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In-Depth: Quantifying Performance and Trade-Offs in Movement Design

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In-Depth: Quantifying Performance and Trade-Offs in Movement Design

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Source Credit:  Content and images from SJX Watches by Tim Lake.  Read the original article - https://watchesbysjx.com/2020/01/quantifying-performance-movement-design.html

There are a lot of traditions in the luxury watch industry. From the use of pegwood to polish bevels, to the Roman “IV” rendered as “IIII”, the culture of watchmaking is full of interesting customs passed down over generations. But the most fundamental tradition remains the reliance on incremental improvements towards better timekeeping.

“Better” might mean absolute performance measured over a defined period such as an observatory trial (the objective of the superstar régleurs), or reliable long-term performance on the wrist. Regardless, for almost four hundred years the quest for better precision was the guiding principle of the trade. To paraphrase from historian David S. Landes’ Revolution in Time, “… it has always been the rule that the quality of [a watch] is a function of [its] precision.”

Omega cal. 47.7 observatory chronometer, where the barrel and balance occupy almost all of the diameter. Image – Omega

Today, some 50 years after mechanical timekeepers were left in the dust by their “better” electronic brethren, some makers of mechanical watches are more pious in their observance of this traditional approach to incremental improvement than their competitors.  And if we look carefully, we can quantify this difference in approach by looking at how different watchmakers choose to use the available energy within their movements.

Our interest was to find a way to quantify which watchmakers are making high-performance timekeeping choices and examine how measures like COSC might not reflect real on-the-wrist performance.

The Analysis

Starting with publicly available data, we compiled a database of the balance inertia, frequency, amplitude, and power reserve for a sample of 43 watch movements, from the enormous Kerbedanz KRB-08 with its 27mm central tourbillon cage, to the slender RMXP1 micro-rotor automatic made by Vaucher inside the RM 33, as well as many familiar staples such as the Rolex 3135, Omega 8500, Jaeger-LeCoultre 899, and ETA 2892.

With such tomes as WOSTEP’s The Theory of Horology as our guide, we calculated the amount of balance power (the amount present in the oscillating balance and a function of its inertia, amplitude, and frequency) and the balance maintaining power (the amount required to maintain the balance oscillation).

The ratio of these is known as ‘Q’ – essentially the rate of energy loss to friction in the balance system. For instance, a Q of 300 means 1/300th of the balance power is lost in each oscillation; the higher the ‘Q’ the better. Doing this for our sample allowed us to estimate the power transfer through the going train from the mainspring and better understand the decisions made by the movement designers.

It should also be noted that chronometric performance is dependent on a host of factors beyond the power of the oscillator. Consistency of delivery of the driving force from the mainspring is key, as well as numerous other factors including positional adjustments and regulation, finishing, choice of materials, care during assembly, the use of a free-sprung balance, and the form and isochronism of the hairspring; all will contribute to the actual performance on the wrist.

The analysis provides insight into which watchmakers are setting themselves up for successful high-performance timing and those that are settling for ‘good enough’.

Understanding Balance Power

Balance power is proportional to the balance inertia, but also the amplitude squared and, most significantly, the cube of the beat frequency.

Q is typically in the range of 200 (for vertical positions) to 300 (for horizontal positions), resulting in an average of 250.  Breguet achieves an exceptional 650 with the friction-defying magnetic pivots in the Classique Chronometrie 10 Hz 7727.

fn_phv small Balance, power= frac{1}{2}cdot balance, inertiacdot amplitude^{2}cdot (2pi cdot frequency)^{3}

fn_phv small Maintaining, balance, power= frac{1}{Q}cdot balance, power

fn_phv small Q= frac{balance, power}{maintaining, balance, power}

Another example, the workhorse Rolex 3135: with a 15mg.cm2 balance, 320 deg amplitude, 4 Hz frequency and Q estimate of 300:

fn_phv small Rolex, 3135, power = frac{15}{2}cdot (frac{2picdot 320}{360})^{2}cdot (2picdot 4)^{3}= 372, mu W

fn_phv small Rolex, 3135, maintaining, power = frac{15}{(2.300)}cdot (frac{2picdot 320}{360})^{2}cdot (2picdot 4)^{3}= 1.24, mu W

We applied these calculations to our sample, and the results are plotted in the chart below.

An analysis of balance power and power reserve of a sample of 42 movements (the Harrison H4 was left out being an extreme outlier)

The Trade-Off

The most important insight we can glean from this analysis is that for a fixed amount of energy stored within a given space, balance power and power reserve vary inversely to one another.

In other words, when you increase one, you must decrease the other. This is a really important insight, because it highlights the trade-offs that engineers have to make to deliver the lengthy power reserves that many consumers now expect.

This has major implications for how watches are made and sold. Simply put, it is easier for a brand to articulate the value of a 100-hour power reserve than to explain the theoretical performance gain made possible by a few extra microwatts of balance power. And as average power reserves have increased, so too have consumer expectations.

We now find ourselves in a situation where anytime a brand releases a new movement with a sub 50-hour power reserve, it’s sure to be met with criticism along the lines of, “It’s 2019, why can’t this brand give us a movement with a longer power reserve?” The answer is that of course they can, but they’ve chosen to spend more of the available energy at the balance to help raise the floor of rate performance.

The key takeaway here is that when you see a watch with a long power reserve, you’re not getting that extra power for free – a movement has to fit within a small, finite space so compromises must be made – and the energy is being robbed from the rate-keeping part of the system.

This is why you rarely see chronometer-certified watches with extended power reserves. It’s also why brands with in-house performance standards more stringent than COSC criteria, like Omega and Rolex, stick to more modest power reserves, usually under 72 hours.

Performance figures for 43 movements with publicly available data (inertia for the Bulgari and Zenith movements are estimates) – the colours of the cells darken as performance deteriorates, and lighten as performance gets better

Additional Insights

It’s hard to look at this table without being impressed by the exceptional balance power – 830 microwatts – achieved by the cal. 574DR inside the Breguet Classique Chronometrie 7727 that runs at an astonishing 10 Hz. That’s 72% more power than the Richard Mille RM 031 – featuring a high-frequency balance and direct-impulse chronometer escapement – that costs almost 25 times as much – it’s amazing what can be achieved with magnetic pivots and dual silicon hairsprings.

In fact, we might have been tempted to doubt our own analysis had Breguet not thoughtfully published these figures when the cal. 574DR was released in 2013. Sure, the Kerbedanz central tourbillon is technically ranked first, but it achieves its balance power through sheer size – its 49mm case dwarfs the comparatively diminutive 41mm Breguet.

The balance bridge holding the magnetic pivots of the Breguet cal. 574DR, showing also the silicon hairspring and escape  wheel. Photo – Breguet

Another interesting trend we can observe is the fact that the Omega 8500, Rolex 3135, Jaeger-LeCoultre 975, and the new Audemars Piguet 4400, which made its debut in the Code 11.59 chronograph, are clustered closely together.

These movements are meant to be the last word in robust precision from their respective manufacturers, so it’s pleasing to see such a close race. At the other end of the power table, we see slim movements like the BVL138 (found in the Bulgari Octo Finissimo) and the RMXP1, which have traded chronometric potential for slender form. Again, it’s all about trade-offs.

The svelte BVL138

The Need for Speed

Given that the amplitude for a traditional sprung balance is essentially limited to at least 220 degrees (otherwise positional performance deteriorates) and cannot be more than 350 due to overbanking (discussed later) – the really influential variables are the inertia and the beat frequency.

For a given level of balance power, some watchmakers prefer to achieve it with a slow, heavy balance, while others opt for a lightweight balance oscillating at a high frequency. It is essentially frequency vs inertia, either one or the other, but not both.

It is also worth considering that testing in fixed positions or even on a multi-arm test winder does not represent the same jarring and harmful transient dynamics that real use entails.  From hard sports use to “desk diving”, enthusiastic applause to simply flicking or shaking your wrist to reposition your loose-fitting watch, normal, everyday movement can wreak havoc with the regularity of an oscillating balance wheel.

To give an idea of the magnitude of this effect, we took well-performing 3 Hz and 4 Hz movements and filmed their behaviour at 30 frames per second (fps) while performing rotary motions similar to raising an arm from the elbow, so as to elicit conditions close to resonance of the balance wheel.

From the time stamps on the film, the instantaneous rate deviations seen over 8 seconds were plotted on the y-axis.

For the 3 Hz movement, there was up to 900 minutes-per-day error for one vibration.  One might wonder if the gains and losses might cancel out; in this case the time gained over these 8 seconds was 0.16 seconds.  If sustained, that would lead to an error of nearly 29 minutes over 24 hours.

The 4 Hz movement performed better with a potential error of 13 minutes over 24 hours; i.e. roughly half.

The graph illustrates large instantaneous rate deviations can be caused by arm motions for 3 Hz movements, but with lower deviations for 4 Hz movements

This begs the question, is there an ideal blend of inertia and frequency? In the dynamic environment of a human wrist, for a given power level, the combination that favours a higher frequency may be closer to the ideal.

The reasons are:

  1. The higher the angular velocity of the balance wheel, and the lower its inertia, the less influence that any given wrist motion can either hinder or enhance it.
  2. It is preferable if the natural frequency of the balance is significantly above the natural frequency range of wrist motions, away from causing resonance.

We should note that this challenges the widely held, traditional belief that a slow, heavy balance is preferable to one that is light and fast. We have to remember that much of the common wisdom about chronometry is a product of the era of observatory competitions, when movements were tested in static positions.

For that reason, historical observatory chronometer movements, like the famous Peseux 260 and Zenith 135, almost always had extra-large and extra-heavy balance wheels – a style that has been replicated in many high-end movement of today, like the Voutilainen cal. 28.

The Voutilainen cal. 28 and its extra-large balance

Under such testing conditions, the lower frequency offered distinct advantages, often with lower lift angles and more detachment, and less energy lost to friction at the escapement. But on the wrist, there are additional forces at play that change the rules of the game. Faced with real-world conditions, faster is probably better, all else being equal. Big balances are sexy, but the laws of physics prevail.

A timely case study that demonstrates this principle in action is the new L155.1 from A. Lange & Söhne, found in its new Odysseus sports watch. This is the manufacturer’s first movement to run at 4 Hz, up from the usual 3 Hz (or less) employed in all its other calibres. This change was apparently made to cater for the intended sporty use of the Odysseus.

Assuming the same spring barrel volume as the L086.1 on which it’s based, our analysis indicates that the balance power of the L155.1 was increased by 44% thanks to the reallocation of energy from the power reserve to the higher frequency oscillator (a reduction in power reserve from 72 to 50 hours). This would improve the stability of the balance motion in the face of the increased shocks that the sportier watch would face.

The new L155.1 from A. Lange & Söhne is their first to run at 4 Hz

With wrist movements in the order of 1 Hz to 6 Hz and watch movements operating from 2.5 Hz to 5 Hz, the challenge is clear. So, what has stopped beat rates going higher? Simply put, as speeds rise the power absorbed in friction climbs steeply too. This tends to mean the forces in the going train get even higher as the power struggles to transfer across to the pallets to reach the balance.

The influence of the inertia of the escape wheel itself begins to become a higher influence and wear in the train increases and power reserve suffers. To run faster needs different solutions: changes in escapement geometry, low friction materials, magnetic bearings, or completely new innovations such as the silicon oscillator in the Zenith Defy Inventor.

Friction and the escapement

When we talk about power, we also have to talk about friction. And in a mechanical watch, the most significant source of energy loss is the escapement. The ubiquitous Swiss lever escapement has many fine qualities that make it well-suited for use in wristwatches, but with a lot of sliding action it has always suffered from poor mechanical efficiency.

While researching this article, we found wildly varying efficiency values; from as low as 25%, all the way up to 50% – all from respected sources and makers. The discrepancy may stem from the fact that, in practice, the actual efficiency of the lever escapement will decrease over time as the lubrication deteriorates.

For the purpose of our analysis, we have used 40% for the basic lever – in other words, of the energy that reaches the escape wheel, only 40% is transmitted to the balance.

In an effort to improve on this figure, Rolex recently introduced its own lever design with revised geometry for its new 32xx calibre family. Rolex claims this new design, dubbed the Chronergy escapement, is 15% more efficient than the traditional Swiss lever.

On the other hand, direct or radial-impulse escapements such as the co-axial, detent, or double-wheel chronometer escapement, are far more efficient at transmitting energy from the escape wheel to the balance. In fact, watchmakers that have dabbled in these types of escapements tend to underestimate their advantages, and initial prototypes often overbank until the watchmaker either reduces the strength of the mainspring or increases the inertia of the balance wheel.

The Charles Frodsham double-wheel escapement

Overbanking (sometimes referred to as knocking or galloping due to the distinctive sound it makes on a timing machine) occurs when the impulse jewel on the balance staff receives so much energy from the pallet fork that it spins all the way around until it runs into the backside of the pallet fork (amplitudes on the order of 350 degrees plus).

For the purposes of our analysis, we assumed 53% efficiency for this class of escapements. Beyond better mechanical efficiency, this class of escapements offers an additional advantage – the efficiency does not decline with age.

Introducing ‘Horological Density’

Larger diameter and thicker movements naturally allow for larger barrel(s), and larger, heavier balance wheels. To normalise for this, we computed a stat we’re calling the Horological Density Factor (HDF).

fn_phv small HDFleft [ mu J/mm^{3} right ]=3600cdot frac{balance, powerleft [ mu W right ]cdot power, reserveleft [ h right ]}{calibre, volumeleft [ mm^{3} right ]}

In simple terms, this stat helps determine which movements are the most efficient in providing energy per unit of volume. The chart below can tell us who has used the space well, be it for balance power or power reserve, and can give us insight into manufacturers’ motives.

HDF by calibre – the number varies over 20 fold across the movements surveyed

Apart from the outstanding Breguets, as expected, the certified chronometric stars from Omega and Rolex are towards the top of the chart. Of the top 10, only two (Jaeger-LeCoultre 877 and Panerai P.2002) are eight-day movements. Mention must also go to the humble ETA 2892 for such a high place.

Intriguing is the spread of more than 20-to-1 for the HDF value across the highest to lowest examples (in comparison, the range of spring energy is 170-to-1). Key to delivering the exceptional performances of Breguet movements (one of which is a flyback chronograph by the way) is the high Q of the balances. Without this high Q factor, much larger spring energies (and hence size of the movement) would be required, which would likely accelerate wear in the drivetrain.

And just what is going on at the bottom of the chart? In some instances, aesthetic choices have been made; in others, technical.

A very good example is where F.P. Journe provides plenty of space around the twin barrels in the cal. 1304 found in the Chronometre Souverain as a design choice for visual impact. It is easy to envisage that if peak performance had been the goal, not only would this movement run at 4 Hz, it would have a balance wheel stretching from the centre wheel pivot to the case, and the spring barrels would have been larger. But if this were the case, the goal of building a movement with no apparent connection between barrels and balance would have been lost.

F.P. Journe cal. 1304. Where aesthetic whimsy limited potential performance. Photo – F.P. Journe

Another interesting example is the cal. 380 in the Jaeger-LeCoultre Duomètre Chronographe. This unique movement features two independent power sources: one for the main timekeeping train, and one for the chronograph train.

The stated aim of this solution is to improve precision by avoiding the variation in amplitude that typically occurs when the chronograph is started and stopped. However, this cure may be worse than the disease, since the deleterious effects of reduced balance power (compared to using both spring barrels for the timekeeping train) are likely more significant than the effects of brief fluctuations in amplitude.

The cal. 380 of the Duomètre chronograph with one spring barrel for timekeeping, and the other to drive a chronograph – limiting the potential performance of both

The Tourbillon: Paragon or Parasite?

For watches that feature a tourbillon, we have to factor in additional energy loss due to friction and the inertia of the cage. For the purposes of this analysis, we originally assumed that a tourbillon consumes 10% of the energy. As we’ll see, this estimate was overly conservative. While manufacturers tend to associate tourbillons with precision, there are several reasons to be sceptical.

For one thing, the tourbillon carriage takes up valuable space inside the movement that could be better spent on a larger balance wheel. In addition, the inertia of the cage eats up energy that could be better spent maintaining a higher inertia balance wheel or a higher frequency.

Case in point: Jaeger-LeCoultre. The brand’s fixed-escapement cal. 975 features a balance with 14 mg.cm2 of inertia, while the cal. 978, a similar movement except with a tourbillon, manages only 11.5 mg.cm2. This example suggests that a tourbillon carriage may consume as much as 20% of the movement’s overall energy; even more as the amplitude of the balance wheel in tourbillons is often less than 300 degrees.

When it comes to reducing the inertia of the tourbillon cage itself, brands like Jaeger-LeCoultre and De Bethune have made enormous strides, or even done away with the cage altogether. But by definition, tourbillons always introduce more inertia and more friction, and reduce the size of the balance, when compared to their fixed-escapement counterparts.

While there are no comparative tests that we can use to study the result of these effects, we can learn from Omega’s experience in the observatory competitions throughout the 1950s and 1960s. In 1947, Omega created the cal. 30I, the first serially produced wristwatch tourbillon movement.

The movement was created solely for the annual observatory competitions. While Omega’s fixed-escapement movements – mostly from 30T2 family of movements, which also formed the base for the 30I tourbillon – regularly dominated the trials, setting new all-time precision records in 1951, 1955, 1959, and 1966, the brand’s tourbillon found glory only once, at the 1950 competition in Geneva.

The Omega 30I tourbillon movement

Why chronometric performance still matters

For collectors who are nostalgic for the days of the observatory competitions, there’s nothing quite like seeing a movement that’s clearly been purpose-built for performance. The quest for the perfect rate has inspired generations of watchmakers to develop extraordinary innovations, even for the smallest of performance gains. Keeping this noble tradition alive is arguably the most important thing the modern luxury watch industry can do to remain culturally relevant in the 21st century.

Watchmakers that can instil this traditional sense of purpose into their modern products are able to relate their current collections to the achievements of the past in a more authentic way. It’s one thing to faithfully reissue a vintage design, but if the movement fails to live up to the norms of the period, the historical connection will ring hollow. Furthermore, an abiding commitment to the fundamental ideals of horology as-the-keeping-of-time will help modern watchmakers differentiate their products from other categories of fashion accessories and luxury goods.

A Patek Philippe tourbillon pocket watch that competed twice at the Geneva observatory time trials, once in 1929 where it landed a first prize, and then again in 1931 where it received only an honourable mention

If we’re to avoid a situation where all we’re left with is a collection of kinetic sculptures with differing aesthetics and questionable performance, something must change. Last year’s Concours International de Chronométrie, the modern-day successor to the observatory time trials of the last century, is instructive: though announced with much fanfare, the contest had just a single competitor, leading to a cancellation of the prize ceremony.

The label “International” was a bit misleading, given that only Swiss-made watches were allowed to enter – “intercantonal” would have been more apt. And this was just one of numerous concessions made to the participating brands to ensure that no one would lose face in the event of a poor performance. Ironically, by shrinking from the challenge of honest competition, the industry itself came away poorer.

As has been written countless times before, accurate mechanical timekeepers are no longer needed. Most of us are surrounded by electronic devices that sync periodically with an atomic clock, which is several orders of magnitude more precise than even the best marine chronometers of old.

In this environment, it can be hard to justify prioritizing timekeeping performance over more saleable characteristics like design or impressive complications. But the most compelling watches are those that manage to blend art and science, that carry on the tradition of scientific inquiry, and do so with designs that educate and inspire, and some brands continue to do just that.


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Source Credit:  Content and images from SJX Watches by Tim Lake.  Read the original article - https://watchesbysjx.com/2020/01/quantifying-performance-movement-design.html

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