Spherical Cube or Hexahedron

Posted: June 29th, 2011 | Author: John Zerning | Filed under: Spherical Cube or Hexahedron | Tags: , , | No Comments »

The geodesic subdivision i.e. tessellation of the sphere derived from the spherical cube is little explored.

I wonder why?

Imagine a cube inscribed in a sphere. Now from the centre of the sphere project the edges of the cube on the circumsphere. The projected edges will follow great circle arcs i.e. geodesics. Each face of the cube can be divided into an orthogonal grid. Again projecting this grid from the centre of the sphere on the circumsphere will give a quadrilateral mesh with a geodesic pattern (all the lines follow great circle arcs). The number of divisions of the cube’s edge will give the frequency breakdown. The figures show a 6 frequency spherical cube.

This geodesic dome has a 4-fold symmetry, which makes it adaptable to plans with right angles, which is the norm.

Nowadays, when any imaginable configuration (sculpture) can be built, we should remind ourselves that the architectural language, for some 5000 years, is primarily based on the discipline of orthogonal ground plans! Also observe how the structures grow directly from the plans.

What is different and new?

Contemporary architects and engineers should ask: how much does their building weigh?

Of course, this design approach is not always appropriate.

Geodesic grid shell, 6 frequency spherical cube. 11 different strut lengths are required to construct this geodesic grid shell.

Geodesic grid shell, 6 frequency spherical cube. 10 different strut lengths are required to construct this geodesic grid shell.

Geodesic grid shell, 6 frequency spherical cube. 10 different strut lengths are required to construct this geodesic grid shell.

Geodesic grid shell, 6 frequency spherical cube. 10 different strut lengths are required to construct this geodesic grid shell.

Geodesic grid shell, 6 frequency spherical cube. 10 different strut lengths are required to construct this geodesic grid shell.

Geodesic grid shell, 6 frequency spherical cube. 10 different strut lengths are required to construct this geodesic grid shell.

Geodesic dome plus orthogonal ground plan and elevation in concert! The grid shell is propped by a trabeated frame.

Geodesic dome plus orthogonal ground plan and elevation in concert! The grid shell is propped by a trabeated frame.

Truncated modular geodesic grid shells that can be tessellated along the X and Y axes.

Truncated modular geodesic grid shells that can be tessellated along the X and Y axes.


Barrel vault capped by half domes

Posted: June 29th, 2011 | Author: John Zerning | Filed under: Barrel Vault | Tags: , | No Comments »

Barrel vaults also known as tunnel vaults (shells with single curvature) are the earliest kind of vaulting used. They are simple structures for roofing rectangular ground plans. How to enclose the arched openings of the barrel vault has always been a challenging structural and aesthetic problem.

The standard solutions are plane lattice structures which resist wind loads via bending. A much more efficient solution is a double curved space frame, which resist wind loads principally in an axial manner (via compression or tension). The figure show a barrel vault capped by half domes. Its geometry is a geodesic envelope!

It is not generally recognised that a series of circles (arches) parallel to one another, and a series of straight lines parallel to one another, intersecting the circles at right angles, form the simplest case of a geodesic pattern on the surface of a cylinder. Indeed, structures with geodesic patterns on single curved surfaces (Euclidean geometry) are nothing new! The geometry of the half dome is derived from the spherical cube.

Returning to lightweight roofs

The transept roof of the Crystal Palace, for the Great Exhibition of 1851, with its barrel vault construction was given lateral stability via diagonal bracing made from wrought iron rods. It was a highly efficient system. It is very instructive to note how Paxton used hierarchical systems for the transfer of loads — nature’s way. This seminal roof structure inspired engineers to develop ligtweight grid shells with rectangular meshes and diagonally pre-stressed cables. If the cladding is transparent the cables become almost invisible!

It resembles a loaf of bread - organic.

Geodesic grid shell with quadrilateral and rectangular meshes. It resembles a loaf of bread - organic.

Geodesic grid shell with quadrilateral and rectangular meshes. It resembles a loaf of bread - organic.

Geodesic grid shell with quadrilateral and rectangular meshes. It resembles a loaf of bread - organic.


Octahedral Ellipsoid

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Ellipsoid | Tags: | No Comments »

Elliptical domes offer interesting alternatives to hemispherical envelops. In hemispherical domes the ratios between the spans and rises are always 2:1. Elliptical domes can be stretched or squashed.

The drawings show a well-proportioned geodesic elliptical dome, modelled on a actual melon! The ratio between its major and minor axes is 1.44:1. It has bilateral symmetry, the breakdown is a 4-frequency octahedral symmetry.

Pictorial view

Pictorial view

Top view

Top view


Cathedral arch with a companion

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Arch Pergola | Tags: | No Comments »

Cathedral-arch with a companion.

Cathedral arch pergola

Cathedral arch pergola


Tetrahelix with spicules

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Tetrahelix | Tags: | No Comments »

Tetrahelix with spicules, analogous to the arrangement of leaves around plant stems.

Tetrahelix

Tetrahelix


A flitting view

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Sphere | No Comments »

A flitting view in our own garden with the geodesic sphere. (18.12.2009)

18.12.2009

18.12.2009


Gourd-shaped geodesic envelop

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Gourd | Tags: , | No Comments »

Truncated geodesic domes of different sizes can be joined together forming a continuous envelop. The drawings show a truncated dome with an apse. The dome has a 6-frequency octahedral symmetry and the apse a 3-frequency octahedral symmetry. Notice the clean geometry along the cross-section where the truncated dome and apse join.

Pictorial view

Pictorial view

Top view

Top view


Geodesic gridshell with a 6-fold symmetry

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Hexagonal | Tags: , | No Comments »

The optimal solution for the enclosure of space is the geodesic dome with a 5-fold icosahedral symmetry. (The most beautiful molecule, carbon-60, “Bucky ball”, has a 5-fold symmetry).

However, truncated geodesic domes with a pentagonal symmetry are difficult to aggregate in two directions, since the geometry along the cross-sections, where the truncated geodesic domes join together, are messy. This problem can be neatly solved in designing domes with a 6-fold symmetry.

The drawings show a geodesic gridshell with a 6-fold hexagonal symmetry. It is derived by projecting the hexagonal face of a truncated tetrahedron, with a triangular subdivision, on a circumsphere. All the lines follow great circle arcs.

The hexagonal face of a truncated tetrahedron marked on a sphere, with a geodesic triangular pattern.

The hexagonal face of a truncated tetrahedron marked on a sphere, with a geodesic triangular pattern.

Gridshell with geodesic triangles having a 6-fold symmetry, supported on columns.

Gridshell with geodesic triangles having a 6-fold symmetry, supported on columns.

Top view. Note how the areas of the geodesic triangles vary. Being relatively large at the crown where the loads are low and smaller towards the supports where the loads increase.

Top view. Note how the areas of the geodesic triangles vary. Being relatively large at the crown where the loads are low and smaller towards the supports where the loads increase.

An aggregate of 3 hexagonal geodesic gridshells. Note the clean geometry along the cross-sections where the truncated domes join.

An aggregate of 3 hexagonal geodesic gridshells. Note the clean geometry along the cross-sections where the truncated domes join.


Prestressing: Dodecahedral cage made rigid via prestressed wires

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Prestressing | Tags: , | No Comments »

Once again, curiosity and the pleasure of finding and working things out motivated this DIY project.

Being a keen cyclist, I am fascinated by the lightweight efficiency of the bicycle wheel with tension spokes. This small and inexpensive project is about applying the structural principle of the bicycle wheel to a spatial closed system.

The starting point were the two polyhedra: the great stellated dodecahedron inscribed in a dodecahedron. For the dodecahedral cage I used Herringbone struts (manufactured by Simpson Strong-Tie) and for the great stellated dodecahedron I used galvanised wires.

Instead of the turnbuckles I used long eye bolts with two nuts. To fix the wire end to the eye bolt I threaded the wire through the eye and bent it over by 180 degrees, then pushed a washer over the two wires and bent the end again.

I began by assembling the dodecahedral cage (the ends of the struts had prepared holes). As the form had “hinged” joints and no triangulation it collapsed! To make it stand up I temporarily stabilised all the 12 pentagonal faces with thin wires (radiating from the centre to each of the five vertices).

Next, piece by piece, the 90 prepared wires, with L-shaped ends, were fixed into their correct positions.

Finally, the exciting bit could begin – prestressing the structure one vertex at a time. With each complete cycle the structure became progressively stronger and stiffer – magic. Indeed, prestressed wires resist forces like columns! The larger the structure the more efficient it becomes.

Yes, I do, and I understand!

This is a good model of the synergy between the opposing forces (tension and compression).
The working together of the two forces to produce an effect greater than the sum of their individual parts.

The constant interaction between two opposing balancing forces in this closed system can stand as a metaphor for Yin and Yang!

Dodecahedron filled with a stellated dodecahedron. Straw model.

Dodecahedron filled with a stellated dodecahedron. Straw model.

The principle of the bicycle wheel applied to a spatial closed system.

The principle of the bicycle wheel applied to a spatial closed system.

Constructional details

Constructional details

Constructional details

Constructional details

Struts and “spider webs”, the latter being almost invisible.

Struts and “spider webs”, the latter being almost invisible.


Lightweight Space Frames

Posted: May 23rd, 2010 | Author: John Zerning | Filed under: Lightweight | Tags: | 1 Comment »
“Less is more”
- Mies van der Rohe
“More with less”
- Anonymous

Applied to architecture and structure, the former is primarily an aesthetic position; the latter is a principle of economy.

Designing lightweight space frames requires rigorous discipline following a few basic rules.

No bending

Take a bamboo cane, and with your hands, subject it to tension, compression and bending. This very simple experiment demonstrates that bending is an indirect inefficient transfer of forces, as compared with the direct-action (vectors) of tension and compression.
Remember, in any structure that is capable of transmitting forces, tension (pulling) and compression (pushing) always coexist! (It is impossible to imagine one without the other).

A truss, which is an assembly of triangulated struts and ties, is much more efficient and lighter than a beam on girder.

A space frame is a three-dimensional truss, transferring forces in an axial manner. Designing highly efficient space frames requires a clear differentiation between these two states of stress, using hollow or angle steel or aluminium sections for the struts (bones) and wires or cables for the ties (ligaments).

Prestressing is a particular effective way of achieving lightness as it enables undesirable compression stress to be converted into tensile stress! The bicycle wheel is a classic example.

Symmetry and Geodesics

The optimal solution of the enclosure of space is the spherical geodesic dome (the sphere encompasses the given volume with a minimum of surface). Increasing the size of this structure will increase its efficiency!

Imagine the straight edges of the 5 regular Platonic solids and the 13 Archimedean solids expanded into curved edges, as if each polyhedron has been blown up like a balloon. These curved edges will form a grid of great circles arcs, i.e. geodesics (the shortest line between two points on a spherical surface is an arc of a great circle). Each geodesic polygon can be divided again into smaller geodesic polygons, i.e. triangles. The number of the subdivision of the polygon edge define its frequency.

Buckminster Fuller recognised that a pattern of great circles arcs with a 5-fold symmetry, based on the icosahedron, is the best solution to the problem he set himself, i.e. how to enclose space with a structure that requires the least amount of material. His iconic design for the U.S. Pavillion, Expo ‘67, Montreal, Canada, is a double grid geodesic dome, 76 meter diameter, with a 5-fold symmetry. The outer triangular grid has a 16-frequency.

Geodesic domes with a 5-fold symmetry are difficult to aggregate in two directions, since the geometry along the cross-section where they join lack order and is messy. This problem can be neatly solved in designing domes with 3-fold, 4-fold or 6-fold symmetries.

Hierarchical systems for the transfer of loads

The strategy in designing lightweight space frames is straightforward. Think of curvatures that are synclastic and anticlastic with “geodesic” triangles. Choose a geometry with symmetrical patterns.

Employ hierarchical systems for the transfer of loads – it is Nature’s way”! Differentiate between the primary structure, its secondary structure and the tertiary structure. Size their elements accordingly. Where it is not absolutely essential – remove inactive material in the structure. Employ elements that act mainly in axial tension or compression as against those acting in bending. Tensile ties are much more economical than compression struts, especially when the former are prestressed!

A minimal space frame can be defined mathematically!

At any chosen cross-sectional area of the structural element, the fraction-stress under maximum load divided by the permissible stress of the material – is equal to one.

God is in the construction details

“God is in the details”
Mies van der Rohe

Indeed, good construction details are the mark of a healthy construction. The Victorian engineers were masters in construction details, made from wrought-iron. The structural forms they used, like trusses, arches and portal frames were primarily one-directional load carrying arrangements. Space frames carry loads in a two-way action. This makes the design of the connection a challenging problem. There are numerous space frame connectors on the market. They are usually made from steel.

The most successful and also conceptually satisfying , is the MERO connectors. It was invented by the engineer and good businessman Max Mengeringhausen (1903-1988). The connector has the form of a rhombicuboctahedron (polyhedron with 26 faces). It is an ingenious spatial nut and bolt fixing. An 18-way joint at angles of 45 degrees. This did put a constraint on the possible space frame configurations that could be built with these connectors.

However, being able to vary the angles between the struts and ties and their lengths in the MERO system via computer numerical controlled (CNC) processing, any imaginable configuration can be built. The MERO connectors come in a range of different sizes (the MERO system was used for the iconic Eden Project in Cornwall). For low-tech DIY space frames my deceptively simple universal connector is hard to beat!


DIY Geodesic Dome that packs into a suitcase

Posted: April 16th, 2009 | Author: John Zerning | Filed under: Shelter | Tags: , | 4 Comments »
Model of the geodesic hemispherical dome, 4- frequency icosahedron.

Model of the geodesic hemispherical dome, 4-frequency icosahedron.

The universal joint using off-the-peg materials.

The universal joint using off-the-peg materials.

Unpacking the struts and ties from the boot of the car.

Unpacking the struts and ties from the boot of the car.

Fixing the cladding to the space frame was as easy as hanging a curtain!

Fixing the cladding to the space frame was as easy as hanging a curtain!

Curtain rods (springs) prestressed  the cladding.

Curtain rods (springs) prestressed the cladding.

Interior view of the parachute shelter. The principles of ancient kite technology applied to a contemporary tent.

Interior view of the parachute shelter. The principles of ancient kite technology applied to a contemporary tent.

An instant temporary private Eden on a camping site in the south of France in 1972.

An instant temporary private Eden on a camping site in the south of France in 1972.

Reminiscent of the iconic photo - Earthrise - taken by Apollo 8 astronaut in 1968.

Reminiscent of the iconic photo - Earthrise - taken by Apollo 8 astronaut in 1968.

Curiosity and the pleasure of finding things out motivated this project.

In order to understand the geometry of geodesic domes and to get a good feel for its structural behaviour, one must build one!

There are two major design problems: connector and cladding.

Connector

Looking into the published images on connectors for geodesic domes, I could not find a really simple joint suitable for DIY.

Starting with the knowledge that in a triangulated frame the connector can be a ‘pin-joint’ (hinge) as it is primarily subjected to axial forces (compression or tension) – no bending!  The Eureka moment came while I was playing in the workshop joining bits of wood and metal. The universal joint (see Figure 2) takes advantage of the bendability, strength and durability of metal.. With this connector there is no need to calculate the axial angles of the struts and ties. By tightening the nut of a long bolt  the metal strips, and the ends of the members, will bend to the correct axial angle.

Struts and Ties Lengths

I wanted my dome to be a hemisphere and without dissecting the triangles at its equator. The lengths of the struts and ties should not exceed 1 metre. A 4-frequency icosahedron met this brief. The chord factors (length of members) were simply worked out using the appropriate table (Dome Book 2, published by Pacific Domes, 1971). For this 6 metre diameter geodesic dome I used birch dowels 18mm dia.

Required:

  1. 93.50 cm. 30 members
  2. 90.00 cm. 70 members
  3. 85.90 cm. 30 members
  4. 80.00 cm. 30 members
  5. 84.75 cm. 60 members
  6. 72.85 cm. 30 members

Total: 250

Note the very high 52/1 slenderness ratio (length divided by diameter) of the struts.

Cladding

To clad a doubly curved surface with prefabricated materials and to make it watertight is a challenge.

For my experimental, lightweight, demountable shelter I chose a parachute (price £4.50, 1971). It is dome shaped and fits loosely inside the 6 metre diameter dome. Curtain rods (springs) fixed the parachute to the joints of the dome, thus prestressing the fabric.

Erection

For the location of my experimental shelter I chose a camping site in the hills near Roquebrune-Cap-Martin on the easterly end of the Cote d’Azur (not far from the ‘hostel’ where Le Corbusier spent the summers and where he dies of a heart attack while swimming in 1965). A slightly sloping spot in a wooded area was ideal.

The assembly of my prefabricated ultra-lightweight geodesic dome resembled the ‘growth’ of cells, expanding in a centrifugal nature. The ends of the struts and ties had a colour code.

I began by assembling a triangulated pentagon on the ground, next adding 5 triangulated hexagons each sharing 1 edge with the former. A shallow dome began to form. I supported this structure on a stool in order to lift it off the ground. Adding 5 more triangulated hexagons, each sharing 2 edges with the above. Next adding 5 triangulated half-hexagons, each sharing 3 edges with the above, thus completing the top part ½ of the 4-frequency icosahedron dome.

The 5-fold symmetry of this structure dictated where the rest of the various lengths of struts and ties should go, making sure, at every stage, that the colour coded ends of the members did match. It took me about 2 hours to erect the dome single-handed.

Fixing the parachute to the space frame was easy and quick, like hanging a curtain! It was exciting to experience how this spherical double layer prestressed system increased the rigidity of the whole structure – synergy.

This project was first published in AD (Architectural Design) 02.1973.

Lighter than Air!

Having read that the geodesic domes (Biomes) at the Eden Project in Cornwall weigh less than the volume of air they enclose, I thought to check whether this is also true with my small geodesic dome?

1.2 kg (density of air per cubic metre) x 56.5 (volume of air enclosed by hemispherical dome, 6 metre diameter) = 67.8 kg.

Weight of the structure + cladding: 38 kg (struts and ties) + 3 kg (parachute) = 41 kg!


Octet Truss Screen

Posted: November 30th, 2008 | Author: John Zerning | Filed under: Octet Truss | Tags: , | No Comments »

The archetypal element to shape space in the garden is the screen. Traditional screens are two-dimensional constructions. Three-dimensional screens require less material, enable sculpted shapes and a richer planting scheme. They also touch the ground very lightly with minimum disturbance to the soil. The modular units of an octet truss are alternating octahedra and tetrahedra, thus it is a truss with omnitriangulation, which results in a highly efficient space frame configuration. Generally octet trusses are constructed of struts all with equal length, in order to simplify construction.

However, with my simple universal joint the strut lengths can vary, allowing easy low tech fabrication. I do not see these minimal octet trusses as sculptures. Their job is to support, train and display plants and thus they become invisible, analogous to the skeletons in animals.

  1. Building blocks – octahedron and tetrahedron – of the octet truss. This example has five different strut lengths.
  2. Octet truss screen with a chamfered top edge.
  3. Octet truss screen on an inclined ground.
  4. Octet truss forming a curved screen.
  5. Octet truss forming a curved screen.
  6. Octet truss forming a screen with a right angle.

 

Building blocks - octahedron and tetrahedron - of the octet truss. This example has five different strut lengths.Octet truss screen with a chamfered top edge.

Octet truss screen with a chamfered top edge.

Octet truss screen with a chamfered top edge.

Octet truss screen on an inclined ground.

Octet truss screen on an inclined ground.

Octet truss forming a curved screen.

Octet truss forming a curved screen.

Octet truss forming a curved screen.

Octet truss forming a curved screen.

Octet truss forming a screen with a right angle.

Octet truss forming a screen with a right angle.


Toroidal Pergola

Posted: November 30th, 2008 | Author: John Zerning | Filed under: Toroidal Pergola | Tags: | No Comments »

A toroidal trellis on stilts gives climbing plants optimum growing conditions due to the hole in the middle, thus minimising shading from the leaves. Also, the open centre is like a clearing in the forest, permitting light to enter the ground.

So why are we not seeing toroidal trellises in our gardens?

  1. Doughnut shaped space frame trellis formed by an octamast (assembly of octahedra) bent into a ring and supported on two octahedra. This toroidal pergola clothed with climbing roses will be a magnificent sight and also perfume the air.
  2. Plan view.
Doughnut shaped space frame trellis formed by an octamast (assembly of octahedra) bent into a ring and supported on two octahedra. This toroidal pergola clothed with climbing roses will be a magnificent sight and also perfume the air.

Doughnut shaped space frame trellis formed by an octamast (assembly of octahedra) bent into a ring and supported on two octahedra. This toroidal pergola clothed with climbing roses will be a magnificent sight and also perfume the air.

Plan View.

Plan View.


Geodesic Gridshell Pergola

Posted: November 30th, 2008 | Author: John Zerning | Filed under: Geodesic Gridshell Pergola | Tags: , | No Comments »

The flat “lattice” (beams and cross members) roofs supported on columns are the most common trellises in our gardens. They are heavy in every sense, materially and visually. Yes, they are easy to make/erect and inexpensive. And these are good reasons why they will continue to be ubiquitous.

However, occasionally we should aim a bit higher and design/build trellises that express contemporary ideas about the geometry of spatial forms. For me this means doing more with less.

The illustrations here show a gridshell pergola. Its surface is synclastic, i.e. having curvatures in the same sense (concave or convex) in all directions through any point. The geometry of this geodesic gridshell is generated by projecting (from the centre) the edges of a cube onto the circumsphere. It is 1/6th of the sphere’s surface. This surface is further subdivided forming a quadrangular mesh following great circle arcs.

Note, a geodesic gridshell lattice cannot be laid out flat, which gives the structure extra stiffness. Structural designs that follow nature’s example, i.e. geodesic principles, will result in obtaining minimal, highly efficient forms which are beautiful, in harmony and at ease with nature.

  1. Sphere with a geodesic quadrangular pattern.
  2. Geodesic gridshell supported on four tetrahedra.
  3. Horizontal projection of the gridshell.
  4. An aggregate of gridshells.

 

Sphere with a geodesic quadrangular pattern.

Sphere with a geodesic quadrangular pattern.

Geodesic gridshell supported on four tetrahedra.

Geodesic gridshell supported on four tetrahedra.

Horizontal projection of the gridshell.

Horizontal projection of the gridshell.

An aggregate of gridshells.

An aggregate of gridshells.


Postscript

Posted: November 30th, 2008 | Author: John Zerning | Filed under: Postscript | Tags: | No Comments »

Space frame trellis design and construction, which is essentially spatial model building on a bigger scale, is an excellent vehicle for structural explorations that can be applied to numerous structural design problems, on many different scales. For the structural maquettes I use paper straws and for the connectors short lengths (30mm) pipe cleaners. You can make a many-way joint (2, 3, 4, 5, 6, 7 etc).

For example, in case of a three-way joint you will need three short lengths of pipe cleaners.. Two go into each end of the straws, thus forming a universal joint.

Explorations in geometry based on the polyhedral approach are the stuff of creativity.
A famous Chinese proverb says:

I hear, I forget; I see, I remember; I do, and I understand.


Space Frame Trellises

Posted: January 14th, 2008 | Author: John Zerning | Filed under: Space Frame Trellis | Tags: , , , | No Comments »

My new and original plant support system was inspired by Buckminster Fuller (1895-1983), the inventor of the geodesic dome. The key feature of the SFT system is its variability, which is made easy with my deceptively simple universal connector.

Form
The structural shapes of the SFT are modelled on molecules. Why look at molecules? – Nature is always the sublime teacher of structural economy.

twin_domed_pergola_19_white.jpgLawrence Bragg pioneered in 1912 the x-ray diffraction technique to ‘see’ the three-dimensional arrangement of individual atoms in crystals. The conjecture by a few scientists that graphite-like sheets (hexagonal lattices) could be bent into geodesic structures was indeed confirmed. These carbon-cage molecules, which form very stable structures, are referred to as ‘fullerenes’ in honour of Buckminster Fuller who first explored and applied these geodesic structures in his architectural designs.

A geodesic is the shortest curve between two points on a curved surfaces laying wholly on the surface. We find geodesic patterns in very different things and very different orders of magnitude and in many disguises. They are present in:

  • Fullerenes
  • Double helix of DNA
  • Protein shells of viruses
  • Pollen grains
  • Skeletons of various tiny marine organisms
  • Shapes of various species of fungi
  • Compound eyes in various species of insects
  • Conical helices in various species of shells and horns of animals
  • Muscular fibres, for example the circular and longitudinal muscles of the mammalian heart
  • Helical twists in many climbing plants

Geodesic space frame structures are efficient regardless of scale.
What is a space frame? – A three-dimensional frame, usually triangulated in all directions, composed of struts and ties interconnected so that they all share in carrying any load.

Application
Trellises are used as obelisks, screens, arches, arbours and pergolas. Trellises have a particular relevance to today’s smaller gardens and ‘gardens in the sky‘. Obelisks and arches can be used to frame a view, define an entrance or path. Obelisks can give instant height to a border. An arbour can partly hide a sitting area.

Trellised walks are surely among the most delightful features in the garden. Their use goes back to antiquity. Imaginative trellises can also be used as sculptures in the garden. Generally, trellises have a rustic appearance and are heavy in every sense, physically and aesthetically. The structural form of 21st century trellises should be minimal, lightweight and almost invisible!

My SFT system, analogous to a Meccano kit, can be used in a new garden project and also to rejuvenate an existing area of the garden. A unique feature of my SFT system is that individual struts can be threaded through the branches of an established plant and assembled into a very strong and unobtrusive trellis.

Cost
My space frame trellises are inexpensive to make as they use standard off the peg materials. They can be fabricated by any blacksmith or any DIY enthusiast.

Arbour

arch_pergola_7.jpg

arch_pergola_81.jpg


Arbour in full bloom

Posted: January 13th, 2008 | Author: John Zerning | Filed under: Arbour | Tags: , , | No Comments »
Arbour

Arbour in the form of half an icosahedron plus two tetrahedra. (The icosahedron and the tetrahedron are two of the five Platonic solids).

The trellis of this arbour has the form of half an icosahedron plus two tetrahedra. (The icosahedron is the basis of Fuller’s geodesic domes).

The rose festooned arbour has a long history. Many years ago someone planted ‘New Dawn’ next to the boundary wall of St. George’s Fields, near Marble Arch, just opposite Hyde Park.

Gradually this vigorous climber grew up the wall and along the ground forming a tangled mass. In order to save and rejuvenate this old rose, I designed the trellis in the form of a modified geodesic dome, made from 17 equal length struts.

First, the tangled rose was lifted and held up by means of a few T-shaped wooden poles.

Next, the trellis was erected piece by piece under the raised rose. Once fully assembled the props were removed.

The massive climber dropped perfectly over the trellis and covered it completely. The rose responded magnificently to its raised support and flowered profusely.

To extend the flowering season an evergreen clematis armandii was planted and trained over the rose. It quickly spread over the arbour and up the wall of the neighbouring house. In full bloom the sight is spectacular. It was most gratifying to see that neglected climbing rose transformed into a garden treasure!

Arbour

The assembled arbour. The minimal space frame is very stable, yet it touches the ground lightly.

Arbour

The space frame trellis is doing its work, whilst being invisible!

Arbour in Winter

To photograph this sight one had to be very quick.


Arch Pergola

Posted: January 12th, 2008 | Author: John Zerning | Filed under: Pergola | Tags: , , , | No Comments »
arch_pergola_5.jpg

The Arch Pergola is formed from four pyramidal units bent into an arc and propped by two internal V-shaped supports.

This space frame trellis is a hybrid between an arch and a pergola.

It is formed from four pyramidal units bent into an arc and propped by two internal V-shaped supports.

The structure works like a three-hinge arch, which makes it not susceptible to differential settlements of the foundation – pegs in this case.

arch_pergola_7.jpg

The space frame trellis is almost invisible amongst the branches of the plants.

arch_pergola_6.jpg

The dynamic and minimal space frame trellis is accentuated by the snow.

arch_pergola_8.jpg

The universal connector, using off the peg materials.

arch_pergola_9.jpg

Another view of the connector.


Sphere

Posted: January 11th, 2008 | Author: John Zerning | Filed under: Sphere | Tags: , , | No Comments »
sphere_10.jpg

St. George’s Fields sphere

This geodesic sphere in stainless steel can be found in St. George’s Fields, near Marble Arch and opposite Hyde Park. It is constructed from ten great circles. (The shortest line between two points on a sphere is an arc of a great circle). This oversized ‘football’ can be moved about in the garden till the ideal spot for it is located. As it is not fixed to the ground cutting the lawn underneath the sphere is not a problem.

sphere_11.jpg

This sphere was placed in the shady part of the garden. An ivy was planted where the sphere touches the ground.


Helical Obelisk

Posted: January 10th, 2008 | Author: John Zerning | Filed under: Helical Obelisk | Tags: , , , | No Comments »

helical_obelisk_12.jpg

Helical Obelisk

helical_obelisk_13.jpg

Helical Obelisk

In this obelisk the tetrahedra are joined face to face to create a twisted column with triangular faces. The edges of this arrangement follow helical lines, it is referred to as a tetrahelix. Note, it forms right-handed helices like in the structure of DNA. The tetrahelix space frame is a beautiful geodesic structure expressing life and growth, which is most appropriate for the support of plants.

Sixteen of these 21st century obelisks were erected in a double rose border over 100 metres long at the RHS Garden Harlow Carr. This project was first shown on the BBC Gardener’s World Roadshow on 09.07.05 and again in Gardener’s World on 02.09.05. A similar photo was included in the RHS poster in 2006 to excite garden lovers to join the RHS.