Tensairity Concept Applied to Lighter-Than-Air Vehicles ...

1 Copyright © 2014 by ASME

TENSAIRITY CONCEPT APPLIED TO LIGHTER-THAN-AIR VEHICLES FOR LIGHT-WEIGHT STRUCTURES

Anna Suñol Vrije Universiteit Brussel,

Department of Mechanical Engineering

Brussels, Belgium

Dean Vucinic Vrije Universiteit Brussel,

Department of Mechanical Engineering

Brussels, Belgium

Lars De Laet Vrije Universiteit Brussel,

Department of Architectural Engineering

Brussels, Belgium

ABSTRACT Airships have the intrinsic advantages of Lighter-Than-Air

(LTA) vehicles: minimal energy consumption and Vertical

Take-Off and Landing (VTOL) characteristics. Due to these

advantages, significant efforts are being taken in order to

investigate new applications and technical improvements. More

specifically, there is a renewed interest in large airships for

heavy payload transportation and for stratospheric airships. The

design of large airships is a big challenge, especially when

considering the structural point of view, since big volumes

imply high loads, and since light weight is a major requirement

for this type of vehicles. In this context, a light-weight structure

is proposed by applying the structural Tensairity concept. A

Tensairity beam consists of a rigid air beam designed on the

basis of complete functional separation of the different

structural elements, allowing for a maximum optimization. In

this paper, the justification of the feasibility of applying

Tensairity components in airships is discussed based on two

criteria. The first criterion is the justification of the need of a

lightweight structure by a state of the art analysis and a study of

the principal characteristics of the existing types of LTA

vehicles structures. The second criterion is a preliminary

technical analysis, which aims to clarify if the load bearing

behavior of airships is suited for the application of the

Tensairity concept. Moreover, the bases for the development of

the concept for the LTA vehicles structures are established.

The advantages and drawbacks of the traditional rigid airships

structure in comparison with a non-rigid structure has been

analyzed, which conclusion is that the use of a rigid structure is

convenient for large airships, since it reduces significantly the

stresses of the envelope, but at the same time decreases the

payload efficiency due to the addition of the structure's weight.

Moreover, the analysis of the load bearing behavior suggests

the technical feasibility of applying Tensairity components,

since airships have to withstand high bending moments and

Tensairity structures are appropriate for withstanding such

loads. Finally, the principal guidelines for defining the various

load cases and for modeling Tensairity beams have been

defined. In order to confirm the hypothesis of the suitability of

Tensairity structures on airships, extensive research on design,

analysis and optimization of Tensairity beam grids in typical

airship loading conditions is needed.

INTRODUCTION It is well known that Lighter-than-air (LTA) vehicles,

like the "zeppelin" airships, were a common transport system in

the beginning of last century. Nowadays, LTA vehicles are

being again intensively researched, by focusing on the use of

new materials, techniques and applications for constructing a

future generation of airships [1]. The reason of this renewed

interest is related to the main advantage of applying the LTAs

concept: LTAs vehicles fly by the presence of the buoyancy

forces, which implies that the propulsive forces are very small

when compared to the standard aircrafts propulsion

requirements. In other words, the buoyancy forces eliminate the

necessity of producing energy to generate the required lift force

in order to counteract the airship weight. Another advantage

intrinsic to LTA is its hovering capabilities, which enables

vertical take-off and landing (VTOL).

One of the main requirements in the structural LTA’s design is

the minimization of weight to increase the transported payload.

In this line, a new light-weight structural concept is proposed,

which applies Tensairity components. Tensairity is a recent

concept of a lightweight structure based on the complete

functional separation of tension and compression elements,

enabling a separated weight-optimization for each structural

element [2]. It consists of air-beams, in combination with rigid

elements for supporting compression and cables to counteract

to the traction stresses. Tensairity beams are expected to reduce

the structural weight significantly for identical span and

maximum load requirement, when compared to the

conventional girders. As an example, a Tensairity beam of 10m

Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014

November 14-20, 2014, Montreal, Quebec, Canada

IMECE2014-38174


span, slenderness γ of 10 and a distributed load of 2kN/m is by

factor of 6 lighter than a steel HEB profile beam, when

designed for similar conditions [3]. The larger the slenderness,

the larger this factor will be. Such reduction in weight, in

combination with the property of an increasing performance

with length, suggests the possibility of applying Tensairity as

primary structural components for airships, expecting to yield

similar results. Such a property makes Tensairity an interesting

alternative for building LTA structures and an attempt following

such approach has been developed and researched in this paper.

The motivation underpinning such idea of applying Tensairity

in LTA vehicles was born within the framework of the

Multibody Advanced Airship for Transport (MAAT) project,

which design involves the structural analysis of a non-

conventional large stratospheric airship [4]. Concerning the

structural design, its main challenges are its large dimensions

and its non-conventional shape. Concerning the dimensions, the

airship is 346m of length, 218m span and 66m height, as shown

in Figure 1. It is conceived as the biggest airship ever designed.

Regarding the shape, the optimal geometries for pressurization

are the sphere or the cylinder, while MAAT geometry is

ellipsoidal and with a central hole due its mission requirements.

Until today, the study of the MAAT design have comprised

different disciplines, such as the preliminary airships

specifications [5], aerodynamic studies [6], power estimations

[7] or the docking procedure [8], among others, and along the

structural analysis the application of Tensairity beams has been

proposed. Consequently, the application of Tensairity beams for

airships has been decided to be further investigated.

Figure 1: MAAT project

The first step to apply Tensairity beams in the MAAT airships is

to investigate the feasibility of Tensairity beams in airships.

Thus, a literature study of the Tensairity structural principle and

its application in the relation to the airship characteristics has

been carried out. Along this line, the section LTA

STRUCTURES explores the existing types of airships

structures and compares their advantages and drawbacks.

Secondly, the section TENSAIRITY defines the principle and

main characteristics of Tensairity beams and presents already

existing applications. In addition, a justification of the use of

light-weight structures from a state-of-the-art perspective is

presented in the section TENSAIRITY APPLIED TO LTA

VEHICLES ADVANTAGES. From a technical perspective, the

application justification can be found in the section

MODELING LTA LOADING CONDITIONS, as well as the

definition of the modeling process to characterize such loads, as

input into the FEA solver. Moreover, in the section SECURITY

FACTORS AND STRUCTURAL DESIGN CRITERIA, the

most important criteria for a structural design in airships is

presented. Finally, in the section MODELING TENSAIRITY

BEAMS, the relevant aspects of the Tensairity beams process is

defined.

In general, the aim of this paper is to investigate the possible

benefits and the feasibility of Tensairity structures in LTA

vehicles and provide the methodological basis needed for the

development of the Tensairity concept application.

LTA STRUCTURES LTA are classified in 3 groups according to their

structure: (a) non-rigid airships, (b) semi-rigid airships and (c)

rigid airships. Figure 2 shows the main structural characteristics

of the three types of airships.

Non-rigid airships, or blimps, are those LTAs, which shape is

maintained solely by the envelope overpressure: the differential

pressure between the inner lifting gas and the outer atmosphere

pushes the envelope to the desired shape, counteracting all

other involved forces. In other words, the envelope is the main

primary structure carrying all the loads: gondola loads,

aerodynamic forces… Simple structures exist in the critical

areas (as the nose cone) where otherwise the fabric would need

to be thicker, in order to withstand the loads only by itself.

Loads are transmitted to the envelope by a system of cables and

distributed by a suspension system (adjustable catenary cable

system). Due to the absence of a rigid structure, non-rigid

airships are light, easy to design, build and maintain. However,

as the volume of the airship increases, drawbacks related to

manufacturing and maximum load bearing of the membrane

appear. Consequently, non-rigid airships are suitable for small

airships [1].

Semi-rigid structures consists both of a rigid keel and a

catenary suspension system that still carries load, although

playing a much reduced load in comparison to the non-rigid

structures. The rigid keel distributes the gondola weight along

the entire length of the airship and eliminates the main function

of the catenary curtain, although the envelope still acts as a

primary structure, due to the poor fit of keel and envelope.

Thus, the envelope still carries aerodynamic bending loads.

Consequently, the envelope is still partially responsible of

maintaining the desired shape by its overpressure [1].

Rigid airships are supported by a framework, which carries all

the loads and by itself maintains the shape of the airship, while

the purpose of the envelope is solely to maintain the presence

of the lifting gas inside. Consequently, the strength requirement

is much lower, allowing the use of lighter fabrics. Rigid

airships allow gas compartmentalization, which increases

safety. Rigid airships are not appropriate for sizes below one

million cubic feet (around 28,300 m3) volume. Its major benefit


is that there is no size restriction due to the envelope fabric

strength, which allows for larger volumes dimensions [9].

Figure 2: Graphical description of non-rigid, semi-rigid and rigid airships (Source, ref. [1])

According to such definitions, the design decision of non-rigid,

semi-rigid and rigid structures depends on the volume of the

airship, being the non-rigid the most suitable for small airships.

In addition, in the case of non-conventional shape airships,

where maintaining the shape only supported by the envelope is

challenging, the use of rigid structures might also be beneficial.

TENSAIRITY Tensairity is a recent light weight structural concept

based on tensegrity or, in other words, by the complete

functional separation of its structural elements. A basic

Tensairity beam consists of a beam made of 3 elements [10]:

cables, which solely withstand traction; a strut, which solely

withstands compression; and a pressurized membrane, which

pretensions the cables and stabilizes the compression element

against buckling. Its innovation, when compared to tensegrity,

is the addition of the pressurized membrane, which provides

cohesion and rigidity to the structure by pre-tensioning its

cables. Figure 3 shows the concept of Tensairity. Cables and

strut are connected, thus transmitting the forces to each other.

They are the only elements carrying load, and the membrane

acts only for stabilization. Tensairity beams are conceived as

effective beams for withstanding bending moments.

Figure 3: A Tensairity beam consists of a tension element (cable), a compression element (strut) and stabilizing element (membrane), each of them solely carrying one type of stress. (Source, ref. [2]).

If compared to a regular beam or a truss girder, the central rigid

elements are eliminated and substituted by an air beam. Such

central rigid elements of the conventional structures are not

optimal; since stresses are concentrated in the upper and lower

areas, and since central elements must be dimensioned for

buckling instead of for yield stress. By the elimination of such

elements and substitution by an air beam, there is automatically

a significant decrease of weight, while conserving high beam

inertia.

In addition to the suppression of central elements, the

membrane increases the buckling load by acting as a

continuous elastic support [3]. In the case of a simply supported

conventional beam which withstands compression, the buckling

force is defined as described in (1). In order to increase the

buckling force, it is common to apply vertical supports, which

effect is analogue to the reduction of the beam length. Equation

(2) shows the buckling force for the simply supported beams

having n vertical supports. Tensairity beams use a membrane as

a continuous elastic support, increasing the buckling force of

the compression element as shown in equation (3), where k is

defined as shown in (4).

𝑃𝑏 = 𝜋2 ·𝐸 · 𝐼

𝐿𝑏2

(1)

𝑃𝑏 = (𝑛 + 1)2 · 𝜋2 ·𝐸 · 𝐼

𝐿𝑏2

(2)

𝑃𝑏 = 𝑘 · 𝜋2 ·𝐸 · 𝐼

𝐿𝑏2

(3)

𝑘 = 𝜋𝑝

(4)

As a consequence, by selecting a proper inertia and internal air

beam pressure, the compression element can be dimensioned to


withstand the yield stress, instead of buckling criteria. Thus, all

the elements are dimensioned for the yield stress, leading to a

weight reduction - optimal structure. Tensairity beams can be

order of magnitude lighter than the girder beams, when

considered for the same span and load conditions [10].

Moreover, as the membrane does not carry loads, but acts as a

stabilization element, its internal pressure and membrane force

are independent of the length and slenderness of the beam.

Thus, large spans can be covered with the application of such

light beams. Considering the mentioned characteristics, Tensairity has an added value, due to its significant reduction on weight, its large span, easy storage, transportation and erection (95% of its volume is air) [3],

having a high potential for being used for wide span roof structures, temporary bridges and temporary buildings. Extensive research is being conducted, aiming to improve the design of the

Tensairity structures for different loads and constraints, as well as for different applications. Indeed, some Tensairity structures have

been already designed and successfully implemented as roof, bridge, or portable hangars. Tensairity horizontal beams are being

continuously researched and optimized [2].

Figure 4 shows already existing Tensairity beams applications,

all of them in the architectural domain.

Figure 4: Tensairity has already been successfully applied as long span beams for a roof and bridge, and for portable hangars.

There is a precedent of a Tensairity in an aeronautic

application, in current development, based on the construction

of inflatable kites. The aim of applying Tensairity on inflatable

wings is to increase the small load-bearing capacity of such

structures, which limits the aspect ratio of this wing type. For

such application, the Tensairity beams were needed to be

curved in order to be able to build wings with dihedral, sweep

and twist. A prototype was made and successfully flied,

demonstrating a higher performance than conventional air

beams in terms of weight, crash resistance, buckling load and

rigidity [11].

TENSAIRITY APPLIED TO LTA VEHICLES ADVANTAGES

In the section LTA structures, from a structural point of

view, three types of airships have been presented and their main

characteristics defined. An important conclusion of such

classification is the drawbacks of the non-rigid airships

structures requiring large volumes, which is principally due to

the high stresses on the envelope. These high stresses come

from the internal over-pressure, which maintains the envelope

shape under the load conditions. The Hoop stress equation (5)

relates a linear dependence of the envelope stress in respect to

the cylinder radius. Although equation (5) does not apply to an

airship, which geometry is not perfectly cylindrical, it provides

a qualitative sense of the effect of the envelope radius on the

envelope stresses.

𝜎ℎ =𝑃 · 𝑟

𝑡

(5)

Indeed, after the state-of-the-art study, it became clear that the

biggest airships ever built were rigid. Figure 5 shows the length

of several airships that have been in use, without considering

the projects currently under development. The conclusion is

that the biggest airships that have ever flown were rigid. It is

relevant to mention that all rigid airships were from the

previous century and not active for more than 90 years. Figure

5, thus compares vehicles designed using new and old

technologies. Nowadays, the use of composite materials and

structural software is enabling the design of higher performance

rigid airships. The data in Figure 5 has been extracted from

[12], [13], [14], [15], [16] and [9].

In addition, Figure 6 shows several current airship projects,

evidencing a nowadays renewed interest for large airships,

principally focusing on heavy payloads and stratospheric high-

altitude airships. The reasons of this new interest are the

advances in the design of higher performance materials,

propulsion, solar panels, and energy storage systems, as well as

the need for a more eco-oriented approach [17]. The data

shown in Figure 6 is obtained from [18], [14], [16] and [4].


Figure 5. Relation between airship Length and Payload for different structural airship types

Figure 6: Relation between airship length and payload for different structural airship types, predicted from the future airship projects base.

From Figure 6, it can be seen that there is a higher interest in

non-rigid airships, when compared to the rigid ones. The reason

of such preference is the requirement to lower the weight of the

structure, since the rigid structure leads inherently to a higher

structure’s weight and consequently to a lower payload

capacity. As example, Table 1 shows the ratio payload-total

weight (KPL), calculated by applying equation (6), for a non-

rigid and a semi-rigid airship with similar characteristics,

respectively, Goodyear GZ 20A (non-rigid airship) and

Goodyear NT (semi-rigid airship).

Due to the higher performance of non-rigid airships, a

significant research on fabric materials is being carried out,

aiming to design new fabric materials which will be able to

sustain the high membrane stresses [19].

𝐾𝑃𝐿 =𝑃𝐿

𝑊

(6)

Airship KPL [-]

non-rigid (Goodyear GZ 20A) 0,26

Semi-rigid (Goodyear NT) 0,20

Table 1: The payload-total weight ratio is 20% higher in a semi-rigid airship than in a non-rigid airship

It is important to mention the research and design of a rigid

airship, which has been built with air beams in 1990, the

Airboat [9]. This structure did not include the tension and

compression elements which give rigidity to the air Tensairity

beams, but already suggests the interest in the air beams

structures to be applied to airships. Airboat showed its main

benefit to be highly flexible in the event of impacts.

Considering the mentioned structural challenges on large

airships and the renewed interest in them, the Tensairity

concept appears as an appropriate light-weight structure

solution to be investigated, and thus substitute the traditional

rigid beams and girders with Tensairity beams. This solution

envisages fulfilling the same structural requirements, but being

much lighter in respect to the resulting weight.

MODELING LTA LOADING CONDITIONS As the first step in a structural design is the

understanding of the loading conditions, the respective analysis

of the most important loads is detailed in this section.

In the case of LTA airships, the primary loads are buoyancy,

internal overpressure, aerodynamic loads (both longitudinal and

lateral), weight and thrust force [20]. Consequently, the

objective is to clarify if the Tensairity keel will be able to

withstand such loads, and as result, decrease its weight by order

of magnitude, in comparison to a equivalent conventional rigid

keel.

The buoyancy force is the result of a difference in pressure

along the axis pointing to the Earth, which is the consequence

of the fluid weight. Such difference of pressure can be

expressed by the Bernoulli equation, by assuming zero velocity

[21]. When integrating the difference of pressure over the

airship surface, we obtain the net buoyant force, as shown in

equation (8) [21]. If this buoyant force is higher or equal to the

vehicle’s weight, the vehicle is labeled to be LTA.

𝑣2

2+ 𝑔𝑧 +

𝑝

𝜌= 𝑐𝑡

(7)

𝐹𝐵 = ∫ (𝑝2 − 𝑝1)𝑑𝐴𝐻 = 𝜌𝑓𝑙𝑢𝑖𝑑𝑔𝑉𝑏𝑜𝑑𝑦

(8)

Internal overpressure is needed in both, the non-rigid and semi-

rigid airships, but not required for rigid airships since, as

mentioned before, the envelope does not carry loads. Similarly

to buoyancy, the pressure distribution is not uniform and must

be modeled as a gradient of pressure following equation (7)

[22]. Atmospheric conditions must be taken into account, since

the variation in temperature implies the variation in pressure.

Figure 7 shows a structural numerical simulation of the MAAT

airship, where only overpressure was applied. The high stresses

on the envelope, especially in the junctures with the form-

finding elements, make evident the need of avoiding high

overpressures. A Tensairity structure will be considered instead.

0

1

2

3

4

5

6

7

0 100 200 300

Pa

ylo

ad

[t]

Lentgh [m]

non-rigid

semi-rigid

rigid

0

10

20

30

40

50

60

0 100 200 300 400

Pa

ylo

ad

[t]

Length [m]

non-rigid

semi-rigid


Figure 7: The MAAT FEA simulation considering only the internal overpressure as load evidences the need of a rigid structure for large non-conventional airships.

Aerodynamic loads are the result of the action of the air due to

the airship’s movement or the wind presence. In order to

estimate the overall value of these forces, it is useful to utilize

the force and moment coefficients, as defined in equations (9),

(10) and (11) [20]. In the case of dynamic analyses, it is also

necessary to take into account the virtual mass, due to the

considered large airships volumes. In practice, the virtual mass

flow implies that the vehicles movement in the air must be

modeled with a larger mass, influencing the accelerations. The

virtual mass force takes into account the force needed to

accelerate a body immersed in the fluid, as the sum of

accelerations related to the involved bodies and the neighboring

flow [23], and it is not negligible for the dense fluids as water,

and also for large volumes. On the contrary, this force is

normally neglected in the airplanes analyses, where the air

density is low and the respective air volume displaced is also

small. There are some tabulated mass coefficients for certain

geometries, and for other cases a 1D transient Computational

Fluid Dynamic (CFD) simulation is needed [20].

𝐶𝐿 =𝐿

0.5𝜌𝑣∞2 𝑉

23

(9)

𝐶𝐷 =𝐷

0.5𝜌𝑣∞2 𝑉

23

(10)

𝐶𝑀 =𝑀𝑦

0.5𝜌𝑣∞2 𝑉

(11)

Such values are useful for computing the required thrust and

dimensioning the control surfaces of the considered airships.

However, it does not contribute on determining the load

distribution along the airship. The aerodynamic bending

moment estimation can be computed by applying the equation

(12) [9].

𝑀𝑚𝑎𝑥 = 0.29 [1 + (𝐿𝑎

𝐷− 4) (0.5624𝐿𝑎

0.02

− 0.5)] 𝜌𝜇𝑣∞𝑉𝐿𝑎0.25

(12)

However, in order to obtain the complete aerodynamic loading

distribution, a CFD analysis must be performed and the

pressure on the envelope computed. Figure 8 shows the

pressure coefficient distribution on the Cruiser envelope while

the feeder is approaching, 15m below its docking position.

Such simulation has been performed considering the

atmospheric conditions at 15 km altitude, and a 5 m/s flying

velocity. In non-rigid airships, where deformations are high, a

Fluid-Structure-Interaction (FSI) simulation is highly

recommended [24]. The simulation shown in Figure 8 has been

conducted using FlowVision software, found appropriate due to

its moving body capabilities, its automatic mesh generation and

its coupling with Abaqus software [25].

Figure 8: Pressure coefficient distribution on the Cruiser airship during the docking operation

The local forces, as a component weight or the thrust force, can

be modeled as point loads in their corresponding positions,

while the weight load of the structure itself can be modeled as

the gravity force. As constraint, the inertial relief will be

imposed for the simulation of in-flight conditions [26]. Inertia

relief is the load distribution required to balance the externally

applied forces which are acting on a free or partially free body.

Inertial relief is thus defined as the loads resulting from the

respective masses accelerations [27].

In the case of semi-rigid airships, the envelope is still carrying

loads and the interaction of the structure-membrane must be

included as part of the structural design and analysis [1].

Although loading conditions are not identical to the situations

where Tensairity has been applied until today, the rigid keels of

airships are primarily carrying the bending loads [20], both due

to the gondola weight and aerodynamic loads. Such similarity

envisages the benefits of integrating Tensairity technology in

airships structural design, introducing it to the semi-rigid and

rigid structures, and thus enabling these new concepts for LTA

vehicles.

Due to the envisaged advantages, Tensairity is currently being

researched in the MAAT project framework under the loading

conditions estimated in [28]. The conceptual design is a rigid

airship where the keel is made of Tensairity frames, as shown in

Figure 9. Such frames are responsible of withstanding the

different loads mentioned in the section “MODELING LTA

LOADING CONDITIONS”, preventing the need of any


internal overpressure. This decision is taken due to the envelope

shape is far from a pressure vessel, reason why it would

generate large stresses if there is an internal overpressure. In

other applications where the decision of using Tensairity beams

is related to the size and not the shape of the envelope it might

be more convenient to design a semi-rigid airship.

Figure 9: Rigid cruiser with the photovoltaic roof (1), the propulsion units (2) the cabin and docking system (3) and the Tensairity keel (4)

SECURITY FACTORS AND STRUCTURAL DESIGN CRITERIA

The criteria for designing and dimensioning the airship

structure is regulated and defined in TAR (Transport Airships

Requirements) [29]. It is relevant to mention that:

- Strength requirements are specified in terms of limit

loads (the maximum loads expected in service) and

ultimate loads (limit loads multiplied by prescribed

factors of safety).

- Unless otherwise specified, a factor of safety of 1.5

must be used.

- The structure must be able to support limit loads

without detrimental permanent deformation. At any

load up to limit loads, the deformation must not

interfere with the safe operation.

- The structure must be able to support ultimate loads

without failure for at least 3 seconds. However, when

proof of strength is shown by dynamic tests simulating

actual load conditions, the 3 second limit does not

apply.

- In membranes the safety factor is 4 to account for

fatigue.

The structural design must consider the load cases shown

in Figure 10.

Figure 10: Scenarios that must be considered during the structural design (source Ref: [29])

MODELING TENSAIRITY BEAMS The main details of modeling Tensairity beams are

detailed in [2]. Due to the Tensairity principle, which is the

complete functional separation of the different components,

each component can be modeled with the corresponding

structural element. Following this concept, the Tensairity beam

membrane can be modeled as MEMBRANE element, which

does not withstand bending moments and, consequently, only

withstands tension. Due to the fabric nature, orthotropic

characteristics must be assigned to the applied fabric material.

The Tensairity beam compression element must be modeled as

BEAM elements, if metal materials are applied; and SHELL

elements composed by orthotropic layers, if the composite

materials are applied.

The cable is the most complex in terms of FEA modeling, since

it must be placed in its initial position, which is near to its

natural position. Otherwise, the numerical simulation can

become unstable. Consequently, it is important to find the

geodesic line, which is defined as the shortest path connecting

two points on a given surface, and then place the cable on it.

The interaction between elements is also important, since the

membrane is responsible for providing the rigidity of the

structure. The compression element is connected tightly to the

membrane, while the tension element is in contact with the

membrane. This condition must be also modeled in the FEA

solver, to prevent relative movement between compression

element and membrane. On the other hand, the tension element

must be modeled in such a way that the movement of the

tension element, when moving away from the membrane, is

allowed, while the movement to the membrane is prevented. All

these mentioned boundary conditions can be modeled by

contact conditions, where the friction can also be considered for

in-plane displacements.

It is highly recommended for the future numerical

investigations related to the Tensairity structures to be

systematically validated with the adequate experimental tests.

(1)

(2)

(3)

(4)


CONCLUSIONS The application of the structural Tensairity concept is an

interesting alternative for building LTA structures. This paper

has detailed the justification of the feasibility of applying the

Tensairity components in airships constructions, and has shown

the promising advantages. The presented justification is based

on two main criteria: the justification of the need of Tensairity

airship structures and a study of the technical feasibility.

Concerning the justification of the need, a state of the art

analysis has been performed, showing a renewed interest in

large LTA vehicles. Combining this interest with the facts that

(a) large non-rigid airships are structurally challenging and (b)

semi-rigid and rigid airships can transport fewer payloads due

to the structure’s weight, the need of lightweight structures is

justified.

Concerning the technical feasibility study, the principle of

Tensairity has been presented, and the airships loads have been

analyzed. The principal Tensairity advantage is that it can be

maximally optimized due to its inherent complete functional

separation, where every element withstand one type of load: the

strut only supports compression, the cable only supports

traction and the membrane stabilizes the system. Moreover, the

compression element can be dimensioned for yield stress

instead of buckling, due to the increase of the buckling force

resulting from the stabilization provided by the membrane.

In order to provide some insights in the external loading that a

Tensairity airship structure would need to support, the main

forces acting on airships have been identified and characterized.

The conclusion of this analysis is that the airship structures

have to withstand high bending moments. Thus it came out

naturally to apply the Tensairity principle, as it is especially

suited to bear bending moments

Taking into account the main conclusions presented, the

application of the Tensairity concept in the airships structural

design appears to be a technically feasible solution. In order to

confirm such hypothesis, extensive research in design and

simulation of Tensairity beams is required, and will be pursuit.

NOMENCLATURE 𝐶𝐷 Drag coefficient

𝐶𝐿 Lift coefficient

𝐶𝑀 Pitch moment equation

CFD Computational Fluid Dynamics

𝐷 Aerodynamic drag force

𝐸 Young modulus

FSI Fluid Structure Interaction

𝑔 Gravity

𝐼 Beam longitudinal inertia

𝐾𝑃𝐿 Payload-total weight

𝐿 Aerodynamic lift force

LTA Lighter-Than-Air

𝐿𝑎 Airship length

𝐿𝑏 Beam longitude

𝑀 Aerodynamic bending moment

MAAT Multibody Advanced Airship for Transport

𝑛 Number of vertical beams

𝑝 Static pressure

𝑃 Internal overpressure

𝑃𝐿 Payload

𝑃𝑏 Buckling force

𝑟 Envelope radius

𝑡 Envelope thickness

𝑣 Air velocity

𝑉 Airship volume

VTOL Vertical Take Off and Landing

𝑣∞ Airship velocity

𝑊 Total weight

𝑧 Altitude

γ Slenderness

𝜌 Air density

𝜎ℎ Hoop pressure

ACKNOWLEDGMENTS The presented work in this paper was performed as

part of the Multibody Advanced Airship for Transport (MAAT)

project with ref. 285602, supported by European Commission

through the 7th

Framework Programme, and which is gratefully

acknowledged.

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