VERTICAL WALL SUNDIAL: simulation of shadow cast by a vertical sundial on the south facing wall of a tower on Midsummer Day at the latitude of Greenwich (London, England).
VERTICAL SUNDIALS can appear on towers or walls and can easily be seen from a distance. Compare with a traditional horizontal garden sundial. On a south facing wall (in the northern hemisphere) the gnomon (the object that casts the shadow) lies at an angle to the dial of 90 degrees minus the latitude. This means that the gnomon lies parallel to the axis of rotation of the Earth (at an approximation the sun can be said to revolve around the gnomon). Consequently, the shadow sweeps out a path that is close to regularly spaced for the hours although some adjustment is needed for complete accuracy. The numbers on the dial are spaced (along a horizontal line) by using the tan of the angle of rotation of the sun (relatively speaking around the gnomon). Thus the gap between the 12 noon point and 1 pm point is proportional to tan 15o. The sun moving through 15o in one hour (360o in 24 hours = 15o in one hour). The gap between 12 noon point and 2 pm is proportional to tan 30o.