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

Friday, March 18, 2011

History of mechanical clocks - the challenge

up: home next: early mechanical clocks - verge and foliot

History of Mechanical Clocks with Animations

Clocks are fascinating, especially the old mechanical ones. They are superbly simple, cyclic and hypnotic to watch. In addition, they are coupled to many, many moving gears and other complex mechanical parts. At their heart, all the successful clocks employ a resonator (a pendulum or a balance wheel) to parcel out the time while the gears translate these parcels into minutes and seconds.

Clocks methodically count out the minutes of our lives, never slowing, never resting. They are an integral part of our modern lives and our society. But where did they come from? Who invented the first mechanical clock? Well, it turns out that they evolved over the last 700 years as one of the first high tech developments of the modern world. In this chapter we explore this development, what drove it, and how these complex devices work. Much of this development was driven by the navigational needs of sailors. Remember, during this time period, many of the dreams, discoveries, and conquests were made possible by the expanding range of travel. Navigation was very central to these endeavers.

Map of Spanish Armada Battle with the Spanish Armada
Figure 1.1a. In 1588 King Phillip II of Spain sent a huge armada of ships and men to conquer England and, in his mind, to save it from the "improper and immoral" Queen Elizabeth I. The armada of 130 ships set sail from Lisbon (under Spanish rule at the time) on May 28, 1588 for the English channel. Image of Phillip II from Wikipedia, public domain. Figure 1.1b. Battle of Gravelines between the Spanish Armada and the English fleet, by artist Jacques de Loutherbourg. Gravelines is a French town on the south side of the English channel. The more nimble ships of the English equipped with longer range canons were able to stand off the more numerous and larger Spanish ships. A violent storm then scattered the weakened Spanish fleet. Wikipedia, public domain.

1.1 The Challenge

During the renaissance, England enjoyed its island status. It was separated from Europe and avoided most of the European wars, at least on its own soil, but yet it was close enough to benefit from the social and technological advancements sweeping the continent. The maritime advances, however, made maintaining this separation increasing difficult.

In 1588 England faced impending demise as a huge armada of 122 ships, 19,000 men, and countless weapons backed by King Phillip II of Spain sailed to capture the island nation. It was saved only by the skill of its navy and the luck that a mighty storm scattered the Spain fleet. The battle compelled England to develop and maintain a first rate navy.

Map English domain

Figure 1.2. Important British sailing routes in 1700.

By the 1700's Britain was flourishing with new international power and wealth, largely due to its naval and maritime strength. While once it relied on its island status for protection from more powerful foes in Europe, after mastering the maritime world, Britain had now had become a major trading and colonizing power itself. The 1713 Treaties of Utrecht officially gave Britain much of present day Canada, present day northeastern United States, Gibraltar, Minorca, and slave trading rights to western Africa making Britain a major maritime and colonial power. Britain also had holdings in the West Indies and India. Managing the large fleet of ships required for this empire placed new demands on maps and navigation.

Next, we start an account of a fictional British sailor of this time. We do this in order to illustrate the importance of a good clock to a sea captain.

1.2 A sailor's story

Our fictitious British sailor of the time, John Kemp, age 18, had shipped out on the HMS Croker (also fictitious) from the port at Portsmouth on July 25th 1706, bound for Lisbon, Portugal. Having worked for the last 6 year aboard ships starting as an apprentice, he was now a mate, the right hand man of Captain Johnston. Since last year, when the Captain promoted him to mate, his most important responsibility became plotting their course on the map board. The captain was very particular about the map and John was the only soul that the captain trusted enough for the job. Captain Johnston was forever reminding John that one screw up on the map could mean death to all. Most of the time, danger didn't seem so pressing, being out in the middle of a large ocean with nothing much to hurt anyone, but bad things seemed to have a way of sneaking up on you in the seas. John remembered last year hearing of the losing of the HMS Gallows off the coast of Wales. The ship had sailed from Boston. The ship's first mate said that they had been expecting to reach land the next afternoon, but unexpectedly reached it and ran aground at 3 am in the morning in fairly high seas. The first mate and three other were all that survived. They were off in plotting their position on their map board and had reached their destination early.

Many of the accidents at sea were due to navigational errors. John was constantly monitoring the ship's bearing and headway. He would check with the helmsman as to the current bearing. Keeping a constant eye on the compass, the helmsman would always attempt to keep the ship on the course the captain had set. John also needed to know the ship's speed. He had a float and string to determine this, but usually he could tell by looking at the set of the sail and how fast the water appeared to be passing by the ship. Every three hours he would enter the bearing and speed in the log book and update their position on the map. He was, however, very aware that the speed was just approximate and that the bearing was only loosely connected to the actual direction of travel. The wind and currents were constantly trying to push the ship sideways. John was supposed to estimate the sideways drift of the ship, but this estimate was just approximate. This method of "dead reckoning", as it is called, was fraught with errors, as the HMS Gallows had proven.

On this voyage they were following the coast of France and then Spain to Lisbon, Portugal. The nearby land was both a boon and a liability. It was reassuring to be able to spot landmarks and to know exactly where you were on the map. Of course it is not all that easy to tell one rocky outcropping from another, so misidentifications were common. John always made a point of studying the map carefully ahead of time to be aware of all the landmarks and potential navigational hazards coming up so he could be sure to spot them. Captain Johnston was forever quizzing him and would, upon occasion, compliment him as being the best mate he'd seen in a long time. It was something to get a compliment out of this captain! Being near land meant that various navigational hazards, such as shoals, rocks, points, etc were a constant headache, especially at night and in fog. Land also meant watching for other ships. The threat of a collision was not very great, but the threat of a pirate or unfriendly enemy ship was a considerable threat to most ships. However, seeing as how the HMS Croker was a warship, there were very few ships that would mess with her. Of course the rocks didn't care if you were a warship or a rowboat.

Astrolab use sextant

Figure 1.3. Sailor using an astrolabe to measure the angle between the sun and horizon. With this angle (taken at noon) and the day of the year, a sailor could consult a navigational table to determine his latitude. Other similar instruments were also used to measure this angle, such as the sextant which was invented in 1736 and is still in use today.

Path of the sun are various latitudes

Figure 1.4. Path of the sun in the southern sky. It reaches its highest point (its zenith) at solar noon. The upper set of suns represent the path on a summer day, while the lower set is for a winter day. The sun will also be higher if the ship is closer to the equator. Sailors carried tables showing the latitude for a measured solar altitude (at noon) and a given day of the year.

Keeping time at sea

Whenever it was clear enough to make out the sun at noon, John was to, without fail, watch for the sun to reach its zenith, the high point in the sky, and carefully measure the sun's elevation above the horizon. He was to shout out the moment of zenith to the apprentices to reset the ship's clocks. The HMS Croker, like most other ships used "hour glasses" as clocks, although the captain had a pocket watch that he would reset upon hearing the call. John would then head for the captain's cabin where he would use a navigational table to read off the ship's latitude using the sextant's reading and the current date. The captain said that a good latitude measurement was like a gift from the Lord. You could count on it being correct. So armed with the latitude, you could go to your map and with confidence mark the east-west line on which the ship lay. Then you could, at that moment, correct for some of the errors in your dead reckoning and account for missed or misidentified landmarks. If only there was a way to use the sun to figure out your longitude, then you would have it all: the exact point on the map where you were. The Captain felt that most navigational accidents would not happen if sailors knew how to measure longitude at sea.

Map of the Atlantic Ocean title="Early map of the Atlantic Ocean and America">

Figure 1.5. Map of America, circa 1678. The Atlantic and Pacific Oceans were huge to the sailors of this time. Better navigational tools such as better clocks were critical to reducing the risks of their perilous voyages. Colored version of image of the US National Oceanic and Atmospheric Administration (NOAA). Public Domain.

The coming fall, the HMS Croker was due to sail across the Atlantic, for Jamaica. It would be John's first Atlantic crossing and he was a little anxious about it, especially since Captain Johnston was expecting him to keep the map board. Sailing across that huge ocean, two to three weeks with no landmarks…nothing! A ship could easily be 300 miles off course after that period of nothing but dead reckoning, even with latitude measurements. The captain had explained that things got quite tense towards the end. The crew was eager for land, but with so much potential for error, one needed to be very cautious. That meant making no headway at nighttime, unless it was clear with a good moon. The bad accidents happened when it was stormy at night and the ship risked being blown into a rocky shore. Even when land was seen, in the Caribbean some islands were friendly and some were not, so a ship had to proceed with extreme caution until one's exact location was figured out. Knowing the latitude was a great help in figuring out which island you might be looking at. Of course if someone were to figure out how to measure longitude at sea, then you would just know where you were, none of this guessing.

The Prize

In 1707 there was another bad accident. Fourteen hundred British sailors lost their lives with the sinking of four warships on the rocks of the Scilly Isles off the coast of England because of another navigating error. To inspire innovation in this area, in 1714 Parliament offered a prize for an improved way to measure longitude: £10,000 for 1 degree accuracy in longitude, £15,000 for 2/3 degree accuracy, and £20,000 for a half degree accuracy. One degree of longitude translates to about 65 miles at the latitude of the West Indies and India. £20,000 at that time was roughly equivalent to ten million U.S. dollars in today's money, a handsome prize! Other sailing nations had previously offered prizes for this same thing, but this was a first for Britain.

By this time, 1714, John was 26 and now a captain of a small brig in the British fleet. He was excited about the prize when he heard about it, because he felt "at least someone is trying to do something about the problem that cost so many lives each year". He figured with such a large and prestigious prize, someone was bound to figure out a solution. John's wife, Mary, was particularly excited by the news, for she, like most wives of sailors, feared accidents more than anything else when she got to fretting about her husband's perilous occupation. John, like most captain had thought about the problem and knew something about the most likely solution. It was all to do with time. If a person were to know "Greenwich time" when he measured the zenith on a particular day, then he would have it: he would know his longitude. The concept had been understood since 1553 when the Dutch astronomer, Gemma Frisius had figured it out. It was based on the idea of a round Earth that rotates to make day and night, the stuff that had gotten Galileo into so much trouble with the church. John explains:

Spinning Earth and time.

Figure 1.6. The Earth seen when 0 degrees longitude (shown in yellow) is closest to the sun. This is the longitude line that passes through Greenwich, England. At this time it is solar noon along this longitude. The Earth turns in the direction of the black arrow. It turns 15 degrees per hour (the distance between two longitude lines shown in this picture). Thus in three hours it will turn to make it solar noon at the southern tip of Greenland and in 5.5 hours it will be solar noon in Florida.

Time related to longitude

"At the zenith when the sun is at its highest, it is solar noon at your position. At that instant, your longitude is closest to the sun and the other longitudes are further away from the sun. But the Earth is rotating. It rotates 360 degrees in a day, or, that works out to 15 degrees longitude in an hour. Points west of a you will rotate closest to the sun after your noon has past. That is, they have their noons delayed, delayed by one hour for every 15 degrees west they are. To us English, the longitude line that passes through Greenwich, England is our longitude zero, or the prime meridian. It's what we use to measure our longitude from. The French use Paris, being as how they are French. So if we were to be 30 degrees west in longitude from Greenwich, then our solar time will be 2 hours delayed from the solar time at Greenwich. Then two hours later, at our zenith, i.e. our noon, it would be 2 pm in Greenwich. No matter where we were on the Earth, if we can determine how many hours our solar time is delayed from Greenwich time, we are that many hours times 15 degrees in longitude west of Greenwich."

"Converting a time difference into a longitude, that is the easy part. The hard part is, how on earth is a sailor in the middle of the Atlantic Ocean to know what time it is in Greenwich, England? A year ago when I was commissioned the captain of this vessel, I was presented with this fine pocket watch, one of the most accurate around. But it is off by about 10 minutes a day, so after a few days at sea, I don't know Greenwich time, so I just keep resetting it every noon by the zenith. I understand that some folks think that they can improve the watches to keep much better time. I don't know if that is possible or not. If they got it down to a few seconds off a day, then we would have something! They have grand pendulum clocks with that sort of accuracy, but you can't put one of those aboard a ship and have it work. They need to be kept upright and level and a pitching ship is not upright and level. Pendulum clocks need to be set on firm earth to work properly."

Figure 1.7. The planet Jupiter and its four largest moons, the ones discovered by Galileo, as seen through a simple telescope. Note that as viewed from the Earth, we are seeing the orbits on edge (not from above). These moons circle their planet much more frequently than our moon does. The moons, from innermost to outermost are Io, Europa, Ganymede and Callisto. They eclipse Jupiter every 21 hours, 43 hours, 86 hours, and 200 hours respectively. Mouse over the illustration to see the action, or over "fast" to speed it up (click on it if it doesn't start). This animation is very speeded up compare with the real moons which appear to move slower than the hour hand of a clock. You might enjoy seeing another animation based on Galileo's actual observations from his note book at strangepaths.

Time via Jupiter's moons

"The other way to figure out Greenwich time has to do with the heavens. The four moons of Jupiter that Galileo discovered, circle Jupiter every few days. You can see these with a telescope, the kind that we sailors carry. The royal mathematicians and astronomers got together and published tables that list the exact times, in Greenwich time, that these moons will eclipse Jupiter. So if we carefully watch the moons at night and observe an eclipse, we can consult the table and it'll tell what Greenwich time is at that instant. We compare that with a clock on board that was set with the zenith on the previous day, and subtract to get the time delay of our time compared with Greenwich time. This gives the longitude. I've used this, and it works, as long as you have great patience, the sky is clear, and the ship is not rocking. Occasionally this will be the case, when the seas are like glass, but usually the method isn't practical on a ship. It's just next to impossible to get a fix with a telescope on the moons of Jupiter aboard a rolling ship, let alone watch them move for a while. I've also heard that someone is working on another method using our moon, but it has yet to work very well either, on board a real ship."

Next, we will go back and survey the development of mechanical clocks that had started in Italy 500 years before John Kemp's day.

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