This page now treats the selected primary and secondary values as instantaneous effective pitch radii. The connected view preserves two variable-radius pulley stations and one continuous belt while separating exact no-slip kinematics from real traction, control and loss behavior.
Instantaneous CVT Pitch-Radius Explorer
Enter declared primary and secondary pitch radii and an input speed. The connected belt view reports no-slip speed ratio, output speed, common pitch-line speed and the ideal lossless torque ratio.
Equation Used
- Rp and Rs are declared instantaneous effective pitch radii, not sheave outside radii.
- The belt is inextensible and does not slip at either pitch line.
- The selected radii are stationary during each displayed operating point.
- Output and input pitch-line speeds are equal.
- The torque ratio is ideal and follows only from lossless steady power.
- Complementary sheave travel, fixed belt length, center-distance constraints, wrap, clamping, traction, efficiency, power capacity, loads, heat, controls, wear and safe operation are excluded.
Replaces a generic efficiency and performance model with exact instantaneous no-slip pitch-radius kinematics and an explicitly ideal lossless torque ratio.
Two variable-radius pulley stations share one pitch-line speed
Bosch describes a pushbelt CVT as a belt running between input and output pairs of conical sheaves, with each pair changing the belt's running radius. At any declared operating point without slip, the same belt pitch-line speed passes both pulley stations.
The connected schematic shows those two effective pitch circles and one continuous belt; it does not prescribe the sheave actuator or shift schedule.
Use this page as an instantaneous kinematic ledger
The worksheet converts declared effective pitch radii and input speed into speed ratio, output speed and belt pitch-line speed. The reciprocal torque ratio is shown only under an ideal lossless-power assumption.
It cannot select, rate, control or validate a real CVT.
Match tangential speed at both pitch radii
Radii are converted from millimetres to metres in the belt-speed calculation. Real torque requires measured efficiency and device-specific traction data.
A transparent instantaneous operating point
For Rp=40 mm, Rs=100 mm and Nin=6000 rpm, Nout/Nin=0.400, ideal output speed is 2400.00 rpm and belt pitch-line speed is 25.133 m/s. Under ideal lossless steady power only, Tout/Tin=2.500.
No capacity or actual efficiency follows.
Pitch-radius kinematics are not a complete CVT design
A real CVT couples sheave travel, belt length, wrap, clamping and traction while managing loads, heat, losses and controls. Those require the specific architecture and manufacturer data.
The former generic efficiency slider, loss percentage and universal performance, vehicle, service-life, maintenance and tuning claims are removed.
CVT pitch-radius questions
Are these pulley outside radii?
No; they are declared effective pitch radii where belt speed is matched.
Does this calculate a shift schedule?
No.
Is the torque ratio an actual measured value?
No; it is the reciprocal ideal ratio under lossless steady power.
Can this size a CVT?
No.
CVT and belt-drive references
- Bosch Mobility, Pushbelt: a CVT pushbelt runs between input and output conical-sheave pairs whose running radii vary.
- Gates, Heavy Duty V-Belt Drive Design Manual: speed ratio and driven speed follow pitch diameters.
- MIT OpenCourseWare, Elements of Mechanical Design, Belt Drives: belt-drive geometry, contact and power-transmission context.
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