Podcast How Watches Work E3 – Movements As Torque Managers

Allen and David sit down in the third installment of the ‘How Watches Work’ series to discuss the subject of torque, what it is and why it is central to the design and operation of any watch, be it quartz or mechanical, simple or complicated.

What Is Torque?

What is torque? At its simplest, torque is the force applied to turn something – literally the rotational equivalent of force. When you push open a door you are applying torque to turn the hinge in order to open the door. Everyone implicitly understands torque whether they realize it or not. When you push on a door to open it, you know to push near the handle rather than near the hinge because if you push there you have to supply a lot more force to generate the required torque to open the door. The unit of torque is the Nm, or newton-meter (pound-foot to my American friends) and that tells us torque is a product of force and distance.

τ = r × F

Torque is calculated as r, the distance from the rotational center, multiplied by F, the force.

So let’s go back to that door… it requires a certain amount of torque, or turning force, to open it as you need to over come the friction in the hinge, the weight of the door and possibly an auto close spring. As we have seen, you can apply a force to generate the torque at the handle side or the hinge side. If you push near the hinge, your hand is much closer to the hinge so the force component you provide must be much higher. If you push near the handle, your hand is much further away and the force component can be less to provide the same torque. It’s basically leverage but applied to something turning.

So What Has Torque Got To Do With Watches?

Actually a lot.  

Torque is what is generated by the watch’s mainspring and so torque is at the root of everything that happens in the watch after it is wound. The mainspring’s torque enables the hands to rotate as time passes. The mainspring’s torque enables to other complications such as a calendrical functions and chronographs to be powered at the same time. Ultimately, the mainspring’s torque dictates how much force is applied to the balance to keep the watch’s timekeeping precise. So you see, torque is everything to the watch’s operation.

Torque’s importance is not just limited to automatic watches, it also drives the design of quartz watches where a very limited amount of power, stored in a small battery or capacitor must drive the watch for months and preferably years. Therefore, torque demands within a quartz watch must be minimized which is why the hands of quartz watches are generally thinner and lighter the mechanical watches. This is especially try of quartz chronograph hands which have to move quickly. Torque minimization is why quartz watches tick once per second since that motion uses less torque. And yes, your mechaquartz sweep hand does use up the watch’s battery 4 or 5 times faster if you leave it running.

The design of a watch’s escapement can also place its own additional torque demands on the main spring. In the late 1960s, Seiko were competing in the Swiss chronometer trials and found that precise long term timekeeping was enhanced by using a large balance with a high oscillation rate. So, when the 36000 vph caliber 45 was produced by Daini Seikosha for the King Seiko range, a mainspring with increased stiffness was required to supply sufficient torque to drive the large balance so quickly. Of course, this led to reliability issues elsewhere in the movement that were not suitably uprated for the increased torque.

In the early 60s when a nascent Grand Seiko was designing watches with large gold hands, more torque was needed from the mainspring to drive those heavier hands around the dial. As the torque is transferred through the going train, it reduces as the speed of the gear wheels increases. Remember from episode two, the purposed of the going train is to speed up the rotation of the barrel to correspond with a rotation of one wheel once per hour and another once per minute. Therefore the faster the hands move, the less torque is available to turn them, which is why the slow hour hand can be heavier, but the faster seconds hand needs to be lighter.

Torque is also a factor when sizing the movements. Larger watch movements can have larger wheels in the going train and larger barrels, resulting in a watch with more torque, a greater power reserve and smoother torque delivery which improves precision. The smoother torque delivery is a function of having more teeth on the wheels.

Isochronism, or Lack Thereof

Escapement isochronism (definition: the quality of being isochronous, meaning occupying equal time) relies on constant torque. So, exactly the same little shove to the balance wheel from the escape wheel on each oscillation. An ideal spring exhibits Hooke’s Law which states that the extension of a spring is exactly proportional to the force applied to it, and conversely, of interest to the watchmaker, the force from the mainspring should be exactly proportional to the extension (the wind). Remember Robert Hooke from the first How It Works episode on escapements? He was the inventor if the microscope and the hairspring balance we are familiar with, among other things, and probably had more input to ‘Newtons’ laws of gravitation than Newton ever gave him credit for. Well, he also discovered the law governing spring extension and the implication of his law for watchmakers is that as the mainspring unwinds, the torque delivery also decreases (as the extension reduces, so must the force exerted if the coefficient of elasticity of the spring remains constant).

Effect of Hookes Law on watch torque
Hooke’s Law decreases watch torque as the mainspring unwinds

Hooke’s Law… (yes, him again)

Torque is not constant due to Hooke’s Law nor linear through out the main spring power reserve. When the the main spring is loosely wound, torque is very low and when it is approaching its elastic limit, akin to overwinding a watch, torque again drops off again. However, the bit in the middle after the spring has been wound a bit until the spring is too tightly wound is almost linear. We call this the operational range of the spring. This is why the mainspring is already wound up in the barrel even when power is fully depleted. The spring needs a certain amount of wind from the get go to avoid that low torque phase when it is loose. This is a bit like preload on a car or bike shock absorber. Spring response is more linear and more predictable when the spring is already squashed a bit.

Have you ever wondered why a mainspring is not normally a simple coil but in fact takes the shape of an S? Well, it is shaped like that to flatten the torque curve and provide an operating range with a more constant torque curve and therefore make the timekeeping more isochronous. A simple helical main spring would start to slow down long before the S-shaped spring does, making the S-shaped spring a better timekeeper for longer. It is worth noting at this point that an automatic watch that is worn is likely to be more isochronous than a manual watch while it is being worn because the automatic winding mechanism will keep the spring ‘topped-off’ near maximum wind.

S-shaped mainspring
Watch mainsprings are typically S-shaped to flatten the torque curve

Most watches make do with pre-wind, S-shaped springs and some material choices to give a mainspring that is good enough for reasonable timekeeping. But ‘good enough’ is often not ‘good enough’ for high horology and so a number of watch complications have been invented to further improve upon the torque delivery within a watch. Technically, they are not complications because they do not give the wearer more information, but they are complicated subsystems and so I think the term is justified for common understanding.

Fuseé and Chain

The first torque complication is the fuseé and chain. A fuseé is a conical gear wheel driven by a chain from the barrel rather than the barrel driving the second wheel directly. The purpose of using a cone is that when the mainspring is fully wound and torque is higher, the chain drives the cone at the top, where the radius is small. Driving the cone at the top requires more torque. Using our door analogy, driving the top of the cone is like pushing the door near the hinge. As the mainspring unwinds, the torque decreases slightly and the chain moves down the fuseé. Driving the cone lower down where it is wider requires less torque, just like opening the door by pushing near the handle.

Therefore, the fuseé counteracts the torque change from the barrel to ensure that the going drain afterwards, only sees constant torque. It’s a smart solution that has its origins in large tower clocks where the torque difference between full wind and wound down was significant and was later miniaturized for pocket watches. The fact that a a tiny fuseé and chain can be built into the going train of a wrist watch is an amazing achievement. A. Lange & Söhne managed to squeeze such a mechanism into it’s 1994 Tourbillon Pour le Mérite with a chain cross section of just 0.6 x 0.3mm! Since then, wrist watches from Breguet, Zenith and Romain Gauthier. Such miniaturization is not inexpensive however… each of these watches will cost you between $75,000 to $175,000.

A. Lange & Söhne Fuseé and chain. Image courtesy of A. Lange & Söhne

The Remontoire

The final complication that has a role to play in torque delivery is the remontoire. A remontoire is a secondary spring driven from the main spring with a much, much smaller power reserve, placed close to the escapement. The principle behind the remontoire is that it evens out the long-term torque variance by constantly winding and unwinding as it drives the balance in a much more isochronous way. A typical remontoire has a power reserve measured in seconds rather than hours and it therefore constrains any timekeeping error due to torque variance to an absolute minimum. As a result, if a remontoire starts taking longer to wind up due to decreasing mainspring torque, it has very little effect on timekeeping as the average torque at the escapement remains fairly constant.

Torque due to remontoire
Result of a remontoire on watch torque