To determine offset of the perceived shadow edge, I built a simple device consisting of a cardboard test pattern, a white cardboard screen, and a stick to separate them about 36". The test pattern was two parallel strips each exactly 1" wide with a 1" gap between them. Over a three month period or so, at different times of day, I would point this at the sun and measure the widths of the shadows and the gap I observed on the white cardboard screen with a dial caliper. The shadows of the 1" strips each averaged about 0.72" wide and the shadow gap between the strips averaged about 1.28" wide (at a distance of 36" away from the test pattern) giving an angular displacement of arcsine(0.28"/2/36") = 0.222° for each edge. For some real excitement, for my test pattern I could have used two parallel strips 1.28" wide with a 0.78" gap between them, and it would have cast two 1.00" wide shadows 1.00" apart!
Hi Pete,
Thanks for the information about your method of measuring the offset of the shadow edge from the center of the Sun's image. I tried out a modification of your method this weekend at a polar, equatorial sundial at the Heritage Plantation in Sandwich, MA. This dial has a 1.00 inch diameter style, and a scale radius of 19.0 inches. The geometrical width of the style's shadow would be 1.00 inch, or an angle of arcsine (1.00/19.0) = 3.017 degrees, or in units of time: (3.017 deg)x(4 min/deg) = 12.07 min = 12 min 4.1 sec.
I measured the offset of the shadow edge in two ways. First, I simply observed that the shadow covered 11.25 minutes on the sundial's scale. Thus difference in the geometric shadow's width and the perceived shadow's width is approximately (12m:4s) - (11m:15s) = 49 sec. Half of this is due to one edge and half to the other, therefore the shadow edge was displaced about 25 sec of time from the center of the Sun's image. This was very simple but not too precise because of the difficulty of reading the width of the shadow in minutes on the dial's scale. (Each minute of time covered only 2 mm on the scale)
A second way to measure the offset was to measure the time, with a stopwatch, for the shadow to pass a given mark on the dial. This procedure is potentially capable of much greater precision than the first. A time interval of some 720 seconds is capable of much greater precision of measurement than the measurement of a space interval of some 25 mm. I measured the time for the shadow to pass over a given mark (from front shadow edge to back shadow edge) to be 10m:52 s. Here the difference in the shadow's geometric width and perceived width was (12m:7s)-(10m:53s) = 74 sec. This includes of offsets at both edges of the shadow, so that the offset at one edge would be 37 sec. This figure is in better agreement with your measurement and with my earlier measurements. However, I found it very difficult to determine just when the shadow had passed the mark. My estimate of last week was based on the shadow of a 20 foot high roof as compared with the shadow of a style 18 inches above a scale. Improvements in this method lie in using either a much larger instrument or using a more precise method of locating the edge of the shadow. Here, I think the "disappearance of the shadow of a thread held parallel to the edge of the shadow," as used at the Great Dial at Jaipur, may be the answer. I am thinking about how to mount such a thread on the dial that I have been using.
Happy dialing,
Bill Walton
Plymouth, MA, USA
42 N 71 W
