DESIGN CALCULATIONS

Centripetal acceleration

	a = v^2 / r 		v = 2pi r / t
	a = 4 pi^2 r / t^2
	r = a t^2 / 4 pi^2

	Specifically, for Spaceport One we want a = .5g = 5 m/s^2
						t = 60 s
						4 pi^2 = 39.48
	r = 455.9m

	This gives a circumference of about 3 km.

	Assume 4m/level:  there is room for 10.5 levels.
	Let the hub be 0 and number the levels 0..9.


Area of a Cylinder:

	a = 2 pi r l

	Assume r = 500m, a = 3141 * l m^2.  Assume a total of
	10m^2/person (counting agriculture and services), that's
	about 300 people per 10m of length.  Half that for the .25g
	wheel of HackTown.   A disk with n levels has n/2 times the
	area of a simple cylinder with the same radius.


Volume of a sphere:

	v = 4/3 pi r^3  = 4.189 r^3

	The area of a sphere is 4 pi r^2, or 12.56 r^2.

	Thus, a sphere with radius 100m has a volume of 4.189e6 cubic
	meters, and an area of 125600 m^2.  If that area were
	covered with 5m cubicles (25 m^2) there would be 5026 of
	them.  There would be 1256 10m cubicles.  Plenty for an
	initial colony.

	a 50m radius sphere would have 1/4 the area, or 31400 m^2.
	That's enough for the initial migration's living space, at
	25m^2/person (_plenty in zero g), and it's _tiny (100m diam.)

	That doesn't handle agriculture, but agriculture doesn't need
	as much shielding and doesn't have to worry about Coriolis
	force.


Volume of a shell:

	let d = thickness and r = inside radius.  Then,

	v = 4/3 pi ((r + d)^3 - r^3) 
	  = 4/3 pi ((r + d) (r^2 + 2dr + d^2)  - r^3)
	  = 4/3 pi (3dr^2 + 3d^2 r + d^3)

	If d = 2 and r = 100,  we have

	v = 4.189 * (60,000 + 1200 + 8) = 256,400 m^3.

	That's about that many tonnes of rock, or 2.6e8 kg (256
	million kg).  You can do it in a year if you launch 1M
	kg/day, or close to 10kg/sec.  Marginal.

	If r = 50 it's a bit over 1/4 that.