Can any Maths expert explain how to make a sun dial?

Question

MATHS PRACTICAL SUN DIAL.

Answer 1

Try here hun, or do your own search asking "How to make a sundial" and choose which explains better.

http://liftoff.msfc.nasa.gov/Academy/Earth/Sundial/Sundial-ConstructSimple.html


Good Luck! :)

Answer 2

Many ornamental sundials are designed to be used at 45 degrees north. By tilting such a sundial, it may be installed so that it will keep time. However, some mass-produced garden sundials are inaccurate because of poor design and cannot be corrected. A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base so that its style or gnomon is parallel to the Earth's axis of rotation, so that it points at the north celestial pole in the northern hemisphere, or the south celestial pole in the southern hemisphere.


Horizontal sundial in Taganrog (1833)A local standard time zone is nominally 15 degrees wide, but may be modified to follow geographic and political boundaries. A sundial can be rotated around its style or gnomon (which must remain pointed at the celestial pole) to adjust to the local time zone. In most cases, a rotation in the range of 7.5 degrees east to 23 degrees west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time, a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter.

Ordinary sundials do not correct apparent solar time to clock time. There is a 15 minute variation through the year, known as the equation of time, because the Earth's orbit is slightly elliptical and its axis is tilted relative to the plane of its orbit. A quality sundial will include a permanently-mounted table or graph giving this correction for at least each month of the year. Some more complex sundials have curved hour-lines, curved gnomons or other arrangements to directly display the clock time.

Answer 3

I believe you need a triangular thing (forgive technical terms) whose angle from the horizontal is the same as your latitude. Aim it true North. Notice that this means there are no sun dials at the equator, at least not the sort we are used to. I suppose you could make one using shadow length. Ask some South American Indian, they have probably been doing that for centuries.

Answer 4

1.an equatorial sundial

For this project, you will need:
a piece of card slightly wider than the protractor and say 25cm (10 in.) long
a drinking straw or knitting needle
a protractor

Draw lines across the card dividing the length into sections of 1, 10, 14, and 1 cm. (The length of 14 is alright for latitudes of 50 deg. or more, but if you live at a lower latitude, you will need to make this length longer) We'll call these lines A, B,and C. Mark the centre point O of line A, and the centre point P of line C. Draw a line OP connecting the two centre points.
Place the centre of the protractor on O and draw round it. Make a pin hole through O, turn the card over, and place the centre of the protractor on the pin hole. Draw round the protractor again so you have two semicircles back to back
Mark 15 degree intervals and number the hours as shown, on both semi-circles.
Score and fold the card along the lines A, B, and C
Enlarge the pin hole at O and push the straw through. Make sure the straw is at 90 deg. to the card around O.
Move the bottom end of the straw along the line OP until the angle it makes with the horizontal is the same as the latitude of the place where you are (this is about 30 deg. for Perth and for New Orleans, 45 deg for Bordeaux and for Minneapolis, 51.5 deg. for London, and 55 deg for Edinburgh)
You may find it easier to calculate the correct angle, and mark off the correct length along the straw. The correct length is 10 x (cotangent of the latitude). In the examples above, the correct lengths would be 17.3 cm. for Perth or for New Orleans, 10 cm for Bordeaux and for Minneapolis, 8 cm for London, and 6.9 cm for Edinburgh

When you've found the correct location for the bottom end of the straw, bend up a tab as shown in the diagram, or put a pin through from the other side to hold the straw in the right place
The straw forms the gnomon. The shadow of the gnomon will fall on the hour lines on the top of the dial in summer, and on the underside in winter.
You can colour your dial and write a motto such as "AIM HIGHER THAN THE MARK" underneath.

You now have a working equatorial sundial. The dial plate, with the 15 degree angles marked on it, is parallel to the equator, and the straw forming the gnomon is parallel to the earth's axis. The sun appears to revolve round the earth's axis at 360 deg. every day, which is 15 deg. every hour (which is why you marked out your hour lines at 15 deg. intervals)

You can also see from your model how a horizontal sundial is constructed. Wait till the shadow is exactly on one of your hour lines, and mark a line where the shadow of the base of your straw falls on the horizontal piece of your card, and mark the hour alongside.

When you have marked out a number of lines in this way, you will see that the angles are not a regular 15 deg. on the horizontal surface. You will also see that the shadow line along the "equator" surface meets the shadow line along the horizontal surface, along the line of the fold B. The hour lines on the horizontal surface are, in fact, the projection, on the horizontal surface, of the 15 deg. lines on the equatorial surface. This forms the basis of the graphical method of determining the hour lines for horizontal sundials, which of course are different for each latitude.

2.a horizontal sundial

To Construct a Horizontal Sundial
The first step is to mark out the hour angles. A base line with a centrally rising perpendicular gives the noon, 6am and 6pm lines

Various methods exist for generating the remaining hour angles, we will use the computational method. The formula for calculating the angles quoted in many works on the subject is:

log tan D = log tan t + log sin Ø

and was used in this form to save the need for long multiplication of fractions. However in these days of pocket calculators we can use the more straightforward:

tan D = (tan t)(sin Ø)

In both these formula D is the angle which the hour line makes with the noon line, t is the is the time measured from noon in degrees and minutes of arc [the earth completes the 360° round the sun in 24 hours so 1 hour = 15° and 1 minute = 15' of arc], and Ø is the latitude of the place where the dial is to be positioned. Each angle calculated for times before noon also gives the angle for the equivalent times after noon
It's best to draw up a table:


time t tan t sin Ø tan D D
9.30 (2.30) 37°30' 0.7673 0.7749 0.5945 30.73°

I have put in one set of figures assuming a latitude of 50°48' (Ø = 50.8). Of course this is an obvious spreadsheet application. Having plotted all the hour angles required, normally hours and half hours, the shadow casting component, known as a gnomon or style, can be fitted along the noon line as shown below. The angle or height of the style is equal to the latitude of the dial location.

It is a good idea to draw the whole thing out on a large sheet of paper fixed to a board and make a style out of thin card. This will check the design before committing it to a more permanent medium. The sundial should be positioned where it will be in the sun for the maximum length of time with the dial plate perfectly level and with the noon line pointing directly north.


Apart from the above there are various methods to make sun dial

another horizontal sundial ( + link to the original French) copiously illustrated
a diptych dial
an equiangular dial
a Capuchin sundial ( + link to the original Swedish) + many illustrations

Answer 5

you gotta know the longitude and latitude of the sundial's location...