

Step 2:
Modeling slew times (continued)
Modeling slew time data
You should now have obtained data files containing tables of measured telescope slew times
in right ascension and declination. If your telescope is housed in an automated dome, you
would also have a data file containing a table of measured dome slew times in azimuth.
Here we will assume that the right ascension, declination, and dome slew time data have
been saved to files RA.txt, Dec.txt,
and Az.txt, respectively, and that these files are located in
directory TAO\regress.
Below we describe the analysis of right ascension slew time data. The analysis of declination
and azimuth slew times is completely analogous.
If you plot the data contained in RA.txt,
you should obtain a welldefined
relationship between angular displacement and slew time, as in the following sample plot
(where three independent slew time measurements are shown for each angular displacement
in right ascension; such a sample of measurements might be obtained by running script
SlewTime three times in succession):


A relationship of this kind can be modeled in a simple and accurate way by a piecewise
linear function, that is, a function which is linear in each of a series of intervals
of the independent variable (angular displacement). The above plot shows that the relationship
is essentially linear for angular displacements greater than 20 deg. In order to compute the
parameters of a straight line which fits the data for displacements greater than 20 deg, one
may use the leastsquares program regress, which
is located in the TAO\regress
directory. To use this program:
 Use a text editor to prepare a text file containing only those lines of
RA.txt whose right ascension displacement is greater than or
equal to 20 deg. For the data shown in the above plot,
this file would contain these lines:
22.8557 37.9
45.7114 60.1
137.3921 139.4
22.8557 39.4
45.7114 57.7
137.3921 135.8
22.8557 38.7
45.7114 55.1
137.3921 135.0

 Save this text file with a different name, e.g., TAO\regress\RA_1.txt.
 Open a DOS window (Command Prompt), cd to the
TAO\regress directory, and type the command
C:TAO\regress\>regress RA_1.txt

After the program executes, the regression results will have been written to file
TAO\regress\RA_1_output.txt. In our example this file would
contain the following results:
Regression results:
y = A + B * x
A = 1.87675E+01
B = 8.58086E01
Coeff. of determination: R^2 = 9.98446E01
Standard error of B: 1.27958E02

The high value of R^{2} (close to unity)
indicates that a good fit has been obtained (as
expected from the plot), and that for angular displacements greater than 20 deg, slew
time in right ascension (T, in seconds) is well approximated by the linear equation
T = 18.768 + 0.8581 x dRA,
where dRA is the angular displacement in right ascension (in degrees). For angular displacements
smaller than 20 deg, this relationship becomes inaccurate, so we examine more closely
the lower left corner of the above plot:


We now see that the relationship is again aproximately linear for angular displacements
between 1 and 20 deg, so we use regress again to fit another straight line to the
corresponding data points:
T = 8.227 + 1.4541 x dRA.
Inspecting the lower left corner of the above plot,


we see that for angular displacements smaller than 1 deg the data do not fit very well
to a straight line, since the errors in the measurements of slew time become significant
when compared to the slew times themselves. In any case, we use regress
to fit a last straight line:
T = 3.893 + 6.36 x dRA.
After finishing the modeling of the telescope slew times in right ascension, the
telescope slew times in
declination and (if applicable) dome slew times in azimuth should be modeled in an
analogous way.
Previous: Obtaining slew time data
Next: Preparing files containing slew time models
© 19992004 Paulo Holvorcem

