I use two sheets of graph paper, which are each 8.5”x11”. I make sure the paper has the grid centered on the hole for the gnomon. You’ll need to use some clear tape to get the graph paper attached to the plate. Then, create a coordinate system using the center of the gnomon hole as the origin (Lx=0, Ly=0).
Figure 11 Graph paper placed on Masonite board with axes (Lx and Ly) set up.
Figure 12 Detail of the coordinate grid on the plate using the graph paper.
The next step is to set up the compass itself. It’s easiest to use a protractor to create the disk of the compass. Depending on your latitude, you’ll have to think about where the shadow will be projected. In the Northern Hemisphere, north of the Tropic of Cancer, the sun will always transit to the south of the local observer, so the shadow at its shortest length will point to true north. The calculations in the spread sheet assume that the center (Lx=0) will be at the local noon. So, taking Lx=0 and drawing a line to the away from the gnomon hole will point to true north. By using the protractor, the compass points can be laid out, with 0o being due north, and 180o being due south.
Figure 13 Laying out the compass disk on the sum compass.
Figure 14 Completed compass disk.
The next step is to lay out the hyperbola. The coordinates listed in red on the spreadsheet should give a series of points that can be labeled with time. A detail of this is shown below for my example on June 14th.
Figure 15 Laying out the hyperbolic trace using the points in the spread sheet (Lx and Ly coordinates) labeled with times.
Once all the points for the hyperbolic trace has been put on the graph paper, they can be connected using a straight-edge. Although there’s some curvature, approximating the curve with a straight line between each pair of points gives a good enough trace.
Figure 16 By connecting the dots of the trace, a full hyperbola can be created.
Figure 17 Detail of the trace around the local noon on the sun compass.
3.) Using the sun compass
Depending on the day of the year, the hyperbolic trace should be good for a number of days around the time it was made for. Even when latitude changes, and the date changes a fair amount, a decent compass can be used by adjusting the height of the gnomon.
Make sure the gnomon is level. Usually this just means that you have a flat surface to use. If you want to go one step further, you can find a set of levels in a hardware store, and use these to level out the plate.
Rotate the plate until the tip of the shadow touches the hyperbolic trace. If you labeled the points with the time, you can also get an estimate of time. This alignment is shown below for 8:45 AM.
Figure 18 Alignment of sun compass for 8:45 AM on June 14th.
Figure 19 Alignment of sun compass at 10:45 on June 14th.
Figure 20 Alignment of the sun compass at 11:45 AM on June 14th.
Figure 21 Alignment of compass at 12:30 on 14 June.
Figure 22 Alignment of compass at 13:00 on 14 June.
you've posted an awesome article, loved it
ReplyDelete