January 2010

THE POLAR SUNDIAL

Building a sun clock

Among the early sundial expressed in this blog are the Equatorial dial clock, the dial Vertical and Horizontal dial. This time we will deal with a sundial sundial which is parallel to the axis of the world, ie the dial and the gnomon are in parallel, which does not occasionally happen with the previous cases.

clock dial in the Equatorial, the sundial is perpendicular to the axis of Nomon and the gnomon is parallel to the axis of the world. In the sundial Polar dial, the dial is parallel to Nomon Solar and both the axis of the world, which makes him a particular case.

Having developed the complicated Azimuth sundial, the Polar watch dial with the clock dial with the Equator are the simplest to make and to calculate.

To understand a little how this Polar watch will support us in Figure 1, which are represented a sundial and a Quadrant Quadrant Equatorial Polar. If the line "NS" represents the axis of rotation of the Earth, in the case of Equatorial watch his Nomon (red stem) should be aligned with this axis to be functional, solar rays generate the shadow (blue line) of the gnomon on the dial according to the angle between the Sun and the vertical. To the extent that the sun rotates around the axis, so does the shadow of the gnomon about copying the movement of the sun, 15 degrees for each hour spent. Being the sun right in the vertical, is 12 pm.

FIGURE 1

If we put a plane parallel to the axis "NS", we are called Polar Quadrant, in this case also the gnomon parallel to the axis must be rectangular, with the top edge that defines the projection of the shadow of this Nomon and therefore time. Similarly, (Figure 1) whether the sun revolves around the axis "NS", the shadow of the gnomon rectangular copy the movement of the sun projected on the plane but with the difference that although the Sun moves regularly as can accuse the Equatorial Dial Watch, at the "Polar" divisions for the hours are not evenly distributed, but are defined by the interception of the hour lines Quadrant clock Equatorial plane "Polar". Solar noon, the shadow of the gnomon is rectangular just below it.

Polar Clock that will dial in this release has the dimensions of 200 mm wide by 310 mm long, with the purpose to develop within the space that allows a sheet of legal size or 216 mm x 330 mm.

In this case the gnomon is rectangular so that the upper edge is parallel to the sundial and is made with measures 40 mm high by 161 mm long. This Nomon we will in cardboard 2 mm thick as the entire quadrant sundial Polar.

To determine the separation of the divisions corresponding to the hours and half hours on the sundial have to settle for an hour and half hour following trigonometric formula:

L = AG x Tan (h).

Where:

L = Distance where is the line showing the time "h" from the line representing at noon and it matches the location of the gnomon on the dial.

AG = The height of the gnomon, which in our case is 40 mm.

Tan (h) = the tangent of the angle taken hours after noon, 11 am and 1 pm corresponds to an hour angle of 15 ° from the vertical (noon) to 9:30 AM and 2:30 PM 37.5 ° corresponds to 10 AM and 2 PM will correspond with the vertical 30 °, etc.

Figure 2 displays the origin of the trigonometric equation to determine the length of the shadow "L" that is where the line will be indicative of the time based on the height "AG" the gnomon and hour angle "h".

FIGURE 2

This sundial, the hour angles are distributed from the gnomon 15 º every hour, but because the shadow of the gnomon is projected onto a plane parallel to it, the lines time plotted on the sundial are not uniformly distributed as shown in Figure 3, which represents the template, and quadrant developed Solar Polar.

FIGURE 3 Note that the separation between the lines indicating the time are not equally spaced, so that the distance between time and time grows as the display away from the central line is at 12 PM. Looking at the centerline of hours under the midday sun will note that this is twofold, the reason is to compensate for the thickness of Nomon made cardboard 2 mm thick, hence, the distance between line and line 12 PM is 2 mm. Right there is the gnomon and tear from these other lines.

Figure 4 shows the template of the gnomon rectangular and quadrant media.

FIGURE 4

on the gnomon no further comments therefore it is very simple its dimensions depend on the clock that we, in this case is a rectangle 40 x 161 x 2 mm as already mentioned. The bases or supports for the dial are designed as a truncated triangle, the slope of the oblique angle is the latitude of the place where he will watch, in my case, this angle is 8.27 º. In the same way as the gnomon, these supports be made from cardboard 2 mm thick, form does not necessarily have to be shown in the template, but the slope of the baseline has to be compulsorily angle the latitude. What you are looking for is that by placing the sundial on the ground, this is parallel to the axis of the poles, we see that the dial and the gnomon are inclined to place them on the floor and directing the highest clock Pole North, but do not forget that the plane of the quadrant and the upper edge of our Nomon are parallel to the axis of rotation of the Earth. Figure 5 shows the final appearance of your clock once assembled and figure we can notice mentioned above.

The bases are placed so that the high side is to the north and sought to achieve the parallelism.

FIGURE 5

We used three media and not two at each end to ensure that the sundial will not deform under its own weight, if the stiffness is sufficient, we employ only two supports equidistant. To avoid the effect of "foot", these bases must be perfectly aligned with each other.

The photograph below shows the sundial template attached to the cardboard base of 2 mm thick.