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Make your own Sundial

The type of sundial shown here is very easy to make - simply print out the one for your area!

The sundial shown below is accurate to within five to ten minutes for places within the province of Gauteng in South Africa, such as Johannesburg or Pretoria. It gives the standard time for southern Africa, which is the time we set on our watches and clocks. (Click on the image for a larger version and data table for making your own):

Sundial for Johannesburg / Pretoria, Gauteng Province, South Africa

The green line is called the "date line". The date is estimated by interpolating between the markers on the line. Stand on the green line at today's date, and the shadow falling on the blue line, called the "timeline", gives the mean Sun time. The offset from the green line to the red figure "8" for today gives the correction (described below) to the mean Sun time. The figure "8" shape is known as the "analemma". The size of the correction to be added to or subtracted from the mean Sun time is shown by the scale at the foot of the analemma.

Setting up the Sundial

To set up the sundial after printing it:

Set your watch accurately to Standard Time (not daylight saving) for your time zone.
get a thin straight rod about 20 to 30 cm long, such as a knitting needle.
Stick one end of the rod into a something which will hold it upright, such as a little putty, or a cork, or transparent plastic.
Near midday, take the sundial and rod into the sunshine and place the sundial on a horizontal surface.
Place the rod onto today's date on the "figure 8" in the centre of the diagram.
Turn the diagram until the shadow of the rod crosses the time line at the correct time. This has oriented the sundial to true north.

To use the sundial:

The rod or stick casting the shadow should be placed on the centreline of the sundial, (shown in green), where today's date falls - interpolate between the marked dates. This will give the mean solar time.
The offset from the centre line (green) to the analemma (red curve) for today is the correction for Sun time not running evenly (which is explained below). This correction is up to 16 minutes in February and November, as can be seen by comparing the offset with markings on the timeline (blue curve).

Here at Hartebeesthoek we have made a large version of the sundial. It is painted onto a flat surface in front of our Visitors Centre. A person can stand on it - the person's shadow crossing the time line then gives the time. One can also use a long (about 2-metre) rod to cast the shadow, to be more accurate.

Sundial in use at HartRAO, viewed from the south.

The Analemma

The type of sundial shown here is called an "analemmatic sundial". The "analemma" is the "figure 8" in the centre which marks the apparent motion of the Sun during the course of the year.

The north-south passage of the Sun during the year is the reason for the north-south extent of the dateline and of the analemma. This apparent motion of the Sun is caused by the Earth's axis being tilted at 23.46 degrees to the plane of its orbit around the Sun. This means that on June 21 the Sun will appear to be almost 47 degrees closer to the northern horizon at midday than on December 21.

There are two reasons why the Sun wanders off to one side and then the other of the dateline, to produce the figure 8:

Firstly, the orbit of the Earth around the Sun is not circular but slightly elliptical, or egg-shaped. On July 4 or 5 the Earth is at its furthest from the Sun, and moving slowest. It then starts to speed up slightly as it moves closer to the Sun, and once past its point of closest approach in January 2 or 3 it starts to slow down again. The speeding up and slowing down of the Earth in its orbit means that the time measured from the Sun's position can be a little early or late compared to Standard Time, the steady rate at which our clocks run.
Secondly, the tilt of the Earth's axis to the plane of its orbit around the Sun also causes the Sun to appear to be early or late. The Sun and planets follow a path across the sky called the Ecliptic. Because of the tilt of the Earth's axis, the ecliptic is tilted at 23.46 degrees to the Celestial equator. The effect of this tilt is to produce an apparent slowing down and speeding up of the Sun as it moves along the ecliptic.

The two effects are similar in size. When added together the combined effect is called "the equation of time", and is shown below.

A sundial is "fast", i.e. ahead of standard time, in May and from September to December. It is about 16 minutes fast at the beginning of November.

A sundial is "slow", i.e. behind standard time, from January to mid-April, and from mid-June to the beginning of August. It is about 14 minutes slow in mid-February.

The picture below shows that the effect is biggest in February and November, and so the loop of the analemma is widest at those times. Sun time matches standard time in mid-April, mid-June, at the beginnning of September, and in late December.

We see the Sun making this figure "8" loop in the sky - these animations show what we see from the southern hemisphere and from the northern hemisphere.

This non-uniform variation in sun time during the year also causes the times of sunrise and sunset to be asymmetric. Graphs of sunrise and sunset for Nairobi, Johannesburg, Durban, Cape Town and SANAE clearly show this effect.

The Seasons

The change in distance from the Earth to the Sun owing to the elliptical orbit is small, up to + or - 1.7% of the mean distance of 150 million km. It is NOT the cause of the seasons. The seasons are a result of the large tilt of the Earth's axis, which causes first the southern hemisphere to be tilted towards the Sun (September to March) and then the northern hemisphere (March to September) as the Earth orbits the Sun. The heating caused by the Sun depends on the sine of its elevation (angle above the horizon), so the closer to the zenith (directly overhead) it passes at midday, the greater the heating. The longer days in summer also let the Sun heat the surface for longer than during the short days in winter.

The Timeline

Looking at the timeline, one can see that 12h00 (noon) does not line up with the dateline running vertically through the centre of the analemma. This is because standard time in southern Africa is set as though the whole of Southern Africa were at longitude 30 degrees east. However, Gauteng is at 28 degrees east longitude. Now, the Sun appears to move through 1 degree of longitude in 4 minutes of time, so the Sun seems to be 8 minutes late compared to Standard Time. Its shadow at midday falls a little west of where we expect it. The Sun's shadow tells us "local time", and to correct to Standard Time the time markers on the timeline have been offset by 8 minutes of time.

The effect is much bigger for Cape Town and Windhoek (see below), which are much further west. The opposite effect is seen on the Durban sundial, as Durban is east of 30 degrees longitude, and local time is then ahead of South African Standard Time.

Sundial for the Equator

It is interesting to see what the sundial would look like for a place on the equator at 30 degrees east (click on the image for a double size version):

The dateline lies symmetrically across the timeline, because the Sun appears to move an equal distance either side of the equator during the course of the year.

Sundial for the Tropic of Capricorn

The Tropic of Capricorn runs through southern Africa. This marks the line furthest south at which the Sun will appear exactly overhead at midsummer. In South Africa, the tropic runs between the towns of Polokwane / Pietersburg and Louis Trichardt. This is what a sundial for the Tropic of Capricorn at 30 degrees east looks like (click on the image for a double size version):

Here the dateline just touches the timeline on which the shadow falls.

More Southern African Sundials

Here are sundials for some other southern African cities and towns. Click on the name for a full size version with a table of the data for making your own "walk-on" sundial.

Sundial for Bloemfontein, Free State Province, South Africa
Sundial for Cape Town, Western Cape, South Africa
Sundial for Dendron, Limpopo Province, South Africa.
Sundial for Durban, Kwazulu-Natal Province, South Africa
Sundial for Giyani, in South Africa's Limpopo / Northern Province.
Sundial for Grahamstown, Eastern Cape, South Africa.
Sundial for Harare, Zimbabwe.
Sundial for Hermanus, Western Cape, South Africa
Sundial for Lydenburg, in South Africa's eastern Mpumulanga Province.
Sundial for Malelane, in South Africa's north-eastern Mpumulanga Province.
Sundial for Nelspruit, in South Africa's north-eastern Mpumulanga Province.
Sundial for Pietermaritzburg, in South Africa's eastern Kwazulu-Natal Province.
Sundial for Polokwane (Pietersburg), in South Africa's Limpopo Province, lies just south of the tropic of Capricorn.
Sundial for Potchefstroom, in South Africa's North-West Province.
Sundial for Richards Bay, Kwazulu-Natal, South Africa.
Sundial for Sasolburg, Vanderbijlpark and Vereeniging, Gauteng and Free State, South Africa.
Sundial for Welkom, Free State, South Africa.
Sundial for Windhoek, Namibia

Make your own sundials live on the Web

Design your own analemmatic dial like those shown above, using Jurgen Giesen's Analemmatic Sundial Java Applet.

Design your own horizontal sundial using Jurgen Giesen's "Pie Sundial" Java Applet. Ingeniously, this design has the gnomon built in.

Design your own horizontal sundial at Andrew Reynold's webpage

All you need to know for these is the longitude and latitude of your location, and the longitude of standard time for your time zone. For example Johannesburg is approximately 26 degrees south and 28 degrees, while South African Standard Time is 2 hours earlier than Greenwich, corresponding to an East Longitude of 30 degrees (the Sun moves through 15 degrees in an hour).

Shadows is a free Windows program you can download for designing sundials. The "Expert" and "Pro" versions with more capability are not free.

De Zonnewijzerkring has ZW_Easy and ZW2000 free Windows programs you can download for designing various types of sundials.

Aligning your sundial

For aligning most sundials one needs to know the direction of true (geographic) north. One can find the time at which sun is true geographic north (or south) of your location for each day of the year at www.solar-noon.com. The shadow of a vertical stick or of a string with a weight suspended from it will point due north (or south) at solar noon.

More about Sundials

Frans Maes' Sundial Site has a good explanation of the rights and wrongs of analemmatic sundials.

Analemmatic sundial mathematics gives you the math behind the sundials shown above.

The Analemma Website has more information on the analemma and equation of time.

Analemmatic Sundials: How to build one and why they work has a simpler explanation about the math.

Sundials on the Internet and The North American Sundial Society provide many general resources and links about sundials.

Sundial links, a page set up by Daniel Roth, has many useful links.

The Sundial Primer by Carl Sabanski has lots of useful information on sundials, descriptions of sundial types, and how to design a sundial.

Last updated 2012/07/05 by M J Gaylard e-mail: mike@hartrao.ac.za