Figure 29: Horizontal sundial
Figure 30: Side view of a horizontal sundial
The horizontal dial is pole - style. It is the one of the most commonly used sundial because it can be used to tell the time whenever the Sun is shining since the dial plate is placed horizontal to the ground. Some other types of sundials, such as the vertical dials can only be used during restricted hours of the day.
A horizontal sundial consists of a flat horizontal dial plate with hour lines which radiate outwards from the tip of the gnomon, which is the upright triangular plate. See Figure 31 for the general configuration. If the line OA is orientated in a true north-south direction, with O toward south and A toward north, the shadow of the style, falling among the hour lines will indicate the time of the day.
We will now show the mathematics of how the hour lines are being drawn for a horizontal sundial.
In Figure 32, OP is the style pointing to the pole, P. PNS is the meridian, NPT is the hour angle and TON is the shadow angle. By using one or more of the relations of spherical trigonometry, we can deduce that
cos NP cos PNT = sin NP cot TON - sin PNT cot NPT
in which PNT = 90º, NP = Ø and TON = 
Since cos PNT = 0, sin PNT = 1, therefore
0 = sin Ø cot - cot (HA)
tan = sin Ø tan (HA)
We will show in the below animation how the shadow of the gnomon is cast in a year.
Click here for the animation.
Most sundials that are available in the market do not work without a little adjusting.
Many of these "popular" horizontal dials have a gnomon which is set at 45º. This means that this dial is, hopefully, designed for use at latitude 45º.
The gnomon needs to point to the north celestial pole, so unless the angle of the gnomon is equal to the latitude, the horizontal dial must be "tipped".
If the gnomon was set at 45 º to the dial plate, but the latitude is 30º, then there is a difference of -15º between the gnomon and the latitude. So we must tip the whole dial so that the gnomon is lowered 15º. If the latitude was greater than the angle of the gnomon then we would tip the whole dial so that the gnomon is raised the correct magnitude.
These adjustments will correctly adjust for the new latitude.
