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Masonary Errors of the Ram YantraThe project started with winter solstice 2009 activities at the Jantar Mantar, which also included discussions and observations using the Ram Yantra, which is a very user friendly instrument for easy measurement of the Altitude and Azimuth of the Sun in daytime. The instrument can also measure the altitude and azimuth of stars and planets at night time, but, more about that, later.  Method used for measuring Altitude and Azimuth of the Sun, using the Ram Yantra at the Delhi Jantar Mantar Observatory Altitude and Azimuth Observations taken by Megha Rajoria and Biplab Dutta Ram Yantra are twin cylindrical instruments for measuring Altitude and Azimuth of celestial objects. In this project we are measuring the altitude and azimuth of Sun during the day time in a time span of almost 5 - 6 hours. The measurement of both altitude and azimuth is done simply by chasing the shadow of the gnomon on the wall and on the strokes of the instrument. The wall, radius of the stroke and the gnomon are of same distance and all three of them have calibrations of degrees on them so that the altitude and azimuth can be read. The image below is showing the shadow on the wall, from where we can read the calibrations for altitude and azimuth tangent to the curve of the shadow.  The shadow moves up and down on the walls and on the strokes at different angles of altitude and azimuth at different times of the day. MEASUREMENTS DONE ON 22nd DEC'09 The Sun was bright on this day with very little clouds. We managed to take almost 30 readings in the Northern Instrument for both Altitude and azimuth of sun, of which the graphs have been plotted below. We found while taking the data that the instrument is in a really bad condition at lot of places where there are no calibration marks of the degrees for altitude. In this case we measured the distance of the wall from the bottom and took that distance to the wall with better calibrations in order to convert the distance in degrees, which definately give rise to errors. (Data to be entered)
The theoretical values were obtained for the corresponding times of observation, from the NASA Horizons Solar System Dynamics ephemerides at: Some graphical representations of the data collected Sun Altitude versus time of observation  Sun Azimuth versus time of observation  Feedback Is the polynomial fit to the observed points? Might do a polynomial fit separately to the observed points and to the theoretical values, and see how close they are in the fitted parameters. Theoretical derivation of the change in Sun altitude as a function of time - you will find it when people talk of Altitude sundials - would be a good idea. There are some outrider data points (very obviously deviant) - remove these points and fir again and then check between the observed and theoretical values. In both the figures above, plot the observed values as discrete data points and the theoretical values as a continous line. The plot should then have - obs Alt or Az vs time and also theoretical Alt and Azm vs time in the same graph. Do not keep the labels as A and B and so on. Make the labels to be the actual quantities plotted - Altitude, Azimuth, Time and so on. Sun Altitude - Theoretical versus Observed  Sun Azimuth - Theoretical versus Observed  Feedback In both the figures above, plot a simple Y=X line to see how the points are scattered around that. Plots of errors in altitude and azimuth as a function of measured lengths to the shadow and the corresponding masonary parameters - like errors in gnomon height, inclination, zero azimuth point and the sector widths for azimuth measurement - should give a handle on these intrinsic errors of the instrument. Starting with the equations defining the Altitude and Azimuth and differentiating these equations, should lead one the the useful equations for these plots. MEASUREMENTS DONE ON 23rd Feb'10 We took around 60 readings on this day in both the cylinders between 10:30hrs to 17:30hrs. The movement of the shadow this time was more on the strokes than on the wall. We also observed that there is a calibration error in the southern cylinder in the azimuth reading of 6 degrees. Later in the evening the trees around and the buildings also stopped the sun ray to make the shadow. We observed overall, that there are lots of calibration error in the instrument which are possibly there because of the bad restoration of the instrument. Acknowledgements (To be written) Useful Reerences |