Abstract: A strong, lightweight structural system wherein curved structural elements are tangentially joined. Compressive forces are distributed in a near continuous manner throughout the matrix. Tensile forces in the system are present primarily to brace, support and pre-stress the compression net. Synetic designs are scaleable from molecular through architectural levels, finding many applications in dome shaped and spherical structures. The system also provides a force interaction model that is applicable to a broad array of real and theoretical problems.
 
 

INTRODUCTION

Synetics is a system of construction which utilizes the compressive properties of structural materials to the fullest advantage. It may be employed in a wide variety of shapes, particularly "pneumatic" shapes and lattices. The range of size appropriate to Synetic design runs from the vanishingly small to the vanishingly large. In general, it is useful wherever it is advantageous to make the largest and strongest structure per pound of structural material employed.

Synetic also refers to a tension-compression modeling system used to teach and explore principles of dynamic forces which apply to intangible and invisible structures. Synetics models the dynamics of structure in pure angle and frequency, in minimal, energetic and self-coordinating terms.

A Synetic building is an airy and lace-like basketry of thin arcs patterned in curvilinear triangulation. Bows of springy material are attached in tangency to one another in such a way that the tendency of arcs to spring outward is symmetrically restrained by the like tendency of other arcs. Synetic frames self-‘inflate.’

Synetics takes the compressive function out of the single column or spar and spreads it relatively evenly throughout the manifold along continuous networks. It resolves a manifold into discrete patterns of tension and compression, which co-function in dynamic equilibrium to produce useful structure.
 
 

THE COMPRESSION NET

Synetic compression elements are curved, continuous, wavilinear and cyclical in nature.

Particularly important Synetic compressive elements are hoops of material having strong tendencies toward circularity, flatness, and a larger radius.

Typical compressive material is stiff, springy rod or tube (or bundles of rods or tubes) bent into arcs and joined to form curved domical spans of a diameter many times that of an individual arc and very many times greater than that of a bundle or rod. Large Synetic frames, using the minimum possible compressive material, have lower weight, air resistance and visual obstruction than other systems. 

In Synetic structure, the hoop is the fundamental structural entity, not the triangle. The hoop is the primary, self-bracing bow, strongest minimum structure, having no induced bending moments, a triangle has three. 

Synetics reduces the aspect of compression in a structure so that, to a greater extent than previously possible, the structure will have the aspect of continuous compression throughout. 

Tension will be subjugated and become involved variously and as required to brace, support and pre-stress the compression net. 
 
 

SYNETIC TENSION

Synetic tension is minimum, discontinuous, axial, chordal, straight, and geodesic. Tensile elements may be apparent and plainly involved in a Synetic structure or may be found to be engaged less visibly as they conform more closely to paths of compression.

Synetic frames are structurally independent of covering, but are greatly strengthened by tensile attachment. Tensile bracing might consist of only the minimum required to maintain the balanced array of bows, and be achieved by inter-linking arcs, or by tying or lashing points of crossing and tangency. 

Further strengthening of a Synetic frame is derived from incremental addition of more circumferentially comprehensive tension portions in the form of lines, nets, or fabric, until the frame is maximally braced in full membrane stress. 
 
 

SYNETIC ATTACHMENT

Synetic attachment is entirely by tangency, the universal cohesive principle of natural structuring.

Tangent connection is structurally integral, distributing dynamic loads with maximum efficiency. 

Tangency provides the structural common denominator joining whole or partial structures, regular or irregular, globally or locally. Tangency joins larger to smaller, high frequency to low, one symmetry to another, planar to curved structure, concave to convex, angular to smooth, tensile to compressive, radial to tangential, rigid to flexible, reticular to Synetic. 
 
 

SYNETIC PATTERN

Synetics provides simple, self-similar, uniform structure, well suited to unlimited symmetric development and polyhedral elaboration or lattice. 

Polygonal Synetic modular units might be individual bowed arcs, pairs or triangles of arcs, or five-, six-, seven-, or eight-fold stars comprised of in-curved arcs. Synetic pattern follows all packings and tilings in planes and lattices, as well as curved manifolds in all higher globally symmetric breakdowns such as are provided by conventional geodesic resolution. Patterns of circle-packing are most relevant to Synetic design.

Basic polyhedral units are balanced symmetric arrays of inwardly curved arcs. These arcs correspond to the edges of tetrahedra, octahedra and icosahedra and to all lattices, compounds truncations and tessellations of them. Other regular polyhedra may be seen as lattice fragments. Radial or tangential balanced arc-paths comprise Synetic polyhedra. Synetic vertexial domains are woven, turbined, empty of knobs, nodes and hubs. Conventional ball-and-stick atomic modeling posits arbitrary and cumbersome shapes where considerations of angle and energy only are appropriate.

A conventional lattice node or vertex is treated in Synetics as a polyhedron, through or around which curved compressive paths are taken uninterruptedly. The conception of space-filling lattice of linear truncated octahedra, for example, becomes one of a curvilinear lattice of Synetic tetrahedra as they replace reticular nodes. Synetic bows cross without compressive interaction.
 
 

EARLY ARTIFACT

The Synetic tetrahedron has the shape of a pinch of clay pressed between thumbs and forefingers, before being rolled into a Paleolithic sphere. The shape is formed as four idealized interpenetrating spheres contract to close off an interstitial space. This is the most efficient and fundamental compressive shape, minimally defined in Synetic terms by six in-curved tangent bows, each amenable to most efficient tensile bracing within the system, that is, tension applied on each side of a bow and lying in its plane of bowing.
 
 

SYNETIC MODELS

Energetic behaviors, which derive directly from topology, and which operate at all scales, form and inform Synetic structure. 

At the quantum level, Synetic wave-form paths are symmetrically impounded curves of least work. Numerically and structurally integral, they provide a framework to model quantized energetic behavior, storage and transport.

At the atomic level, tangent articulation represents sites of valency, patterns of vectored connectivity which are symmetrically disposed by the same dynamic that forms orbital and radial Synetic paths.

In molecular modeling, Synetics accommodates all regular and irregular lattices. Balanced bowed arcs, self-adjusting in angle and distance, self-coordinate in structure of any complexity. 

Synetic flexibility allows construction of open arrays, cages, and zeolites. The introduction of heptagonal pattern yields structure with negative curvature, saddles, toroids, helical tubes, etc. 
 
 

NANO

Synetic tetrahedra model silicate elaboration and carbon structure.

The Synetic tetrahedron does away with the ball as model of an atom, replacing it with four points of valency by means of a balanced array of six equal, energetic arcs. Tetrahedral arcs are close to one-fifth of circle. A ring of five Synetic tetrahedra is a lowest energy configuration, setting angular and distance conditions for further low energy attachment leading to a dodecahedral array of twenty tetrahedra and higher fullerenes. Twelve rings of five model a functionalized carbon-60 molecule. 

A ring of six Synetic tetrahedra can bea low energy configuration if it is non-planar, if tets are alternately rotated in respect to one another. This ring sets angular conditions for further low energy attachment in the form of the diamond lattice. 
 
 

SYNBIOTIC

On the scale of cellular architecture, Synetics models the tangent relations between fibers and membranes, fiber and fiber, conforming to minutely accretive structure as well as to branching, tree-like growth. 

Nowhere in natural structure is found a spar poking a membrane. Curves in tangent cohesion are found everywhere.

Synetics models packing lattices, the interstitial architecture of minimal tension surfaces: relations between membrane and membrane, cells, bubbles and foam. 
 
 

FLYBALL

At larger scale, a toy ball in the form of a Synetic framework is extremely light in weight, yet displays much resilience, bounce without much mass, surface tension without much surface. Minimal in structure, without the drag of a balloon, it carries across the room, and small children can grasp it easily, toy and concept.
 
 

WOVEN DOMES

At the domestic scale, domes are made of bows of springy material attached to one another in patterns that turn hoop-strength into sphere-strength. Bows may be variously overlapped and inter-woven to achieve different effects such as collapsibility or to achieve construction or modular advantages.

Synetic frames are entirely curvilinear yet readily conform to rectilinear or irregular intersections such as might be imposed by a rectangular plan or by attachment to orthogonal buildings. Under load, Synetic tangent articulation is in balanced thrust, allowing a variety of simple attachments involving small and identical fittings.

Because of its flexibility, Synetic structure has great capacity for combination, aggregation and truncation. In construction, energy is added incrementally, with advantages of compression-tension equilibrium being apparent and useful in modular portions. Buildings may be built upside-down then rolled over, no scaffolding required. At any stage of construction, Synetic frames are not capable of catastrophic failure. They do not require foundation, only tying down. 
 
 

EARTHQUAKE-PROOF

Structures are in stressed dynamic equilibrium, low-energy configurations which are strongly restored after any dynamic load. Spheres, domes, tubes and toroids behave as tough pneumatic membranes, bouncy and resilient even at large diameters. Synetic frames are exceptionally resilient and are capable of rebounding from extreme distortion. In severe gross deformation, individual members are not brought close to a radius of curvature at which they might fail. In many applications, the flexibility of structures can safely be increased to re-configure dynamic loads through a frame.
 
 

COVERING

Synetic domes are structurally independent of a covering and thus may be wrapped, using material too weak to be used in conventional tents and domes where their structural involvement would be required. 

This independence allows covers to be made using simple gores and patterns relatively unrelated to the dome geometry. Being curvilinear throughout, they are particularly accommodating to thin material, fabric, nets and membranes, supporting them widely. The tensile re-enforcing detail of conventional tents is not needed.

The radially expansive nature of Synetic frames allows such material to be maintained easily in uniform tension overall, providing smooth, structurally rational surfaces, perhaps for further rigidifying. Uniform membrane tension diminishes flapping and mechanical degradation. It reduces air resistance and drag caused by induced vibrational modes, and it uniformly pre-stresses the compression net.
 
 

NEW INDIGENOUS BUILDING

Synetic dome design is singularly effective in low-tech applications, being tolerant of distortion, inaccuracy, and inconsistency. 

Synetics gives to compressive material structural advantages similar to those conferred on tensile material by fine division, bundling, networking, etc. Employing a minimum of compressive material, Synetic structuring makes good use of common but small and inconsistent material. For example, poor quality bamboo, of short length, split and bundled, is bowed into hoops to make large, high frequency domes. Techniques of lashing and weaving provide basic effective Synetic attachment.

Other advantages appear in the extreme simplicity and low cost of Synetic construction, in its modularity, and in its ability to employ a wide variety of material. 

An important feature of Synetic construction is its potential for incremental strengthening by the addition of materials which are abundant, widespread and cheap, which are, specifically, poor quality compressive material, and high-quality tensile material.
 
 

THE SUBTRACTION METHOD

Conversely to their radially expansive nature, Synetic spheres present optimal compressive paths in response to external loading, which acts to pre-stress and strengthen the structure. 

Centro-symmetric loading on a Synetic sphere may be provided by partial de-pressurizing of a covered frame. Such a pressure differential further engages the covering as it is caused to cling to the frame, and to form deep, radially inward curves between the curved bights of the frame. 

These in-curved tensile portions act as structural members to oppose arc deflection, to decrease membrane vibration and to add stability to the structure, enabling it to carry heavy external loads.

Covered with membrane material, relative de-pressurization will cause a dome to be pressed strongly to the ground or water surface.
 
 

SYNETIC AIRSHIP

At sufficient size, Synetic spheres are sufficiently lightweight and strong to be buoyant in air when appropriately covered and partially de-pressurized. 

In a Synetic airship there is structural independence between the lifting body, the aerodynamic body, and the airframe. The load imposed by pressure differential may be used only to pre-stress and strengthen a framework light enough to be lifted by other means of buoyancy. Accurately controlled dynamic effects in Synetic structure further supply lift and propulsion to an airship.
 
 

DRIVEN DYNAMIC

Synetic resolution of a manifold into discrete patterns of compression makes possible accurate, electronically controlled local deformation of the structure. Adjustments to compressive elements are made co-functionally with those to tension elements, maintaining tension-compression equilibrium while the structure deforms. Synetics provides a dynamic continuum between rigid mechanical behavior and flexible pneumatic behavior. 

Dynamic effects might include induced de-resonation of the structure, or induced motion, oscillation, or traveling wave-form. They might take the form of expanding or contracting volumetric portions in order to maintain accurately manageable pressure differentials, or they might act as a pump to move air or water, or they might directly entrain air with wing-like motion.
 
 

BALLS

Problems inherent in conventional geodesic and tensegrity theory have prevented their development as widely deployed building systems, and also have stopped their usefulness as models of natural structure. Limits to popular use of geodesics and tensegrities are soon apparent as increasingly large simple shapes are found to require ever more complex, numerous, and consistently accurate components. Particularly problematic is the insistence that compression be treated as rectilinear and discontinuous.

Also, at all scales from molecular description to geodesic building, the dynamics of articulation are not addressed. As tensegrity resolution increases in frequency, revealing tensegrity spars comprised of ever finer tensegrity spars, the exact nature of the attachment of spar to tendon remains unexplained.

Contrary to the prediction of tensegrity, a spar under increasing compression will not catastrophically fail but will continue to bow until reaching a characteristic curve of least work between the two ends as they are brought together. It will not buckle unless it is supplied with an induced bending moment in the form of a hinge, fault, node, vertex or some other singularity.

Conventional ball-and-stick atomic modeling posits arbitrary objects where only considerations of angle and energy are appropriate. In large geodesic structure, the essentials of connection is obscured with hubs, extra-strong and re-enforced, over-engineered to anticipate and overwhelm the inclination to fail in any direction, at all of the induced bending moments provided by the vertices of chords. 

Vertexial and nodal systems are not found in natural structuring, nor are stacked spheres or the triangular arrays deriving form them. Spider-webs and connect-the-dot pictures yield triangles.
 
 

SYNETIC + GEODESIC = SYNERGETIC

Synetic design lets the compressive member bow, then braces that bow. As a bow may be freely rotated around the string, so the Synetic arc is rotated to lie within a useful manifold, such as spherical. In this position, tangential and curved as opposed to straight and chordal, the spar is available for bracing throughout its length by tensile patterns which also conform to the manifold.

Synetic curved spars are made continuous, allowing really continuous tensile bracing which un-interruptedly crosses compression everywhere at right angles, the optimal condition for comprehensive pre-stress. Synetic tensile attachment is in-line, not acute. Tensile integrity is not vulnerable to local compressive failure. 

A hoop is best braced by tension in its plane. Of all possible curved paths on a spherical manifold, the least amenable to tension in its plane, and therefore the least efficient in compression, is a geodesic. Most efficient is Synetic, non great-circular, non-equatorial, non-geodesic, but everywhere ideally braced by the most efficient tensile pattern, geodesic. 

Geodesic is the path of least distance; Synetic the path of least time. Geodesic is the string, Synetic is the bow.