Some sundials divide up the time between the hours but not this one. Sundials are made so their time is correct by the sun. This is called solar time and is a local time. Clock time is different and it can be confusing to check a sundial and clock together. It depends on the place and the time of year. In the real world it can also be assumed that the ground plane is not horizontal, but nothing changes in the reasoning: the plumb lines that descend from the time points form a sort of vertical cage of lines which do not depend on the level of the courtyard on which they end.
Their figure, like the mutual arrangement of the points Kn relating to the dates, seen in the plan view, is immutable. It is therefore sufficient to mark the ends of both the time mark and Kn plumb lines on this horizontal or inclined plane, making sure that the "mobile stylus" is always vertical [to the true earth].
The human style, even if the dial is drawn on the side of a hill, will attempt to be vertical to the true earth I therefore believe that the tracing of an Analemmatic Sundial on a courtyard, garden, or playground, even when inclined or declining, can take place in a manner similar to those construction workers who trace a new building: they operate on a hypothetical horizontal plane, then transfer their plans with vertical poles and plumb lines onto the irregular ground.
Obviously there is no interest in constructing and analemmatic dial on an unpaved surface. It is also possible to broaden the discussion: instead of considering plumb lines, as has been done here, it is possible to create similar projections with variable inclinations using variously horizontal or inclined surfaces.
The chosen inclinations are identified by their respective gnomons. The so-called "Foster - Lambert" dial is one of them. The limiting feature of this research is when the gnomon has a fixed position and is not dependent on the date: the result of course] is the "normal" sundial on any plane with a polar gnomon. But I must repeat that the gnomon or at least the gnomon point must always be in the plane of the local meridian.
The sundial consists of the gnomon and the dial plate. For a horizontal sundial like you find in your garden , the gnomon rises at an angle equal to the sundial site's latitude. But what about the hour lines on the dial plate?
They must also match the sundial's latitude. Bannekar's sundial showed how to do this graphically. Here we'll use a simple formula and allow our screen calcuator to do the work See column on the right.
The hours are minus in the morning ante meridian and positive in the afternoon post meridian. We measure HA using the meridian as the reference. At 10 AM, the sun is 2 hours before the meridian.
Since the earth rotates degrees in 24 hours, that's 15 degrees in 1 hour. To use the javascript calculator below, convert your latitude into a decimal number for entry. Example: 48 o 45' N would be entered as Your Latitude:. Sundial Mathematics. Repeat these steps every 30 minutes, each time marking the time of day at the top of your shadow. While you are waiting to trace your shadow use a pencil or pen to carefully poke a hole through the center of your paper plate.
Check the time, round up to the nearest hour, and write this number at the very edge of your plate with a crayon or marker. For example, if the clock says A. Use your ruler to draw a straight line from the number you wrote to the hole in the center of the plate. Wait until the clock reads the hour that you wrote before proceeding to the next step for example, if you started at A. Take your plate and plastic straw outside.
Put the plate on the ground and poke the straw through the hole you made. Slant the straw slightly toward the line you drew. Carefully rotate the plate so the shadow of the straw lines up with the line you drew. Do you think the shadow will stay in the same place all day?
Why or why not? Place the paperweight or stones on the very edges of the plate to hold it in place. Every hour check your sundial and the position of the shadow on your plate. If you started at 10 A. Each time you check the sundial, write the hour on the edge of the plate where the shadow falls. Why do think the shadow is moving? What does your sundial remind you of? After several hours of tracing your own shadow observe the positions of each tracing. Did your shadow move during the day?
What else changed about your shadow with each tracing? What do you think caused these changes?
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