New Trigger Tower Coordinates                                   6-NOV-1990
-----------------------------

    There was a problem with the routine that generates the Trigger Tower
geometry (ACTUAL_GEOMETRY by Sylvain Tisserant). It was obtaining
coordinates from a file ('D0$STP:CALTOWER_STP.DAT'), which did not contain
the correct tower coordinates. This file was intended to only be used for
testing the Calorimeter-coordinate software. The file containing the true
geometry of the Calorimeter is 'D0$STP:CAL_STPFILE.DAT'.

    There are two major differences between the coordinates in these two files.
First, There is a region in the Calorimeter at ETA +/-7, where only 2 plates,
rather than 4 plates, are summed to create the EM tower. The test version of
the coordinates had incorrect data on which plates existed.

    The other major difference between the coordinates in these two files is
the coordinates given for the endcap regions of the Calorimeter (|ETA| > 7).
There is a difference ranging from 2% to 7% over these coordinates.

    The table below shows the % errors in Z by eta (it is constant over PHI):

EM TOWER         |EM TOWER         | HD TOWER       | HD TOWER
ETA    % Error   |ETA    % Error   | ETA  % Error   | ETA  % Error
-----------------+-----------------+----------------+---------------
-1     0.0000000 | 1     0.0000000 | -1   0.0000000 | 1   0.0000000
-2     0.0000000 | 2     0.0000000 | -2   0.0000000 | 2   0.0000000
-3     0.0000000 | 3     0.0000000 | -3   0.0000000 | 3   0.0000000
-4     0.0000000 | 4     0.0000000 | -4   0.0000000 | 4   0.0000000
-5     0.0000000 | 5     0.0000000 | -5  -0.0662423 | 5  -0.0662423
-6    -0.0446248 | 6    -0.0446248 | -6   0.3150651 | 6   0.3150651
-7    -0.5253955 | 7    50.15616   | -7   0.4256613 | 7   0.4256613
-8    -0.1118753 | 8    -0.1118753 | -8   0.4682124 | 8   0.4682124
-9    -0.1119349 | 9    -0.1119349 | -9   2.204729  | 9   2.204729
-10   -0.1120455 | 10   -0.1120455 | -10  3.680666  | 10  3.680666
-11   -0.1121561 | 11   -0.1122158 | -11  3.680517  | 11  3.680517
-12   -0.1117647 | 12   -0.1117647 | -12  3.680711  | 12  3.680711
-13   -0.1118240 | 13   -0.1118240 | -13  3.680472  | 13  3.680472
-14   -0.1123777 | 14   -0.1123777 | -14  3.680173  | 14  3.680173
-15   -0.1119349 | 15   -0.1119349 | -15  3.680420  | 15  3.680420
-16   -0.1118751 | 16   -0.1118751 | -16  3.681547  | 16  3.681547
-17   -0.1122672 | 17   -0.1122672 | -17  3.681107  | 17  3.681107
-18   -0.1116024 | 18   -0.1116024 | -18  3.678807  | 18  3.678807
-19   -0.0859189 | 19   -0.0859189 | -19  3.681839  | 19  3.681839
                 |                 | -20  3.897319  | 20  3.897319


    The table below shows the % errors in R by eta



EM TOWER         |EM TOWER
ETA    % Error   |ETA    % Error
-----------------+---------------
-1     0.1134087 | 1   0.1134254
-2     0.1183566 | 2   0.1183733
-3     0.1199087 | 3   0.1199253
-4     0.1196583 | 4   0.1196834
-5     0.1200422 | 5   0.1200338
-6     0.1125827 | 6   0.1125994
-7    10.35351   | 7   4.102435
-8    -5.762737  | 8   0.0456931
-9     0.0040321 | 9   0.0403212
-10    0.0376269 | 10  0.0376269
-11    0.0357592 | 11  0.0357335
-12    0.0348372 | 12  0.0348372
-13   -5.762737  | 13  0.0336376
-14   -2.366645  | 14 -2.366645
-15   -2.358949  | 15 -2.358902
-16   -2.354545  | 16 -2.354545
-17   -4.786382  | 17 -4.786382
-18   -5.850428  | 18 -5.850428
-19   -5.762737  | 19 -5.762737
                 |

    The Z coordinate is completely identical over PHI. The R coordinate is
almost identical over PHI for channel EM. The largest deviation between smallest
and largest value for a particular ETA over all PHI is less than 1.0E-4%.

    The actual angle given for each PHI coordinate is almost exactly:
        (2*(PHI-1) + 1)  * 360.0/32.0  degrees
(within 0.3%). In the incorrect tower coordinates, this is the value exactly.

    Also of interest is the amount of error in the quantity SIN(THETA). The
table below shows the % error in SIN(THETA) for different values of ETA.


EM TOWER

ETA = -19...-1, 1...19
 -5.671288      -5.725695      -4.653492      -2.226730      -2.221971
 -2.215748      0.1417447      0.1409612      0.1394102      0.1369735
 0.1333055      0.1291496       8.599196      0.098592237    0.061709657
 0.043845270    0.025691753    0.010077676    0.0011262090

 0.0011262090   0.010077676    0.025691753    0.043845270    0.061709657
 0.098582461    -22.78804      0.1291496      0.1333055      0.1369836
 0.1394658      0.1409612      0.1417447      -2.215748      -2.221971
 -2.226730      -4.653492      -5.725695      -5.671288


HD TOWER

ETA = -20...-1, 1...20
  3.267769       1.405378      0.3839497      1.1390125E-02 -0.4688259
-0.4639536     -0.4620837     -0.4563295     -0.4467643     -0.4331616
-0.4127594     -0.4407308     -6.7770816E-02 -7.0942469E-02  -1.724064
  1.500855      0.3514096      0.2051506      8.1402436E-02  9.2252428E-03

 9.2252428E-03  8.1402436E-02  0.2051506      0.3514096       1.500890
 -1.724064     -7.0942469E-02 -6.7770816E-02 -0.4407308     -0.4127594
-0.4331616     -0.4467643     -0.4563295     -0.4620505     -0.4639536
-0.4688259      1.1390125E-02  0.3839497       1.405378       3.267769


    The errors are fairly small for the central calorimeter towers. This is
important, because at the time of this writing the resistors used in the ADC
scaling have already been ordered.