuals e. This slope was calculated for both tangential and radial components as values relative to the mean pedal force corresponding to the tangential pedal force.

An example of slope calculation, with the mean pedal force divided into six groups, is shown in Figure 2. Figure 2(a) shows waveforms for each group, with measured crank angles at 30° intervals on the horizontal axis and the instantaneous pedal force on the vertical axis. The results of plotting the mean pedal force on the horizontal axis and the instantaneous pedal force at each angle on the vertical axis are shown in Figure 2(b). This figure demonstrates that the instantaneous pedal force at each angle can be approximated well by a linear function with respect to increases in the mean load. The validity of the regression calculation was assessed by calculating the root mean square (RMS) error and examining the error distribution and magnitude.

Figure 2

2.3. Statistical analysis

Statistical analyses were performed to compare PC1 and PC2 scores between professional and nonprofessional participants. Differences in central tendency were assessed using the Wilcoxon rank-sum test, and differences in dispersion were evaluated using the Brown–Forsythe test. The significance level was set to p < 0.05. All statistical analyses, including PCA, were conducted using JMP Student Edition 18.2.0.

3.1. Evaluation of participants and data preprocessing

As shown in Table 1, participants with Pro attribute exhibited sufficiently high FTP/BW characteristics, showing a difference from those of participants without Pro attribute. Participants without Pro attribute rode regularly (2–5.5 times/W per week), and their FTP/BW indicates they were intermediate to advanced hobby racers.

Figure 3 presents the mean load (power) for 219 cases. The quartile values and median were 80.4–93.9–107.0 (W), which corresponds to approximately 200 W when converted to the total output from both legs. The dataset also included a wide range of workload outputs, from a minimum of 23 W to a maximum of 362 W (both legs combined).

Figure 3

3.2. Evaluation of slope values

Linear regression was performed for both radial and tangential directions at each angle for pedal force data from 219 cases to calculate slope values. The logarithmic distribution of the RMS error, representing the residuals of the regression calculation, closely approximated a normal distribution, and no difference in variance was observed across angles. Therefore, the mean ± standard deviation (SD) in the logarithmic distribution of the RMS error was calculated and back-transformed. Figure 4 presents the mean value and values corresponding to mean ± SD values of the RMS error for each angle from 0° to 330° and overall.

Figure 4

3.3. Principal component analysis

PCA was performed using slope data at 30° intervals for both radial and tangential directions, yielding 24 points per dataset of the 219 cases. Table 2 shows the eigenvalues and cumulative contribution ratios for the top four principal components and the standard deviation as distribution information for principal component values. The results showed that eigenvalues exceeded 1 for principal components up to PC3, and the cumulative contribution ratio reached 64.6% for PC1 and PC2 combined, and 83.4% for PC1 through PC4.

Figure 5 shows the baseline waveform $\overline{a}(\theta )$ on the left axis and the angle-specific slope waveforms PC ₁(θ) and PC ₂(θ) on the right axis. Panels (a) and (b) show tangential and radial components, respectively.

Figure 5

3.4. Pedaling strategy by principal component value differences

The results of pedaling characteristics for each of the five types described are shown in Figures 6 and 7. Figure 6 shows pedal force waveforms when pedaling at workloads virtually equivalent to 100, 200, and 300 W for both legs combined, with (a) tangential and (b) radial forces. In the figures, Type 1 is positioned at the center, Types 2 and 3 (which vary only in PC1) are positioned on the right and left, and Types 4 and 5 (which vary only in PC2) are positioned above and below, enabling easy comparison with PC1 and PC2 magnitudes, similar to a scatter plot.

Figure 6

Figure 7

In addition, Figure 7 presents pedal force vectors at 200 W for each type in the same arrangement as shown in Figure 6, plotted according to the pedal position at that moment in a circular representation. From these figures, it can be observed that, compared to Type 1 (average pedaling in the center), Type 2 on the right has less downstroke force and stronger upstroke force, Type 3 on the left is dominated by downstroke force, Type 4 above demonstrates delayed timing for downstroke force, and Type 5 below exhibits early timing for downstroke force.

Figure 8 shows a scatterplot of PC1 and PC2 for each participant. In the figure, participants with Pro attribute are indicated by ○ and non-Pro participants by ●. The × marks indicate the center of the two principal components and points at distances of ±σ _k from the center for PC1 and PC2, representing the principal component values for the five pedaling types.

Figure 8

3.5. Statistical test results for principal component value differences

Statistical comparisons between Pro and non-Pro participants were performed using the Wilcoxon rank-sum test for central tendency and the Brown–Forsythe test for variability. For PC1, the median (p < 0.0001) and variability (p = 0.0007) differed significantly between the Pro and non-Pro participants. In contrast, for PC2, no significant difference was observed in the median, whereas variability differed significantly (p < 0.0001). Detailed results are presented in Table 3.

4.1. Data conditions

The data analyzed in this study were extracted from outdoor cycling sessions. While the typical workload during outdoor activities was approximately 200 W, data of extremely high or low workloads were also included, representing a wide range of pedaling conditions. Although the RMS error values (shown in Figure 4) varied in magnitude across angles, the mean value was approximately 1–3 N (at most less than 10 N), which was sufficiently small compared with the average load of 100 W (shown in Figure 3) for regression calculations. Thus, even for outdoor cycling data measured in various outdoor environments, the linear relationship between the instantaneous pedal force variation at each angle and workload variation was well maintained, and slope calculation through linear approximation could be appropriately performed for most participants by properly extracting pedaling data during cycling.

In addition, as the present method relies on the slope of pedal force with respect to total load, systematic errors in sensor sensitivity are expected to be largely canceled out, representing an advantage of this approach.

4.2. Results of principal component analysis

PCA using all calculated slope values (24 degrees of freedom in total: 12 elements at 30° intervals for both radial and tangential directions) demonstrated that each participant’s pedaling strategy characteristics could be explained primarily by approximately four principal components based on eigenvalue magnitudes and cumulative contribution ratios (shown in Table 2). In the PCA conducted in this study, data were mean centered but not scaled. This approach was adopted because the importance of pedaling force inclination varies across crank angles; for example, angles where pedaling force is large have a high impact, while regions such as the top dead center have a low impact. Therefore, the study aimed to preserve the influence of inclination at each crank angle as is. In this study, we focused on the fact that the cumulative contribution ratio of the top two principal components (PC1 and PC2) was sufficiently large at 64.6% and conducted subsequent analyses considering that important characteristics of the pedaling strategy are contained in these principal components. Incorporating PC3 and PC4 increased the cumulative contribution ratio to 83.4%, enabling a more detailed analysis of the pedaling strategy; however, analysis of higher-order principal components remains a topic for future research.

4.3. Pedaling strategy represented by principal component values

The pedaling strategy represented by PC1 differed between Types 2 and 3, indicating a coordinated force application between the downstroke and upstroke legs.

From the changes in pedal force vector waveforms (shown in Figure 6), the increase in the tangential force during the downstroke phase (30°–150°) with increasing load was greater for Type 3 than for Type 2. Conversely, during the leg pull-up phase (210°–330°), the negative pedal force due to decreases in leg weight in Type 2 (particularly at a high load of 300 W, where the pedal force is nearly zero), whereas Type 3 shows no change in pedal forces. Similarly, in the radial direction, Type 3 generated larger pedal forces than Type 2, resulting in a greater nonpropulsive force. Furthermore, Type 2 produced a tangential component output of the pedal force vector for a prolonged duration, reflecting a pedaling strategy that effectively converts forces to propulsion. In contrast, Type 3 responded to increased load only with downstroke forces, generating downward vectors that resulted in inefficient pedaling with large pedal forces near the bottom dead center but with little propulsive component. Thus, the pedaling strategy represented by PC1 reflected the overall coordination of force application between the downstroke and upstroke legs, and higher PC1 values indicated a more effective pedaling strategy.

As shown in Figure 6, at 300 W load, the angle at which the maximum pedal force is achieved is 110° (late) for Type 4 and 90° (early) for Type 5. Additionally, as shown in Figure 7, the direction of pedal force vectors is diagonally backward near the bottom dead center for Type 4 and diagonally forward during downstroke phase for Type 5, generating a more propulsive force than Type 3 but relatively low overall efficiency. Thus, the pedaling strategy associated with PC2 manifests as differences in downstroke timing, and excessively early or late timing reflects a suboptimal pedaling strategy.

Thus, PC1, which represents coordinated force application during downstroke and upstroke, and PC2, which represents differences in downstroke timings, can be used as indicators of the pedaling strategy.

4.4. Evaluation of pedaling strategy using principal component values

Figure 8 shows a scatter plot of PC1 and PC2 values. While non-Pro participants (●) are widely distributed, participants with Pro attribute (○) are concentrated in a narrow region with positive PC1 values and PC2 values centered around zero, and the principal component values for Type 2 align with the center of this region. Table 3 shows that statistically significant differences were observed between professional and nonprofessional participants in the distribution of principal component values (PC1 and PC2). Thus, the pedaling strategy of participants with Pro attributes primarily exhibited Type 2 characteristics, which can be considered a desirable pedaling strategy that produces stable propulsion by coordinating force application between the downstroke and upstroke legs based on PC1.

Previous research has also shown that in elite cyclists’ pedaling movements, negative forces that were present at low loads increased to nearly zero as upstroke movement increased at higher loads [20]. Moreover, in the pedaling strategies of cyclists at different competitive levels, professional cyclists showed a smaller minimum downstroke force with increasing load compared to recreational cyclists [19]. These findings support Type 2 as a desirable pedaling strategy.

Conversely, when PC2 values deviate from the moderate range, the timing of the pedal downstroke under increasing load becomes either too late or too early, resulting in a pedaling strategy with poor overall efficiency that cannot be considered desirable pedaling. Previous research has reported that more experienced cyclists have more stable and relatively less variable pedal force timing and waveforms [24], and in elite cyclists’ pedaling movements, the crank angle at which the maximum load force appears gradually decreases [20]. These findings suggest that consistent control and stability are essential conditions for better pedaling.

Thus, Type 2 pedaling with positive PC1 and PC2 values near zero is considered a “desirable pedaling strategy”. Using the PCA method proposed in this study, individual cyclists’ pedaling strategies can be evaluated based on PC1 and PC2 values.

4.5. Comparison with conventional efficiency indices

Studies evaluating the IFE, which has been used as a pedaling technique indicator [16,17], focused on the leg pull-up movement and reported that while a constant pull-up movement increases the IFE, the physiological cost of the pull-up movement is high and decreases GE. In addition, the IFE does not necessarily represent effective or performant pedaling [18]. However, previous studies were conducted under artificial conditions with intentional emphasis on pull-up movements at constant load. The pedaling strategy observed in this study, “increasing pull-up movement in response to increased load”, differs from the constant pull-up movement observed in previous studies and can be interpreted as situation-adaptive motor control for maintaining power output, which is not contradictory to previous research findings. Rather, the present study findings indicate a realistic pedaling strategy: “under outdoor cycling conditions”, “with naturally varying load”, and “pull-up movement increases only to the minimum necessary level in response to increased load”. Specifically, at a low load, power was generated primarily through a downstroke movement without a significant pull-up movement; at a moderate load, the pull-up movement gradually increased in a supplementary manner; and at a high load, the pull-up movement increased while minimizing efficiency loss. This indicates that a “pedaling strategy of pulling only when and as much as necessary” is effective, representing a novel finding.

Thus, the efficiency index (IFE), which is conventionally used to evaluate pedaling techniques using values at a specific point in time, does not capture the pedaling strategy in response to varying loads. In contrast, the “principal component values calculated from slopes against load increase” proposed in this study can quantify the characteristics of the pedaling strategy and therefore represent a conceptually new type of indicator.

4.6. Limitations of the current study

This study included only 91 participants, and data of 219 cases were used in the final analysis when the left and right legs were analyzed separately. Furthermore, participant cadence was not restricted, and pedal force, rather than power values, was used directly for analysis. Moreover, outliers were excluded through data preprocessing, and mean values were divided into six levels for slope calculation. Nevertheless, linear regression performed well even with such limited pedaling data, and a wide range of pedaling strategies could be analyzed using principal component values from all calculated slope data, indicating that the analysis method proposed in this study is sufficiently robust. However, the current analysis method does not consider measurement-related issues, such as measurement variability in outdoor cycling data, inconsistent measurement conditions, and systematic errors in pedal force sensors, as well as the effects of participant saddle height, gear ratio, crank length, and cadence; furthermore, the potential confounding effects of these factors were not explicitly controlled for in this study. In addition, because the participants regularly ride bicycles equipped with pedal force vector sensors, a selection bias may be present, as such individuals are likely to be more conscious of their pedaling and may therefore represent a relatively more skilled cycling population.

Additionally, because only two principal components were used for evaluation in this study, there may be room for expressing pedaling strategies through higher-order principal component terms that were not addressed.

Furthermore, because this study was an observation-based retrospective data analysis and focused on proposing an analysis method, all obtained data were used for analysis, and validation with external data was not performed. Therefore, future research should evaluate the validity and appropriateness of the method proposed in this study by analyzing pedaling data from participants with clearly established pedaling characteristics or by comparing participant pedaling characteristics with measurement data obtained from other tools to quantify pedaling characteristics.

4.7. Possibilities for future research

As mentioned in Section 4.6, several research constraints necessitate caution when directly generalizing the findings of this study to other cyclist populations or data measured in external environments.

This study proposes the principal component values as a hypothesis. By comparing with values from other measurement devices used in laboratories, the actual meaning of principal components is expected to become clearer. Additionally, although this study limited the analysis to two principal components, further research is required for a more detailed pedaling strategy analysis by incorporating additional principal components.

Furthermore, while this study examined the analysis method using all activities as the analysis target, the SHIMANO CONNECT Lab also accumulates road gradient information and GPS information simultaneously, suggesting the possibility of evaluating pedaling movement under specific conditions, such as climbing, descending, or curved roads. Additionally, all analyses in this study used measurement data during seated pedaling and did not include out-of-saddle pedaling data. These issues should be addressed in future research.

Using the values obtained from the PCA, weight values corresponding to the current principal component values were calculated for newly measured pedal force data. In other words, because pedaling indicator values corresponding to PC1 and PC2 values can be calculated even for newly obtained measurement data, the position of participants from the PC1–PC2 scatter plot can be clearly indicated, enabling quantification of the pedaling strategy for each participant. This would enable quantification of the difference between each participant s pedaling strategy and a more desirable pedaling strategy, and could also indicate the direction for improving the participant s technique.

As a further application possibility, if weight values corresponding to principal component values could be presented to participants in real time, cyclists could receive immediate feedback for improving pedaling movements. The possibility of using such real-time analysis methods remains a topic for future research.