A Sundial For South Africa

A sundial can enhance one's garden and be a talking point. Or it can merely be an interesting project. Sundials are fairly easy to make, however the average person might find the simple mathematics involved a bit daunting.
So - no calculations here, just simple and straightforward instructions on how to go about making a sundial. We will use a standard sheet of A4 paper as a template. A4 paper is 210mm by 297mm. We will also need a ruler and a sharp pencil (and possibly an eraser if you are like me and make lots of mistakes).
A sundial consists, basically, of two parts - the dial and the gnomon. Which is a fancy name for the triangular bit that sticks up in the centre.
The type of sundial we will make is known as a "horizontal" sundial.
Before you can commence making a dial you must determine the latitude of the place you live in - or where you are going to use the sundial. You can do this by looking in the gazetteer of a standard atlas. I include a list of some South African towns and cities. All of South Africa lies between 22 degrees South and 35 degrees South. If the minutes of latitude are greater than 30 then take the next whole number as your latitude. Example: De Aar is 30 degrees and 39 minutes South - the Latitude you want is 31 degrees. Bloemfontein is 29 degrees and 06 minutes South - the Latitude you want is 29 degrees.

CITY	DEGREES LAT	MINUTES LAT
BEAUFORT WEST	32	18
BLOEMFONTEIN	29	06
CAPE TOWN	33	59
DE AAR	30	39
DURBAN	29	57
EAST LONDON	33	00
GRAHAMSTOWN	33	19
JOHANNESBURG	26	10
KIMBERLEY	28	43
KOEKENAAP	31	32
KURUMAN	27	28
LANGEBAANWEG	32	59
MOSSEL BAY	34	11
OUDTSHOORN	33	35
PIETERMARITZBURG	29	35
PIETERSBURG	23	54
POFADDER	29	10
PORT ELIZABETH	33	58
PRETORIA	25	45
PRIESKA	29	40
QUEENSTOWN	31	52
SPRINGBOK	29	42
SUTHERLAND	32	23
UPINGTON	28	25
WELKOM	28	00
WORCESTER	33	39

Having found your "reference" latitude you are ready to commence making your sundial template.

Divide your sheet of A4 paper by drawing a line in the middle of the long side across the sheet. Measure 148.5 from the top, on both sides, and draw a line across the sheet.

Now turn the sheet of paper sideways. The point P at the top of the sheet of paper will be the axis from which you will draw the radiating lines for the dial face.

From the following table select the column under your reference latitude.

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176

Assuming we chose 29° for our reference latitude .....

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176

we should now have a column of figures that looks like this:

13
27
42
59
78
102
133
33
83
128
170

These figures represent distances in millimetres from the bisector at the bottom edge of the paper. Mark, on both sides, each distance. When the figures suddenly get smaller (those that are underlined) it means you must "turn the corner" and start marking from the bottom of the paper towards the top line.

As shown in the following figure.

From the center point draw radiating lines to each of your outer edge marks. Remember the more accurately you work the more accurate will be your sundial. Perhaps you wish to mark those lines reperesenting hours differently. By now you will have gathered that each of these marks represents 30 minutes of time starting from 6am through to 6pm - these two hours represented by the top edge of the paper. 12 noon is represented by the bisector.

Your dial face template is now finished. You could use it to transfer the drawing to something more permanent like a thick piece of cardboard, a piece of wood or metal. You could also "clean it up" as in the following drawing and mark the times at the appropriate lines.

Now we need to make the gnomon. Take a fresh sheet of A4 paper. Using your reference latitude select the relevant number from the following table:

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
85	89	93	98	102	107	112	116	121	126	131	136	142	147

Using the number we found in the table measure in millimetres from the bottom of the sheet of A4 paper as shown in the figure. Draw a line from the opposite corner to the mark on the opposite edge. The triangle represents the gnomon. The size is not important, just the angle. Of course it should be large enough to cast a shadow on the dial we have made.

Mount the gnomon on the 12 o'clock line of the dial with the sharp side pointing toward the top as shown in the figure below.

Aligning the Sundial

Our sundial is complete. It should be mounted with the 12 o'clock line on a true North-South axis. It is not sufficient that you line it up with the clock time for that moment.
Now for the bad news.......

Reconciling "clock" time with "sundial" time for complete accuracy!

The Effect of Longitude

One fly in the ointment is longitude. In South Africa our time is based on the 30° East line of longitude. Thus our sundial would truly only be correct with clock time, even allowing for all other factors, if installed on this line.
However all is not lost. Every 1° of longitude represents 4 minutes of time. And every minute of longitude represents 4 seconds of time. Determine your longitude by looking in the gazetteer once again.
Convert the degrees and minutes to decimal degrees by dividing the minutes of longitude by sixty and adding them to the degrees. Thus 18° 22 minutes would become 18° plus 22/60 = 0.3666.... or 18.37° rounded off to the nearest 100th. Now subtract this from 30°. 30 - 18.37 = 11.63. Multiply that by 4 and the answer is 46.52 minutes of time. Or 46 minutes and 31 seconds of time (0.52 times 60 to get seconds).
You need do this calculation only once. If you live west of the 30° line (most of South Africa) then you must remember to add this sum to the sundial time. If you live East it must be subtracted.
To sum up:

Find your longitude from an Atlas.
Convert it to decimal longitude by multiplying the minutes by 60 and adding them to the degrees.
Subtract the decimal longitude from 30.
Multiply the result by 4 to obtain the "difference" between clock and sundial time.
Convert this sum from decimal minutes to minutes and seconds by multiplying the fractional part by 60.

It is a good idea to add this information to your dial face so that you will remember it always. Something like: Longitude correction: Add 41 minutes 22 seconds printed on the face would help.

More bad news......
Bad news part one: A sundial does not tell "clock" time. It tells "local apparent sun time". Clock time is known as "mean solar time" which is an average having no real relationship to the sun.
Bad news part two: Because the length of "real" days vary the sundial is only accurate on a few days every year. This is partially explained in the following section.
Bad news part three: Refraction causes errors too!
The Sundial makes use of the apparent solar day to tell time. Unfortunately the apparent solar day has varying lengths which are inconvenient to modern man. Thus the "mean solar day" has been adopted as a convenient average.
However when one depends on a shadow made by the real sun then it becomes difficult to reconcile "sundial time" with "civil time" as the two times are known.

If one were to observe, from the exact same spot, the sun every ten days at exactly the same "civil time" for each observation and plot its position on a chart the following graph will be produced: (this is known as the "analemma" or daily declination of the sun which is from Latin but derived from Greek "analemma" meaning "pedestal" which originally referred to the base of a sundial.)

As we have seen the sun "wanders" around the sky during the year, and we depend on the shadow it casts for our sundial time, we need some method of correcting for this "wander".

Intially, assuming our dial is correctly aligned, we would make the correction for longitude by adding or subtracting the sum we worked out earlier. However this could bring us only within 20 minutes or so of clock time! Further adjustments are needed. Most of them require some advanced mathematical skills.

Refraction is the way the sun's rays are "bent" as they move through our atmosphere. It varies from a maximum at sunrise to a minimum at local noon. The effect is greater in winter than in summer. In fact refraction causes a different error all the time.

The equation of time is affected by factors such as the tilt of the earth's axis and the speed around the sun. Other factors such as precession and nutation also play a role. Calculating the corrections for these influences becomes quite a nightmare to a novice and necessitates knowledge of annual variations not easily come by.

Programs are available on the Web which take out the slog work and output a "total correction" for your locality. A nice easy one to use is the Dialists Companion which is available to download as Shareware from the North American Sundial Society

The North American Sundial Society can be found on by clicking here.

Conclusion

If your appetite is now whetted and you want to make a truly accurate sundial for where you live, and you feel you are up to the math, try the following link:

Sundials on the Web

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176

A Sundial For South Africa

Aligning the Sundial

Reconciling "clock" time with "sundial" time for complete accuracy!

The Effect of Longitude

More bad news......

Conclusion

Copyright: Eugene Griessel, May 2000

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176

22°	23°	24°	25°	26°	27°	28°	29°	30°	31°	32°	33°	34°	35°
10	11	11	12	12	13	13	13	14	14	15	15	15	16
21	22	23	24	25	26	26	27	28	29	30	31	31	32
33	34	35	37	38	39	41	42	43	45	46	47	49	50
45	47	49	51	53	55	57	59	61	62	64	66	68	70
60	63	66	68	71	73	76	78	81	83	85	88	90	92
79	82	85	89	92	95	99	102	105	108	111	114	117	120
103	107	111	116	120	124	128	133	137	141	145	1	6	11
136	142	148	7	14	21	27	33	39	44	48	53	57	61
46	53	59	64	70	75	79	83	87	91	94	97	100	103
104	108	112	116	119	122	125	128	130	133	135	137	139	141
158	160	162	164	165	167	168	170	171	172	173	174	175	176