Dear John Carmichael, Well done John, Your simple question again triggered an avalanche* of responses from us nit picking old timers.
By now the difference between accuracy and precision is well defined. I would like to return the discussion to sundial design. The accuracy of a dial depends on the skill of the designer, builder and installer. It should take into account the latitude, longitude and orientation of the dial. The precision of a sundial is limited by the fact that the sun is not a point source of light but is a disk about half a degree wide. The shadow edge is fuzzy for half a degree as the sun is partially covered (penumbra shadow) and then totally covered by the umbra shadow. Size does not matter. A small dial seems to have a sharper shadow but it cannot be read as precisely. A large dial allows division into smaller units of time but the shadow is too fuzzy to read precisely. For a rod type of gnomon, the problem is even worse. It may be too narrow to completely cover the sun and produce the dark umbral shadow. There is a simple demonstration of this phenomenon that I observed one morning. Stand by a window with the sun at your back and casting your shadow on the floor. Move away from the window until the shadow of your head is about 4 inches (10 cm) from the shadow of the top of the window. Then slowly more to bring your shadow up to the window shadow. As the penumbra shadows of your head and the window start to intersect, the dark shadow will grow. The top of your head will seem to swell upward as the shadows come together. Repeat to confirm the phenomenon. This is best done in the privacy of your own home. In that twilight zone of partial shadow, a sundial cannot be precise. Half a degree is two minutes of time. But there are techniques to minimize the problem and read a dial to a precision of less than a minute. One is to use a disk or ball on the gnomon to cast the shadow. A properly sized disk will project a small dark umbral shadow at the center of the large fuzzy penumbral shadow. The Romans used this technique by topping their obelisks with spheres. Cheers from a swelled headed, nit picking, old timer, Roger Bailey Walking Shadow Designs N 51 W 115 *where triggering an avalanche is not just a figure of speech!
