Given: barrel arbour core diameter 3mm, barrel inner diameter 9mm, mainspring thickness 0.1. Calculate the theoretical length of the mainspring.

Given: barrel arbour core diameter 3mm, barrel inner diameter 9mm, mainspring thickness 0.1. Calculate the theoretical length of the mainspring. 

Pi x (R²-r²)
2e

3.14 x (4.5²-1.5²)
2 x 0.1

3.14 x (20.25-2.25)
0.2

3.14 x 18
0.2

56.52
0.2

282.6 turns

Given: centre wheel 80 teeth, third wheel 75 teeth, fourth wheel 70 teeth, escape wheel 15 teeth, third pinion 10 leaves, fourth pinion 10 leaves, escape pinion 7 leaves. Calculate the number of vibrations per hour, per second and the frequency (in Hertz) of the pocket watch.Vh = Z1•Z3•Z5•(2Ze) = N1
Z2•Z4•Z6

Vh = 80•75•70•(2 x 15) = 18,000
10•10•7

Given: minute wheel 48 teeth, minute wheel pinion 12 leaves, hour wheel 36 teeth. How many leaves does the cannon pinion have?Motion work ratio is almost always 12:1

N1 = Z1 Z3
N2 Z2 Z4

1 = 12 x ? 
12 48 x 36

1 x ? 
4 x 36

1 x ? 
144

144/12 = 12

Given: hour wheel 48 teeth, minute wheel pinion 10 leaves, cannon pinion 12 leaves. Calculate the number of teeth of the minute wheel.Motion work ratio is almost always 12:1

N1 = Z1 Z3
N2 Z2 Z4

1 = 10 x 12
12 48 x ? 

1 x 10
4 x ? 

10
120

120/4 = 30

Given: hour wheel 64 teeth, minute wheel 42 teeth, cannon pinion 16 leaves. Calculate the number of leaves of the pinion.N1 = Z1 Z3
N2 Z2 Z4

1 = 16 x ? 
12 64 x 48

1 x ? 
4 x 48

1 x ? 
192

192/12 = 16