[american institute of aeronautics and astronautics aiaa 5th atio and16th lighter-than-air sys tech....

American Institute of Aeronautics and Astronautics1

The Design of Robust Helium Aerostats

Jonathan I. Miller* and Meyer Nahon†

McGill University, Montreal, Quebec, H3A 2K6, Canada

Tethered helium aerostats are receiving renewed attention in the scientific andsurveillance communities. However, conventional aerostats cannot consistently survive highwinds. The goal of this research was to design an aerostat that could be deployed for verylong periods, thus reducing operating costs and interruptions in data acquisition. Existingdesigns and fabrication techniques were first reviewed and replicated in the construction ofa 2.5 m diameter spherical aerostat. The constructed balloon was then flown outdoors toobserve its operational qualities. A low-cost data acquisition system was assembled tocharacterize the balloon’s dynamics. The results were used to inform a Finite Element modelevaluating the critical stresses in a 10.15 m diameter balloon envelope. A second model wascreated to appraise the performance of an aerostat with a partial-hard carbon fiber shell incritical areas.

I. IntroductionHE tethered helium aerostat is an old concept that is being revitalized due to the advent of new materials andapplications. A typical tethered aerostat system consists of a fabric envelope to contain the lifting gas, one or

more tethers to moor the balloon to the ground, a flying harness to distribute the tether load over the aerostat, loadpatches through which the flying harness is attached to the envelope, and occasionally a pressure regulation systemknown as a ballonet.

Aerostats are commonly used for positioning aerial platforms for environmental, astrophysical, communications,and surveillance applications. In many of these applications it is critical, with respect to minimizing the operatingcosts as well as maintaining a constant stream of data acquisition, that the balloon remain aloft for long durations oftime. Yet today’s typical tethered aerostat is not reliably able to survive high winds due to “dimpling” (a loss inenvelope shape caused by high surface pressures), and due to the point loads produced where the mooring linesattach to the envelope. The use of synthetic materials and laminates with high strength-to-weight ratios hasimproved the survivability and reliability of modern aerostats. To create a near-perpetually deployed aerostat,however, other changes, such as the use of an ultra-robust envelope partially made from a hard material, must beinvestigated. Such an investigation requires knowledge of the conventional materials and construction techniquesused to build tethered balloons, the dynamics of the buoyant bodies, and how the stresses from the tether loads aredistributed over the envelope. The research discussed here was performed on spherically shaped aerostats. Althoughthey have a higher drag coefficient than their blimp-shaped, streamlined counterparts, they also cost less and aresimpler to manufacture and operate, are subject to lower hoop stresses, and do not require a special ground-mooringapparatus to allow weathervaning.1

Tethered aerostat systems have received limited attention in recent literature and this work has predominantlyfocused on the dynamics of streamlined aerostats. The techniques used for fabricating gas balloons have changedlittle over the last century, however, and the 1926 work by Upson2 remains a key reference for the design andconstruction of envelopes and mooring structures. In 1997 and 1998 Recks provided very thorough and moremodern guides to building small Helium blimps.3,4 These guides contain a wealth of information about envelopematerials, plotting 2-dimensional gores, and assembly procedures that can be extended to the domain of sphericalaerostats. More recently, in 1999, Khoury and Gillett wrote a comprehensive review of numerous aspects of airshipdesign,1 including higher-level information on the materials and bonding procedures that are used in classical andmodern airship envelopes and are also applicable to aerostat construction.

On the topic of the dynamics of tethered, buoyant spheres, Williamson and Govardhan performed the mostrelevant body of work. They found that the spheres would not maintain a constant inclination angle in the flow, but

* M.Eng. Candidate, Department of Mechanical Engineering, 817 Sherbrooke St. West.† Associate Professor, Department of Mechanical Engineering, 817 Sherbrooke St. West, Senior Member AIAA.

T

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would tend to oscillate in a characteristic figure-of-8 motion.5 They reported that the oscillation amplitudes weredependent on the flow speed, and that the drag coefficients of the spheres were up to 100% higher than those forsmooth, fixed spheres. Williamson and Govardhan also went on to investigate the influence of vortex shedding inexciting tethered spheres of differing sizes and tether lengths.6 They found that there was a resonance when thestationary shedding frequency coincided with the natural pendulum frequency of the tethered systems, known as the‘lock in’ phenomenon.

The only study found of the hull stresses on a tethered aerostat in flight was performed in 1982 by Hunt forTCOM.7 Hunt used NASTRAN to evaluate the stress contours over TCOM’s larger aerostats subjected to differentinternal pressures, gravitational forces, and experimentally determined aerodynamic pressures for a range of windspeeds from 0 – 90 knots. He found the highest stresses were at the maximum diameter of the balloon and the loadpatches. The analysis was limited, though, as it considered only small deflections and used a coarse mesh,constrained by the computational power available, that did not allow for detailed stress concentration results. Huntperformed a second finite element stress analysis in 1993 to determine the survivability of a lightweight nosestructure for mooring an aerostat in high winds.8 The analysis demonstrated that the structure could withstand90-knot winds with the appropriate safety factor, but it provided little information about the stresses in the hull. Asfor the finite element analyses of related tethered, fabric systems or lighter than air systems, such as parachutes,sails, and airships, the available studies did not focus on detailed stress contours, and were not appropriate to thetask of evaluating aerostat failure.

In 1980, Durney outlined the causes of local failure in large aerostat envelopes.9 He devised a means ofpreventing the propagation of local failures into catastrophic failures by installing a network of high-strength rip-stop material, thereby reducing damage and repair costs, but did not look into preventing local failures in the firstplace.

The research described here was directed at investigating new concepts for the design of a robust tethered,spherical balloon capable of withstanding high winds for long periods of time. As a first step, existing constructionand design techniques were reviewed and replicated by building a small spherical balloon. The constructed balloonwas then flown at different altitudes to study its drag coefficient and oscillatory behavior in various natural windconditions. The results of the flights were used to inform a Finite Element (FEA) model of the balloon, whichdetermined the critical stresses in the envelope for the wind speed at which the aerostat would first dimple. An ultra-robust aerostat with a partially hard shell, made of carbon fiber, in critical areas was then designed and a secondFEA model assembled to evaluate the structural performance of this partial-hard aerostat against the fully fabricmodel.

II. Construction of a Small Helium AerostatTo achieve a good compromise between cost, ease of storage and handling, and a usable product, it was decided

to construct the smallest balloon possible that would stay aloft in a 10 m/s wind. It was determined that the aerostatshould have at least 44.1 N (4.5 kg) of net static lift when considering only the weight of the Helium and envelope inthe lift calculation. It was also decided that the balloon would need a rapid deflation device in case of an emergency.A final constraint was that the material employed in the envelope had to be workable and not require the use ofspecial equipment for construction of the aerostat. Following a review of construction methods and materialscommonly used on modern aerostat envelopes, a suitable envelope size, configuration, and tether attachment methodwere selected. The balloon was then constructed with the aid of simple tools and flown to observe its operationalqualities.

A. Envelope Materials and DesignRecks supplied a list of distributors who specialize in fabrics for smaller Helium inflatables,3,4 from which

Lamcotec was chosen as the optimum supplier because of their experience dealing with amateur and professionalballoonists. Lamcotec’s 142 g/m2 (4.2 oz/yd2) single-coated heat-sealable #109 70 denier urethane-coated nylontaffeta was selected for the envelope, as it was the lightest material available that could be easily manipulated. Thenylon is 0.15 mm thick and has a break strength of 181 MPa and 152 MPa in the warp and weft directionsrespectively.

Knowing the weight of the material to be used, the minimum radius of the aerostat needed to meet the liftrequirement of 44.1 N at sea level and 25°C was determined to be 1.19 m. A radius of 1.25 m was chosen for theaerostat, which would produce a net lift of 53.2 N. It was calculated that when considering a drag coefficient of 0.7for the sphere (the reason for which is discussed later), the main tether in a balloon of this size would see at most aload of 217 N during a 10 m/s wind. Assuming the worst-case scenario of the main tether being attached directly to


End Patch

Seam

RipPanel

Net

Figure 4. The Finished Balloon

the aerostat through a standard 25 mm wide tether attachment strap, and considering the 0.15 mm thickness of theLamcotec material, the corresponding stress in the envelope is 57.9 MPa, well below the 152 MPa breaking strengthof the chosen urethane-coated nylon in the weaker weft direction.

To reduce the number of seams, and consequently the build time and chance for fabrication errors, cylindrical,single-piece gores were used in the aerostat rather than conical or multi-piece gores (Fig. 1). A 6-gore configuration,the minimum required to maintain a sphericalshape, was chosen for the aerostat. The gorescould have been either heat sealed or gluedtogether. Following the construction of a series of2 m long test seams, heat sealing was selected asit produced a smoother seam with fewerpenetrations and had a shorter curing time. Thegores were heat sealed coating-to-coating using a1” seam, resulting in a balloon in which thedirection the coating faces alternates from gore to gore.

B. Tether AttachmentThe most common methods of securing the tethers to the envelope are through a net draped over the top of the of

the aerostat; or straps that start at the top of the balloon and run down its perimeter; or through load patches, largepatches of material bonded to the side of the envelope (Fig. 2).Though it is the heaviest approach, using a net was deemedmost appropriate as it best distributes load and is easiest toimplement. The net was sourced from Qued Seaway PlasticsLtd, a local distributor. Their 2-180B untreated, 1 ¾” meshnatural nylon netting was selected as it is their lightest, with aspecific weight of 170 g/m2, and has a break strength of 890 N,well above the 217 N maximum load for the 2.5 m aerostatmentioned above. The size of the net was selected to cover theballoon down to 35° below its equator so the tethers wouldattach to the tangent of the balloon at that point and make a

35° angle with the vertical, as recommended by Upson.2 The entire net weighed 2.5 kg, which reduced the lift of theballoon from 53.2 N to 28.6 N.

C. Envelope ConstructionTo assemble the aerostat, the gores were first traced onto the sheets of urethane-coated nylon using a Smalley

Chart.11 They were then cut out with ordinary scissors and heat-sealed together using a Teflon-coated Hobbicohobby iron at 175°C. The heat-sealing was performed over a flat, 1 1/2” x 1/8” steel bar bent to the curvature of thefinal balloon’s surface so the seam between two gores would lie down as a perfectly straight and flat line. Once allsix seams were made, the holes at the top and bottom of the sphere where thegores met were covered using an end patch and a filler valve respectively. Boththe end patch and filler valve were bonded to the balloon using vinyl cement.

With the balloon built, a device had to be installed in the envelope thatwould induce a controlled descent in case of an emergency. Either a burnout ora rip panel could have been used. A burnout is a relatively new method ofinducing a controlled descent in small blimps, and consists of a patch ofmaterial with a heat element or chemically reactive substance that burns a holein the envelope on command.3 Since this requires the complexities of actuatorsand electrical power, the more common rip panel was used. The rip panel,shown in Fig. 4 as part of the finished balloon, consisted of a large slit in theenvelope that started at the top of the balloon and ran 1/5th the circumferencedown, covered by a reinforced piece of fabric. Opening the rip panel quicklydeflates the balloon without seriously damaging the envelope.2

D. Flight Dynamics of the Tethered Spherical AerostatThe 2.5 m diameter spherical aerostat was flown outdoors at tether lengths of 15, 30, and 45 m while moored to

the ground by a single tether to evaluate its motion characteristics and drag coefficient. The load in the main tether

Cylindrical Conical

Figure 1. Gore Types10

Load Patch Strap Net

Figure 2. Tether Attachment Methods


3DReferencePosition

Wind Speedand

Direction

3D BalloonPosition

Load

MainTether

Winch

Figure 5. Experimental Setup

of the balloon was recorded with a TransducerTechniques load cell. The wind speed wasmeasured at 3 m and 10 m altitudes usingCampbell Scientific RM Young Wind Monitors,and the wind direction was measured at analtitude of 10 m using the monitors. The 3-dimensional position of the balloon wasrecorded with a low-cost Delorme differentialGPS system, typically used for hikingapplications, that consisted of a roving remotestation receiver attached to the top of theballoon along the axis of the tether, and a staticbase station receiver placed at a known, fixedlocation on the ground. The position of thewinch was recorded at the beginning of eachday of testing by the differential GPS systemand was used during post processing to determine the 3-dimensional position of the balloon relative to the mooringwinch. The lift of the aerostat was also measured at the start of each day of testing.

Williamson and Govardhan observed that a buoyant, tethered sphere in a steady stream flow will tend to oscillateboth inline and transverse to the flow, rather than maintain a steady inclination angle, and that the combination of

these two oscillations produces a figure-of-8 motion.5 Our 2.5 m aerostatdid oscillate in a direction transverse to the stream flow, Fig. 6, but due tovarying wind conditions caused by gusts, it did not exhibit a discernablefigure-of-8 pattern. More details on the test conditions and data collectedcan be found in Ref. 12.

If the motion of the balloon is averaged over several periods ofoscillation, the inertial terms due to the balloon accelerations will averageto zero and a quasi-static state may be assumed. In this case, a free bodydiagram of the balloon is as seen in Fig. 7, where FL denotes the lift force,FD the drag force, FT the load in the main tether, θ the inclination angle,hereon referred to as the blowdown angle, and the overbar indicatesaveraging over several periods. Using the quasi-static assumption the drag

force on the tethered sphere was determined from its blowdown angle and lift force. The drag coefficient of thetethered sphere,

DC , was then calculated with

22

2

1ru

FC

air

DD

πρ= (1)

where u is the mean wind speed that the sphere is subjected to, which is found by extrapolating the measured windspeed. The radius of the balloon is denoted by r, while ρair is the density of the surrounding air.

The Reynolds number range investigated was 2.8x105 – 8.2x105. Taking into account the surface roughnesscaused by the net over the 2.5 m balloon, the flow was considered to be supercritical in this range.14 An average dragcoefficient of 0.88 was calculated for the aerostat, much higherthan the value of 0.15 for a smooth, fixed sphere insupercritical flow, and higher than the value of 0.7 found byWilliamson and Govardhan for smooth, tethered spheres insubcritical flow.6 This value was also higher than the value of0.75 for a rough, free sphere in high Reynolds number flowpresented by Scoggins.14 A possible reason for the high dragcoefficient of the 2.5 m balloon is that the aerostat was notperfectly spherical due to the use of only 6 gores, giving it aless streamlined, hexagonal shape. A second possible source is the surface roughness caused by the net. Finally, dueto offsets and inaccuracies in the GPS system used, the drag coefficient found is tentative at best. The existence of

-8 -6 -4 -2 0 2

-20

-15

-10

-5

0

5

WindDirection

NoFigure-of-8

Figure 6. Motion of the Aerostatfor a Typical 30 m Flight

Horizontal Distance from the Winch

Distance East, m

DF

LF

TF

θ

Figure 7. Free Body Diagram of a TetheredAerostat


Figure 8. 10.15 m Diameter Aerostat Model

higher drag coefficients for buoyant, tethered spheres as compared to fixed, smooth spheres, however, will prove tobe key knowledge for the analysis of the stresses seen in the balloon’s envelope during flight.

III. Finite Element Analysis of a Fabric AerostatThe catastrophic failure of aerostats in high winds tends to occur when a local failure of the envelope propagates

into a massive tear.9 To quantify exactly how and why aerostats fail, a Finite Element Analysis of the stresses in theenvelope was conducted to see where stress concentrations exist and what limits fabric aerostats from operating inhigh wind speeds. A nonlinear static analysis of the envelope was performed, as it was expected that the envelopedeflection would be large.15 The analysis assumed a quasi-static state for the balloon with the inertial terms beingequal to zero.

A. Finite Element ModelThe 2.5 m aerostat described previously is not very suitable for carrying useful payloads, and so the investigation

was performed on a 10.15 m diameter aerostat, being considered for NRC’s 1/3 scale Large Adaptive Reflectorexperiment.16 The ballonets and seams were omitted for simplicity due to their lack of influence on the major hullstresses. The model, Fig. 8, featured 8 tethers that each separate into 8 sub tethers before attaching to the tangent of

the balloon through 0.5 m diameter load patchesspaced at equal intervals around a ring 35° belowthe equator of the sphere. The tethers andsubtethers were modeled as cylinders of 11 mmand 15 mm in diameter respectively, theappropriate diameters for a balloon of this size.The load patches were approximated as circularareas of the envelope where the thickness doubles,which assumes a perfect bond between the two.

The 10.15 m diameter balloon was made fromLamcotec’s 205 g/m2 (6.05 oz/yd2) urethane-coated nylon. In the absence of detailedorthotropic mechanical properties for thismaterial, the envelope material was approximatedas being linear elastic isotropic Nylon 6, used as

the load-bearing component of some airship envelope materials,1 but with the thickness, areal density, and breakstrength of the Lamcotec fabric. The tethers were made of Cortland’s Plasma 12-strand rope and were alsoapproximated as being linear elastic isotropic. The properties of the envelope and tether materials are shown inTable 1.

Table 1. Material Properties

Nylon 617 Cortland Plasma RopeYoung’sModulus

2.5 GPa Thickness 0.18 mm Young’sModulus

37.4 GPa SubtetherDiameter

15 mm

Poisson’sRatio

0.39 ArealDensity

205 g/m2 Density 980 kg/m3 Tether BreakStrength

93.4 kN

Density 1140 kg/m3 BreakStrength

142 MPa TetherDiameter

11 mm SubtetherBreak Strength

169 kN

The envelope was made from linear triangular elements, as they conform better to curved boundaries than linearrectangular ones and have reduced computational needs over those of quadratic triangular elements.18 To avoidinstabilities in the equations used by NASTRAN for the nonlinear analysis, beam and shell elements with smallbending stiffnesses had to be used for the envelope and tethers respectively.

It was found that constraining the model only at the confluence point of the tethers led to singularities in thestiffness matrix that caused diverging displacements to be generated by NASTRAN. The next most realistic solutionwas to constrain each tether, but not the subtethers, in its entirety from translating in any direction. This is equivalentto having infinitely stiff tethers. Since the main interest of the analysis was the stress distribution in the balloon’senvelope, this approximation was deemed acceptable.

LoadPatch


B. Simulated LoadsThe forces applied to the model included aerodynamic and internal pressures, and gravity. The static pressure

distribution over a tethered, buoyant sphere as it moves through the air is not available in literature, and theaerodynamic load was approximated using the distribution over a smooth, fixed sphere in high Reynolds numbersteady flow. The highest Reynolds number for which this staticpressure distribution is available was published by Achenbachfor Re = 5x106 and is shown in Fig 9.19 It is of interest toanalyze envelope stresses at high wind speeds, and a Reynoldsnumber of this magnitude corresponds to a relatively low7.1 m/s wind speed for a 10.15 m diameter spherical aerostat.As seen in Fig. 9, however, the static pressure profile does notchange dramatically for high Reynolds numbers since theseparation point of the flow from the sphere remains relativelyconstant. It was therefore deemed reasonable to use thisdistribution for higher Reynolds numbers. A further issue withusing the depicted distribution is that it implies a dragcoefficient of only 0.23. As discussed in Section II, the dragcoefficient of tethered, buoyant spheres tends to be much higherthan this, an issue that will be addressed later.

Helium has a lower density than air, and its pressure decreases more slowly over a change in height, z. Referringto the balloon in Fig. 10, if the pressures of the two gases are equal at some reference height, zo, a differentialpressure will act outwards to the envelope above that height with the resultant being an upward, buoyant force. Itfollows that buoyancy was simulated in the program by varying the internal pressure of the balloon as

eHeairii gzpp )( ρρ −+= (2)

where ρHe is the density of helium, g is the gravitational acceleration of 9.81 m/s2,ip is the mean internal

overpressure for the balloon, taken to be 249 Pa (1 inWG), and ze is the vertical distance in meters from the center ofthe balloon. Integrating the pressure profile described by Eq. 2over the surface of the 10.15 m aerostat yields a gross lift of5621 N. With gravity simulated as an acceleration equal to g andapplied to the entire model, the net lift of the aerostat isdetermined by NASTRAN to be 4969 N.

The highest wind speed at which the model can be evaluatedis constrained by “dimpling,” or a loss of aerostat’s sphericalshape when the dynamic pressure of the wind exceeds theinternal pressure of the balloon. Dimpling will first occur at thestagnation point because, referring to Fig. 9, the aerodynamicpressure has its highest positive value there. Once a dimple isformed, the balloon turns into more of a sail, causing the dragforces to rise as the entire dimpled area is exposed to thestagnation pressure, and rendering the assumed static pressure

distribution invalid. Since the stagnation point will always be at the center of the balloon, where pi = 249 Pa,dimpling occurs when ½ρairu

2 > 249 Pa, or when u > 20 m/s corresponding to a Reynolds number of 14.1x106 forthe 10.15 m aerostat.

C. Results of the Finite Element AnalysisThe constraint force, FT in Fig. 7, and the hoop stress in the envelope at the point that is diametrically opposite

the stagnation point, far from the influence of the tethers, were predicted with simple analytic expressions to be8230 N and 4.10 MPa respectively. The constraint force and hoop stress returned by NASTRAN were both within0.8% of the expected values, supporting the accuracy of the model.

The distribution of the stresses over the envelope is shown in Fig 11 a). Those areas in which a mesh is seenrepresent regions where the deformed shape of the aerostat is internal to the original shape. Away from the influenceof the tether attachment points the stress in the envelope changes with a profile similar to the static pressuredistribution, due to the hoop stress in the membrane being proportional to the pressure on the fabric. From Fig. 9 it is

Angle Back from the Stagnation Point, deg

x- Re = 1.62x105

- Re = 3.18x105

- Re = 1.14x106

- Re = 5.00x106

Figure 9. Static Pressure Distribution Overa Smooth, Fixed Sphere19

z po – ρairgz

po - ρHegz

po

zo

Figure 10. The Mechanism of Buoyant Lift1


seen that the aerodynamic pressure of highest magnitude occurs approximately 80° from the stagnation point, and isdue to a suction on the surface. The high aerodynamic suction combines with the large internal pressure at the top ofthe balloon to create a region of large skin stress, where the stresses reach up to 9.7 MPa.

The highest stresses in the envelope were concentrated around the load patches. However, due to the variablemembrane stresses caused by the aerodynamic pressures, these concentrations were not even amongst all 8 patches.The maximum stress occurred at the lower load patch on the side of the balloon in Fig. 11 a), located approximately75 - 80° back from the stagnation point in the region of high aerodynamic pressure, and was equal to 19.9 MPa. Thetensile stress was concentrated just above the load patch, a consequence of the membrane thickness halving whenmoving from the load patch to the envelope.

The lowest stresses in the envelope, around 1.02 MPa, are in the region of the stagnation point. This is becausein the near-dimpling wind speed of 20 m/s, the aerodynamic pressure is equal in magnitude and opposite in sense tothe internal pressure, and so they cancel each other out. The region of the stagnation point also displaces backslightly farther than those areas around it, about 12 mm as compared to 7 mm, illustrated in Fig. 11 b), indicating theonset of dimple.

D. Practical ConsiderationsThere are two important assumptions made in the preceding analysis. The first is the relatively low drag

coefficient of 0.23 for the aerostat. Williamson and Govardhan published the only experimental drag coefficient datafor tethered, buoyant spheres. They found that at a subcriticalReynolds number of 14000 the drag coefficient would be around 0.7.6

Since supercritical drag coefficients tend to be lower than subcritical,the drag coefficient of 0.7 was conservatively used for analysispurposes and design purposes, as described later in Section IV.

To determine the relationship between the drag coefficient of thetethered sphere and the maximum stress in the envelope, thesimulation was run for 7 different wind speeds from 0 m/s to 20 m/sand the maximum stress in the envelope as well as the drag force wereevaluated. Figure 13 shows the correspondence between the dragforce and the maximum stress for each test case, and we can see thatthere is a linear relationship between the two. Since the drag force onthe tethered sphere depends proportionately on the drag coefficient, asillustrated by Eq. 1, it follows that the maximum stress in the envelopewill then depend proportionately on the drag coefficient. Hence, when considering the more realistic drag coefficientof 0.7, the highest stress in the envelope of the aerostat in a 20 m/s wind is expected to be 19.9 MPa(0.7/0.23) =60.6 MPa.

The second idealization in the analysis is that the loads are distributed evenly amongst the tethers. However, asan aerostat moves through the air it is very common for the tethers to become unevenly loaded. Consider a situationwhere the aerostat pitches slightly about the confluence point, and the tether in the region of maximum stresses

80°

Wind

4.12 MPa

BalloonCenter

9.7 MPa

Tether

19.9 MPa

Stress, MPa(Range Narrowedto 1.02 - 12 MPa)

Spot of HigherDisplacement About the

Stagnation Point

Displacement, mm(Range Narrowed

to 0.1 – 40 mm)

a) Stresses (exaggerated view) b) Displacements (unexaggerated view)

Figure 11. Stress and Deformation Profiles Over the Fabric Aerostat in a 20 m/s Wind

0 1000 2000 3000 4000 50000

2

4

6

8

10

12

14

16

18

20

22

Drag Force, N

Max

imum

Str

ess,

MP

a

Results from NASTRAN

Linear Approximation

Figure 12. Rise in MaximumEnvelope Stress with Drag Force


Lip

BondedRegion

d = 0.0120.21

0.255

0.063

0.015

Figure 13. TetherAttachment Plate

momentarily experiences the entire load while still oriented tangent to the balloon. In this case the maximum stressexperienced by the envelope will rise by 8 times, from 60.6 MPa to 484 MPa, above the 142 MPa breaking strengthof the 205 g/m2 envelope laminate. It follows that the fabric balloon would be incapable of surviving wind speedseven below the dimple speed. Since 20 m/s winds can regularly occur in some environments, it becomes relevant toconsider how an aerostat might be redesigned in order to survive much higher wind speeds.

IV. Partial-Hard Aerostat DesignThere are aerostats in existence that can survive winds higher than 20 m/s: TCOM’s largest, 16000 m3 aerostats

can survive up to a 46.3 m/s (90 knot) wind, equivalent to a grade 2 hurricane. TCOM achieves this reliability byusing heavier materials unsuitable for smaller balloons, and avoids dimpling by using very large internal pressures,which proportionally raises the envelope stresses. An alternative solution for increasing an aerostat’s resistance topoint loads and dimpling is to reinforce the envelope using a hard shell in the critical areas of the balloon. Based onSection III, these critical areas include the region of tether attachment and the stagnation point, both of which lieapproximately on the bottom 1/3 of the aerostat for wind speeds above the dimple speed. It was decided to design a10.15 m diameter spherical partial-hard aerostat that would be operable in a 46.3 m/s wind with a safety factor of1.5.

A. Designing the Partial-Hard BalloonMaintaining a low weight, and consequently a high lift, is a critical factor when designing an aerostat. It follows

that a hard material with a high strength-to-weight ratio must be used for the shell, such as carbon fiber. AdvancedComposites Group’s LTM25/CF0511 woven prepreg carbon fiber, with the mechanical properties shown in Table 2,was selected for the analysis. Woven carbon fiber was chosen as it can have quasi-isotropic mechanical properties, ifat least 2 layers are used with fiber directions oriented at their largest angles from each other,20 and is less expensiveand more readily available than multiaxial carbon fiber. Furthermore, a prepreg was preferred as it ensures that theresin is evenly distributed amongst the fiber reinforcement, improving strength and reducing the variance inmechanical properties across the composite, and eases the molding process by allowing for a “hand-layup.”21

Table 2. Material Properties for Advanced Composites Group’s LTM25/CF0511 Carbon Fiber

Fiber Direction Modulus 65.6 GPa Fiber Compression Strength 405 MPaShear Modulus 3.17 GPa Shear Strength 78.2 MPaPoisson’s Ratio 0.03 Areal Density 0.435 kg/m2

Fiber Tensile Strength 562 MPa Per-Layer Thickness 0.28 mm

The LTM25 epoxy resin used in the carbon fiber composite is not Helium impermeable, thus requiring the use ofa full 10.15 m Helium-enclosing fabric envelope embedded in the carbon fiber shell. The fabric chosen for theenvelope was Lamcotec’s 142 g/m2 (4.2 oz/yd2) urethane-coated nylon, presented in Section II, as it is light andworkable.

The tethers were designed to attach to the tangent of the aerostat 35° below its equator using mildly curvedrectangular plates bonded to the side of the carbon fiber shell. The design of the tether attachment plates was kept

simple, as the main interest of the analysis is the protective shell. The plates, Fig. 13,have a bonded region and a protruding lip with a hole lined by a grommet throughwhich the tethers pass. The recommended adhesive for the plates is Loctite’s HysolE-20HP, which has a tensile strength of 39.3 MPa and a shear strength of 28.6 MPawhen bonded to epoxy.

The tether attachment plates were designed so they would withstand the loadingscenario in which one tether takes the entire load in a 46.3 m/s wind while still comingoff the tangent of the balloon. Based on a drag coefficient of 0.7 and a factor of safetyof 1.5, the expected tether load would be 1.12x105 N, requiring a 12 mm CortlandPlasma rope. It was found that in order to resist the shear stresses in their lips and the

tensile stress concentrations at their holes, the tether attachment plates would have to be made out of 10 layers ofcarbon fiber and have the dimensions shown in Fig. 13.12

The edges of the adhered region of the tether attachment plates are bonded to the shell 35° below the equator ofthe spherical aerostat. To clear the plates, the carbon fiber shell was brought up to 33° below the equator. A fullyfabric 10.15 m balloon with a drag coefficient of 0.23 will experience a blowdown angle of 42.5° when subjected tothe dimpling wind speed of 20 m/s. At this speed the stagnation point of the wind lies on the carbon fiber shell


42.5° - 33° = 9.5° below the fabric-carbon fiber interface, and so dimpling is prevented. In fact, the extra weight ofthe partial-hard balloon combined with the higher drag coefficient of a tethered, buoyant sphere will result in asteeper blowdown angle, thus moving the stagnation point further toward the bottom of the balloon.

It was found that the radius of the simulated 10.15 m aerostat of Section IV would expand by a maximum of0.011 m when subjected to only internal pressure and gravity, and it was decided to make the radius of the carbonfiber shell 0.011 m larger than that of the fabric balloon, or 5.086 m total, to account for the bulging. The number oflayers needed for the shell was determined iteratively by first predicting the maximum stress the fabric aerostat ofSection III would see in a 46.3 m/s wind based on the rise in drag force, calculating the number of layers of carbonfiber needed to resist the stress, checking for failure using a finite element model of the partial hard balloon(described later), and revising the design as necessary. The best results were found when using 2 layers of carbonfiber in the shell and a ring of 5 layers that started 45.2° below the equator of the balloon and rose to 33° below,Fig. 14, thus encompassing the tether attachment region.

Eight 1” wide and 3.0 mm thick nylon straps were employed to attach the fabric envelope to the carbon fibershell. The straps ran over the top of the balloon and were sewn directly into the envelope. At the end of each strapwas a metal ring through which one of the 8 tethers passes before going through the hole of a tether attachmentplate, as illustrated in Fig. 14. This alleviates some of the load seen by the plates. The fabric envelope was also gluedto the carbon fiber along the rim of the shell using an epoxy glue in order to minimize movement between the two.

B. Finite Element ModelIn the absence of detailed matrix and fiber information, the LTM25/CF0511 carbon fiber was modeled as being

linear elastic isotropic with the mechanical properties shown in Table 2. This was deemed acceptable because, asstated above, when using more than one layer of the woven prepreg it is expected to have quasi-isotropic properties.The number of layers of the composite used was described in the model by the thickness of the carbon fiber, inmultiples of the single-layer thickness, thus assuming a perfect bond between the sheets.

The carbon fiber shell was created as a spherical section covering the bottom of a theoretical sphere of 5.086 min radius starting 33° below its equator. Eight tethers emanated from the tangent of the shell 35° below the equatorof the sphere. The tethers were modeled identically to those of Section III, save that their diameter was increased to12 mm to accommodate the higher loads in the present model. The end node of each tether was tied to a node on thelip just below the edge of the adhered region of a tether attachment plate to approximate the attachment interface.The carbon fiber shell and tether attachment plates were all made out of triangular shell elements.

The Helium-enclosing fabric envelope was modeled similarly to the 10.15 m aerostat of Section III. The gluedregion was approximated by tying nodes around the rim of the carbon fiber shell to the fabric envelope. The strapsseparated from the envelope 1° above the fabric-carbon fiber interface and ran to the tether attachment point on thelips of the attachment plates. One node on the end of each strap was tied to both the lip and the end of each tether.The material for the fabric balloon was assumed to be linear elastic isotropic nylon 6 with a thickness of 0.15 mmand an areal density of 142 g/m2.

The simulated loads and constraints for the partial-hard model were similar to those of the fabric model inSection III. The aerodynamic pressure was applied only to exposed surfaces and not to protected areas such as thefabric enclosed within the carbon fiber shell. The internal pressure profile described by Eq. 2 was applied only to the

Strap

Tether

AttachmentPlate

MetalRing

45.2° 33°

5 LayerRing

2 Layershell

Strap

SeparationPoint

PointAttachment

Fabric-CarbonFiber Interface

Strap inthe

Fabric

0.063 m

0.27 m

0.21 m

Tether

Figure 14. The Simulated Carbon Fiber Shell, Straps, and Tether Attachment Plates


fabric sphere and straps. The tethers were constrained from translating in any direction identically to the model ofSection III.

C. Results of the Finite Element AnalysisA plot of the fabric envelope is shown in Fig. 15 a). The highest stress is equal to 45.5 MPa and occurs at the top

of the balloon approximately 80° back from the stagnation point. It is speculated that this maximum stress will notrise much with a rise in drag coefficient from 0.23 to 0.7. To illustrate this, we refer to Fig. 9. When the flow over afixed, smooth sphere changes from being subcritical to supercritical at Re = 3x105, there is a change in the staticpressure distribution on the back half of the sphere, which leads to the change in drag coefficient. However, themagnitudes of the maximum pressure coefficients 75° - 80° past the stagnation point are lower in the subcriticalstate, where the drag coefficient is higher, as compared to the supercritical state. Similarly, the increased drag in atethered sphere as compared to a fixed sphere is likely not caused by a rise in magnitude of the aerodynamicpressure coefficients, but by a change in the pressure distribution over the back of the sphere.

The resultant of the negative aerodynamic pressure over the back of the fabric sphere will try to suck it out of thecarbon fiber shell, loading the straps. The stress in the fabric balloon, however, does not appear to concentratearound the strap attachment points. The reason for this is that the glued area alleviates some of the tension in thestraps and ensures they are evenly loaded, resulting in a maximum stress of just 17 MPa in that region. If one wereto take into account the more realistic drag coefficient for a tethered buoyant sphere of 0.7, rather than the value of0.23 assumed for the simulation, the maximum stress of 17 MPa rises to 51.7 MPa. Considering the 152 MPabreaking strength of the 142 g/m2 Lamcotec fabric in the weft direction, there is a safety factor of 2.9 in the fabricenvelope.

A plot of the stresses in the carbon fiber shell can be seen in Fig 15 b). Due to using a ring of 5 layers around thetether attachment plates and a shell of 2 layers elsewhere, the stresses are fairly evenly distributed throughout theentire carbon fiber section. The stresses on the bottom of the shell were 2 – 3 MPa larger than at the top, however, aconsequence of the buoyant fabric sphere pulling upwards on the carbon fiber shell.

The highest stresses in the carbon fiber section were from 6.5 MPa up to 10.2 MPa and occurred in the regionsaround and below the tether attachment plates, and behind the lips of the plates. Furthermore, there were relativelylarge stresses, around 8 MPa, just at the rim of the hard shell where the fabric sphere came in contact with thecarbon fiber section. Following the logic presented in Section III, if the drag coefficient for a tethered buoyantsphere of 0.7 were taken into account, and if one tether coming off the tangent of the shell briefly undertook theentire load, the maximum stress of 10.2 MPa will rise to (10.2 MPa)(0.7/0.23)(8) = 248 MPa. The resulting safetyfactor is 1.6 when considering the carbon fiber’s 405 MPa compressive strength, above the target value of 1.5.

D. Practical ConsiderationsThe envelope and shell of the partial-hard aerostat presented weigh 165 kg together, while the envelope of a

conventional 10.15 m diameter spherical balloon only weighs 79.5 kg. This equates to an increase in the alreadysteep blowdown angle in a 20 m/s wind from 70.5° in the fully-fabric case to 73.9° in the partial-hard case,calculated using a CD of 0.7. To regain the original blowdown angle the diameter of the partial-hard aerostat wouldhave to be increased to approximately 11.75 m. If an increase in diameter of this magnitude is not acceptable, the

Stress, MPa

45.5 MPa

No StressConcentrations

Wind

10.2 MPaStress, MPa

(Range Narrowedto 0.01 – 7.5 MPa)

High StressRegion

Tether

AttachmentPlate

a) Fabric Envelope b) Carbon Fiber Shell

Figure 15. Stress Profile Over the Partial Hard Aerostat


weight of the partial-hard balloon could be reduced by using a lightweight 2.5 oz/yd2 urethane bladder for theprotected bottom 1/3 of the fabric balloon, and by removing those sections of the carbon fiber shell that see lowstresses and do not risk being exposed to the stagnation pressure in wind speeds above the dimple speed. Using thesetwo strategies would cut the weight difference as well as the increase in blowdown angle by more than a third.

There are large ovens and autoclaves that canaccommodate curing the hard shell of the 10.15 mpartial-hard balloon in one piece. However, making theshell in one piece would then require a means to transportthat piece to the launch site. A more practical solution isto make the carbon fiber shell out of 8 cylindrical goresthat would fit into a standard 14.6 m (48’) long x 2.6 m(102”) wide x 2.8m (110”) tall semi-truck trailer, Fig. 16,and then assemble it by adhesive bonding on site. The useof 8 cylindrical gores is beneficial as it allows the loadfrom each tether to be taken by a solid piece of carbonfiber. Another solution would be to lay the carbon fiber inits mold and cure it at a low temperature in a heatedhangar on site, allowing the strength of a single-pieceshell to be retained.

V. ConclusionsThe design of a robust helium aerostat began with the construction of a 2.5 m diameter spherical balloon to

review conventional design and construction methods. It was found that although building an aerostat in-house is 3to 5-times cheaper than buying one off the shelf, construction time is lengthy, the potential for error is large, and thefinal result is of poorer quality. This led us to conclude that the purchase of experimental balloons from aprofessional supplier would be warranted for future research. The 2.5 m aerostat was flown outdoors while mooredto the ground by a single tether, and due to the erratic nature of the wind it did not exhibit the figure-of-8 motionpredicted for tethered, buoyant spheres. The drag coefficient of the aerostat was observed to be 0.88, high even fortethered spheres. However, the value found is not reliable due to inaccuracies with the GPS system used.

A finite element analysis of the stresses in the envelope of a 10.15 m diameter spherical fabric aerostat in a20 m/s wind detected the onset of dimple. The analysis further showed the aerostat would fail when uneven loadingamongst the 8 tethers as well as a more realistic drag coefficient were considered. A hard shell was designed toprotect the bottom 1/3 of the 10.15 m spherical aerostat so that it could operate in a 46.3 m/s (90 knot) wind. In thehigh wind, the fabric envelope saw relatively low stresses, yielding a safety factor of 2.9. Using a 2 layer carbonfiber shell with a ring of 5 layers around the tether attachment points, a general safety factor of 1.6 was attained forthe balloon. The weight of the aerostat was doubled for the ultra-robust aerostat design, however, increasing theblowdown angle, but considering there is not a comparably sized balloon that can survive 46.3 m/s winds, the costincurred may be deemed acceptable.

The analysis performed was limited by the approximations made. In future analyses, more detailed mechanicalproperties should be determined for the simulated materials, as well as better approximations for the drag-causingaerodynamic pressure profiles on the aerostat before and after dimpling.

AcknowledgmentsThe funding for this project was provided by the Natural Sciences and Engineering Research Council of Canada.

We would also like to acknowledge Profs. Lessard, Hubert, Sharf, and Nemes of McGill University, and Dr.Dewdney of the National Research Council for their technical suggestions and discussions.

References1 G. A. Khoury, J. D. Gillett, Airship Technology, Cambridge Aerospace Series 10, Cambridge University Press, 19992 R. H. Upson, Free and Captive Balloons, The Ronald Press Company, NY, 19263 R. J. Recks, A Practical Guide to Building Small Gas Blimps, Recks Publications, Chula Vista, Ca, 19974 R. J. Recks, An Introduction to Muscle Powered Ultra-Light Gas Blimps, Recks Publications, Chula Vista, Ca, 19985 C. H. K. Williamson, R. Govardhan, “Dynamics and Forcing of a Tethered Sphere in a Fluid Flow,” Journal of Fluids and

Structures, Vol. 11, 1997, pp. 293 – 305

4.85 m

0.62 m

33°5.086 m

2.8 m

2.6 m

3.8 m

3.26 m

45°

5.086cos33°= 4.27 m

Figure 16. Fitting the Shell into a Standard Semi-Truck Trailer


6 R. Govardhan, C. H. K. Williamson, “Vortex-Induced Motions of a Tethered Sphere,” Journal of Wind Engineering andIndustrial Aerodynamics, Vol. 69, 1997, pp. 375 – 385

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10 E. G. Pare, R. O. Loving, I. L. Hill, Descriptive Geometry, 4th Ed., The Macmillan Company, NY, 197111 J. H. Smalley, “Development of the e-Balloon,” Technical report AFCRL-70-0543, National Center for Atmospheric

Research, Boulder, CO, 197012 J. Miller, “The Design of Robust Helium Aerostats”, M.Eng. Thesis, Dept. of Mechanical Engineering, McGill Univ.,

Montreal, QC, Canada, 200513 F. M. White, Fluid Mechanics, 4th Ed., WCB/McGraw-Hill, 199914 J. R. Scoggins, “Sphere Behavior and the Measurement of Wind Profiles,” NASA Technical Note D-3994, June 196715 R. D. Cook, D. S. Malkus, M. E. Plesha, R. J. Witt, Concepts and Applications of Finite Element Analysis, 4th Ed., John

Wiley & Sons, Inc., 200216 C. Lambert, “Dynamics Modeling and Conceptual Design of a Multi-Tethered Aerostat System,” M.A.Sc. Thesis, Dept. of

Mechanical Engineering, University of Victoria, Victoria, BC, Canada, 200217 C. A. Harper, Modern Plastics, Modern Plastics Handbook, McGraw-Hill Handbooks, McGraw-Hill, 200018 S. Moaveni, Finite Element Analysis, Theory and Application with Ansys, 2nd Ed., Pearsons Education, Inc., 200319 E. Achenbach, “Experiments on the Flow Past Spheres at Very High Reynolds Numbers,” Journal of Fluid Mechanics,

Vol. 54, No. 3, 1972, pp. 565 – 57520 J. W. Weeton, D. M. Peters, K. L. Thomas, Engineer’s Guide to Composite Materials, American Society for Metals, 198721 U.S. Department of Defense, “Plastic Matrix Composites with Continuous Fiber Reinforcement,” Military Handbook,

MIL-HDBK-754(AR), 1991

[american institute of aeronautics and astronautics aiaa 5th atio and16th lighter-than-air sys tech....

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