I was curious how quickly (or slowly) the various gears in the Schatz standard 400 day clock turned, and especially wanted to know how many rotations the mainspring barrel makes in a year and in 400 days.
Here are the results:
Beats per hour: 480 (8 beats per minute)
The escape wheel rotates every 5 minutes.
The center wheel rotates once per hour
T4 (the wheel driving the center wheel) rotates every 7.5 hours
T3 rotates every 2 days
T2 rotates every 256 hours (10.67 days)
The mainspring barrel rotates every 76 days. It rotates 4.77 times per year, and 5.23 times in 400 days.
First, the number of teeth were counted in each gear:
Barrel 86 teeth
T2 64 teeth (gear) 12 leaves (pinion)
T3 64 12
T4 60 10
T5 (center wheel) 96 8
T6 (escape wheel) 20 8
For all calculations, the center wheel is used as the starting point, we know that it makes one turn per hour. We then multiply a series of ratios to find the rotation speed of the other gears, and the number of beats per hour of the escape wheel.
For number of beats per hour, the escape wheel rotates faster by the ratio of the number of center wheel teeth to the number of leaves in the escape wheel pinion, times the number of escape wheel teeth times 2 (because each tooth of the escape wheel needs to escape twice – from both the entrance and the exit pallet).
Beats per hour = (96 / 8 ) x 20 x 2 = 480
Dividing by 60 minutes per hour gives 8 beats per minute.
For the rotation speed of the barrel, we multiply ratios of the gears driving the center wheel:
Rotation time in hours = 1 hour x (60 / 8 ) x (64 / 10) x (64 / 12) x (86 / 12) = 1835 hours
= 76 days,
corresponding to 4.77 rotations per year or 5.23 rotations per 400 days.