BIG BANG DESIGN NOTES
6/22/05

Size and shape:

  Equatorial diameter 172" (14' 4")
  Aspect ratio 0.8 -> height is 137.6"

Central sphere: 

  28" diameter

Mapping of radius (from center of sphere) to cosmic expansion factor:

  86" (7 ft 2 in) = present day
  Every 7.2" in = universe a factor of 2 smaller
  14" (radius of central sphere) corresponds to 1/a = 2^10 = 1024, close to
    size of universe at last scattering
  50" (inner edge of zone 1 clusters) corresponds to 1/a = 2^{36/7.2} = 32,
    roughly appearance of first stars and galaxies

Zones and rod distribution:

  Rods are categorized into four zones based on length 
     (radius = length + rsphere)

  Zone 1: 36"-45" (radius 50"-59"), redshift z=31 to z=12.5 
          first light
  Zone 2: 45"-54" (radius 59"-68"), redshift z=12.5 to z=4.65 
          end of the dark ages
  Zone 3: 54"-63" (radius 68"-77"), redshift z=4.65 to z=1.38 
          buildup of galaxies, quasar era
  Zone 4: 63"-72" (radius 77"-86"), redshift z=1.38 to z=0 
          settling down, growth of clusters

  On average, 40% of cluster rods are zones 1 and 2; 60% are zones 3 and 4
  Lengths are evenly distributed within each of these two categories.
  Lengths are rounded to the nearest 2".
  Rods of exactly 54" are counted as zone 3.

Lamps (quasars):
  
  75 total
  3 wattages: faint, medium, bright
  15 Zone 1, all faint
  15 Zone 2, half faint, half medium
  30 Zone 3, half medium, half bright
  15 Zone 4, half faint, half medium

Conflict resolution:

  Lamp and cluster rod holes are required to be at least 3.875" from the
  cable connection at the "north pole" of the sphere.  

  The following minimum center-to-center separations are enforced for 
  all pairs of holes on the sphere:
    any cluster rod to zone 2-4 cluster rod 	1.54 inches
    cluster rod to zone 1 cluster rod		1.35 inches
    lamp rod to lamp rod             		1.35 inches
    lamp rod to zone 1 cluster rod   		1.35 inches
    lamp rod to zone 2-4 cluster rod 		1.54 inches

  Clusters are separated by at least 1.04 times the sum of their radii.

  The perpendicular distance between a rod and any cluster on a shorter
  rod is at least 1.04 times the cluster radius.
  
Galaxies:

  Type 1 galaxies are disks, type 2 galaxies are spheres
  Spherical galaxy diameters are 1.5", 2.0", 2.5"
  Disk galaxy diameters are 1.75", 2.25", 2.75"

Clusters:

  Cluster spheres are 1.125" diameter for zones 1/2, 1.625" for zones 3/4
  All galaxy attachment rod lengths are rounded to nearest 0.5"

  Zone 1 clusters: 
    1-3 galaxies
    all size 1
    all disks
    spherically distributed
    rmin = 3 in
    rmax = 6 in

  Zone 2 clusters:
    3-5 galaxies
    all size 1
    all disks
    spherically distributed
    rmin = 3 in 
    rmax = 6 in

  Zone 3 clusters:

    5-8 galaxies

    5/6 clusters are
      spherically distributed
      rmin = 3 in
      rmax = 5 in
      1/2 size 1, 1/2 size 2
      all disks

    7/8 clusters have two-component structure
      core:
	4 galaxies
	spherically distributed
	rmin = 3 in 
	rmax = 5 in
	1/3 size 1, 1/3 size 2, 1/3 size 3
	size 1 are all spheres
	size 2 are all disks
	size 3 are 1/2 spheres, 1/2 disks
      filament:  
	remaining galaxies
	anisotropically distributed
	xmin,ymin = 2 in
	xmax,ymax = 4 in
	zmin = 4 in
	zmax = 7 in
	1/2 size 1, 1/2 size 2
	all disks

  Zone 4 clusters:

    8/9 clusters are 1-component
	anisotropically distributed
	xmin,ymin = 2 in
	xmax,ymax = 4 in
	zmin = 4 in
	zmax = 9 in
	1/4 size 1, 1/2 size 2, 1/4 size 3
	size 1 are all disks
	size 2 and 3 are 3/4 disks, 1/4 spheres

    10-15 clusters have two-component structure
      core:
	1/2 of galaxies in cluster (rounded down)
	spherically distributed
	rmin = 3 in 
	rmax = 5 in
	1/4 size 1, 1/4 size 2, 1/2 size 3
	size 1 are all spheres
	size 2 are 1/2 spheres, 1/2 disks
	size 3 are 3/4 spheres, 1/4 disks
      filament:  
	remaining galaxies
	anisotropically distributed
	xmin,ymin = 2 in
	xmax,ymax = 4 in
	zmin = 4 in
	zmax = 9 in
	1/4 size 1, 1/2 size 2, 1/4 size 3
	size 1 are all disks
	size 2 are 3/4 disks, 1/4 spheres
	size 3 are 1/2 disks, 1/2 spheres

Clusters conflicts:

  Cluster spheres are 1.125" diameter for zones 1 and 2, 1.625" for 
  zones 3 and 4.

  The centers of galaxy rod holes are required to be 0.6" away from 
  the attachment point in all zones.

  Galaxy rod holes must be at least 0.23" away from each other on the
  surface of cluster sphere.  The same limit is imposed for 1.125" and
  for 1.625".

  Two galaxies may not be separated by less than 1.2 times the sum of
  their radii.

  A rod may not pass within 0.6 times the diameter of an interior galaxy.

Weights:

  Central sphere (lbs): 75 lbs (approximate for aluminum plus harness, welds)
  
  Cluster spheres (lbs): 0.071, 0.071, 0.210, 0.210 for zones 1, 2, 3, 4
  Lamps (lbs): 0.125

  Disk galaxies (GRAMS):   35, 55, 95  for sizes 1, 2, 3
  Sphere galaxies (GRAMS): 60, 90, 120 for sizes 1, 2, 3
  Galaxy support rods assumed to be 0.0017 pounds/inch

  Lamp rods (including estimate for cord) assumed to be 0.030 pounds/inch

  Cluster rods assumed to be
    0.065  lbs/inch for 1.25"
    0.028  lbs/inch for 1.0"
    0.023  lbs/inch for 0.75"

  CM calculations use approximate treatment of Carlson rod breakdown