Typical setups
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Drive
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Variator shifting from low to overdrive
Belt CVT geometry for scooters, ATVs and push-belt car gearboxes: ratio range and spread, secondary diameter at every primary position, sheave travel, belt wrap and the road speed at every ratio.
| Primary Ø | Secondary Ø | CVT | Overall | Speed |
|---|
A longer belt sits deeper in the secondary at low ratio and higher at overdrive. Same pulleys, other belts:
| Belt length | Low | Overdrive | Spread |
|---|
The belt length is fixed. When the primary sheaves close and push the belt out to a larger diameter, the secondary sheaves must open and let the belt sink, so the ratio changes continuously.
Scooter and ATV rubber belts use about 26–30° included angle, steel push-belt car CVTs about 22°. A spread of 3–4.5 is typical for scooters, 5–7.5 for car CVTs. Keep at least about 150° of wrap on the smaller pulley and a little travel to spare at both ends so the belt never bottoms on the hub or rides off the top of the sheaves.
This calculator models a belt CVT (variator) of the kind used in scooters, ATVs, snowmobiles and small cars. From the center distance, belt length, primary pulley range and largest secondary diameter it finds where the belt sits at each end of the shift, the low and overdrive ratios, ratio spread, sheave travel, belt wrap and road speed. Scooter tuners use it to predict the effect of a different belt or variator, and students and engineers use it to understand and lay out a variator drive.
This variator spans 2.65 to 0.65 with a spread of 4.06, typical for a scooter, and would reach about 69 km/h (43 mph) at 7500 RPM if the engine can pull full overdrive. All figures ignore belt slip, so real speeds are a few percent lower.
A belt CVT has two pulleys whose sheave halves slide apart or together. The belt length is fixed, so when the primary sheaves close and push the belt out to a larger diameter, the secondary sheaves must open and let the belt sink to a smaller diameter. The ratio is i = d₂ / d₁, the secondary belt diameter over the primary belt diameter, and it changes continuously between the low and overdrive limits. In scooters, centrifugal rollers in the variator close the primary as engine speed rises, and a spring and torque cam on the secondary resist it.
Ratio spread is the low ratio divided by the overdrive ratio, i_low / i_overdrive. It tells you how wide the CVT's range is, like the gap between first and top gear in a manual gearbox. A scooter variator going from 2.65 to 0.65 has a spread of about 4.1. Typical spreads are 3 to 4.5 for scooter and ATV rubber-belt CVTs and about 5 to 7.5 for car CVTs with steel push belts or chains. A larger spread needs larger pulleys or more sheave travel.
Usually not. With the same center distance, a longer belt sits higher on the secondary pulley for any given primary diameter, so both ratios become numerically higher. In the example scooter, going from a 730 mm to a 740 mm belt raises the overdrive ratio from 0.654 to 0.725, which lowers top speed by about 10%. A shorter belt does the opposite but can weaken the launch ratio. If the low end is already limited by a full secondary pulley, extra length mostly costs top speed.
Each moving sheave half moves axially by x = Δd · tan(α/2), which is the same as 2 · Δr · tan(α/2), where Δd is the change in belt diameter on that pulley and α is the included sheave angle. A scooter primary that goes from 41 mm to 92 mm with a 28° sheave needs (92 − 41) · tan 14° = 12.7 mm of travel. Belt wear makes the belt narrower and sink deeper, which uses up part of this travel, so leave a little spare at both ends.
Rubber CVT belts for scooters, ATVs and snowmobiles usually run in sheaves with an included angle of about 26° to 30°, and 28° is very common. Steel push belts in car CVTs run at about 22°. The belt's own side angle must match the sheave, or it will contact only on one edge, slip and wear unevenly. A smaller angle wedges the belt harder for more grip but needs more axial travel for the same change in diameter.
Divide engine speed by the overall ratio to get wheel speed, then multiply by the tire circumference: v (km/h) = rpm / (i_CVT · i_final) · π · D_tire (m) · 60 / 1000. For 7500 RPM, an overdrive ratio of 0.654, a 13.5 : 1 final drive and a 430 mm tire: 7500 / 8.82 = 850 RPM, and 850 · π · 0.43 · 0.06 = 68.9 km/h (42.8 mph). This assumes full overdrive and no belt slip. Real top speed also depends on whether the engine has enough power to pull that ratio.