Bernard's Sundial

Location: Brunswick, Melbourne, Australia
37º46'12" South,
144º58'12" East

Background

I decided I wanted a reasonably scientifically accurate, and decorative, sundial as the perfect finishing touch for my home renovations. Unfortunately, the sundials in shops looked very basic and there seemed to be no way to calibrate them to a location, nor markings to indicate that they were designed for Melbourne. They were either the standard horizontal dial with an angled gnomon (the part of a sundial that casts a shadow so you can tell the time), or in a couple of cases were the spherical type made of intersecting metal circles, which cost a few hundred dollars yet looked rather wonky.

Plus it's nice to know where the sun is, as it earns me money via my roof-top photovoltaic cells:

(click for larger image of the power generated on 21 Dec 2004, which totalled 4.9 kWh)
average daily power, sampled monthly

Solution & Design

I looked on the Internet to see whether I could build my own (using up some of my hardware junk if possible!); I was amazed to see the variety of types of sundials, and there were also several sites that were great at explaining things like the Earth's orbit, the Analemma and so on.

I formulated a design: if I could line up a circle to be parallel with the equator (which means that the axis of the circle is parallel with the axis through the Earth's North & South poles) then the sun will appear to rotate around the circle at a constant rate, viz. 24 hours for one rotation, or 15º an hour; with a slight seasonal variation - see below. Also during the course of a day, the sun will stay at a fixed angle above or below my 'equator' circle - during the course of a year this angle moves from 23.5º at the solstices to 0º at the equinoxes. This arrangement is called an Equatorial Sundial.

So now, I just needed a circle (the dial) and a gnomon of some sort (to cast a shadow). Luckily, my local bike shop had an old, slightly rusty, but still very circular, wheel that they were about to throw out and were happy to let me have it- perfect as the dial in the design. If I replaced the axle of the wheel with a long rod, it would cast a shadow onto the wheel's rim that could be used to tell the time. I purchased a long threaded rod from the local hardware store.

The sundial is located in the North-facing rear courtyard of my house. I didn't want people to crash into it; and it needed to take into account the shading from 2-story factory walls next door to the West and to the North, and a couple of tall trees next door to the East and North-East. I attached it to the upstairs wall which makes it a little bit harder to read from a distance but it gets around most of the shading problems.

Construction and Installation

I put the threaded rod through the axle of the wheel (with nuts on each side of the wheel to keep it rigid) and fixed the top end to the wall, letting the rim of the wheel rest on the wall. The angle of the wheel could be adjusted by tightening a nut where the rod goes through the wall bracket. The rod needed to extend below the wheel by at least 13cm so that it casts a shadow on the rim in winter.

Side view

North view (not all spokes shown on wheel)

The best way to get everything lined up right was to make use of the Equinox, where for a couple of days, the sun was very close to being side-on to the rim. This is where I discovered that the wall wasn't facing Due North as I had thought, but angled about 11º East. I resolved the problem by placing a block of wood under one side of the rim so that the wheel was angled a bit to one side.

Getting the alignment right at the Equinox (September 2004) - note that the sun is edge-on to the rim, hence the shadow of the rim on the wall is a straight line. Also the wheel had to be angled out from the wall slightly (using the plank of wood) so that the rod/axle lines up with the Earth's axis.

The point of light that is around 120º from the top of the wheel (anticlockwise) is probably from the sun shining through the valve hole at the top of the wheel.

The next phase was to make the sundial tell the time! The wheel has 36 spokes, exacly 10º apart. This corresponds to 40 minutes per spoke... not the easiest dial to read, but a start. I rotated the wheel so that the hole in the rim (where the valve pokes through when you have a tyre on it) was at the top, and the little circle of light that it projects lined up with the axle at noon. With everything set in place I used a variety of fasteners (mainly screws and silicone sealant) to keep it there.

When it is not the equinox, the rod/axle casts a shadow on the rim, and by counting the number of spokes that the shadow is from noon (at 40 minutes a spoke) you can get a very accurate reading of the time. When it is right on the equinox, you can use the beam of light from the valve hole (at 20 minutes a spoke, since you're effectively using a gnomon that's twice as far away), or you can judge where the shadow would be on the rim by lining up the rod's shadow on the wall.

Eventually I attached some markers to the rim (angle brackets for 6am, 9am, noon, 3pm, 6pm; and nails the other hours) to make it a bit easier to read.

The Analemma

A basic sundial actually runs fast or slow, based on the time of year. In November it can be as much as 15 minutes fast. This is due to the fact that Earth's orbit is slightly elliptical, so Earth speeds up and slows down a bit during the year relative to the Sun. Also the tilt of the Earth (23.5º) has an effect. So, rather than the sun being in the same spot in the sky at the same time each day, it traces out a figure-8 shape called the 'Analemma'.

There is a formula that can be used to calculate the time correction according to the date, but many sundials show this correction graphically which is what I've done as well. I made a plaque out of a small piece of polished marble that I found buried in the backyard (possibly a benchtop from a long-forgotton renovation?), by engraving into it a rough Analemma and graph of time correction and elevation above the equator, according to time of year; using an angle grinder (which isn't the most dextrous of engraving tools, but it's what I had handy!). I stuck the plaque on a handy pole where it can be read in conjunction with the sundial. I used photos of analemmas on other sundials to obtain the correct shape. Note that my analemma is not to scale - the real analemma is a lot narrower but this would have made mine harder to read.

The horizontal lines represent the sun's elevation North of the equator in increments of 5º. The vertical lines indicate how fast or slow the sundial is, in increments of 5 minutes. In the centre is an 'X' that marks zero degrees and zero minutes of time.

One circuit of the analemma corresponds to a year, starting with the First of January at the notch marked with an (inverted) 'J' at the bottom of the circuit. The year progresses up the right side, then diagonally up to the left, then across the top to the right and finally diagonally down to the left. The first of each month is marked with a notch. The top and bottom of the Analemma corresponds to the Solstices (approx June 21 and December 21) and the zero-elevation intersections, halfway up the graph, are the Equinoxes (approx September 21 and March 21).

To use the Analemma, read the time on the Sundial. Then, use the current date to find the corresponding point on the Analemma. If the date lies on the right side of the analemma, add the appropriate number of minutes (counting grid lines) to the time from the sundial. If the date lies to the left, you subtract minutes.

For example, if it was 14th February, you find the part of the curve halfway between the 'February' and 'March' notches (the right-most part of the curve), and note that this is about 14 minutes. If the Sundial reads 2:30pm, that means that the actual time must be 2:44pm Australian Eastern Standard Time, or 3:44pm Daylight Savings time. We also see that the sun is about 13º south of the equator, not that this helps read the time!

Paved Analemma

I've created another Analemma graph using "cats' eyes" road reflectors that I've scavenged over the years; glued to the concreted surface of the courtyard with Liquid Nails.

I am using the lines in the concrete as grid lines: the centre point is marked by a white/red reflector; the side lines (extending towards the house) represent +/-15 minutes, and the lines parallel to the back wall represent +24, +8, -8 and -24 degrees (the last is out of shot near the camera).

1st January is marked by a blue reflector (near the door) and 1st July by a red reflector (near camera). The 1st of other months are marked with white reflectors with yellow reflectors indicating approximately the 15th of each month... note that it's all a bit approximate. February and March are to the left of January in this photo.

Daytime/nighttime globe

The sundial was looking good, but it needed a finishing touch, also I was a bit worried about the rod taking someone's eye out. The solution was to put a sphere on the end of the rod, and by drawing a map of the Earth on the sphere, it would be able to show which part of the planet is in sunlight or nighttime. The best sphere I could find was a 15cm diameter brass float at the local plumbing shop - it looked really nice and was durable and light (but was a bit pricey and subject to dinting). It had the great advantage that it had the right thread to be screwed straight on to the rod. I traced on the map using my sister's boyfriend's globe (thanks Rob!), and spent several weeks trying various methods of etching on the design using Brasso and hydrochloric acid. In the end, I polished the globe to a high shine and applied a lacquer that is designed for sealing stone paving to the 'land' areas of the globe. This preserved the shine on these parts allowing the 'ocean' parts to oxidise nicely. I trimmed the rod so that it was just long enough to cast the correct shadow during summer solstice, and screwed on the globe with Melbourne was on top (so that it lines up with its location on the Earth).

Daylight Saving

The Sundial doesn't correct for daylight saving - you have to do this yourself! Daylight Saving applies in Melbourne from the last Sunday in October to the last Sunday in March.

Cost

Bicycle wheel: $0 (courtesy Ray's Bicycle Centre, Sydney Road, Brunswick)
Threaded metal rod: around $5
Brass float: $90
Assorted hardware (brackets, bolts, nuts, screws, nails, sealant, acid, lacquer): loose change, or were there to be used

Related/useful links

The Hyatt Regency Jersey City Sundial
The Seattle, Washington Equatorial Sundial (similar design to mine)
Heavens Above (solar data)
Analemma.com (fantastic description of the Analemma)

Results

It works! Even from a distance you can normally judge the time to within a couple of minutes, and up close you can improve the accuracy to less than a minute. It looks quite nice (I reckon) and acts as a reminder, of sorts, of the world outside.

The Summer Solstice video (818kB) is a time-lapse of 22nd/23rd December 2004 (combined, due to weather conditions), starting around 12 hours after the exact solstice. The video starts at 5:30:00 AEDT and finishes at 21:20:00 AEDT. Sunrise was at 5:55 AEDT and sunset at 20:42 AEDT. Each frame corresponds to 10 minutes - note that every four frames the shadow has moved to the next spoke.

It's not very clear, but you can just see the shadow of the gnomon first appear on the rim of the wheel at 9:10 AEDT (before that, too much of the wheel is in the shadow of the eaves). It last appears (faintly) at 16:10 AEDT - after this the sun is too far around the West side of the house.

The camera was positioned to look up at the sundial, along the line of the North/South axis. This makes it easier to read the dial, as the rod's shadow acts as an approximate hour hand. Conveniently this 'hand' moves clockwise. I suspect that 'clockwise' was originally defined as the direction a shadow moves in the northern hemisphere, but this still works for us in this case as we read the sundial from underneath.

You can also see the Daytime/Nighttime globe working well in the video (from this angle, it's in the centre of the wheel). For example, the North pole (pointing straight at the camera) does not receive any direct sunlight - and will not until the next March equinox. Asia is near the top right of visible part of the globe, Europe and North Africa towards the bottom right, and North America towards the bottom left.

The November video [1 month from Summer Solstice] (934kB) is a time lapse of 21 Nov 2005 (prior to 7am footage from 22 Nov). Sunrise 5:56am AEDT, Sunset 20:16pm AEDT. The sundial 'acquires' the sun just before 8:00am AEDT and loses it again just after 4:20pm AEDT.

The February video [2 months from Summer Solstice] (781kB) is from 21 Feb 2006, Sunrise 6:55am AEDT, Sunset 20:11pm AEDT. It was cloudy early in the day, first confirmed shadow at 9:40am AEDT and the last time reading 5:50pm AEDT.

The Autumn Equinox video [3 months from Summer Solstice] (716kB) is a time lapse of 20th March 2005 (exact time of equinox was at 23:33 AEDT). Sunrise was at 7:22 AEDT, sunset at 19:32 AEDT. This video shows very clearly how the wheel (parallel to the equator) lines up with the sun throughout the Equinox. See how the shadow of the wheel appears to 'roll' in a perfectly straight line across the wall. The sundial 'works' from around 8:00 AEDT until about 18:30 AEDT - several hours longer than the summer solstice (due to better 'lines of sight' - the house isn't in the way of the sun so much).

The April video [4 months from Summer Solstice] (669kB): 25th April 2006, Sunrise 6:55, Sunset 17:40. Sundial effective from 7:50am (possibly 7:30 except for shadow of tree), until 16:10.

The May video [5 months from Summer Solstice] (637kB): 20th May 2005, Sunrise 7:17, Sunset 17:15 AEST. Sundial effective from 7:50am (possibly earlier, fog affected) until 15:50. Note that there is significant shading from neighboring trees (and fog) until 10:20.

The Winter Solstice (approx) video [6 months from Summer Solstice] (627kB): 18 June 2005, Sunrise 7:34, Sunset 17:07. Sundial effective from 8:10 (possibly earlier, cloud affected) until 15:40. This video is 3 days early for the solstice, due to bad weather for the solstice. Note how the shadow of the globe brushes against the shadow of the rim all day.

I am planning to add more time-lapse videos to eventually show the sundial at 1-month intervals.

This side-on photo was taken at exactly noon (sundial time, without the Analemma correction) approximately 12 hours after the summer solstice. Notes:

the southern Indian Ocean is decidedly green - this is oxidised copper resulting from my aborted attempts at etching the oceans; I expect that this will gradually dissolve/blend in with the oxidised northern hemisphere oceans.
There is a point of light visible just where the collar of the globe is screwed on to the rod. This is where the sun is shining through the valve hole at the top of the wheel rim; I used this alignment to calibrate the sundial; also I trimmed the rod so that it was just long enough to 'catch' this point of light; this means that in winter the rod will be just long enough to cast a shadow on the rim.
Melbourne is at the top of the globe (to coincide with where the sundial is installed) - it's just dawning on the East coast of India and in Madagascar; the big shiny areas are Africa to the right and Saudi Arabia to the left of the Red Sea.

Note - it doesn't work on cloudy days...

View of Sundial from rear courtyard. Note that it now has large 3-hour markers (and smaller 1-hour markers not quite visible here)

Queries: bfdeAAA@alphalink.com.au (spam deterrent: remove AAA to send me an email)
January 2005

Last updated: June 2005