Presets
Playback
Drivetrain and gear
Hub input speed = cadence x chainring / sprocket; road speed = input x hub ratio x wheel circumference. The efficiency per gear is an assumed teaching value, highest in direct drive. Choose which planetary stage to animate and which member drives it with the buttons below.
Model checks
The science
What is modelled
The hub has fourteen output ratios between 0.279 and 1.467. Three simple planetary stages (sun, four planets on a carrier, ring) provide the ratios in the 3D model; here one of them is animated with exact kinematics for three drive arrangements, next to a drivetrain calculator that takes cadence, chainring, sprocket and wheel size.
Equations
- Willis equation:
Zs ωs + Zr ωr = (Zs + Zr) ωc, with the ring fixedωc/ωs = Zs / (Zs + Zr). - Planet spin:
ωp = ωc - (Zs/Zp)(ωs - ωc). - Road speed:
v = ncrank (Nring/Nsprocket) r π D / 60. - Power:
F v = η Prider.
Checks run in the page
- The Willis equation for all three stages and drive modes, with an independent mesh-point derivation.
- The near-geometric ladder of the 14 ratios.
- The total range of 526 %.
- The power chain from rider to road.
Honest simplifications
The 14 ratios are illustrative values taken from the 3D model and are not derived from the three stages shown (a real hub combines stages in series with a selector). Efficiency per gear is an assumed teaching value. Not a real product's specification.
What to try
- Press Steep climb, lowest gear and compare the ground force with the top gear.
- Use the three mode buttons and watch which member of the planetary set stands still.
- Change the stage and compare the carrier speed ratios 0.286, 0.313 and 0.333.