# Vertical sundial

The vertical sundial is a sundial with a vertical dial . It is usually located on a building wall, where there is often free space and should be embellished. It is therefore the most common sundial.

Vertical sundial with pole rod for true local time on a wall slightly deviating from the west (the scale contains one more hour line for the afternoon than for the morning)

## description

In contrast to the horizontal sundial, this is not an all-day sundial . For the longest time (on the northern half of the earth) a wall facing south is illuminated by the sun, namely 12 hours on the days of the equinox . On the longer summer days it is even less than 12 hours, and the early morning and late evening hours can be shown on a north wall sundial . With a corresponding limitation of the display time, any wall can be fitted with a vertical sundial. An east or west sundial shows between sunrise and noon ( true local time ) or between noon and sunset. Twin sundials, which combine east and west sundials, can occasionally be found in large courtyards of castles or monasteries.

## calculation

If the wall points due south, the dial is symmetrical and the following equation applies:

${\ displaystyle \ alpha = \ arctan (\ cos \ phi \ cdot \ tan \ tau)}$

α is the angle between the hour line and the meridian (vertical) which, in addition to a function of the hour angle τ, is also one of the location constants Φ ( geographical latitude ). The angle α = 0 ° applies to the 12 o'clock line ( true local time ).

Most of the time the wall used does not point exactly south. It's twisted a little east or west. For the now asymmetrical scale the equation applies:

${\ displaystyle \ alpha = \ arctan (\ cos \ phi \ div (\ sin \ phi \ cdot \ sin d + \ cot \ tau \ cdot \ cos d))}$

d is the angle of rotation of the wall (positive if it deviates from the west). The 12 o'clock line remains vertical (τ = 0 ° → α = 0 °).

## Individual evidence

1. Out of a total of 3341 sundials in Austria, 3161 are vertical sundials (status: January 1, 2006; Karl Schwarzinger: Catalog of fixed sundials in Austria. Austrian Astronomical Association , Vienna 2006).
2. ^ Arnold Zenkert: Fascination Sundial. Verlag Harri Deutsch, Thun and Frankfurt am Main 2002, page 54.
3. ^ Arnold Zenkert: Fascination Sundial. Verlag Harri Deutsch, Thun and Frankfurt am Main 2002, page 62.