Basic Energy Balance Equations for Cycling

Working draft, version 0.2, 2026-09-13. Markdown master for the Streamlines Knowledgebase, converted from the author's draft Basic Energy Equations.docx; figures in figures/, rebuilt by build_figures.py.

Energy balance

Rider Work + Kinetic Work + Gravitational Work + Rolling Resistance Work + Aero Work = 0 — **Figure 1.** The energy balance.

Where:

Rider Work = Rider Power × Time
Kinetic Work = −½ × Mass × (Final Speed² − Initial Speed²)
Gravitational Work = −1 × Mass × Gravity × (Final Elevation − Initial Elevation)
Rolling Resistance Work = −1 × Crr × Mass × Gravity × Distance
Aero Work = −1 × CdA × Alpha

and Alpha is dynamic pressure integrated over the distance:

\[\text{Alpha} = \int_0^{\text{Distance}} \text{Dynamic Pressure} \cdot dx\]

Note: Sign convention is positive propulsive, negative retarding. Rider Work will always be positive, Rolling Resistance work always negative, and Kinetic and Gravitational will vary.

CdA Equation using a fixed Crr

Measurement is based upon the conservation of energy.

Rider Work + Kinetic Work + Gravitational Work + Rolling Resistance Work, divided by Alpha, equals CdA — **Figure 2.** CdA from the energy balance with Crr held fixed.

Crr Equation using a fixed CdA

Rider Work + Kinetic Work + Gravitational Work + Aero Work, divided by Mass × Gravity × Distance, equals Crr — **Figure 3.** Crr from the energy balance with CdA held fixed.