As is generally known, both the velocity of rotation and the centrifugal force at the various points of a rotating object are proportional to the distance from its center of rotation, the axis (Figure 83); i.e., the velocity is that much greater, the further the point in question is distant from the axis and that much less, the closer it is to the axis; it is equal to zero on the theoretical axis of rotation itself.
Figure 83. Velocity of rotation and centrifugal force on a rotating object.
Key: 1. Centrifugal force; 2. Velocity of rotation; 3. Distance from the center of rotation; 4. Center of rotation; 5. Rotating object; 6. Axis of rotation.
Accordingly, the rotating part of the space station must be structured in such a manner that its air lock and the cable connections in the center of the entire structure are in the axis of rotation because the least motion exists at that point, and that those parts, in which a gravitational effect is to be produced by centrifugal force, are distant from the axis on the perimeter because the centrifugal force is the strongest at that point.
Figure 84. The Habitat Wheel. Left: Axial cross section. Right: View of the side constantly facing the sun, without a concave mirror, partially in cross section.
Key: 1. Wheel rim; 2. Well of the staircase; 3. Elevator shaft; 4. Axial segment; 5. Circular corridor; 6. Turnable air lock; 7. Elevator; 8. Bull's eyes with mirrors; 9. Condenser pipes; 10. Evaporation tube; 11. Bull's eye (window); 12. Cable connection.
These conditions are, however, best fulfilled when the station is laid out in the shape of a large wheel as previously indicated (Figures 84, 89 and 90): the rim of the wheel is composed out of cells and has the form of a ring braced by wire spokes towards the axis. Its interior is separated into individual rooms by partitions; all rooms are accessible from a wide corridor going around the entire station. There are individual rooms, larger sleeping bays, work and study areas, mess hall, laboratory, workshop, dark room, etc., as well as the usual utility areas, such as a kitchen, bath room, laundry room and similar areas. All rooms are furnished with modern day comforts; even cold and warm water lines are available. In general, the rooms are similar to those of a modern ship. They can be furnished just like on Earth because an almost normal, terrestrial gravitational state exists in these rooms.
Figure 85. Directional relationships in the habitat wheel.
Key: 1. Direction of the centrifugal force, that is, of apparent gravity; 2. Everything vertical is tilted instead of parallel; 3. "Lowest" region; 4. Partition; 5. Down; 6. Up; 7. Bathtub; 8. The water level is curved instead of straight (flat); 9. Vertical direction; 10. Vertical; 11. Axis of rotation (center) of the habitat wheel; 12. "Highest" point.
However, to create this gravitational state, the entire station, assuming a diameter of 30 meters, for example, must rotate in such a manner that it performs a complete rotation in about 8 seconds, thus producing a centrifugal force in the rim of the wheel that is just as large as the gravitational force on the Earth's surface.
While the force of gravity is directed towards the center of mass, the centrifugal force, on the other hand, is directed away from the center. Therefore, "vertical" in the habitat wheel means the reverse of on Earth: the radial direction from the center (from the axis of rotation) directed outward (Figure 85). Accordingly, "down" now points towards the perimeter and at the same time to the "lowest" part, while "up" now points towards the axis and at the same time to the "highest" point of this manmade celestial body. Taking its smallness into account, the radial orientation of the vertical direction, which in most cases is irrelevant on the Earth due to its size, now clearly becomes evident in the space station. The consequence of this is that all "vertical" directions (such as those for human beings standing erect, the partitions of the rooms, etc.) are now convergent instead of parallel to one another, and everything "horizontal" (e.g., water surface of the bathtub) appears curved instead of flat (see Figure 85).
A further peculiarity is the fact that both the velocity of rotation and the centrifugal force, as a result of their decrease towards the center of rotation, are somewhat less at the head of a person standing in the habitat wheel than at his feet (by approximately 1/9 for a wheel diameter of 30 meters) (Figure 83). The difference in the centrifugal forces should hardly be noticeable, while that of the velocities of rotation should be noticeable to some degree, especially when performing up and down (i.e., radial) movements, such as lifting a hand, sitting down, etc.
Figure 86. a) Top view onto the external door of the rotating air lock of the habitat wheel. b) Axial cross section through the rotating air lock of the habitat wheel.
(See Figure 84 and the text.)
The ball bearings are designed in such a manner that they allow movement in the direction of the axis through which closing and/or releasing is possible of the external air seal which connects the air lock airtight to the inside of the habitat wheel when the inside door is open.
Key: 1. Rotation of the habitat wheel; 2. Rotation of the air lock; 3. Axial segment; 4. Inside door; 5. To the air pump; 6. Air intake valve; 7. External air seal; 8. Motor pinion gear; 9. Gear on the rotor of the lock; 10. Outside door; 11. Ball bearing; 12. Rotating air lock, movement in the axial direction.
However, all of these phenomena make themselves felt that much less, the larger the diameter of the wheel. In the previously selected case (30 meters in diameter), only a slight effect would be perceptible.
Since the equipment for connecting to the outside is installed in near the axis (because at that point the least motion exists!), the axial segment forms a kind of "entrance hall" of the entire station. This segment has a cylindrical shape. At its ends (near those points where it is penetrated by the theoretical axis of rotation), the air lock is positioned on one side and the cable connection on the other side (Figure 84, S and K).
The air lock is made rotatable in order to ease the transition between the rotational movement of the habitat wheel and the state of rest of outer space (Figure 86). When "outgoing," the air lock is stationary with respect to the habitat wheel (thus, it is rotating with respect to outer space). People can, therefore, move easily out of the habitat wheel into the air lock. Then, the latter begins to rotate by electrical power opposite to the direction of rotation of the habitat wheel until it reaches the same rotational speed as the habitat wheel. As a result, the air lock is stationary in relation to outer space and can now be departed just as if the habitat wheel were not even rotating. The process is reversed for "incoming." With some training, rotating the air lock can, however, be dispensed with because the habitat wheel rotates only relatively slowly at any rate (one complete revolution in approximately 8 seconds in the previously assumed case with a 30 meter diameter of the wheel).
Even the cable connection at the other side of the axle segment is designed in a basically similar manner in order to prevent the cable from becoming twisted by the rotation of the habitat wheel. For this reason, the cable extends out from the end of a shaft (Figure 87), which is positioned on the theoretical axis of rotation of the habitat wheel and is continually driven by an electrical motor in such a manner that it rotates at exactly the same speed as the habitat wheel, but in the opposite direction. As a result, the shaft is continually stationary in relation to outer space. The cable extending from the shaft cannot, in fact, be affected by the rotation of the habitat wheel.
Figure 87. A. Top view onto the cable connection of the habitat wheel. B. Axial cross section through the cable connection of the habitat wheel.
(See Figures 84, K, and the text.)
Key: 1. Rotation of the habitat wheel; 2. Rotation of the shaft; 3. Cable; 4. Shaft; 5. Compound cable; 6. Ball bearings; 7. Passageways sealed airtight; 8. Vacuum;
9. Sliding contact rings; 10. Pressurized; 11. High and low voltage lines on the inside of the habitat wheel;
12. Heating tube.
Stairs and electrical elevators installed in tubular shafts connect the axial segment and the rim of the wheel. These shafts run "vertically" for the elevators, i.e., radially (Figure 84, A). On the other hand, for the stairs, which must be inclined, the shafts are taking the divergence of the vertical direction into account curved along logarithmic spirals that gradually become steeper towards "up" (towards the center) (Figures 88 and 84, T) because the gravitational effect (centrifugal force) decreases more and more towards that point. By using the stairs and/or elevators in an appropriately slow manner, the transition can be performed gradually and arbitrarily between the gravitational state existing in the rim of the wheel and the absence of gravity in outer space.
Figure 88. Well of the living wheel staircase.
Key: 1. Axial beam; 2. Elevator shaft; 3. Rim of the wheel; 4. Well of the staircase; 5. Railing; 6. Logarithmic spiral with a slope of 30°.
Supplying the habitat wheel with light, heat, air and water takes place in the fashion previously specified in general for the space station by employing the engineering equipment described there. The only difference being that the wall of the wheel rim always facing the sun also acts to heat the habitat wheel; for this reason, this wall is colored dull black (Figures 89 and 84), in contrast to the otherwise completely highly polished external surfaces of the station. A small solar power plant sufficient for emergency needs of the habitat wheel is also available.
Figure 89. Total view of the side of the habitat wheel facing the sun. The center concave mirror could be done away with and replaced by appropriately enlarging the external mirror.
All storage rooms and tanks for adequate supplies of air, water, food and other materials, as well as all mechanical equipment are in the wheel rim. The concave mirrors associated with this equipment and the dull black colored steam generator and condenser pipes are attached to the habitat wheel on the outside in an appropriate manner and are rotating with the habitat wheel (Figures 84, 89 and 90).
Figure 90. Total view of the shadow side of the habitat wheel.
Finally, attitude control motors and thrusters are provided; besides the purposes previously indicated, they will also generate the rotational motion of the habitat wheel and stop it again; they can also control the rate of rotation.