6.1. Tether Sizing, Radiation Concerns, and Hab Layout
Devin Cummings
Nomenclature
acentripetal = centripetal acceleration, m/s2
w = angular velocity, rad/s
r = length from c.g. of spinning object to c.g. of system
aCoriolis = Coriolis acceleration
v = velocity vector of a moving astronaut
α = angle between w and v
6.1.1 Introduction
Many people think that the best reason to not go to Mars is the possible risk to human life. They believe that the human body and mind are not up to the challenge of traveling the vast reaches of space. In this section, we intend to show that human factors problems such as microgravity concerns, radiation exposure, and habitat layout are easily solvable through the use of artificial gravity, radiation shielding, and efficient habitat design.
6.1.2 Hab and ERV Tether Sizing
One major concern in manned flight to Mars is the effect of the microgravity environment on astronauts for an extended time period. The simplest solution to solving the microgravity problem is to create artificial gravity through the use of a tether connecting the living module to the spent last stage of its propulsive rocket. By spinning these two countermasses about the center of gravity, we can create a centripetal acceleration, thereby artificially creating gravity.
A Matlab code (Appendix 6.1.1) was written to calculate the accelerations and velocities needed to determine the length of tether necessary for astronauts to comfortably tolerate artificial gravity. The following plots are the outputs of this code.
Figure 6.1.1 Angular Velocity for Mars Gravity vs. Tether Radius
In Figure 6.1.1, centripetal acceleration was used to determine the angular velocities needed for Mars gravity at a given tether radius. This equation is:
acentripetal = w2r (6.1.1)
where w is angular velocity and r is radius of tether. Using this equation, it is found that Mars gravity can be created at a spin rate of 3rpm with a tether of 38m, at a spin rate of 2rpm with a tether of 85m, and at a spin rate of 1rpm with a tether of 340m.
The two limiting factors in how short we can make the tether are the gravity gradient and Coriolis effects. The first to be considered is the gravity gradient, or change in gravity as you move toward the center of gravity. The gravity gradient should not exceed a change of 0.01 g’s per foot, or 0.122 rad/s2 to avoid astronaut disorientation.1 This limits the tether to an angular velocity of 0.35 rad/s, or 3.3rpm. Figure 6.1.2 shows the percent difference in gravity between a 2m tall person’s head and feet with respect to tether radius.
Figure 6.1.2 Percent Difference in Gravity vs. Tether Radius
The final consideration is Coriolis effect. This is the dizzying effect caused by trying to move perpendicular to the plane you are rotating in. Coriolis acceleration is measured using the following equation:
ACoriolis = 2wvsinα (6.1.2)
where w is the angular velocity vector, v is the velocity vector of an astronaut walking within the hab module, and α is the angle between them. Coriolis acceleration must be kept under 0.25*acentripetal, or 0.93m/s2, for astronaut comfort.1 To meet this, angular velocity must be held under 4.5rpm. Figure 3 shows centripetal acceleration for an astronaut walking at 1 m/s versus tether radius.
Figure 6.1.3 Coriolis Acceleration (m/s2) vs. Tether Radius (m)
The limiting factor for the tether, then, is gravitation gradient, which limits angular velocity to under 3.3rpm. While this is liveable, it isn’t pleasurable. Therefore, a tether length of 85m, with an angular velocity of 2rpm, is the suggested minimum tether length. An 85m tether gives a gravitational gradient of 0.04 1/s2, well below the maximum allowed value of 0.12 1/s2, and a Coriolis acceleration of 0.42 m/s2, well below the max allowable value of 0.93 m/s2, putting the astronauts into their optimum comfort zone.
For the ERV module, the above procedure was used. However, it has been decided to gradually spin up the ERV over the course of a month after leaving Mars to a centripetal acceleration equivalent to 1g. This will help ensure that the astronauts are healthy upon Earth arrival. In order to do this and still meet the gravity gradient and Coriolis acceleration factors mentioned above, a tether length of 223m from ERV to the center of gravity of the system is needed.
6.1.3 Radiation Considerations
Another large concern for a crew expected to survive the hostile environments of space and Mars is radiation exposure. There are two major sources of radiation that cause harmful exposure – Galactic Cosmic Rays (GCR’s) and Solar Cosmic Rays (SCR’s)2.
Galactic Cosmic Rays are high-energy particles that originate from deep space. They are not a major design concern for two reasons. First, their high energies of approximately 1x109V make it impossible to shield them without adding a very significant amount of mass to the hab module. Second, they are luckily not a major concern because they occur only as a small, continuous shower throughout the voyage and never in one major dose.
Solar Cosmic Rays are of much more concern because they do not occur as a steady shower, but rather as occasional large doses. Solar Cosmic Rays, sometimes called solar flares, consist of high-quantity doses of protons with energies of approximately 1x106 V, and occur on an average of approximately two solar flares per year. Although the energies of the individual protons are much lower than those of GCR’s, their high concentration can produce doses of several hundred cSv, enough to kill an unprotected human. Fortunately, their lower energy level allows them to be shielded fairly easily through the use of a radiation storm shelter.
Since one of the best ways to shield SCR’s is through the use of materials containing Hydrogen atoms to dissipate their kinetic energy, the simplest solution to the SCR shielding problem is to use a resource that is already abundant on the Hab module – water.
The first thing to consider in radiation shield sizing is how much radiation an individual can be exposed to. The following figure shows general guidelines for human exposure.
Table 6.1.1 3 shows the acceptable radiation doses for various body tissues in a human body over set lengths of time. This table establishes that the limiting factor for humans is the exposure of blood-forming organs to the radiation. Next, we study known solar flares to determine the thickness of water needed to properly shield the astronauts.
Figure 6.1.4 Radiation Dose(cSv) vs. Water Shield Thickness(cm) for Ordinary Solar Flares 4
The X in Figure 6.1.4 shows that a thickness of 25cm will reduce the radiation dose of a solar flare from a lethal unshielded dose of 1000cSv to a shielded dose of approximately 2cSv, well within the tolerance range of a human being.
Figure 6.1.5 Radiation Dose (cSv) vs. Water Shield Thickness (cm) for Large Solar Flares 4
One major concern that remains, though, is what happens if an unusually large flare occurs while the Mars crew is in space. In Figure 6.1.5, we see a comparison of water depth to recorded dose for the six largest recorded solar flares since 1950. With a water shield thickness of 25cm, the maximum dose a person might receive is approximately 15.8cSv. Exposure through this thickness is still well within human tolerances for even the largest solar flare in the past 50 years.
To size the storm shelter for solar flares, we must look at three requirements. First, the storm shelter requires a thickness of 25cm H2O to properly shield the astronauts. Second, the amount of water being taken along is 5.5m3. Finally, the storm shelter needs an interior volume large enough to accommodate four astronauts for the length of a solar flare, approximately a few hours. Through the use of a simple MATLAB code (Appendix 6.1.2), we find a suitable storm shelter to be a cylindrical storm shelter with an inside diameter of 1.6m and inside height of 2m. This configuration requires a total of 4.64m3 water to protect the crew, allowing the remainder to be in use by other systems without compromising protection. Storage for the remaining water is put above the storm shelter, increasing the outer dimensions of the storm shelter to 2.1m in diameter and 2.75m in height.
By using water to shield astronauts from SCR’s, we solve two problems at once. The water has a suitable storage, and a large amount of mass is saved by not having to take along extra shielding material for the storm shelter.
6.1.4 Thermal Concerns
Heating issues on the Habitat module were also an initial concern when designing the mission. According to the mission plan, the Hab module continues on a free-return trajectory in the event of a mission failure before arrival on Mars. This free-return trajectory takes the Hab very close to the sun as it uses a gravity assist from Venus to return back to Earth. As a result of this free-return, we must determine the temperatures that the skin of the Habitat module will reach during the Venus flyby and ensure that its thermal controls can withstand the higher temperatures associated with this route.
Heat is produced on a spacecraft by four sources – solar radiation, reflected solar radiation from nearby planets, planetary radiation, and internal heat dissipation.5 When performing the thermal design analysis, we choose to neglect the effects of planetary radiation and internal heat dissipation. This is a reasonable assumption because when the spacecraft is as close to the sun as it is, these sources account for less than five percent of the total heating.
Because the Hab’s temperature is affected by direct solar radiation and reflected solar radiation from Venus, it is unclear whether the point of maximum temperature will occur when the spacecraft is closest to the Sun or Venus. We use a MATLAB program (Appendix 6.1.3) to calculate the skin temperature of the spacecraft at each of these two points. At case 1, the Hab’s closest distance from the Sun, the skin reaches an equilibrium temperature of 448 K, and at case 2, the Hab’s closest distance from Venus, the skin reaches an equilibrium temperature of 453 K, or approximately 350° Fahrenheit. These results are promising, because the Hab has more than adequate thermal protection without adding any additional weight. The Habitat module’s skin, designed to take temperatures of several thousand Kelvin during planetary descent, can easily handle these temperatures with no ill effects, and internal cooling units keep the interior of the Hab at a comfortable living temperature.
6.1.5 Habitat Module Internal Layout
As we design the internal layout of the Mars Habitat Module, there are two issues we must consider. First, aerodynamic concerns dictate the overall sizing of the Hab structure. Second, we must be extremely efficient with the interior volume available to make the astronauts’ time aboard the Hab as stress-free as possible.
Level Layout
Figure 6.1.6 Overall Habitat Module Layout
The overall layout of the Hab module can be seen in Figure 6.1.6. Its dimensions are an interior height of 7.17m and an interior diameter of 8.74m. This height poses a major problem because if we split the Hab up into two floors of equal height, each floor is almost 3m in height, wasting valuable space in high ceilings. However, if we split the Hab into three floors, each floor is approximately 2m in height. With a 2m ceiling, a taller astronaut is prone to bumping his or her head at all times. We remedy this problem by creating a three-floor Hab in which only two of the three floors are full-size. These two floors, the second and third levels, are 2.5m in height, giving astronauts enough head room for comfort without wasting valuable space. The smaller floor, the first level, measures only 1.4m in height, and houses the ejection seats and controls for takeoff, as well as the oxygen and nitrogen tanks for the trip.
Level 3
Figure 6.1.7 Level 3 Isometric View Figure 6.1.8 Level 3 Top View
Figures 6.1.7 and 6.1.8 show Level 3, which contains the sleeping and hygiene quarters for the crew of the Hab module. We use a hub-based design for this floor because it allows us to avoid having rooms with deep, sharp back corners that waste space. This configuration also provides walled rooms for the astronauts, giving them welcome privacy for parts of the day.
Figure 6.1.9 Bedroom View
Figure 6.1.9 shows the configuration of each bedroom. Each bedroom is wedge-shaped, with the narrow end opening up into the inner corridor, and has a floor area of approximately 5m2. The furnishings include one 1m x 2m bed and two dressers, 1m wide x0.3m deep, for storage of clothing and personal belongings. Each bedroom is also equipped with a personal communications console, which the astronauts use to send and receive messages from home and keep journals.
Figure 6.1.10 Hygiene Facilities
The room in the upper right of Figure 6.1.8 is the Hygiene Room, better seen in Figure 6.1.10. This room contains the necessary hygiene and cleaning facilities needed for the astronauts. From left to right of the cabinet structure shown in Figure 6.1.10, these facilities include two individual laundry hampers, a clothes washer and clothes dryer, two sinks, two showers, and finally two more individual laundry hampers. The free-standing object in the room is the toilet.
Level 2
Figure 6.1.11 Level 2 Isometric View Figure 6.1.12 Level 2 Top View
Figure 6.1.11 and Figure 6.1.12 show the second level, which was designed to contain most group activity areas. To maximize space in this area, the floor was left without walls. Also, this larger area helps reduce feelings of confinement the astronauts might feel. The area at the direct top of Figure 6.1.12 is devoted to physical fitness, with exercise machines such as treadmills and strengthening machines using rubber bands for tension. The upper right part of the figure is the wardroom. This region has a conference table and chairs for use in meetings or work, and also has a control and communication center for spacecraft control and contact with mission control. Also, when not in use, the conference table can be folded up to the outer wall, freeing up interior space.