# Power-Cadence Relationships in Cycling: Building Models from a Limited Number of Data Points
## 1 Introduction  
The Force-Velocity test performed on a stationary cycle ergometer is a well-established method used by researchers and practitioners to assess the neuromuscular function of the lower limbs. The experimental data collected during this test are often analyzed to estimate maximal anaerobic power [1, 2, 3, 4, 5], a physiological parameter of interest for evaluating athletic performance [6, 7, 8, 9, 10, 11, 12, 13, 14, 15], fatigue [16, 17, 18, 19], or age-related changes in neuromuscular function [20, 21]. Since the early development of this testing approach, various protocols and ergometer designs have been proposed, each of which can influence the quality and characteristics of the data collected. A central objective of any Force-Velocity testing protocol is to generate data that reflects the participant's true maximal force and power output across a wide range of cadences [5]. However, fatigue and suboptimal execution of the pedaling task canlead to the collection of data points that do not reflect true maximal values. To mitigate this issue, most protocols limit the duration of each sprint to approximately 6-7 s, restrict the number of maximal efforts (typically 3 to 6), and incorporate 3-5 min of rest between efforts. Despite these precautions, it remains common to observe substantial variability in power output at similar cadences across maximal efforts and across pedal cycles [5; 7; 22]. As previously demonstrated by our group, such variability is associated with differences in lower limb muscle activation levels [5]. To improve the consistency of maximal power expression during testing, some researchers have recommended the use of familiarization sessions in which participants repeat the protocol across multiple days [21; 23; 24], for a better assessment of their maximal power generating capacities. This somehow mirrors the standard practice used in neuromuscular assessments involving maximal voluntary contractions, where several attempts are made to capture a true maximum. Similarly, collecting multiple data points at the same cadence during a single testing session increases the likelihood of capturing cadence-specific maximal power outputs. However, applying this principle during a single force-velocity test must be done cautiously to avoid excessive fatigue, which may arise from accumulating too many maximal efforts or an overly long total duration of the Force-Velocity testing. In addition to variability in testing protocols, notable differences exist in how experimental data collected during Force-Velocity testing in cycling are processed. These differences pertain to three main aspects. First, researchers have modeled different types of relationships. Some have estimated Pmax by extrapolating the y- and x-intercepts of the force or torque vs. cadence relationships [4; 8; 9; 15; 16; 17; 25; 26; 27; 28], while others have relied on modeling the power vs. cadence relationship to estimate Pmax more directly [1; 5; 7; 10; 11; 12; 13; 15; 21; 22; 29; 30; 31; 32]. Second, various modeling approaches have been employed to characterize the power-cadence relationship. A commonly used method assumes that this relationship follows a symmetric parabola and applies second-order polynomial regression [1; 4; 7; 9; 13; 15; 16; 17; 18; 25; 26; 27; 28; 29; 30; 32; 33; 34; 35; 36; 37; 38]. In contrast, an alternative approach recognizes that the shape of the power-cadence curve may differ between individuals and deviate from symmetry, thus requiring a third-order polynomial model [5; 10; 11; 12; 22; 39]. The superiority of this latter approach has been demonstrated by two different studies [5; 10]. Third, strategies for selecting and aggregating data points vary substantially. These include processing each maximal effort independently [15; 16; 21; 22], aggregating all data across multiple efforts [1; 4; 7; 9; 11; 12; 13; 26; 27; 28; 29; 30; 32; 33; 34; 39], or selecting a single maximal data point per cadence or cadence interval [3; 5; 10; 11; 12; 15; 18; 37; 38].