The
Sundial Primer created by Carl Sabanski 
Cylinder Sundial Cylinder Sundial: (also known as a shepherd's dial or pillar dial): a portable, altitude dial in which hour lines for different dates are delineated around the surface of a cylinder, which is allowed to stand or hang vertically. A horizontal gnomon projects radially from the top of the cylinder, and is adjusted to the appropriate date around its periphery. Sometimes two gnomons are supplied; a long one for winter and a short one for summer. The dial is held with the gnomon facing the sun so that the shadow falls vertically. Latitude specific. Altitude Sundial: (or elevation dial): any dial which uses the sun's altitude, rather than its azimuth, for indicating the time. Usually does not need to be aligned NS. Examples are ring dials, flag dials and shepherds' dials. Altitude dials were often incorporated in quadrants and folding rules. Altitude (of the sun) (a, ALT): the angular distance of the centre of the sun's disk above the observer's horizon (negative numbers indicate that the sun is below the horizon). It is measured along the principal plane to the sun's centre, and is the complement of the zenith distance. It is part of the horizontal coordinate system. This was a widely used portable dial as it was easy to make and inexpensive. The shepherd's dial indicates the time by the sun's altitude, which depends on the latitude and the time of year. The dial must be designed for a particular latitude and is adjustable for the date. Figure 1 illustrates the dial. The hour lines appear as curved lines on the cylinder amongst the vertical date lines. The gnomon is a horizontal pin mounted at the top and can be rotated so that it aligns with a particular day of the year. The date scale is inscribed below the movable gnomon. Once the gnomon is aligned with the appropriate date, the dial is held facing the sun and turned until the shadow is parallel to the vertical date lines. The time can then be read.
Figure 1: Cylinder Sundial (SONNE/CAD) A chart of the hour lines can be drawn on paper and attached to a cylinder or they may placed directly on the cylinder's surface. As the chart is to be attached around the cylinder, its width should be equal to or slightly larger than the circumference of the cylinder. The height of the chart is related to the length of the gnomon and is determined by the longest shadow that will be cast by the gnomon. As shown in Figure 1 this will occur at the summer solstice when the sun's altitude is at its maximum. The height of the chart "H" is determined as follows: H= G tan (90  ø +23.44) = G tan (113.44  ø) where ø is latitude of the location where the sundial will be used and G is the length of the gnomon. Knowing the dimensions of the chart, the width can be divided into 12 vertical bands that represent the 12 months. Additional lines can be added to further divide the months into smaller periods. The position of the hour lines can now be determined. First the sun's altitude "a" must be determined for a given hour (Local Apparent Time) of a particular day. The distance "D" of the hour line from the top of the chart is determined as follows: D= G tan a where G is the length of the gnomon. Figure 2 illustrates the layout of the hour lines for a cylinder sundial. As this dial indicates local apparent time (LAT), the hour lines are symmetrical about noon. The calculations need only be done for the morning hour lines as the afternoon hour lines are the same. This is because the sun's altitude is the same for equivalent time periods before and after noon (LAT), e.g. 8 am and 4 pm.
Figure 2: Cylinder Sundial Hour Lines  Local Apparent Time (SONNE/CAD) From this figure it can be seen that the dial is least accurate during the winter and around noon as the hour lines are very close together. It is also possible to correct the hour lines for longitude as is illustrated in Figure 3. This is the same dial as in Figure 2 but it indicates zonal solar time. Because of the longitude correction each time will have a unique hour line.
Figure 3: Cylinder Sundial Hour Lines  Zonal Solar Time (SONNE/CAD) As all the days on the year are represented on a cylinder sundial, it is also possible to apply the correction for the Equation of Time to the hour lines. For clarity, Figure 4 illustrates this for only the full hours. The hour lines have been corrected for both longitude and the Equation of Time and the sundial now indicates clock time.
Figure 4: Cylinder Sundial Hour Lines  Clock Time (SONNE2.1/CAD) Usually a cylinder sundial is constructed to be a portable dial and is relatively small. Here is an idea for a large scale sundial. This would work well in a childrens' playground. If you considered building a carousel the cylinder sundial would form the central rotating hub of the carousel. The seats would be mounted at the bottom of the cylinder. The sundial could be painted in the upper portion of the cylinder. The pointer is mounted at the top of the cylinder with the date scale below it. The pointer would have to rotate on its own to line up with the appropriate date as well as with the cylinder to allow alignment with the sun. This would be a very unique playground structure. And the kids would always be home on time.
