Science, Maths & Technology

# Build an accurate clock challenge

Updated Monday 28th January 2008

The science behind clocks, sundials and keeping time, part of the BBC/OU's programme website for Rough Science 2

Copyright: Used with permission To tell the time in a Rough Science environment - where we only have access to a tool kit, rope, buckets, hoses and old scrap - it is probably easiest to use the sun, a local ingredient which was thankfully in plentiful supply.

The one point that is relatively easy to determine by using a sundial is local noon. But how do we make the sundial tell the time accurately, how do we get a clock to chime, and with the rough components on the island, how will we ever make a wristwatch?

How does an accurate clock work?

As the earth turns on its axis, the sun appears to move across our sky and the shadows cast by objects North of the tropics move in a clockwise direction.

If you watch a shadow during the day cast by a rock, a tree, or even your own body, you will notice that it is quite long in the morning and decreases in length until noon when it is at its shortest. The shadow will then grow longer again as night approaches. You can tell what time of day it is by observing a shadow but it's not as simple as it sounds.

The shadow stick was the earliest form of sundial. People judged the time of day by the length and position of the stick's shadow. If the sun rose and set at the same spot on the horizon every day, a shadow stick would be pretty accurate.

However, the sun's path through the sky changes each day because the earth's axis is tilted. On the earth's yearly trip around the sun, the North Pole is tilted towards the sun half of the time and away from the sun for the other half.

In addition, because the sun doesn't often pass directly overhead at noon and the earth's surface is curved, the shadow cast by a shadow stick doesn't move at a uniform rate. So even if we mark the shadows at sunrise, noon and sunset we cannot evenly divide the space up to mark the individual hours.

We could build a horizontal sundial on a flat, level base plate and make sure that the shadow stick is angled so that it is parallel to the earth's north-south axis. However, marking the points where the shadow will fall at each hour is not as simple as it might seem. These points change depending on latitude.

At a high northerly latitude the marks would look like this:

Whilst closer to the equator, they would look like this:

As a result, there are two significant drawbacks:

1. Trigonometric calculations are required to work out the hour mark positions - easy to do with a calculator but very tricky without.
2. Even if the hour marks could be calculated the gaps between them would be unequal, making measurement of periods shorter than an hour difficult.

Another solution is the equinoctial sundial. The hour marks are drawn on a circular dial which is not flat on the floor but at an angle to the ground. This angle varies depending on where you are in the world but always results in the dial being parallel to the equator. The gnomon points at the North star, which means that it is at right angles to the dial.

This type of sundial is very easy to set up. Once the gnomon is pointed at the North star and the dial is constructed at right angles to the gnomon, the sundial is set up in the right direction and elevation to give us equal gaps between the hour marks.

The shadow falls on the lowest point of the dial at noon and will be a quarter of a turn anti-clockwise from the bottom at 6am and a quarter turn clockwise from the bottom at 6pm. We decided to make a big equinoctial sundial, because the bigger it is, the more accurate it will be. On top of that, the only suitable metal rings knocking around on the island were very big!

Of course, experts will know that there are still small inaccuracies in measurement. Local time is usually slightly different to mean solar time because of the path that the earth uses to orbit the sun. These inaccuracies can be corrected by using the equation of time.

How can we make a chiming clock?

Copyright: Used with permission In an attempt to make a chiming clock, we constructed a water clock as we couldn't think of a way of making a chiming clock out of a sundial.

We placed a huge barrel at a height of about three metres and a second large barrel lower down. Size was important - the bigger the barrel, the higher the volume of water and the more power to make a big noise.

For the clock to be accurate, we need a constant flow of water. Drilling a hole in the higher barrel and allowing the water to flow freely wouldn't work because as the water level drops so too does the water pressure.

We placed a pipe into the upper barrel partially filled with liquid. The pipe was then extended down to a lower barrel. To start the siphon, suction was needed at the bottom of the tube. A partial vacuum is formed at the bottom which allows atmospheric pressure to force water along the tube. This causes water to flow up the tube, over bend (X), and along the tube towards the lower barrel.

Copyright: Used with permission Once the water reaches the same level as the end of the tube in the top barrel (point Y) the mass of water descending the pipe continues to draw more water from the upper container unaided. The longer the pipe descends from point Y, the faster the water will flow through the tube.

The most important thing is that the rate at which the water flows is independent of the volume of water in the top barrel. It flows to the lower barrel at the same speed whether the top barrel is nearly full or almost empty.

How did the clock chime?

Copyright: Used with permission This is where the science more or less ends. We made a float that rose as the water level moved up in the lower barrel. By using bamboo, string, nails, scraps of wood and other odds and ends we linked this to a triggering mechanism which released coconuts or calabashes on the hour so that they would roll down rails to make a chiming noise on an old disused lime juice machine. Perhaps we were out in the tropical sun for too long!

To calibrate the water clock, we used the sundial and worked out how far the float rose each hour.

How was the portable clock made?

Copyright: Used with permission Making a portable clock or wrist watch, with no small springs, no battery and no precision tools ruled out making a mechanical clock, so we opted for a mini sundial. To make sure that the sundial wristwatch was accurate, the gnomon had to point at the correct angle. This meant that the wristwatch had to be kept level using a plumb line or spirit level. The gnomon also had to face north so a compass was needed.

Roll up Mike Leahy's 'compact two-piece time-piece': a ridiculous contraption that looked like a mini radar station. Amazingly, it worked and even more incredible is the fact that during the sixteenth to eighteenth centuries people actually used to carry portable sundials around, complete with compasses and they're still made in India. No doubt they looked a little smarter than the Rough Science creation though!

The BBC and the Open University are not responsible for the content of external websites.

Building a Sundial - from the web book “From Stargazers to Starships” by David P. Stern, on the International Solar-Terrestrial Physics page, part of the NASA site

Sundial Links - from The North American Sundial Society site

Sundials on the Internet - information about all aspects of sundials

Clepsydra - from Rees’s Clocks, Watches and Chronometers, 1819 on Gordon T. Uber’s Home Page

How do Clocks Keep Time? - on the Physical Science Lessons page on the University of Michigan website

Books

Sundials, History, Theory and Practice by RRJ Rohr, Dover Publications

Making a Clock-Accurate Sundial Customized to Your Location (for the Northern Hemisphere) by Sam Muller, Naturegraph Publishers

Longitude by Dava Sobel, Fourth Estate

The Illustrated Longitude by Dava Sobel, Fourth Estate

Mapping Time by E. G. Richards, pub Oxford

Sundials by Albert Waugh, pub Dover

Sundials by Christopher St J. H. Daniel, pub Shire Album

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