Figure 1. Schematic of a CRTS reflector
Large deployable reflectors are required when designing high-gain antenna systems for spacecraft, particularly for land-mobile telecommunications payloads. A novel deployable reflector concept is presented here which is based on the inherent properties of doubly curved surfaces. The new reflector consists of three basic elements: a parabolic membrane, a number of collapsible ribs, and an expandable hub. The membrane itself serves both as the structure and as the radio-frequency reflective surface, resulting in a highly versatile lightweight antenna with substantial applications potential.
Large reflectors are a key element of high-gain antenna systems for spacecraft, particularly those carrying land-mobile telecommunications payloads, where there is a strong desire to keep the mobile ground terminals as small as possible. Such reflectors inevitably need to be foldable for launch and at the same time they have to fulfil a number of sometimes conflicting electrical and mechanical requirements.
In this field of large spacecraft antennas, one is constantly searching for reflector designs with improved specific mass (i.e. mass per unit aperture area), compact stowage volumes, and high deployment reliabilities. These requirements are driven both by the limited payload-accommodation envelopes of today's launchers and the high cost per kilogramme of placing payloads into orbit.
There are currently several designs of deployable reflector in various stages of development, ranging from outline concepts to fully qualified reflectors which have already been used on operational satellites. The vast majority of the well-developed concepts are based on a rigid deployable structure which, after it has attained its final shape, functions as a stable platform to which a reflective surface - such as an electrically conductive mesh - is attached. The key to the geometrical stability of this kind of reflector is therefore the stiffness and stability of this support structure.
Few concepts, however, make use of the inherent geometrical stability of a doubly curved, nonelastic membrane. A membrane of this type, properly shaped and tensioned, can function both as the structural element and as the reflecting surface, and as such has the potential of providing a truly lightweight reflector. This characteristic of doubly curved surfaces is exploited in the ESA-developed Collapsible Rib Tensioned Surface (CRTS) reflector presented here, which is the subject of ESA patents in France and the USA.
The CRTS reflector is based on the inherent geometrical stability of a doubly curved, non-elastic membrane which is maintained in a tensioned condition. A non-elastic membrane is one that behaves like a piece of cloth rather than, for example, a sheet of rubber. To achieve the required tensioned state, the reflector has three basic elements: the parabolic membrane itself, a series of thin-walled collapsible ribs with C-shaped cross-section, arranged radially and supported by an expandable hub.
The hub is contracted during folding and deployment, so that the ribs can deploy the membrane without having to pre-stress it at the same time. Once the membrane is fully deployed, the hub is expanded to apply a state of prestress to the membrane and thus to set it into its proper shape (Figs.1&2). of applications also. In fact, it may very well be that this
Figure 1. Schematic of a CRTS reflector
Figure 2. Three-dimensional view of the CRTS reflector
The membrane itself consists of a set of flat gores, i.e. pie-shaped pieces of material, attached together at the seam. When the reflector is deployed, each gore takes the shape of what is called a 'parabolic cylinder'. This can be pictured as a tube with a parabolic cross-section. Hence, the overall shape of the reflector is not an exact paraboloid, but only an approximation to it whose accuracy improves as the number of gores is increased. Each rib is typically held in a pocket attached to the membrane at the seam between the two adjacent gores. It is positioned with the convex side facing upwards, i.e. towards the focus of the reflector. The ribs are firmly attached only to the outer rim of the membrane.
The reflector ribs
The radial ribs consist of thin
slender metal blades of C-shaped cross-section, which are pre-formed
to the nominal - usually parabolic - reflector profile.
The ribs are therefore doubly curved structural members, with a
high curvature (i.e. small radius) in the cross-section plane and
a low curvature (i.e. large radius) in the plane of the rib
itself. The ribs are firmly fixed to the membrane at the rim of
the reflector, and are allowed to slide relative to the membrane
at the intermediate positions. Near the vertex of the reflector,
they are connected to the expandable hub.
Owing to the curved cross-section of the ribs, they function as a beam up to a certain threshold bending moment. For bending moments higher than this threshold, the cross-section will snap into a flat shape, thereby reducing its local bending stiffness by a factor of up to 50. This basically creates an instant hinge line at any desired location along the rib. It is this feature that allows the reflector to be folded into a small volume for launch.
This unique behaviour of the C-shaped ribs has been investigated analytically, numerically and experimentally. The conclusion of this study is that the ribs' snap-through behaviour can be predicted reasonably well by finite-element analysis, but that all predictive techniques tend to underestimate the actual snap-through bending moment observed experimentally. Typical results from this work are presented in Figure 3.
Figure 3. Typical snap-through behaviour of a rib with C-
shaped cross-section --- finite-element results x, o Experimental
results
The most suitable material for the ribs is copper-beryllium, mainly because of its low creep behaviour, its relatively low stiffness and its high elastic limit. In addition, it is easily formed when in an annealed condition, and can be hardened with a rather simple thermal process. The low-creep attribute is particularly important as the antenna may be stored for prolonged periods in a folded condition and there should be no plastic setting of the rib.
The three key parameters of the rib's design are its width, the enclosed cross-sectional angle and the thickness of the blade material. They need to be optimised as a function of antenna size, required accuracy (the main factor determining the number of ribs needed) and deployed natural frequency. The rib design is not necessarily limited to a single blade, a multi-blade rib probably resulting in an even more optimised design, since the bending moment along the rib increases towards the reflector vertex.
Expandable hub
The expandable hub is designed to
provide the proper boundary conditions to the ribs at the vertex
of the reflector, and to supply a radial force (and displacement)
to these ribs for tensioning the membrane. It also provides the
rigid mechanical interface for the whole reflector. Within the
hub, the ribs are attached to sliding elements which can only
move in a radial direction. All other possible motions are
constrained. The force- and displacement-generating device, which
in essence pushes outwards on the sliding elements and therefore
on the ribs, can be based on a spring action or on a motor-driven
mechanism.
Membrane
The reflector membrane is required to have
a high in-plane stiffness, which provides a high and stable
surface accuracy, in combination with a low bending stiffness,
which facilitates folding. In addition to these essentially
mechanical requirements, it needs to be radio-frequency (RF)
reflective and exhibit low creep. A good candidate material that
can fulfil these requirements is a fibre-reinforced metallised
plastic foil. The membrane can be assembled from high-precision
gore segments whose seams coincide with the locations of the
ribs.
As the membrane of a CRTS reflector serves both as the prime structural element and as the RF-reflecting surface, it is important to note that the accuracy of the reflector is in principle determined by the accuracy of the membrane, with the ribs serving only as tensioning elements. This is fundamentally different from almost all other reflector designs, where the supporting structure controls the reflector accuracy to a large extent.
One additional desirable characteristic for the membrane is optical transparency. This stems from the fact that these kinds of reflectors will mainly be used for antennas that are large compared with the size of the host spacecraft. In this case, the solar radiation pressure becomes an important disturbing factor for the satellite's attitude control. Having a surface that is RF-reflective yet optically transparent minimises this effect, and would therefore be very desirable. One option for achieving this goal is to replace the metallised plastic foil with a nonelastic metallic mesh. Such a mesh would differ fundamentally from the knitted elastic type used on reflectors with a rigid support structure, and would most likely be a woven mesh with inherent high in-plane stiffness.
Auxiliary elements
Other elements required for a
CRTS reflector are a stowage container and a (pyrotechnic)
release system. The stowage container protects the folded antenna
package during ground handling, testing and launch, and is
released just before in-orbit deployment is initiated. The
release system, which holds the ribs and the membrane in folded
condition, initiates the actual deployment of the reflector by
releasing the ribs to deploy due to their stored elastic energy.
It is not inconceivable that both the functions of the stowage
enclosure and the release system can be combined into a single
device.
A CRTS reflector is composed of a foldable membrane and continuous ribs with no built-in hinges at fixed locations. This means that the same reflector can be folded in different ways, and this unique characteristic can be used to good advantage to fit the reflector into different, externally imposed, payload envelopes. However, the folding scheme selected does have an influence on the deployment behaviour of the reflector. These aspects have been studied in some detail and the results of this work are summarised below.
Folding schemes
Three different folding scenarios
are considered here:
Figure 4. Folding scheme 1
Figure 5. Folding scheme 2
Figure 6. Folding scheme 3
A comparison of the three packaging methods, based on packaging efficiency, complexity of the folding process, and the possibility that the reflector might deploy into a non-nominal configuration, shows Scheme 2 to be the most promising.
In terms of packaging efficiency, Schemes 2 and 3 are the best because they minimise the volume of gaps in the package. Scheme 2 is more flexible, because the height and diameter of the package can be readily modified to suit mission requirements. In Scheme 3, some space is taken by the region where the ribs bend and twist near the hub, but from this point onward the ribs wrap nicely around the package. With this scheme, however, changing the size of the folded reflector requires a careful re-analysis of the whole packing scheme.
As far as the complexity of the folding process itself is concerned, Scheme 2 is clearly superior and its practical implementation has therefore been tested experimentally. Implementing Scheme 1 should also be relatively straightforward, even though it may be difficult to ensure that the rib folds remain in the required position after packaging, while the implementation of Scheme 3 appears to be rather complex.
Only preliminary assessments can be made so far regarding the possibility of the reflector deploying in a non-nominal configuration. With Scheme 1, there is the possibility that the tip segments of the ribs might become interlocked during deployment, because all ribs are bent towards the centre of the hub in the packaged configuration, and they tend to move over centre during deployment.
For Scheme 2, two aspects are important. Firstly, a rib with several up and down folds is not naturally stable and needs to be suitably restrained to prevent it from buckling out of plane within the volume of the package itself. This aspect has been investigated experimentally and was found to be of no major concern. Secondly, there is the possibility that the membrane might go past the hub during deployment and, having deployed too far outward, be unable to flip back to the front of the hub, remaining in a concave, rather than a convex shape. This is a potentially serious problem, and indeed some deployment tests have shown this kind of behaviour. The problem can, however, be eliminated by contracting the hub diameter further than strictly required by pre-stressing considerations.
Scheme 3 appears to have potentially the lowest risk in terms of non-nominal deployment. The fact that the ribs are wrapped around the central part is likely to induce a kind of natural synchronisation of the deployment, thereby reducing the risk of non-nominal conditions.
Deployment
As noted above, the deployment behaviour
of a CRTS reflector has been studied both theoretically and
experimentally with a 1 m-diameter model. The theoretical work
concentrated on modelling the deployment of a single rib,
initially with a simple two-degree-of-freedom model of a rib
with a single fold, and finally with a finite-element model of
a rib with multiple folds. Based on this work, it is possible to
predict the global deployment behaviour of the reflector, and to
make a first estimate of the time needed to deploy a full-sized
reflector. One specific case analysed indicated that a 5 m-diameter
CRTS reflector will deploy in approximately 5 seconds.
Following the theoretical investigations, a series of deployment tests were carried out on the 1-m model packaged according to Scheme 2. This model differs in two respects from an actual CRTS reflector. Firstly, it has straight, instead of parabolically curved ribs, and hence the gores become flat when the model is fully deployed. Secondly, the model does not have an automatic hub contraction/expansion mechanism, and therefore tensioning of the membrane is not possible. Due to these simplifications, the model has to be considered a deployment model rather than a fully functional scale model.
For the test, the model was folded with a dedicated folding device and suspended horizontally. Deployment was initiated by cutting the restraining string, and recorded with a video camera. Figure 7 shows the successful deployment sequence. The reflector was deployed pointing downward, otherwise gravity effects would have been too large for the root folds of the ribs to snap-in. The time interval between consecutive frames in Figure 7 is 0.12 s.
Figure 7. Deployment sequence of the 1-m model folded
according to Scheme 2
The anticipated performance advantages of a CRTS reflector compared to reflectors with a rigid support structure are:
A less desirable attribute of the reflector is the rather uncontrolled deployment. The actual deployment progression, from initiation to fully open, is not kinematically controlled as in most - but certainly not all - other deployable reflectors. However, the division of the deployment into two distinctly separate phases, namely the actual deployment phase itself and the membrane tensioning phase, means that the ribs deploy without external constraint. They will therefore naturally return to their lowest energy state, which is their fully deployed position in a zero-gravity environment.
Other performance characteristics such as surface accuracy, deployed natural frequency, etc. have not been quantified so far but are currently being studied. They are not expected to differ substantially compared with other deployable reflector designs.
Whereas the primary application today for large deployable reflectors in general, and for the CRTS reflector in particular, is for land-mobile telecommunications payloads in geostationary orbit, other applications are also being considered, such as high-resolution radio telescopes based on Very Long Baseline Interferometric (VLBI) techniques, and Earth-observation weather radars.
An important aspect that is frequently overlooked is that deployable reflectors are not only required for large antennas, but are also beneficial for providing small to medium size antennas for small satellites. The low mass and the compact and flexible stowage characteristics of CRTS reflectors are strong assets that make them potentially very suitable for these kinds field of application will emerge as the more commercially appealing in the shorter term.
A special word of thanks is due to Dr. S. Pellegrino, Dr. Z. You and their co-workers in the Department of Engineering at Cambridge University (UK) for their substantial and enthusiastic contributions to the development of the CRTS reflector.
ESA Bulletin Nr. 88.