The Digital Toolbox for Watchmakers

At the workbench, we repeatedly make the same calculations: Which mainspring should we order when the original is missing? Will an available spring fit the barrel? Through how many degrees must we turn the collet? How many turns does the rating nut need? This page brings together the calculators for these tasks and the interactive models from the blog. Each calculator shows its working so that the result can be checked.

The calculators follow the flow of power through the movement: power source, going train, escapement and oscillator. The escapement models come first because the pallet adjustment model is the most useful one at the workbench. It is worth bookmarking this page; every section has its own direct link.

Contents

1. 1Models of the Swiss lever escapement
   1. 1.1Pallet adjustment model (coming with Part 2)
   2. 1.2Escapement test bench
   3. 1.3Lever escapement in 3D
   4. 1.4The five phases
   5. 1.5Balance amplitude
   6. 1.6Fault atlas (coming later)
2. 2Power source
   1. 2.1Calculating a mainspring when the original is missing
   2. 2.2Checking and shortening an available mainspring
3. 3Going train
   1. 3.1Beat rate from tooth counts
4. 4Oscillator
   1. 4.1Balance: beat error in degrees
   2. 4.2Pendulum: adjusting the rating nut
5. 5Rate checking
   1. 5.1Daily rate from time error
   2. 5.2Timegrapher for pendulum clocks (in development)
6. 6Other tools
   1. 6.1Lignes and millimetres
   2. 6.2Dew point at the crystal
   3. 6.3Amplitude from lift time

1 Models of the Swiss lever escapement

The models accompany the article The Swiss Lever Escapement and run in the browser, including on a phone. Clicking ‘Start model’ opens the model here in the article.

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2 Power source

2.1 Calculating a mainspring when the original is missing

If the mainspring is missing or broken, we need its width, thickness and length to order a replacement. The thickness follows two rules of thumb from the literature: the arbor radius should be 10 to 14 times the spring thickness, and the thickness should be between one hundredth and one seventieth of the barrel diameter. The ideal length fills half the available area inside the barrel, giving the greatest number of barrel turns. The original spring or the manufacturer's specification always takes precedence.

2.2 Checking and shortening an available mainspring

For clocks, we often shorten an available spring to the required length, or check whether a catalogue spring is an exact fit. The deciding quantity is the fill factor: the proportion of the available area inside the barrel occupied by the spring. In practice, 50 to 53% is used. A longer spring gives fewer barrel turns, so we shorten it.

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3 Going train

3.1 Beat rate from tooth counts

If the beat rate is unknown, we count the wheel teeth and pinion leaves. We start with a wheel whose rotational speed is known, usually the centre wheel. If the movement has no true centre wheel, we use the fourth wheel or another wheel with a known speed. If there is no third wheel, leave a row blank. If the seconds hand is mounted directly on the escape wheel, its tooth count alone is enough. Each escape-wheel tooth gives two vibrations.

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4 Oscillator

4.1 Balance: beat error in degrees

The timegrapher shows beat error in milliseconds; on the movement, we adjust it in degrees. On pocket watches, we turn the collet on the balance staff. With a movable stud carrier, we turn the carrier together with the stud. The calculator gives the angle and, if the balance diameter is entered, the corresponding distance at the balance rim.

Turn through the full calculated angle, not half of it. The beat error displayed by the timegrapher is already half the difference between tick and tock, directly giving the displacement of the rest position from the centre of the escapement. If an instrument displays the full difference, halve its reading before entering it. A start-up test or a small initial adjustment shows the required direction.

4.2 Pendulum: adjusting the rating nut

We usually do not know a clock's beat rate. For regulation, the approximate pendulum length is enough, measured from the bending point of the suspension spring to roughly the centre of the bob. If the estimate is 10% out, the result is also only 10% out. If the clock gains, lower the bob; if it loses, raise it.

The calculation is idealised and assumes a simple pendulum. The empirical factor of 2.25 rather than 2 allows for the fact that only the bob moves during adjustment, while the rod also oscillates. This is itself an average drawn from practical experience. We measure again after making the adjustment.

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5 Rate checking

5.1 Daily rate from time error

To check the rate over several days, we set the watch or clock to a time signal and later read off the deviation. A gain is positive; a loss is negative.

5.2 Timegrapher for pendulum clocks

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6 Other tools

6.1 Lignes and millimetres

Movement sizes are given in lignes, written '''. One ligne measures 2.256 mm. The calculator converts in both directions.

6.2 Dew point at the crystal

If the inside of the crystal fogs up, the crystal is colder than the dew point of the air inside the case. The calculator shows the crystal temperature at which water starts to condense.

6.3 Amplitude from lift time

The timegrapher measures lift time and calculates the amplitude using the selected lift angle.

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