Airship Buoyancy Control Using Inflatable Vacuum

JOURNAL OF AIRCRAFT
Vol. , No. ,
Airship Buoyancy Control Using Inflatable Vacuum Chambers
Sean A. Barton∗
Florida State University, Tallahassee, Florida 32306
DOI: 10.2514/1.C031654
1
Buoyancy control is identified as a significant problem in airships, past and present. An existing proposal to
enhance the control of buoyancy in lighter-than-air aircraft is reviewed, and a new method of buoyancy control (the
inflatable vacuum chamber) is proposed. The differences between the existing proposal and new proposal are
highlighted, including the new possibility of an airship that lands vertically onto the ground without a mooring mast, a
ground handling party, or a runway. Theory of lightweight stiff inflatable structures is discussed and a specific design
and construction method is proposed. The design is optimized and confirmed elastically stable; design specifications
are given. A typical operation cycle (including liftoff, flight, and touchdown) is detailed. An area of potential
theoretical advancement is identified.
I.
techniques involving pressurization or compression appear to be
more practical than those involving heating or liquefaction.
The new Aeroscraft (Worldwide Aeros Corporation) is anticipated
to use compressed air storage to control buoyancy reversibly. The
Aeroscraft will be outfitted with high-pressure tanks in which air can
be pumped to gradually increase the weight of the ship. When the
tanks are full, weight can be discharged rapidly by venting the tanks.
This capability could assist with fuel weight compensation, vertical
ground takeoff (instead of mooring), and rapid loading of cargo. But
without a method of rapidly adding weight the operations of vertical
ground landing and rapid unloading of cargo remain difficult. These
cannot be accomplished with a compressed air tank, because air
pumps are too slow or too heavy. It can be shown that if the pump is
of equal weight as the storage container, it could take hours to fill
the tank, yet only seconds to empty it. Thus, rapidly and reversibly
adding weight to an airship in-flight can be accomplished only with a
tank of negative pressure. Unfortunately, conventional vacuum
chambers are impractical for this purpose because of their large mass
(high weight). However, in a recent development, the inflatable
vacuum chamber (IVC) [2,3] allows for vacuum chambers of smaller
mass (low weight) and, thus, it is now interesting to explore the
potential application of vacuum to airship buoyancy control. The
idea of using vacuum in an airship is not new. It dates back to 1670
when it was first proposed by Italian monk Francesco Lana de Terzi
[4] (see Fig. 2).
We now introduce this new possibility for buoyancy control, the
IVC. Buoyancy control using an IVC is most closely related to the
before-mentioned techniques involving pressurization or compression. These techniques will be briefly reviewed first. The IVC will
then be discussed.
Introduction
E
DWIN Mowforth [1], Vice President of the Airship Association,
vice president of the Airship Heritage Trust, states, “Many of
the airship’s principal operational problems are associated with
the functions of buoyancy control : : : ” This fact is demonstrated in
airship history. The U.S. Ship (USS) Akron was lost when it was
forced into the sea by a strong downdraft. The USS Macon was lost
after its captain, in a panic over a potential loss of buoyancy, ordered a
massive and irreversible discharge of ballast; the Macon rose above
pressure height (the altitude at which the gas bags expand beyond the
total volume of the airframe), lost lifting gas, and eventually crashed
into the sea. The loss of the USS Shenandoah might have been caused
by airframe damage resulting from a breach of pressure height. Of
the U.S. Navy’s airships, only the USS Los Angeles met its end of old
age; however, it too suffered from an inability to adjust its weight to
meet changing conditions (see Fig. 1).
In modern airships, the usual buoyancy control problem is that of
compensating for the weight of fuel consumed in-flight.† Inability to
control buoyancy effectively also creates difficulty with landing,
takeoff, and load exchange. Difficulties with the weight of fuel consumed during flight can be handled in many ways. Fuels of various
densities (gases and liquids) can be used (as in the LZ 127 Graf
Zeppelin). Vectored thrust and flight control can compensate to an
extent. Difficulties with landing and takeoff are often avoided by
not landing and instead mooring some tens of feet above the ground.
An airship that actually lands and takes off can solve some of the
buoyancy problem with aerodynamic lift, but this requires the airship
to make a run along the ground (a runway) for takeoff and landing
and, thus, erodes the airship’s prized land anywhere ability. Airships
can also discharge ballast on liftoff, but discharge of lifting gas on
touchdown is cost prohibitive. Load exchanges must be balanced,
thus a load cannot be dropped except where sufficient ballast is
available.
There are a variety of standing proposals to allow an airship to
reversibly change its weight in-flight. They include pressurization or
heating of the entire gas contents of the airship, compressed storage of
the lifting gas or air, and liquefaction of the lifting gas or air. A good
review of these techniques can be found in [1]. It is concluded that
II.
Buoyancy Control Using Compressed Air Storage
First, we explore the idea of storing compressed air on the airship.
For such a system it is important to know the weight of the container
and the weight of air it will be able to store. Often the limiting factor
for a buoyancy control system is its weight. An ideal system would
allow the airship to change its weight by a large amount quickly while
adding only a small amount of weight to the airship itself.
We first propose that the air be stored in long cylinders of
continuously wound fiberglass composite.
pInsuch cylinders, the
glass fibers are wound at an angle of arctan 2 ≈ 54.74 deg to the
Presented at the SDM 2011, Denver, CO, 4–7 April 2011; received 6
September 2011; revision received 5 January 2013; accepted for publication
21 January 2013; published online XX epubMonth XXXX. Copyright ©
2013 by the American Institute of Aeronautics and Astronautics, Inc. All
rights reserved. Copies of this paper may be made for personal or internal use,
on condition that the copier pay the $10.00 per-copy fee to the Copyright
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*Postdoctoral Associate, Department of Physics, 77 Chieftan Way.
Member AIAA.
†
Personal correspondence with Edwin Mowforth, 14 August 2010.
axis of the cylinder to provide strength around the circumference that
is twice the strength along the axis. (When a cylinder is subject to
hydrostatic loading the stresses in the circumference are twice those
along the axis.) It can then be shown that the total weight of the
container (excluding end effects) is
σ composite −1
3P
mtank mair-stored air
(1)
ρair ρcomposite
1
2
BARTON
Fig. 1 The USS Los Angeles after being struck by a tailwind while
moored on 25 August 1927.
container is in tension only (no compressive forces). (For a proof
of the previous statement, see the Appendix.) Because Eq. (1) is
applicable to general shapes it is also valid for pressurizing the entire
volume of lifting gas in the airship. In that case, however, one
considers the stress-to-density ratio of the fabric (not composite) that
carries the pressure load in the surface of the airship. Mowforth ([1]
pp. 360–363), appears to contradict the idea that Eq. (1) is valid
for pressurizing the entire envelope of the airship. He, however,
acknowledges in private correspondence with the present author‡ that
the choice ks 10 in ([1] p. 362), does not follow from any known
discussion and is likely in error. It is the belief of the present author
that Eq. (1) is applicable to any pressure container, including the
entire envelope of a nonrigid airship.)
For air at 15°C, Pair ∕ρair ≈ 0.083 km2 ∕s2 . For a 60/40 composite
of E-glass/epoxy loaded at a safety factor of 4, σ composite ∕
ρcomposite ≈ 0.25 km2 ∕s2 . Thus, the mass of the tank will be
approximately equal to the mass of the air the tank can store. If one
substitutes a 70/30 composite of aramid/lightweight epoxy loaded
at a safety factor of 4 we find σ composite ∕ρcomposite ≈ 0.47 km2 ∕s2 and,
thus, the mass of the container would be about one-half the mass of air
stored. It appears that containers of wound carbon fiber might have a
mass 2.5 times smaller than the mass of air they can contain with the
same safety factor.
Energy consumption of the required air pumps will likely not
exceed 3% of the airship’s total energy budget [1]. A survey of air
compressor pumps (and vacuum pumps) on the market today
indicates that they can easily pump a weight of air equal to their own
weight in about 45 min. If engineered for minimal weight (for airship
application) this could likely be improved by a factor of 2.
III.
Fig. 2
Francesco Lana de Terzi’s flying boat concept circa 1670.
where m is mass, P is pressure, ρ is mass density, and σ composite is the
strength of a unidirectional sample of the composite material on its
strong axis. Note that Pair ∕ρair depends only on the temperature and
not on the storage pressure (ideal gas law). It is also true (and more
difficult to show) that Eq. (1) is also valid for containers of arbitrary
shapes including cylinders with hemispherical ends, spheres, and
ellipsoids as long as the material comprising the structure of the
Inflatable-Vacuum-Chamber Concept
We now shift our attention to the potentially complementary
system, the inflatable vacuum chamber. We can begin to understand
the mechanics of the IVC by considering the following idealized
structure. One imagines that there is a dense three-dimensional
isotropic network of thin tensile fibers. These fibers are placed
randomly and densely, having all possible orientations and approaching a continuum. These fibers can be imagined to be glass,
aramid, carbon, or otherwise. One then imagines removing regions of
the tensile fibers to leave behind structures of a desired shape. For
example, one might imagine leaving behind a spherical container
consisting of the fiber segments in a volume between two concentric
spheres of different radii and all other volumes void of fibers. One
then imagines placing gas-impermeable barriers along every surface,
where the volume of removed fibers meets the volume of remaining
fibers. For the example of the spherical container mentioned
previously this would consist of two spherical membranes coincident
with the before-mentioned spherical surfaces. Because the fibers
carry only tension and not compression the space between the fibers
must be pressurized to provide the idealized solid with the ability to
transmit compressive forces. One thus imagines that the severed ends
of the fibers are mechanically connected to the membrane, so that the
space occupied by the fibers can be pressurized, and the resulting
tensions in the fibers will be terminated in the membrane (see Fig. 3).
The distance between the fibers is considered to be small compared to
the thickness of the membrane, so that the stresses in the membrane
can be neglected. Note that the membrane does not carry any of the
stresses resulting from pressurization. The force imparted to the
membrane by fiber attachments is balanced by the pressure force.
A structure such as this is filled mostly with gas and, thus, has a low
density. Pressure and fiber cross-sectional areas can be reduced
proportionally to reduce the effective strength of the structure. This
reduction, however, does not affect the effective strength-to-stiffness
ratio of the idealized continuous solid or structure that it forms. This
is in contrast to traditional compressive structures which, when
designed for lighter loads, lose stiffness at a proportion much greater
than the proportion by which they lose strength. Corrugations and
complex networks of compressive members are often used to address
‡
Personal correspondence with Edwin Mowforth, 13 March 2011.
3
BARTON
We average this for all orientations of the fibers to find the average
elastic energy per unit volume of fiber material:
Z Z
1 π π
u sin θ dϕ dθ
4π 0 −π
2
εx εy ε2y εy εz ε2z εz εx
ε
≈E x 10
15
10
15
10
15
u Fig. 3 A cross-sectional view of the idealized spherical IVC: the thin
lines represent tensile fibers and the thick lines represent gasimpermeable membranes.
this problem, but as the design load further lightens, it becomes nearly
impossible to maintain the ratio of stiffness to strength, hence the
difficulty in designing lightweight vacuum containers as compressive
structures. This is the motivation for the idealized inflatable solid
just described. Its design load can be reduced arbitrarily while
maintaining its strength-to-stiffness ratio. Thus, it can then be shown
that, if this idealized spherical shell is sufficiently thick, the linear
mass density of the fibers is sufficiently small, and the space between
the fibers is sufficiently pressurized; the structure remains elastically
stable when vacuum is introduced into the central space. Let us
further consider this pressurized network of fibers.
In the idealized case, a pressurized matrix of tension fibers can be
described mechanically as a continuous solid having a specified
strength and elasticity. We will here show that, if the tension fibers are
isotropic, the idealized bulk solid has isotropic elasticity and
Poisson's ratio of one-fourth. We will also show that the elastic
modulus per mass and single-axis strength per mass of this idealized
continuous material is one-sixth that of the fiber material.
We imagine a dense isotropic network of thin elastic tensile fibers
having all possible orientations:
2
3
cos θ
a 4 sin θ cos ϕ 5
(2)
sin θ sin ϕ
We identify this as the elastic energy of an isotropic elastic solid with
an elastic modulus of E∕6 times the fiber volume fraction and
Poisson's ratio of one-fourth. This consideration is valid only if the
strain on all three principal axes is positive. Under negative strain,
some fibers relax to zero tension and the analysis become nonlinear.
Notice that with such a network of fibers it is not possible to
have zero tension along any single axis without having zero tension
along all axes. This is because only a very small number of fibers
carry tension along a specific axis or in specific planes, and none of
the fibers carry compressive force. This means that such a tensile
network always has a background tension, the transmission of which
requires extra weight and extra pressurization to create force balance.
For an example, consider the hydrostatically compressed spherical
shell. The ratios of the tensions on the principal stress axes in the
shell are 0∶1∶1 (radial∶circumferential∶circumferential). The idea
of the pressurized tension network is to use pressures to achieve the
isotropic positive part 1∶1∶1 and then use the tensile network to
provide the additional reduction −1∶0∶0 needed to bring the total to
0∶1∶1. However, the requirement of only positive strain requires a
“background tension” of 1/2 and, thus, we must substitute −1∶0∶0
with −3∕2∶ − 1∕2∶ − 1∕2. Thus, pressure (and the initial loading of
all fibers) has to be increased by 50% to provide the background
tension to prevent negative strain on loading.
These difficulties can be reduced, however, if the fibers are not
placed isotropically but instead are placed primarily along the
anticipated axes of principal strain when loaded. Unfortunately, this
approach increases difficulties with elastic stability and the analysis
thereof. Because stress in the tensile fibers will be isotropic when the
IVC is vented and will be primarily in the radial direction when
vacuum is present we find that practical IVCs have a large population
of tensile fibers in the almost radial direction. This almost direction
is necessary to mitigate issues of elastic stability. The structures of
Figs. 1 and 7a in [2,3] (reproduced as Figs. 4 and 5, respectively)
illustrate this philosophy of exactly radial and almost radial,
respectively. In this example, the tensile fibers are part of a textile
membrane. We propose the structure of Fig. 5 for use in buoyancy
control. Though spherical IVCs have better theoretical properties we
avoid them for difficulties in automating their construction and
difficulties in producing double-curved (spherically curved) fabric
membranes.
for all θ and ϕ.
We then imagine stretching the network of fibers on three principal
axes of strain resulting in new orientations:
3
2
0
0
1 εx
0 5a
(3)
1 εy
b4 0
0
0
1 εz
where is the strain. ε These new orientations have elastic energy per
unit volume of fiber material equal to
1
u Ejbj − 12
2
(4)
where E is the elastic modulus of the fiber material. To second order
in ε this is found to be
1
u ≈ Eεx cos2 θ εy sin2 θ cos2 ϕ εz sin2 θ sin2 ϕ2
2
(5)
(6)
Fig. 4
Upper right quadrant of Fig. 1 from [2,3].
4
BARTON
Fig. 7 Method of constructing the proposed structure.
Fig. 5
IV.
Figure 7a from [2,3].
Proposed Structure
The structure has a cross section shown in Fig. 6 and is invariant in
its length. In the figure, the lightly shaded exterior region represents
low-pressure helium, heavily shaded regions represent high-pressure
helium, the unshaded interior region represents vacuum, thick lines
represent gas-impermeable fabric, and thin lines represent gaspermeable fabric. Its inner radius is about 1 m, and its total length
(continuous or noncontinuous) is approximately 600 m. It provides
about 7.5 tons of buoyancy control range. The ends are closed crudely
by wetting the fabrics near the end of the structure with a sealant,
placing a constricting band around the structure at that point, and then
tightening the band until gas leakage is minimized. Ports and ducting
are added to facilitate inflation and deflation.
It should be noted that buoyancy control systems that occupy large
volumes create different amounts of buoyancy at different altitudes
even if their gas contents do not change. For example, because the
proposed vacuum volume displaces about 2 tons of air at sea level and
does not change its volume at altitude, its buoyancy is reduced by
0.62 tons at an altitude of 10,000 ft.
V.
Construction of the Proposed Structure
The proposed structure is formed of five layers of fabric. The
innermost and outermost fabric layers (layers 1 and 5, respectively),
are gas impermeable, that is the fabric has been impregnated with
some gas-impermeable resin or laminated with some gas-impermeable
layer. These five fabrics are sewn together with a lock-stitch sewing
machine as shown in Fig. 7. The structure is closed by bonding each of
the five layers back to itself with a butt joint secured with an adhesive.
The structure is preliminarily inflated at low pressure to give it shape.
Lines of sealant are then placed between the lobes on the sewn seams to
slow the gas leakage passing through the holes created by the sewing
needle.
The author has built preliminary structures of polyurethane-coated
polyester fabric. The fabric layers were sewn together as described
and sealed from the exterior with a paintable two-part polyurethane
sealant. After three coats of polyurethane sealant were applied
leak rates were found to be low. Fabric layers were closed onto
themselves by heat welding of the polyurethane fabric coating.
Special sewing machine fixtures were designed to aid in maintaining
correct dimensions.
A superior way of bonding two fabrics edge to edge is by means
of a butt strap adhered to the face of each fabric with an adhesive. This
is the current state of the art in the manufacture of nonrigid airships
[5,6]. Although sewing the fabrics together is simpler it does not
allow for a natural termination of the tensions in the fibers that are cut
along the cut edge of the fabric. This can result in the position of the
fibers shifting over time, especially in the fibers parallel to the seam
that are between the stitching and the cut edge of the fabric. Shifting
of the fibers is often slowed by the immobilizing effect of the sealant,
but this results in the undesirable situation in which the sealant is
transmitting part of the structural load. This usually results in failure
of the sealant and leaks. In general, sewing together the cut fabric
edges is undesirable for these reasons.
In construction of the vacuum tank design proposed in this work
there are five of these butt joints (one to close each of the five layers
of fabric onto itself), and it is recommended that these butt joints
be made in the discussed state-of-the-art way. The remaining joints in
the structure (approximately 100 in number) are fundamentally
different. They cannot be created with adhesives because the stresses
present tend to peal the fabrics apart and fail the adhesive.
Additionally, the known difficulties that follow from sewing of cut
fabric edges do not apply because the fabric does not have cut edges at
these joints. The present author recommends that these 88 structural
joints be created by sewing the several layers of fabric together and
applying a sealant over the stitches from the inside of layer 1 and the
outside of layer 5.
VI.
Fig. 6
Cross section of the proposed structure.
Stability of the Proposed Structure
The stability of the proposed structure is analyzed with techniques
similar to those found in [2,3] with the following exceptions. The
effective-tension concept is not used. The angles of arc in the outer
and inner lobes are added as additional degrees of freedom bringing
the total number of degrees of freedom per unit cell from four up to
six. The design strength of each membrane is calculated from the
tensions present in the absence of vacuum. These tensions do not
have a unique solution, until one imposes the additional constraint
that the tensions in layer 2 and layer 4 must be equal. This constraint is
arbitrary. It may be found that releasing this constraint will allow the
optimized mass of the structure to be slightly lower and, thus, further
investigation is required. The elasticity of each membrane is set by
assuming that the elastic modulus divided by the tensile strength
is 34 (characteristic of aramid fiber fabrics) [7]. The outside radius,
number of lobes, and pressure are then varied keeping the inside
radius fixed to find the structure with the smallest total membrane
5
BARTON
Fig. 8
Failure mode of the proposed structure.
mass per unit volume of vacuum that has both elastic stability and
positive tension in all membranes. As shown in the Appendix the
mass of gas the structure contains when vacuum is not present is
directly proportional to the total membrane mass. Thus, the weight of
the pressurizing gas is not considered when optimizing the structure.
The optimized structure is found to have an outside radius that is
1.50 times its inner radius, 44 lobes, and a pressure of 3.08 absolute
atmospheres in its wall. The failure mode of the structure is shown in
Fig. 8. Tables 1 and 2 give the specification of the specific design.
VII.
System Operation
The 2 t system proposed here (schematically shown in Fig. 9 for a
nonrigid airship) is designed to aid with vertical takeoff (or liftoff),
weight compensation for fuel consumed during flight, and vertical
landing (or touchdown). Larger systems would be required to adjust
buoyancy for onloading and offloading of cargo.
The IVC functions as both a vacuum chamber and a pressure
vessel. Its weight efficiency as a pressure vessel is equal to that of
pressure vessels of simpler designs (see the Appendix). It, however,
has the additional ability to contain vacuum (in addition to pressure)
Table 1
when sufficient pressure is present. An IVC buoyancy control system
thus has the same weight and buoyancy control range as a system that
only compresses gases but has the additional benefit of being able to
rapidly add weight. This comes at the cost of having a storage vessel
of more complex geometry.
We consider here an airship displacing approximately 100 t of air at
sea level having a fuel capacity of about 5 (metric) tons. It experiences
a drag force of about 2 t (metric ton force) at its top speed of about
100 km∕h. It is equipped with a 2000 hp engine and has a range of
1000 km. It flies at altitudes up to 10,000 ft.
We begin with the airship on the ground, at sea level, no vacuum in
the center of the IVC, full pressure (about 30.6 psi gauge) in the wall
of the IVC, and no fuel. In this condition, the airship has been
designed to have a net buoyancy of −2.00 tons, giving it traction with
the ground. It is not moored. In preparation for liftoff 5.55 tons of fuel
are added. The net buoyancy is now −7.55 tons.
As time for liftoff approaches, engines are started and engine
exhaust is directed through the heat exchangers warming the helium
contents of the airship to produce 5.55 tons of superheat buoyancy.
One notes that the superheat must be maintained only until the
moment of liftoff at which time the pressure/vacuum system will add
the buoyancy to the airship permanently. Thus, the difficulties of
maintaining superheat for extended periods or at high velocity are
avoided. Although it appears feasible to augment buoyancy with
superheat for a short period of time [1], more investigation is needed
to confirm this. The net buoyancy is now −2.00 tons.
When the ship is prepared for liftoff the wall of the IVC is vented
releasing compressed helium into the envelope of the ship. The
helium cools adiabatically as it expands. The increase in lifting gas
volume rapidly forces air off the ship. (In a nonrigid ship this air exits
through the overpressure protection valves.) Buoyancy surges by
4.53 tons. Net buoyancy is now 2.53 tons. In absence of vertical
winds or assistance from vectored thrust this produces about 1∕40g
of vertical acceleration. Thus the airship rises to an altitude of 100 ft in
about 15 s.
Immediately after liftoff the heat exchangers are closed and thus
heating of the lifting gas is discontinued. The airship's lifting gas
now contains a pocket of hot helium (resulting from the lifting-gas
heating) and a pocket of cold helium (resulting from the adiabatic
expansion of the helium released from the IVC). As these
temperature variations dissipate to the atmosphere during the next
15 min, 2.48 tons of buoyancy are lost, bringing the net buoyancy to
0.00 tons. The IVC system is now fully discharged. Simultaneously,
as the airship climbs to 10,000 ft, the valves venting the interior and
General specifications for the inflatable vacuum chamber
Parameter
Value
General design specifications
Radius to inside sewn seam
1.00 m
Radius to outside sewn seam
1.50 m
Number of lobes
44
Absolute pressure in wall
3.079 atmospheres
Absolute pressure in central space
As low as 0.00 atmospheres
Safety factor
4
Total noncontinuous length
581.1 m
Volume of central space
1632 m3
Pressurized volume
2965 m3
Total volume
4597 m3
Fabric of epoxy-impregnated aramid fibers
Density of fibers
1.44 g∕cm3
Strength of fibers
3.6 GPa
Elastic modulus of fibers
124 GPa
Total fabric weight
2998 kg
Total weight of axial fibers
999 kg 1∕3 total
Total weight of perpendicular fibers
1999 kg 2∕3 total
Fabric densities
Layer 1
36.16 g∕m2 (not including gas-impermeable resin or layer)
Layer 2
122.68 g∕m2
Layer 3
45.94 g∕m2
Layer 4
122.69 g∕m2
Layer 5
54.24 g∕m2 (not including gas-impermeable resin or layer)
6
BARTON
Table 2
Weight components of an operational inflatable
vacuum chamber
Weight components
Fabric weight
Extra helium required to pressurize
Helium removed when evacuated
Total weight added to airship when fully charged
Reduction in payload assuming discharge on takeoff
Total buoyancy control range
Weight of air displaced when central space is evacuated
Weight of air undisplaced when central space is vented
Weight of air immediately undisplaced on venting
Weight of air displaced when wall is vented
Weight of air immediately displaced when wall is vented
Table 3
Initial state
2.998 tons
1.042 tons
0.276 tons
3.764 tons
2.998 tons
7.552 tons
2000 kg
2000 kg
1429 kg
7552 kg
4531 kg
Buoyancy control capabilities of the inflatable vacuum
chamber
Immediate weight
change
Pressure Vacuum
First
Second
C
C
1.43 t
0
C
C
1.43 t −4.53 t
C
C
−3.10 t
0
C
D
−4.53 t
0
Delayed
weight
change
0.57 t
−2.45 t
−2.45 t
−3.02 t
Final state
Pressure Vacuum
C
D
D
D
D
D
D
D
C charged, C discharged.
Note: Delayed weight change occurs as adiabatic heating/cooling
dissipates.
wall of the IVC remain open allowing the reduction in ambient
pressure to further evacuate all parts of the IVC, thus buoyancy
remains balanced.
Once an altitude of 10,000 ft is reached, valves to the IVC are shut,
locking-in the density of the IVC system. Because of the fixed
volume of the IVC the airship will tend to stay at 10,000 ft. Avariation
of 1000 ft in altitude will create a change in buoyancy of about
0.13 tons that will tend to return the airship to 10,000 ft. This
oscillation of the airship's altitude will have an approximate period
of 17 min.
For the next 10 h or so, the airship flies its course of approximately
1000 km during which it consumes almost all of the 5.55 tons of fuel
added. Simultaneously, a helium pump (thought to weigh about half a
ton) removes helium from the interior of the IVC and from the
envelope of the airship and forces it into the wall of the IVC to create a
near vacuum in the interior of the IVC and a pressure of close to
28.0 psi gauge in its wall. This net compacting of the helium results in
a reduction of buoyancy of close to 5.55 tons, precisely balancing the
Fig. 9 Schematic representation of the IVC buoyancy control system for
a nonrigid airship.
weight of lost fuel. The net buoyancy remains at 0.00 tons, and the
fuel tank is close to empty.
As the helium pump continues to increase the gauge pressure in the
wall of the IVC beyond close to 28.0 psi (where close to corresponds
to the small weight of fuel remaining), the altitude for aerostatic
equilibrium (which was 10,000 ft) begins to decrease, and the airship
begins to descend. As the density and pressure of the ambient
atmosphere increases, the buoyancy of the IVC system begins to rise
and (in absence of continued pumping) the gauge pressure in the wall
of the IVC would begin to drop. Thus, pumping continues to surpass
changes in ambient pressure and bring the gauge pressure in the wall
of the IVC to close to 30.6 psi as the airship approaches the ground.
Net buoyancy remains at 0.00 tons.
As touchdown approaches the pilot prepares to vent the vacuum in
the central space of the IVC. When first contact with the ground is
made an auxiliary air ballonet in the central space of the IVC is vented
rapidly decreasing the net buoyancy by 1.43 tons. Net buoyancy is
now −1.43 tons and, thus, traction with the ground is secured. During
the next 15 min, as frictional heat dissipates to atmosphere, an
addition 0.57 tons of weight are added to the ship increasing traction
with the ground. For rapid return to the air, refueling and superheating
of the lifting gas occur simultaneously. The auxiliary air ballonet is
gradually emptied by allowing helium into the central compartment
of the vacuum tank.
Note that in this proposed system, the IVC vacuum space is finally
filled with helium and not air. Note that the buoyancy of the ship is the
same in either condition. In both cases, some gas already in the ship is
moved into the IVC to make room for more air to flow into the airship.
The addition of new air to the airship is what actually changes the
weight of the ship. Additionally, moving helium instead of air into
the IVC has the advantage of increasing the pressure height of the
ship whenever vacuum is vented. This might be useful in the event
that the IVC system is used in-flight for disaster avoidance. A similar
argument shows the advantage of pressurizing the wall of the IVC
with helium. Furthermore it is useful for the central space of the IVC
and the wall of the IVC to contain the same gas, so that only one pump
is required to manipulate the gas. Alternately, placing the vacuum
system into an air atmosphere (and filling it with air) has the
advantage of being able to rapidly exhaust gas to the exterior of the
ship (which reduces the retention of thermally disturbed gas on
takeoff, eliminates the need for overpressurization protection in a
nonrigid airship, and simplifies structural considerations in a rigid 2
airship (see Sec. IX). It has the disadvantage of permanently reducing
pressure height and/or payload capacity of the airship.
VIII.
Use of Oversized Vacuum Tanks
Once the airship designer has specified the buoyancy change
capability (2 tons in our examples) there still remains some choice
in the total volume of the vacuum tank. Until now we have only
considered tanks from which the vast majority of gas in the central
space is removed. As an alternative, one can consider a tank of larger
volume with less structural strength, so that only a fraction of the gas
in the central space is removed. In any case, the same amount of gas is
moved, the same change in buoyancy is achieved, and the structural
weight of each tank is the same.
The major advantage of the larger tank is a reduction in pumping
energy because the same amount of gas is moved with less back
pressure on the pump. This makes possible a faster or lighter pump
and further reduces the already small amount of engine power
required to recharge the system. As an example, we consider a 100 t
airship having a 2 t vacuum buoyancy system inside the helium
lifting-gas volume. If the vacuum tank is of minimum size (designed
for full evacuation) the energies required to charge the pressurized
wall and central vacuum are 492 and 276 MJ, respectively. (These
energies assume fast adiabatic compression in the pump and slow
isothermal compression in the tank. Actual energy consumed will
be almost double because of mechanical friction in the pump.) An
example alternative is to increase the total volume of the tank by a
factor of 2 and remove only half of the gas in the central space. The
energies required to charge the pressure and vacuum in this case are
7
BARTON
276 and 55 MJ, respectively. At four times the volume and one-fourth
evacuation these become 148 and 24 MJ, respectively. Assuming
adiabatic compression in the pump and isothermal compression in the
tank, the energy E required to pressurize or vacuumize a volume V to
a pressure P in an atmosphere of pressure P0 and inverse relative heat
capacity at constant pressure Γ (2/7 for ideal diatomic gasses) is given
in Eqs. (7) and (8), respectively:
1Γ
P V
PV
P0 V
P
Epressure 0 −
(7)
1Γ
Γ
Γ1 Γ P0
Evacuum P∕P0 − P∕P0 1−Γ 1 − P∕P0 1−Γ
Γ1 − Γ
(8)
The benefit of minimizing energy required to charge the vacuum
system is mainly in the weight and speed of the pump. A 2000 hp
engine delivers 1000 MJ of mechanical energy every 11 min. Thus, in
the extreme case when the flight is short (perhaps 4 h) the vacuum
tank is small (requiring full evacuation), and the pump is 50%
efficient; the energy required to charge the vacuum system is only 7%
of the total engine power. Although compact vacuum systems require
mechanical vacuum pumps and mechanical air compressors to reach
the required pressures, systems of larger volume use roots blowers
and multistage centrifugal blowers with attendant reductions in
weight or increases in speed.
A secondary benefit of using an oversized tank is the reduction in
weight of the primary vent and primary exhaust valves (the large
valves used at touchdown and takeoff, respectively, to provide rapid
movement of gas and rapid buoyancy change) because of the reduced
pressure differences. The rates of buoyancy change are limited by
these valves (and the capacity of the overpressure protection louvers).
Assuming a set amount of weight budgeted to these valves, vent times
can be reduced by a factor roughly equal to the factor of increase in
tank size, see Sec. XI.
Pumping required to reach aerostatic equilibrium when altitude is
changed is relatively unaffected by tank size. For example, when the
ship moves from pressure height (11,865 ft) to sea level, ambient air
density changes by 30% of sea level air density. When the vacuum
system is in the lifting gas and compact (4597 m3 ) this corresponds to
an increase in buoyancy of 1.689 tons, thus 1379 m3 of helium must
be compacted away to maintain neutral buoyancy. This is about 22%
of the total volume required to charge the pressurized wall. For a tank
having twice the volume buoyancy change is doubled and, thus, an
amount of gas equal to 44% of the total charge must be pumped, but
this pumping occurs at roughly half the back pressure and with a pump
of the same weight is thought to occur in approximately the same time.
It can be shown [see Sec. XI, Eq. (14)] that, even though a tank
of double the minimum volume has less pressure difference available
to drive gas into the tank, its total fill time (with a valve of equal
aperture) is less by a few percent.
The natural oscillations of the airship's altitude when the vacuum
system is locked in increase in frequency when larger tanks are used.
IX.
is difficult to provide a sufficiently large conduit from the rapidly
deflating gas cells to the outside, so that the rapid movement of air
does not put excessive compressive forces on the structure of the
airship. A third option, which resolves both of these issues (and is
the recommendation of the author), is to place inside the central
space of the vacuum tank and auxiliary air ballonet. When the space
is under vacuum, the auxiliary ballonet is empty. When the airship
lands a primary valve is opened connecting the auxiliary ballonet
to the outside atmosphere. The forces of vacuum rapidly fill the
auxiliary ballonet with air creating the weight gain needed to secure
the landing. A secondary valve, which connects the central vacuum
space (outside the auxiliary ballonet) to the lifting-gas volume is then
opened allowing lifting gas to gradually move into the central space
of the vacuum tank thus slowly deflating the auxiliary ballonet. In a
nonrigid airship this happens naturally under the slight pressure
generated by the primary air ballonet blower and corresponds to an
increase in the volume of the primary air ballonet. In a rigid airship, a
small blower is used to transport the contents of one or several gas
cells into the central space of the vacuum tank, thus making more
volume for other gas cells to expand when altitude increases. This
exhausting of the auxiliary ballonet must be completed prior to the
airship returning to pressure height to provide enough volume for the
altitude expansion of the lifting gas.
When the ship again takes to the air, the helium in the wall of the
vacuum tank must be released to create the surge in buoyancy that
will provide a safe and rapid takeoff. The resulting increase in liftinggas volume forces air out of the ship. This change in volume is again
too rapid for the air ballonet blower backflow (in a nonrigid ship) to
discharge without overpressurization of the ship. In a rigid ship, it is
also difficult to have such a large conduit from the rapidly inflating
gas cells to the outside atmosphere as to prevent excessive tensile
forces on the structure of the ship. Unlike the central space of the
vacuum tank, placing auxiliary ballonets in the wall of the vacuum
tank is not feasible, because the volume is divided into many smaller
volumes by structural gas-permeable fabrics. If auxiliary ballonets
were possible, one could pressurize the wall of the vacuum tank with
the right proportion of air and helium, so that upon depressurizing the
wall on takeoff only air is discharged from the wall, and only helium
remains in the wall. In this way the discharge could be dumped
directly to atmosphere and the pressure height of the ship would be
preserved. Perhaps an inflatable vacuum tank of a different geometry
can be designed, so that the pressurized volume is more consolidated;
this is the subject of future research. For the present, the author
recommends that the airship be outfitted with an overpressurization
protection system. In a nonrigid airship, this might consist of a
number of pressure relief valves (having a total exhaust aperture area
roughly 10 times larger than that of the primary exhaust valve for an
airship pressurized at 0.01 atm) connecting the primary air ballonet to
the atmosphere, so that the ballonet can be exhausted sufficiently fast
to ensure a safe and rapid takeoff. The exhausting of the vacuum tank
wall could not exceed the volume flow capacity of the primary ballonet
exhaust system. In a rigid airship, one would need to carefully consider
which gas cells the wall of the vacuum tank should be exhausted into,
and if the air around these rapidly expanding gas cells can escape the
airship with sufficient ease to prevent structural damage.
Management of High-Volume Gas Flows
When the airship lands the central space of the vacuum tank must
be vented to gain traction with the Earth. There are several ways this
can be accomplished. A first option is to vent directly with atmospheric air resulting in direct weight gain. This first option has the
disadvantage of reducing payload capacity or pressure height of the
airship. The airship can reach full pressure height only if 100% of its
gas volume is occupied by helium. The presence of any air volumes
that cannot be exhausted results in a loss of payload capacity or
pressure height. A second option (which resolves this first issue) is
to vent with helium from the lifting-gas volume causing the volume of
the lifting gas to decrease and, thereby, causing the air ballonet to
increase in volume creating the increase in weight indirectly. With
this second option, one finds that the air ballonet blower is generally
unable to keep up with the massive volume of air that must be moved
to prevent implosion of a nonrigid airship. Even in a rigid airship, it
X.
Isentropic Expansion vs Isenthalpic Expansion
When calculating the buoyancy changes resulting from a release
of vacuum or a release of pressurized gas the distinction between
isentropic expansion and isenthalpic expansion must be considered.
This was not considered in previous work [8]. When an ideal gas is
expanded in a manner in which the maximum amount of work is
extracted (e.g., with a piston) the temperature of the gas decreases,
and the entropy of the gas remains unchanged. This is isentropic
expansion. Similarly, isentropic compression of an ideal gas results
in heating. Alternately, when an ideal gas is expanded in a manner
in which no work is extracted (e.g., through a porous plug), the
temperature and enthalpy of the gas immediately prior to and immediately after the expansion are the same (assuming that velocity and
bulk kinetic energy is negligible). This is isenthalpic expansion.
8
BARTON
As an example, we consider an evacuated vacuum tank being
opened to the atmosphere (not inside an airship). In this generic case
of a vacuum being released the expansion of the ambient atmosphere
into the vacuum tank can occur either isentropically or isenthalpically. For the most rapid expansion, an orifice or nozzle is opened
between the atmosphere and the interior of the vacuum tank. The
work energy from the isentropic expansion of the gas accelerates the
gas into the tank as it passes through the nozzle. Thus, the temperature
of the gas decreases, but its velocity increases. The total of the thermal
energy, kinetic energy, and potential energy (from atmospheric
work) must remain unchanged as required by energy conservation.
As this kinetic energy dissipates through the action of viscosity it is
converted back to thermal energy and, thus, the final state is the same
as if the expansion had been isenthalpic, wherein the kinetic energies
are dissipated as they are produced inside the porous plug. In either
case, the work that the atmosphere does to push the gas through the
orifice, nozzle, or porous plug is finally found in the vacuum tank as
thermal energy. As more gas enters the tank, gas already in the tank is
compressed isentropically causing its temperature to rise. In the final
state, when pressures inside and outside the tank are equal, we find
that the potential energy of the atmosphere has decreased by an
amount P0 ΔV atm , where P0 is the atmospheric pressure, and ΔV atm is
the volume of the atmosphere, which has moved into the vacuum
tank. Ideal gas properties for the gas in the tank in the final state give
P0 V tank NkT tank
Utank
5
NkT tank
2
(9)
P0 ΔV atm NkT 0
(11)
5
U0 NkT 0
2
(12)
In the final state, its internal energy must increase by the amount of
atmospheric work:
(13)
Combining Eqs. (9–13) we find
7
T tank T 0
5
Dynamics of Filling the Vacuum Tank
P
v2
P
0
Γρ0
Γρ 2
where
Γ≡
NkB
CP
2
5
2
7
and thus we find
s
Γ 2P0
P
v
1−
Γρ0
P0
The rate at which volume is removed from the atmosphere is
Avρ
V_ ρ0
(14)
where A is the area of the orifice through which the tank is vented. The
average thermal energy in the tank during and immediately after
venting is equal to the sum of the thermal energy and work energy that
has entered the tank during venting (see Sec. X):
1
1
− 1 NkT tank − 1 NkT 0 P0 V
Γ
Γ
1
T0
NkT 0 → T tank Γ
1−Γ
This heating of the gas (which comes from the work energy that was
required to create the vacuum initially) results in the tank filling to
only 3/5 and 5/7 of its total mass capacity for monatomic and
diatomic gases, respectively. The tank fills to full capacity only once
this frictional heat has dissipated. In a medium-sized airship this will
take about 15 min. The pressure in the tank is given by
5
ΔV atm V tank
7
Thus, the change in buoyancy of the vacuum tank upon venting is
only five-sevenths of its change in buoyancy on evacuation. The
remaining two-sevenths of the buoyancy change is realized when the
frictional heat has dissipated to the environment. In an atmosphere of
helium
(a
monatomic gas), these fractions are three-fifths and two-fifths, respectively.
Thus, for an airship with an inflatable vacuum tank inside its
lifting-gas volume that is vented with air at the moment of touchdown
71% of the buoyancy decrease comes immediately; the remaining
29% comes gradually over the next 15 to 20 min (the time required for
lifting-gas heat to dissipate in a medium sized airship). (The heat
capacity of the fabric forming the vacuum tank is approximately equal
to the heat capacity of the helium it contains when unpressurized, thus
half of this heat might be soaked up by solids that the helium comes in
contact with during the first 5 min.)
The average temperature in the vacuum tank during the entire
filling process is seven-fifths ambient temperature. Early during the
filling, all of the gas is this temperature. Late in the filling, the gas that
entered earlier is hotter, and the gas that entered later is cooler, but the
average remains unchanged.
for ideal monatomic gases
for ideal diatomic gases
Here, P and ρ are the pressure and density in the flow, respectively,
and P0 and ρ0 are the stagnation/ambient pressure and density. The
adiabatic condition requires
1−Γ
P
ρ ρ0
P0
(10)
This same gas in the initial state also obeys ideal gas properties:
Utank U0 P0 ΔV atm
XI.
When the vacuum tank is vented some time is required for the gas
to move into the central space. Once the valve is opened gas accelerates toward the valve opening expanding adiabatically according to
Bernoulli's equation for compressible fluids:
Ptank P0
V T tank
P1
V0 T0
where V is the total volume removed from the atmosphere, V 0 is the
volume of the tank, and P1 is the pressure already present in the tank
at ambient temperature (nonzero of oversized tanks). The time
required to fill the tank is then
V 0 1−Γ 1−P1 ∕P0 Z
t
0
1
V 1−Γ
dV 0 p
A
V_
Γ
ss
Γ
2ρ0
P1
1−
P0
P0
Thus, when the tank volume is 1632 m3 and fully evacuated (not
oversized) and fitted with a valve having an orifice area of 0.25 m2 (a
valve weighing approximately 200 kg), the fill time for helium and air
is 11.3 and 42.9 s, respectively. (Note that fill time for oversized tanks
with a valve of the same weight is less.) Helium and air will fill the
tank to three-fifths and five-sevenths full mass capacity, the mass
defect being related to the frictional heat of filling the tank. When the
medium is air, one might consider exhausting this heated air to
atmosphere to replace it with air of ambient temperature to acquire the
9
BARTON
remaining 2/7 of the capacity, however, one finds that to exchange
this volume of air in 1 min requires a blower weighing approximately
1000 kg and a valve orifice of approximately 2 m2. Avalve of this size
would weight approximately 1500 kg. Thus, it is concluded that the
vacuum tank should be sized to give the desired weight change during
its initial fast filling period when it is driven by the large pressure
difference built up over hours by the work of the vacuum pump.
XII.
Failure of the Inflatable Vacuum System
The vacuum tank can fail in two primary ways: leakage and
explosion. First, the vacuum tank’s gas impermeable skin can fail,
leaking helium into the lifting-gas volume of the airship. In the case of
slow leaks, the helium pump can replace the leaking helium with no
effect on the airship. In the case of faster leaks, the vacuum volume (if
charged) can be used to temporarily take up some of the leaking
helium thus temporarily preventing the buoyancy of the ship from
changing. As pressure continues to drop in the wall of the vacuum
tank the vacuum must be released to prevent geometric instability of
the vacuum tank structure. Finally, when pumping and venting of
vacuum can no longer keep pace with the leak, the extra helium will
begin to accumulate in the lifting-gas volume forcing air off the ship.
This loss of air will result in an uncontrollable increase in buoyancy.
A discharge of lifting gas may then be required to prevent a breach of
pressure height and safely land the ship.
If the leak is fast or results from a violent tearing of the vacuum
tank's fabric, the available pathways for exhausting air may be insufficient to prevent overpressurization of the airship and the resulting
structural damage. In anticipation of such difficulties, one could
potentially design the airship to fail in a very specific way when overpressurized, so that pressure is quickly relieved, damage is confined
to a single area, and the remainder of the lifting gas is retained. This is
the subject of future research.
After the vacuum tank system has failed it can no longer provide
the buoyancy control function required to land the ship. An emergency landing will be secured by other means (loss of aerodynamic
lift [runway landing], mooring, ground handling party, vectored
thrust, jettison of lifting gas, etc.).
XIII.
Future Theoretical Work
When pressure in the wall of an IVC containing vacuum is
sufficiently reduced instability will occur. This instability may
potentially collapse a large fraction of the volume occupied by the
vacuum. It might also be true that, immediately after the collapse,
slightly increasing the pressure in the wall might restore the volume
of vacuum. If such a tipping point phenomenon occurs it might be
useful in airship design. If one can manipulate such a tipping point
with only small changes in pressure, then one might move large
volumes of gas with only small amounts of pumping. This may lead
to a buoyancy control system that does not need charging, one that
can switch back and forth from its heavy state to its light state at will
by simply collapsing and uncollapsing its IVC at this tipping point of
stability/instability.
XIV.
Conclusions
In the current work, we have re-established the need for buoyancy
control in airships, discussed existing proposals to control buoyancy
with the storage of compressed air, re-introduced the inflatablevacuum-chamber (IVC) concept, optimized a specific IVC design for
buoyancy-control application, considered methods of constructing
the proposed structure, analyzed the elastic stability of the proposed
structure, given specifications for the proposed structure, discussed
the operation of the proposed buoyancy-control system, considered
vacuum tanks of different volumes, discussed the logistics of venting
the vacuum tank, discussed the heating and cooling effect that occur
upon venting, discussed the dynamics of venting, considered the
potential failure of the system, and illuminated potential avenues for
future investigation. We continue to develop and test the techniques
necessary to construct a working IVC approximately 50 m3 in total
volume. We are also investigating experimentally the isenthalpic
heating upon venting to gain a better understanding of the time scales
involved in delayed buoyancy change.
Appendix: Proof of Equation 1
We here prove that Eq. (1) is applicable to arbitrary shapes. We
consider a number of tensile fibers bonded together with a resin
to form tensile shells (or membranes). These tensile shells form
structures, which contain pressurized gas. We assume that fibers are
only placed where needed for strength and, thus, all fibers are at their
maximum working load when the pressure is introduced. We first
integrate the trace of the stress tensor σ ij over a volume that contains
the entire structure (including all fibers, resin, and pressurized gas).
We offset the stress tensor everywhere by the ambient pressure such
that the pressures considered are gauge pressures, and the stress
tensor outside the structure is zero:
3
2
0
0
Pgas
Z
7
6
0 7
Pgas
trσ ij dV tr6
5V gas
4 0
allvolume
0
2
Z
composite volume
6
tr6
4
0
Pgas
3
−σ composite working load
0
0
0
7
07
5 dV
0
0
0
0
3Pgas V gas − σ composite working load V composite
(A1)
Note that the tension in the composite is shown to occur only in the x
direction. This is clearly not true but also does not affect the result,
because the trace is invariant under rotations of the coordinate
system.
Because the stress tensor at the boundary of the volume is
everywhere zero, and because the divergence of the stress tensor is
zero (momentum conservation), it is true that ∫ all volume σ ij dV 0ij .
Also, because the trace of the integral is the integral of the trace, it is
true that
Z
Z
trσ ij dV tr
σ ij dV tr0ij 0 (A2)
all volume
all volume
and, thus, from Eq. (A1)
V composite mgas
3Pgas V gas
thus mcomposite
σ composite working load
3Pgas
ρcomposite
ρgas σ composite working load
(A3)
which is Eq. (1).
Acknowledgments
The author would like to acknowledge Jack Sams for bringing
together the right people to generate this idea, Ian Winger for
developing techniques for constructing inflatable structure from
fabrics, Helena Safron for editing this document and illuminating
errors in the author's logic, Edwin Mowforth for sharing his lifetime
of experience with lighter-than-air aircraft, and Frank Flaherty and
Robin Winton for useful discussion. The author would also like to
acknowledge David Van Winkle for making possible the trip to
Denver to present this work, Juan Ordonez for administering the
continued fabrication research, and the anonymous reviewer that has
helped bring the manuscript into its current form.
Reference
[1] Mowforth, E., “Improvements,” Airship Technology, edited by Khoury,
G. A., and Gillett, J. D., Cambridge Aerospace Series 10, Cambridge
Univ. Press, New York, 1999, pp. 359–384.
3
10
BARTON
[2] Barton, S. A., “Stability Analysis of an Inflatable Vacuum Chamber,”
Journal of Applied Mechanics, Vol. 75, No. 4, 2008, p. 041010.
doi:10.1115/1.2912742
[3] Barton, S. A., “Stability Analysis of an Inflatable Vacuum Chamber,”
Journal of Applied Mechanics, Vol. 76, No. 1, 2008, p 017001.
[4] Terzi, F., Prodromo: Overo, Saggio di alcune inventioni nuove
premesso all'Arte maestra, Rizzardi, Brescia, Italy, 1670.
[5] Bradley, P., “Materials,” Airship Technology, edited by Khoury, G. A.,
and Gillett, J. D., Cambridge Aerospace Series 10, Cambridge Univ.
Press, New York, 1999, p. 151.
[6] Zhai, H., and Euler, A., “Material Challenges for Lighter-Than-Air
Systems in High Altitude Applications,” AIAA 5th Aviation,
Technology, Integration, and Operations Conference, Arlington, VA,
AIAA 2005-7488, 26–28 Sept. 2005.
[7] Kevlar Aramid Fiber Technical Guide, DuPont, Publication H-77848 4/
00, E. I. du Pont de Nemours and Company, Wilmington, DE,
April 2000, http://www2.dupont.com/Kevlar/en_US/assets/downloads/
KEVLAR_Technical_Guide.pdf [retrieved 21 March 2011].
[8] Barton, S. A., “Airship Buoyancy Control using Inflatable Vacuum
Chambers,” Proceedings from the 52nd AIAA/ASME/ASCE/AHS/
ASC Structures, Structural Dynamics and Materials Conference,
April 2011.
BARTON
11
Queries
1. AU: Please review the revised proof carefully to ensure your corrections have been inserted properly and to your satisfaction.
2. AU: As per journal style, section citations in the text denoted by their respective label numbers only.
3. AU: Please check and confirm the references and their respective citations in the text.