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A general truss system for very large space base foundations, with application to the solar power satellite
A GENERALTRUSS SYSTEM FOR VERY LARGE SPACE BASE FOUNDATIONS, WITH APPLICATION TO THE SOLAR POllER SATELLITE Anthony P. Coppa General Electric Company, Astro Space Division Philadelphia, PA 19101 shells (T-bacteriophages) and thin shell bucklina patterns which I had studied previously.(4,5,6] Finding that I was able to describe a number of such viruses within the framework of formulas that I had derived f o r the buckling patterns and having learned that the virus shells were composed largely of protein structures, I had then proceeded to attempt the same f o r protein and DNA backbone structures. While I was successful in this endeavor considerably late r(7) , at that early point in the study, while trying to model DNA, I produced with my formulas an extraordinary fold structure. This provided the insight f o r the COPPATRUSS. The p a r t i c u l a r fold structure is unique among an i n f i n i t e family of related structures any of which are specified by the base angle of the isosceles triangles that make up f a m i l i a r thin shell buckling patterns. In approaching construction of this f i r s t model, rather than choosing a value of the angle a r b i t r a r i l y , I u t i l i z e d instead a prominent angle that is present in protein chains, namely the tetrahedral angle (2 cos-1 I/V-3 or 109.5° ) and employed this as the sum of the base angles. Due to this fortuitous choice, the resulting structure immediately exhibited the remarkable property that when twisted at i t s ends i t crystallized into a geometrically perfect equilateral triangular prism. Further, by simple manipulations of the folded prism, i t was found possible to " c r y s t a l l i z e " numerous other prismatic structures of various forms. The choice of the tetrahedral angle f o r the model had produced the perfect-packing isosceles tetrahedron as the structural unit.
Abstract The paper presents a general three-dimensional truss system (COPPATRUSS) that appears uniquely capable of satisfying the requirements f o r very large foundation structures in space. The currently patented system obtains perhaps the highest structural efficiency (strength/mass and s t i f f ness/mass) possible in a general space truss. In addition i t offers great architectural variety, modularity, fabrication economy, low package volume f o r launch, and rapid, p r i n c i p a l l y automated, assembly in space. An example of an application to the Solar Power S a t e l l i t e is discussed. Introduction Very large space systems are foreseen f o r the Space Station era and beyond. An example of one that has been studied considerably is the Solar Power S a t e l l i t e ( I ) described as reqyirT ing a structural platform area of 60-120 km.[Z,~) Previous studies which h a v e discussed design concepts and methods of constructing such super large structures have estimated overall system masses in the tens of thousands of metric tons and the need f o r hundreds of space construction workers operating over extended periods of time. Obviously, such enormous enterprises will exert great demands on all related technologies and system design aspects. One of the greatest challenges will be to construct structures of unprecedented size u n d e r working conditions almost t o t a l l y foreign to experience. A large part of this challenge l i e s in the fact that when these structures are b u i l t in space, they will be b u i l t f o r the f i r s t time: there will be l i t t l e margin f o r error or a b i l i t y to correct unforseen problems in the construction process. Hence i t is important to u t i l i z e a process that has been proven out to a maximum extent p r i o r to i t s application in space.
Two properties of this structure were immediately evident: (1) the crystallized structures w e r e continuously triangulated and hence rigid and (2) the parent structure embodied a self-building principal. Both of these properties were seen at the time to be p o t e n t i a l l y valuable f o r space trusses. The isosceles tetrahedral cell became the geometrical unit of COPPATRUSS.
Given the a b i l i t y to construct such structures in space i t is crucial to u t i l i z e a highly e f f i cient structural system, one that provides the required strength, stiffness, architectural shape, dimensional stability, and d u r a b i l i t y at minimum l i f e - c y c l e cost. Minimum mass, material cost, launch stowage volume, and construction time associated with the structure and constructional implements are important performance measurements.
Development of the COPPATRUSS system was i n i t i a t e d in 1983 with the submission of a patent disclosure f o r a truss beam of equilateral triangular cross section.(8) The truss is unique in that i t is assembled from separate triangular frame elements, each of which contains the necessary node f i t t i n g s f o r connecting them together. This wa followed by a series of inventions( 9, 10, 11)s which describe structural details and methods of construction, including automated methods. Additional inventions are currently in the patent process.
This paper presents a general, three dimensional truss system (COPPATRUSS) that has the potent i a l of being the optimum of a l l possible truss systems f o r providing very large structures f o r space.
Ideal Truss Characteristics
COPPATRUSS is the result of a discovery that I made early in 1970 while engaged in a private study of the structures of helical protein chains and DNA. Immediately p r i o r to this event, my interest had been aroused by the apparent similari t y between the e x t e r i o r form of certain virus
The ideal truss system f o r constructing general large structures in space may be described as having the following characteristics: (1) I t is capable of uniformly triangulating 3-dimensional space; (2) the unit triangular cell is
Copyright ~1987 General Electric Co. Published by the American I n s t i t u t e of Aeronautics and Astronautics Inc. with p~rmission. A A IS--L
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equilateral; (3) i t offers a great variety of useful architectural forms; (4) i t can be constructed by assembling modules together; and (5) i t is suitable for automated construction, especially at the module level. Characteristic (I) signifies that any derived truss will exhibit a triangular relationship among any three adjacent strut elements and a tetrahedral arrangement among any six adjacent strut elements that are interconnected by four nodes. Such properties assure structural r i g i d i t y under general 3-dimensional loading and obtain highest stiffness and strength per unit weight. Characteristic (2) obtains an optimal balance of structural efficiency between tension and compression forces imposed on strut elements and also provides constructional simplicity. General space foundation trusses will be usually subject to free-free oscillations and at times attitude control torques. As a result strut elements will be usually subject to alternating tension and compression forces. The strength of the truss will be limited by strut s t a b i l i t y under compression loading. I f for instance, the limitation is due to strut column buckling, for which the resistance varies inversely with the square of the strut length, then strut length disparity results in strut weight and volume penalties. Characteristic (3) anticipates the evolutionary aspect of large projects in space. Large projects will tend to have extended lifetimes during which modification in size and/or shape of the initial truss configuration may be expected. This characteristic w i l l , of course, also provide the a b i l i t y to configure the i n i t i a l structure to satisfy ongoing design requirements. Characteristic (4) enables construction of the large structure from discrete building blocks, which themselves may be formed of lower order building blocks. This permits the planning and execution of more efficient construction processes. I t also may permit removal of building blocks from a given structure at a later time for re-use elsewhere. Characteristic (5) is necessary to reduce construction time as well as manual construction operations to a minimum. Automated assembly is necessary at the lower construction levels of a thoroughly modular system which has many constituent building blocks. Basic COPPATRUSSGeometry If the equilateral tetrahedron possessed the property of perfect packing, a truss geometry u t i l i z i n g i t as a unit cell would satisfy both characteristics (1) and (2). But since the equilateral tetrahedron does not possess this property, i t has l i t t l e value for a general three-dimensional truss system. The only unit cell that satisfies characteristic (I) and very nearly satisfies characteristic (2) is the isosceles tetrahedron whose base angles sum to the tetrahedral angle (2cos- I I/~-3). This is the geometrical cell of the COPPATRUSSsystem.
Because of its perfect packing property, such cells when packed together with their v e r t i ces in register everywhere generate a threedimensional grid of straight lines which uniformly subdivides space into equal triangular elements. A region about a cell is shown in Figure 1. I f strut elements are placed along this grid and node joints at all intersections of the grid, a completely triangulated three-dimensional truss entirely f i l l i n g the utilized space is obtained. Such a truss is rigid everywhere. Moreover, i f tetrahedral cells are selectively removed from the general space, open networks of cells are obtained. When the resulting arrangement of remaining cells is in the form of a triangulated truss, rigid open trusses are thereby obtained. This characteristic provides great choice of architectural form with assurance of structural r i g i d i t y on every case. Because of this property of generating many structural forms, we call this cell the prototetrahedron ( P T ) . Examples of open truss networks are given later. With regard to characteristic (2), strut length disparity derived from the PT cell is quite small. The edges of the PT are made up of four shorter edges ~f = 1.151ength5s ~and two longer edges of length 2s/ ~3 . . Hence, the penalty due to the longer edge per se is small. As pointed out later, moreover, the longer and shorter edges are associated with certain symmetries in the COPPATRUSS which minimizes the penalty due to edge disparity. In contrast, a general truss system that is based on a cubical cell (also perfect packing) suffers from the lack of natural diagonals in the three-dimensional grid. The grid generates only orthogonal cell arrays. Hence in general such a system does not produce rigid open truss networks. Diagonals can be devised to stabilize open trusses but these are structurally i n e f f i cient. Because of i t s basic geometry, therefore, COPPATRUSS is perceived to offer the highest structural efficiency possible in a 3-dimensional truss system. This advantage translates immediately into the least mass and cost of basic truss materials for a given truss size. While these factors have an important impact of the overall cost of a large space structures project, other factors such as construction t i m e and implementation will of course contribute heavily. These matters relate to the other characteristics (3),(4), and (5) stated above and will be discussed later. System Description Protoframe:
The Basic Building Block
In the COPPATRUSSsystem as presently defined, the PT is a geometrical and not a physical entity. The basic material building block is the protoframe (PF) (8) which has the form of one PT cell face. A protoframe model is shown in Figure 2. I t consists Oaf two equal struts, A and,J} of length s and strut, C of length 2 s/Y3 joined together at their ends by vertex f i t t i n g s .
173 The end struts also shown in the Figure are used to complete the ends of truss beams whenever this is required. In that case, there are three such struts per beam, irrespective of the beam length. There are three d i s t i n c t vertex f i t t i n g s in a protoframe, labeled A', B', and C' and positioned opposite their respectively labeled sides. The f i t t i n g s shown in Figure 2 contain all hardware elements that are needed to assemble the protoframes into truss beams. The struts can be connected either d i r e c t l y to the f i t t i n g s or via connectors preassembled into the strut ends. The l a t t e r design permits the f i t t i n g s to be smaller in cross sectional bulk than the struts. Strut end connectors permit greater design choice in joining the struts into the protoframe. The vertex f i t t i n g s depicted in the model exhibit a mechanical fastening design but other joining schemes are also possible. A given f i t t i n g , say C', of one protoframe mates with a A' f i t t i n g of another PF and a B' f i t t i n g of a third PF to form a complete node of a truss beam assembled f r o m protoframes. Such node connections can be accomplished very simply and rapidly. This joining scheme permits the rapid manual or automated assembly of truss beams(9,11). Vertex f i t t i n g s are not fabricated individually but rather derived from a master f i t t i n g . This is shown at the center of Figure 3 together with the derived fittings.(10) All fabrication operations are performed on the master and once completed i t is cut into 3 parts thereby yielding the individual A', B', and C' f i t t i n g s , This procedure obtains very accurate and precise fits between mating surfaces and alignments among other vertex f i t t i n g s of the frame at r e l a t i v e l y low cost. Protoframes are prefabricated prior to being assembled to form truss beams. For very large truss construction, protoframes are prefabricated in space by automated means. Truss Beams Examples of truss beams assembled from protoframes are shown in Figures 4 and 5. Figure 4 shows a beam of equilateral triangular cross section (Type T) as assembled from 12 protoframes (comprising 4 beam bays) and 3 end struts.(8) (A bay is defined as the smallest portion of the beam having a protoframe in each lateral face; a typical beam might have about 50 bays.) This model was made to demonstrate the rapid assembly property of the beam and not strut length/diameter proportions that are representative of a space structure. The l a t t e r would show struts about four times longer than those shown in Figure 4 for the same strut diameter and f i t t i n g proportions. APT cell is identified in dashed lines in Figure 4. I t is composed of the center lines of protoframe ABC situated on the right face, B struts of the protoframes on the bottom and l e f t faces, and the C end strut on the front face of the beam. This i l l u strates the fact that the PT is a geometrical rather t h a n physical entity of such a beam. Protoframes, on the other hand, such as the one cited above, are distinct structural building
blocks. The dashed lines also i l l u s t r a t e that the strut centerlines intersect at a point at a typical beam node. The vertex f i t t i n g s accomplish the sequential joining of three protoframes together at a node. In the assembly process, each time a third protoframe is added to two existing protoframes at a node, only one joining operation is required to secure the complete node. Thus, i f a beam is composed of 3N protoframes, where N is the number of bays, a total of only 3N joining operations (one per protoframe) is required to assemble the entire beam. The length of such a beam would be equal to Ns where s is the short side length of the protoframe. The protoframes can also be assembled to form a square cross section beam (Type S), illustrated by the computer-aided design model of Figure 5. This capability is due to the two basic 60° and 90° symmetries of the PT c e l l , a most remarkable feature. This results in the a b i l i t y to produce Type T truss beams whose 1ongerons consist entirely of short CA or B) sides of the PF and Type S beams whose longerons consist entirely of the longer (C) side~ The beam of Figure 5 is an assembly of 10 PFS, 4 end struts, and internal diagonal struts. The beam consists entirely of PT cells. I t is noted that the internal diagonals are exactly equal in length to the longer protoframe side (C). Thus, only two different strut lengths are present in both type beams. This is also the case for all COPPATRUSS structures that are based on a specific PF design. A Type S truss beam assembled from 4N protoframes, where N is the number of beam bays, has a length of 2Ns/~t~. Hence for equal numbers of bays, a Type S beam has a length of 2/ir'~ times that of the associated type T beam. This is the same length relationship that exists in the protoframe i t s e l f . A total of 4N joining operations Cone per frame) is necessary to assemble the frames. The Type S beam also requires 2 internal diagonal struts per bay or a total of 2N C type struts. Truss BeamAssemblies Types T and S trussbeams may be used individua l l y or as building blocks of larger structures. The remarkable aggregational properties of these building blocks is indicated in Figure 6, which shows paper constructions of them. Two versions of the Type T beam are shown, each constructed of identical protoframes but differing in the direction of helical sequence involved in assembling the frames. The TCL) beam has a left-handed sequence and the T(R) a right-handed sequence. The Type S beam on the other hand has a balanced helical sequence. In these models protoframes are indicated by the triangular regions having the letters A, B, and C on their interior. Struts are represented by the dark lines and nodes by strut intersections. Protoframes do not exist in regions without internal letters. Hence, the upper right longeron of the Type S beam is composed of the C struts of protoframes existing in the right Cvertical) face, whereas the upper l e f t longeron is composed of C struts of protoframes existing in the top face. It
174 is noted that both the lateral and end faces of these beams possess protoframe facets ABC. The end face of the Type S beam, in particular is subdivided into two such facets by the internal diagonal strut, C. Because of this property, the various beams can be connected to one another in any manner by matching the facet of one to the facet of another and securing the associated protoframe vertex f i t t i n g s . Thus any type beam may be attached end to end, end to side, and side to side to a same or d i f f e r e n t type beam, with the exception that Type T beams of the same helical sign cannot in general be connected side face to side face. The actual connections themselves are accomplished with f i t t i n g s that are derived from the previously described vertex f i t t i n g s . These obtain a common intersection point f o r all struts joining a given node. Replication of Building Blocks The connective v e r s a t i l i t y of COPPATRUSS beams is due d i r e c t l y to the perfect-packing property of the basic tetrahedral c e l l , aggregates of which can f i l l space in innumerable ways. Thereby, not only is great architectural variety obtained but also the a b i l i t y to replicate the basic geometry of building blocks at higher levels of assembly. For example the basic protoframe can be replicated at higher levels by u t i l i z i n g truss beam components in place of strut elements. The replication property greatly facilitates design conceptualization and definition of systematic construction processes. Zero-Order Building Blocks The replication property makes i t possible to devise modular building blocks which are p a r t i c u l a r l y suitable f o r assembling a specific architectural design or a family of related designs. The simplest of these are called zero-order building blocks and provide the transition from the material (protoframe) order to the architectural orders (n = I, 2, 3. . . . ) of the COPPATRUSS system. Depending on the truss designs envisioned, a zero-order building block is devised according to combined architectural and constructional considerations. Assembled from truss beam components which themselves are assembled from protoframes, zeroorder building blocks represent a judicious partitioning of the overall space construction process. L a r g e quantities of basic parts (protoframes) are machine-assembled to form much smaller quantities of much larger components (truss beams). These in turn are assembled by less automated means into s t i l l fewer and larger structural units (zero-order building blocks). Finally these identical, t r u l y modular units are assembled to form the f i n a l structure or structures possibly by s t i l l less automated means. Each phase of the construction process therefore involves repetitious assembly operations of identical parts u t i l i z i n g equipment and procedures s p e c i f i c a l l y fashioned f o r i t . This systematization of the overall construction process obtains the rapid and precise assembly of very large trusses in space.
Zero-order building blocks contain the means f o r connecting them together to form the f i n a l structure. They are t r u l y modular, i . e . , capable of being removed from the structure as well as reassembled into i t . The present paper is focused on the use of triangular truss frames (triframes) to construct higher order structures. In i t s vertex-to-vertex geometry a triframe is a larger-scale replicate of the protoframe. Hence, the lengths of i t s sides h a v e the same relative proportions as those of the protoframe. The shorter sides of the triframe have a length, Lo=nos and the larger side a length of 2nos/~'~, where no is a design specified integer and s the shorter side length of the protoframe. Higher Order Structures Because of the replication property, COPPATRUSS is a hierarchical system involving higher order structural configurations that are assembled from lower order building blocks. Thus a structure of any given order number (1, 2, 3. . . . . n) can be assembled from identical parts of lower complexity. This capability f a c i l i t a t e s the design of very large space trusses as well as the planning and execution of e f f i c i e n t construction processes. Numerous models of higher order structures have been constructed. Several of these will be presented in a l a t e r paper, disclosure at this time not being permissable due to on-going patent a c t i v i t i e s . SPS Application The Solar Power S a t e l l i t e is taken as an example of a possible applicatioo of COPPATRUSS. The 5GW SPS system is described(2) as requiring a generally f l a t structural platform having an overall area of 64.6 km2, of which 90% is employed to support the photovoltaic cell blanket. A microwave antenna support structure is connected to the platform within the remaining area. The antenna plan is described as approximating the area of a i km diameter circle. In the present discussion the truss is assumed to extend uniformly over the entire 64.6 km2 area and the corresponding mass estimate to include the mass of the antenna support structure (assumed here to be about 10% of the total structural mass). Platform Design Concept The platform truss is configured in the form of a rhombic slab having symmetrically beveled edges, as shown in Figure 7 (a rectangular platform can also be formed). I t i s composed of a number of mutually p a r a l l e l f i r s t - o r d e r COPPATRUSS t r i a n g u l a r section beams that are interconnected along t h e i r longitudinal base edges. Their apex longitudinal edges are interconnected by a series o f z e r o - o r d e r t r i f r a m e s whose v e r t i c e s are in r e g i s t e r with corresponding v e r t i c e s of the f i r s t order beams. The r e s u l t i n g s t r u c t u r e is t h e r e f o r e composed completely o f interconnected t e t r a h e d r a l truss elements and has r i g i d i t y in a l l d i r e c t i o n s . The s p e c i f i c arrangement r e s u l t s in a platform bending r i g i d i t y in the l o n g i t u d i n a l d i r e c t i o n of the i s t order beams of about twice t h a t in the transverse
175 direction. The protoframes consist of graphite/epoxy composite tubes (EL:234 GPa) mechanically joined to v e r t e x f i t t i n g s via s t r u t end connectors. The end connectors are assumed to be constructed o f a composite, such as g r a p h i t e / e p o x y , with incorporated m e t a l l i c f a s t e n i n g elements. The s p e c i f i c g r a v i t i e s of the tubes and f i t t i n g s are assumed to be 1.50 and 2.77 r e s p e c t i v e l y . The z e r o - o r d e r t r i f r a m e s consist o f z e r o - o r d e r truss beams. The beam components are connected together by means of v e r t e x j o i n t s which also provide for attachment to other triframes. Thus composed, the t r i f r a m e s are completely modular and may be connected to or removed from the s t r u c t u r e at any l o c a t i o n . The f i r s t - o r d e r beams are assembled d i r e c t l y from t r i f r a m e s and end z e r o - o r d e r beam elements. S t r u c t u r a l Sizin 9 The truss designs were sized according to a s p e c i f i e d maximum s t r u t load, P which was applied to a l l s t r u t s . The s p e c i f i e d load was based on stati~n~eeping thruster reactions cited f o r the SPS~I~J. In the f o l l o w i n g discussion P=3110 N (700 Ib) is assumed. This i s estimated to represent an ultimate s a f e t y f a c t o r of 7.5 r e l a t i v e to the s t r u t load due to the nominal t h r u s t e r r e a c t i o n s . The s a f e t y margin is expected to be more than adequate to cover a d d i t i o n a l loads due to s o l a r blanket t e n s i o n , thermal expansion, dynamic a m p l i f i c a t i o n , and geometrical e c c e n t r i c i t y . The s t r u t lengths were determined by equating the Euler column capacity o f the longer (C) s t r u t to the load P f o r a given tube diameter and wall thickness, Euler buckling representing the l i m i t i n g f a i l u r e mechanism of the system. This established the o v e r a l l size of the p r o t o frame. The geometry o f the o v e r a l l platform is defined by the parameters nO and n I ( i n t e g e r s ) and the l e n g t h , s of the protoframe A side. nO is the number of s t r u t s present in the outer base edge of the c o n s t i t u e n t z e r o - o r d e r t r i f r a m e , whose edge length is t h e r e f o r e equal to n O s. S i m i l a r l y , n I is the number o f such edge length segments present in the outer edge of the n I x n I rhombic p l a t f o r m , whose length t h e r e f o r e equals nonls. Since the rhombus formed by such edges provides the surface over which the s o l a r blanket is spread, we have: (nonls sin c ' ) 2 = A
(I)
where c' is the angle opposite the c side of the protoframe (c' = cos - I 1/3, also the acute angle of the rhombus) and A the required blanket area. n I is also the s p e c i f i e d number of f i r s t order beams t h a t comprise the platform s t r u c t u r e . Hence, the product nos must s a t i s f y equation ( I ) in such a way t h a t nO is the l a r g e s t i n t e g e r f o r which the Euler capacity associated with s is g r e a t e r than P. This was accomplished by a simple i t e r a t i v e calculation. With n O and s obtained, the truss geometry of the e n t i r e s t r u c t u r e is determined f o r the s p e c i f i e d values of n I and A.
Buckling capacity of the z e r o - o r d e r beam columns and pl at f or m v i b r a t i o n frequency were the other design c r i t e r i a applied. The beams were required to have an indicated Euler buckling strength >3P to provide assurance of some degree o f tolerance to d e v i a t i o n s from ideal truss geometry. Frequency c r i t e r i a were l i m i t e d to fundamental bending of the o v e r a l l platform both with and without the s o l a r blanket dead mass e f f e c t . Frequencies above 5 cycles per hour were considered acceptable(12) but obtained values were g e n e r a l l y found to exceed t h i s by a f a c t o r of 4. Properties of several platform designs having different values of n I are l i s t e d in Tables I and 2. The designs are based on a s t r u t outside diameter and wall thickness o f 64 and .51 mm r e s p e c t i v e l y and a s t r u t loading of 3114 N (700 Ib). In Table i , WT is the t o t a l weight o f the platform truss ( i n c l u d i n g antenna support structure); s, the length o f the protoframe A side; Lo, the length o f the outer edge o f the t r i f r a m e , (L/H) 0 and (L/H) I , the l e n g t h / depth ratio of the triframe and pl at f or m respectively, as measured along t h e i r outer edge, Po/3P the r a t i o o f the indicated column buckling resistance o f the z e r o - o r d e r Type T t r uss beam to i t s local s t r u t r e s i s t a n c e , and f, the f i r s t f l e x u r a l v i b r a t i o n frequency o f the pl at f or m with s o l a r blanket attached. In Table 2, NTF and NpF are the t o t a l number o f t r i f r a m e s and protoframes in the e n t i r e truss r e s p e c t i v e l y whereas NTF/and NpF/T F are the number o f t r i f r a m e s per f i r s t - o r d e r beam and the number of protoframes per t r i f r a m e respectively. Other parts such as connector frames and end connector s t r u t s are not l i s t e d because o f minor importance to the parts count, but t h e i r weights are included in WT. WTF and WpF are the complete weights o f an i n d i v i d u a l t r i f r a m e and protoframe r e s p e c t i v e l y . Increase in the value of n I produces a decrease in nO, both o f which e f f e c t s bring about a reduct i o n o f the t r i f r a m e size and t h e r e f o r e a densification of z e r o - o r d e r beams throughout the t r u s s . Hence, both the o v e r a l l weight and part quantities increase with l a r g e r values o f n I. Another e f f e c t of t h i s i s to reduce the pl at f or m depth and ( t o g e t h e r with the mass increase) bring about a reduction o f o v e r a l l stiffness, as r e f l e c t e d in the lower values of f. The c h i e f b e n e f i t of increasing n I i s to obtain lower slenderness r a t i o s f o r the z e r o - o r d e r beams. From a design poi nt o f view it i s obviously best to choose the smallest value o f n I t h a t obtains adequate o v e r a l l buckling resistance o f the z e r o - o r d e r truss beams. This also obtains greater flexural resistance in these elements, d e s i r a b l e f o r r e s i s t i n g local loadings. Antenna Support Truss COPPATRUSS obtains a hexagonal truss c o n f i g u r a t i o n t h a t may be useful f o r constructing the SPS microwave antenna primary and secondary support s t r u c t u r e s by means o f a planar a r r a y of triframes. To i l l u s t r a t e t h i s consider the t r i f r a m e s o f the n=16 design of Table i . The area w i t h i n the t r i a n g u l a r envelope of the t r i frame base i s equal to ½ Lo 2 sin C'. As shown
176
in Figure 8 six such triframes situated about a common center and joined with their neighbors along common edges together comprise a hexagon whose area is equal to 3(.516) 2 sin 70.53°=.753 km2, which comes close to the area of a I km diameter circle. Six equal d e p t h layers of this configuration involving progressively smaller triframes in the successive layers provide an overall truss depth of 26 m. which is considered appropriate for the SPS antenna(2). Such a structure is obtained by the assembly of 72 triframes and provides the basic foundation for the antenna support. Figure 8 shows a version of the structure, consisting of 3 hexagonal layers. The primary structure can be subdivided so as to provide adequate support for the secondary structure. The l a t t e r can be integrated into the triframe layer of the antenna radiating face by further subdividing the spaces to provide the appropriate bay size for supporting the microwave waveguide subarrays. I t is noted that the above antenna structure concept is constructed from the same protoframe building blocks that are used to build the primary platform of the SPS. I t employs triframes identical to those used for the platform as well as similar triframes, differing only in the lengths of their constituent zero-order beam lengths, for assembling other portions of the primary as well as secondary support structures. This commonality of parts as well as the resulting commonality of associated construction processes are indeed significant advantages of the COPPATRUSS system. Possible locations for mounting the microwave antenna to the platform include the center or corners, as shown in Figure 7. At all places the outside shape of the antenna conforms exactly to the cutout on the platform that is required to accommodate the antenna. From structural and mounting convenience points of view i t would seem preferable to u t i l i z e one of the corners of the platform. This might, however, result in objectionable motions transmitted to the antenna by overall platform vibration.
and triframe j o i n t connectors (TFC). These parts are furnished in a completely finished form, ready for assembly in space. The struts, for example, are furnished complete with end connectors and accurate end-to-end length; the f i t t i n g s and connectors contain all fastener hardware elements required for assembly. The various parts are packaged in appropriate dispensers that are designed to accommodate the associated parts feed-mechanisms. Stowage of basic parts in the space transportation system is efficient for launch into LEO. T h i s results from combining r e l a t i v e l y low density packages, like t u b e bundles with much higher density items like f i t t i n g s and solar blanket modules. Triframe Assembler The basic space construction f a c i l i t y component is the Triframe Assembler (TFA), four of which are recommended for building the SPS trusses. These are integrated together to form the major construction f a c i l i t y which produces complete first order beams ( B 1 ) with attached apex triframes. The TFA consists essentially of an oversized triframe and three Automated Assembly Centers (AAC), one attached near each triframe vertex. The AAC's are delivered to LEO in an operationally r e a d y condition. Each AAC incorporates three operational modules, which effect the automated assembly of protoframes and zero-order truss beams (Bo) and the manual assembly of triframe joints (TFJ). The protoframe assembly module (PFAM) provides automated delivery of struts and vertex f i t t i n g s to the PF assembly fixtures which automatically assemble the protoframes. The assembly operations are supervised by crew members (working in a "shirt sleeve" environment) who can manually override them whenever required. Manual override is accomlished through electromechanical linkup with the PF assembly fixtures, which are situated on the exterior (space side) of the AAC.
The Zero-Order Beam Assembler (BAo) consists of the combined PF assembly fixtures, the positioning drive, and bay locking and release Construction Process mechanisms. The BAo acts to assemble a complete truss bay f r o m the most recently assembled The SPS can be constructed by a r e l a t i v e l y protoframes and attach i t to previously assembled straightforward process with the COPPATRUSS truss bays in an incrementally continuous truss system. The process obtains rapid assembly building process. BAo operations are conducted of platform and antenna support trusses because automatically in the space environment and are of the following features: (a) immediate supervised by crew members (EVA). commencement of construction after initial delivery of f a c i l i t y components and basic truss The Triframe Joint Assembler (TFJA) provides parts to the LEO assembly site; (b) minimal a "shirt sleeve" working environment for crew need for space construction facilities; (c) members who assemble the TFJ's. Manual assembly extensive use of robotic assembly operations is efficient because of the three-dimensional (usually manually supervised); (d) continuous bulk of the TFJ and the r e l a t i v e l y small number assembly process from basic parts to completion required during assembly of a TF. When complete, of platform subassembly components ( f i r s t order a TFJ is attached to a transfer device, passed beams with attached apex triframes); and (e) through the TFJA a i r lock, and moved to the minimal assembly operations in GEO. TF assembly plane. Similar TF transfer operations are performed at the other AAC sites of the The basic construction strategy for the SPS various TFA's more or less in unison. The last trusses is (a) space assembly of zero-order three TJF's that are required during assembly triframes (TF), the principal "building block" of the current TF are transferred prior to of the SPS platform and antenna trusses and completion of the component Bo's. These TF's (b) groundbased precision fabrication of basic remain attached to the actuator posts of the hardware parts such as protoframe (PF) struts
177 transfer mechanisms. When the Bo'S have been completed t h e i r e n d s are attached to t h e i r respective TF's by members of the TFA EVA crew. Only relatively few and simple fastening operations are required to effect this. The TFJ's form the TF vertices and are d i r e c t l y analogous to the PF vertex f i t t i n g s . At this point the completed TF is held in position on the three TFJ transfer posts. Subsequently the posts are stroked further, thereby moving the TF to the f i r s t - o r d e r beam assembly plane located nearby. The parallelism between this plane and the TF plane can be precisely controlled by the TFJM crew members at the three AAC sites via the TFJ transfer drives. This action when coordinated with the e x t e r i o r EVA crew f a c i l i t a t e s subsequent joining operations whereby triframes are assembled to form a f i r s t order COPPATRUSS beam. The Triframe Assembler is constructed as follows: Upon delivery to LEO and activation, the three component AAC's e a c h assemble an appropriate zero-order truss beam (longer than those to be used in the SPS TF's) and a TFJ. The resulting beams and TFJ's are then joined together to form an oversized triframe. This is accomplished by f i r s t separating the beams from t h e i r respective AAC's and using the AAC's to maneuver the beam ends into the required positions near t h e i r mating TFJ's. The beams are then connected to the appropriate TFJ's by members of the TFA crew, thereby completing the TFA structural backbone. The AAC's are then attached at t h e i r designated positions on the frame. Construction is complete upon verificaton that the TFJ support posts which will locate the TF vertices are properly aligned. The other three TFA's are constructed similarly. The backbone trusses of the TFA may be constructed with higher stiffness than the standard TF, i f necessary, to provide a more stable assembly platform. This would be done p r i n c i p a l l y by increasing the wall thickness of the struts while maintaining the same strut OD as that of the standard PF struts. This permits processing the heavier backbone PF's with the standard assembly apparatus. Each TFA represents an independent f a c i l i t y f o r constructing TF's from basic PF struts and vertex f i t t i n g s . Production of TF's can begin immediately u p o n checkout of the f a c i l i t y . Since the SPS platform is composed e n t i r e l y of TF's, except f o r a r e l a t i v e l y small number of end truss beam components, several assembly options are admissable. One is to assemble the SPS d i r e c t l y from a stockpile of TF's. This procedure, however, is not the best f o r rapid production. A better way is to assemble TF's into f i r s t order beams, then connect the beams together, and f i n a l l y attach the apex TF's to them. This in fact could be accomplished using a total of only three TFA's. The preferred procedure f o r the SPS, however, in view of the great need f o r rapid assembly, is to construct the f i r s t - o r d e r beams complete with attached apex TF's in one continuous process. To accomplish t h i s , three TRA's are attached together in the same r e l a t i v e position as TF's are arranged in a f i r s t - o r d e r triangular beam
or PF's in a zero-order triangular beam. The fourth TFA is attached to this assembly in the same r e l a t i v e position as an apex TF when attached to an adjacent f i r s t - o r d e r beam. This assemblage of four TFA's comprises the f i r s t - o r d e r triangular beam assembler (BA1). W i t h this one f a c i l i t y a l l of the major components of the SPS platform can be rapidly assembled from basic parts. Assembly of the BA1 f a c i l i t y can begin following construction of the f i r s t two TFA units and is completed upon attachment of the fourth unit. The assembly process involves maneuvering the units into position, u t i l i z i n g the vehicle control systems of the AAC's, and f i n a l l y fastening the backbone TFJ's together. A previously constructed zero-order truss beam is f i n a l l y connected between the base and apex TFA's to help support the free vertex of the apex TFA. Assembly of the f i r s t - o r d e r beams (BI) with attached a p e x TF's proceeds as follows: Upon completion of TF construction, in each of the four TFA's (a concurrent process), the four TF's remain supported on t h e i r respective TFJ transfer posts. The posts of the three TF's that will form a complete bay of B1 are then extended, thereby placing them in t h e i r respective B1 assembly planes. This also brings the mating connectors of the TFJ's into mutual contact. These are attached together with the fastening hardware contained in the TFJ connectors (EVA). Then the apex TF is extended from i t s TFA into the assembly plane and attached to the completed B1 bay. Finally, the completed bay is released from the TFJ supoprt posts and displaced longitudinally by one bay length (distance l o ) . Assembly of the next bay proceeds once the next set of TF's becomes available. In the previously cited example (n1=16, Table 1) sixteen such steps are required to complete the assembly of a f i r s t - o r d e r beam with attached apex TF's. When finished, the B1 is parked in a nearby location to await completion of the next B1, upon which the two are mated together (EVA) by fastening the mating TFJ connectors of the B1 base edges and those along the apex edges. At this point, to use again the n1=16 example, one-eighth of the entire SPS platform truss has been constructed (8.2 x 1.02 km.). Attachment of the photovoltaic blanket and harness can then proceed as desired. In the cited design example the two center B1 beams are interrupted to provide space f o r a central antenna location on the platform. This is accomplished by constructing four B1 beams, each having seven bays and assembling them to adjacent f u l l - l e n g t h beams in the manner described above, thereby leaving a central opening in the platform of the required size. Construction of the antenna support truss can proceed upon completion of the f i n a l B1 beam of the platform. As described previously, the basic structure is composed of TF's, arranged in six layers of decreasing plan size, and t o t a l l i n g 36 in number. The recommended procedure is to use one TFA to assemble a l l TF's, beginning with six TF's of the size employed throughout the platform truss. The next set of TF's would be constructed a f t e r removing one bay from each
178 leg of the backbone truss. This would result in T F ' s smaller t h a n the previous TF's by precisely one zero-order bay, which is exactly what is required for the structure depicted in Figure 8. T F ' s for each succeeding layer would be constructed similarly, i . e . , after removing one bay from each leg of the backbone truss. Modifying a TFA in this manner would be a r e l a t i v e l y minor matter. To remove a bay would require loosening only six local fasteners. The beam sections could be drawn together by means of simple fixtures clamped to each longeron. The various TF layers would be attached together at their TFJ's and at intermediate beam vertex nodes. Antenna secondary structures are not considered herein for lack of sufficient requirements definitions. Estimates of overall time and personnel required to construct the SPS, once parts and f a c i l i t y components have been delivered to LEO are currently under study and will be published when available. Indications are that requirements will be substantially lower, especially assembly time, than previous estimates employing other approaches. Concludin9 Remarks The purpose of this paper has been twofold: to introduce the COPPATRUSS system and to test its application to a superlarge spacecraft like the 5 GW Solar Power Satellite. Regarding the l a t t e r , uniquely configured and apparently high performance design concepts have emerged both for the SPS platform and antenna structures. Specifically, a combined mass of 4000-5000 metric tons has been estimated for b o t h structures (trusses), based on an area coverage of 64.5 km2. The writer believes this estimate to be considerably lower than previous ones. Relative to other performance aspects COPPATRUSS seems to measure up well in the excellent launch stowability, modular construction processes, s u i t a b i l i t y for automation, and architectural variety that i t offers. The basic geometry of COPPATRUSS gives i t a unique position among all possible linear truss systems for i t alone has the capability to uniformly subdivide space into quasi-regular tetrahedral cells and triangular partitions. In other truss systems either the strut network is not everywhere triangulated or else large length disparity exists among some of the constituent struts. Both characteristics reduce structural efficiency under general 3-dimensional loading. Hence COPPATRUSS inherently possesses the highest structural efficiency among all possible truss systems. This gives rise to a question, namely, "Granted that i t is structurally best, is i t the optimum truss system for space? For i f i t (or any other system) can be shown to be so, then perhaps we can develop a worldwide standard for building large space trusses that would be applicable far into the future. Structural performance, while only one necessary ingredient of a desirable system, is nevertheless quite important because i t signifies lower structural mass. In a system like SPS this could mean a saving of over 1000 tons. But, of course, there are other important considerations. Assuming that competing systems
stow equally well for launch, construction efficiency, design v e r s a t i l i t y , and configuration variety are very important factors. Here too, however, COPPATRUSS appears to be eminently qualified. References i. Glaser, P., "The Earth Benefits of Solar Power Satellites," Space Solar Power Reviews, Vol. 1, pp. 9-38, 1980. 2. Nathan, C. A., "A Near Term Space Demonstration Program for Large Structures," Advances in the Astronautical Sciences, Eds. R. A. Van Patten et al, Volume 36, Part I, pp. 57-78, 1978. 3. Miller, K. H., "Solar Power Satellite Construction Concepts," Advances in the Astronautical Sciences, Eds. R. A. Van Patten et al, Volume 36, Part 1, pp. 79-99, 1978. 4. Coppa, A. P., "On the Mechanism of Bucking of a Circular Cylindrical Shell Under Longitudinal Impact," Proceedings of the 10th International Congress of Applied Mechanics (1960), F. Rolla and W. T. Koiter, Eds. 1 9 6 2 ; also Mechanics (U.S.S.R.), Periodical Selection of Foreign Papers, No. 6; also General Electric TIS Report No. R60SD494, September, 1960. 5. Coppa, A. P., "Inextensional Buckling Configurations of Conical Shells," AIAA Journal, Vol. 5, No. 4, 1967. 6. Coppa, A. P., "A Family of Rigid Shell Structures, Self-Deployable f r o m Folded Configurations of Small I n i t i a l Volume," Paper No. 68-359, 9th AIAA/ASME Structures, Structural Dynamics, and Materials Conference, April. 1968. 7. Coppa, A. P., "Biomolecular Implications of Fold Structures, (unpublished), 1979. 8. Coppa, A. P., "Truss Structure and Method of Construction," U.S. Patent No. 4,601,152, July 22, 1986. 9. Coppa, A. P., "Method of Truss Structure Construction," U . S . Patent No. 4,644,628, Feb. 24, 1987. 10. Coppa, A. P., "Vertex Fittings Derived from a Master Fitting," U.S. Patent No. 4,580,922, April 18, 1986. 11. Coppa, A. P., "Apparatus and Method for Constructing and Disassembling a Truss Structure," U . S . Patent No. 4,633,566, Jan. 6, 1987. 12. Engler, E. E. and Muench, W. K., "Automated Space Fabrication of Structural Elements," Advances in the Astronautical Sciences, Eds. R. A. Van Patten et al, Volume 36, Part I, pp. 27-77, 1978. Table i. nI
WT metric tons
16 20 24
s
Platform Structure Data no
m
3983 5.32 5029 5.29 6072 5.29
Lo
,~/i~L,O _~pPo ,_~_/IL~if
m 97 78 65
516.0 416.2 343.8
cph 118 96 65
1.19 20 30 1.83 25 26 2.64 29 23
179
Table 2. nl
Component Part Quantities and Weights
NTF
NpF
NTF/B1 NpF/TF WTF -
16 20 24
961 1521 2209
923,036 1,169,475 1,409,340
46 58 70
kg
956 766 636
WpF kg
4 1 2 2 4.28 3 2 9 4 4.26 2 7 4 0 4.26
Figure 3.
Protoframe Master and Derived Vertex Fittings
Figure 4.
Type T Zero-Order Truss Beam Showing Tetrahedral Cell.
J Figure 1.
Tetrahedral Grid
c,
--.
Figure 2.
--
._=___
ee
?
~
__._==_
l
r.C'
~
-
4e
q m
p
Protoframe Model, also End Struts Figure 5.
Type S Zero-Order Truss Beam
180
Figure 6. Models of the Zero-Order Truss Beams of the COPPATRUSSSystem (Paper Constructions. Protoframes indicated by triangles ABC.)
dge Sun-facing ~
Figure 7.
Earth-fa,clng~
Rhombic COPPATRUSSDesign Concept for to Solar PowerSatellite Platform, ni=9 (showing possible antenna locations)
_#~,?Trlfram
Sectton A-A Figure 8.
~-Base Edge
AntennaSupport Truss Concept for for Solar PowerSatellite
Abstract The paper presents a general three-dimensional truss system (COPPATRUSS) that appears uniquely capable of satisfying the requirements f o r very large foundation structures in space. The currently patented system obtains perhaps the highest structural efficiency (strength/mass and s t i f f ness/mass) possible in a general space truss. In addition i t offers great architectural variety, modularity, fabrication economy, low package volume f o r launch, and rapid, p r i n c i p a l l y automated, assembly in space. An example of an application to the Solar Power S a t e l l i t e is discussed. Introduction Very large space systems are foreseen f o r the Space Station era and beyond. An example of one that has been studied considerably is the Solar Power S a t e l l i t e ( I ) described as reqyirT ing a structural platform area of 60-120 km.[Z,~) Previous studies which h a v e discussed design concepts and methods of constructing such super large structures have estimated overall system masses in the tens of thousands of metric tons and the need f o r hundreds of space construction workers operating over extended periods of time. Obviously, such enormous enterprises will exert great demands on all related technologies and system design aspects. One of the greatest challenges will be to construct structures of unprecedented size u n d e r working conditions almost t o t a l l y foreign to experience. A large part of this challenge l i e s in the fact that when these structures are b u i l t in space, they will be b u i l t f o r the f i r s t time: there will be l i t t l e margin f o r error or a b i l i t y to correct unforseen problems in the construction process. Hence i t is important to u t i l i z e a process that has been proven out to a maximum extent p r i o r to i t s application in space.
Two properties of this structure were immediately evident: (1) the crystallized structures w e r e continuously triangulated and hence rigid and (2) the parent structure embodied a self-building principal. Both of these properties were seen at the time to be p o t e n t i a l l y valuable f o r space trusses. The isosceles tetrahedral cell became the geometrical unit of COPPATRUSS.
Given the a b i l i t y to construct such structures in space i t is crucial to u t i l i z e a highly e f f i cient structural system, one that provides the required strength, stiffness, architectural shape, dimensional stability, and d u r a b i l i t y at minimum l i f e - c y c l e cost. Minimum mass, material cost, launch stowage volume, and construction time associated with the structure and constructional implements are important performance measurements.
Development of the COPPATRUSS system was i n i t i a t e d in 1983 with the submission of a patent disclosure f o r a truss beam of equilateral triangular cross section.(8) The truss is unique in that i t is assembled from separate triangular frame elements, each of which contains the necessary node f i t t i n g s f o r connecting them together. This wa followed by a series of inventions( 9, 10, 11)s which describe structural details and methods of construction, including automated methods. Additional inventions are currently in the patent process.
This paper presents a general, three dimensional truss system (COPPATRUSS) that has the potent i a l of being the optimum of a l l possible truss systems f o r providing very large structures f o r space.
Ideal Truss Characteristics
COPPATRUSS is the result of a discovery that I made early in 1970 while engaged in a private study of the structures of helical protein chains and DNA. Immediately p r i o r to this event, my interest had been aroused by the apparent similari t y between the e x t e r i o r form of certain virus
The ideal truss system f o r constructing general large structures in space may be described as having the following characteristics: (1) I t is capable of uniformly triangulating 3-dimensional space; (2) the unit triangular cell is
Copyright ~1987 General Electric Co. Published by the American I n s t i t u t e of Aeronautics and Astronautics Inc. with p~rmission. A A IS--L
171
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equilateral; (3) i t offers a great variety of useful architectural forms; (4) i t can be constructed by assembling modules together; and (5) i t is suitable for automated construction, especially at the module level. Characteristic (I) signifies that any derived truss will exhibit a triangular relationship among any three adjacent strut elements and a tetrahedral arrangement among any six adjacent strut elements that are interconnected by four nodes. Such properties assure structural r i g i d i t y under general 3-dimensional loading and obtain highest stiffness and strength per unit weight. Characteristic (2) obtains an optimal balance of structural efficiency between tension and compression forces imposed on strut elements and also provides constructional simplicity. General space foundation trusses will be usually subject to free-free oscillations and at times attitude control torques. As a result strut elements will be usually subject to alternating tension and compression forces. The strength of the truss will be limited by strut s t a b i l i t y under compression loading. I f for instance, the limitation is due to strut column buckling, for which the resistance varies inversely with the square of the strut length, then strut length disparity results in strut weight and volume penalties. Characteristic (3) anticipates the evolutionary aspect of large projects in space. Large projects will tend to have extended lifetimes during which modification in size and/or shape of the initial truss configuration may be expected. This characteristic w i l l , of course, also provide the a b i l i t y to configure the i n i t i a l structure to satisfy ongoing design requirements. Characteristic (4) enables construction of the large structure from discrete building blocks, which themselves may be formed of lower order building blocks. This permits the planning and execution of more efficient construction processes. I t also may permit removal of building blocks from a given structure at a later time for re-use elsewhere. Characteristic (5) is necessary to reduce construction time as well as manual construction operations to a minimum. Automated assembly is necessary at the lower construction levels of a thoroughly modular system which has many constituent building blocks. Basic COPPATRUSSGeometry If the equilateral tetrahedron possessed the property of perfect packing, a truss geometry u t i l i z i n g i t as a unit cell would satisfy both characteristics (1) and (2). But since the equilateral tetrahedron does not possess this property, i t has l i t t l e value for a general three-dimensional truss system. The only unit cell that satisfies characteristic (I) and very nearly satisfies characteristic (2) is the isosceles tetrahedron whose base angles sum to the tetrahedral angle (2cos- I I/~-3). This is the geometrical cell of the COPPATRUSSsystem.
Because of its perfect packing property, such cells when packed together with their v e r t i ces in register everywhere generate a threedimensional grid of straight lines which uniformly subdivides space into equal triangular elements. A region about a cell is shown in Figure 1. I f strut elements are placed along this grid and node joints at all intersections of the grid, a completely triangulated three-dimensional truss entirely f i l l i n g the utilized space is obtained. Such a truss is rigid everywhere. Moreover, i f tetrahedral cells are selectively removed from the general space, open networks of cells are obtained. When the resulting arrangement of remaining cells is in the form of a triangulated truss, rigid open trusses are thereby obtained. This characteristic provides great choice of architectural form with assurance of structural r i g i d i t y on every case. Because of this property of generating many structural forms, we call this cell the prototetrahedron ( P T ) . Examples of open truss networks are given later. With regard to characteristic (2), strut length disparity derived from the PT cell is quite small. The edges of the PT are made up of four shorter edges ~f = 1.151ength5s ~and two longer edges of length 2s/ ~3 . . Hence, the penalty due to the longer edge per se is small. As pointed out later, moreover, the longer and shorter edges are associated with certain symmetries in the COPPATRUSS which minimizes the penalty due to edge disparity. In contrast, a general truss system that is based on a cubical cell (also perfect packing) suffers from the lack of natural diagonals in the three-dimensional grid. The grid generates only orthogonal cell arrays. Hence in general such a system does not produce rigid open truss networks. Diagonals can be devised to stabilize open trusses but these are structurally i n e f f i cient. Because of i t s basic geometry, therefore, COPPATRUSS is perceived to offer the highest structural efficiency possible in a 3-dimensional truss system. This advantage translates immediately into the least mass and cost of basic truss materials for a given truss size. While these factors have an important impact of the overall cost of a large space structures project, other factors such as construction t i m e and implementation will of course contribute heavily. These matters relate to the other characteristics (3),(4), and (5) stated above and will be discussed later. System Description Protoframe:
The Basic Building Block
In the COPPATRUSSsystem as presently defined, the PT is a geometrical and not a physical entity. The basic material building block is the protoframe (PF) (8) which has the form of one PT cell face. A protoframe model is shown in Figure 2. I t consists Oaf two equal struts, A and,J} of length s and strut, C of length 2 s/Y3 joined together at their ends by vertex f i t t i n g s .
173 The end struts also shown in the Figure are used to complete the ends of truss beams whenever this is required. In that case, there are three such struts per beam, irrespective of the beam length. There are three d i s t i n c t vertex f i t t i n g s in a protoframe, labeled A', B', and C' and positioned opposite their respectively labeled sides. The f i t t i n g s shown in Figure 2 contain all hardware elements that are needed to assemble the protoframes into truss beams. The struts can be connected either d i r e c t l y to the f i t t i n g s or via connectors preassembled into the strut ends. The l a t t e r design permits the f i t t i n g s to be smaller in cross sectional bulk than the struts. Strut end connectors permit greater design choice in joining the struts into the protoframe. The vertex f i t t i n g s depicted in the model exhibit a mechanical fastening design but other joining schemes are also possible. A given f i t t i n g , say C', of one protoframe mates with a A' f i t t i n g of another PF and a B' f i t t i n g of a third PF to form a complete node of a truss beam assembled f r o m protoframes. Such node connections can be accomplished very simply and rapidly. This joining scheme permits the rapid manual or automated assembly of truss beams(9,11). Vertex f i t t i n g s are not fabricated individually but rather derived from a master f i t t i n g . This is shown at the center of Figure 3 together with the derived fittings.(10) All fabrication operations are performed on the master and once completed i t is cut into 3 parts thereby yielding the individual A', B', and C' f i t t i n g s , This procedure obtains very accurate and precise fits between mating surfaces and alignments among other vertex f i t t i n g s of the frame at r e l a t i v e l y low cost. Protoframes are prefabricated prior to being assembled to form truss beams. For very large truss construction, protoframes are prefabricated in space by automated means. Truss Beams Examples of truss beams assembled from protoframes are shown in Figures 4 and 5. Figure 4 shows a beam of equilateral triangular cross section (Type T) as assembled from 12 protoframes (comprising 4 beam bays) and 3 end struts.(8) (A bay is defined as the smallest portion of the beam having a protoframe in each lateral face; a typical beam might have about 50 bays.) This model was made to demonstrate the rapid assembly property of the beam and not strut length/diameter proportions that are representative of a space structure. The l a t t e r would show struts about four times longer than those shown in Figure 4 for the same strut diameter and f i t t i n g proportions. APT cell is identified in dashed lines in Figure 4. I t is composed of the center lines of protoframe ABC situated on the right face, B struts of the protoframes on the bottom and l e f t faces, and the C end strut on the front face of the beam. This i l l u strates the fact that the PT is a geometrical rather t h a n physical entity of such a beam. Protoframes, on the other hand, such as the one cited above, are distinct structural building
blocks. The dashed lines also i l l u s t r a t e that the strut centerlines intersect at a point at a typical beam node. The vertex f i t t i n g s accomplish the sequential joining of three protoframes together at a node. In the assembly process, each time a third protoframe is added to two existing protoframes at a node, only one joining operation is required to secure the complete node. Thus, i f a beam is composed of 3N protoframes, where N is the number of bays, a total of only 3N joining operations (one per protoframe) is required to assemble the entire beam. The length of such a beam would be equal to Ns where s is the short side length of the protoframe. The protoframes can also be assembled to form a square cross section beam (Type S), illustrated by the computer-aided design model of Figure 5. This capability is due to the two basic 60° and 90° symmetries of the PT c e l l , a most remarkable feature. This results in the a b i l i t y to produce Type T truss beams whose 1ongerons consist entirely of short CA or B) sides of the PF and Type S beams whose longerons consist entirely of the longer (C) side~ The beam of Figure 5 is an assembly of 10 PFS, 4 end struts, and internal diagonal struts. The beam consists entirely of PT cells. I t is noted that the internal diagonals are exactly equal in length to the longer protoframe side (C). Thus, only two different strut lengths are present in both type beams. This is also the case for all COPPATRUSS structures that are based on a specific PF design. A Type S truss beam assembled from 4N protoframes, where N is the number of beam bays, has a length of 2Ns/~t~. Hence for equal numbers of bays, a Type S beam has a length of 2/ir'~ times that of the associated type T beam. This is the same length relationship that exists in the protoframe i t s e l f . A total of 4N joining operations Cone per frame) is necessary to assemble the frames. The Type S beam also requires 2 internal diagonal struts per bay or a total of 2N C type struts. Truss BeamAssemblies Types T and S trussbeams may be used individua l l y or as building blocks of larger structures. The remarkable aggregational properties of these building blocks is indicated in Figure 6, which shows paper constructions of them. Two versions of the Type T beam are shown, each constructed of identical protoframes but differing in the direction of helical sequence involved in assembling the frames. The TCL) beam has a left-handed sequence and the T(R) a right-handed sequence. The Type S beam on the other hand has a balanced helical sequence. In these models protoframes are indicated by the triangular regions having the letters A, B, and C on their interior. Struts are represented by the dark lines and nodes by strut intersections. Protoframes do not exist in regions without internal letters. Hence, the upper right longeron of the Type S beam is composed of the C struts of protoframes existing in the right Cvertical) face, whereas the upper l e f t longeron is composed of C struts of protoframes existing in the top face. It
174 is noted that both the lateral and end faces of these beams possess protoframe facets ABC. The end face of the Type S beam, in particular is subdivided into two such facets by the internal diagonal strut, C. Because of this property, the various beams can be connected to one another in any manner by matching the facet of one to the facet of another and securing the associated protoframe vertex f i t t i n g s . Thus any type beam may be attached end to end, end to side, and side to side to a same or d i f f e r e n t type beam, with the exception that Type T beams of the same helical sign cannot in general be connected side face to side face. The actual connections themselves are accomplished with f i t t i n g s that are derived from the previously described vertex f i t t i n g s . These obtain a common intersection point f o r all struts joining a given node. Replication of Building Blocks The connective v e r s a t i l i t y of COPPATRUSS beams is due d i r e c t l y to the perfect-packing property of the basic tetrahedral c e l l , aggregates of which can f i l l space in innumerable ways. Thereby, not only is great architectural variety obtained but also the a b i l i t y to replicate the basic geometry of building blocks at higher levels of assembly. For example the basic protoframe can be replicated at higher levels by u t i l i z i n g truss beam components in place of strut elements. The replication property greatly facilitates design conceptualization and definition of systematic construction processes. Zero-Order Building Blocks The replication property makes i t possible to devise modular building blocks which are p a r t i c u l a r l y suitable f o r assembling a specific architectural design or a family of related designs. The simplest of these are called zero-order building blocks and provide the transition from the material (protoframe) order to the architectural orders (n = I, 2, 3. . . . ) of the COPPATRUSS system. Depending on the truss designs envisioned, a zero-order building block is devised according to combined architectural and constructional considerations. Assembled from truss beam components which themselves are assembled from protoframes, zeroorder building blocks represent a judicious partitioning of the overall space construction process. L a r g e quantities of basic parts (protoframes) are machine-assembled to form much smaller quantities of much larger components (truss beams). These in turn are assembled by less automated means into s t i l l fewer and larger structural units (zero-order building blocks). Finally these identical, t r u l y modular units are assembled to form the f i n a l structure or structures possibly by s t i l l less automated means. Each phase of the construction process therefore involves repetitious assembly operations of identical parts u t i l i z i n g equipment and procedures s p e c i f i c a l l y fashioned f o r i t . This systematization of the overall construction process obtains the rapid and precise assembly of very large trusses in space.
Zero-order building blocks contain the means f o r connecting them together to form the f i n a l structure. They are t r u l y modular, i . e . , capable of being removed from the structure as well as reassembled into i t . The present paper is focused on the use of triangular truss frames (triframes) to construct higher order structures. In i t s vertex-to-vertex geometry a triframe is a larger-scale replicate of the protoframe. Hence, the lengths of i t s sides h a v e the same relative proportions as those of the protoframe. The shorter sides of the triframe have a length, Lo=nos and the larger side a length of 2nos/~'~, where no is a design specified integer and s the shorter side length of the protoframe. Higher Order Structures Because of the replication property, COPPATRUSS is a hierarchical system involving higher order structural configurations that are assembled from lower order building blocks. Thus a structure of any given order number (1, 2, 3. . . . . n) can be assembled from identical parts of lower complexity. This capability f a c i l i t a t e s the design of very large space trusses as well as the planning and execution of e f f i c i e n t construction processes. Numerous models of higher order structures have been constructed. Several of these will be presented in a l a t e r paper, disclosure at this time not being permissable due to on-going patent a c t i v i t i e s . SPS Application The Solar Power S a t e l l i t e is taken as an example of a possible applicatioo of COPPATRUSS. The 5GW SPS system is described(2) as requiring a generally f l a t structural platform having an overall area of 64.6 km2, of which 90% is employed to support the photovoltaic cell blanket. A microwave antenna support structure is connected to the platform within the remaining area. The antenna plan is described as approximating the area of a i km diameter circle. In the present discussion the truss is assumed to extend uniformly over the entire 64.6 km2 area and the corresponding mass estimate to include the mass of the antenna support structure (assumed here to be about 10% of the total structural mass). Platform Design Concept The platform truss is configured in the form of a rhombic slab having symmetrically beveled edges, as shown in Figure 7 (a rectangular platform can also be formed). I t i s composed of a number of mutually p a r a l l e l f i r s t - o r d e r COPPATRUSS t r i a n g u l a r section beams that are interconnected along t h e i r longitudinal base edges. Their apex longitudinal edges are interconnected by a series o f z e r o - o r d e r t r i f r a m e s whose v e r t i c e s are in r e g i s t e r with corresponding v e r t i c e s of the f i r s t order beams. The r e s u l t i n g s t r u c t u r e is t h e r e f o r e composed completely o f interconnected t e t r a h e d r a l truss elements and has r i g i d i t y in a l l d i r e c t i o n s . The s p e c i f i c arrangement r e s u l t s in a platform bending r i g i d i t y in the l o n g i t u d i n a l d i r e c t i o n of the i s t order beams of about twice t h a t in the transverse
175 direction. The protoframes consist of graphite/epoxy composite tubes (EL:234 GPa) mechanically joined to v e r t e x f i t t i n g s via s t r u t end connectors. The end connectors are assumed to be constructed o f a composite, such as g r a p h i t e / e p o x y , with incorporated m e t a l l i c f a s t e n i n g elements. The s p e c i f i c g r a v i t i e s of the tubes and f i t t i n g s are assumed to be 1.50 and 2.77 r e s p e c t i v e l y . The z e r o - o r d e r t r i f r a m e s consist o f z e r o - o r d e r truss beams. The beam components are connected together by means of v e r t e x j o i n t s which also provide for attachment to other triframes. Thus composed, the t r i f r a m e s are completely modular and may be connected to or removed from the s t r u c t u r e at any l o c a t i o n . The f i r s t - o r d e r beams are assembled d i r e c t l y from t r i f r a m e s and end z e r o - o r d e r beam elements. S t r u c t u r a l Sizin 9 The truss designs were sized according to a s p e c i f i e d maximum s t r u t load, P which was applied to a l l s t r u t s . The s p e c i f i e d load was based on stati~n~eeping thruster reactions cited f o r the SPS~I~J. In the f o l l o w i n g discussion P=3110 N (700 Ib) is assumed. This i s estimated to represent an ultimate s a f e t y f a c t o r of 7.5 r e l a t i v e to the s t r u t load due to the nominal t h r u s t e r r e a c t i o n s . The s a f e t y margin is expected to be more than adequate to cover a d d i t i o n a l loads due to s o l a r blanket t e n s i o n , thermal expansion, dynamic a m p l i f i c a t i o n , and geometrical e c c e n t r i c i t y . The s t r u t lengths were determined by equating the Euler column capacity o f the longer (C) s t r u t to the load P f o r a given tube diameter and wall thickness, Euler buckling representing the l i m i t i n g f a i l u r e mechanism of the system. This established the o v e r a l l size of the p r o t o frame. The geometry o f the o v e r a l l platform is defined by the parameters nO and n I ( i n t e g e r s ) and the l e n g t h , s of the protoframe A side. nO is the number of s t r u t s present in the outer base edge of the c o n s t i t u e n t z e r o - o r d e r t r i f r a m e , whose edge length is t h e r e f o r e equal to n O s. S i m i l a r l y , n I is the number o f such edge length segments present in the outer edge of the n I x n I rhombic p l a t f o r m , whose length t h e r e f o r e equals nonls. Since the rhombus formed by such edges provides the surface over which the s o l a r blanket is spread, we have: (nonls sin c ' ) 2 = A
(I)
where c' is the angle opposite the c side of the protoframe (c' = cos - I 1/3, also the acute angle of the rhombus) and A the required blanket area. n I is also the s p e c i f i e d number of f i r s t order beams t h a t comprise the platform s t r u c t u r e . Hence, the product nos must s a t i s f y equation ( I ) in such a way t h a t nO is the l a r g e s t i n t e g e r f o r which the Euler capacity associated with s is g r e a t e r than P. This was accomplished by a simple i t e r a t i v e calculation. With n O and s obtained, the truss geometry of the e n t i r e s t r u c t u r e is determined f o r the s p e c i f i e d values of n I and A.
Buckling capacity of the z e r o - o r d e r beam columns and pl at f or m v i b r a t i o n frequency were the other design c r i t e r i a applied. The beams were required to have an indicated Euler buckling strength >3P to provide assurance of some degree o f tolerance to d e v i a t i o n s from ideal truss geometry. Frequency c r i t e r i a were l i m i t e d to fundamental bending of the o v e r a l l platform both with and without the s o l a r blanket dead mass e f f e c t . Frequencies above 5 cycles per hour were considered acceptable(12) but obtained values were g e n e r a l l y found to exceed t h i s by a f a c t o r of 4. Properties of several platform designs having different values of n I are l i s t e d in Tables I and 2. The designs are based on a s t r u t outside diameter and wall thickness o f 64 and .51 mm r e s p e c t i v e l y and a s t r u t loading of 3114 N (700 Ib). In Table i , WT is the t o t a l weight o f the platform truss ( i n c l u d i n g antenna support structure); s, the length o f the protoframe A side; Lo, the length o f the outer edge o f the t r i f r a m e , (L/H) 0 and (L/H) I , the l e n g t h / depth ratio of the triframe and pl at f or m respectively, as measured along t h e i r outer edge, Po/3P the r a t i o o f the indicated column buckling resistance o f the z e r o - o r d e r Type T t r uss beam to i t s local s t r u t r e s i s t a n c e , and f, the f i r s t f l e x u r a l v i b r a t i o n frequency o f the pl at f or m with s o l a r blanket attached. In Table 2, NTF and NpF are the t o t a l number o f t r i f r a m e s and protoframes in the e n t i r e truss r e s p e c t i v e l y whereas NTF/and NpF/T F are the number o f t r i f r a m e s per f i r s t - o r d e r beam and the number of protoframes per t r i f r a m e respectively. Other parts such as connector frames and end connector s t r u t s are not l i s t e d because o f minor importance to the parts count, but t h e i r weights are included in WT. WTF and WpF are the complete weights o f an i n d i v i d u a l t r i f r a m e and protoframe r e s p e c t i v e l y . Increase in the value of n I produces a decrease in nO, both o f which e f f e c t s bring about a reduct i o n o f the t r i f r a m e size and t h e r e f o r e a densification of z e r o - o r d e r beams throughout the t r u s s . Hence, both the o v e r a l l weight and part quantities increase with l a r g e r values o f n I. Another e f f e c t of t h i s i s to reduce the pl at f or m depth and ( t o g e t h e r with the mass increase) bring about a reduction o f o v e r a l l stiffness, as r e f l e c t e d in the lower values of f. The c h i e f b e n e f i t of increasing n I i s to obtain lower slenderness r a t i o s f o r the z e r o - o r d e r beams. From a design poi nt o f view it i s obviously best to choose the smallest value o f n I t h a t obtains adequate o v e r a l l buckling resistance o f the z e r o - o r d e r truss beams. This also obtains greater flexural resistance in these elements, d e s i r a b l e f o r r e s i s t i n g local loadings. Antenna Support Truss COPPATRUSS obtains a hexagonal truss c o n f i g u r a t i o n t h a t may be useful f o r constructing the SPS microwave antenna primary and secondary support s t r u c t u r e s by means o f a planar a r r a y of triframes. To i l l u s t r a t e t h i s consider the t r i f r a m e s o f the n=16 design of Table i . The area w i t h i n the t r i a n g u l a r envelope of the t r i frame base i s equal to ½ Lo 2 sin C'. As shown
176
in Figure 8 six such triframes situated about a common center and joined with their neighbors along common edges together comprise a hexagon whose area is equal to 3(.516) 2 sin 70.53°=.753 km2, which comes close to the area of a I km diameter circle. Six equal d e p t h layers of this configuration involving progressively smaller triframes in the successive layers provide an overall truss depth of 26 m. which is considered appropriate for the SPS antenna(2). Such a structure is obtained by the assembly of 72 triframes and provides the basic foundation for the antenna support. Figure 8 shows a version of the structure, consisting of 3 hexagonal layers. The primary structure can be subdivided so as to provide adequate support for the secondary structure. The l a t t e r can be integrated into the triframe layer of the antenna radiating face by further subdividing the spaces to provide the appropriate bay size for supporting the microwave waveguide subarrays. I t is noted that the above antenna structure concept is constructed from the same protoframe building blocks that are used to build the primary platform of the SPS. I t employs triframes identical to those used for the platform as well as similar triframes, differing only in the lengths of their constituent zero-order beam lengths, for assembling other portions of the primary as well as secondary support structures. This commonality of parts as well as the resulting commonality of associated construction processes are indeed significant advantages of the COPPATRUSS system. Possible locations for mounting the microwave antenna to the platform include the center or corners, as shown in Figure 7. At all places the outside shape of the antenna conforms exactly to the cutout on the platform that is required to accommodate the antenna. From structural and mounting convenience points of view i t would seem preferable to u t i l i z e one of the corners of the platform. This might, however, result in objectionable motions transmitted to the antenna by overall platform vibration.
and triframe j o i n t connectors (TFC). These parts are furnished in a completely finished form, ready for assembly in space. The struts, for example, are furnished complete with end connectors and accurate end-to-end length; the f i t t i n g s and connectors contain all fastener hardware elements required for assembly. The various parts are packaged in appropriate dispensers that are designed to accommodate the associated parts feed-mechanisms. Stowage of basic parts in the space transportation system is efficient for launch into LEO. T h i s results from combining r e l a t i v e l y low density packages, like t u b e bundles with much higher density items like f i t t i n g s and solar blanket modules. Triframe Assembler The basic space construction f a c i l i t y component is the Triframe Assembler (TFA), four of which are recommended for building the SPS trusses. These are integrated together to form the major construction f a c i l i t y which produces complete first order beams ( B 1 ) with attached apex triframes. The TFA consists essentially of an oversized triframe and three Automated Assembly Centers (AAC), one attached near each triframe vertex. The AAC's are delivered to LEO in an operationally r e a d y condition. Each AAC incorporates three operational modules, which effect the automated assembly of protoframes and zero-order truss beams (Bo) and the manual assembly of triframe joints (TFJ). The protoframe assembly module (PFAM) provides automated delivery of struts and vertex f i t t i n g s to the PF assembly fixtures which automatically assemble the protoframes. The assembly operations are supervised by crew members (working in a "shirt sleeve" environment) who can manually override them whenever required. Manual override is accomlished through electromechanical linkup with the PF assembly fixtures, which are situated on the exterior (space side) of the AAC.
The Zero-Order Beam Assembler (BAo) consists of the combined PF assembly fixtures, the positioning drive, and bay locking and release Construction Process mechanisms. The BAo acts to assemble a complete truss bay f r o m the most recently assembled The SPS can be constructed by a r e l a t i v e l y protoframes and attach i t to previously assembled straightforward process with the COPPATRUSS truss bays in an incrementally continuous truss system. The process obtains rapid assembly building process. BAo operations are conducted of platform and antenna support trusses because automatically in the space environment and are of the following features: (a) immediate supervised by crew members (EVA). commencement of construction after initial delivery of f a c i l i t y components and basic truss The Triframe Joint Assembler (TFJA) provides parts to the LEO assembly site; (b) minimal a "shirt sleeve" working environment for crew need for space construction facilities; (c) members who assemble the TFJ's. Manual assembly extensive use of robotic assembly operations is efficient because of the three-dimensional (usually manually supervised); (d) continuous bulk of the TFJ and the r e l a t i v e l y small number assembly process from basic parts to completion required during assembly of a TF. When complete, of platform subassembly components ( f i r s t order a TFJ is attached to a transfer device, passed beams with attached apex triframes); and (e) through the TFJA a i r lock, and moved to the minimal assembly operations in GEO. TF assembly plane. Similar TF transfer operations are performed at the other AAC sites of the The basic construction strategy for the SPS various TFA's more or less in unison. The last trusses is (a) space assembly of zero-order three TJF's that are required during assembly triframes (TF), the principal "building block" of the current TF are transferred prior to of the SPS platform and antenna trusses and completion of the component Bo's. These TF's (b) groundbased precision fabrication of basic remain attached to the actuator posts of the hardware parts such as protoframe (PF) struts
177 transfer mechanisms. When the Bo'S have been completed t h e i r e n d s are attached to t h e i r respective TF's by members of the TFA EVA crew. Only relatively few and simple fastening operations are required to effect this. The TFJ's form the TF vertices and are d i r e c t l y analogous to the PF vertex f i t t i n g s . At this point the completed TF is held in position on the three TFJ transfer posts. Subsequently the posts are stroked further, thereby moving the TF to the f i r s t - o r d e r beam assembly plane located nearby. The parallelism between this plane and the TF plane can be precisely controlled by the TFJM crew members at the three AAC sites via the TFJ transfer drives. This action when coordinated with the e x t e r i o r EVA crew f a c i l i t a t e s subsequent joining operations whereby triframes are assembled to form a f i r s t order COPPATRUSS beam. The Triframe Assembler is constructed as follows: Upon delivery to LEO and activation, the three component AAC's e a c h assemble an appropriate zero-order truss beam (longer than those to be used in the SPS TF's) and a TFJ. The resulting beams and TFJ's are then joined together to form an oversized triframe. This is accomplished by f i r s t separating the beams from t h e i r respective AAC's and using the AAC's to maneuver the beam ends into the required positions near t h e i r mating TFJ's. The beams are then connected to the appropriate TFJ's by members of the TFA crew, thereby completing the TFA structural backbone. The AAC's are then attached at t h e i r designated positions on the frame. Construction is complete upon verificaton that the TFJ support posts which will locate the TF vertices are properly aligned. The other three TFA's are constructed similarly. The backbone trusses of the TFA may be constructed with higher stiffness than the standard TF, i f necessary, to provide a more stable assembly platform. This would be done p r i n c i p a l l y by increasing the wall thickness of the struts while maintaining the same strut OD as that of the standard PF struts. This permits processing the heavier backbone PF's with the standard assembly apparatus. Each TFA represents an independent f a c i l i t y f o r constructing TF's from basic PF struts and vertex f i t t i n g s . Production of TF's can begin immediately u p o n checkout of the f a c i l i t y . Since the SPS platform is composed e n t i r e l y of TF's, except f o r a r e l a t i v e l y small number of end truss beam components, several assembly options are admissable. One is to assemble the SPS d i r e c t l y from a stockpile of TF's. This procedure, however, is not the best f o r rapid production. A better way is to assemble TF's into f i r s t order beams, then connect the beams together, and f i n a l l y attach the apex TF's to them. This in fact could be accomplished using a total of only three TFA's. The preferred procedure f o r the SPS, however, in view of the great need f o r rapid assembly, is to construct the f i r s t - o r d e r beams complete with attached apex TF's in one continuous process. To accomplish t h i s , three TRA's are attached together in the same r e l a t i v e position as TF's are arranged in a f i r s t - o r d e r triangular beam
or PF's in a zero-order triangular beam. The fourth TFA is attached to this assembly in the same r e l a t i v e position as an apex TF when attached to an adjacent f i r s t - o r d e r beam. This assemblage of four TFA's comprises the f i r s t - o r d e r triangular beam assembler (BA1). W i t h this one f a c i l i t y a l l of the major components of the SPS platform can be rapidly assembled from basic parts. Assembly of the BA1 f a c i l i t y can begin following construction of the f i r s t two TFA units and is completed upon attachment of the fourth unit. The assembly process involves maneuvering the units into position, u t i l i z i n g the vehicle control systems of the AAC's, and f i n a l l y fastening the backbone TFJ's together. A previously constructed zero-order truss beam is f i n a l l y connected between the base and apex TFA's to help support the free vertex of the apex TFA. Assembly of the f i r s t - o r d e r beams (BI) with attached a p e x TF's proceeds as follows: Upon completion of TF construction, in each of the four TFA's (a concurrent process), the four TF's remain supported on t h e i r respective TFJ transfer posts. The posts of the three TF's that will form a complete bay of B1 are then extended, thereby placing them in t h e i r respective B1 assembly planes. This also brings the mating connectors of the TFJ's into mutual contact. These are attached together with the fastening hardware contained in the TFJ connectors (EVA). Then the apex TF is extended from i t s TFA into the assembly plane and attached to the completed B1 bay. Finally, the completed bay is released from the TFJ supoprt posts and displaced longitudinally by one bay length (distance l o ) . Assembly of the next bay proceeds once the next set of TF's becomes available. In the previously cited example (n1=16, Table 1) sixteen such steps are required to complete the assembly of a f i r s t - o r d e r beam with attached apex TF's. When finished, the B1 is parked in a nearby location to await completion of the next B1, upon which the two are mated together (EVA) by fastening the mating TFJ connectors of the B1 base edges and those along the apex edges. At this point, to use again the n1=16 example, one-eighth of the entire SPS platform truss has been constructed (8.2 x 1.02 km.). Attachment of the photovoltaic blanket and harness can then proceed as desired. In the cited design example the two center B1 beams are interrupted to provide space f o r a central antenna location on the platform. This is accomplished by constructing four B1 beams, each having seven bays and assembling them to adjacent f u l l - l e n g t h beams in the manner described above, thereby leaving a central opening in the platform of the required size. Construction of the antenna support truss can proceed upon completion of the f i n a l B1 beam of the platform. As described previously, the basic structure is composed of TF's, arranged in six layers of decreasing plan size, and t o t a l l i n g 36 in number. The recommended procedure is to use one TFA to assemble a l l TF's, beginning with six TF's of the size employed throughout the platform truss. The next set of TF's would be constructed a f t e r removing one bay from each
178 leg of the backbone truss. This would result in T F ' s smaller t h a n the previous TF's by precisely one zero-order bay, which is exactly what is required for the structure depicted in Figure 8. T F ' s for each succeeding layer would be constructed similarly, i . e . , after removing one bay from each leg of the backbone truss. Modifying a TFA in this manner would be a r e l a t i v e l y minor matter. To remove a bay would require loosening only six local fasteners. The beam sections could be drawn together by means of simple fixtures clamped to each longeron. The various TF layers would be attached together at their TFJ's and at intermediate beam vertex nodes. Antenna secondary structures are not considered herein for lack of sufficient requirements definitions. Estimates of overall time and personnel required to construct the SPS, once parts and f a c i l i t y components have been delivered to LEO are currently under study and will be published when available. Indications are that requirements will be substantially lower, especially assembly time, than previous estimates employing other approaches. Concludin9 Remarks The purpose of this paper has been twofold: to introduce the COPPATRUSS system and to test its application to a superlarge spacecraft like the 5 GW Solar Power Satellite. Regarding the l a t t e r , uniquely configured and apparently high performance design concepts have emerged both for the SPS platform and antenna structures. Specifically, a combined mass of 4000-5000 metric tons has been estimated for b o t h structures (trusses), based on an area coverage of 64.5 km2. The writer believes this estimate to be considerably lower than previous ones. Relative to other performance aspects COPPATRUSS seems to measure up well in the excellent launch stowability, modular construction processes, s u i t a b i l i t y for automation, and architectural variety that i t offers. The basic geometry of COPPATRUSS gives i t a unique position among all possible linear truss systems for i t alone has the capability to uniformly subdivide space into quasi-regular tetrahedral cells and triangular partitions. In other truss systems either the strut network is not everywhere triangulated or else large length disparity exists among some of the constituent struts. Both characteristics reduce structural efficiency under general 3-dimensional loading. Hence COPPATRUSS inherently possesses the highest structural efficiency among all possible truss systems. This gives rise to a question, namely, "Granted that i t is structurally best, is i t the optimum truss system for space? For i f i t (or any other system) can be shown to be so, then perhaps we can develop a worldwide standard for building large space trusses that would be applicable far into the future. Structural performance, while only one necessary ingredient of a desirable system, is nevertheless quite important because i t signifies lower structural mass. In a system like SPS this could mean a saving of over 1000 tons. But, of course, there are other important considerations. Assuming that competing systems
stow equally well for launch, construction efficiency, design v e r s a t i l i t y , and configuration variety are very important factors. Here too, however, COPPATRUSS appears to be eminently qualified. References i. Glaser, P., "The Earth Benefits of Solar Power Satellites," Space Solar Power Reviews, Vol. 1, pp. 9-38, 1980. 2. Nathan, C. A., "A Near Term Space Demonstration Program for Large Structures," Advances in the Astronautical Sciences, Eds. R. A. Van Patten et al, Volume 36, Part I, pp. 57-78, 1978. 3. Miller, K. H., "Solar Power Satellite Construction Concepts," Advances in the Astronautical Sciences, Eds. R. A. Van Patten et al, Volume 36, Part 1, pp. 79-99, 1978. 4. Coppa, A. P., "On the Mechanism of Bucking of a Circular Cylindrical Shell Under Longitudinal Impact," Proceedings of the 10th International Congress of Applied Mechanics (1960), F. Rolla and W. T. Koiter, Eds. 1 9 6 2 ; also Mechanics (U.S.S.R.), Periodical Selection of Foreign Papers, No. 6; also General Electric TIS Report No. R60SD494, September, 1960. 5. Coppa, A. P., "Inextensional Buckling Configurations of Conical Shells," AIAA Journal, Vol. 5, No. 4, 1967. 6. Coppa, A. P., "A Family of Rigid Shell Structures, Self-Deployable f r o m Folded Configurations of Small I n i t i a l Volume," Paper No. 68-359, 9th AIAA/ASME Structures, Structural Dynamics, and Materials Conference, April. 1968. 7. Coppa, A. P., "Biomolecular Implications of Fold Structures, (unpublished), 1979. 8. Coppa, A. P., "Truss Structure and Method of Construction," U.S. Patent No. 4,601,152, July 22, 1986. 9. Coppa, A. P., "Method of Truss Structure Construction," U . S . Patent No. 4,644,628, Feb. 24, 1987. 10. Coppa, A. P., "Vertex Fittings Derived from a Master Fitting," U.S. Patent No. 4,580,922, April 18, 1986. 11. Coppa, A. P., "Apparatus and Method for Constructing and Disassembling a Truss Structure," U . S . Patent No. 4,633,566, Jan. 6, 1987. 12. Engler, E. E. and Muench, W. K., "Automated Space Fabrication of Structural Elements," Advances in the Astronautical Sciences, Eds. R. A. Van Patten et al, Volume 36, Part I, pp. 27-77, 1978. Table i. nI
WT metric tons
16 20 24
s
Platform Structure Data no
m
3983 5.32 5029 5.29 6072 5.29
Lo
,~/i~L,O _~pPo ,_~_/IL~if
m 97 78 65
516.0 416.2 343.8
cph 118 96 65
1.19 20 30 1.83 25 26 2.64 29 23
179
Table 2. nl
Component Part Quantities and Weights
NTF
NpF
NTF/B1 NpF/TF WTF -
16 20 24
961 1521 2209
923,036 1,169,475 1,409,340
46 58 70
kg
956 766 636
WpF kg
4 1 2 2 4.28 3 2 9 4 4.26 2 7 4 0 4.26
Figure 3.
Protoframe Master and Derived Vertex Fittings
Figure 4.
Type T Zero-Order Truss Beam Showing Tetrahedral Cell.
J Figure 1.
Tetrahedral Grid
c,
--.
Figure 2.
--
._=___
ee
?
~
__._==_
l
r.C'
~
-
4e
q m
p
Protoframe Model, also End Struts Figure 5.
Type S Zero-Order Truss Beam
180
Figure 6. Models of the Zero-Order Truss Beams of the COPPATRUSSSystem (Paper Constructions. Protoframes indicated by triangles ABC.)
dge Sun-facing ~
Figure 7.
Earth-fa,clng~
Rhombic COPPATRUSSDesign Concept for to Solar PowerSatellite Platform, ni=9 (showing possible antenna locations)
_#~,?Trlfram
Sectton A-A Figure 8.
~-Base Edge
AntennaSupport Truss Concept for for Solar PowerSatellite