Tangential Pedal Force Calibration: Hardware Compensation and Strain Gauge Scaling

1. Strain Gauge Instrumentation and Signal Chain

In high-frequency telemetry systems, measuring the tangential pedal force requires a rigid array of strain gauges bonded directly to the crank arm. These sensors operate within a Wheatstone bridge configuration. The small differential voltage generated by mechanical deflection must undergo low-noise amplification. An analog-to-digital converter (ADC) then digitizes this analog signal.

The microcontroller processes these raw samples. Thermal variations shift the baseline resistance of the metal foil, creating offset errors. Consequently, executing a zero-offset calibration before data collection is mandatory. The system registers the unloaded voltage level. We write these offset values directly into the configuration non-volatile memory. This ensures subsequent strain measurements reflect actual force rather than thermal drift.

2. Mathematical Formulation & Torque Dynamics

The instantaneous mechanical power and crank torque relation of tangential pedal force is modeled as:

Where:

• $P(t)$ is the instantaneous power in Watts.
• $\tau(t)$ represents the crank torque vector, which is the cross product of the crank arm position vector and the applied pedal force vector.
• $\omega(t)$ is the dynamic angular velocity of the crank, which varies slightly within each stroke due to resistance changes.
• $\text{TE}$ and $\text{PS}$ represent Torque Effectiveness and Pedal Smoothness, respectively, tracking force application efficiency.

Calculating $\tau(t)$ relies on isolating the force vector perpendicular to the crank arm. Radial forces yield zero torque. Thus, we isolate $F_{\text{tangential}}$ to compute the output power. During $360^{\circ}$ rotations, the angle of force application changes continuously.

3. Calibration Register Mapping & Protocol Specs

To maintain accuracy within $\pm 1%$, the firmware utilizes a specific calibration routine. The microcontroller communicates with the instrumentation amplifier via I2C. The calibration parameters are stored in specific registers.

Data serialization occurs in the interrupt service routine (ISR). High-frequency sampling requires low interrupt latency. The system writes the digitized force data to a ring buffer. The UART buffer then transmits these packets to the main processor.

We verify packet integrity using a 16-bit checksum verification. If the checksum fails, the receiver discards the corrupted data frame. This safeguards against transmission line noise. Furthermore, thread safety is enforced to prevent race conditions during calibration write cycles.

References

1. Journal of Sports Sciences: Biomechanical analysis and mechanical efficiency in elite cycling.
2. DIDI.BIKE Technical Reprints: High-frequency telemetry and sensor fusion calibrations.
3. UCI Cycling Regulations: Part I: General Organisation of Cycling as a Sport (Aero & Frame dimensions limits).
4. Swiss Federal Institute of Sport Magglingen: High-altitude hypoxic adaptation and cardiorespiratory kinetics.