The first step is to mark out the hour angles. A base line with a centrally rising perpendicular gives the noon, 6am and 6pm lines as follows:-
Various methods exist for generating the remaining hour angles, we will use the computational method. The formula for calculating the angles quoted in many works on the subject is:
log tan D = log tan t + log sin Ø
and was used in this form to save the need for long multiplication of fractions. However in these days of pocket calculators we can use the more straightforward:
tan D = (tan t)(sin Ø)
In both these formula D is the angle which the hour line makes with the noon line, t is the time measured from noon in degrees and minutes of arc [the earth completes the 360° round the sun in 24 hours so 1 hour = 15° and 1 minute = 15' of arc], and Ø is the latitude of the place where the dial is to be positioned. Each angle calculated for times before noon also gives the angle for the equivalent times after noon:-
It's best to draw up a table:
| time | t | tan t | sin Ø | tan D | D |
|---|---|---|---|---|---|
| 9.30 (2.30) | 37°30' | 0.7673 | 0.7749 | 0.5945 | 30.73° |
I have put in one set of figures assuming a latitude of 50°48' (Ø = 50.8). Of course this is an obvious spreadsheet application. Having plotted all the hour angles required, normally hours and half hours, the shadow casting component, known as a gnomon or style, can be fitted along the noon line as shown below. The angle or height of the style is equal to the latitude of the dial location.
It is a good idea to draw the whole thing out on a large sheet of paper fixed to a board and make a style out of thin card. This will check the design before committing it to a more permanent medium. The sundial should be positioned where it will be in the sun for the maximum length of time with the dial plate perfectly level and with the noon line pointing directly north.
Happy dialling!