finding barrel mainspring length

[willofiam]

I was looking for something else and came across this, William

DSCN9083_01.JPG (11.31 KiB) Viewed 6833 times

[gerene]

Thanks William for this formule which certainly can come in handy.
Would this be for watches, clocks or both?

Jan

[david pierce]

Jan,
Pi R^2 = the area of the space inside the barrel. Pi r^2 = the area taken out by the barrel arbor. The area of the cylindrical space between the outer wall of the barrel and the arbor is Pi R^2 - Pi ^r^2. If you factor out Pi, this becomes Pi(R^2 - r^2). Since the area of something = Length x Thickness, the length of the spring will be Length = Area / Thickness or L = Pi(R^2 - r^2) / T. Also since the spring must coil and uncoil, space must be allowed in the barrel for this to happen. If you want 1/2 of the space to hold the wound coil and the other 1/2 of the space to allow the coil a place to go, then you can multiply (Pi(R^2 - r^2) / T) by 1/2. The result will be William's formula which now becomes L = Pi(R^2 - r^2) / 2t. The number 2 is the control parameter that determines the amount of space taken up by the coiled spring and the amount of empty space that gives the coil a place to go when it uncoils. If necessary, you can change this value to suite the particular mechanism you are working on.
david

[gerene]

Thanks David for your lengthy and clear explanation of the formula. I guess my question should have been phrased: is the value of the constant in the denominator for clocks and/or watches?
I do understand that 2 in this case represents that the spring occupies about half of the width between the barrel arbor and the inside of the barrel wall.
De Carle states in his book "Practical Watch Repairing" that this should be less than 1/3 for watches. We can change the constant to 3 to calculate the length of the mainspring for watches.
Suppossing that half the width would be good for clocks then the formula is geared to clocks. I couldn't find the ratio for clocks in the literature I have at hand.

Jan

[david pierce]

Jan,
The "experts" who write watch repair books are really no different than the rest of us. They get their information from various sources such as books wirtten by other experts, articles, interviews and practical experience. A lot of times when a number is thrown out to the rest of us it may be nothing more than an estimated guess. If one source says 1/3 and another source says 1/2 it does not mean that one is wrong and the other is correct. One number will simply run the mechanism longer than the other number.
That said, I feel that the smaller the watch, the more critical the issue of wasted space becomes. Larger watches and particularly clocks can afford a wider latitude in this area. In the end result the way the mechanism behaves determines the correct ratio of coil thickness to barrel space. Since the inversely proportionly control parameter controls the length of the spring, as the number gets larger you simply end up with a shorter spring and more barrel space. The margin of error is then the length of time the mechanism will run between windings.
david

[maitai11]

David:

We haven't met - my name is Tim - but, after reading your formulation explanation, I gotta wonder: were you ever a candidate for the Nobel Prize in Mathematics? If not, it may be time for your name to be submitted for consideration. I'm going to come to you with all my math questions, since math, to me, is very much a foreign language!

Awesome breakdown of that formula!

Tim

[david pierce]

Tim,
I am simply a humble truck driver.
david