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Different combinations of the radius R of the structure and the angular velocity w can generate 1 g (9.81 m/s2) :
g = w^2 . R
If w is expressed in rpm (revolutions per minute), then 1 rpm means that the structure will cover 2 p radians in one minute :
1 rpm = 2.pi / 60 s = 0.105 1/s
Substituting in the above equation:
(0.105 .w)^2.R = g
Expressing R in terms of w :
R (w) = g / (0.105 . w)^2
The following graph depicts the mathematical relationship between R and w :
The table below shows possible radii for desirable rotation rates of between 0.5 and 2 revolutions per minute.
Due to pseudo gravity considerations, solids of revolution are the obvious choice for shapes. This is so due to the fact that the lines of equal gravity will be circular, and it would be desirable to have the same gravity at all points along the surface.
Sharp ends should be avoided for structural reasons. The main stress of this structure will result from internal pressurization, so membrane oriented shapes are better suited for the job. Possible shapes are:
Two radically different concepts are implicit in the suggested shapes.
Spheres or cylinders of huge radii result in a huge space colony with considerable volumes of trapped atmosphere. The size of this atmosphere and of the settlement itself leads to the concept of naturally regenerative environment, in which the Earth like natural mechanisms could be recreated.
Being able to reproduce natural processes and having a big sized colony is undoubtedly an important design factor, for it gives designers the chance to rely on natures buffers for security. Although life support system solutions would still have to be engineered, it could be said that, if all parameters are properly calculated, the system can be switched on and it will take care of itself. The clear drawbacks to this solution have to do with research and the difficulties associated with constructing such a mammoth structure and terraforming an atmosphere in it.
On the other hand the ring like structure reduces the size of the atmosphere with opposite advantages and disadvantages with respect to the above mentioned options. That is, the structure itself will be easier to construct but a careful watch must be kept over the now smaller atmosphere. Any mismanagement of the atmospheric parameters could result disastrous, for the relatively reduced size of everything does not allow for nature to compensate imbalances.
These two opposed alternatives seem, however, to fulfill their own unique role in the goal of colonizing space. While the ring structure could be envisaged as a first step in achieving the goal due to its manageable construction and also act as a test bed for the systems that will need to be engineered, only the mammoth cylinders or spheres will actually provide a stable, self-sufficient quasi natural environment for humans to dwell for years to come.
For the above reasons, further studies will be conducted for both options: a relatively small ring shaped colony as a first step and a huge spherical or cylindrical colony to follow in the evolution of space settlements.
A good way to decide upon the suitability of each shape would be to compare the surface areas that could be utilized in comparably sized spheres and cylinder.
Taking a sphere of radius R and a cylinder of radius R and equal height (2R) the surface areas would be :
Sphere = 4. PI . R^2Cylinder = 2.PI.R. 2 R = 4. PI . R^2
That is, in both cases the surface area is the same.
However, a cylinder can be designed with a greater height to radius ratio that could increase disposable surface, while the sphere constitutes a locked geometry. Anticipating future considerations, a sphere appears to be of more difficult construction and assembly, and will offer a considerable challenge from the point of view of illumination. Although the final closed shape of the structure will be determined according to other considerations, it is then decided that the main body of the big colony will be constituted by a cylinder.
Determining the exact dimensions and spinning rates
In order to be consistent with the objectives that were outlined above and the structural design reasons that led to the adopting of both shapes, a big radius and consequently slow rotation rate should be chosen for the cylinder and a relatively smaller radius and a thus faster rotation rate should be chosen for the ring colony.
In this way, the ring would constitute a space colony that will be more confined and perhaps not so pleasant to live in, but that will pave the way for a bigger cylinder that could host colonists in more favorable earth like conditions.
Based on gravity considerations, a rotation rate of 1.25 rpm is adopted for the ring structure, with an external radius at the surface of 570 m
The diameter of the cross section will determine both the horizontal area and the ceiling of the colony. A possible diameter of 250 m will still roughly (considering a total diameter of 1100) allow for 600m of free space in between the edges of the colony.
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