A pulley-based continuously variable transmission changes its ratio by moving the belt to different contact radii between conical pulley halves. A small primary contact radius and large secondary radius reduce output speed and increase ideal output torque. Reversing that radius relationship gives overdrive.
Continuously Variable Transmission (CVT) Interactive Calculator
Compare ideal CVT speed and torque using two effective belt-contact radii. The conical pulley sections show why the belt climbs outward as the halves close. Each radius remains independently adjustable for comparison.
Equation Used
- Same-direction rotation through an uncrossed belt, with no slip.
- Ideal power conservation; no efficiency loss or hydraulic power consumption.
- Inputs specify effective contact radii in a common relative unit, not outer pulley diameters.
- Independent radii compare configurations. Fixed-belt centre-distance and length constraints are not enforced by these sliders.
- Constant outside sheave diameter and illustrative 15 degree face slope; housing, sections and belt thickness are explanatory geometry.
An uncrossed belt turns both shafts in the same direction. This ideal ratio calculator assumes no slip or losses. Real CVTs coordinate both pulley positions to accommodate one fixed belt length; not every independent radius pair belongs to the same installed transmission.
Contact radius changes inside a fixed-size pulley
The conical pulley halves move along their shaft. Closing the gap pushes the belt outward; opening it lets the belt run closer to the axis. The animation keeps the outer pulley diameter fixed and shows the changing belt-contact circle.
The main view cuts away the front halves to expose the belt. The two axial sections show the V-shaped faces and the belt seated between them. Both shafts turn in the same direction because the belt is uncrossed. Belt markers travel at the same surface speed as both contact circles.
What this comparison can tell you
The calculator compares the speed and ideal torque at a selected pulley ratio. It does not include a launch clutch, torque converter, reverse gearset, final drive or vehicle model.
Input speed and torque are entered operating conditions. Selecting them here does not establish that a particular belt or transmission can carry that load.
The no-slip ratio
Equal belt-contact speed requires n_in Rp=n_out Rs. Therefore the input-to-output speed ratio is Rs/Rp and output speed is n_in Rp/Rs.
For the lossless comparison, T_out=T_in Rs/Rp. Multiplying torque by angular speed gives equal power on both shafts. Real losses would reduce available output power.
The relative-radius inputs set a ratio without specifying physical millimetres. The drawing uses one consistent radius scale and an illustrative 20-unit centre distance. It also reports the resulting belt length, making changes in the required belt loop visible.
Underdrive and overdrive
For 6000 rpm input, 400 N·m input torque, Rp=1 and Rs=6: They give a 6:1 ratio, 1000 rpm output and 2400 N·m ideal torque. These are mathematical inputs, not an approved hardware rating.
Swapping the two radii gives a 1:6 ratio, 36000 rpm output and about 66.7 N·m ideal torque. The negative 500% reduction result means a 500% speed increase. Equal radii give 1:1 speed and equal ideal torque.
Independent inputs versus a real shift
A physical CVT must accommodate one belt of essentially fixed length between its shaft centres. Both pulley positions therefore need coordination. This calculator leaves the two radius inputs independent to compare ideal configurations; changing them freely can imply a different belt length.
Clamping load, friction, slip, thermal limits, belt stress and actuator control are not modeled. Playback shows steady rotation at each chosen configuration, rather than claiming every transition is a feasible controlled shift.
Questions about the CVT model
Do the pulley discs grow or shrink?
No. The belt contact radius changes between conical halves while the outer disc size stays fixed.
Why do both pulleys turn the same way?
The belt is uncrossed. Their angular speeds differ, but their belt-contact surface speeds match.
Why can RPM reduction be negative?
In overdrive, output speed exceeds input speed. A negative reduction reports that increase.
Does the output torque establish a safe rating?
No. It is an ideal power-conserving result. Hardware capacity and slip require additional information.
Can I choose both radii freely on one real CVT?
Not generally. A fixed belt length and fixed shaft spacing couple their possible positions.
References
MathWorks, Continuously Variable Transmission, describes pulley kinematics, ratio, belt geometry and the additional dynamics needed to model slip.
Bosch Annual Report 2012, discusses axially movable pulley cones and changing belt pitch radius.
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