There are all sorts of resonances around us, in the world, in our culture, and in our technology. A tidal resonance causes the 55 foot tides in the Bay of Fundy. Mechanical and acoustical resonances and their control are at the center of practically every musical instrument that ever existed. Even our voices and speech are based on controlling the resonances in our throat and mouth. Technology is also a heavy user of resonance. All clocks, radios, televisions, and gps navigating systems use electronic resonators at their very core. Doctors use magnetic resonance imaging or MRI to sense the resonances in atomic nuclei to map the insides of their patients. In spite of the great diversity of resonators, they all share many common properties. In this blog, we will delve into their various aspects. It is hoped that this will serve both the students and professionals who would like to understand more about resonators. I hope all will enjoy the animations.

For a list of all topics discussed, scroll down to the very bottom of the blog, or click here.

Origins of Newton's laws of motion

Non-mathematical introduction to relativity

Three types of waves: traveling waves, standing waves and rotating waves new

History of mechanical clocks with animations
Understanding a mechanical clock with animations
includes pendulum, balance wheel, and quartz clocks

Water waves, Fourier analysis

Saturday, March 19, 2011

John Harrison - conclusion

previous: the balance wheel clock up: home next: references

History of Mechanical Clocks with Animations

John Harrison portrait

Figure 5.1. John Harrison (1693-1776), self taught horologist (expert on clocks). Son of a carpenter, his passion for clocks led him to be one of the most respected innovators of clocks. After a lifetime of pursuit of the longitude prize, he officially was presented the prize when he was 79 years old. Wikipedia, public domain.

1.6 John Harrison

John Harrison was born in 1693 as the first son of a carpenter. Legend has it that he received a pocket watch when he was six and sick in bed with the small pox and that he spent hours listening to it and studying its moving parts. It is unclear why a boy of the working class would be permitted to play with such a expensive item. In any case, he did take up the building and repairing of clocks in his spare time. At some point Harrison took to improving clocks and developed his "gridiron pendulum" invention that used both iron and brass rods to compensate for the normal small lengthening of a pendulum when the temperature rises. Later he developed his "grasshopper escapement" which was almost frictionless even when it was not lubricated. He next turned his attention to the marine clock prize. At age 35 in the year 1727, he met with the well known astronomer Edmond Halley, discoverer of Halley's comet, to solicit a grant to build a marine clock. Halley sent him with his plans to George Graham, Britain's foremost clockmaker or horologist. Graham was so impressed with Harrison and his ideas that he personally loaned Harrison 500 pounds to make a working model of his invention. Seven years later Harrison presented the model to the Royal Society.

Harrison Stamp Ascension

Figure 5.2. Modern postage stamp with picture of Harrison's first navigational clock, the "H1".

What sort of resonator did Harrison's design employ? It was a balance wheel resonator, of course, but a special type of balance wheel resonator. To completely cancel out the effect of a pitching ship at sea, he used two coupled, counter-rotating balance wheels, locked together in opposing motions by a set of very fine wires. You can see a video of the operation of a modern reproduction of this clock on, including its escapement and tolerance to shock and motion. Perhaps because of Harrison's humble upbringing and desire to economize on the construction of this clock, this state-of-the-art clock oddly employed wooden gears. This clock was later to be dubbed "H1", as the first of Harrison's navigational clocks. It weighed 72 pounds. The Royal Society insisted on a trial at sea with the clock.

Figure 5.3. Harrison's counter-rotating balance wheel resonator used in H1 and H2. Mouse over to start. The two wires (colored red and blue in this illustration) force the two oscillating structures to mirror each others' motion. The springs are shown in gray. The metal balls are brass and provide much of the moment of inertia of the resonator.

In 1736 he and his clock traveled to Lisbon aboard the Centurion. John suspended the clock from one of the beams below deck to somewhat isolate it from the ship's swaying. During the voyage, the clock predicted the longitude within 1.5 degrees, which was better than the ship captain's estimate, but not quite good enough for the prize. Being a perfectionist and knowing the flaws in his design, he decided not to request a second trial but instead requested additional financial assistance from Board of Longitude to make another clock, one having metal gears.

His next clock, the "H2" was heavier, but basically the same design. Within three years he had become jaded by the design, gave it up and started yet another clock, the H3 which he worked on for 19 years. While the H3 did not reach board's goals, it did have innovative features, including a bimetallic strip to compensate for the temperature sensitivity of the balance spring (hair spring) and caged roller bearings. Both are used in machinery today. The H3 was large and weighed more than his previous clocks. All his designs used complex double balance wheels (see Fig. 5.3) that, because of transverse forces that the coupling wires exerted on the bearing, were more energy consuming that the simple balance wheels of Huygens. More power was required to operate it. Also, because it required a stronger drive force which would vary somewhat due to lubrication, wear, temperature, etc., it also made the double balance wheel more subject to outside influences. This was the opposite of the effect that Harrison had intended by using the counter-rotating balance wheel.

The ideal clock resonator would require no outside power to oscillate and would oscillate on its own, independent of the world around it. While no resonator is totally without damping, the closer one comes to the ideal lossless balance wheel, the better its potential as a clock resonator. In resonator theory we call the efficiency of a resonator to oscillate, the quality factor, or "Q" for short. The simple balance wheel had a higher Q than the double balance wheel. It also may be that the H3 was plagued by a non-linear balance wheel springs which would cause the period to vary with the amplitude of the balance wheel swing (not isochronous). While this is possible, horologists (experts on clocks) of the day were very aware of the problem of non-linear balance springs and we would guess that Harrison would have taken steps to remedy this.

Bandwidth of a resonator.

Bandwidth of a Resonator

One of the properties of a resonator is its bandwidth, i.e. how it responds to various frequencies of excitation. This is related to its resonance curve and its Q. Because in a timepiece one wants the resonator to oscillate in a very narrow range of frequencies, the bandwidth is also an indication of how stable a timepiece can be built with a particular resonator at its core.

The less friction or loss a resonator has, the higher the Q and the more narrow this peak is.

See Wikipedia for more information on Q.

Harrison subcontracts out a clock

Harrison had so far built all his clocks himself. In 1752, perhaps because of his age, his feeble fingers, weariness of years, or because of his appreciation of commercial watch builders, Harrison commissioned London watchmaker John Jefferys to make him a watch with special improvements, for his own personal and experimental uses. He was so impressed by the result that he decided that with a few more improvements it might win the prize. Sometimes true progress is made when a dreaming researcher teams up with a first rate artisan or practitioner of the trade. Apparently that happened here. In 1755 he asked for more support to continue work on the H3, but also for support to have two more similar watches made with improvements, one of pocket size and one somewhat larger. The larger of these, now called the "H4", was 13 cm (5.2 inches) in diameter, weighed 1.45kg (3.2 pounds), and had the appearance of a very large pocket watch. While large for a pocket watch, it was small compared to his previous navigational clocks, an advantage on a crowded ship deck. Unlike his previous clocks, this "watch" had a simple balance wheel and therefore had less friction than his previous clocks. This watch proved to be quite accurate, but, as before, it needed to be tested on the open ocean.

On November 18th 1761, his new clock and his son set sail on the Deptford for Jamaica. John Harrison, having spent his life in pursuit of a dream, was now 68 and was too old to make the long trip and would have to be content to wait for the ship to return. For some reason, the clock was not secured in a gimbal, as we might suppose, but reportedly positioned on a cushion which his son would adjust depending on the lie of the ship.

1993 Harrison Stamps

Figure 5.4. Modern postage stamps honoring Harrison. The stamps show the elaborately decorated outside and the inside of the H4.

Success at last!

When the ship returned on the next January 19th, the results were truly amazing. The watch was found to be only 5.1 seconds slow, after two months at sea! This was infinitely better than the allowed 2 to 4 minutes to win the prize. Was John Harrison declared the winner and given the prize? No! The longitude board was skeptical and required more tests. Even after more successful tests, it turned out that the board was not about to award Harrison the prize. While the board might have just wanted to be careful, some people felt it was because of John Harrison's lowly social status as a carpenter; some felt that it was because the board was populated mostly by astronomers and wanted an astronomy solution; or perhaps it was due to the 48 year old board's not wishing to vote itself out of existence by awarding the prize. Whatever the reason, the board proceeded to add additional requirements. John met some of these and was awarded half the prize, but eventually had to appeal to King George III to pressure Parliament into awarding the balance of the prize to John. He finally had his money, however the most important thing to him was that in June 1773, at age 79, John Harrison was officially recognized as the winner of the longitude problem! His lifelong dream and pursuit had finally become reality.

We now return to our fictional story of the Kemp family.

Captain Cooks portrait.

Figure 5.5. Captain James Cook. Wikipedia, public domain photo. Born in 1728 in Yorkshire England, son of a farmer of Scottish descent.

As a teenager he apprenticed to a sea-faring family and in 1755 he joined the royal navy. He proved himself an expert navigator and soon after made lieutenant rank. He was chosen by the Royal Society of London to undertake a scientific journey to Tahiti to observe and document the planet Venus transiting the sun. This measurement would help calculate the distance from the earth to the sun.

To combat the ever present illnesses and afflictions of sailors, he insisted that his men eat onions and pickled cabbage every day and fresh fruit and vegetables whenever possible. His men were also to bathe every day, clean their clothes, and air out their bedding.

He died in Hawaii on Feb 14, 1779 on his epic third voyage in a minor fight with Hawaiian natives.

Second Voyage of James Cook.

Figure 5.6. Route of Captain Cook's second, three year voyage, 1772-1775. He and his crew sailed from Britain to the South Atlantic Ocean, round the Cape of Good Hope and to the South Pacific, where he spent extensive time. His circular paths in the South Pacific followed the trade winds as he headed north in the winters to restock in warmer water and back south again in the summers. He was the first explorer to sail south of the Antarctic circle. He completed his voyage by continuing eastward, circumnavigating the southern end of the globe. Once back in the South Atlantic, he sailed north, back to Britain.

1.7 The second voyage of Captain Cook

A test of Harrison's clock

While the Kemp family did not directly witness these famous trials, John Kemp's grandson, Jessie Kemp did play a part in a related way. On July 13th, 1772 he shipped out on the HMS Resolution from Plymouth with Captain Cook on Cook's famous second voyage. Like his grandfather, Jessie was the ship's mate and responsible for navigation, under the watchful eye of his captain. Captain Cook was especially interested in the navigation on this voyage because he planned to go where no ship had ever sailed, to the far reaches of the South Pacific and he wanted to know exactly where they were at all times. After sailing from England to the southern tip of Africa, he sailed east, south of Australia to New Zealand. There he spent the next 18 months following the prevailing winds, sailing around in the south Pacific from the equator to as far south as the Antarctic Circle. Jessie reported later, that Captain Cook was determined to find the gates of Hell and then sail through them.

Although he never did discover the Antarctic landmass, he was the first sailor to sail south of the Antarctic circle. He sailed back to England via the Straits of Magellan, thereby circumnavigating the southern end of the globe. Due to his political connections, Captain Cook had been able to borrow the first copy of Harrison's famous H4 clock, the "K1", and proceeded to take it on this voyage. Jessie Kemp, being the navigator, was entrusted with this prized timepiece, making sure that it was level, carefully wound, and generally cared for. When the ship returned on March 24th, 1776, Captain Cook was noted to have remarked that the clock had been "our faithful guide through all the vicissitudes of climates". Jessie noted that if any ship had witnessed those "vicissitudes", it had been theirs, the HMS Resolution, and the most the clock had ever been off was 8 seconds a day. It had allowed them unprecedented accuracy and confidence in charting the largely unknown and huge South Pacific Ocean.

1.8 Conclusion

John Harrison died one year after Captain Cook's return on March 24th, 1776 on his 83rd birthday. Mechanical clocks had truly come of age.

Only a few copies of Harrison's famous clock were ever made, mostly because it was very complex and expensive, even having diamond jewels for bearings. However by 1785 John Arnold and Thomas Earnshaw had worked over the design and turned it into a practical marine clock, or chronometer as it is called. In fact, Jessie Kemp later purchased one of Arnold's pocket watches for himself for use in his profession as a navigator. This chronometer and other similar ones were extensively used for longitude measurement for the next century until the invention of the wireless telegraph allowed easy synchronization of all clocks around the world. Even after that, they were very popular among professionals who needed accurate time, such as railroad conductors.

It may seem odd that a captain on the open sea should depend on a clock for his location and so perhaps his very survival. Even stranger is that the critical element in that clock is a tiny balance wheel resonator, weighing less than the heart of a tiny mouse, yet it is guiding the rough and tumble sailors in their large sailing ships. We might be surprised to learn that the new navigational wonder child of our generation, the GPS (global positioning system), also uses clocks at its very core, and these clocks and their resonators must have orders of magnitude greater accuracy than the H4. They are even smaller than the balance wheel of the previous generation and guide even more immense ships.

The next big step in the evolution of clocks involves a different type of resonator, an electronic quartz resonator, which proved to be even more accurate; but we will cover that in another chapter.

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