48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<br>15th AIAA 2007-2290

23 - 26 April 2007, Honolulu, Hawaii

Spherical Cryogenic Hydrogen Tank Preliminary Design

Trade Studies

Steven M. Arnold1
NASA Glenn Research Center, Cleveland, OH, 44135

Brett A. Bednarcyk2
Ohio Aerospace Institute, Cleveland, OH, 44142

Craig S. Collier3 and Phillip W. Yarrington4

Collier Research Corp., Hampton, VA, 23666

A structural analysis, sizing optimization, and weight prediction study was performed by
Collier Research Corporation and NASA Glenn on a spherical cryogenic hydrogen tank.
The tank consisted of an inner and outer wall separated by a vacuum for thermal insulation
purposes. HyperSizer®, a commercial automated structural analysis and sizing software
package was used to design the lightest feasible tank for a given overall size and
thermomechanical loading environment. Weight trade studies were completed for different
panel concepts and metallic and composite material systems. Extensive failure analyses were
performed for each combination of dimensional variables, materials, and layups to establish
the structural integrity of tank designs. Detailed stress and strain fields were computed from
operational temperature changes and pressure loads. The inner tank wall is sized by the
resulting biaxial tensile stresses which cause it to be strength driven, and leads to an
optimum panel concept that need not be stiffened. Conversely, the outer tank wall is sized by
a biaxial compressive stress field, induced by the pressure differential between atmospheric
pressure and the vacuum between the tanks, thereby causing the design to be stability driven
and thus stiffened to prevent buckling. Induced thermal stresses become a major sizing
driver when a composite or hybrid composite/metallic material systems are used for the
inner tank wall for purposes such as liners to contain the fuel and reduce hydrogen
permeation.

I. Introduction

N ASA is investing in technology development efforts and alternate fuel foundation technologies that will greatly
reduce or even eliminate environmentally harmful emissions. Because of this, liquid hydrogen (LH2) has
emerged as a propellant to supply the fuel needs for future aircraft due to its high energy per unit mass. Durable,
lightweight cryogenic propellant storage and feed systems are required to enable the development of hydrogen-
fueled aircraft. As a result, there is a need for hydrogen tank storage systems for these aircraft applications, which
are expected to provide sufficient capacity for flight durations ranging from a few minutes to several days. It is
understood that the development of a large, lightweight, reusable cryogenic liquid storage tank is crucial to meet the
goals of and supply power to hydrogen-fueled aircraft, especially for long flight durations. For short-duration flight
applications, simple tank designs may suffice. However, for longer duration flight applications, a double-wall
construction with a vacuum-based insulation system appears to be the most optimum design1, 2. Current preliminary
mission requirements that are pushing the long-flight-duration hydrogen aircraft development include 14-day (336-
hr) flight duration with a payload capacity that is sufficient to accommodate the instrumentation required for the
various missions. It is precisely these types of aircraft with relatively long flight durations on the order of days that
provide the greatest engineering challenges to develop long-term and lightweight hydrogen storage systems, since
1
Chief, Mechanics and Life Prediction Branch, ASME Member, Steven.M.Arnold@nasa.gov.
2
Senior Scientist, AIAA Member, Bednarcyk@oai.org.
3
Senior Research Engineer, AIAA Senior Member, Craig.Collier@hypersizer.com
4
Senior Research Engineer, AIAA Member, Phil.Yarrington@hypersizer.com

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This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
boiloff of the cryogenic fluid can become a significant problem. For example, space shuttle operation accepts a loss
rate (boiloff) of approximately 1.6 percent of LH2 by weight per hour, whereas for long flight duration aircraft
applications an acceptable rate of boiloff of LH2 would be on the order of 0.1 percent by weight per hour.
Consequently, the need for reduced weight in combination with good insulating properties for long-term storage
provides a new challenge for cryogenic tank design. These new designs provide an opportunity to apply advanced
materials and structural concepts in an effort to reduce the overall weight of the tank and keep the volume at an
acceptable and practical level. Although, the design of a cryogenic LH2 storage tank, coupled with the use of LH2
as aircraft fuel, involves many challenges, the most dominate structural ones include geometry, temperature,
permeation, hydrogen embrittlement, and safety factors as reviewed recently by Mital et al.1 In the present study we
will revisit prior work1, 2 and perform preliminary material and structural trade studies on a doubled-walled, vacuum
jacketed, spherical cryogenic tank concept; wherein 1) increased factors of safeties, 2) reduced strain allowables to
prevent leakage are imposed, 3) multiple failure criteria, 4) metallic inner tank liner materials are introduced, and 5)
additional materials are utilized for the sizing of both inner and outer tanks.

II. Basic Design Considerations

Multiple design configurations can be, and have been, envisioned from a single tank with insulation to hybrid
tanks with either insulating materials or pure vacuum in between walls or various combinations thereof 1. The
overall objective of the designs is to have a safe, lightweight, thermally efficient cryogenic storage system. Some
important tank system parameters relative to flight durations are presented in Table 1. The materials, tank structural
configurations, and insulation system options are numerous and interdependent. Some of these key considerations
are: 1) the functional requirement that LH2 be maintained between its freezing and boiling points, –259 °C (–435
°F) and –253 °C (–423 °F), respectively; 2) the temperature difference between ambient conditions and LH2, which
can be as high as ΔT = 300 °C (540 °F); 3) tank wall and/or liner permeation by hydrogen or just leakage of the
hydrogen through micro-cracks thus greatly impacting material selection of the tank wall and/or the need for a liner;
and 4) the CTE mismatches between the components of the tank system. There are other important issues associated
with cryogenic tank design such as vapor management (a proper vent system), fuel transfer, pumping a saturated
cryogenic fluid such as LH2, and the possibility of the cold energy utilization. However, these system design issues
are beyond the scope of this paper and thus will not be addressed here.

Table 1. Important Tank System Parameters Relative To Flight

Duration

[Listed in order of importance.]

Short flight Mass density
duration Strength and toughness
Coefficient of thermal expansion
Stiffness
Thermal diffusivity
Thermal conductivity
Long Mass density
flight Thermal conductivity
duration Strength and toughness
Coefficient of thermal expansion
Stiffness
Thermal diffusivity

One approach, to reduce the number of design choices is to turn to the concept of performance indices (e.g.,
material and structural), as put forth by Ashby3; where the performance, P, of a structural element is a function of
three, typically independent, aspects: the functional requirements, F, the geometry, G, and the properties of the
material, M, of which it is made,
P = f (F, G, M) (1)

When this group of parameters is assumed to be separable, then

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 P = f1 (F) ⋅ f2 (G) ⋅ f3 (M) (2)

In this case the functions, f1, f2, and f3 are assumed to be independent of each other; that is, the optimal choice of
materials is independent of the geometry of the structural component; thus enabling one to identify the optimal
subset of materials without solving the complete design problem. While this is clearly a simplification of the full
coupled design problem, it can provide a great deal of insight in the preliminary design stage. The key material
indices applicable for both thermal and mechanical issues of interest here are shown in Table 2. Constructing
material property diagrams [see refs. 1 and 3] for examples], enable one to assess the pertinent thermal and
mechanical performance indices given in Table 2 and provide insight in designing an efficient insulation scheme for
long duration flights. These diagrams also aid in narrowing the viable choices of engineering materials to be used.

Table 2. Performance Indices For Thermal And Mechanical Components of

Cryogenic Storage Tank

Function and constraints Performance index, maximize

Thermal
Minimum heat flux at steady state, fixed thickness 1/k
Minimum temperature rise in specified time, fixed 1/a
thickness
Maximum energy stored for given temperature rise
k/α1/2
and time
Minimum thermal distortion k/α

Mechanical
Strength-limiting design with minimum mass σf /ρ
Damage-tolerant design with minimum mass KIc/ρ
Deformation-limiting design with minimum mass E/ρ

k = thermal conductivity
a = thermal diffusivity (k/ρCp)
ρ = mass density
Cp = specific heat
α = coefficient of thermal expansion
σf = strength
KIc = mode I fracture toughness
E = Young’s modulus
Time, t = w2/2a with w = wall thickness.

Additional basic design considerations for the LH2 tank are discussed below:
Thermal Insulation
The four thermal performance indices come into play when considering designs concepts involving single or
multiple layers of insulating materials. However, these types of concepts typically require large volumes of
materials. Therefore, to deal with the significant thermal challenges the current state of the art suggests that a high
vacuum with highly polished wall surfaces, with or without a multi layer insulation (MLI) system, can provide the
required insulation needs for lightweight long-term cryogenic fluid storage applications. The MLI provides
additional insulation against radiation heat transfer relative to a simple vacuum jacket system. However, either
system is very sensitive and dependent on maintaining a very high level of vacuum, as any degradation in the
vacuum level significantly degrades the systems insulating properties, thus potentially leading to mission failure.

Tank wall material selection

When selecting tank wall material one can see from Table 2 that the most desirable materials will possess high
specific strength, high specific fracture toughness, and high specific stiffness, as well as low permeability to liquid
and gaseous hydrogen; however, no single material provides all these attributes simultaneously. In Mital et al.1 it

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was demonstrated that continuous-fiber-reinforced polymer (CFRP) composites, discontinuous reinforced metallic
composites (DRX) – specifically discontinuous reinforced aluminum (DRA)4, and metallic materials offer the best
compromise relative to the performance indices. Note, however, that the use of continuous fiber reinforced
composite materials most likely will involve higher initial manufacturing costs, while DRAs are essentially isotropic
and can be manufactured using less expensive techniques such as casting. Furthermore DRA materials have the
added benefit of extremely low (if not negligible) hydrogen gas permeability, an issue typically associated with
polymer matrix composite systems. Ceramic materials also offer high specific strength, stiffness and low
permeability, but because of their low fracture toughness they are not considered viable for tank wall material.
Two other key material properties that are important considerations for the design of high-pressure vessels but
may also be applicable to low-pressure cryogenic storage tanks are yield-before-break, KIc/σy, and the leak-before-
break, (KIc)2/σf, performance indices. Higher fracture toughness materials are desirable as they provide more
damage-tolerant systems. Any crack that propagates into the insulation system can compromise the thermal
properties of the insulation system – resulting in the loss of the mission due to rapid boiloff of the cryogenic fuel. It
should be noted that composite materials, in general, provide high specific fracture toughness, which makes them
desirable for this application. Yet, fracture toughness can become an issue especially at cryogenic temperatures,
where many materials become excessively brittle.
Lastly, there is an advantage in using monolithic materials for tank construction since using one material for the
tank wall eliminates thermally induced internal stresses due to different CTE factors of various materials such as the
typical constituents of a composite material. However, most likely monolithic metallic tanks will not be as light as
their PMC or DRX counterparts. Consequently, a metallic structure is fine for ground-based systems where weight
is not as significant of a constraint as it is for any mobile or flight (be it aeronautics or space-based) hardware
systems. It has been estimated that composites can offer a 25 percent weight savings relative to the latest monolithic
aluminum tanks in these applications5. Although, the resins used with polymer matrix composites do tend to allow
higher hydrogen permeation than metals; thus leading to the recent investigation into advanced nanoclay enhanced
resins discussed in ref. 2.

Tank wall architecture

Although material selection for the tank wall is a critical issue in the design process, tank wall geometry (albeit
single-wall or double-wall construction) is another interrelated issue. Various tank wall geometries have been
utilized in the past1, however, due to the long duration missions of interest here most likely the insulation system
utilized would be a high vacuum-based system which would dictate the use of a double-walled tank construction.
As such, herein, we will only examine a doubled-walled vacuum jacketed spherical tank system. Clearly, the shape
of the tank will affect its ability to accommodate bending stresses which will arise from fuel slosh and loads induced
at the supports. Therefore, certain geometrical shapes, such as a sphere, can minimize bending stresses better within
the wall of the tank, while cylindrical configurations or more complex conformal geometries may require selection
of a wall construction that can accommodate bending.

Liner
A linerless tank (a tank without the need for a liner) is the preferred choice in order to minimize cost, weight, and
compatibility issues. However, for advanced fiber-reinforced composites, even the state-of-the-art resin systems2
may be too permeable to contain liquid and gaseous hydrogen when subjected to high strains resulting from
mechanical and thermal loads that are characteristic of efficient tanks. In addition, the thermal cycling associated
with repeated filling and draining may cause material fatigue damage in the form of matrix microcracking, which
may result in the leakage of hydrogen. And since composite spherical tanks are subjected predominantly to biaxial
stresses, which may result in transverse microcracking at levels of strain significantly below the strain to failure, thin
metallic or nonmetallic liners may be required. In addition, since all polymeric resins are gas permeable to a certain
degree, metallic liners will be considered in the trades conducted herein.

III. Structural Analysis Approach

Herein, a structural analysis, sizing optimization, and weight prediction study is performed on a spherical
cryogenic hydrogen tank. The tank consists of an inner and outer wall separated by a vacuum for thermal insulation
purposes. The outer tank provides the vacuum jacket and carries external atmospheric pressure, while the inner tank
contains the cryogenic hydrogen under the operating internal pressure. The specific 106 inch diameter double-
walled tank design analyzed herein contains a central rod support which passes through the center of the tanks,

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protruding through the tanks at the top and bottom poles and enables the elimination of globally induced thermal
forces between tanks. The central rod support provides structural rigidity to the 102 inch diameter inner tank, a port
for filling and draining propellant, and a means of mounting the tank to the vehicle. The central rod is
approximately 10 ft long, so that the rod extends from both poles approximately 9 inches, allowing enough length
for mounting hardware to attach the tank to the vehicle structure. It was assumed to have a 4 inch diameter2.
Figure 1 depicts both the inner and outer walls of the tank via a transparency view of the corresponding finite
element mesh. The color bands represent identified optimization zones which are the fundamental structural
components that will be used by HyperSizer (see discussion in section II.A below). Each band (referred to as a
“component” within HyperSizer) can be sized independently to a different design concept (i.e., different skin
thickness, panel cross sectional dimensions, layup, etc.). In doing so, the lightest feasible tank for a given overall
size and thermomechanical loading environment may be obtained by HyperSizer.
The inner tank wall is sized based on biaxial tensile stresses, resulting from applied internal pressure, which
causes it to be strength driven, and an optimum panel concept need not be stiffened. However, the external tank wall
is sized mechanically by the pressure differential between atmospheric pressure and the vacuum between the tanks,
causing it to be stability driven and thus stiffened to prevent buckling. Other loadings that affect the design are
vehicle accelerations. Design attempts to minimize detrimental effects from tank supports were successful in
reducing localized concentrated forces, however they did cause additional wall pad up and weights at the top and
bottom tank poles caused primarily from vertical accelerations.

2
1

4
106.4 in.

Figure 1. A spherical cryogenic hydrogen tank analyzed and sized by HyperSizer, consisting of
an cinner and douter wall separated by a vacuum for thermal insulation purposes.
Optimization zones are identified by the color bands e. The left image is looking at the tank
from the side, the right image is looking at the tank from the top/bottom. Supports are attached
at the tank north5 and southf poles. A column is placed vertically between the poles.

A. Background on HyperSizer®
HyperSizer6 is a structural analysis and sizing software tool developed by the Collier Research Corp. that
automates the types of structural analyses that a typical aerospace stress engineer performs using closed-form,
empirical based, and state-of-the-art numerical solutions. HyperSizer contains specialized aerospace structures
knowledge and methods and provides a computational framework for performing non-FEA based analyses.
However, the HyperSizer software seamlessly links with NASTRAN finite element models as well, so that loads can
be extracted automatically, and then used to size a section of the structure, including the effects of stiffeners. If

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needed, HyperSizer can then update the NASTRAN model with new properties based on the sizing results of the
section. The HyperSizer approach is to perform comprehensive failure analysis for all specified load cases and
structural locations. These failure analyses are either not possible or not practical to perform with FEA. HyperSizer
analyses are very rapid as panel concepts are analyzed without the need to discretely mesh with finite elements the
shape of the stiffeners or their spacing. This permits tremendous flexibility and rapid turn around of trades with
different panel concepts all from the same coarsely meshed global structural representation. Consequently,
HyperSizer can find the lightest structural weight for a given set of candidate materials and panel concepts while
ensuring that all potential failure modes are prevented from occurring during the sizing optimization.
Typical HyperSizer analyses consist of the following seven steps:
1. Use finite element mesh to define structural geometry
2. Assign material directionalities
3. Apply boundary conditions
4. Apply load cases
5. Select material and panel concept constraints
6. Define failure criteria, limit and ultimate factors of safety, and buckling factors
7. Perform sizing analysis – where margins of safety are calculated throughout the structure

B. Finite Element Model

The NASTRAN finite element model employed was shown in Fig. 1. Both the inner and outer tanks were
meshed with 6400 NASTRAN CQUAD4 shell elements; assuming a vacuum between the tanks. The interior post
and beam support structure shown in Fig. 2 is meshed with 884 CBAR elements. This support structure is part of
the inner tank with the purpose of carrying the imposed g-loads given in Table 3. The effect of this support structure
on the outer tank design is minimal. Figure 3 shows the assigned material direction for both tanks, where the
preferred direction runs longitudinally from the north to south poles. Results from the NASTRAN finite element
model were extracted by HyperSizer and applied to various sections (“components”) of the tank. These components
(colored circumferential bands) were shown in Fig. 1. In general, the HyperSizer software enables each component
to be sized independently according to its local loads in order to minimize the overall weight of the structure.
However, because the local loads in the components near the poles of the outer tank are highly dependent on the
design of the attachments between the inner and outer tanks at the poles, the preliminary sizing of the outer tank was
performed based solely on a component at the tank equator, the sizing component indicated in Fig. 3. Thus, the
minimum acceptable unit weight (weight per unit area) determined by HyperSizer for this component was multiplied
by the total outer tank area (i.e., 247 ft2) to arrive at the estimate for the outer tank weight. Similarly, the weight
estimate for the inner tank is established by multiplying the resulting weight per unit area by the total inner tank area
of 228 ft2.

Outer Tank
Polar Region

Inner Tank
Polar Region

Figure 2. Beam elements are used to transfer the vertical pole (green) and boundary
condition concentrated forces to the four polar rings to support both inner and outer tank
walls.

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 Sizing
Component

Figure 3. HyperSizer graphics of material angles used to determine the direction of

primary stiffening as well as the 0 degree reference for composite materials.

C. Load Factors, Failure Criteria, Buckling Factors and Verification

Mechanical loads on the tanks are derived from (1) the difference between the pressure within the tank and the
ambient conditions, (2) fuel weight, (3) vehicle acceleration loads, (4) fuel slosh due to aircraft maneuvers, and (5)
tank system weight and its supports. Fuel slosh is bound to be encountered as the aircraft maneuvers or as it
encounters air turbulence during the flight. Consequently, six independent and seven combined load cases (LC) were
examined as summarized in Table 3. The first six cases are the unique fundamental mechanical loadings cases. The
3.5g anticipated acceleration is added to gravity for a net 4.5g load vertical acceleration LC. With load cases 7
through 12 being derivative cases that are a combined superposition of the fundamental load cases, 1 through 6.
Case 13 is the thermal condition that is superimposed on all the mechanical conditions. The highlighted cases are the
three controlling load cases that sized the inner and outer tanks. The outer tank wall is sized by LC 2 and the inner
wall is sized by LC 12 & 13 superimposed. The other load cases were identified separately for early trade studies.
The pressures were applied to the NASTRAN FEM using PLOAD4 data type. This included the internal and
external static pressures and the hydrostatic head from acceleration, i.e., head pressure = density * acceleration*
height of tank. The horizontal pressure was applied likewise. The dry mass of the walls were included as Non-
Structural Mass (NSM) on the element data records and their inertia acceleration applied with GRAVITY data type.
The NSM was entered automatically from HyperSizer.

Table 3. Load Cases

LC Loading Combined Load Sets
1 Static 30 psi internal fuel pressure
2 Static 14.7 psi external atmospheric pressure (worst case)
3 4.5g vertical acceleration - of the fuel
4 4.5g vertical acceleration - of the tank structure
5 0.5g lateral acceleration - of the fuel
6 0.5g lateral acceleration - of the tank structure
7 Vertical acceleration (fuel + structure) 3, 4
8 Lateral acceleration (fuel + structure) 5, 6
9 Total acceleration 3, 4, 5, 6
10 Static 30 psi + vertical acceleration 1, 3, 4
11 Static 30 psi + horizontal acceleration 1, 5, 6
12 Static 30 psi + total acceleration 1, 3, 4, 5, 6
13 Thermal: -423°F internal tank, 72°F external tank

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Typically FEM is used to compute internal design-to forces; however in the present spherical tank problem the
primary driving pressure induced hoop loads can be calculated without the need of FEA. Yet FEA is required to
quantify wall forces due to acceleration loadings; however these loadings were found to produce only secondary
effects. The inner wall internal (outward) pressure and outer wall external (inward) pressure can be determined quite
accurately with closed form equations, below:

Internal wall running loads resulting from the 30 psi delta pressure.

Pr 30(51.19)
NX = Ny = = = 768 (lb / in ) (3)
2 2
External wall running loads resulting from the -14.69 psi delta pressure.

Pr −14.69(53.21)
NX = Ny = = = −390.8 (lb / in) (4)
2 2
The thermally induced stresses, when applicable, can also be calculated in closed form without the need of FEA.
HyperSizer automatically does this by using the materials thermal coefficients, elastic modulus, reference
temperature, and operating temperature. This capability was used to quantify the resulting thermally-induced
stresses between the composite and metallic liner.
Total mass and acceleration forces were verified with FEA diagnostic. The FEA solution was verified to have
net zero forces on FEM grid constraints (SPC) for pressure, thus indicating that the loads were in balance and these
same forces were equal to the closed form computed net force caused by acceleration. The FEA computed outer
wall forces had an extremely slight variation in them (i.e., Nx and Ny ranged between 385-390 lb/in), the largest
deviation being in the polar regions. The inner tank had larger, but still small variations in forces. The polar caps had
bending moments that caused the inner wall to deform significantly when unstiffened. The solution was to stiffen
these north and south pole regions. Similarly, the typical process of iterating between FEA and HyperSizer to obtain
convergence of loading was done; in this case the issue is bending moments on the inner wall panels caused by
vertical acceleration and the changing reference plane due to panel thickness sizing.

D. Load Factors, Failure Criteria, Buckling Factors and Verification

Load Factors
A limit load factor of 1.33, and an ultimate load factor of 1.65 where utilized throughout the analysis. These
factors are thought to be appropriate for pressurized vessels even though NASA typically uses an ultimate load
factor of 2.0 for space flight pressure vessels. These factors are higher than those used in ref. 2, which used a limit
load factor = 1.0, and ultimate load factor of = 1.5 in accordance with U.S. federal aviation regulations (U.S. FAA7),
and had an impact of not only increasing the weight slightly but also modified the final selected stiffening concept
for the outer tank.

Composite Failure Criteria

Different failure criteria are appropriate for different tank hardware. HyperSizer has a large body of test data
embedded in its database associated with composite materials at cryogenic temperatures and has specific correlation
factors for almost all commonly used failure criteria; with the Tsai-Hahn criteria having the best correlation to test
data. Herein, seven failure criteria were examined during the analysis of the outer tank, i.e., maximum strain,
maximum stress, Tsai-Hill, Tsai-Wu, Tsai-Hahn, Hoffman, and LaRC03. However, for the inner tank wall (which in
stark contrast to the outer tank is subjected to cryogenic temperatures) a different composite analysis approach is
required because of the need to reduce or eliminate permeation of the hydrogen due to thermally induced matrix
cracking. Consequently, for this analysis, we chose to employ the maximum strain in the fiber direction as the
failure criteria, with an imposed reduced strain allowable of 0.006 in/in.

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 Panel Buckling
Curved panel buckling analysis, a buckling knockdown factor and buckling lengths must be specified. The
buckling knockdown factor is employed to correlate theoretical (Raleigh-Ritz) curved panel buckling loads (which
are typically highly non-conservative) with experimental buckling loads. This is due to the fact that curved panel
buckling is highly dependent on slight variations in thickness and flaws that occur randomly in structures. The
necessary buckling knockdown factor is also a function of thickness, as the small variations and flaws become of
greater importance as the structure becomes thinner8, 9. The buckling lengths characterize the controlling buckling
mode shapes for the curved panel and are a function of the thickness and radius of curvature of the panel. These
buckling lengths must be verified through an independent finite element analysis of the curved panel.
Given the fact that the outer tank is subjected to a state of biaxial compression and thus its sizing is stability
driven, performing an accurate buckling analysis is critical. Consequently, due to the curvature of tank walls we
chose to employ the cylindrical Raleigh Ritz energy solution contained within HyperSizer instead of the more
commonly used flat plate closed form solution, even though the optimization run times are longer. Although, this
cylindrical solution fully accounts for anisotropic panel stiffness’s, it is limited to single curvature. Thus to account
for the spherical shape, the buckling lengths were calibrated to FEA eigenvalue analyses. An FEA eigenvalue
analysis was performed to measure the distance of the sphere half mode shapes which were assigned as a
HyperSizer buckling length. In the case of a stiffened panel this length was 7 inches, whereas in the unstiffened case
it was 6 inches, see Fig. 4 and Table 4.

Figure 4. FEA eigenvalue determination of appropriate buckling span for the outer wall. The left
mode shape is for a stiffened panel that shows 7” half modes. The right mode shape is for an
unstiffened panel and shows 6” modes.

Table 4 provides the factors of safety, buckling lengths, and buckling knockdown factors employed in the sizing of
the outer tank. In HyperSizer, global buckling, such as panel buckling, crippling, and buckling-crippling interaction
are treated as ultimate failure events and thus employ the ultimate load factor. Local buckling, on the other hand, is
a local failure event and the structure can typically support a great deal of additional load prior to collapse after the
onset of local buckling as stresses are redistributed10. Consequently, local buckling of the facesheet and the grid
stiffeners within HyperSizer thus employ the limit load factor. The buckling knockdown factors employed are based
on NASA SP80078 which penalizes theoretical buckling loads as a function of the (r/t) ratio, which is radius divided
by thickness. Furthermore, HyperSizer adds to the methods of NASA SP8007 by including the effects of the D11,
D22, and D33 bending stiffness terms and reliability analysis, see ref. 9. These factors are different for the stiffened
and unstiffened configurations because they have different effective thicknesses.

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 Table 4..Factors of safety and buckling parameters used in the outer tank sizing.
Limit Load Factor Ultimate Load Factor Buckling Lengths Buckling
Concept
(Local Buckling) (Global Buckling, Crippling) (in) Knockdown Factor
Unstiffened 1.33 1.65 6×6 0.4
Grid
1.33 1.65 7×7 0.75
Stiffened

An assessment was also made as to whether the overall global linear elastic deformations of the inner and outer
walls are compatible. The issue is the possible ballooning type deformation of the unstiffened inner wall due to
internal pressurization, and a tear drop type deformation due to vertical acceleration and inertia of the fuel mass. The
concern is that the inner tank wall will displace beyond the 2 inch clearance available between it and the outer tank
wall, and thus bear against it. The correct analysis would entail a non-linear geometric FEA solution; however, this
level of analysis detail is beyond the scope of the present paper. A non-linear FEA analysis (for the acceleration load
case) however, would likely show deformations smaller than the linear elastic analysis, which computes
displacements based on bending stiffness only of the panels and does not include membrane resistance to curvature
(think of a sagging cable resisted by tensile forces). So for this reason, it is assumed that the linear static FEA
analysis conservatively computes total, overall wall displacements. In the present case it showed a total
displacement of the inner tank wall of only 0.39 inches. This is well below the available 2 inch clearance between
inner and outer tanks.

E. Materials
Given our initial screening of materials via the performance indices described earlier, four basic materials were
selected for study. Three were isotropic metallic based materials (i.e., Al 2024, LiAl 2090 and DRA (with 20% and
55% particle volume content) and the fourth was a continuous graphite reinforced polymeric composite (i.e.,
IM7/977-2) with a fiber volume fraction of 60%. The material properties employed are given in Table 5; where the
IM7/977-2 system ply-level properties are given. The composition of the DRA material is Al-10Si-1Mg with 20% or
55% SiC particles11.
Many different layup ply orientation percentages were attempted, but because of the biaxial nature of the hoop
loading, the optimum layups tended to be those that had equal amounts of 0 and 90 degree plies. The layup that was
settled on was an 8-ply quasi isotropic, symmetric laminate, i.e. [45/-45/0/90]s, where during sizing the individual
ply thicknesses were uniformly scaled so as to achieve positive margins. Each ply utilized the properties given in
Table 5. It should also be noted that the allowables of the ply material, as given in Table 5, have also been knocked
down to account for matrix cracking, which must be avoided in a pressure vessel configuration. For our baseline
inner tank wall we chose a more established material: Al 2024 T81. The -423oF strength data used shows it to
increase dramatically as compared to room temperature strength. This is questionable and could cause this material
to be less weight competitive than currently quantified. Lastly since the external tank wall is subjected to a
compressive state and thus stability driven, those materials in Table 5 with high specific stiffness’s, i.e., DRA and
graphite/epoxy, should be the best outer tank candidate materials.

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 Table 5. Material properties.
DRA DRA Graphite/Epoxy*
Property LiAl 2090 Al 2024 T81
20% 55% IM7/977-2 Ply
ρ (lb/in3) 0.0975 0.11 0.099 0.11 0.057
RT -423oF RT -423oF RT RT RT -423oF
E1 tension (Msi) 11.6 12.9 10.5 11.8 15.7 29 23.3 20.8
E1 compression
11.6 12.9 10.5 12 15.7 29 21.5 20.4
(Msi)
E2 tension (Msi) 11.6 12.9 10.5 11.8 15.7 29 1.35 2.8
E2 compression
11.6 12.9 10.5 12 15.7 29 1.35 2.8
(Msi)
ν12 0.315 0.301 0.313 0.283 0.33 0.24 0.3 0.3
G12 (Msi) 4.41 4.96 4 4.6 6.04 11.7 0.75 1.16
αL=-0.1 αL=--0.3
α (x10-6/oF) 12.1 0.02 12.55 8.5 9.28 5.6
αT=15 αT=15
Stress Allowables
σ 11u tension (ksi) 72.5 78 67 100 50 55 139.8 124.8
σ 11u compression 72.5 78 67 100 50 55 129 122.4
(ksi)
σ 22u tension (ksi) 72.5 78 67 100 50 55 8.1 16.9
σ 22u compression
72.5 78 67 100 50 55 8.1 16.9
(ksi)
σ 11y tension (ksi) 68.2 73 59 88 35 30 139.8 124.8
σ 11y compression 68.2 73 59 88 35 30 129 122.4
(ksi)
σ 22y tension (ksi) 68.2 73 58 88 35 30 8.1 16.9
σ 22y compression
68.2 73 58 88 35 30 8.1 16.9
(ksi)
τ 12u (ksi) 54 54 40 39 39 39 11.6 15.8
* Considered both standard and reduced (0.006 in/in) strain allowables.

IV. Inner Tank Sizing Results

Here sizing results are presented for the unstiffened portion of the inner tank wall. We begin by examining a
representative acreage component, see Fig. 3, subjected to the fundamental load case 1 which results in biaxial
circumferential tensile forces. Note no minimum gage constraint has been imposed on the facesheet or liner
thicknesses, as only structural viability, and not permeability or manufacturability is being assessed. Table 6 shows
the resulting panel unit weights considering the five materials given in Table 5. Clearly, the graphite/epoxy,
IM7/977-2, system is significantly lighter than the comparable metallic based designs as one might suspect since the
specific strength of this PMC system is significantly greater than its metallic counterparts. Also when reduced strain
allowables are utilized for the Gr/Ep system wall thickness is increased as is tank weight. Further it is interesting to
note that a linerless IM7/977-2 concept (even when strain allowables are reduced to ensure no microcracking) is 23
% lighter than the lightest of the Gr/Ep with metallic liner systems considered.

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 Table 6. Results of inner tank wall trade studies when subjected to 30 psi internal pressure only at RT.
Material Material Liner Total Unit Weight
Thick. Matl & Thickness Weight (lb)
(in) thickness (in) (psf)
Gr/Ep 1 0.0154 none 0.0154 0.126 28.7
Gr/Ep 2 0.0198 none 0.0198 0.162 36.9
Gr/Ep 0.0154 0.00591” LiAL 2090 0.0213 0.2094 47.7
Gr/Ep 0.0154 0.00606” Al 2024 0.0215 0.2145 48.9
Gr/Ep 0.022 0.01667” DRA 20% 0.0387 0.4182 95.3
Gr/Ep 0.044 0.01939” DRA 55% 0.0634 0.6683 152
LiAL 2090 0.0176 NA 0.0176 0.2467 56.2
Al 2024 0.0189 NA 0.0189 0.2754 62.8
DRA 20% 0.0292 NA 0.0292 0.4161 94.9
DRA 55% 0.0341 NA 0.0341 0.5393 123
1
MS for Gr/Ep = min of (max strain, Tsai-Hahn)
2
MS for Gr/Ep = min of (max strain, Tsai-Hahn), with reduced leak criteria strain allowable of
0.006 in/in this is a baseline case w/o a liner
In order to demonstrate that the 30 psi internal pressure is the dominant loading case for sizing the inner tank
wall, a similar sizing analysis for the four metallic materials was conducted, but with the sizing component force
resultants obtained via a finite element analysis using load case 12 of Table 3. Clearly, the resulting inner tank
weights (see Table 7) are increased by less than 7% thereby substantiating our earlier hypothesis, that acceleration
loads produce only secondary effects.

Table 7. Sizing results for inner tank wall when both 30 psi internal pressure and all accelerations
from Table 3, load case 12, are examined at room temperature.
Material Material Total Unit Weight (lb)
Thick. (in) Thickness (in) Weight (psf)
LiAL 2090 Varies slightly Varies slightly Avg. 0.2610 59.5
Al 2024 Varies slightly Varies slightly Avg. 0.2926 66.7
DRA 20% Varies slightly Varies slightly Avg. 0.4424 101
DRA 55% Varies slightly Varies slightly Avg. 0.5735 131

As the inner wall (and not the outer wall) is subjected to a severe thermal environment, trade studies must be
conducted under combined mechanical and thermal load histories. Note in general the stress allowable will be
greater at cryogenic temperatures, see Table 5. Also, within HyperSizer thermo-elastic lamination theory is utilized
to perform a ply-by-ply failure analysis wherein internal thermal residual stresses due to thermal expansion
mismatch are account for. Table 8 presents inner tank weight results given a combined 30 psi internal pressure and
a -423oF thermal loading. Note that the reduced leak criteria strain allowable of 0.006 in/in, for both RT (room
temperature) and -423oF temperatures, was applied. Interaction failure criteria are known to work well with RT
material strength properties, but are questionable at cryogenic temperatures, as demonstrated by the fact that when
the interaction criteria were turned on the laminate could not size due to internal thermal stresses. Consequently, for
the combined thermal-mechanical case only the maximum strain failure theory was considered. When the maximum
strain in the 1 direction (fiber direction) was activated the laminate sized strictly to fiber strain. Alternatively, when
the maximum strain in the 2 direction was used, the laminate could not size again without exceeding the matrix
strain allowable due to the thermal residual stress/strain developed from the large change in temperature. This
explains why the baseline graphite/epoxy case without a liner found in Table 8 has the same weight (36.9 lbs) as it
does in Table 6, i.e., in both cases, the inner tank was sized by the reduced 0.006 in/in strain allowable. Thus it can
be concluded that matrix cracking within the Gr/Ep system should be expected to occur just from thermal loading

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alone. Consequently, some type of liner material would be required to ensure no hydrogen permeation. This is in
sharp contrast to the conclusion found in previous work2 for a nanoclay enhanced resin system, wherein
approximately 2.5 times the current matrix strain allowable was used.

Table 8: Results of inner tank wall material and unstiffened panel weight trade studies. Loading consists of
30 psi internal pressure and -423 oF temperature differential. Area = 228 ft2
Material Material Liner Total Unit Weight
Thickness (in) Material Thickness Thickness (in) Weight (psf) (lb)
Gr/Ep 0.0198 none 0.0198 0.162 36.9

Gr/Ep 0.011 0.01526” 0.02626 0.3045 69.4

LiAL 2090
Gr/Ep 0.011 0.00943” 0.0204 0.2274 51.8
Al 2024
Al 2024 0.01269 NA 0.01269 0.1845 42.0

LiAL 0.01636 NA 0.01636 0.2293 52.3

2090

As one might expect, the monolithic, Al 2024 T81, tank actually sized up to be 33% lighter at -423 oF than at RT
(i.e., 42 lbs versus 62.8 lbs) due to the fact that the cryogenic strength properties are 50% higher than RT properties
(see Table 5). This increase in strength, however, is questionable as it was based on behavior of AL 2024 T81
tempered rod and bar forms per MIL-HDBK-5E12. Note, however, in the case of Gr/Ep tanks with metallic liners
the thickness of the metallic liners slightly increased (and thus the inner tank weight) as a result of the additional
induced thermal stresses within the tank, compare Table 6 with Table 8. Lastly, due to the lack of cryogenic data for
the DRA material no additional results beyond those of Tables 6 and 7 can be reported for the imposed thermal
environment. Furthermore, thermal material incompatibility prevented a workable design for the case of a DRA liner
and Gr/Ep inner tank.

V. Outer Tank Sizing Results

As stated earlier the outer tank wall is sized mechanically by the pressure differential between atmospheric
pressure and vacuum (a biaxial compressive loading condition), causing the controlling failure analysis to be
stability driven. Consequently, specific compressive stiffness, Ec/ρ, is more important than specific strength. One
clear option to lighten the design is to stiffen the outer tank to prevent buckling. The grid stiffened structural
concepts considered for the outer tank sizing are shown in Fig. 5. For comparison purposes an unstiffened uniform
thickness concept, for each material was also considered. It should be noted that HyperSizer admits a great deal of
freedom in optimizing the grid stiffened panels shown in Fig. 5. For instance, the iso-grid panel concept allows the
grid stiffeners in each direction to be independent materials and have independent heights, thicknesses, and spacing.
For the sizing performed in this section, many of these sizing variables were linked such that the entire panel was
required to be the same material, while four independent geometric variables remained. These four independent
geometric variables are: facesheet thickness, stiffener thickness, stiffener height, and stiffener spacing. HyperSizer
optimizes the panel by varying these geometric variables, each within a specified range, while also varying the
materials and or concepts in order to determine the lightest weight configuration that satisfies all failure analysis
checks. Note that, since within a sphere the hoop loads are the same in both directions (with near zero in-plane
shear) the angle-grid and bi-grid are essentially equivalent designs; as it is merely a matter of orientation of the
stiffening ribs in relation to the sphere, which has no effect. Consequently, HyperSizer would obtain the same
optimum weight for either angle-grid or bi-grid concepts for the analytical biaxial loads (see Eq. 3). Furthermore,
note that both concepts may be slightly lighter and/or easier to fabricate than the iso-grid concept.

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 60°

Figure 5: HyperSizer grid stiffened panel concepts considered in the sizing of the outer tank.

Sizing results of the outer tank are summarized in Table 9, where the table is divided into stiffened and
unstiffened configurations. Recall that the weight for each design is simply the unit weight determined by the
HyperSizer sizing optimization multiplied by the tank area (247 ft2). For the unstiffened configurations, the only
design parameter is the tank thickness, and in all five cases curved panel buckling was the controlling failure
mechanism. For the grid stiffened configurations, the four geometric design parameters are given in Table 9.
Further, the table indicates that a bi-grid configuration was chosen as the optimum for all materials except the
graphite/epoxy system, which utilized an iso-grid configuration. In addition, the controlling failure mode for the
stiffened LiAl 2090 was curved panel buckling, while for the Al 2024, DRAs and graphite/epoxy stiffened panels;
the controlling failure mode was crippling-buckling interaction.
In terms of the weights for each outer tank designs, Table 9 indicates that all stiffened configurations are lighter
than all unstiffened configurations. The graphite/epoxy composite design was the lightest material choice for both
the stiffened and unstiffened configurations; with the 55% DRA material system being a close second, especially in
the stiffened configuration. Given the assumptions employed in the sizing analysis outlined previously, the iso-grid
stiffened graphite/epoxy composite system provided the lowest overall weight at 108 lbs. However, the 55% DRA
and 20% DRA bi-grid configurations were also very lightweight at 111 and 129 lbs, respectively and could possibly
be a better choice if the manufacturing costs (likely dominated by machining (or casting) of the grid stiffeners) were
significantly lower than the PMC composite manufacturing costs. Remember, these weights are for the acreage area
of the tank, and do not include the closeout and fitting material required to withstand the localized forces at the tank
attachments. The non-optimum weight factor within HyperSizer was set to 1.0, meaning these are ideal weights that
do not include such closeout details and items such as weld fillets, brackets, clips, etc. Traditional non-optimum
weight factors account for added weight and analysis inaccuracies. A range of 1.2 to 1.5 has been used in the past.
However, we believe that HyperSizer is considerably more accurate than previous weight prediction analysis tools
to the point where the non-optimum weight factor should be based strictly on historical data that compares as
fabricated weights to theoretical weights, and should not include analysis inaccuracy. For this reason, if one applies
a weight non-optimum, it should be on the low range of traditionally used values.

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 Table 9. Summary of outer tank designs performed at RT.
Design Solution Unit Weight Facesheet Stiffener Stiffener Stiffener Controlling
Weight (lb) Thickness Thickness Height Spacing Failure Mode
(lb/ft2) (in) (in) (in) (in)
Aluminum Curved Panel
(LiAl 2090) 1.862 460 0.1326 – – – Buckling
Aluminum Curved Panel
1.973 487 0.1356 – – –
Unstiffened

(2024-T81) Buckling
DRA 20% Curved Panel
1.691 418 0.1186 – – –
Buckling
DRA 55% Curved Panel
1.490 368 0.0941 – – –
Buckling
Graphite/ Curved Panel
1.246 307 0.1518 – – –
Epoxy Buckling
LiAl 2090 Curved Panel
0.557 138 0.019 0.015 0.35 0.5
(bi-grid) Buckling
Al 2024-T81 Crippling-
(bi-grid) 0.606 150 0.019 0.016 0.36 0.5 Buckling
Interaction
DRA 20% Crippling-
Stiffened

(bi-grid) 0.524 129 0.018* 0.014* 0.34 0.5 Buckling

Interaction
DRA 55% Crippling-
(bi-grid) 0.448 111 0.017* 0.011* 0.31 0.6 Buckling
Interaction
Graphite/ Crippling-
Epoxy 0.436 108 0.033 0.0154 0.31 0.7 Buckling
(iso-grid) Interaction
Graphite/ Crippling-
Epoxy @-70oF 0.428 106 0.0242 0.0198 0.29 0.6 Buckling
(iso-grid) Interaction
* A manufacturing minimum gage limit may need to be applied.
.
Recall that the sizing analysis performed on the outer tank did not consider any thermal loading. Yet from our
inner tank work, one might suspect that the sizing of the outer tank, given a graphite/epoxy material system, would
be affected by any temperature change as the graphite/epoxy plies exhibit thermal expansion mismatches that give
rise to thermally induced stresses that combine with the mechanically induced stresses. Consequently, a single sizing
analysis involving a Gr/Ep outer tank at altitude (i.e. 65,000ft which results in an outer tank surface temperature of -
70oF, see ref. 2) was conducted. The result is shown in the last row of Table 9, where it is clear that the resulting
outer tank weight is slightly lower (106 lbs) as compared to the ground based, i.e., RT, weight of 108 lbs. Thus
indicating that ground conditions are controlling for the sizing of the outer tank and that microcracking due to
thermally induced stresses, at altitude, is not a concern.
Note, if minimum gage manufacturing limits are imposed the outer tank weight will increase significantly. For
example, in the case of 55% DRA, when a minimum gage of 0.03 inches is imposed the outer tank weight increases
from 111 lbs to 160 lbs and the controlling failure mode would switch from crippling buckling interaction to that of
face sheet local buckling. Also, note the weights in Table 9 are based on membrane compressive forces, and do not
include the outer fiber stresses/strain variations caused by secondary bending moments due to pressure on the
facesheet skin as supported between the rib stiffeners. Since this is a strength driven effect, the DRA materials will
still be better performing as compared to the Al 2024 and LiAL 2090 materials, but the advantage may not be as
great. Including these additional stresses and strains may exceed the material’s yield stress but not the materials
ultimate stress; meaning the panel could withstand the loading without static failure. However, allowing the panel to
go beyond the material yield could present a fatigue concern, and also in essence, the skin pockets would be in a
post buckled mode shape that could present other operational disadvantages.

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 Lastly, the entire outer tank was sized (not just a representative acreage component) given the resulting FEA
distribution of loadings. Figures 6, 7 and 8 illustrate the outer tank wall unit weight, margin of safety, and
controlling failure mode distribution over the entire outer tank results, respectively. In Fig. 6 one clearly sees how
the polar regions pad up (become thicker and thus heavier) to accommodate the increased loads in these regions due
to bending and load transfer from the center post. Figure 7 depicts how uniform and close to zero (i.e., MS = 0.001
to 0.006) the margin of safety is over the entire outer tank wall, thus indicating the near optimum solution that was
obtain. Finally, Fig. 8 shows that over 85% of the outer tank is controlled by crippling-buckling interaction failure
criteria, while in the polar regions both strength and local buckling modes are controlling instead.

Figure 6. Outer wall unit weights of iso-grid stiffened panel concept, wherein the magenta color
indicates lightest weight and red the heaviest weight. Figure on left represents the north pole
and the right side the south pole.

Figure 7. Outer wall minimum margin-of-safety (MS) for all failure modes. Color variation shows
a range of MS from 0.001(blue) to 0.006 (orange), which are very desirable since they are close to
zero. This shows a very near optimum solution on the entire tank wall.

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 Figure 8. Illustrates the controlling failure modes for the outer tank wall. Same result for opposite
polar region.

VI. Conclusion
A structural analysis and sizing optimization study was performed on a doubled-wall spherical cryogenic
hydrogen tank concept. The tank consists of an inner and outer wall separated by a vacuum for thermal insulation
purposes. The outer tank provides the vacuum jacket and carries external atmospheric pressure, while the inner tank
contains the cryogenic liquid hydrogen under the operating internal pressure. Weight trade studies were completed
for different panel concepts and material systems (both metallic and composite). Extensive failure analyses were
also performed for each combination of dimensional variables, materials, and layups to establish structural integrity
of the various tank designs. Detailed stresses and strains were computed from operational temperature changes and
pressure loads for both inner and outer tanks. Results demonstrate that composite materials (e.g., PMCs, and
DRAs), with their tailorable stiffness and strength properties lead to lower mass outer tank designs as compared with
traditional metal tank designs. Furthermore, Gr/Ep (i.e., IM7/977-2) based inner tank designs will exhibit
microcracking due to thermally induced stresses. As a result Gr/Ep inner tank designs will require a liner material to
ensure no hydrogen permeation (both through microcracking and thinness of gage), unless the nanoclay enhanced
graphite/epoxy systems discussed in Sullivan et al2 are shown to be viable.
The final baseline estimated metallic based tank weight came in at about 153 lbs for both inner (mostly
unstiffened Al 2024 = 42 lbs) and outer (bi-grid stiffened DRA 55% = 111 lbs) tank walls. With the graphite/epoxy
based design weight coming in at 160 lbs for both inner (Gr/Ep with Al2024 liner = 51.8 lbs) and outer (iso-grid
stiffened Gr/Ep = 108 lbs) tank walls. Note if the Gr/Ep based tank design’s inner tank is replaced with an all
aluminum inner tank (i.e., Al 2024) the overall weight is decreased to 150 lbs. Either composite/hybrid design is
approximately 10 to 16% lighter than the lightest weight alternative all monolithic metallic design of 180 lbs, inner
tank (Al 2024 = 42lbs) and outer tank (bi grid LiAl 2090 = 138 lbs). Note, although higher factors of safety and
lower strain allowables were imposed in this study as compared with previous work2, the final overall hybrid tank
system weight (composed of an Al 2024 inner tank and Gr/Ep outer tank) was approximately 60 lbs lighter. This
decrease in weight is mainly attributable to the fact that no minimum gage thickness was imposed in this study; with
the result being a 3 times thinner inner tank wall thickness as compared to previous work2. Clearly then weight
growth is to be expected, due to minimum gage thickness either for manufacturing limitations or for hydrogen
permeation requirements, as well as closeout details and items such as weld fillets, brackets, clips, etc. The final
choice regarding which tank design would be selected will most likely be determined by manufacturing and
inspectability costs and requirements.

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 References
1
Mital, S.K., Gyekenyesi, J.Z., Arnold, S.M., Sullivan, R.M., Manderscheid, J.M., and Murthy, P.L.N, “Review of Current
State of the Art and Key Design Issues With Potential Solutions for Liquid Hydrogen Cryogenic Storage Tank Structures for
Aircraft Applications, NASA TM-2006-214346, October 2006.
2
Sullivan, R.M., Palko, J.L., Tornabene, R.T., Bednarcyk, B.A., Powers, L.M., Mital, S.K., Smith, L.M, Wang, X.J., and
Hunter, J.E., “Engineering Analysis Studies for Preliminary Design of Lightweight Cryogenic Hydrogen Tanks in UAV
Applications”, NASA TP-2006-214094, May 2006.
3
Ashby, M.F., Materials Selection in Mechanical Design, 3rd ed, Elsevier Butterworth-Heinemann, Oxford, England, 2005.
4
Miracle,D.B., “Metal Matrix Composites for Space Systems: Current Uses and Future Opportunities. Affordable Metal-
matrix Composites for High Performance Applications, Awadh B. Pandey, Kevin L. Kendig, and Thomas, J. Watson, eds., TMS ,
Warrendale, PA, 2001, pp. 1-21.
5
Sharke, P., “Technology Focus. Fluid Handling and Fluid Power. H2 Tank Testing.” Mechanical Engineering, April 2004.
6
HyperSizer Structural Sizing Software, Collier Research Corp., Hampton, VA, http://www.hypersizer.com, 2006.
7
Federal Aviation Administration Regulation. FAR section 27.303. http://www.flightsimaviation.com/data/FARS/part_27-
303.html, Accessed Mar. 16, 2006.
8
NASA Space Vehicle Design Criteria, NASA – SP8007 Buckling of Thin Walled Cylinders, National Aeronautics and Space
Administration, Office of Advanced Research and Technology, Washington, D.C., August 1968.
9
Collier C. and Yarrington, P., “Consistent Structural Integrity in Preliminary Design", 46th AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics & Materials Conference, Austin, TX, April 2005.
10
Collier, C., Yarrington, P., and Van West, B., “Composite, Grid-Stiffened Panel Design for Post Buckling Using
HyperSizer”, AIAA−2002−1222, 2002.
11
Arnold, S.M., Powers, L., and Glovan, R., “Design/Analysis and Manufacturability of Lightweight, Hybrid,
Discontinuously Reinforced Aluminum Flat-Faced Propellant Duct Flanges”, NASA TM-2004-213130, July 2004.
12
Mil-Hdbk-5, Metallic materials: DOD, pages 3-87 and 3-88.
13
Mil-Hdbk-17-3E, Composite materials: DOD Coordination Working Draft, 1998

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