A going train is the gear train that transmits power from a clock or watch’s driving source to its escapement. Wheels and pinions set the relationship between the slow power-source rotation and the faster downstream arbors. This calculator follows four ideal external-gear stages from barrel to escape wheel, starting with an entered centre-wheel rate.
Going Train Interactive Calculator
Propagate a user-defined centre-wheel rate through four ideal external-gear ratios and inspect each mesh with exact angular marker motion.
Equation Used
- Four ideal external-gear meshes: barrel-centre, centre-third, third-fourth and fourth-escape.
- Each entered ratio is a positive speed-magnitude ratio; every mesh reverses direction.
- Rigid gears with no slip, backlash, losses or deformation.
- No tooth counts, module, centre distance, torque, efficiency, strength, bearing or escapement model.
Ideal gear-speed calculation. Each entered ratio is the magnitude of driven speed divided by driver speed for one external mesh. The panels are scaled independently and do not design tooth counts, module, centre distances, torque capacity, losses or an escapement.
Compound clock-train stages
A going train carries motion from the barrel through the centre, third and fourth arbors to the escape wheel. A wheel on one arbor drives a pinion on the next. Where a wheel and pinion share an arbor they have the same angular speed.
The animation separates the four meshes into panels. Marker angles use the exact entered ratios and reverse direction at each external mesh; panel sizes are independently scaled for readability.
Going trains in timekeepers
Mechanical clocks and watches use a going train to connect the power source, time display and escapement. The number of stages and the arrangement of hands vary; the four-stage layout here is one idealized arrangement.
The escapement and oscillator regulate the rate of a working timekeeper. A falling mainspring torque does not simply make each wheel run independently slower while preserving correct time. Reduced drive can affect oscillator amplitude and ultimately stop the movement, but this ratio calculator does not model those effects.
The British Museum’s record of watch movement 1958,1201.1152 gives actual wheel and pinion counts and documents a separate centre-seconds train. Such records illustrate why the details of an identified movement matter.
Calculating gear speeds
Let r1 through r4 be the positive driven-speed/driver-speed magnitudes of the four meshes. The barrel-to-escape magnitude is r1r2r3r4. Starting from centre rate n_c, fourth speed is n_c r2r3 and escape speed is n_c r2r3r4. Hourly rates are divided by 60 for rpm.
The barrel rate is n_c/r1, so its period is r1/n_c hours per revolution. External meshes reverse direction; output tiles report speed magnitudes.
Example: four entered ratios
Use centre rate 1 revolution/hour and stage ratios 12, 8, 7.5 and 10. The corresponding example wheel/pinion pairs are 96/8, 80/10, 75/10 and 70/7.
- Total barrel-to-escape speed ratio: 12 × 8 × 7.5 × 10 = 7200.
- Fourth-wheel speed: 1 × 8 × 7.5 / 60 = 1 rpm.
- Escape-wheel speed: 1 × 8 × 7.5 × 10 / 60 = 10 rpm.
- Barrel period: 12 / 1 = 12 hours per revolution.
The numerical ratios determine relative speeds. They do not establish a beat rate without the escape-wheel tooth count and the escapement’s release sequence. Nor is one barrel revolution the same as the total power reserve.
From ratios to a working clock
Ratio arithmetic alone does not design a clock train. A buildable train requires integer wheel and pinion tooth counts, module or pitch, centre distances, arbor layout, tooth form, backlash, torque and power losses, bearing loads, strength and an escapement compatible with the intended beat rate.
Frequently asked questions
Are the panel circles the actual gear sizes?
No. Each panel is scaled independently to show its ratio. Gears sharing an arbor appear in adjacent panels; the drawing is not a single physical layout.
Why do directions alternate?
Each external gear mesh reverses rotation. A wheel and pinion fixed to the same arbor turn together.
Why does changing Barrel-Centre not change Escape Speed?
Centre Rate is the specified reference speed. The first ratio changes barrel speed and total ratio; downstream speeds depend on Centre Rate and ratios 2, 3 and 4.
Why does changing Centre Rate not change playback speed?
Playback shows relative angular motion on a fixed time scale. Centre Rate changes the calculated speeds and barrel period, while the displayed ratios remain the same.
Can I infer escapement beat rate from Escape Speed alone?
No. You also need the escape-wheel tooth count and the actual release pattern per beat. The calculator has no escapement model.
Does Barrel Period give the clock’s run time?
No. It gives hours per barrel revolution at the entered centre rate. Run time also depends on usable barrel turns and the power source.
Horological references
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