Balance wheel in a cheap 1950s alarm clock, the Apollo, by Lux Mfg. Co. showing the balance spring (1) and regulator (2).

The balance wheel is the part of a mechanical watch that controls its rate, analogous to the pendulum in a pendulum clock. The balance wheel rotates back and forth, being returned toward its center position by a spiral spring, the balance spring or hairspring. It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balace wheel is part of a scientific invention of the 1500's. Each swing of the wheel (called a 'tick' or 'beat') allows the gear train to advance a set amount, moving the hands forward. The combination of the mass of the balance wheel and the elasticity of the spring keep the time between each oscillation or ‘tick’ very constant, accounting for its near universal use as the timekeeper in mechanical watches and small clocks up to the present. Image File history File links Metadata Size of this preview: 797 × 600 pixelsFull resolution (1803 × 1357 pixel, file size: 337 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Metadata Size of this preview: 797 × 600 pixelsFull resolution (1803 × 1357 pixel, file size: 337 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... It has been suggested that this article or section be merged into Watch. ... For other uses, see Pendulum (disambiguation). ... A pendulum clock uses a pendulum as its time base. ... Look up spring in Wiktionary, the free dictionary. ... The balance spring is a scientific device invented by Robert Hooke. ... A simple escapement. ... Elasticity is a branch of physics which studies the properties of elastic materials. ... Oscillation is the variation, typically in time, of some measure as seen, for example, in a swinging pendulum. ...

Perhaps the earliest existing drawing of a balance wheel, in Giovanni De Dondi's astronomical clock, built 1364, Padua, Italy. The balance wheel (crown shape, top) had a beat of 2 seconds. Tracing of an illustration from his 1364 clock treatise, Il Tractatus Astarii.

Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Jacopo and Giovanni deDondi (father and son) were scholars active in 14th century Padua, Italy, and are remembered today as being pioneers in the art of clock design and construction. ... Prague astronomical clock Astronomical clock in Lund Cathedral An astronomical clock is a clock with special mechanisms and dials to display the relative positions of the sun, moon, zodiacal constellations, and sometimes major planets. ...

Origin

The balance wheel appeared with the first mechanical clocks, in 14th century Europe, but it seems unknown exactly when or where it was first used. It is an improved version of the foliot, a primitive inertial timekeeper consisting of a straight bar with weights on the ends. The first clocks in northern Europe used foliots, while those in southern Europe used balance wheels (White 1966, p. 124). As clocks were made smaller, first as table clocks and then as the first large watches after 1500, balance wheels began to be used in place of foliots (Milham 1923, p. 92). The wheel shape had less air resistance, and its geometry partly compensated for thermal expansion error due to temperature changes (Headrick 2002). Since more of its weight is located on the rim away from the axis, a balance could have a larger moment of inertia and keep better time. The verge escapement is the earliest known type of escapement, the mechanism in a clock that maintains the swinging of a pendulum. ... In physics, thermal expansion is the tendency of matter to increase in volume or pressure when heated. ... Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg m², Former British units slug ft2), is the rotational analog of mass. ...

Addition of Balance Spring

Early balance wheel with spring in an 18th century French watch.

These early balance wheels were crude timekeepers because they lacked the other essential element: the balance spring. Early balance wheels rotated freely in each direction until the escapement pushed it back the other way. This made the timekeeping strongly dependent on the driving force, so the watch slowed down as the mainspring unwound. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... The balance spring is a scientific device invented by Robert Hooke. ... A simple escapement. ... Mainspring (U.S.A. motor spring): In a watch, long strip of hardened and blued steel or of a specially alloyed steel, between 2oo & 3oo millimeters in length and 0. ...

A way forward opened when it was noticed that springy hog bristle curbs, added to limit the rotation of the wheel, increased its accuracy (Britten 1898, p. 9). Robert Hooke first applied a metal spring to the balance in 1658 and John Hautefeuille and Christian Huygens improved it to its present spiral form in 1674 (Headrick 2002)(Milham 1923, p. 224). The addition of the spring made the balance wheel a harmonic oscillator, the basis of every modern clock, with a natural resonant frequency or ‘beat’ resistant to changes in the drive force or friction. This crucial innovation greatly increased the accuracy of watches, from several hours per day (Milham 1923, p. 226) to perhaps 10 minutes per day (NIST 2002, p. 3), changing them from expensive novelties into useful timekeepers. Robert Hooke, FRS (July 18, 1635 – March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. ... Christiaan Huygens Christiaan Huygens (approximate pronunciation: HOW-khens; SAMPA /h9yGEns/ or /h@YG@ns/) (April 14, 1629–July 8, 1695), was a Dutch mathematician and physicist; born in The Hague as the son of Constantijn Huygens. ... In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ... For other uses, see Clock (disambiguation). ... This article is about resonance in physics. ...

Temperature Error

After the spring was added, a major remaining source of inaccuracy was the effect of temperature changes. An increase in temperature, for example, made the spring and the balance get longer from thermal expansion. A more important effect however was that the elasticity of the spring decreased. The weaker spring would take longer to return the balance wheel back toward the center, so the frequency of oscillation or ‘beat’ would get slower and the watch would lose time. George Airy found that a brass balance would lose 6 minutes 6 seconds per day from a 60 degree F. temperature increase, of which 4 minutes 7 seconds was due to spring elasticity decrease (Glasgow 1885, p. 238). In physics, thermal expansion is the tendency of matter to increase in volume or pressure when heated. ... Elasticity is a branch of physics which studies the properties of elastic materials. ... George Biddell Airy Sir George Biddell Airy (or Airey) FRS (July 27, 1801–January 2, 1892) was British Astronomer Royal from 1835 to 1881. ...

Temperature Compensated Balance Wheels

Need for an accurate clock to determine longitude during sea voyages drove many advances in balance technology in 18th century Britain. Even a 1 second per day error in a chronometer could result in a 17 mile error in ship's position after a 2 month voyage. John Harrison was first to apply temperature compensation to a balance wheel in 1753, using a bimetallic ‘compensation curb’ on the spring, in the first successful marine chronometers, H4 and H5. These achieved an accuracy of a fraction of a second per day (NIST 2002, p. 3). Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... A marine chronometer is a timekeeper precise enough to be used as a portable time standard, used to determine longitude by means of celestial navigation. ... John Harrison John Harrison (March 24, 1693–March 24, 1776) was an English clockmaker, who designed and built the worlds first successful chronometer (maritime clock), one whose accuracy was great enough to allow the determination of longitude over long distances. ... thermocouple and Peltier_Seebeck effect. ... A marine chronometer is a timekeeper precise enough to be used as a portable time standard, used to determine longitude by means of celestial navigation. ...

Bimetallic temperature compensated balance wheel, from an early 1900s pocket watch. 17mm dia. (1) Moving opposing pairs of weights closer to the ends of the arms increases temperature compensation. (2) Unscrewing pairs of weights near the spokes slows the oscillation rate. Adjusting a single weight changes the poise, or balance.

A simpler solution was devised around 1765 by Pierre Le Roy, and improved by John Arnold, and Thomas Earnshaw: the compensating balance wheel (Milham 1923, p. 233). The key was to make the balance wheel change size with temperature. If the balance could be made to shrink in diameter as it got warmer, conservation of angular momentum would make it rotate faster, like a spinning ice skater that pulls in her arms. The faster balance would take less time to oscillate back and forth, compensating for the slowing caused by the weaker spring. Image File history File links Metadata Size of this preview: 600 × 600 pixelsFull resolution (1612 × 1612 pixel, file size: 287 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Metadata Size of this preview: 600 × 600 pixelsFull resolution (1612 × 1612 pixel, file size: 287 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... London watchmaker John Arnold (1736–99), was one of the true master clockmakers from what was unarguably England’s golden age of horology. ... Thomas Earnshaw (born on February 4, 1749 in in Ashton-under-Lyne - died March 1, 1829 in London) was an English watchmaker who first simplified the process of chronometer production, making them available to the general public. ... In physics, angular momentum intuitively measures how much the linear momentum is directed around a certain point called the origin; the moment of momentum. ...

To accomplish this, the outer rim of the balance was made of a ‘sandwich’ of two metals; a layer of steel on the inside fused to a layer of brass on the outside. Strips of this bimetallic construction bend toward the steel side when they are heated, because the thermal expansion of brass is greater than steel. The rim was cut open at two points next to the spokes of the wheel, so it resembled an S-shape (see figure) with two circular bimetallic ‘arms’. A temperature increase makes the arms bend inward toward the center of the wheel, and the shift in mass inward makes the balance spin faster, cancelling out the slowing due to the spring. The amount of compensation is adjusted by moveable weights on the arms. Marine chronometers with this type of balance had errors of only 3 - 4 seconds per day over a wide temperature range. (Glasgow 1885). By the 1870s compensated balances began to be used in watches. thermocouple and Peltier_Seebeck effect. ...

Middle Temperature Error

Marine chronometer balance wheels from the mid 1800s, with various 'auxiliary compensation' systems to reduce middle temperature error.

The standard Earnshaw compensation balance dramatically reduced error due to temperature variations, but it didn't eliminate it. As first described by J. G. Ulrich, a balance adjusted to keep correct time at a given low and high temperature will be a few seconds per day fast at intermediate temperatures (Gould 1923, p. 176-177). The reason is that the moment of inertia of the balance is a quadratic function of the radius of the compensation arms, and thus of the temperature. But the elasticity of the balance spring is a linear function of temperature. Image File history File links Size of this preview: 800 × 157 pixelsFull resolution (1169 × 229 pixel, file size: 25 KB, MIME type: image/png) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Size of this preview: 800 × 157 pixelsFull resolution (1169 × 229 pixel, file size: 25 KB, MIME type: image/png) File historyClick on a date/time to view the file as it appeared at that time. ... f(x) = x2 - x - 2 A quadratic function, in mathematics, is a polynomial function of the form , where are real numbers and . ... A linear function is a mathematical function term of the form: f(x) = m x + c where c is a constant. ...

Chronometer makers adopted 'auxiliary compensation' schemes, which reduced error below 1 second per day. Most of the chronometers that came in first in the annual Greenwich Observatory trials between 1850 and 1914 were auxiliary compensation designs(Gould 1923, p. 265-266). Auxiliary compensation was never used in watches because of its complexity.

Better Materials

Low temperature coefficient alloy balance and spring, in an ETA 1280 movement from a Benrus Co. watch made in the 1950s.

The bimetallic compensated balance wheel was made obsolete in the early 1900s by advances in metallurgy. Charles Edouard Guillaume won a Nobel prize for the 1899 invention of Invar, a nickel steel alloy with very low thermal expansion, and Elinvar (from El asticité invar iable) an alloy whose elasticity is unchanged over a wide temperature range, for balance springs (Milham 1923, p. 234). This led to a series of improved low temperature coefficient alloys for balances and springs. A solid alloy balance with a spring of Elinvar was largely unaffected by temperature, so it replaced the difficult-to-adjust bimetallic balance. Image File history File links Metadata Size of this preview: 798 × 599 pixelsFull resolution (908 × 682 pixel, file size: 117 KB, MIME type: image/jpeg) Balance wheel in a Benrus DN21 watch, probably made in the 1950s. ... Image File history File links Metadata Size of this preview: 798 × 599 pixelsFull resolution (908 × 682 pixel, file size: 117 KB, MIME type: image/jpeg) Balance wheel in a Benrus DN21 watch, probably made in the 1950s. ... Charles Édouard Guillaume (February 15, 1861, Fleurier – June 13, 1938, Sèvres), was a French-Swiss Physicist that received the Nobel Prize in Physics in 1920 in recognition of the service he had rendered to precision measurements in Physics by his discovery of anomalies in nickel steel alloys. ... Invar, also called FeNi36, is an alloy of iron (64%) and nickel (36%) with some carbon and chromium. ... Elinvar is the name of a type of metallic alloy with a modulus of elasticity which does not vary with temperature; the name means elastically invariable. ...

Some chronometer designers, such as Paul Ditisheim (Gould 1923, p. 202) still used compensation on the balance to cancel out the small remaining temperature coefficient of the Elinvar balance spring. These have a solid balance wheel (not cut as in the conventional bimetallic balance) but with adjusting screws mounted along the rim to adjust the amount of compensation. In the design used by Paul Ditisheim, the balance wheel rim is of one material while the spokes are of another. In the chronometers built by the Hamilton Watch Company in the 1940s, the rim is bimetallic but not cut. In either case, the effect of temperature change is to change the wheel shape from circular to slightly oval. The amount of compensation is small, so no auxiliary compensation is used.

Modern Balance Wheels

Modern balance wheel (arrows), in a Chinese watch movement.

Until the 1980s balance wheels were used in chronometers, bank vault time locks, alarm clocks, kitchen timers, stopwatches, and time fuzes for bombs, but quartz technology has taken over these applications, and the main remaining use is in quality watches. Image File history File links Metadata No higher resolution available. ... Image File history File links Metadata No higher resolution available. ... A marine chronometer is a timekeeper precise enough to be used as a portable time standard, used to determine longitude by means of celestial navigation. ... A time lock is a locking mechanism commonly found in bank vaults and other high-security containers. ... A basic digital clock radio with analog tuning A wind-up, spring-driven alarm clock An alarm clock is a clock that is designed to make an alert sound at a specific date and/or time. ... A timer is a specialized type of clock. ... A stopwatch is a timepiece designed to measure the amount of time elapsed from a particular time when activated to when the piece is deactivated. ... Fuze is a brand of beverage. ... A quartz clock A quartz clock is a timepiece that uses an electronic oscillator which is made up by a quartz crystal to keep precise time. ...

Modern (2007) watch balance wheels are usually made of Glucydur, an alloy of beryllium, copper and iron, with springs of alloys such as Nivarox (Odets 2007). They are smooth, to reduce air friction. Instead of weight screws to adjust the poise, they are computer-poised at the factory, using a laser to burn a precise pit in the rim to make them balanced (Odets 2005). Balances rotate about 1½ turns in each direction. The rate of the balance is adjusted with the regulator, a lever with a narrow slit on the end through which the balance spring passes. Moving the lever slides the slit up and down the balance spring, changing its effective length, and thus the resonant vibration rate of the balance. Since the regulator interferes with the spring’s action, some precision watches have ‘free sprung’ balances with no regulator, such as the Gyromax (Odets 2007). Glucydur is the trade name of a metal alloy with low thermal expansion, used for making balance wheels and other parts of mechanical watches. ... General Name, symbol, number beryllium, Be, 4 Chemical series alkaline earth metals Group, period, block 2, 2, s Appearance white-gray metallic Standard atomic weight 9. ... For other uses, see Copper (disambiguation). ... For other uses, see Iron (disambiguation). ... Nivarox (full business name Nivarox - FAR SA) is a Swiss business entity that is the result of a merger in 1984 between Nivarox SA and Fabriques dAssortiments Réunis (FAR). ... Gyromax balance wheel, not showing the spokes and center arbor. ...

A balance’s vibration rate is measured in beats (ticks) per hour, or BPH. The length of a beat is one swing of the balance wheel, between reversals of direction, so there are two beats in a complete cycle. Balances in precision watches are designed with faster beats, because they are less affected by motions of the wrist (Arnstein 2007). Watches made prior to the 1970s usually had a rate of 18,000 BPH (5 beats per second). Current watches have beats of 21,600, 28,800, and a few have 36,000 BPH (10 beats per second). During WW2, Elgin produced a very precise stopwatch that ran at 40 beats per second (144,000 BPH), earning it the nickname 'Jitterbug' (Schlitt 2002).

The precision of the best balance wheel watches on the wrist is around a few seconds per day.

References

• Arnstein, Walt (2007), Does faster mean more accurate?, TimeZone.com, <http://www.timezone.com/library/comarticles/comarticles0017>. Retrieved on June 15, 2007.
• Brittanica (2007), Marine Chronometers article, Encyclopedia Brittanica online, <http://www.britannica.com/ebc/article-9360740>. Retrieved on June 15, 2007.
• Britten, Frederick J. (1898), On the Springing and Adjusting of Watches, Spon & Chamberlain, <http://books.google.com/books?id=1SgJAAAAIAAJ&q=hog+bristle#search>. Has detailed account of development of balance spring.
• Glasgow, David (1885), Watch and Clock Making, MacMillan, <http://books.google.com/books?id=9wUFAAAAQAAJ>. Detailed section on balance temperature error and auxiliary compensation.
• Gould, Rupert T. (1923), The Marine Chronometer. Its History and Development, London: J. D. Potter, pp. 176-177, ISBN 0-907462-05-7
• Headrick, Michael (2002), "Origin and Evolution of the Anchor Clock Escapement", Control Systems magazine, Inst. of Electrical and Electronic Engineers 22 (2), <http://www.geocities.com/mvhw/anchor.html>. Retrieved on June 6, 2007. Good engineering overview of development of clock and watch escapements, focusing on sources of error.
• "Inventing the Clock". John H. Lienhard. The Engines of Our Ingenuity. NPR. KUHF-FM Houston. 2000. No. 1535. Transcript. Transcript page shows one of the earliest drawings of a balance wheel: the Di Dondi clock, 1379.
• Milham, Willis I. (1923), Time and Timekeepers, MacMillan, ISBN 0780800087. Comprehensive 616p. book by astronomy professor, good account of origin of clock parts, but historical research dated. Long bibliography.
• NIST (2002), A Walk Through Time, part 3: A Revolution in Timekeeping, <http://physics.nist.gov/GenInt/Time/revol.html>. Retrieved on June 6, 2007. Nontechnical history of clocks and watches, by National Institute of Standards and Technology.
• Odets, Walt (2005), Balance Wheel Assembly, Glossary of Watch Parts, TimeZone Watch School, <http://www.timezonewatchschool.com/WatchSchool/Glossary/Glossary%20-%20Balance%20Assembly/glossary%20-%20balance%20assembly.shtml>. Retrieved on June 15, 2007. Detailed illustrations of parts of a modern watch, on watch repair website
• Odets, Walt (2007), The Balance Wheel of a Watch, The Horologium,TimeZone.com, <http://www.timezone.com/library/horologium/horologium0013>. Retrieved on June 15, 2007. Technical article on construction of watch balance wheels, starting with compensation balances, by a professional watchmaker, on watch repair website
• Perez, Carlos (2001), TimeZone, Artifacts of the Golden Age, part 1, <http://www.timezone.com/library/cjrml/cjrml0006>. Retrieved on June 6, 2007. Narrative history of watches, by antique watch afficionado, on watch collector's website.
• Schlitt, Wayne (2002), The Elgin Collector's Site, <http://elginwatches.org/databases/watch_codes.html>. Retrieved on June 20, 2007.
• White, Lynn Jr. (1966), Medieval Technology and Social Change, Oxford Press, ISBN 978-0195002669. Has in-depth historical analysis of medieval clock development, copious references to original sources.

The Engines of Our Ingenuity is a radio program that is regularly broadcast on National Public Radio. ... Year 2000 (MM) was a leap year starting on Saturday (link will display full 2000 Gregorian calendar). ...

External Links

• Video of antique mid-1800s watch showing the balance wheel turning
• Costa, Alan (1998), The History of Watches,, <http://www.atmos-man.com/historyo.html>. Retrieved on June 19, 2007 History of watches, on commercial website.
• The Watch Cabinet Pictures of an extensive private collection of antique watches from 1710 to 1908, showing many different varieties of balance wheel.