Ram Yantra
The above is a view from the North, of the twin cylindrical Ram Yantra masonry instruments, at the Delhi Jantar Mantar. In the foreground of the picture, half of the hemispherical bowls of the twin Jayaprakas instruments can be seen.
Ram Yantra seems to be constructed precisely to make it very easy for any one to make local co-ordinate measurements of objects in the sky. Each of the cylindrical instruments consists of a circular wall and a gnomon at the center. The height of the walls and the gnomon, has been designed to be exactly equal to the inside radius of the building measured from the outer circumference of the thick gnomon - that is, the height of the gnomon is exactly equal to the length of the floor of the instrument measured from the outer circumference of the gnomon to the inner circumference of the wall.
The walls and floor are graduated for reading Azimuth and Altitude angles. An inside view of the Ram Yantra is shown below -
What is needed is to observe the shadow of the gnomon - determine its centre and mark it on the floor or the walls of the instrument - wherever it falls.
The floor is divided into thirty sectors and thirty gaps of the same dimensions as the sectors. Each of the sectors are thus spanning 6 degrees of Azimuth and they are further sub-divided into 6 degree markings. Thus angles of 1 degree each can just be read of from the Azimuth markings - finer graduations seem to be missing from the Delhi instrument, in its present condition, but, temporary calibrations for finer accuracy can always be achived using tape measure placed parallel to Azimuth circles.
The gaps are for facilitating the movement of observers to read the markings and hence, the complimentary instrument is designed in such a way that, the shadow falls on a sector of one of the instruments, if it falls in the gap for the other instrument.
The walls of the instrument are also graduated similar to the floor - each of the markings representing one degree in Azimuth and one degree in Altitude.
It is the Altitude markings in tangents of scale, that form the beautiful simplicity of usage of this instrument. When the shadow falls at the top of the wall of the instrument - the Altitude of Sun being zero - 45 markings on the wall giving rise to an altitude of 45 degrees for the Sun, if the shadow falls at the junction of the walls and the floor and another 45 degrees inward from the wall towards the circumference of the Gnomon - so that, altitudes between 45 to 90 degrees can be read off on the floor of the instrument. Finer graduations than a degree are marked on some of the sectors - where missing - one needs to remember that the scale is not linear any more (unlike for the Azimuth) and thus more accurate Altitude measurements (where fine graduations are missing) could be inferred by measuring accurately, the length of the shadow and knowing that the height of the gnomon is equal to the length of the floor sector.
Tan (Altitude) = Gnomon Length / Shadow Length
It is interesting to think of the accuracies possible with this instrument - a first time observer, initially fels rather disheartened due to the uncertainities in estimating the center of the Gnomon Shadow, the blurring between the Umbra and the Penumbra and so on. But, simply because the instrument is built on such a massive scale - the errors induced by these uncertainities are minimal and wonderful accuracies (for educational purposes) can be achieved with this instrument.
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