# Horizontal Sundial

Figure 29: Horizontal sundial

Figure 30: Side view of a horizontal sundial

## Characteristics

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.

## General Appearance

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.

Figure 31: Dial plate of a horizontal sundial

## The Mathematics of Horizontal Sundial

We will now show the mathematics of how the hour lines are being drawn for a horizontal sundial.

Figure 32

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)

Figure 33: The calculated shadow angles at latitude 51ºN.

## How it works

We will show in the below animation how the shadow of the gnomon is cast in a year.