Let's get Mathematical Part 7

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