At 07:29 PM 3/1/00 +0100, Alain MORY wrote: >Hi, all diallists ! >> >I'm asked to realise a vertical sundial on a circular tower. I don't >know exactly (it's a truism !) how to proceed. >This sundial will probably be built on stone, but we can't curve the >stone. Then I think that it will be possible to realise like a multiface >dial. >What does the sundial list think about such a challenge ? >Completely crazy or just a half ? > Bonjour Alain,
Your question is a good challenge. The answer is not easy. There is a good example of this type of dial in the town of Anduze in southern France (Gard). The "Cadrans Solaires Francais Catalogues" describes the setting as a "tour de l'horloge". The cylindrical tower now has a clock and a sundial but its original purpose was a watch tower or barbican, a remnant of the fortifications around the old town. The dial demonstrates some of the features of a dial laid out on a cylinder. As Dan Wenger mentioned, it is useful for only a few hours as the cylindrical plane of projection curves away from the gnomon. The Anduze dial is essentially a noon mark, showing hour marks for only one hour on either side of noon. It has declination lines with zodiac marks so it shows the seasons well. It also shows that the hour lines are curves on the cylindrical surface. The curvature increases with the time from noon as the shadow moves around the cylinder. A simple model will demonstrate these effects. Stick a pin in a paper tube at an angle equal to your co-latitude. Hold it in the sun and rotate it to show different time angles. You will find that the shadow of the gnomon pin is curved and the dial is only useful for about two hours before and after noon. My suggestion to calculate the hour lines is to treat the cylinder like a polygon with a series of flat vertical faces. Calculate the lines for each face the usual way as a series of vertical declining dials. Lay out the design for each facet and draw a smooth curve through the mid points for each face to approximate the hour angles. I am sure there are more elegant solutions but the mathematics is beyond me. Your challenge remains. The alternative but practical way to lay out the dial is to do it on site. Install the gnomon, facing south at a slope to the vertical equal to your co-latitude. At local noon the shadow will be vertical. For each time increment from noon, mark the shadow of the gnomon on the cylinder surface for each hour line. This may take some time as a cloud will pass just as the time gets critical. Roger Bailey Walking Shadow Designs N 51 W 115
