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CORRECTING THE DAILY RATE

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1. Introduction

Many factors influence how well a watch runs. Thus, over the course of its life and various events, a watch may tend to run fast or slow. The daily advance or delay of a watch compared to a reference time is called: daily rate. Fortunately, watchmakers have devised different ways of adjusting the daily rate of a movement.

Recall that if a watch runs fast, it is because the Frequency of oscillation of its Regulating organ is too high. Conversely, if it runs slow, it is because its frequency is too low.

Two methods allow the frequency of the regulating organ to be corrected: modifying the active length of the Hairspring (balance spring) and that of the Moment of inertia of the Balance. The choice of one or the other of these methods, or their combination, is made during the design of the Movement.

2. Correction of the Daily rate by modifying the active Length of the Hairspring (balance spring)

This is, to this day, the more common of the two methods used. It consists in modifying the Frequency of the Oscillations of the Regulating organ by adjusting the active Length of the Hairspring (balance spring). The Hairspring (balance spring) is a spring Blade of rectangular cross-section, wound in an Archimedean spiral. Just like a guitar string, the greater its Length, the lower its Frequency. Conversely, the shorter its Length, the higher its Frequency. This correction method requires the presence of a Regulator. The position of the regulator pins determines the active length of the hairspring. When the regulator pins are brought closer to the stud (hairspring stud), the active length of the hairspring increases, the frequency decreases, and this causes a delay. Conversely, when the regulator pins are moved away from the stud (hairspring stud), the active length of the hairspring decreases, the frequency increases, which results in gaining time (Figure 1).

Figure 1

Correction of the daily rate by modifying the active length of the hairspring

Click on the animation to enlarge it

For informational purposes. If a medium-sized wristwatch is running 10 s/day slow, the active Length of the Hairspring (balance spring) must be shortened by about 0.02 mm (approximate value for a hairspring with a Length of 100 mm at the counting point and a Balance of 11 mm diameter oscillating at 28,800 A/h).

3. Correction of the Daily rate by modifying the Moment of inertia of the Balance

The Moment of inertia is the physical quantity that measures the resistance of a body to a change in its rotational speed around an Axis.

• The more the Mass is far from the Axis → the greater the moment of inertia

• The more the Mass is close to the Axis → the weaker it is

• At equal mass, the distribution changes everything

Thus, the Moment of inertia of a Balance depends on its Mass and its radius according to the following formula:

The Balances with variable inertia exploit this physical law. Thus, screws are arranged around the periphery of the Balance or split weights (usually in Gold) on the Felloe (rim base) of the Balance. By moving their Mass toward the inside of the Balance, its Moment of inertia is decreased and its Frequency (rotational speed) increases, causing the watch to run fast. Conversely, by moving the Mass of the Screws or weights toward the outside of the Balance, its moment of inertia is increased and its Frequency decreases, causing the watch to run slow (Figures 2 and 3).

Figure 2

Correction of the Daily rate by modifying the Moment of inertia of the Balance

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Figure 3

Ratio of the Balance’s moment of inertia – Daily rate

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Although at the scale of a wristwatch the correction range is smaller than when modifying the active Length of the Hairspring (balance spring), this solution has the advantage of being less prone to being thrown off by a shock. Moreover, and above all, it makes it possible to do without a Regulator and to eliminate the influence of the friction of the Regulator pins and the Hairspring (balance spring) on the Isochronism.