Customized Horizontal Sundial

I wanted a sundial for the garden that would tell the approximate time at my latitude, 41.67 degrees north of the equator. I found some basic instructions and the mathematics to calculate the layout of the dial at sundials.co.uk/projects. I'm going to 3D print my sundial, but it could also be built from metal, wood, or cardboard.

A 3D printer, if available, or

an 12 inch x 12 inch (320 mm x 320 mm) sheet of metal or wood

glue, paint, and markers

a ruler

a protractor for measuring angles

a magnetic compass or smart phone with compass app

I started with a circle 7.5 inches (190 mm) diameter. The lines and numbers that mark the hours need to be located based on your latitude, P, in degrees. First, calculate the sine of P. In my case, at 41.67 degrees north, sine (P) = 0.665. As the earth revolves, the sun's position changes by 15 degrees each hour. A gnomon, the pointer on the sundial, will cast a shadow on the face of the dial, but the position of the lines and numbers is calculated using tan(D) = tan (t) * sin (P) where

D = angle from 12 o'clock position, in degrees

t = time difference in hours from 12 noon times 15 degrees

time from noon, hrs ------t, earth degrees-------- tan D --- angle D

6 -------------------------------------90----------------------1.085E+16---90

5 -------------------------------------75-----------------------2.481---------68

4 -------------------------------------60-----------------------1.152---------49

3 -------------------------------------45-----------------------0.665---------33.6

2 -------------------------------------30-----------------------0.384---------21

1 -------------------------------------15-----------------------0.178---------10.1

So, from the center of my circle, I laid out lines about 2.5 inches long at the angles listed above to the left and right of the 12 o'clock position. In the northern hemisphere, we start at the 6 a.m. position to the left of the center, numbering the hours to noon and then 1 to 6 p.m. to the right side. In the southern hemisphere, 6 a.m. is to the right, 6 p.m. to the left.

To create the gnomon, make a right triangle with the angle at the bottom the same as your latitude, 41.67 degrees in my case. The base leg of the triangle is about 2.5 inches. Place the tip of the triangle at the center of the circle with opposite leg at the 12 o'clock noon position. Attach the gnomon to the circle. If you 3D print the sundial, the gnomon can be part of the solid. You can also add words of inspiration.

I attached an .STL file of my sundial which I printed on an Ender 3 printer. It took about 8 hours to print. If you live within + or - about 5 degrees of latitude, that is, 36 to 47 degrees north, the design is close enough to give good results.

The sundial can be placed on the ground or mounted on a post. The circular disk must be level. Turn the disk so that the gnomon points to true north. A compass will point to magnetic north but a correction must be made for the location of the north magnetic pole. Search online for a map of magnetic declination to find the correction for your location. In my case, a compass will point about 14 degrees west of true north, so I need to adjust the position of the sundial to compensate. If you have a smart phone with a compass app, it may show you where true north is. When the position of the sundial is correct, sighting along the angle of the gnomon should point directly at the North Star.

On sunny days, the gnomon will cast a shadow on the sundial showing the approximate time. However, the indicated time may be 5-30 minutes off from the time your computer or smart phone says. This is because the actual length of a day changes as the earth makes its elliptical orbit around the sun. Also, the sundial doesn't adjust for daylight time.

My sundial says it's almost 4:00 pm, time for a cup of tea!