8e0cd8f2-488e-487c-8df1-2e569a3ca859.doc 1/3 19/02/2010 HOW TO MAKE A SUNDIAL o o o The Sun’s position in the sky will move by 15 each hour (360 movement / 24 hours = 15 / hour). BUT The horizontal or vertical sundial plate is angled to the Sun’s rays due to our latitude. This means that o the shadow cast does not move by 15 every hour. It will move through larger angles for one hour at dawn and dusk, and smaller angles for one hour near noon. I’ve found two good methods to get the angles for the dial. In each calculated example, I am using the o latitude of Cranbrook – 51 N. If you live elsewhere, find your home latitude on the Internet. Method 1 – calculations Draw your 12 noon line on your dial. o The first line either side of the noon line (11am and 1pm) will not be 15 away from noon, due to the latitude problem. To calculate the angle, use the following formula: Horizontal dial Vertical dial o o tan(angle) = sin(latitude) x tan(15 ) tan(angle) = cos(latitude) x tan(15 ) o E.g. for a horizontal dial at a latitude of 51 , the calculation would be o o tan(angle) = sin(51 ) x tan(15 ) = 0.777 x 0.268 = 0.208 o angle = inverse tan(0.208) = 11.8 o The lines are drawn at 11.8 either side of the noon line. o o For the 10am and 2pm lines, you repeat the process but use 30 instead of 15 in the calculation. This o will give you a result of 24.2 and is the angle of the 10am and 2pm lines from the noon line. o This continues until you get to 6am and 6pm. These lines are just drawn at 90 to the noon line. The finished dial will look something like: noon 1pm 2pm 3pm o angle of 11.8 to noon line 4pm o angle of 24.2 to noon line 5pm (Same arrangement of lines this side of noon line) 6pm 8e0cd8f2-488e-487c-8df1-2e569a3ca859.doc 2/3 19/02/2010 Method 2 – drawing circles Draw a large circle to be your sundial face. Measure the radius of this circle. Calculate the radius of the smaller circle that you will need to draw the hour lines using the following formulae: Horizontal dial Vertical dial small radius = sin(latitude) x large radius small radius = cos(latitude) x large radius Place the two circles on a large sheet of paper. The circles should be just touching each other. Draw a line joining the centres of the two circles. At the point where they touch, draw another line at right angles to the first line (see below) perpendicular line line between centres The original line between the centres is the noon line. o On the smaller circle, draw in hour lines at 15 to each other, starting from the noon line and working outwards. You need to go five lines either side of the noon line. Extend these new lines to hit the perpendicular line between the circles. From the perpendicular line, draw back to the centre of the large circle. Add the 6am and 6pm lines at right angles to the noon line. 6am o all lines at 15 to each other noon line 6pm 8e0cd8f2-488e-487c-8df1-2e569a3ca859.doc 3/3 19/02/2010 The style (often called the gnomon) o This is the pointy bit that casts the shadow. If you put this at 90 to the dial face then the shadow that it casts will change length during the day. To make sure that the shadow length stays the same, we angle the style to the dial. (You actually angle it so that the style points to the pole star.) Horizontal dial Vertical dial style angle o = 90 - latitude style angle = latitude of dial The style needs to be positioned so that, from above, it points along the noon line: noon style The horizontal dial needs to be mounted so that the noon line and nail points directly north. This does need to be true north, not magnetic north, or you will be out by a noticeable amount. The vertical dial needs to be mounted so that the dial faces directly towards south. You will need an east-west wall, or fix a vertical post so that the dial can be positioned along an east-west line and face south. In all cases, you will measure local solar time with the dial. It won’t measure clock time due to the problems with the non-uniform motion of the sun (see the equation of time) and the additional complication of British Summer Time. It will measure solar time instead. It will also measure local solar time as the dial will almost certainly be east or west of Greenwich and so local noon will not be the same as that at Greenwich. For the horizontal dial, you can compensate for that by angling the noon line away from north by the longitude of your dial. For further information and useful web sites, check Moodle.