How an eCVT shifts an e-bike without any gears

Some e-bike mid-drives threw the derailleur away. No cassette, no shifter clicks, no chain hopping sideways while you stand on the pedals — and the bike still has a low gear for the fire road and a high gear for the flat. Nothing steps. The ratio just slides.

I wanted to understand that properly, so I built an interactive 3D model of the gearset you can assemble part by part and then drive with sliders. This post is the short version of what is going on inside it.

The problem: a motor likes one speed, a hill does not

Electric motors make their best torque and efficiency in a fairly narrow speed band. Riders are not narrow: you grind up a climb at 40 rpm and spin along the flat at 95 rpm. Something has to sit between the two.

A derailleur solves this mechanically, by moving the chain onto a different sprocket. That gives you discrete steps, a moment where nothing drives, and a mechanism that hates being shifted under full load — which is exactly the moment a mid-drive is pushing hardest.

An eCVT solves it without moving anything. The chainline never changes. The ratio between your cranks and the chainring is set electronically, by how fast a second motor spins one gear.

One gearset, three shafts

The whole trick is a single planetary gearset. It has three concentric connections instead of the usual two:

• Ring gear (63 teeth) — the input. Bolted to your crank spindle, so it always turns at pedalling speed. The main assist motor adds its torque here too.
• Sun gear (27 teeth) — the control. Driven by a second, smaller motor. This is the shifter: not a lever, just a commanded speed.
• Planet carrier — the output. The plate carrying the three planet gears (18 teeth each). Whatever speed it turns, the chainring turns.

In a normal gearbox you drive one shaft and read the other. Here you drive two and the third is decided for you.

The whole thing is one equation

That is it. That single line — engineers call it the Willis equation — explains every behaviour of the drivetrain. The output is a fixed weighted average of two speeds you control: one with your legs, one with a motor. A bigger ring and a smaller sun means your legs have more say in the answer.

And because the sun motor can be commanded to any speed, the output can be any value the equation allows. There are no gears to be in. That continuum is the CV in CVT.

Four things the speed motor can do

Hold your cadence at 80 rpm and watch what the chainring does as the second motor changes speed:

Neutral is my favourite row, because it is the one that proves nothing is disengaging. Put −(63 ÷ 27) × 80 = −187 rpm into the sun and the two terms of the equation cancel exactly. The gearset is fully engaged, meshing, spinning — and delivering zero output speed.

Nothing in that table is a "gear". There are no steps between the rows: every sun speed in between is equally valid. On a real bike you never command the sun directly anyway. You ask for a cadence or a support level, and the controller solves the same equation backwards to decide what the speed motor should do.

Speed is free. Torque is not.

Here is the part that took me longest to accept. Gearing down multiplies torque — at half output speed you get roughly double output torque, same as any gearbox. But the torques on the ring, sun and carrier are also locked to each other by the tooth counts, and they do not care which direction power is flowing.

In low gear the sun is being driven backwards while the gearset pushes it forwards. Power flows into the speed motor. It is generating, not driving, and that recovered electricity is what feeds the main assist motor on the ring.

That recirculating loop is the real engineering story of an eCVT. It is why these drivetrains are quiet and stepless, and also why they give up a few percent of efficiency compared with a chain sitting on a well-chosen sprocket. Every ratio you ask for is paid for in watts moving between two motors.

Which motor actually shifts?

There are two motors in the housing and it is easy to mix up their jobs. Turn the assist motor up and you do not change gear — it is geared to the ring, which is tied to your crank, so it simply pedals harder for you. It sets how much force goes in.

Only the sun's speed relative to the crank sets the ratio. One motor pushes, the other one shifts, and the equation keeps them honest.

What this model simplifies

The 63/27/18 tooth counts keep the arithmetic readable while still being a valid gearset: no undercut, the planetary assembly conditions satisfied, standard 20° involute teeth. The model on the page is engineering-grade geometry — true involute flanks, exact mesh phasing, and non-interpenetration proved by a 63-check harness, with a live subset of those checks running in the page itself.

The packaging is idealised, though: I draw the speed motor coaxial with the sun and the assist motor driving the ring through a single pinion, where real units route both through extra reduction stages and lay them out very differently. Losses, freewheels, sensors and thermal limits are all left out.

Go drive it

Reading about a gearset is a poor substitute for turning one. The interactive page builds the mechanism one part at a time in a nine-step tour, then hands you the sliders: change your cadence, change the speed motor, hit the low / direct / high / neutral presets, explode the assembly, cut away the housing, or click any part to see what it does. Try to predict the readout before you move a slider — the equation is short enough to do in your head.

Try it: lucaslongo.com/pages/ecvt