Unit 6 : Equatorial Sundials : Variations : Horizontal and Vertical Sundials : Tech Notes : Unit Questionniare

# Horizontal and Vertical Sundials

Horizontal and Vertical Sundials

Many people like to have a sundial that is horizontal (in the garden or on a deck) or vertical (on a south-facing wall).  This is a little more complicated to construct, because the projection of the shadow of a gnomon on a horizontal or vertical surface does not move 15 degrees per hour but sometimes more and sometimes less.

A common variety of sundial uses the position of the shadow of the edge of a gnomon aligned with the North / South Celestial Pole to tell time (not pointing to your local zenith straight up).  This makes the sundial more accurate than one with a vertical gnomon.

To construct a horizontal sundial for use with such a gnomon at a given latitude, the most simple method is as follows:

Step 1

Draw a circle of radius 1 unit.  This unit can be one inch, one foot, one meter, 1 decimeter (= 10 cm) or whatever unit is most convenient for you to work with.  This circle will be your sundial face.

Step 2

For a horizontal dial, draw a second circle tangent to the first one (tangent means touching at one point, in this case) and with a radius that is sin(latitude) units. (The sine of the latitude, sin(latitude), is a number less than or equal to 1, so the second circle will always be smaller than the first.  The radius of the smaller circle is sin(latitude) units.

Click on the following link to open a  page of sine latitude calculations.  Click here.

Using the table linked above, sin(42 degrees) is 0.669 which is very close to the fraction 2/3.  Therefore, if you chose your large circle to be three inches in radius or diameter your smaller circle will be about two inches in radius or diameter.

Why sin(latitude)?  What we are doing is projecting the sunlight through an imaginary equatorial dial and on down to the ground.  Trig then tells us that the lengths on the ground are related to the lengths on the equatorial dial by this factor sin(latitude).

The angle A is equal to the local latitude.  Therefore, by trig properties of triangles ("Sin(angle) = opposite over hypotenuse"), Sin(A) = Y / X

Step 3

Draw a line connecting the centers of the two circles.  This is the noon line.

Step 4

Draw a dividing line perpendicular to the noon line through the point where the two circles touch.

Step 5

Continue drawing lines on the SMALLER circle to divide this into 15 degree sections.  This is the same as you did on the dial face for the equatorial dial in the previous subunit.

Step 6

Extend the lines on half of this circle to the dividing line drawn in Step 4 above.

Step 7

From the intersection of these lines and the dividing line, draw new lines to the center of the larger circle.  These lines will be the hour lines on your sundial.  The geometry behind this construction is illustrated for latitude 42 degrees north in the diagram linked in the box to the right.

Step 8

Finally, add your gnomon.  It must have one edge pointing to the North Celestial Pole. This edge will cast the shadow that you will use to tell time.  Beyond that, the design of the gnomon is part of the artistic side of designing a sundial.

The following images illustrate how to mount the gnomon for a horizontal sundial.

Click here to open a one page example of the geometry you are working out in these steps. Remember that this diagram has been worked out specifically for Lat 42 degrees N.  When you are finished viewing the diagram, click Back on your browser to return to this page.

For a vertical sundial, follow the same procedure as outlined above, but make the smaller circle's radius equal to cos(latitude).  Again, you can click here to use the sine and cosine table.