Keeping Time · Part 7 of 7
Faults as Physics
Every watch in Tick Again arrives with something wrong with it, and the game never tells you what. You find out the way a watchmaker does: it will not wind, or it winds and will not run, or it runs and gains three minutes an hour. That only works if a fault is not a label on the watch but a change to the model, so that the symptoms come out of the same physics as everything else. This last article is about how the faults are made, and how a watch’s rate is put together from them.
The rate, term by term
A watch’s rate, how many seconds a day it gains or loses, is composed from a handful of terms, each standing for something a watchmaker would recognise:
public var rate: Double {
var r = baseRate + regulator * Watch.regulatorSpan
if faults.contains(.magnetizedHairspring) { r += 3 * 60 * 24 }
if amplitude > 0 { r += (caliber.escapement.amplitude - amplitude) * 0.08 }
if !dialUp { r -= 3 }
return r
}The base rate is the watch’s own error as it came in, set for each watch in its envelope. The regulator is the index on the balance cock, which lengthens or shortens the working part of the hairspring; moved from the middle of its scale to either end, it changes the rate by 240 seconds a day, an estimate of a period index marked for review. Magnetism makes the coils of the hairspring cling together, which shortens it and makes the watch gain a great deal: three minutes an hour. The short-swing term is the one from the last article but one, 0.08 seconds a day for every degree under 270. And lying dial down costs three seconds a day, a position error of the kind every real watch has in some measure.
The model then runs the watch at that rate: for every second of real time, 1 + rate/86,400 seconds pass on the watch. So the rate is not only a number on the timegrapher: the hands drift by it, the ticks come faster by it, and the trace climbs by it, all from the same term.
Faults as changes to the physics
The faults themselves are an enumeration in the source, and each one changes something specific. A few of C1’s, with what they do:
- A broken mainspring. The crown turns and the click clicks, sixteen to a turn, and nothing is stored, because there is nothing for the ratchet to wind against.
- A tired mainspring. It winds and runs, but pulls with less force, so the swing settles at 0.72 of its healthy figure.
- A rusted click spring. The click does not hold. The spring winds, and a fifth of a second after you let go of the crown, it unwinds again.
- A loose cannon pinion. The watch runs perfectly, the seconds hand turns, and the hands never move, because the friction that should carry them slips exactly as fast as the train drives them.
- A broken balance staff. Nothing can swing. The settled amplitude is zero; the watch winds and never starts.
- A cracked jewel. A pivot drags in a damaged hole. The swing falls to 0.6 of its figure, so the watch runs short, and runs fast with it.
- A magnetized hairspring. Three minutes an hour fast, until it is demagnetized.
- Out of beat. The trace splits in two, and stays split until the collet is turned.
- A broken stem. The crown turns freely and neither winds nor sets.
Before you read on
A watch comes in with a cracked jewel. Does it gain or lose?
It gains. The crack does not change the balance’s frequency; it costs the balance its swing, the swing falls to about 160 degrees, and a short swing runs fast at 0.08 seconds a day for every degree short. A test checks both halves: the amplitude falls below seven tenths of healthy, and the rate rises by more than five seconds a day. It is the kind of symptom a watchmaker reads backwards, from a fast watch with a poor swing to something dragging in the train.
Oil
The quietest faults are about oil. Every jewel and bush in the movement has its oiling point, and each takes a particular lubricant: the slow arbors under the mainspring’s pull, the barrel and the centre, take heavy oil; the fast ones, from the third wheel to the balance, take fine oil; the pallet stones take their own, applied only with the balance cock off; the keyless works take grease. Each pivot carries a weight for how much of the swing it costs when it is not properly oiled, the balance most at 0.14, the barrel least at 0.03, and how it is wrong matters:
public var efficiency: Double {
var loss = 0.0
for p in points {
switch state(p.id) {
case .fresh: break
case .dry: loss += p.weight
case .old: loss += p.weight * 0.8
case .wrong: loss += p.weight * 0.6
case .flooded: loss += p.weight * 0.5
}
}
return max(1 - loss, 0.3)
}Dry is worst, old oil nearly as bad, the wrong oil better than none, and too much, a second drop that floods the seat, costs half. The efficiency multiplies the swing, so a carelessly oiled watch does not stop; it runs, short and fast, which is exactly how a real one fails a watchmaker’s check. The weights are estimates waiting for review, but the order of them is not: a dry balance pivot costs far more than a dry barrel arbor, as anyone who has oiled one will say.
Where the model stops
The model is a watch as a watchmaker reads one, and it stops where the bench does: at the rate, the amplitude, the beat error, the reserve, and the order the parts come out. It does not model the escape wheel’s teeth sliding across the pallet face, or the hairspring breathing, or temperature. Several of its figures, the ones marked as estimates through this series, are waiting for a watchmaker to read the source and correct them. The tooth counts, the order of the work and the arithmetic that ties them together are the parts I can vouch for, because the tests hold them, and they are the parts the game is built on.
If you want to see the model run, it is on the bench in Tick Again.