A polar sundial is a sundial where the entire sundial face is tilted relative to the ground at an angle equal to the location's latitude. The gnomon is either a solid rectangular piece, or a thin rod, parallel to the sundial face. The only thing to calculate is the distance X, from the base of the gnomon, where the shadow will fall at a given time, for a gnomon of height L.
This type of dial can only show times between about 7am and 5pm, because the hour lines at 6am and 6pm are infinitely far away. The spacing of the lines is the same for all places on Earth, the only thing that changes is the tilt of the face of the dial. So the hour line graphic below can simply be scaled to any width needed. Just be aware that at there are two 12p marks, one on each side of the gnomon, and all of the marks will need to be shifted the width of the gnomon. For the values in the table, these should be measured from the base of the gnomon (not the center).