A vertical sundial is a dial that is placed on a wall. It is therefore vertical to the ground. There are two types of vertical dials; the direct vertical (these dials are upon surfaces that face a cardinal direction, which is to say they face true north, south, east or west) and the declining vertical dial (these dials DO NOT face a true compass point).
These directions are for a vertical declining dial.
NOTE: This is one of the HARDEST dials to create, if you are not familar with sundial "language" please read ALL my related pages before trying this.
Before we can start there are a few things we need to know. What is the latitude of the place where the dial is to be used and what is the declination of the wall on which the dial is to be placed?
The diagram below shows the four possible directions that a wall can decline. The lines P are perpendicular to the face of the wall, the lines M lie along the meridan the angles D are the declination of the wall and North is as shown.
The four possible directions of declination are: Southwest, Southeast, Northwest and Northeast.
We must now determine the amount that the wall declines. Take care when finding this angle since all other values rely upon its accuracy.
In the diagram below AB represents the side of the wall where we wish to place a dial. A board 1234 is placed horizontally against the wall (AB) and leveled. Find the meridian line NS. Draw the line EW parallel to AB bisecting the line NS at D. From the point D draw the line DC perpendicular to the line EW. The angle CDS is the declination of the wall.
The above diagram shows a wall the faces south and declines east.
To complete a vertical dial we will need to determine three items. The first is the sub-style distance (SD). This is the line along which the gnomon will lie (perpendicular to the dial face). Recall that on a horizontal dial the sub-style line is the same as the 12:00 (noon) line. This is not the case in a vertical dial.
The second item is the style height (SH). This is the angle that the gnomon makes with the face of the dial. Recall that in a horizontal dial the style height is equal to the latitude of the place where the horizontal dial is to be used.
The final item is the positions of the hour lines.
Draw AB as a horizontal line. At C draw the line CD perpendicular to line AB. Now draw a semi-circle centered at C to form the semi-circle ADB.
Draw line CG so that the angle DCG is equal to the colatitude of the place where the dial is to be used. The colatitude is equal to 90 (degrees) minus the latitude (in degrees). If the latitude is 40 degrees then the colatitude is 50 degrees. From G draw line GH such that it is parallel to AB, crossing line CD at H.
NOTE: If the dial declines toward the West the angle DCG will lie to the right of line CD, if the dial declines to the East the angle DCG will lie to the left of line CD. In this example we are using a declination to the East.
On the side of CD opposite the line CG draw the line CJ such that the angle DCJ equals the angle of the dial's declination. To find the point K lay off on the line CJ (from C) a distance equal to GH (use the compass). Draw line KL from the point K that is parallel to line AB and intersects line CD at L.
On line HG lay off line HM so that line HM is equal to line KL. Draw a line from C through M and tangent to the semi-circle. Label this point N.
This completes the first step! The angle DCN is the sub-style distance (SD).
Draw line KP such that it is parallel to line CD and intersects line AB at point P. Find point R on the semi-circle such that the line MR is equal to the line KP (use the compass). Draw a line from point C to point R.
This completes the second step! The angle NCR is the style height distance (SH).
The final step is to determine the positions of the hour lines. Let us use a new diagram, using only the line from the preceding diagram(s) which are necessary to the hour line construction. We need the lines AB, CD, CN and CR from the above diagrams.
At some point along the line CN pick a point M and draw the line ST such that it is perpendicular to line CN. The distance of CM will determine the scale of the final diagram (so make it as large as your paper will allow).
Draw line ME such that is perpendicular to line CR. Find the point O along the line CN such that the line ME is equal to the line MO (use the compass).
With point O as the center draw a circle of any radius. Label the intersection of line CD and line ST point d. Draw a line from point O to point d.
Starting at line Od divide the circle into 15 degree sections, draw lines from O that intersect line ST using these 15 degree marks on the circle centered at O.
Draw lines from the 15 degree intersections along line ST to the point C. These are the hour lines of the vertical sundial.
Now attach the dial to the wall it was calculated for, remember to make sure that the 12:00 line (noon) is vertical (Perpendicular to the ground).
NOTE: If the wall declines to the NORTH then the dial is placed such that the hour line radiate UPWARDS (in the diagrams above the hour lines radiate downward [a southern dial]). Also, in a NORTH dial the 12:00 line is no longer Noon but Midnight. It is not usual to place dials on Northern walls since they receive little sunshine.