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Estimating the mainspring size from barrel diameter


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Just throwing this out there to see your opinions.

Typically I trust that the mainspring that I find in a watch is the correct one.  However, I recently opened a watch and found that it was definitely not the correct mainspring.  Someone hacked a T-end mainspring into a normal manual bridle.

I could not find any information about the movement online, so I endeavored to find out what the proper mainspring might have been.

Assuming that mainsprings are designed to follow the 1/3 area rule (that the unwound mainspring in the barrel should occupy 1/3 of the barrel width), then thickness and length must scale with the barrel diameter.

I took every available mainspring being sold on Cousins, and plotted the thickness of the mainspring vs the barrel diameter, and I found an extremely statistically significant relationship between the two (see picture).

From the results, we find that the thickness of the mainspring is equal to 1.18% of the barrel diameter, minus 0.0036 mm (this tiny subtraction can probably be ignored).

Alternatively, you can take the average of all the thickness/diameter ratios, and you get 1.14%.  If you have a low-grade non-jeweled watch, you can add one standard deviation, which will bring you to 1.26%.  If you have a very high grade 21 jewel watch, you can subtract a standard deviation, which will bring you to 1.02%.

When reading this page about estimating thicknesses (https://www.vintagewatchstraps.com/mainsprings.php), the author says that deCarle and Daniels have suggested anywhere between barrel diameter/100, up to barrel diameter/84.

These figures suggest anywhere between 1% and 1.19%, so I don't think my method is too far from reality.

thicc.png

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Wow, what a diligent work!
You confirmed by your method (maybe for the 1st time, I never read of similar work before), what not only deCarle and Daniels have suggested, but can be found in any horological textbook: average thickness recommended is D / 85. Fine, full jewelled watches D/90, rather coarse watches D/80. From that range you have to choose first, then length can be found from the known dimensions.

Figures for clock springs are different, however.

How did you find the barrel diameters? Diameter given with springs is that of its retaining ring usually. 

Thank you for this interesting post,
Frank

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Really interesting work there! One thing I noticed is spring thickness equals ligne size of the movement in most cases. For higher beat watches add 10% or so. This is just an odd coincidence, but I've even dug through the Generale Ressorts book comparing and it really holds true.

 

The formula for length is:

Length = π(Rb² - Ra²) / 2x thickness

Rb is barrel radius, Ra is arbor radius

To the result add about 20%

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2 hours ago, praezis said:

How did you find the barrel diameters? Diameter given with springs is that of its retaining ring usually. 

When I purchase a mainspring, I try to get the largest size that is smaller than the actual barrel diameter.  So if the true ID is 10 mm, I'll try to buy a 9.5 mm so that it can easily slot in.  As long as the retaining ring and the barrel ID are close, then the 1/3 relationship should still hold true, so the model I built should still apply.

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