5.2 Structures
Nicholas Czapla
Nomenclature
A / = Cross sectional area, m2SA / = Surface area, m2
I / = Inertia, m4
V / = Volume, m3
d / = Diameter, m
h / = Height, m
t / = Thickness, m
m / = Mass, kg
P, p / = Load, N, Pressure, Pa
n / = number of landing struts
mT / = Metric tonne (1000kg)
SF / = Safety factor
Pcr / = Critical buckling load, N
y / = Yield stress of material, Pa
H / = Hoop Stress, Pa
L / = Longitudinal stress Stress, Pa
E / = Modulus of elasticity, Pa
/ = Density, kg/m3
5.2.1 Introduction
During the Earth to Mars transit, the primary structure in use by the crew will be the habitat module (HAB). It contains everything the crew needs to survive en route to Mars as well as on the surface of Mars: crew living areas, solar storm shelter, communications station, main science laboratories, and a garage that houses the short-range rover (SRR). Figure 5.2.1 shows what the HAB will look like on the surface of Mars.
En route to Mars, the HAB vehicle is tethered to the burnt out stage of the nuclear thermal rocket (NTR) stage of the Earth launch vehicle (ELV). The tether supplies approximately 0.38g’s of gravity, the same gravity force the astronauts experience on the surface of Mars. Figure 5.2.2 shows the tethered HAB as it approaches Mars. Prior to the aero-capture maneuver, the tether releases and we safely dispose of the NTR. After entering the atmosphere successfully, the nosecone of the heat shield (HS) separates and the HAB continues it’s descent and lands on the surface.
On the surface the HAB becomes the base of operations for the mission. The extended rover missions account for the only lengthy periods of time where crewmembers are away from the HAB. The HAB, therefore, is both mission-critical and life-critical.
5.2.2 Material Selection
Habitat Outer Structure
When choosing the materials for the outer walls of the Habitat structure, we require that the material meet several characteristics. First and foremost, the material needs to be lightweight. In addition to being lightweight, the materials need to be strong enough to handle the severe loading conditions the vehicle sees during the mission. Another major concern is that of reparability. The material needs to be easy enough to repair, so that one or two astronauts can perform emergency repairs as well as routine maintenance while on the surface. In addition, since the HAB is both mission and life critical, we desire a material with a well-proven history of success. We considered several materials. Among these were aluminum alloys, aluminum-lithium alloys, titanium, and composite materials. In comparing the list of materials with the requirements for the mission, we narrow the materials down to aluminum alloys and composite materials. After preliminary research we narrow the choices down to three configurations for materials: standard, composites, and honeycomb. Here standard aluminum refers to a sheet of material, composites refer to a laminate structure, and honeycomb refers to a sandwich configuration.
For the first choice, we choose standard aluminum. It has a well-proven history of success, good strength, and is very easy to repair. Figure 5.2.3 shows a plot of HAB mass vs. D/h ratio. This plot compares HAB masses for the three materials and configurations. It is easy to see that aluminum is considerably heavier than either composites or an aluminum honeycomb structure. Due to the large difference in HAB masses between standard aluminum and the other two categories, standard aluminum is not the material configuration that meets the necessary conditions for the HAB structure.
Fig. 5.2.3 HAB outer wall mass versus D/h, constant thickness.
This narrows the selection down to either composites or honeycomb structures. Honeycomb structures, which are excellent at resisting bending loads because of their high inertias, are very lightweight. Composite materials offer the same types of advantages for different reasons. Reparability concerns arise with the use of composite materials because of the nature of the repairing process. The standard way to repair composite materials involves epoxying a patch of the same material over the damage. The epoxy needs time for baking and curing to be effective. This is a much more difficult and expensive task than riveting an aluminum patch over the same area. For this reason we choose an aluminum honeycomb structure for the outer walls of the HAB structure.
Landing Struts
The landing struts need to be both lightweight and strong. A historical database provides the material choices for the landing struts: aluminum, beryllium, steel and titanium. A simple stress analysis to analyze the landing loads shows that of the four materials, landing struts built out of beryllium are the lightest weight. More detail on this analysis is shown in section 5.2.6, Vehicle Sizing.
5.2.3 Shape Considerations
The shape of the HAB depends primarily upon the internal pressure applied throughout the mission. We pressurize the HAB at 1 atm, the same as on the surface of Earth. The internal volume requirements for the HAB rule out the spherical shape, the best pressure vessel, because for the necessary volume the diameter of the spherical vessel would be too large to mount on the launch vehicle. Thus, we choose a cylinder for the shape since it is the most practical shape available for the HAB. Details of the HAB vehicle sizing are provided in section 5.2.7 Vehicle Sizing.
5.2.4 Volume Breakdowns
The HAB vehicle volume breaks down into three main areas: HAB interior, HAB exterior, and propulsion system. The interior section contains everything that is within the cylindrical HAB structure as well as the cylindrical garage that the HAB sits on. The exterior section contains everything outside the cylindrical HAB but inside the HS, except for the propulsion systems, which composes the final area. The following three tables present the breakdowns for these respective areas.
Table 5.2.1 Propulsion System Volume BreakdownRCS-Tanks / Volume (m^3)
Propellant Tanks (4) / 17.49
Pressurant Tanks (2) / 6.11
RCS-Engines / Volume (m^3)
Engines (10) / 0.07
Retro Thrusters / 3.07
PROP SYSTEM TOTAL / 26.74
Tables 5.2.1 and 5.2.2 show propulsion system breakdowns and exterior volumes.
These two tables tally up the total volume of systems outside the HAB living area but inside the HS. Ideally, we want to occupy all of the volume between the HAB and the HS. In our design a considerable amount of volume is wasted because the shape of the HS is not
concentric to the HAB. The rounded triangular shape of the HS provides the necessary lift to keep the g loading at reasonable levels during Mars entry. Optimization to reduce the wasted volume is left for future work.
Table 5.2.2 Exterior Volume BreakdownExterior / Volume (m^3)
Solar Panels / 19.50
Parachutes / 2.64
Com Antenna / 0.30
Landing Gear / 0.74
EXTERIOR TOTAL / 23.18
Table 5.2.3 shows the interior volume breakdown. This table determines the size of the HAB. The total interior volume necessary on the inside of the HAB living area is 426.1 m3, and the necessary volume for the garage is 88.6 m3. The total interior volume is 514.7 m3. Figure 5.2.4 is a schematic that shows the internal layout of the vehicle.
Table 5.2.3 Interior Volume BreakdownWater / Volume (m^3)
Potable Water / 1.28
Hygienic Water / 4.22
Water Containers / 1.00
Pressurization System / Volume (m^3)
Tanks-8
4 N2 / 4.00
4 O2 / 4.56
Food / Volume (m^3)
Food / 16.99
Miscellaneous / Volume (m^3)
Crew living area / 350.00
Crew / 30.00
Ejector Seats / 4.50
Space Suits (10) / Volume (m^3)
Space Suits Regular (6) / 5.73
Space Suits- EVA (4) / 3.82
TOTAL / 426.10
Garage / Volume (m^3)
Rover / 12.00
General (Inflatables/Experiments) / 60.00
Airlock / 10.00
Generator / 6.60
TOTAL / 88.60
INTERIOR TOTAL / 514.70
Fig. 5.2.4 Schematic of internal HAB layout.
5.2.5 Weights
One of the most critical aspects of a manned Mars mission is the total weight, both during launch from Earth, as well as launch from Mars. The first previously mentioned weight is one of the primary driving forces in the mission. It costs approximately $100 million dollars to launch 1 mT (1000kg) to Mars Therefore, we determine that any weight savings are important and reduce weights wherever possible.
We present several weight breakdowns since this area is an important part of the design. First, Table 5.2.4, shows a weight breakdown of the structures that comprise the HAB.
Table 5.2.4 Structural Weight BreakdownMass (kg) / Mass (mT)
HAB / 4665.19 / 4.67
Garage / 2621.32 / 2.62
Solar Shelter / 1244.48 / 1.24
STRUCTURE TOTAL / 8530.99 / 8.53
The next breakdown is for the exterior section of the HAB. This section corresponds to the exterior referred to in section 5.2.5 Volumes.
Table 5.2.5 Exterior Weight BreakdownMass (kg) / Mass (mT)
Solar Panels / 2000 / 2
Parachutes / 1900 / 1.9
Com Antenna / 800 / 0.8
Landing Gear / 244 / 0.244
Heat Shield Attachments / 1000 / 1
NTR mating structure / 2000 / 2
Tether/Power Cable / 500 / 0.5
EXTERIOR TOTAL / 8444 / 8.444
Table 5.2.6 shows the breakdown of the interior weights of the cargo on the HAB.
Table 5.2.6 Interior Cargo Weight Breakdown
Water / Mass (kg) / Mass (mT)Potable Water / 1280 / 1.28
Hygienic Water / 4220 / 4.22
Inert Water / 360 / 0.36
Water Containers / 600 / 0.60
Gases / Mass (kg) / Mass (mT)
O_2 / 716 / 0.72
N_2 / 225 / 0.23
Pressurization System / Mass (kg) / Mass (mT)
Tanks-8 / 0.00
4 N2 / 867.5 / 0.87
4 O2 / 867.5 / 0.87
Food / Mass (kg) / Mass (mT)
Food / 1984 / 1.98
Power / Mass (kg) / Mass (mT)
Wiring, Electronics / 5000 / 5.00
Miscellaneous / Mass (kg) / Mass (mT)
Crew living area / 2000 / 2.00
Crew / 500 / 0.50
Ejector Seats / 864 / 0.86
Space Suits (10) / Mass (kg) / Mass (mT)
Space Suits Regular (6) / 330 / 0.33
Space Suits- EVA (4) / 500 / 0.50
TOTAL / 20.31
Garage / Mass (kg) / Mass (mT)
Rover / 800 / 0.80
General (Inflatables/Experiments) / 1500 / 1.50
Airlock / 3000 / 3.00
Generator / 3300 / 3.30
TOTAL / 8.60
INTERIOR TOTAL / 28.91
The next breakdown in Table 5.2.7 provides the breakdown weights of the propulsion systems. It is important to note here, there are two RCS propulsion systems en route to Mars. One is located on the HAB, and the other is located on the burnt out NTR stage on the opposite end of tether. The propulsion systems weight breakdown includes the RCS thrusters and tanks that are located on the NTR. It also includes the tether and reel system that is located on the NTR.
Table 5.2.7 Propulsion System Weight BreakdownRCS / Mass (kg) / Mass (mT)
Propellant Tanks (4) / 65.68 / 0.07
Pressurant Tanks (2) / 13.88 / 0.01
Propellant / 9730.90 / 9.73
Pressurrant / 267.19 / 0.27
Engines (10) / Mass (kg) / Mass (mT)
Per Engine / 38.68 / 0.04
Total (10) / 386.80 / 0.39
Retro Thrusters / 104.54 / 0.10
PROP SYSTEM TOTAL / 10568.99 / 10.57
Combining the previous totals with the weight of the HS gives the total launch weight of the HAB, 73.53 mT. To better understand the weight breakdown see Figure 5.2.2. This chart shows the total launch weight and its breakdown into the five major components,
Fig. 5.2.4 Weight breakdown for launch from Earth.
Once the HAB reaches Mars and lands on the surface, its weight drastically reduces. The main bulk of the weight loss occurs because the front part of the HS detaches. There are other factors that contribute to the loss such as the fuel and oxidizers burning out, and some of the consumables being eaten. The consumables contribution is very small and is negligible. Figure 5.2.3 show the same chart as Figure 5.2.2 does, except it is for landing on Mars.
Fig. 5.2.5 Weight breakdown for landing on Mars.
The weights are presented along with their percent of the total weight for both launch and landing in Table 5.2.8.
Table 5.2.8 Component Weights During Launch and Landing with % of Total WeightLaunch Weights (mT) / % Total Weight / Landing Weights (mT) / % Total Weight
Hab Structure / 8.53 / 11.60% / 8.53 / 15.91%
Propulsion System / 10.57 / 14.37% / 2.07 / 3.86%
Heat Shield / 17.07 / 23.22% / 5.65 / 10.54%
Exterior / 8.44 / 11.48% / 8.44 / 15.75%
Interior / 28.91 / 39.32% / 28.91 / 53.94%
Total / 73.53 / 53.61
The sizing of the vehicle is closely related to the volumes and weights of the individual components, and also to the materials and shape.
5.2.6 Vehicle Sizing
HAB
At this point several constraints have already been placed on the size of the HAB. The material and shape have both been determined, and also we set a minimum volume requirement for the interior of the vehicle.
The first step in the process choosing a height and diameter for the HAB that satisfies all of the requirements. Next we choose a reasonable skin thickness. With these dimensions, we perform a hoop stress analysis. The assumption for this analysis is that the HAB is a simple thin-walled cylindrical pressure vessel. The hoop stress for such a vessel is well known and is
H=pd/2t (5.2.1)1
A hoop stress in a pressure vessel is a principal stress, therefore the maximum shear stress criterion determines if the body will fail. The shear stress criterion is
1Y/SF (5.2.2)1
If this condition holds true, the body does not fail due to the internal pressure. The results of this analysis produce a hoop stress of 14.6 Mpa, which is less than one half of the yield stress of aluminum. This calculation is performed in the Microsoft Excel spreadsheet Habitat.xls in Appendix 5.2.
The next significant loading occurs during launch. The most important issue during launch is the frequencies of vibration of the vehicle. A preliminary vibration analysis shows that the natural frequencies of the HAB vehicle are larger than the natural frequencies of the ELV, which indicates that a failure due to vibration does not occur. The estimated natural frequencies of the ELV are 35 Hz and 15 Hz, in the axial and lateral directions respectively. The results of the analysis determine the HAB’s natural frequencies to be 70 Hz in the axial and 50 Hz in the lateral direction. These results are a bit high and this is due to the model used for the analysis. The HAB was assumed to be a thin cylindrical shell of uniform thickness and density. Equations 5.2.3 and 5.2.4 give the natural frequencies using this assumption. This is not a very accurate representation
(fnat)A=0.25(EA/mL)0.5 (5.2.3)2
(fnat)L=0.56(EI/mL3)0.5 (5.2.4)2
of the actual HAB, but it does give a rough estimate of what the launch frequencies would be. This calculation is also found in Habitat.xls in Appendix 5.2.
The next loading we consider is the loading during aerobraking around Mars. We use a thin walled model, with a triangular cross section to represent the HAB in this analysis. The loading is modeled as three point bending and the stress is evaluated at several location along the length of the HAB. The stress in this case is
=My/I (5.2.5)4
This stress is compared to yield stress according to Eq. 5.2.2. The Matlab code, bending_mom.m, in Appendix 5.1 is used for this analysis.
In this way we determine the proper sizing of the HAB to withstand all of the loading it experiences during the mission. We iterate on this process until the HAB satisfies all of the above loadings. This is the size of the HAB. The final dimensions of HAB are a 8.75 m diameter, and a 9.25 m height. This height breaks down to a height of 7.15 m height for the HAB living area and 2.1 m for the garage height. The thickness of the outer walls is 0.0304 m. The sizing of the HS was determined in collaboration with the Aerodynamics group. The details can be found in Section 2.1 of this report.
Landing Legs
Another type of structural analysis determines the size of the landing struts. There are two main failure modes for landing structures yield and buckling. Buckling is the major driving force in the design of the landing legs, because the landing legs are long and relatively thin. We perform the analysis on several cross sections, including a thin walled cylinder, a cylinder, and a square. A thin walled cylinder was chosen as the best shape for the legs. The reasons for this decision are they provide the lightest structural weight and that the landing legs are retractable. That is, when they are stowed en route to Mars and while on Earth, the legs are compressed. Once the Martian atmosphere is breached and the front cone of the HS falls away, the landing legs extend to the position they will be in for landing. Once on the surface after landing, the astronauts can exit the HAB, and proceed to remove the retro thruster nozzle. With this part removed, the landing legs are then compressed again to their final position and are used to lower the HAB to the ground and also to level the vehicle so it is not on a slant. The design of this type of landing system is beyond the scope of this project, but would be the ideal type of landing system for a long-term mission base. The two analyses are done simultaneously with a SF of 2, to ensure that the legs are robust enough to withstand all of the loading during the landing. The equation for stress in the yield analysis is
Y=P/An (5.2.6)
From this we find a cross sectional area that will resist yielding. With this cross sectional area, a thickness is chosen for the struts and the buckling analysis is performed. A fixed-free column buckling analysis is performed since the critical buckling load for this type of configuration is the smallest. This is a conservative calculation to provide a more robust landing system. The equation for critical buckling load with these boundary conditions is
Pcr=2EIn/4L2 (5.2.7)
The critical buckling load is equal to force applied during landing. The propulsion system was designed to provide a maximum landing acceleration of 1 m/s2. Therefore the applied landing load is
P=mHAB(gmars+aland) (5.2.8)
and is equal to 253.5 kN. Using this in the critical buckling equation, the inertia of the cross section required to withstand the landing loading is found. From the cross sectional area determined in the yield analysis, and the chosen thickness, the inertia of the landing leg can be calculated. This value is then compared to the required inertia and the process is repeated both the area and inertia of the landing leg are sufficient enough to withstand all landing loads encountered. A Matlab code was written to iterate through this process and four materials were done simultaneously: aluminum, beryllium, titanium, and steel. This file, llthin.m, is found in Appendix 5.2. The results of this analysis show that 6, 9.75 m fully extended landing legs with a 15.3 cm diameter and thickness of 1.27cm are the lightest struts that will resist failure during landing. Placing the struts around the diameter of the HAB at 60o intervals evenly distributed the landing loads. However, with the triangular cross section of the HS, extra struts are needed on the HS to provide stability during landing. Two struts provide the needed stability when they are placed at the corners of the base of the triangular cross section of the HS.