Intro:

• The x,y,z coordinate system for the reflector has:
• x (positive East)
• y (positive North)
• z (positive up)
  
• The center of curvature of the sphere defines the center of the coordinate system. The radius is 870 ft.
  
• Often time z0 is translated to the point x=0,y=0 point on the dish (close to ao9).
  
• The suspension cables:
• The main cables run north-south.
• They are spaced every 25 feet in x (east-west) (x+ is eastward).
  
• The smaller  cables
• run east- west
• are spaced every 3 (or 3.25) feet
• They are attached to the  main cables at each 25 foot crossing
• The 3 x 6 foot panels lay with the long direction in the east-west direction.
• there are 4 panels between each main cable.
• The N/S and E/W cables are laid out on an x/y  grid.
• The panel connection points to the cables are on this east west grid.

Terminology

• Panel spacing: this is the  distance in the x,y plane between the panel connection points.
• Panel length: This is the  actual length of the panel.
• to  compute the length:
• Let R0 be the radius of the sphere (870 feet).
  
• get the x,locations of the panel edges (x0,x1)
  
• using the arcsin(x0/R0), arcsin(x1/r0) measure the angle  dTh between the edges
• the length is then dTh*R0
• It is similar when measuring the y length.

The 2002 primary survey was used to measure the panel spacing and size.

• The survey measured optical reflectors on the the NW corner of each panel
  

Measuring the panel spacing:

    The survey x,y locations of each panel corner was used.

The first plot shows the panel spacing in the E/W direction (6.25') (.pdf)

• Page 1 : plot all differences > 5 feet
• sort the data in x, subtract adjacent points, and then ignore points < 5 feet
• Top :the difference  is plotted vs the X (E/W) distance from the center of the dish
• the average value is 6.256ft
  
• there are a number of outliers around x=0
  
• Bottom:The difference is plotted vs the Y (N/S) distance from the center of the dish.
• The outliers are now appearing at  |y| > 450 ft
• Page 2: plots the x,y locations for  all points with difference < 6 ft
  
• The N/S edges around x=0 have shorter distances as well as the points along the northern edge.
• Page 3: The spacing computed using the median value for each N/S line of panels
• I stepped through the x dimension 6.25 feet at a time.
• Every 4 steps this would sit atop a main cable.
  
• the median was computed for all points within 6.25/2 feet of the position and was used for the xoffset.
• The dashed green lines are the positions of the N/S main cables (every 25 feet).
  
• You can see a pattern that repeats every 25 feet.
• The panel size plots (below) show that this comes from using 4 fixed length panels between each main cable.

The 2nd plot shows the panel spacing in the N/S direction (3') (.pdf)

• Page 1: Plot all spacing
• Top: panel spacing vs X (E/W) distance from center.
• There are two sets centered around 3.25 and 3.0 ft
• Bottom:; panel spacing vs Y (N/S) distance from center.
• -290 < y < 295 has a spacing of 3.25 feet
• outside this area has a spacing of 3.0 feet
• Page 2: Spacing  computed from the median of each E/W panel set
• The processing is similar to the the N/S processing.
• The median value along each e/w cable was used to compute the difference.
• There is no obvious pattern in the distance.

processing: x101/p50/panels/panelspacing.pro

Measuring the panel lengths.

    The survey x,y locations were used to compute the length of the panels. The length measures the arclength of the panel on the sphere.

For the long direction (E/W) , the median location of each N/S panel column was used to compute the panel location and  length
For the short direction (N/S), the median location of each E/W panel set was used to compute the panel location and length.
The length was compute by:

• take the x or y locations of the panel corners
• compute the arcsin relative to the center of curvature for each edge
• compute the angular difference of the 2 edges
• compute the length as the arclength of this dTheta

The plots show the panel lengths (.ps) (.pdf)

• Page 1: short (N/S) panel lengths
• Top length vs Y offset from center of dish
• The + are computed from the median position of each e/w row of panels
• the red line is computed using a fixed length of 3.0 and 3.25 feet
• Bottom: blowup of panel lengths -300 to 300 feet
• looking at the + , there may be a grouping of panels with similar length.
• Page2: long (E/W) panel lengths
• Top: the measured panel spacing is replotted to show the spacing pattern between main cables.
• Bottom: The panel lengths vs x offset from center of dish.
• the + use the measured median value of each n/s set of panels
• the red line assumes a fixed 6.25 foot spacing between the panels.
• The jaggedness in the  E/W spacing is caused by using a FIXED length panel between each main cable.

Summary

• Long east/west panel direction
• panels are located about every 6.25 feet on the x,y grid
• There is a jaggedness in this location because fixed length panels are used between each main cable.
• The actual panel lengths vary from 6.25  to 7.4 feet.
• Short north south panel direction.
• The panel spacing in the  x,y plane is
• 3.25 for -290 < y < 295 feet
• 3.0  for y< -290  or y > 295
• The  panel length varies from 3.2 to 3.6 feet.
• There may be a grouping of panel lengths in the y direction, but it is not as obvious as the long direction grouping.
• Note the panel spacing/length for panels  > 490 feet from the center were not included (looks like things changed a bit at the very edge.
  

 home_~phil