Modeling Divergence: Gravity Mechanics vs. Fluid Dynamics in Ergs

By the Forwod Research & Engineering Team | January 24, 2026

A persistent, unresolved challenge in quantifying modern athletic capacity is rectifying the extreme mechanical differences across disparate training modalities.

In traditional commercial fitness, athletes trained in highly predictable, siloed environments. An endurance athlete ran on a track; a strength athlete lifted a barbell. Analytical models only needed to understand one physical domain at a time. Today, however, an athlete might transition from a heavy deadlift straight into a maximal-effort sprint on an indoor rowing machine within seconds.

From an informatics perspective, this is a metrological nightmare. When processing bioenergetic data, a calculation engine cannot treat these two movements as equals. They are governed by fundamentally opposed constructs of physics: Conservative Forces and Non-Conservative Forces.

Attempting to track an athlete’s output across these domains using a single linear algorithm or a basic "rep counting" framework does not just lead to inaccurate data—it mathematically violates the laws of thermodynamics.

The Gravity Barrier: Conservative Forces

In traditional weightlifting permutations (e.g., deadlifts, squats, or presses), the resistance the athlete faces is purely gravitational.

Newtonian gravity is a Conservative Force. It pulls downward on a barbell with a constant force, regardless of the athlete’s intent or speed. The mechanical work ($W$) required to displace that mass against gravity relies strictly on the mass ($m$), the gravitational constant ($g$), and the change in vertical height ($\Delta y$):

Crucially, the net external mechanical work required to displace a load against gravity from a static start to a static finish is mathematically independent of velocity. While an explosive lift requires a massive peak force to overcome static inertia and impart kinetic energy ($E_k = \frac{1}{2}mv^2$)—drastically increasing the athlete's internal metabolic work—that external kinetic energy is ultimately absorbed by gravitational potential at the apex and the athlete's active eccentric braking force.

According to the Work-Energy Theorem, whether the athlete completes the lift in $1 \text{ second}$ or $5 \text{ seconds}$, the net external work done on the barbell against the conservative field remains strictly bounded at $981 \text{ Joules}$.

Furthermore, gravitational resistance operates as a binary step-function: if an athlete can only generate $99\%$ of the required force to overcome the barbell's static inertia, zero displacement occurs, and zero mechanical work is accomplished.

The Non-Linear Fluid Curve: Non-Conservative Forces

Conversely, monostructural ergometers—such as air bikes, ski-ergs, and rowing machines—do not fight gravity. They fight fluid friction and aerodynamic drag.

Fluid drag is a Non-Conservative Force. Unlike a barbell, an ergometer's fan blade cares intimately about how fast it is moving. As the flywheel accelerates, it must actively displace air molecules. In fluid dynamics, the resistance an object faces scales with the square of its velocity ($v^2$), but the power ($P$) required to overcome that resistance scales with the cube of its velocity:

For a standard air-resistance ergometer, the relationship between power output and the velocity of the flywheel is mathematically universally modelled via a specific aerodynamic drag coefficient ($c$):

While advanced clinical hardware internally measures angular deceleration stroke-by-stroke ($I \cdot \alpha$) to continuously map the precise drag factor, computational models operating on abstracted field data cannot see the machine's damper setting. Analytical engines must mathematically anchor this aerodynamic drag coefficient ($c$) to standardised competition medians to allow for rigorous cross-modal normalisation.

Because velocity is cubed ($v^3$), the metrology completely diverges from barbell mechanics. If an athlete decides to pull the handle twice as fast, it does not require twice the power; it requires eight times the power. Furthermore, because force dynamically increases with speed, the total physical Work (Joules) required to row $1,000 \text{ metres}$ at a sprint is mathematically far greater than the Work required to row $1,000 \text{ metres}$ at a walking pace.

The Metrological Collision

When generic algorithms apply linear math to a non-linear velocity cube, they hallucinate data.

If a platform processes a mixed-modal workout and does not strictly delineate between conservative and non-conservative physics, it creates a massive cross-modal blind spot. A model cannot apply a linear pacing algorithm to an ergometer, nor can it apply a velocity-dependent multiplier to the external mechanical work of a barbell. If an algorithm attempts to blend them into a singular points system, it systematically robs elite athletes of the massive, exponential fluid-drag Joules they actually produced.

The Forwod Resolution

To achieve true equivalency, the physics cannot be compromised.

When building the Forwod Calculation Engine, we made the architectural decision to deliberately bifurcate our algorithms into distinct archetype silos. When telemetry reaches our engine, it acts as an intelligent metrological router. Weightlifting geometries are anchored strictly to our conservative biomechanical pipelines, isolating the gravitational constants. Simultaneously, ergometer data is routed through our proprietary non-linear fluid dynamics arrays.

Mapping these drag coefficients and resolving velocity non-linearities from abstracted telemetry remains an ongoing area of active research. Forwod is a moving target, continuously calibrating our internal models against live clinical data. But by structurally respecting this divergence in our architecture, we ensure practitioners utilizing the Forwod framework can normalize a $1 \text{ km}$ row against a 1-Rep Max power clean with peerless accuracy.

Selected Clinical Context & Further Reading

• Baudouin, A., & Hawkins, D. (2002). A biomechanical review of factors affecting rowing performance. British Journal of Sports Medicine.
• Boyas, S., et al. (2006). Power responses of a rowing ergometer: Mechanical sensors vs Concept2 measurement system. International Journal of Sports Medicine.
• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of physics (10th ed.). John Wiley & Sons.