Declining vertical sundial calculator

ANY CALCULATOR DECLINING VERTICAL SUNDIAL CALCULATOR

Before you start carving one out of a solid block of marble, please test it out on a cardboard version first!

All the information on this page applies to sundial design for the northern hemisphere. If you live in the southern hemisphere you will have to take account of the fact that the sun is north at noon, not south..

A book reference is "Sundials Their Theory and Construction" by Albert E.Waugh. It contains lots of information on the design and setting up of various types of sundial.

Sundials are not accurate at all times of the year due to the effects of the equation of time, the error can be in excess of 16 minutes.
It is however possible to design a sundial that should be accurate to within around 2 minutes throughout the year. This has traditionally taken the form of the noon dial called the Analemma.
If the shadow cast by the tip of the gnomon, 'A' in the diagram, and cast on the dial face at 'F' was marked on the face on the hour by clock time for each day of the year, it would be seen to have made a distorted figure of eight shape.
The position of point 'F' can be calculated for any day of the year by finding what the equation of time and declination of the sun is. Horizontal distance 'FG' and vertical distance 'CG' give the co-ordinates for the point.
The equation of time is quoted in minutes. As each hour is entered in this calculator as multiples of 15 degrees, the equation of time in minutes (et) need dividing by 4 (60/15) to convert it to degrees, and adding to or subtracting from the hour, which would be 0 ą et, 15 ą et, 30 ą et etc.
Things to be aware of...the appropriate wall angle is required for a noon Analemma (hour angle = 0) depending on whether point 'F' is plotted on the east or west face of the dial, and deciding when the equation of time is to be added or subtracted from the hour angle depends not only whether 'et' is fast or slow on clock time, but also whether the hour angle is on the east or west face of the dial..
Longitude correction should also be included.

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Quick start:-
To calculate the shadow angles for a direct south facing wall dial fill in the boxes in the blue panel as follows.
Latitude:- Your latitude in decimal degrees, eg for New York enter 40.71
Wall angle:- Enter 90
Length BC:- Enter 1
Declination:- Enter 0
Hour angle:- Hour angle in decimal degrees. One hour =15 for 11am and 1pm shadow angle, 30 for 10am and 2pm shadow angle etc.
The Calculated shadow angle appears in the yellow panel after clicking the calculate button.

LATITUDE...
In the US your angle of latitude can be found Here. The angle needs converting from degrees, minutes and seconds to decimal degrees, eg 52° 30' would become 52.5

WALL ANGLE...
For a dial mounted on a south facing wall the Wall angle is 90. This is the angle the side of the gnomon makes with the wall, (line AB). The gnomon points south along line AB. So if the wall is declined 30 degrees towards the west, the wall angle on the west face of the dial is 120°, and on the east face 60°, (the two angles always add up to 180°).
Except when the angle is 90, run calculations for both wall angles. Note that when calculating for shadow angles with the dial west face, the resultant marking out of the west face will be for the morning sun as it comes up from the east.

LENGTH BC...
This is the vertical length of the gnomon where it joins the wall.

DECLINATION...
The range is 23.44 for the sun's highest point in the summer, to -23.44 for the mid winter sun. The equinoxes have a declination of 0. On the dial, the lines of declination across the dial face are tracked by the shadow from the end of the gnomon, point `A', this shows as the tip of the shadow at point `F'.

HOUR ANGLE...
One hour is represented by 15 degrees, (360/24). Multiples of 15 up to 90 represent the range of hours on one side of the the dial. West face and east face being calculated separately except when the wall angle is 90. Any fractions of angles can be calculated.

GNOMON...
The geometery of the gnomon is shown as lengths 'AB' 'AD' 'BD' and 'CD'. And angles 'ACD ' and 'BCD'.
Length 'AC' represents the shadow casting style of the gnomon. Length 'AB' projects from the dial pointing south. A gnomon can be made as triangle 'BAC' or 'DAC'.

SHADOW...
The shadow angle, is measured from vertical line 'CG' and radiates from point 'C'
The length of the shadow, as measured from point 'C' to point 'F' (shadow length CF) is affected by the declination for a given wall and hour angle. Distance 'FG' and 'CG' can be used as an alternative way of finding point 'F'.

LONGITUDE...
Longitude correction can be added to the hour angle.

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