# Motions and angles

#### aug17

in the focal plane
how big can ao40 be
pointing errors.

# In the focal plane:

• Plate scales:
• from german's alfa memo page 37 (atoms 2001-03.pdf)
• x axis  in za direction. Positive is away from secondary
• y axis  perpendicular to az arm. Positive it toward the stairwell
• z axis in along focus. Positive is pointing toward

 az,za vs focal plane motions moving horn uphill same as moving dome uphill moving horn ccw (toward stairwell) increases turret angle same as moving azimuth CCW (to a lower azimuth angle) plate scales x<0 46.79 asecs/inch         18.42 asecs/cm x along za direction positive pointing downhill x>0 42.21 asecs/inch        16.62 asecs/cm y 37.08 asecs/inch    14.60 asecs/cm y perpendicular to az arm positive pointing toward stairwell turret motion increasing turret angle moves horn from focus  toward the stairwell (+y direction). same as moving azimuth CCW (to lower angle) moving turret 1 deg: =1.276 inches = 3.241 cm =47.3 asecs on sky = 45 asecs on sky (from measurements) (1)*!dtor*73.125=1.276 inches 1.276*37.08secs/in=47.3 asecs on sky 45 asecsSky/degTur comes from measurements on sky. horn position ft in cm 70.48 179.02 radius for center of horn mount (on the floor). Assumes feed tower position relative to the 2ndary did not changes after kevlar cable installation (2004). 69.41 176.30 radius for center of horn on floor (alfa/ao40) germans 1.07" offset 8.11 degrees horn angle relative to floor perpendicular, tilted so horn is closer to secondary. 18.75 47.63 vertical distance top of floor to horn phase center. 73.151 184.34 radius center of floor to horn phase center 70.48 + 18.75*tan(8.11) inches 70.611 179.35 scribe mark on rotary floor. motion of coma lobe moving horn uphill (away from optical axis) creates coma lobe in - za direction in spider scan, shows up in -za offset. moving horn CCW (away from optical axis, increasing turret degree) causes coma lobe in + azimuth direction of beam map (see alfa beam maps) turret floor from gregorian upgrade drawings page s-42. More recent measurements show slightly different values... ft in cm 8'  7.75" 103.75 263.53 radius of rotary floor 50deg 40deg pi sections on the floor they alternate 50deg,40deg 4'  6.5" 54.4 138.47 diameter 50 deg wedge opening 6'  4.75" 76.75 195.00 radius center of 50 deg wedge opening (radiusFloor - 1/2 opening diameter) 3' 6" 30 106.71 diameter 40 deg wedge opening

Notes:
• be a little suspicious of the 73.125 inches radius for the horn focal point. This assumes the feed tower was not changed at all when kevlar cables installed. Better to look at where the coma lobes show up.

# Trying to figure out how big ao40 can be:

Assumptions:

• radius of floor 263.53 cm
• radius of c channel around lower  edge of floor 2.26"= 5.74cm
• Radius to use when lowering ao40 through the floor (to clear the c channel): 263.53- 5.74=257.8 cm
•  radius for center of horn mount on the floor:
• single pixel: 70.48" (179.02 cm)
• alfa/ao40:  69.41" (176.30 cm)  This includes  german's 2.72 cm offset (inward on the radius).
• Assumptions:
• the opening diameter goes from the edge of the floor to the cross beam of the pi wedge without hitting the pi wedge Ibeams..
• Use 257.8 cm for the floor radius (so you don't hit the c channel around the inner edge of the floor).

 Diameter of Hole Opening cm Radius on floor @center of opening cm Radius on floor for Focus mount cm Opening Center to floor Focus mount cm useable Diameter cm Source of opening diameter 138.47 188.6 std 179.02 9.55  radially in 119.37 upgrade drawing with  -2.72cm offset 176.30 12.27 radially in 113.93 142.0 186.8 std 179.02 7.78 radially in 126.44 ao40 report with -2.72cm offset 176.30 10.5  radially in 121.0

We tried checking these numbers by measuring the wedge holding alfa, relative to the edge of the rotary floor
The image shows the measurement  results:

If we assume that the alfa focal radius is at the center of the wedge (either the top or the bottom of the wedge) then we can
compute what the radius for the center of alfa on the floor should be. (more info) This will check if the floor radius, focal radius used above are correct.
I just subtracted the center of the wedge from the floor radius to get the mount location on the floor.
For these computations use 264.23 cm for the floor radius since the above measurements were made from the top of the floor (the c channel was not in the way).

 flrRad cm Floor Radius @ wedge Center cm Floor Radius for focus mount alfa Wedge Center to german's offset focus on floor notes normal with German's 2.72 cm downhill offset 264.23 176.26 179.02 176.30 .04 cm radially out assume bottom of wedge centered 264.23 177.92 179.02 176.30 1.1 cm radially in assume top of wedge centered and 8.17 deg tilt moves 1.65 cm radially out

So using the bottom of the alfa wedge as the center, we get the canonical  horn floor focal radius fir multibeam feeds.

## AO40Summary

• Using the bottom center of the alfa wedge as the floor radius to position alfa and assuming:
• the floor radius : 264.23 cm
• We get:
• 179.02 cm floor radius for single pixel focus.
• 176.30 cm floor radius for multi beam (alfa,ao40) focus
• Forcing ao40 to be centered at one of the focii gives a useable opening diameter of :
•    opening diameter cm allowable diameter using singlePixFocus cm allowable diameter using multiBmFocus cm 138.47 119.37 113.93 142.0 126.44 121.0
We should probably see how many cm there is between the edge of alfa and the constraining beams.

When installing ao40, it will be lowered through the floor, and then tilted by 8.11 degrees. This let s the inner part of ao40 pass underneath the inner cross beam of the floor pi wedge support.

# pointing errors

• model values get added to the computed az,za
• pointing errors from cross scans should be subtracted from az,za used
• pointing errors from turret scans should be added to the az,za used.
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