Message text written by INTERNET:[EMAIL PROTECTED] > Since a caustic is a very different animal from an image, is there any chance of getting around the 2 minute limit on sundial accuracy due to the sun's angular diameter? <
I don't think anyone has yet come back on the specific point made by Art on use of the caustic and I was very interested in its possible use as a means to obtain greater accuracy in sundialing applications. I cannot pretend to be a mathematician - just an engineer - but it seems to me that the appeal of the cusp idea comes from: 1. The cusp of the caustic is actually formed from those rays that are nearest to and parallel to the axis. Other rays parallel to the axis but which are increasingly off-axis are directed increasingly more toward the mirror that those nearer to the axis. This is what forms the caustic. 2. Slightly divergent rays arriving at the mirror at the same point as some that are parallel to the axis will be directed nearer to the cusp that those parallel to the axis so perhaps providing an element of compensation (or focusing) for such penumbral rays. The contra-indications are: 1. In any spherical (or cylindrical) reflexions the cusp so produced is situated at a point mid way between the centre of the reflecting circle and the pole of the mirror making the whole dial twice the physical size 2. From experiment, the width of the cusp is approx 0.6mm across for a mirror of some 125mm in diameter. 3. If we consider an equatorial dial design with (say) a 125mm diam cylindrical mirror surface positioned around a circular frosted glass plate; the whole in line with the ecliptic: Radius of mirror equals 62.5mm Radius of time scale on which the cusp 'sits' is (0.5 x 62.5) = 31.25mm Arc length of semicircular time scale available to accommodate 6 hours (720 mins) is PI*31.25 = 98.17mm If we assume that one can just discern a shift of a quarter of the spot size this would permit a theoretical time precision of: 720*0.15/98.17 = 1.1mins. I suspect, though do not know, that the width of the cusp will be roughly proportional to mirror diameter so maintaining this approximate relationship. If so we shall probably not be able to use a reflected cusp to obtain a significant improvement on the precision with which we may read dial time. However, I guess we probably knew that from the 'free lunch' argument! Patrick
