Verticle Gnomon Sundial Plotter

If you place a stick vertically in the ground and watch the shadow of the stick, the stick is called a gnomon. The location of the tip of the shadow of the gnomon falling on a horizontal plane will depend upon the time of day, the time of year, and the latitude and longitude of the gnomon.

Instructions: Click on the "Draw" button below this paragraph to get a graphic showing some sweeping curves. (This JAVA applet will draw curves which will represent the paths the tip of the shadow takes for a simple verticle gnomon sundial.)

You can enter your own longitude and latitude to get the custom sundial for your exact location and click "draw" again.

If one traces the tip of the shadow of a gnomon every hour of the day for selected days of the year one gets a set of curves (on the horizontal plane) resembling the green curves shown in the graphic above. The graphics is a view from above. The gnomon is at the center of the red circle. The height of the gnomon is just equal to the radius of the red circle. North is to the top of the graphic, west to the left, etc.

Pick one of the green curves. The shadow tip starts in the morning at the western edge of the graphics; as the day progresses the tip follows the green curve and near sunset the tip is near the eastern edge of the graphic on that same green curve.

The green curve which is overall farthest south represents the path for June 21. Just north of that are two curves, one is for July 21; just north again are two more, one is August 21, then one of the next pair is September 20, then one of the next pair is October 21, and one of the next pair is November 21. The curve farthest north is December 21. Moving back toward the south (taking one of each pair encountered) we have January 20, February 20, March 21, April 21, May 21 and again June 21. See the figure below.

The lazy eight black and blue curves are called analemma. Each represents the position of the shadow tip at a particular time of day for various days of the year. The analemma which runs most nearly north and south represents locations of the tip at noon. The next one to the east represents locations of the tip at 1 p.m.; farther east are 2 p.m., 3. p.m. etc. The analemma to the west of the noon analemma represent 11 a.m., 10 a.m. etc. as shown in the labeled figure below.

The point where a green curve (indicating a particular date) crosses an analemma (representing a particular time of day) is the point of the tip of the shadow for that date and time. (The black side of the analemma represents dates from December 21 to June 21 and the blue side represents dates from June 21 to December 21.)

Thus for example the point P on the figure below represents the shadow tip on about February 20 at 10 a.m. The shadow would extend from the center of the red circle (representing the base of the analemma) out to point P. You can interpolate between the green curves for dates between the green curve values, and you can interpolate between the analemma for times of day between the hourly values

Click photo to get larger view of a paperclip sundial. It shows about 9:00 a.m. on January 25.

Bend your paperclip carefully so the height is equal to the radius of the red circle and fix it to your plot with tape.

On the control panel above enter the latitude and longitude of your favorite location using negative numbers for southern latitudes and positive numbers for northern latitudes. Enter longitudes expressed between -180 and +180. Hit the "Draw" button to get the graphic for that location. (We don't do locations beyond the arctic circles. Sorry.) Print it on your printer. Make a gnomon which is as high as the radius of the circle. Paste it pointing straight up at the center of your circle on your copy. (I find a bent paperclip and some clear tape gets a pretty good gnomon; spend a little time getting it straight up and the correct length.) Find some sun. Orient the diagram so the line running north south through the circle points North at your location. The tip of the shadow should point at the time of day and date! Just that easy. (Or alternately if you do not know where north is, but you do know the time and date, orient the printed graphic with gnomon attached so that the shadow tip hits the correct time and date. The lines through the circle now point to the cardinal compass points. Be sure to get the correct side of the analemma curves for the particular date.)

This page prepared by C.Hartley, Director of the Ernest B. Wright Observatory at the Department of Physics at Hartwick College in the City of Oneonta, NY. More things from C. Hartley at his home.