**SIZE AND SHAPE OF MARKING SURFACE**

**The size of your marking surface will be determined by how far the shadow
moves with the change in elevation of the sun.**

**HEIGHT**

**The full angular elevation change of the sun will be 46 degrees and 54 minutes,
twice the amount that the earth's axis is tilted with respect to the plane in which the earth orbits the sun.**

**The vertical distance that the sun's shadow will move on your marking surface
will depend upon the distance between the object that causes the shadow and the marking surface.**

**If the shadow object is a roof line and the marking surface is 10 feet away
then from trigonometry:**

**The sine of an angle = height of the opposite side / the length of the hypotenuse
side.**

**For this purpose, the height of the opposite side is the length of the shadow
movement and the length of the hypotenuse is the distance from the shadowing object to the marking board.**

**From trigonometry tables we find that the sine of 46 degrees 54 minutes =
0.696 = length of shadow movement / 10**

**Or, re-arranging the equation, the shadow movement = 10 times 0.696 = 6.96
feet**

**Thus, a seven foot long marker would cover the full year, and only a one foot
marker would be required for the month period surrounding the solstice.**

**Greater shadow object heights would cause proportionately larger shadow movements,
and vice-versa.**

**WIDTH**

**The required width of the marking surface depends upon the consistency of
the time on which you make your observations.**

**The sun will move horizontally on the order of 0.25 degrees per minute.**

**From the trig tables, the sine of 0.25 degrees is 0.00873.**

**Thus, for the same ten feet distance used above, the sun dial marker will
move**

**10 times 0.00873 feet = 0.0873 feet or 1.04 inch.**

**Thus, a one inch wide strip of masking tape will provide approximately 1 minute
for you to make your elevation mark. (The change in elevation during that one minute is very small and may be ignored.)**

**However, as you approach the solstice and start to have over-lapping marks
you will need to have additional width so as to be able to make separate marks which you can then use for plotting
back to the day of the solstice.**

**Since you will not need much height at this time, a horizontal strip of masking
tape may suffice, as shown in this enlarged sketch.**