Tad Dunne wrote; >I suggest a good measure is not the largest dial but the most accurate to the >naked eye. Some really big ones might fail to take the equation of time into >account. Small ones with an analemma might read to the nearest 5 minutes or >so, while larger ones with an analemma might read to less than a minute.
>A consistent way of measuring this is a) does it tell accurate local time and >b) how wide, in seconds, is the width of the gnomen's shadow. >- Tad Dunne Tad, although it is off the major point intended in my own "World's Largest Sundial," I agree with you that we might justifiably rate dials for operational performance, rather than for size. Fer deVries has already well addressed the issue of "accuracy" vs precision as as it relates to : your "a) does it tell accurate local time." That leaves your : "b) how wide, in seconds, is the width of the gnomen's shadow." Firstly, I suggest the structure of the graded transition from shadow to full illumination at the edge of the gnomon's shadow limits performance. This is a function of the about 0.5 degree apparent angular diameter of the sun, but it is significantly affected by atmospheric scattering, refraction, by contrast dillution from secondary light, by the reflective properties of the surface upon which the shadow is projected, and so forth. Let us lump all this together, and call it the angular limit of the shadow's resolution, and for this discussion's purposes, assign to it a rough value of 1/2 degree of arc. (The hour angle of the sun of course changes by this amount in 2 minutes of time, or 4 seconds time per minute arc.) Secondly, let us adopt the optician's standard accomodation near-point for the "naked eye" as 25 cm, (10 inches,) and the rule-of-thumb eye's resolution of 1 minute of arc as another limit. Finally, let me state that given the task of visually "cutting" a symmetrical image-object for measurement purposes, most observers can find the symmetry axis to better than 1 part in 60 of the object's width, and many can do so quite consistantly to 1 part in 120 as verified by experiment. (This assumes that the image-object angle is large enough for the least count interval to equal or exceed the previously invoked 1 minute visual resolution practical limit.) That suggests that we can shoot for a reading limit of roughly 1 second of time. This is not a "hard" figure, but is one resulting from the above empirical assumptions. Experience suggests that under GOOD conditions this can be met, and perhaps improved upon a bit. (The error for the nonsymmetrical readings of a single shadow edge is much greater.) Without presenting all of the intermediate steps, qualifiers, and exceptions of my argument here on the list, I believe that it can be estimated that in order to get maximal time-measurement performanance from a sundial, there is little need to make a dial larger than is capable of fitting within a cubical box, 50 cm (20 inches) on a side and that a minimum size full-performance dial will require at least a 25 cm (10 inch) box. (With a bow to Tony Moss for the prismatic form of that quantification.) Again, these estimated limits cannot be taken as exact, but are an "honest try." As an independant test of my assertions, I suggest comparison to the dimensions of historical specimens of the class of dials known as heliochronometers. Many expert designers and experienced builders, seeking highest performance, have produced instruments that fall within my estimated size limits. This in no way speaks to the many other good reasons for building larger-scale dials, but only addresses the restricted question as outlined above. May you enjoy building dials, Bill Maddux.
