The "Mach-7 Crash": Proportional Pacing and the Physics of Blind Telemetry

By the Forwod Research & Engineering Team | March 28, 2026

In applied kinematics, there is a fundamental difference between building a physics engine for a university biomechanics laboratory and building one for a commercial tracking environment.

In a clinical laboratory, researchers possess total environmental control. They utilize bluetooth-networked ergometers and 3D motion-capture arrays to stream continuous, high-frequency kinetic telemetry. Outside the lab, however, analytical models must operate on what we call blind telemetry.

When a standard application assesses a user's workout, it rarely possesses a live, second-by-second data stream. It receives a highly abstracted payload: the athlete’s biometrics, the movements performed, the repetition volume, and a single timestamp representing the global workout duration.

When tracking purely gravitational movements—like a barbell back squat—this lack of velocity data is largely immaterial to the net external work calculation. Because gravity is a conservative force, mechanical Work (Joules) is independent of time. But when an athlete incorporates a non-conservative ergometer into the bout, blind telemetry becomes a critical metrological problem.

The Velocity Cube Problem

As we discussed in previous articles, fluid dynamics dictates a non-linear relationship between aerodynamic resistance and speed. For a fan-based indoor rower or air bike, the power required to spin the flywheel scales with the cube of the athlete's velocity ($P \propto v^3$).

Consequently, an analytical model cannot calculate the mechanical Joules of a rowing session without knowing exactly how fast the athlete was moving.

Imagine evaluating a popular benchmark workout consisting of a $1,000 \text{ m}$ row followed by $50$ heavy barbell thrusters and $30$ pull-ups. The analytical model only knows that an elite athlete completed the entire session in exactly 5 minutes ($300 \text{ seconds}$).

How does the software determine the athlete's rowing pace? They could have rowed a world-record sprint and rested for two minutes before touching the barbell, or they could have rowed at a walking pace and sprinted the weightlifting. If a naïve algorithm simply assumes a slow "default" rowing speed for this elite athlete, it systematically robs them of the massive, exponential $v^3$ Joules they actually produced.

Conversely, if the algorithm forces the total rowing distance into whatever time is "leftover" after subtracting the barbell movements, it triggers a catastrophic mathematical failure.

The Mach-7 Crash

During early analytical stress-testing across the industry, we observed what happens when models attempt to linearly compress global time domains without strict physiological boundaries.

If an algorithm subtracts an estimated baseline time for the barbell and gymnastics components from a highly elite global time, the remaining time window for the $1,000 \text{ m}$ row becomes impossibly small. The mathematical model forces the athlete to complete the rowing distance in a fraction of a second.

Because power scales with velocity cubed, passing this physically impossible speed through the fluid dynamics equation results in what we internally termed the "Mach-7 Crash." The model hallucinates power outputs in the tens of thousands of Watts—briefly implying the human athlete generated enough kinetic energy to break the sound barrier.

The Bioenergetic Defense of Proportional Pacing

To resolve blind telemetry without crashing the physical boundaries of human capability, a model must rely on a bioenergetic pacing heuristic. Rather than randomly guessing split times, the most biologically defensible approach is proportional scaling.

High-Intensity Functional Training (HIFT) is designed to rapidly deplete finite anaerobic work capacity ($W'$). From a bioenergetic standpoint, if an athlete operates at an absolute supramaximal threshold on an ergometer, the resulting intracellular perturbation—specifically the accumulation of inorganic phosphate ($P_i$) and hydrogen ions ($H^+$)—physically impairs excitation-contraction coupling within the muscle fibres.

An athlete cannot biologically execute a maximal sprint and then seamlessly resume baseline pacing on heavy barbell movements without a requisite recovery period to reconstitute ATP stores and clear metabolites. Therefore, proportional pacing establishes the most physiologically sound boundary, reflecting the systemic, holistic down-regulation of mechanical power output across all modalities.

Furthermore, in fluid dynamics, resting is heavily penalized. If an athlete rows $500 \text{ m}$ at a blistering pace, completely stops for two minutes, and rows another $500 \text{ m}$, their mean velocity for the interval is drastically reduced. Starting and stopping a heavy flywheel destroys average mechanical power. Utilizing proportional pacing logically penalizes excessive resting exactly the way physics penalizes a boat that stops rowing.

Resolving the Abstract

At Forwod, ensuring our calculation models operate safely against extreme telemetry variations is a core analytical mandate.

By engineering intelligent, proportional pacing logic directly into our computational orchestrator, we established a deterministic mathematical bridge over the blind telemetry gap. Our engine evaluates the structural demands of a mixed-modal bout, establishes a mechanical baseline, and scales fluid dynamics predictably. This ensures that even when data is sparse, the Forwod Calculation Engine consistently respects the absolute limits of human bioenergetics, turning chaotic abstracted data into clean, verifiable physics.

Selected Clinical Context & Further Reading

• Abbiss, C. R., & Laursen, P. B. (2008). Describing and understanding pacing strategies during athletic competition. Sports Medicine.
• Gorostiaga, E. M., et al. (2012). Energy metabolism during repeated sets of leg press exercise leading to failure or not. PLOS ONE.
• Maté-Muñoz, J. L., et al. (2017). Muscular fatigue in response to different modalities of CrossFit sessions. PLOS ONE.