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Shimming the elevation rails

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feb, 2002

The pitch, roll, and focus errors measured in
aug01 can be corrected by rotating the dome by .12 degrees in roll and
shimming a linear ramp in pitch of .125 degrees between za=10 and za=20
degrees (see
the simulation).
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How the shim distances were computed:

A beam of length 21.5 feet (the distance between the
main beams of the dome support) was moved along a radius of 420.75 feet
(the radius of the rolling surface). Let y2, y1 be the vertical positions
of the two ends of this beam (y2 is the uphill coordinate). The za is just
asin((y2-y1)/lenbeam). After shimming we will have yp2, yp1. The change
in pitch is dpitch=asin((yp2-yp1)/lenbeam)-asin((y2-y1)/lenbeam).
To compute the relative shim changes we can set y2,y1=0. So:
dp=asin((yp2-yp1)/lenbeam )--> yp2=sin(dp)*lenbeam +
yp1

The change in pitch we want for our linear ramp as a function of za
is :
pslope=.125/(20-10)
dp=(pslope*(za-10)) for za > 10.

Solving for yp2 :
yp2=sin(pslope*(za-10))*lenBeam + yp1

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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