The requested pitch change is for the center of the
beam. The halfangle of the beam is BmHangle= asin(21.5/2/420.75)=1.464
degrees. So yp1 is 1.464 degrees below the central za and yp2 is
1.464 deg above the central za. The computation starts with a vertical
offset dy(za)=0. At each za step it looks up dy(za-bmHangle) and then computes
dy(za+bmHangle) via yp2 above. These are vertical distances. The shims
are radial so the dy's must be multiplited by 1/(cos(za)) to get the shim
lengths.
The figure shows the needed
vertical offsets and shim distances.
The black line is the vertical distance, the red line line is
the radial distance or shim lengths needed. The * are the locations of
the panel points where the shims are inserted. The vertical lines
are spaced every BmHalfAngle. The discontinuites are spaced by beamlength
feet. This is where the trailing wheel starts to see the shim changes caused
by the leading wheel. The table at the bottom shows the shim length
and vertical distance for each shim position.
The pitch, roll, and focus model, as well as the shim locations use the encoder zenith angle reading as the parameter. The support beam is centered on the mechanical center of the dome. The optic axis of the system passes 1.1113 degrees uphill from the mechanical center of the dome. The black and red lines assumed that y2 and y1 were spaced equidistant from the center of the za position. In reality, y2 is 1.464 degrees uphill from the center of the beam while the za optic axis is 1.1113 degrees uphill from the center of the beam suport. The green and blue lines redo the computation recomputing y1 = (-1.464-1.1113) degrees downhill and y2=(1.464-1.1113) degrees uphill from the encoder (optical) za. The bottom most table has the shim values for this computation.
processing: idl/prf/shimcmp.pro
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