Symmetry equals strength
Stiffness and spoke-tension engine ported from Matt Ford's bike-wheel-calc (Mode Matrix method, Ford 2018) and verified against it to floating-point precision. Strength figures are first-spoke-slack thresholds built on those stiffnesses.
Rim lateral bending stiffness — resists the rim bowing sideways. Typical alloy double-wall rims: 40–80 N·m².
Rim in-plane bending stiffness — how the rim spreads load around its hoop. Usually 3–10× EI_lat (100–300 N·m²).
Rim torsional stiffness. Because the rim is curved, bending and twist are coupled, so GJ shapes lateral flexibility more than EI_lat does. Typical: 15–35 N·m².
Rim hoop (axial) stiffness, used for the rim's in-plane response and the tension-softening terms. Typical alloy: 8–15 MN.
Fourier modes in the Mode Matrix sum. Results converge by ~16–24 modes; more adds precision at negligible cost.
| Build | T_c avg (kgf) | T_c as DS (kgf) | Used |
|---|---|---|---|
| 148 | — | — | — |
| 157 | — | — | — |
Method. Tension balance, lateral stiffness K_lat, radial stiffness K_rad, and buckling tension T_c are computed with a JavaScript port of Matt Ford's open-source bike-wheel-calc library (Mode Matrix method; Ford 2018, A Theoretical Analysis of the Bicycle Wheel, Northwestern University) using smeared spokes, N Fourier modes, tension softening, and the linear buckling approximation. The port matches the library to floating-point precision across the full hub catalogue. Strength figures (F_lat, F_rad) are not library outputs: they are linearized first-spoke-slack thresholds — the load at which the lowest-tension spoke at the load point reaches zero tension — marking the onset of lost preload, not wheel collapse. Spoke geometry uses the rim beam-centroid radius (ERD/2 + 11 mm) per Ford §3.2; 3-cross lacing; steel spokes, E = 210 GPa. Hub flange dimensions compiled from manufacturer documentation. This project could not have been possible without the work of Mechanical Engineer Matt Ford.