**Appendix
A - Design Calculations**

i)
__Torus__

Floor area required at 1g: 1,442,640m^{2}

Floor area of torus: _{}

Where _{}
= radius to torus floor

*r *= minor radius

Rotation rate required to get 1g
acceleration at torus floor: _{}

Where _{}
= acceleration due to gravity (9.806ms^{-2})

_{}
= angular velocity (rad/sec)

_{}
= radius to torus floor

Limit of rotation rate: 1 rpm = 0.1047 rad/sec

=> minimum radius to torus floor: 894.5m

=> maximum minor radius: 128m (+ radiation shielding)

Line of sight (i.e. - how far you can see before floor reaches eye level)

Equation of a circle: x^{2 }+
y^{2} = r^{2}

Where x and y are co-ordinates of point, i.e. - ordered pair (x, y) and r = radius of circle

For line of sight, x = radius - height above floor (1.7m), r = radius to torus floor

=> Line of sight (y) = _{}

*Comparison of radii *

Minor radius (incl. shielding) |
100m |
125m |
150m |

Radius to torus floor (m) |
1183.52 |
940.997 |
780.96 |

Line of sight (m) |
63.412 |
56.54 |
51.5 |

rpm required for 1g |
0.869 |
0.9748 |
1.07 |

ii)
Moveable spheres (see
*fig. 7.1b*)

Floor area required: 9,000m^{2 } (2,250m^{2 }per sphere)

Door to lift: every 18m

Area of sleeves: _{} =
86.59m^{2} in each floor

Floor 2 (door at centre) => floor 1.5m below equator.

*x ^{2} + y^{2} = r^{2}*

=> *x ^{2 }= r^{ 2 }- (1.5)^{2}*

=> Floor area = _{}

Floor 1, 16.5m above equator

Floor area = _{}

Floor 3, 19.5m below equator

Floor area = _{}

Floor area required = S floor areas 1, 2, 3

=>2250 = _{}

=> *r ^{2 }*= 484.545

* r *= 22m