I was showing one of my daughters some of the research resources on-line at our local county library system. Pulled up Britannica, and entered Sundial (of course.) There were a number of useful articles, and I followed through to an article on laying-out a dial. The author chose a geometric layout method, to make a horizontal dial for Chicago, IL. So far, so good. I followed the details, and played with it a bit, before realizing there was what looked like a glaring error. Or is it me??
======================================================== Gnomon Construction Sundial construction depends upon principles of constructive, or gnomonic, geometry. A horizontal dial designed for Chicago's latitude radiates as a 42 deg ellipse. For this example we use a 42 deg ellipse to determine the hour lines' radiation on a horizontal dial at 42 deg latitude. To construct such an ellipse, we need concern ourselves only with the relative lengths of the ellipse's major and minor axes. Since we require only the radials and not the ellipse's perimeter, exact size is unnecessary. One way to constructively deduce these lengths is by drawing a gnomonic triangle for the selected latitude (Fig. 2). Construct right triangle ABC such that < ABC equals the desired ellipse for a given latitude, in this case, 42 deg. Where (X) represents the dial face ellipse's minor axis, (X) is used to determine the length of a 42 deg ellipse's major axis. Those with a trigonometry background and a scientific calculator can also use the formula (1/sin 42) to derive the exact proportions. Dial Plate Construction The gnomonic triangle holds all the information you need to draw a sundial plate and its hour lines by the elliptical coordinate method. See Fig. 3. 1. Using the data from the previous gnomon example, draw two concentric circles such that the inner circle has a radius of 1 and the outer circle has a radius 1.3426. =========================================================== Since I don't live at Chicago's latitude, I naturally went to compute the ratio I would need here, in not-so-northern California. That's when I discovered that 1/sin(42) is more like 1.49+, and asin(1/1.3426) = 48.1. Did the author just screw up, or am I missing something? Dave 37.28N 121.97W -
