Objective: Develop and validate a kinematic analysis framework for extracting mechanical behavior metrics of the bicycle-rider system from FIT files generated by cycling devices (cycling computers, power meters, cadence sensors, and heart rate monitors).
Core problem: FIT files contain signals with multiple instrumental noise sources — GPS positioning errors, ANT+/BLE sensor dropout, cadence quantization, barometric altitude drift — that make direct metric computation invalid without explicit statistical treatment. A tool that ignores these uncertainty sources produces diagnostics of apparent technical depth but fragile statistical foundation.
Methodology: Five primary metrics are defined, each with physical justification, per-variable uncertainty model, contextual validity criteria, and Monte Carlo simulation structure. Classification thresholds are not universal constants but functions of four bicycle configuration variables: discipline, suspension type, drivetrain, and wheel diameter. The framework adopts the principle of statistical honesty: each result is reported as a probability distribution over the classification space, not as a single value.
Key results:
The FIT protocol (Flexible and Interoperable Data Transfer), developed and maintained by Garmin Ltd., is the de facto standard for activity recording in cycling devices. Its adoption is broad: Garmin, Wahoo, Coros, Polar, Suunto, Bryton, and other manufacturers generate .fit files compatible with the public FIT SDK specification (Garmin, 2024).
The record message (global type 20) stores 1 Hz time series of variables relevant to this analysis: speed, cadence, altitude, distance, power, heart rate, and timestamps. This dataset, although designed for athletic tracking, contains sufficient kinematic information to infer characteristics of the mechanical behavior of the bicycle-rider system under defined validity conditions.
The literature on cycling performance analysis (Faria et al., 2005; Abbiss & Laursen, 2008; Korff et al., 2007) focuses predominantly on physiological performance metrics. Mechanical behavior diagnostics of the bicycle-rider interface from field data remains largely unexplored territory, in part because it requires honest confrontation with signal limitations.
Unlike controlled laboratory measurements, field FIT data exhibits: random wireless sensor dropout (5–15% of samples depending on RF conditions), cadence quantization from magnetic magnet detection, GPS speed noise (±0.3 m/s typical at 1 Hz), barometric altitude drift (±2 m), and temporal gaps of up to 10 seconds interrupting local continuity.
Ignoring these uncertainty sources is equivalent to presenting diagnostic labels without statistical foundation. The present framework treats them explicitly through Monte Carlo simulation.
Cadence is typically recorded via magnetic magnet detection on the crank arm or via internal accelerometer (Garmin, Wahoo). Uncertainty sources include:
Speed is obtained from the GPS module (positional difference or Doppler effect depending on device). At 1 Hz:
Altitude is recorded via barometric sensor in most modern devices:
When available, power comes from a pedaling power meter (crank, pedal, or hub):
A direct consequence of the noise model is that not all samples in a FIT file are equally valid for kinematic metric computation. The framework defines two filtering levels:
Segment continuity is broken when the temporal gap between consecutive samples exceeds a configurable threshold (typically 3–5 s for cadence and speed metrics, 5 s for power). Segments with fewer than Nmin valid samples are discarded. This criterion prevents GPS gaps, traffic stops, or technical stops from contaminating local variance computation.
Local variance metrics (cadence, speed/cadence ratio, climbing stability index) are physically interpretable only under quasi-stationary regime. Windows containing the following are excluded:
This exclusion is conservative but necessary: including transients in local variance computation produces false positive instability diagnostics that are actually physiological or tactical, not mechanical.
Physical justification: Under quasi-stationary regime (relatively constant speed and load), a trained cyclist maintains cadence with low relative variation. Persistent cadence oscillations within the same regime reflect disturbances in the continuity of useful torque — whether from terrain irregularities the suspension system does not fully absorb, traction losses, instability in saddle position, or frequent gear changes. Faria et al. (2005) and Hansen et al. (2007) document that optimal cadence for minimizing metabolic cost falls in the 80–100 rpm range for road cycling, with greater tolerable dispersion in MTB due to terrain variability.
Calculation principle: The coefficient of variation (CV) of cadence over quasi-stationary windows. Complemented by the scaled median absolute deviation (MAD) for robustness against outliers produced by dropout or defective interpolation. CV is computed over valid active cadence samples (effective pedaling detected), excluding zero transitions.
Validity conditions: Quasi-stationary regime, cadence ∈ [30, 160] rpm, speed > 1 m/s, gap between samples ≤ 3 s. Not applicable during accelerations, open corners, evident gear changes, or traffic stops.
Classification: Stable / Warning / Critical. Numerical thresholds depend on bicycle configuration (see Section 5).
Physical justification: The ratio between bicycle linear speed and pedaling cadence is a direct function of total effective development (transmission ratio × wheel circumference). Under stable regime with fixed gear, this ratio should be approximately constant. Its coefficient of variation captures the dispersion produced by frequent gear changes, speed instability over variable terrain, or elevated GPS noise. Its absolute value, normalized by wheel circumference if known, approximates the effective transmission ratio in use.
Calculation principle: Ri = 60 · vi / ci, expressed in meters advanced per crank revolution. The CV of R over quasi-stationary segments without detectable gear changes is the primary metric. The median of R allows inferring the average development used.
Validity conditions: Speed ≥ 2.5 m/s (GPS reliability threshold), cadence ≥ 30 rpm, no gear changes within the window, quasi-stationary regime. At low speeds, the relative GPS error over R becomes dominant and the metric is unreliable.
Declared limitation: This metric does not distinguish between genuine mechanical instability and legitimate tactical behavior (frequent gear changes due to variable terrain). Prior segmentation reduces but does not eliminate this ambiguity.
Physical justification: Climbing is the highest mechanical demand regime for the bicycle-rider system. Under sustained gradient, speed and cadence tend to stabilize when the system operates in equilibrium between available power and gravitational resistance. Simultaneous dispersion of both variables reflects system disturbances: traction losses on irregular terrain, rider position instability from poor geometry or saddle fit, inadequate suspension response to traction demand, or pedaling patterns that fragment useful torque.
Calculation principle: The CSI combines the coefficient of variation of speed and the coefficient of variation of cadence over identified climbing segments, with equal weighting (0.5 + 0.5). Gradient is computed over a spatial window large enough to overcome barometric noise. Altitude is smoothed prior to gradient computation.
Validity conditions: Smoothed gradient ≥ 3%, minimum segment length, mean speed ≥ GPS reliability threshold, barometric altimeter available. If no sustained climbs are detected, the metric is reported as not applicable with an explanatory note.
Physical justification: The Variability Index, defined as the ratio of Normalized Power (NP) to Average Power (AP), quantifies the irregularity of the pedaling effort. NP is computed via a 30-second moving average raised to the fourth power, which disproportionately penalizes power spikes relative to the arithmetic mean. A high VI indicates erratic effort: whether from highly variable terrain, inefficient pedaling pattern in the context of the route, or frequent tactical changes. Abbiss & Laursen (2008) document the relationship between VI and metabolic cost in competitive cycling.
Noise robustness: This is the most robust metric in the set. The NP/AP ratio is relatively insensitive to small random power meter noise because the 30 s moving average filters part of the instrumental variability. The relative error of the power meter (1–3%) propagates multiplicatively and approximately uniformly in numerator and denominator, resulting in partial cancellation.
Classification: Four bands: Very Stable / Stable / Variable / Critical. Absolute thresholds are adjusted by discipline and suspension (see Section 5). Wheel diameter dependence is negligible for this metric.
Physical justification: The power-to-heart-rate ratio (EF, Efficiency Factor) tends to decrease over a prolonged effort at constant load due to cardiovascular drift (HR increase without power increase). The percentage change in EF between the first and second half of the segment (decoupling) is an indicator of cardiovascular fatigue and the cardiovascular system's ability to sustain the effort. Barsumyan et al. (2025) document the use of Pw:HR metrics in AI-powered performance analysis.
Declared methodological caveat: This metric is dominated by physiology, not mechanics. Temperature, hydration, accumulated fatigue, autonomic state, and type of heart rate sensor (chest strap vs. optical sensor) are determinant influences. It must not be interpreted as an indicator of drivetrain mechanical efficiency or of the body-bicycle interface. It is included because it is mathematically computable and provides utility for the cyclist as a physiological state indicator in the context of the analyzed activity.
Concept: The difference in the speed-gradient relationship between the ascending and descending branches of an identical gradient would capture drivetrain mechanical losses or inefficient suspension response.
Rejection reason: With GPS speed noise of ±0.3 m/s and altitude noise of ±2 m, small differences between branches are not distinguishable from the combined measurement and segmentation error with confidence. Only normalized discrepancies greater than ~10% emerge above the noise floor. Also requires very specific conditions (bidirectional route, absence of micro-undulations) not guaranteed in general use. Verdict: modelable with medium-low confidence. Rejected as primary metric.
Concept: Longitudinal acceleration captures the dynamic response of the system to terrain perturbations.
Rejection reason: The numerical derivative of GPS speed at 1 Hz strongly amplifies noise. Analytical uncertainty propagation for forward difference with εv ~ Uniform(−0.3, 0.3) m/s produces σa ≈ 0.245 m/s² of pure noise per measurement, independent of any real acceleration. At this noise level, most mechanically relevant real accelerations of interest are submerged. Strong prior smoothing would destroy the signal the metric is meant to measure. Verdict: not modelable with sufficient confidence as a mechanical interaction metric under 1 Hz GPS.
A frequent error in sport activity analysis tools is applying universal thresholds to metrics whose expected value under normal conditions varies significantly with system configuration. An MTB cyclist with full suspension on technical terrain will necessarily exhibit greater cadence variance than a road cyclist on flat terrain — not because the system is failing, but because the external mechanical excitation is different.
The present framework adopts the principle of linear additive correction over base thresholds:
where each Δj exists only when there is a clear physical reason to modify the threshold of metric m. The explicit rule is: variables that do not produce a physically defensible correction for a given metric receive Δ = 0 for that metric. This keeps the system finite and the adjustments auditable.
The external excitation environment differs fundamentally between disciplines. MTB on technical terrain introduces cadence and speed perturbations that are normal system responses, not mechanical failure indicators. Gravel represents an intermediate case. This variable produces the most consistent corrections across all kinematic metrics.
Suspension decouples part of the vertical terrain excitation from the frame and rider motion, but also introduces dynamic losses and small changes in the effective continuity of pedaling. Greater cadence dispersion in a full suspension system on rough terrain does not automatically imply poor body-machine interaction. The adjustment is more relevant for climbing metrics (CSI) than for the V/C ratio.
1x (single chainring) systems present relatively larger jumps between available ratios than 2x (double chainring) systems. This produces greater expected V/C ratio dispersion in variable terrain — not because the system is unstable but because the available ratio space is more dispersed. The effect on cadence variance is smaller. This variable does not affect VI or cardiac decoupling in a defensible way.
Smaller diameter wheels traverse equivalent irregularities less smoothly (greater impact angle for a fixed-height obstacle), inducing more perturbation in speed and cadence. The effect is primarily relevant for kinematic metrics (cadence, V/C, CSI) and negligible for VI and decoupling.
Several variables that might appear relevant do not appear as threshold corrections but as invalidity flags: very technical terrain with frequent stops, routes with intense drafting, extreme mud conditions, degraded GPS signal (HDOP > 5), activities with multiple gaps > 10 s.
The reason is important: these variables should not relax the threshold — they should directly nullify the metric's interpretability. A threshold corrected for "very technical muddy terrain" would be arbitrary; the correct decision is to flag the metric as non-estimable under those conditions.
Additional variables excluded to prevent overfitting: tire width, inflation pressure, crank length, rider weight, fork offset, suspension sag. The robustness of the system requires limiting corrections to variables with documentable and non-redundant physical effect.
Analytical uncertainty propagation is impractical for non-linear metrics such as cadence CV or CSI, because they involve operations on distributions of signals with random dropout, conditional interpolation, and data-dependent segmentation. Monte Carlo simulation allows quantifying the result distribution under the instrumental noise model without requiring analytical approximations.
The question the MC answers is not "what is the metric value?" but "given the plausible instrumental noise model for this type of FIT signal, with what probability would this result have been classified as stable, in warning, or critical?"
Noise model per variable:
Implemented version: Minimal robust version — bicycle configuration fixed (dynamic thresholds constant within run). MC propagates instrumental uncertainty only. N = 500 iterations (balance between statistical confidence and browser performance).
Output per metric:
A result of P(critical) = 0.73 does not mean the system "fails" with 73% probability. It means that under the assumed instrumental noise model, 73% of plausible realizations of the observed signal would have been classified as critical. It is a measure of classification robustness against noise, not of real mechanical failure probability.
The distinction matters: a "critical" classification with P(critical) = 0.95 is highly robust to noise. A "critical" classification with P(critical) = 0.52 is marginal and should be interpreted with caution. The tool presents this information explicitly to avoid false positive diagnoses.
The specific segmentation parameters, exact dynamic thresholds per configuration combination, noise model coefficients, and dropout imputation algorithm are proprietary to BikeLab Studio. The production code is obfuscated and protected via domain trap techniques that silently poison results in unauthorized implementations outside the official domain.
The formulas described in this document correspond to the implemented calculation principles. The exact numerical parameters and post-calculation corrections are not included in this public description.
The architectural decisions of the present framework — in particular the choice to report probability distributions over classification space rather than single values, the explicit documentation of rejected metrics and their reasons, and the principle that a variable producing no physically defensible correction receives Δ = 0 — are direct consequences of applying the operational principles of the Dynamic Coherence Model (DCM), a proprietary framework developed by Carlos Ravello (2025).
The DCM postulates that a technical system achieves optimal functional coherence not by eliminating its uncertainty but by integrating it as an explicit variable of the process. In the present context: the Monte Carlo confidence band, the limitations documentation, and the finite dynamic threshold architecture are direct expressions of the Ω principle of dynamic coherence applied to the domain of cycling kinematic analysis.
The DCM framework is not published in its complete form. — Ravello, C. (2025). Dynamic Coherence Model. Unpublished internal document. BikeLab Studio.
Kinematic analysis of FIT files for mechanical diagnostics of the bicycle-rider interface is technically viable under explicit validity conditions and with honest statistical treatment of instrumental noise sources. The cadence variance, speed/cadence ratio, climbing stability index, and Variability Index (with power meter) metrics constitute a coherent and complementary set of indicators of the system's kinematic behavior.
The central contribution of this framework is twofold: first, the explicit documentation of conditions under which each metric is valid (and those under which it is not); second, the dynamic threshold system that recognizes that the "expected normal value" of these metrics is not universal but a function of the bicycle system configuration.
Monte Carlo simulation does not improve the precision of the computation; it provides statistical honesty about its robustness. A result classified as "critical" with P(critical) = 0.90 under the instrumental noise model is a solid conclusion. A marginal result with P(critical) = 0.55 should be presented as such — not as a definitive diagnosis.
The rejected metrics — speed/gradient hysteresis and derived longitudinal acceleration — are examples of conceptually interesting indicators that are instrumentally non-viable with the signal quality available in 1 Hz field FIT data. Documenting the rejection is part of methodological rigor.
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