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