Friday, January 24, 2014.

San Antonio, Texas

 Minimal Surface Blog Entry

More Research on Minimal Surfaces

Besides circus tents, nomad tents or clearance sale tents, minimum surface construction has evolved into something more sophisticated, substituting mesh for steel as in the case of Kenzo Tenge in Japan, thin structural concrete like in the case of Felix Candela in Mexico, Argentina and Spain.

A Denver Circus Tent from 1914

A Denver Circus Tent from 1914

Palacio de los Deportes. Mexico 1968

Palacio de los Deportes. Mexico 1968

A minimal structure is a building made from minimal materials that can be assembled quickly, efficiently, economically and safely.

In some of our research, architects such as Felix Candela used the same concept – but he utilized the thinnest layer of concrete possible.    Kenzo Tenge had the same idea but utilized steel instead.  (Ohlenbusch, April 2-11, 2013).

Soap film is a minimal surface.  It takes it shape when all of the forces that are exerted on it are in equilibrium.    By default this shape would the optimal shape or the most stable and balanced.   Both Felix Candela and Kenzo Tenge utilized this form in some of their structures.

Other Characteristics

It is light, safe, economical and can be assembled or dismantled easily.

Some of the minimal structures we researched have been standing for more then 50 years such as the 1964 Kenzo Tenge Tokyo’s Olympic Stadium from 1964 resisting high winds and rain storms.

Tokyo's Olympic Stadium 1964

Tokyo’s Olympic Stadium 1964

Tokyo Olympic stadium scale model 1964

Tokyo Olympic stadium scale model 1964

A minimal structure is respectful to nature and for it does not always require a slab, too many columns or much tree leveling.  Its appearance is organic and nature-like, resembling a mountain, a valley, a jellyfish or a cell under a microscope.   It also supports a large spans.   This is the case with the Munich Olympic stadium built in 1972 by Frei Otto:

Olympic Stadium.  Munich. 1972

Olympic Stadium. Munich. 1972


Minimum Surface construction has many shapes:

  1. Hump tents
  2. Peak tents
  3. 4 point cross over tents
  4. Double curve
  5. Parabolic
  6. Hyperbolic
  7. Single curve

Materials  (A revised list)

These structures can be made of:

  1. Wood
  2. Cables
  3. Steel mesh
  4. Steel skin
  5. Steel masts
  6. Plastic skin
  7. Canvas
  8. PVC polyester fabric membrane materials.
  9. Ropes
  10. Concrete anchors to tie the cables at the end at angle of 120 degrees from the horizon.

The Evolution of Minimum Surface construction changes further

Tents or membrane structures of yesterday have evolved a lot lately.

Now these structures are made from polyvinyl polyester resisting winds pressures, rain and snow.

At the All of Russia in 1896, the Shukov Rotunda was presented to the public as the first minimal surface tensile membrane structure giving many architects and engineers at the time a lot to talk about.  (Beeson, Summer 2013). 

Nowadays, technology has evolved more.  For example, when Kenzo Tenge designed and built the 1964 Tokyo Olympic stadium – the minimum surface / tensile structures were now ready to defy the high winds and typhoon weather that Japan sometimes experiences and it has been standing for 50 years now.

Kenzo Tange used instead of a mesh, a membrane from Steel anchored with cables attached to concrete anchors.    (Ohlenbusch, April 11, 2013).

Another examples would be the Feira da Cidade in Brazil, using minimum surfaces.  It does have a space frame and a combination of branch structure as well as a minimum surface membrane above.   There are some gaps in the ceiling for ventilation and light.  (Beeson, Summer 2013).

Feira da Cidade

Feira da Cidade

Additional Definitions 

Tension and compression are the basis for minimum surface structures.   This is the basis for its stability and strength.  (Nerdinger, pages 18-22).

A dome is not any stronger by being round but by being conical or catenary.  When we hold two parallel rings together with soap of film between them the result would be a catenary shaped soap film.

Additional Description

The shapes of the minimal structures are:

  1. Hyperbolic,
  2. Parabolic,
  3.  Square,
  4. Circular,
  5. Semicircular,
  6. Cloverleaf shaped

 Revised Objective

Our objective is to successfully design a minimal transitional structure, with a iconoclastic membrane connecting the old Mc Nay to its new wing, providing an interesting path, for people to contemplate nature and transition from the classic collections to the new modern collection housed at the new wing.

We also need a connection with nature through its gardens.

We plan to use these shapes:

  1. Hyperbolic,
  2. Circle,
  3.  Parabolic,
  4. Circular,
  5. Triangular,
  6. Square,
  7. Square prism
  8. Triangular prism
  9. Tetrahedron


 A Minimum structure can be built using tension and compression, tensile material or fabric, and anchor support.    We plan simulate our model by increasing our scale to an object that is 4 feet long and about a feet wide.

We plan to design a tank with Plexiglas which will hold the soapy water so that we can dip our model and show our patrons how the soap film will provide the form we need.


Model Materials

We would need about four times the recipe amounts we concocted last week:

24 oz. of Glycerin

96 oz. of Walgreen’s Orange Liquid Dish Soap

264 oz. Walgreen’s Distilled Water

(As inspired by Frei Otto’s soap recipe.) (Nerdinger, page 19)

4 feet by 1-foot tank for our large model

Green plastic mixing bowl

Copper wire

1/16th of an inch wire roll  (picture hanging wire)

18-gauge copper wire


1mm elastic cord (Bead Landing Brand)

1mm transparent elastic cord (Stretch Magic Brand)

18 w to 30 w soldering device

Soldering Wire

A ruler

Masking tape


Our Experiment:

On our third day of class, Friday January 17, 2014, we made about 5 more models.    The pictures were not available until after the first post of our blog entry.  But this time, we did more complex compositions producing prism like surfaces.

We used the recipe for soap from last week, and we attached the models to the Plexiglas walls.

We soldered some pieces, soldering copper wire together along with silver soldering wire making a tetrahedron, a square prism, a triangular prism, and a crown.    After the models cooled down, we dipped them in the soap, and we were able to capture the soap film in color using a portable Canon digital camera and a drafting light.

An extruded square

An extruded square

Crossover square forming two triangles

Crossover square forming two triangles

We mounted one of our models on Plexiglas to visualize the constraint of a wall and then the soap film acted as a curvature.

Our Plexiglas box

Our Plexiglas box

Through the 1/16th of an inch holes, we secured the 1/16th inch wire roll, to its wall and base.   This worked very well, for the Plexiglas provided the support we wanted and the soap film remained intact.

An Extruded Circle

An Extruded Circle

Spring-like Structure

Spring-like Structure





Triangle Prism

Triangle Prism





Andres Mulet                  Aleksandr Mikhailov                    Troy O’Connor

(The Minimal Surfaces Group).


Bill Addis, 2005. Frei otto: Complete works. Construction History 21, 115, (accessed January 17, 2014).

Edward Allen, Fundamental of Building Construction:  Materials and Methods 4th Ed.  John Wiley and Sons    Hoboken New Jersey 2004  (page 424).

Bedouin Camp – El Dohous Village  – Desert Life  (accessed Jan 24, 2014).

Sadet Beeson, Ph. D, Lecture on Membrane Structures, Building Technology 3 Summer Semester 2013- University of Texas at San Antonio June 5, 2012.

Frei Otto in Conversation with the Emergence and Design Group: Architectural design, ISSN 0003-8504, Nº. 3, 2004, pages. 18-25.

GRACE GLUECK. 1971. Art: Frei Otto’s ‘minimal structures’ subject of display here. New York Times (1923-Current file) 1971. (accessed January 17, 2014).

Guillermo José Jacobo, Ejemplo Diseño estructural experimental en arquitectura como metodología de diseño arquitectónico. -: Universidad del Nordeste, Facultad de Arquitectura y Urbanismo, Resistencia, Provincia de Corrientes y del Chaco – Argentina.  (accessed Jan 24, 2014).

Karl L. King and the Sells-Floto & Buffalo Bill Wild West Combined Shows Band 1914 to 1916  (accessed Jan 14, 2014).

Achim Menges. 2006. Michael Hensel; Frei Otto. Architectural Design 76, (2): 78-87, (accessed January 17, 2014).

Winfried Nerdinger, Frei Otto, and Technische Universität München. Architekturmuseum. 2005

Frei Otto: Complete works: Lightweight construction, natural design Birkhäuser, (accessed January 17, 2014).

Darryl Ohlenbusch , M. Arch, Lecture on Modern Mexican Architecture – Spanish Architect Felix Candela History of Modern, ARC 6973 Section 903  – University of Texas at San Antonio  April 2, 2013.

Darryl Ohlenbusch , M. Arch, Lecture on Modern Japanese Architecture – Kenzo Tenge  History of Modern, ARC 6973 Section 903  – University of Texas at San Antonio  April 11, 2013.

Frei Otto1969. Design quarterly (74/75): 25-27; (accessed January 17, 2014).

Positioning of Olympic Stadium Roof  (accessed Jan 24, 2014).

Train Model Circus Tent from a Hobby Shop  (accessed Jan 24, 2014).

Tokyo National Olympic Gymnasium by Kenzo Tange  (Kenzo Tange – Olympic Stadium of Tokyo) (It uses minimal surfaces, tension and compression) accessed Jan 24, 2014).

Torsione primaria e torsione secondaria: differenze ed esempi: Article about The Oaka Stadium in Athens – Membrane Construction by Structural Engineer Onorio Francisco Salvatore     (accessed June 5, 2012, and Jan 24, 2014).

William J. Curtis, Modern Architecture since 1900, 3rd edition (Upper Saddle River, NJ: Prentice Hall, 1996).

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