How would I figure out the positions of the hour markings and month markings for
this sundial without paying $499?
... Ah, perhaps
this: building an analemmatic sundial. I'm finding it a little hard to follow, but I think I have it.
- Draw the N-S and E-W axes.
- Draw the circle, any desired radius a.
- Draw the angle phi, which equals your latitude.
- Draw the third side of a right triangle where two of the sides are the E-W segment OW, and the line you've just drawn at angle phi from OW. Now you have lengths c and b. (You figure out where to draw the third side by moving a right angle along the c line until the perpendicular line intersects the origin O. You could also construct a line perpendicular to the c line that intersects O.)
- Mark distance b from O north along the N-S line. This is where the ellipse will intersect the N-S line; call it N.
-
- Measure distance c along the E-W line, starting from O, in both directions, to find the foci F and F' of the ellipse.
- Draw the ellipse with string length F-N-F', or F-W-F'. (Should be equal.)
- Mark 15-degree marks on the circle. Project them directly south to the ellipse for the hour markings.
- Mark the adjustments for the gnomon/person/analemma as shown in the diagram below, where the angles are measured from the focus F.
This doesn't comletely incorporate in the equation of time corrections into the central analemma as done in the southern hemisphere sundial pictured
here. It is missing E-W deviations from the N-S line of the analemma.