CHAPTER IV

 

Important functional elements of the Settlement

 

IV.1. Thermal stress

 

Considering the rotation movement of the Settlement it is easy to imagine that the position of a certain point of the torus towards the Sun is permanently changing. Therefore we can assume the temperatures of the different parts of the torus suffer constant variation depending on their position towards the Sun. The temperature of a certain surface will naturally tend to rise when facing the Sun and will tend to drop as soon as it begins to face the opposite direction.

 

According to Stefan’s law, the power radiated by a black body in space is, where  is Stefan’s Constant (), A is the surface area of the body ( [A]= m2 ) and T is the temperature of the body ( [T]=K ). Therefore the power radiated is directly proportional to T4 for an identical body, which explains why the total energy under a black body increases so much for a relatively small increase in temperature. 

 

We can also expect some dilation and contraction phenomena to occur during a complete rotation of the torus, although its exterior surface (the side facing the sun) will be covered with the solar panels supplying the electromagnetic coils. The solar panels will absorb 15% of the total solar energy; the rest of it will be transformed into heat. As the exterior solar panels are somehow isolated from the ring, only small amounts of heat will be transmitted to it. Moreover, the rotation period of 127s will not allow great temerature differences between the different parts of the torus. Therefore, the heat reaching the metallic exterior of the Settlement will not have considerable effects upon its shape and dimensions.

 

Still we must consider the three possible types of dilation: in length, surface and volume.

 

  [1]

 

, where is the linear dilation coefficient ()  

 

By disregarding the terms containing, we obtain:

 

    [2]

 

 

By disregarding the terms containing , we obtain:

 

    [3]

 

Relations [1], [2] and [3] represent the expressions of the three dilation laws.

,  and are the initial dimensions corresponding to the temperature T0=273.15K (t0=0oC)

 

We can now determine the final dimensions by considering an intermediary phase:

 

 

 

As  we can disregard the terms containing it. Therefore,

 

   [4]

 

  [5]

 

   [6]

 

 

, where  and

 

 

 

The temperature variations will cause small deformation forces to act upon the exterior of the torus. The deformation forces can be assimilated to forces caused by the dilation phenomena. According to Hooke’s law,

 

 

   [7]

 

- the dilation effect

 - the initial length

 - the time elapsed

 - the deformation force

 - the dilation force

S- the surface area of the transversal section of the body

E-  the module of eleasticity

 

As  is a constant, the dilation force varies according to time:

 

The dilation force can also be assimilated to an elastic force:

 

 

Therefore, the dilation force can theoretically cause harmonic vibrations to occur within the body of the torus. But practically the ring suffers chaotic vibrations. Therefore we must provide the inner circumference of the torus with a thermal shield to minimize the thermal stress and thus the chaotic vibrations.  

IV.2. The Coriolis force and its effects

As the Coriolis force is a force which acts upon any moving body in an independently rotating system, its effects can also be felt by colonists onboard the space settlement. The effect of the Coriolis force is an apparent deflection of the path of an object that moves within the rotating coordinate system. The object does not actually deviate from its path, but it appears to do so because of the motion of the coordinate system. The coriolis force is larger for parcels moving at faster speeds, it's zero if a parcel is not moving and is not that large for slow-moving objects or for those moving over short distances. That is why the Coriolis force will not represent a major inconvenient for colonists moving along the torus, as it is only felt by those traveling towards  the center of the settlement.

Therefore, the four elevators connecting the main residential areas with the 0 gravity center must integrate special mechanical systems to ensure that travelers will not feel the effects of the Coriolis force. For achieving this, the composite force acting on the traveler must pass through its symmetry axis. One option would be providing the elevators with mobile floors which will change their angulations according to speed, total acceleration and distance towards the 0 gravity center. As the Coriolis force is larger for objects moving at faster speeds, it will certainly reach its maximum in points situated on the extreme circumference of the torus. In this case, the Coriolis force will reach its utmost at the base of the elevators, where the floor angulations will be maximum. While getting closer to the center of the torus, the angulations of the floors will slowly decrease, reaching 0o at destination.

 

 

Knowing the angular velocity of the space settlement () and the elevator’s time of travel (t) we can determine the floors’ angulations depending on these two data.

 

 

 

Assuming the relative speed of the elevator, implicitly that of the traveler is , the acceleration associated to the Coriolis force is:

 

              

 

 - the gravitational acceleration

 – the position vector

t  -   the time of  travel of the elevator

 

 

 

For reducing the friction between the elevator room and its tube caused by the Coriolis force (which changes its direction accordingly to the direction of movement) the elevator must be fitted with small lateral bearings or wheals. 

 

IV.3. Radiators

 This chapter consists of a few points about the role of radiators in the temperature regulation of the space colony.

Any habitat needs light. This may be provided as sunlight or artificial light, but whichever; it will introduce energy will end up as heat, thus tending to increase the temperature of the habitat. The activities of the colonists and their artifacts may add to the heat generated, particularly if they rely on further imported energy.

The main type of heating and cooling will be electric radiators and coolers with intelligent centralized thermostat.

They would be mounted under the 'floor' of the habitat and would obviously require active pumping of the transfer medium. Still there would be no need for a rotating connection.

The “Thermic Valve” Principle with applicability in non-electric radiators and coolers
 
The temperature of an object suspended in space, in this case the space settlement, will be hot or cold depending upon the amount of radiation that it absorbs. So in shadows it gets very cold, and in the sunlight it gets very hot. This is the main idea for our non-electrical radiator and cooler.
 
  (Thermo equilibrium)
 
We must put a thermoconductor material up and under the 0 gravity zone, as shown in the image below for maintaining this zone to a normal temperature without electric heaters powered from the photovoltaic cells. The thermoconductor material can have a circulating caloric agent like water or any other.
      This makes two advantages:
·               This is a secondary source of power
·               In case the electric system failures the colonists can use the 0 gravity center as a “life boat”.
The position of the rectangular thin panel will be auto orientated by a thermo sensible material located inside the 0 gravity zone thus its angle with the sun rays will be controlled.
If its angle with the solar rays is 90o the panel will receive the maximum amount of radiation thus it will heat the interior of the torus, and if its angle is 0o it will cool the 0 gravity zone.
In an intermediary angle (between 0o and 90o) ,the luminous flux will decrease ,hence, the energy absorbed by the heat conducting material will be the appropriate for maintaining the 0 gravity zone temperature to 20o C.
The heat conducting material will have one black side for better taking the beam energy.
The Wiedemann-Franz law says that the boundary resistances of heat and electricity are proportional. We must use a resistant material because of the great difference between high and low temperatures of the thermo conductor. These are some good heat conductors materials but not resistant to such big radiation and temperature.
 
 
 
 
 
 
 
 
 
 
 
 

Material

Thermal conductivity
(cal/sec)/(cm^2 C/cm)

Thermal conductivity
(W/m K)*

Silver

1.01

406.0

Copper

0.99

385.0

Aluminum

0.50

205.0

Lead

0.083

34.7

Studying the table below we find out that the most suitable material for the radiator panel will be the carbon foam.

 

                     Carbon Foam Properties

Density

0.2 - 0.6 g/cm3

Thermal Conductivity

50 - 150 W/m·K

Specific Conductivity

258

Compressive Strength

3.4 MPa

Compressive Modulus

144 MPa

Specific Surface Area

4 - 34 m2/g

 

For determining the amount of solar energy (ES) absorbed by one of the panels, we will consider a flat thermo conductor panel of surface S1 and a surface S0.  

The solar energy absorbed on the panel will be:

, for a panel inclination of 45o

The small temperature differences between different areas of the torus will generate little breezes which will improve the air circulation.

 

IV.3. Mirrors and solar panels

 

  1. The benefits of natural Sunlight

 

Light is one of the most important elements which contribute to the development of natural life and human activities. It is known that the absence of light or the insufficient amount of light can cause severe damage to living organisms, including human beings, leading to biological extinction. Light plays also a major role by influencing people’s morale and mentality. Therefore, we can not imagine long-term life on the orbital colony without light. This chapter will discuss the distinction between the light we receive from natural sources and that provided by human technology. Most of the direct and indirect effects of artificial lighting will be debated in detail.

 

The importance of adequate sunshine on the body, on exposed skin, on a regular basis is important for human health. Without adequate sunshine, we cannot expect to achieve superior health onboard the space settlement. Also, there are definite negative health effects from artificial lighting. For optimum well-being on the colony, it is necessary to be aware of any influence which upsets the natural order of life.

 

Natural sunlight is needed by all the more highly developed forms of life in all conditions of health and ill-health and throughout their existence. It is a valuable factor in all states and conditions of the human body. As artificial light does not produce a complete spectrum of light, its influence tends to change the natural body rhythms especially accustomed to the light of nature. The only way we may avoid these negative effects is to avoid their causes. Natural sunlight enhances bodily nutritive processes overall. Also, it specifically facilitates phosphorus and calcium absorption and catalyzes the production of vitamin D in the skin.

 

Sunlight is of value in all states and conditions of the body and in all stages of development.

Its role in proper bone development is due to the fact that only through the aid of natural sunlight, particularly the ultraviolet rays, may the laying down and fixation of the calcium and phosphorus salts be accomplished in an ideal fashion as to make for the transformation of cartilage into bone. When insufficient sunlight is obtained, the result is defective, misshapen, brittle and easily broken bones. Sunlight also proves invaluable in cases of glandular inactivity and aids in increasing the coagulating power of the blood, being of inestimable value to sufferers from hemorrhage disorders. The influence of sunlight is also directly related to the number of red cells and hemoglobin in the blood. An insufficiency of light will cause an increase in the serum or watery portion of the blood and a corresponding decrease in the quantity of blood fibrin and red corpuscles, resulting in anemia. But with sufficient sunlight, the oxygen-carrying power of the blood is increased, the circulation of the blood is improved, and consequently the blood’s power to repair and build tissue is increased. Sunlight’s influence on the muscles is to add to their size and quality and to enhance their contractile powers by improving the condition of the entire body, including the nerves that control the muscles.  Regarding the pregnant mother and her unborn child onboard the orbital colony, it must be noted that the benefits to be derived from sunlight are greatest during periods of development and rapid gains in flesh. Sunshine, again, by improving overall health and vitality, aids in the skeletal development of the baby and helps preserve the normal alkalinity of his blood. Another benefit is that pregnant mothers who get sufficient sunlight experience little if any tiredness, backaches and loss of appetite. All anabolic activities in the body ultimately depend on sunlight for most effective function.

 

As human activity is very important onboard the settlement, full-spectrum lighting in closed work places will create significantly lower stress on the nervous system than standard cool-white lighting and will reduce the number of absences due to illness. Full-spectrum lighting will act to boost the immune system in the same way as natural sunlight and will also be used in open-door spaces during orbital nights.

 

Still the effects of artificial lighting have been noticed in both plants and animals. For example, plants grown in artificial light lack the rugged constitution of plants grown under natural lighting conditions. Their growth may be stimulated by subjecting them to longer hours of light, as compared to the natural light cycle of the revolving earth. But this forced growth produces plants bearing flowers and fruit of lesser quality and color appeal than those grown in sunlight. The animal world is also adversely affected by variance of light wavelengths. Fluorescent lighting can cause genetic mutations, cancer and death in the cells of many life forms, including humans.

 

Aside from the facts concerning the direct negative effects of unnatural lighting, we must also consider their more indirect effect on our body rhythms. Their presence, by turning night into day, tend to imbalance the circadian rhythms- the regular cycles of rising and falling body temperature, variations in body chemicals that naturally occur approximately once every 24 hours. The result may be ‘light stress.” All plants and animals require alternating periods of light and dark so that some vital processes may rest while others become activated. The anabolic activities during the night can take place efficiently only when not interfered with by lighting, which continues to stimulate activity in the living cells.

 

That is why the space settlement must dispose of artificial 14-hour days and 10-hour nights. Open spaces inside the torus will have natural sunlight during day time and full-spectrum illumination during the night.

 

 

b. Mirrors and light generation

 

The only feasible option for illuming the residential and recreation areas inside the torus using natural sunlight is to dispose of two large mirrors to reflect the solar rays in the desired location of the colony. The two mirrors will be placed symmetrically towards the center of the ring (or the 0 gravity center), being directly connected to the central body by two long cylindrical bars made of titanium. Taking into account that the angle between the apparent orbit of the Moon and Earth’s ecliptic is 5o9, the two mirrors have to be slightly prone towards the main ring of the torus, as shown in the diagram below. We will consider a mirror inclination of 45o.

 

    

The two Helio sensors containing photoreceptor cells will permanently determine the position of the Sun towards the mirrors. By connecting them to the rotating system of the mirrors, they will always keep them face to the Sun, so that the amount of light reflected onto the surface of the torus will be maximum. 

 

 

 

 

For determining the amount of solar energy (ES) reflected by one of the mirrors, we will consider a flat mirror of surface S1 and a light source of surface S0.  

 

 

 

The solar energy reflected on the ring will be:

 

, for a mirror angulation of 45o

 

 

If the mirrors are slightly curved, then their convex shape will allow the reflection of the light on a wider area. In this case, we can determine the convexity of the mirrors by calculating their radius:

 

 

 

 

 

  [1]

 

 

  [2]

 

    [3]

 

    [4]

 

 

 

 

 

   [5]

 

 

   [6]

 

If , then:

 

 

   [7]

 

   [8]

 

 

 [9]

 

 

  [10]

 

- the radius of curvature of the convex mirror

 - the distance between the mirror and the 0 gravity zone (the length of the bars which connect the central body with the mirrors)            

 

 

c. Simulating the circadian cycle

 

For an easier, less stressful and more rapid accommodation of people in space, creating an artificial “sky” seems to be an imperative condition. Therefore, we will generate the illusion of having a sky by using a transparent ceiling made of special glass, which will not allow the passing of UV radiations. To achieve this, Pb2+ ions will be introduced in the process of clear glass fabrication. The solar light reflected by the two main mirrors will be subsequently reflected by smaller, independent mirrors situated around the 0 gravity center of the torus. Each of them will reflect light onto a well defined sector of the ceiling. To properly illumine the interior of the torus, the solar rays must be reflected perpendicularly on its transparent glass ceiling. Hereby, the illusion of a lightsome sky will be produced. The principle is shown in the drawings below.

 

 

 

 

 

 

 

 

As we said, the regular sequence of days and nights plays a major role in the proper development of human beings, affecting both metabolism and social activity. There are three possibilities for simulating the circadian cycle.

 

1.The first and most efficient, involving only small amounts of energy and simple technological means, is the independent rotation of the adjustable mirrors, so that the reflection angle will not allow light to reach the transparent ceiling of the torus. It can be achieved by using common rotating mechanisms which will orientate the mirrors at an angle of  0o towards the solar rays, so that the reflection angle will become null. The 0o angulations will accord with the night periods inside the torus. The principle is shown in the diagram below.

 

 

 

2.Another way of simulating Terrestrial nights inside the orbital colony will imply a different positioning of the adjustable mirrors. In this case, they should be placed on the inner circumference of the torus, in the immediate vicinity of its ceiling. The idea is lowering the main mirrors so that the light reflected by them will cover a more limited area, avoiding the adjustable mirrors, thence avoiding being reflected inside the torus.

 

 

 

 

 

The lowering of the two large mirrors will imply the use of complex technology and considerable amounts of energy. Disposing the adjustable mirrors along the inner contour of the ring will require much more material than disposing them near its center. Therefore, this option is too uneconomical to be considered.  

 

3. The third solution consists in covering the ceiling of the torus with two superposed titanium “nets”. During the day period, the light reflected by the adjustable mirrors would pass through the nets’ empty spaces. For simulating night periods and even crepuscules, these empty spaces will be slowly narrowed by shifting the exterior net over the interior one, until the surface of the ceiling will be completely covered. Still this option would entail the use of large quantities  of titanium thence a considerable amount of economic resources.

 

 


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