“What is the declination of the wall for a sundial?” A stone sculptor asked us just this question recently . It is a good question because you must know the declination if you are making a sundial that is accurate for the wall. The sculptor was not confident about their own measurements and calculations so they asked us for help.
In fact, the mathematics of sundials can be simple but the practicalities are almost always confusing. Wall declination is the direction the wall faces to the sun. A wall facing the sun in the afternoon declines to the west, while one facing the sun in the morning declines east. A wall facing due south has a declination angle of 0°. Knowing the declination angle is necessary for designing a sundial for the wall. It is needed to determine the angles of the hour lines on the dial, the gnomon rotation among the hour lines, and the gnomon elevation.
The diagram illustrates a method for calculating wall declination. The first step is to measure the protractor angle between sun direction and the wall, and then to calculate the azimuth angle between sun direction and south at the time of day. Wall declination is the difference between azimuth angle and protractor angle plus 90°. There are online tools including map data and azimuth calculators, and the excellent sundial software ShadowsPro is very popular.
The stone sculptor has our results and is delighted with them. The sculpting work is complete, and the metal gnomon will be ready soon, for a beautiful new sundial.