Van Woerd's Sawtooth Balance by American Waltham

Mary Rohs

Registered User
Jun 15, 2017
Was the sawtooth balance incapable of adjusting to accuracy (design failure) or was there simply a cumbersome issue with ongoing adjustments of the balance itself? I've read both hypotheses.

I can't imagine how the watch would be produced (whatever the small number was made with the sawtooth) only to find out mid-production that the time keeping was not accurate or the balance was literally incapable of accuracy. Does anyone have any information?

I started thinking as I saw an old thread here of Van Woerd's personal chronograph, which I believe had the sawtooth balance. So he must've adjusted it well enough to use it and rely on its timekeeping. Why else keep it in the watch.

Thank you.

Tom McIntyre

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Aug 24, 2000
Charles Vander Woerd's intent was to eliminate middle temperature error. It was based on his theory that the strain between the steel and brass portions of the balance contributed to the error.

The actual problem was that the elastic modulus (stiffness) of the hairspring is linear with temperature while the moment of inertia of the balance is non-linear. As a result, the temperature compensation is only correct where the two curves cross. Those points were usually around 35 to 40 degrees and 75 to 80 degrees. In the middle of that range around 55 to 60 degrees there is a temperature compensation error.

Woerd's balance also has most of the weights out on the end of the balance arm, which makes it vulnerable to another error because of the centrifugal force on the balance which makes it sensitive to the amount of force applied to the escapement. That is observed as an error in isochronism, which is a standard test that watchmakers apply to high grade watches.

If you want to know more about precision timekeeping and what Woerd was attempting, there is a discussion in this Power Point presentation on the Evolution of the Marine Chronometer.

Joe Brown wrote an article for the Watch & Clock Bulletin where he tried to demonstrate the correction of middle temperature error and Tom De Fazio wrote a more detailed analysis of the design where he discusses the centrifugal error.

As to your original question, it is no harder to adjust than any other high grade pocket watch. It was probably rejected by the trade because it was just too different.

The Paris Exposition of 1878 gave Woerd a bronze medal for the work. His over enthusiasm about his own inventions was likely one of the reasons he was replaced by Fitch and Church in the Waltham factory.

Dr. Jon

NAWCC Member
Dec 14, 2001
New Hampshire
My view is that for middle temperature error the saw tooth balance was wrong and he should/could have known better. The Swiss were looking at this and publishing work on it starting in 1868 and the nature of the problem was described by Dent in 1848. Chronometer makers were playing with auxiliaries devices like the Poole device. The real problem with the saw tooth is that with that many cuts it requires great precision just to get equal response on both arms. The centripetal force effects also well known thanks to Airy's work but due to manufacturing issues, the large problem with the saw tooth was that it was likely respond unequally and go out of poise.

Trial records show that even in the marine chronometer class, temperature performance eve by top makers was usually less than possible even with the middle temperature error. The problem was that the devices did not respond as expected due to "stiction" and other less known real world issues, The largest gains in temperature performance were in simple devices that could be made very well. Adding complexity in terms of more parts that had to work together usually made performance worse. This is effectively what the sawtooth balance did.
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Clint Geller

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Jul 12, 2002
Pittsburgh, PA
The irony of it is that if Woerd's sawtooth balance had been really successful, like say, Fogg's pinion, it wouldn't be rare, and collectors wouldn't go nuts over it. Only a few relatively technical collectors would care about the earliest examples. For example, watches with Fogg's vibrating stud are rare and sought after, whereas watches with Fogg's much more successful safety pinion aren't so much. And sometimes noble failures like Woerd's Balance can reveal more about the nature of their inventors than successful inventions.
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NAWCC Member
Jan 7, 2011
Breamore, Hampshire, UK
Hi Dr. Jon,

and the nature of the problem was described by Dent in 1848.
In the October issue of the HJ, David Boettcher has written the second part of his exploration of the balance spring and in it he dissects the concept of middle temperature error in some considerable detail. I shall not attempt to precis the article but I think it's well worth reading if you have an interest in the physics of escapements.



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