Sweating Paper Architecture

Guillaume Dumont Maria Larsson Dejan Mojic

Primary Advisor: Professor Yusuke Obuchi Collaborative Advisors: Professor Jun Sato Professor Masayuki Mae Course Assistants: Toshikatsu Kiuchi So Sugita Computational Support: Masaaki Miki

Cybernetic Urbanism V.2, 2014 Obuchi Laboratory Editing: Guillaume Dumont Maria Larsson Dejan Mojic Alisha Ivelich Printed in Tokyo, Japan, 2014 For more information on Obuchi Lab Visit www.obuchilab.com Obuchi Laboratory University of Tokyo Graduate School of Engineering Department of Architecture 7-3-1 Hongo, Bunkyo-ku Tokyo, 113-8656 Japan

Acknowledgements We owe special gratitude to Assistant Professor Yusuke Obuchi and Course Assistants Toshikatsu Kiuchi and So Sugita for their endless support throughout the project.

We would also like to thank Assistant Professor Jun Sato for his keen interest in the project and for providing guidance with regard to structural performance. Professor Sato was also invited us to the Architectural Institute of Japan to build a structural prototype.

We would like to thank Professor Masayuki Mae for his advice on developing and evaluating environmental performance.

We would further like to thank all of the students at Obuchi Laboratory. We include special thanks for Yushi Saada for his contribution to the team during the first semester of research, and the construction team for the 1:1 scale proto-structure—Ana Ilić, Risa Kagami, and Yasemin Sahiner.

We would like to thank Alisha Ivelich for editing this book and various other materials related to the project.

Finally, we are grateful to all the staff and faculty at the Department of Architecture.

Table of Contents

1. Introduction

9

2. Production Process

23

2.1 Initial Experiments 2.2 Development of Pressing Method 2.2.1 Mold 2.2.2 Hyper-parabola Press 2.3 Digitalization 2.3.1 2D Scanning 2.3.2 3D Scanning

3. Assembly

53

3.1 Initial Experiments 3.2 Digital Assembly 3.2.1 Extruded Geometries 3.2.2 Deformed Cylinders 3.2.3 Physical Assembly Test 3.2.4 Doubly-Curved Geometries 3.3 Physical Joint

4. Material

85

4.1 Material Composition 4.2 Mass-Customization Process 4.3 Digitalization 4.4 Feedback Process 4.5 Urban Context Paper Flow 4.6 Performative Material

5. Evaporation 5.1 Urban Integration 5.2 Early Prototypes 5.3 System Principles 5.4 Thermodynamics 5.5 Wind Patterns 5.6 Mรถbius Analysis

131

6. Structure

131

6.1 Structural Simulation 6.2 Composing the Monocoque

7. Application

262

7.1 Modular Aggregation 7.2 Urban Application 7.2.1 Pattern Layout 7.2.2 Performance Evaluation

8. Conclusion

203

Appendices Appendix I

Appendix II

Appendix III

Performance, Application, and Impact of Waste Paper-Based Components for Urban Cooling Systems, by Dejan Mojic Adaptive Assembly System: Research On Organization of Differentiated Components for Hydrotectonic Shell Structures, by Maria Larsson Material composition and experimentation, by Guillaume Dumont

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SWEATING PAPER ARCHITECTURE

1. INTRODUCTION

1

Introduction The aim of this thesis project is to establish a design system based on a production process.

Other digitally designed componentbased geometries are typically fabricated either by assembling identical units in specific positions with the precision of a robotic arm, or by fabricating unique components one by one. We instead tap into the low-tech, established technology of mass-production and update it to fabricate a series of diverse components at one time.

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SWEATING PAPER ARCHITECTURE

TARGET #1

Maximize geometrical possibilities while minimizing use of production formwork and dependence on high-tech fabrication tools Many building materials such as plywood, pressed fibre panels, and other boards of various kinds are produced by pressing particles and fibres into a solid plate. This production technique is employed, but with a crucial tweak; the produced plates are layered and pressed in a stack as opposed to one by one. Additionally, rather than pressing the components between two flat surfaces, both the top and bottom pressing heads are sharp. The result of this production process is a series of differentiated components with incremental changes in curvature in two directions. This variety suggests a number of possible shapes can be generated through strategic assembly of the plates.

1. INTRODUCTION

Mold framework

The paper press produces a series of differentiated components. The degree of curvature is a result of the sharpness of the top and bottom pressing heads.

11

45째 top & bottom press

Resulting stack of paper plates

Separated stack

60째 top & bottom press

Resulting stack of paper plates

Separated stack

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SWEATING PAPER ARCHITECTURE

1. INTRODUCTION

Global shape generated by aggregation of the local geometries of the components.

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Paper plate assembly - curvilinear geometry fabricated with massproduction process.

Gramazio and Kohler brick wall. Identical components placed in specific positions with the precision of the robotic arm. Retrieved July 25, 2014, from: http://www.gramaziokohler.com

Zaha Hadid bent glass structure. Each glass panel is custom-made to fit the geometry. Retrieved July 25, 2014, from: http://www. designtoproduction.ch

1. INTRODUCTION

TARGET #2

Build with what is already available: the by-products of the city Cities do not only consume material resources; they also produce waste, leakage, and more. Our team advocates for creativity and freedom in the use of materials. Paper is readily available in urban areas. We propose that the existing material flow be expanded by using waste paper as a building material before recycling it.

Pressed plates

Recycling

Forest

Paper mill

Material flow diagram. The paper plates are produced from waste paper and are then re-integrated into the existing flow.

Consumption

Waste

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TARGET #3

Celebrate the “paperness” of paper Perhaps the most well-known example of paper as a construction material is Shigeru Ban’s paper tube structures. This is a genuinely responsible consumption of resources. The material is exposed and acts structurally.

But we aim to push the materiality even further. Because paper is an unstable and perishable material that easily reacts to local conditions, we propose it be used for temporary structures. Further, we propose the utilization of its natural ability to absorb water and cool its immediate surroundings as evaporation takes place.

Absorbent paper plate

IE Paper Pavilion, Shigeru Ban Architects. Madrid, Spain 2013.

Retrieved July 25 2014 from: http://www.archdaily.mx/mx/02248744/ie-paper-pavilion-shigeru-ban-architects/515c35acb3fc4b 9d4f00005b

1. INTRODUCTION

Integration The research targets are integrated into a comprehensive and intelligent design system. To balance moisture and structural performance—which often work against each other—the material composition is manipulated to produce plates with a range of absorption properties, from hydrophilic to hydrophobic. The result is a monocoque structure with local distributions of strength and absorbability.

The research team explored the possibility of fabricating a curvilinear geometry with a mass-production process, while aiming to integrate the existing material flow of the city and maximize the effects of the reactive properties of paper.

Composite monocoque shell

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Design Proposal The site for the final proposal is Chuo Dori in Ginza, which is an exceptionally urbanized area with almost exclusively hard surfaces and an exceedingly hot climate.

During weekends, car traffic on the streets in Ginza is sometimes cut off in favour of pedestrian and festival activities. During such events, we propose the creation of a series of temporary outdoor spaces (for use over a three day period). The chosen space is challenging in that these unrecognizable and variable new forms lack clear hierarchies and boundaries, and thus demand interaction and engagement. It is a collective and social experience; people are encouraged to physically interact with the temporary forms by bringing secondary use water to sprinkle on the structures, thus initiating a cooling effect.

Chuo Dori, Ginza. Source: Obuchi, Y. (Photographer) (2013) Chou Dori [Photograph]

Uchimizu - cooling by evaporation. Retrieved July 25, 2014, from: http://www.akibanation.com/tradisi-uchimizu-untuk-mengurangipemanasan-global/

1. INTRODUCTION

19

Street level view of design proposal on Chuo Dori in Ginza

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1. INTRODUCTION

21

2

Production Process

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SWEATING PAPER ARCHITECTURE

Searching for a Generative Production Process The initial material experiments aimed to produce a series of differently shaped components in one formwork. The core issues for consideration were how to shape the material, solidify it in the shaped state, and achieve variety among the produced components overall.

Cloth + Wax. Hung cloth was hardened with melted wax.

Wet noodles. The noodles were deformed with water. Some shapes translated between the layers.

2. PRODUCTION PROCESS

A wooden stick was used to create an indent in the wet, pressed paper.

A solid object was used to make an indent in paper.

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Paper + Glue / Paper + Sugar. Wet paper with glue and sugar was pressed into a solid brick in a rectangular formwork. The more force applied in the pressing, the harder the form became. The sugar-filled brick was brittle and crumbled easily.

Paper + Glue. In an effort to move away from the generic brick shape, the material was pressed and bent between two plastic sheets that were fixed with tape. This process made it difficult for the paper mass to solidify.

2. PRODUCTION PROCESS

Paper patches. Five sizes of patches were tested, ranging in size from 2 mm X 2 mm to 50 mm X 50 mm.

Patches were mixed with water and pressed in a pile. Cellophane wrap separated each level. After pressing, the layers were separated and spread out. Layers created using small pieces crumbled, but those created with large patches maintained brick shapes.

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SWEATING PAPER ARCHITECTURE

Top plate

Bottom plate

Different shapes were produced as a result of variations in pressing force for each layer. The top plate was pressed along its centre line, which is flat and smooth. The unpressed edges curl freely. On the bottom plate, force was distributed uniformly across the surface.

2. PRODUCTION PROCESS

Thick

a째 Thin

b째

A

Bent

B B' C C' D D'

A B

E E'

C

F F'

D E

G G'

F

H H'

G H I

I I'

J

J Stack

Flat Relating surfaces

Shape

Axonometry

The plates share surface geometries with their neighbours. The top side of one plate has the same press lines and angles as the bottom surface of the plate above.

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Cut type: Shreds Paper type: White copy paper Layer separator: Plastic sheet

Cut type: Large patches Paper type: White copy paper Layer separator: Rubber sheet

2. PRODUCTION PROCESS

Cut type: Full patches Paper type: Recycled copy paper Layer separator: Rubber sheet

Cut type: Shreds Paper type: Recycled copy paper Layer separator: Rubber sheet

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Developing the Production Process Layers are separated with rubber sheets

Waste paper

Shredded

Dampen with water and glue mixture Open pressing frame

Close pressing frame

2. PRODUCTION PROCESS

Scaling up the production process. The previous formwork had inner dimensions of 120 mm x 120 mm, making paper plates of the same size. In order to produce plates more suitable for construction, a new larger mold with inner dimensions of 180 mm x 180 mm was built. Also, rather than using man power to perform the press, the mold was placed in a pressing machine normally used to test the strength of concrete (by crushing it).

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SWEATING PAPER ARCHITECTURE

2. PRODUCTION PROCESS

Copy paper, 35 A4 sheets Glue and water, 1:15

Copy paper, 30 A4 sheets 18 m of toilet paper Water

35

Newspaper, 15 pages Copy paper, 35 A4 Glue and water, 1:15 sheets Glue and water, 1:15

Different materials were tested out in the mold. In these experiments, hard pressed shredded copy paper mixed with glue and water was the material that performed best in that the plates assumed the desired V-shape and became relatively hard after drying.

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Establishing the Parameters of the Production Process

Parameters of the production process: sharpness of top and bottom pressing heads

45° 45°

60°

75°

60° 75°

Mold framework

90° 90°

Increasing angle of top and bottom pressing heads

2. PRODUCTION PROCESS

45° 45°

60° 60°

75° 75°

90° 90°

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Digitizing the Component Geometries A crucial step in the design process was the simulation or digitalization of components in the digital world. This allowed our research team to organize geometrical and material information for the targeted design. Simulation indicated which elements were required to achieve a given design. For this research, pressing heads and pressing force were adjusted through a feedback loop of pressing heads, elements produced, and assembly.

To create digitally simulated components which exhibit the behaviour of physical paper, all angles and dimensions of the produced plates were measured with a scanner. Next, production of the plates in the computer environment worked to find a best match with the elements from the physical world. When the damp paper and press were precisely reproduced in the Maya software, a series of components could be generated with a variety of pressing angles. Various combinations of angles could be tested and re-input in the digital design environment.

2. PRODUCTION PROCESS

13.8 cm

14 cm

12 cm

9.5 cm

10 cm

8 cm

6 cm

4 cm

2 cm 0 cm

Measuring components and determining angles. In the first approach, measurements were taken with a protractor and ruler. The aim was to define the angles for each plate and determine the thickness of the elements at various locations.

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SWEATING PAPER ARCHITECTURE

low density t=15mm d=35mm

middle density t=11mm d= 5mm

full density t=3mm d=32mm

middle density t=7mm d=11mm

low density t=14mm d=59mm

initial angle =60째

final angle

center point displacement

Sections of paper components cut in half. Another method was ultimately used to measure the geometry of our components. Plates were scored in half to get a precise section and then scanned with an office scanner. Angles were precisely studied. This process indicated that final angles may differ from the initial pressing head. This is due to the manipulation of the element during the drying process.

2. PRODUCTION PROCESS

41 9

47°

78° 8 92°

112°

7

121° 144° 6 138°

153° 5 147°

152° 4 153°

160° 3 156° 9 8 7 6 5 4 3 2 1

167° 2 163° 175° 1 169°

The nine elements of a stack were separately and precisely studied. Bottom and top angles were measured.

The angles will be used for further geometrical assembly of components in the design process.

178°

42

SWEATING PAPER ARCHITECTURE angle 45° A-A’ section Top and bottom angle, 60 degrees:

164°

angle 60° B-B’ section

A-A’ section

48° 170°

157°

96°

169°

146° 145° 138°

123°

116°

150°

136°

144°

142°

133°

159°

128°

162°

106° 87°

165°

58°

166°

115° 108°

86°

angle 60°

A-A' section A-A’ section

B-B’ section

B’

A’ B A

170°

70°

169°

112°

150°

131°

144°

149°

133°

155°

128°

115°

168° 160° 174°

108°

174° 86°

A’

B B-B' section

B’

A

B

2. PRODUCTION PROCESS angle 75° A-A’ section Top and bottom angle, 75 degrees:

B-B’ section

79°

173°

104°

174°

161°

126°

155°

135° 142°

149° 125°

149°

120°

157°

168°

98°

B-B' section

169°

82° angle 75°

angle 90° B-B’ section

A-A' sectionA-A’ section

B-B’ section

B’

A’ B A

79°

174°

104°

174°

90° 110°

126°

168°

126°

135°

145°

139°

132°

151°

142° 149°

128°

157°

118°

168°

108°

169°

90°

B-B' section

168° 173° 176° 179°

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SWEATING PAPER ARCHITECTURE

The behaviour of paper was expanded upon in the digital environment. Multiple parameters in the Maya software allow for creation of digital behaviours which are identical to physical behaviours. The rigidity parameter was particularly influential in creating a sufficient paper simulation.

The exact same mold and original mesh were set up. The mesh requires an important balance between the size of the mesh in octet and the precision of the geometry. The same mesh will be used in an assembly design with more than one thousand elements.

Model of paper plates 9 bricks of mesh Mesh as ncloth Gap between two plates = 4 mm Plate setup in Maya environment Mesh as ncloth Length = 12.0 cm Width = 12.0 cm Height = 4.0 cm Top and bottom surfaces: u = 8 divisions v = 8 divisions

Mold setup in Maya environment Mesh as passive collider Internal walls distance = 12.05 cm Height of the mold = 55.00 cm Thickness of interaction between passive collider and ncloth objects = 0.112 cm

Front, back, left, right surfaces: u = 8 divisions v = 5 divisions

2. PRODUCTION PROCESS

Digital press simulation. The analog press was reproduced using a model of a similar setup and by identifying material properties of the damp paper.

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Physically pressed plates:

7

8

9

4

5

6

1

2

3

Parameters of matching physical experiment Shredded copy paper, glue, and water 15 sheets of A4 paper per layer 9 layers Flexible rubber separating layers Resulting geometry Overall height = 12.0 cm Maximum angle = 58째

Physically created components have corresponding digital components. The digital manufacturing can easily be modified, depending on the targeted assembly. The digital material behaves very similarly to paper. A closed feedback loop was created between the physically and digitally fabricated components. Additionally, requirements for the overall assembly (in terms of pressing) were also incorporated.

9 8 7 6 5 4 3 2 1

2. PRODUCTION PROCESS

Digitally pressed plates:

7

8

9

4

5

6

1

2

3

Parameters of mesh-plate setup External thickness during simulation = 0.110 Stretch resistance = 20.0 Resistance compression = 10.0 Bend resistance = 0.100 Rigidity = 0.005 Mass = 1.00 Lift = 0.05 Resulting geometry Overall height = 12.0 cm Maximum angle = 58째

9 8 7 6 5 4 3 2 1

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45° 60°

45°

45° 60° 180°

Produced series of digital components with angles and behaviour similar to paper.

2. PRODUCTION PROCESS

75°

90° 140°

75°

90°

140°

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Feedback Process A feedback process through the use of a 3D scanner was established to verify the accuracy of the components in both the physical and digital world. Coordinates are closely compared, and precise data is produced, including the average amount of difference between the physical and digital components. The elements are scanned with a system of structured light. After scanning a number of physical elements, the simulation of the digitally pressed elements was adjusted. Using the feedback process between the physical elements and the digitally simulated components allowed our research team to control the final design and the pressing angles necessary for production.

Scanned plate

0.002mm

Digitally pressed plate

13.52mm

2. PRODUCTION PROCESS

Camera

Plate Projector Structured light system.

Component scanning.

To reconstruct components in the digital world, a structured light system was chosen. It applied a series of 40 consecutive patterns capable of determining the particular topography of the produced plates in less than a minute. This system was very easy to use, the tools were very accessible and the scanning process was fast. Free software with these capabilities is available on the web. David Laser Scanner was used in these experiments.

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3. ASSEMBLY

3

Assembly The most straightforward way of making a curvilinear, component-based structure is to apply a top-down process; that is, to define a target geometry, divide it into components, and fabricate the components. By doing so, however, a multitude of unique components are defined, and these must be customized one by one.

By starting instead with the fabrication of differentiated components, the problem is turned around. Paper plates can effectively be produced, but one question remains: how can they be fit together?

The potential for customized fabrication of a curvilinear assembly lies within the infinite variety of doubly curved shapes possible for paper plate components. Each unique local shape of the global surface is accommodated by a specific paper plate.

This chapter will explore the approach to the organization using various computational strategies to generate an order of assembly, and further, how the digital connections are translated to a physical joint. Finally, we will explore how the geometry is aggregated into a larger modular system.

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3.1. Initial Experiments After testing several ways of connecting the differentiated paper plates, it became clear that an assembly type in which the corners of the plates connected in an overlap was the most desirable organization because the geometry of each plate affects the curvature; the geometries can potentially generate curvatures in two directions, thus producing a three-dimensional curvilinear surface.

3. ASSEMBLY

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3. ASSEMBLY

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3.2 Digital Assembly To make the assembly system a design tool, and to explore what geometries are possible to assemble with the paper plates, algorithms were used to generate various basic assemblies.

3.2.1. Extruded Geometries The first version of the digital assembly explored the relationship between the sharpness of the pressing head and the curve it produced. With singly-curved plates, the tests only indicated extruded geometries.

3.2.2. Deformed Cylinders Two-directional curvatures were not mastered until an assembly of deformed cylinders (next page) were tested.

In these tests, particular sequences fit a certain radius according the plan, and the curvature of the section was an unpredicted consequence of the sequence.

3. ASSEMBLY

Sharper pressing heads generate sharper curvatures

An extruded wall with a custumizable curvature is made by vertical repetition of a particular sequence of components.

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3. ASSEMBLY

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3.2.3. Physical Assembly Test This digitally pre-determined assembly was tested out in a 1:1 proto-structure and was constructed in both the courtyard of the AIJ and in the lounge of Engineering Building 8 at the University of Tokyo during the summer of 2012. The plates fit together in this mock-up, but the topology had some architectural limitations—making an entrance was not possible.

3. ASSEMBLY

H1

M1

M2 G1

M1 M3

M3

M6

M7

M9

45

M9

E6 G9

G 150

45

M 150

flat

M 150

flat

M 150

E9

K9

60

45

60

45

K6 K9

60

150

140

E 140

F 140

F 140

C 130

C 130

D 130

Assembly and production diagram

K9

D 130

A8

K6 K9

A9 A6

D9

B9

45

K 130

flat

K 130

flat

K 130

flat

K 130

flat

K 130

flat

K 130

flat

K 130

45

60

60

130

45

C9

K9 C6

K9

45

K5

K6 K9

60

D9

60

flat

K

C8

K8

K9

B9

K3

C5

K6

C7

K7

K8

A9

D6 K4

D3

K5

A6

K6

K7

A8

C3 K2

C4

K3

A5

K3

K6

A7

C2 K1

D2

K4

B3

A5 H9

K9 C6

K6 D9

flat

E

K9

K5

K3

B6

K1

K2 D1

K2

A4 A7

C8

K8 C5

B6

B3

60

flat

M

K8

K3

K1

B2

A4

C1

K2

A3

A3

C7

K7 D3

K5 C9

K9

K9

45

K5

C6

K7

K4

A2 B1

B2 D6

K6 C4

K3 C8

K8 C5

K6 F9

K3

B1

K2

K1

A1

A2

D3

K3

K6

A1

D2 K1

C2

K4 C7

K7

K8

K3

D6

K1

K2 C1

K2

K4

D3

K5

E6 F9

60 flat

150

E8

D3

K6

K7

K2 K1

K2

C4

K3

E5 E9

M6

K6

E7

E8

K3

D1

K1

D2 K1

C2

K4

F3

E5 H9

M9 H6

M9

E7

M5

K3

F6

K1

K2 C1

K2

E4

F3 H8

M8

E3

F6

H7

K2 K1

F2

E4

M3

H5

M6

G6

M7

M8 M5

E3

D1

K1

E2 F1

F2

M4

G3

M3

F1 H3

M6

E1

E2

M2

H4

M4

E1

H2 M1

G2

M2

H

M1

M2

flat

A 120

A 120

B 120

B 120

C 130

C 130

D 130

D 130

K 130

flat

K 130

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3.2.4. Doubly-Curved Geometries In the final version of the assembly, the same process of iteration was used to match one plate to the next窶馬ot just to fit the same radius in plan, but to fit unique local curvatures in both horizontal and vertical directions. With this system, however, it was still not possible to build any free form geometry because of the way the plates were attached (by overlapping). The distance between two plates can increase slightly, which results in a porous surface and creates opportunities for light filtration, wind filtration, and visual connections; however, if the surface stretches more than 30 percent, the overlap is no longer a stable connection. This knowledge provided the basic criteria for a topology.

These limitations allude to the Mﾃｶbius strip, a continuous surface that has only one side. It can be created by twisting a strip an uneven number of times. The main character of this topology is the spatial and mathematical ambiguity between interior and exterior. As the twist progresses, it forms roofs, walls, and openings. Unlike the cylindrical topology of the proto-structure, it has the potential to create an architectural space.

3. ASSEMBLY

Stretch:

0% stretch 0%

No stretch

10% 10%

20% 20%

Max stretch

Technical surface criteria, full grid of developable surface

Technical surface criteria, full grid of developable surface

30% 30%

50% 50%

70% 70%

Exceeding stretch limit

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The basic process of the assembly system starts with defining a target geometry that meets the topological criteria. An algorithm negotiates between the pressing angles and order of assembly in order to find the solution with the lowest tolerance. Then, the plates can be produced and physically assembled according to the digitally defined recipe. Geometry constructed following these instructions is a result of the aggregation of the shape of the components.

β

α-β=0

α

Line angle difference = 0

-θ α

β

α-β=-θ

α

Line angle difference = - θ

β

θ

α-β=θ

Plate matching calculation

Line angle difference = θ

3. ASSEMBLY

3 twists

1 twist

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C o m p onent geom et r y / p re ssi ng a ng l es

14

5

27 13

26 19

25 6

3

0 33

12 32

11

37

18

4

44

15 7

23

21 46

22

As sem bl y g ri d

TA R G E T G E O M E T RY

35 47

36

24

10 29

9

30 40

34 42

28

16

45 2

1 43

20

8

41 31

17 38

39

3. ASSEMBLY

FEEDBACK S ca n n i n g

PRESSING ANGLES PRODUCTION

ORDER OF ASSEMBLY

CONSTRUCTION

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Full assembly grid

Detail

A1-0

A1-1

A1-8

A1-7

A2-6

A1-2

A2-7

A1-3

A1-4

A2-4

A4-3

A4-4

A3-5

A4-8

B3-3

B3-5

A4-6

A4-7

B4-3

B3-6

A3-8

B4-0

B4-1

B4-4

B4-5

B4-8

A2-8

B2-4

B2-3

B2-6

A4-1

A3-7

B3-4

B2-2

A3-6

B1-3

B2-5

B3-2

A3-3

A4-2

B1-8

B1-2

A1-6

B1-5

B3-0

B1-4

A3-2

A3-0

B1-6

A1-5

A3-4

A3-1

B2-1

B1-7

A4-5

A2-1

A4-0

A2-0

A2-5

A2-3

A2-2

B2-0

B4-7

B3-8

B3-7

B2-7

40° 50° Production molds

A1

110° 130° 120° A4 A2 A3

130° 100° 110° 80°

90°

70° B2

B1 130°

50°

130 B3

B4

80°

90°

Minimal formwork

40°

50°

60°

70°

70°

80°

3. ASSEMBLY

71

972 plates 108 molds 14 pressing heads

C2-0

B1-0

C3-0

C1-7

C4-0

C1-4

B1-1

C1-8

C1-0

C2-1

B4-2

C4-2

C3-5

C1-5

C4-5

C2-5

C4-7

B4-6

C2-6

C4-8

C3-8

D1-2

C4-6

C3-7

D3-2

D3-0

D4-3

C2-7

C4-1

D3-4

D4-2

D4-1

E3-0

D4-7

D3-8

E1-7

D4-8

60°

0°

80° C3

120° C1

C2

°

130° 90°

90°

100°

110°

50°

110°

140°

70°

60° 130°

C4

D1

D2

110°

90°

120° 130° 140°

120°

130°

140°

D3

150°

D4

E1 70°

E3-5

E4-7

50°

E2

E3-7

E1-8

F1

100°

E3

E4

110° 80°

70°

F2-5

F4-1

F4-4

F2-6

F3-3

F4-2

E4-6

F2-8

F3-2

F3-1

F1-8

F2-4

F4-0

E3-8

F2-7

F1-4

F2-3

F2-1

F3-6

F2-2

E4-2

E4-5

E4-8

50° 80°

E4-3

F1-7

F1-3

E3-3

F4-6

F1-1

F1-2

E3-4

E4-1

E4-4

F1-6

E2-6

E3-2

F2-0

F1-5

E2-5

E2-3

E4-0

D4-4

E2-7

E2-4

E3-1

F1-0

E2-1

E1-6

E2-2

D3-6

D4-6

E3-6

E1-3

D3-5

E2-8

E1-1

E1-2

D2-7

D3-3

D3-1

C3-6

C2-8

B2-8

C4-4

E1-5

D3-7

D4-5

E2-0

E1-4

D1-6

D2-6

D1-1

C4-3

D2-8

D2-5

D2-3

C3-2

E1-0

D2-2

D1-7

D1-0

C2-2

C3-3

C3-4

D1-8

D2-4

C1-1

D1-4

D2-1

D1-5

C1-3

C2-3

D4-0

D1-3

C3-1

C2-4

C1-2

B3-1

D2-0

C1-6

F3-4

F3-5

F4-5

F4-3

F3-0

60°

50°

F1

F2

F4-7

F3-8

F3-7

80° F3

100° 120° 60°

F4-8

130° F4

60°

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SWEATING PAPER ARCHITECTURE

3. ASSEMBLY

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SWEATING PAPER ARCHITECTURE

3.3 Physical Joint In transitioning to the physical assembly, the digital plateto-plate relationship needed to be translated to a stable joint that secured alignment and plate distances.

In the first attempt to create this stable joint, two plates were simply attached with a screw. Some limitations and difficulties with the screw joint were identified. By assembling a structure plate by plate in this fashion, there is no guide for how much the plates should overlap before the screw is added. This motivated a development of a tie joint. Two plates were first joined loosely by tucking their corners under a shrinkable string tied around each plate.

This made it possible for distances to be adjusted following assembly, but before fixing the joint by shrinking the string with water. This joint also produced a surface pattern.

When testing at the 1:1 scale, however, some problems were encountered. Distances did not self-organize easily, the structure was weak in some places, and plates often popped out.

These experiences led to further improvements of the tie joint. By placing the string through a hole in the plate, a cross could be tied. The loop was thus closed, ensuring plates would not pop out. Furthermore, the distances between plates could be controlled using specific hole positions that were pre-drilled according to the position of the corner of the adjacent plate. This accommodated a variety of stretches on the surface. In places where the plates were tightly assembled, a single hole was placed in the centre. At maximum stretch in both directions, four holes were measured with a laser template. While the geometry was a result of the aggregation of the shape of the components, the spacing was determined via the hole positions of each joint.

3. ASSEMBLY

Joint 1 - screw

Joint 2 - weave

Joint 3 - woven through holes

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SWEATING PAPER ARCHITECTURE

Joint set up - holes drilled in plates, a 70 cm long shrinkable string

20.5 cm

+ water

15.0 cm Shrinkable string

3. ASSEMBLY

Tied joint detail

Woven joint surface pattern

77

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SWEATING PAPER ARCHITECTURE

No stretch

Horizontal stretch

Vertical stretch

Horizontal and vertical stretch

3. ASSEMBLY

Maximum stretch in both directions

79

80

SWEATING PAPER ARCHITECTURE

No stretch

3. ASSEMBLY

Maximum stretch in both directions

81

82

SWEATING PAPER ARCHITECTURE

3. ASSEMBLY

Although the geometry is produced by specific local shapes, the spacing of each component is generated via specific hole positions of each joint.

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SWEATING PAPER ARCHITECTURE

4. MATERIAL

4

Material Bearing in mind that most industrial products are homogeneous, stable, and sometimes lose their properties during the manufacturing process, we aimed to develop a building material that could benefit from the characteristics of a pure material with smarter qualities.

Experimenting with the qualities of the produced material and its behaviour, the research team created a series of differentiated elements with the aim of producing a high volume. Mass-produced, highly customized components were integrated into the final design process.

Fabricating via pressing contributed to the special arrangement and to the structural performance of the paper. The exact same components were pressed in a digital environment, and expressed the same behaviour exhibited in the real world. A feedback process in which the components were scanned helped to intimately control the produced elements and the design with its simulated components.

Using a resource that was readily available in everyday life but unconventional in architecture became an additional inspiration for our team. It led

85

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SWEATING PAPER ARCHITECTURE

to an understanding of existing schemes in contemporary society, material flows within the city, and the social and economic impacts these schemes and flows imply. Consequently, we established an extended closed loop that transformed waste products into building materials.

With the aim of designing a temporary cooling system, one of the properties of the produced material we sought to emphasize was its ability to act as a watercontaining element. The absorbability of the plate was directly controlled by the manufacturing process and in the treatment of the material. Finally, each element has its own composition, specificities, characteristics, and performance within the design process.

A truck picking up shredded paper and cardboard and subsequently turning it into very compacted bricks was the initial inspiration for the use of paper as a research material. Recycling is typically a complex loop that requires many transport/collection points.

Paper recycling truck on the University of Tokyo campus (2013)

4. MATERIAL

3.1. Material Composition An in-depth research on paper was conducted to display properties and behaviours applicable to industrially manufactured products with a focus on specific strengths, orientation of fibres, and active ingredients. Experiments were simultaneously conducted using different paper qualities, fabrication techniques, and processes. The paper was manipulated and pressed in specific arrangements to create a series of structural and differentiated but related components.

Paper Flow in Urban Context For a long time, resources have been abandoned after they are used, or their natural energies have been ignored. In contrast, materials and energies in nature are constantly being converted or being reused without any waste.

The flow of matter in nature forms a complex network of parallel dynamic systems. In the developed system, the flow of paper within the city is extended in a closed feedback loop and is interdependent with urban water and climate loops.

Paper is used as a secondary resource directly available within the city that can be transferred to the building industry. To introduce this system, our research examined the consumption of paper in Japan, at its recovery rate, at the precise flow of paper for our chosen site (Chuo-Dori) and at the extension of the paper recycling loop for the production of the researched plates.

Compacted paper bricks on the University of Tokyo campus (2013)

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SWEATING PAPER ARCHITECTURE

Facts Despite the invention of the computer and the digitalization of information, the amount of paper remaining in use is considerable. The amount of paper consumed peaked at about 16 millions tons annually.

Considering paper as a secondary resource for the building industry suggests great potential.

(million tons) 35

35

30

30

25

25

20

20

15

15

10

10

5

5

0

0

Annual consumption of paperboard

recovery of paper and paperboard

Annual consumption of paper

1955 1960 1955

1970 1970

1980

1990 1990

Annual consumption of paper - paperboard and its rate of recovery.

2000

2010 2010

4. MATERIAL

Furthermore, after being disposed of, paper is used in the building industry, thus indirectly reducing the number of cut trees required for construction.

(millions tons) 55 55

50 50

45

45

40

40 Supply of domestic wood

35

35

30

30

25

25

20

20

15

15

10

10

5

5

0

0

recovery of paper and paperboard

Annual consumption of paper

1955 1960 1955

1970 1970

1980

1990 1990

2000

2010 2010

Annual consumption of paper, recovery of paper - paperboard and supply of domestic wood in Japan.

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SWEATING PAPER ARCHITECTURE

Extended paper recycling loop in Tokyo

Soka Mill

Ueno Shinjuku

Akihabara Tokyo

Shibuya

Ginza

1. Newly produced paper on the edges of Tokyo is sent to a wholesale office supplier in a targeted area.

Akihabara

Tokyo

Ginza

2. New paper from the wholesale office supplier is delivered to office buildings and utilized.

4. MATERIAL

91

Akihabara

Tokyo

Ginza

3. Used paper is collected and then sent to large dedicated collection points. Plates are fabricated with selected paper.

Akihabara

Tokyo

Ginza

4. Plates are expedited to the chosen site in Ginza (Chuo-Dori) and the temporary structure is built.

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SWEATING PAPER ARCHITECTURE

Akihabara

Tokyo

Ginza

5. Paper plates are dissolved and the paper is collected. The paper is sent back again to the collection points to finally join the existing loop of paper recycling. The extended loop for the creation of both a building material and an architecture is closed.

Soka Mill

Ueno Shinjuku

Akihabara Tokyo

Shibuya

Ginza

6. Waste paper is either recycled at the paper mill or incinerated.

4. MATERIAL

One unit is ------ 4450 plates, which is about ------ 605.2 kg of paper. 7262 yen is required for recycling. By recycling 605.2 kg of paper, the process saves: ------ 1.5 trees, ------ 2317 litres of water, ------ 154 litres of oil, ------ 24 kg of air pollution, ------ 0.2 m3 of landfill space, ------ 359 kW hours of energy.

The economical and environmental impact of our project is considerable. We are able to produce an architecture from resources which exist within the city for a low price. This also preserves essential, pure resources.

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SWEATING PAPER ARCHITECTURE

Performative Material Paper exhibits great potential for water absorbency due to the organization of its fibres and the ingredients it contains.

In most cases, this absorbency is seen as a disadvantage of paper. In the developed prototype, however, this property is emphasized to respond to urban and environmental problems with a performative and variegated material design. Optimization of water-absorbing properties implies a sharpening of each step in the manufacturing process, in the testing of composite materials, and in the elaboration of special paper treatments inspired by the paper industry.

Examining arrangements of paper on a different scale (like the micro-scale) is crucial. Such explorations provide precise information concerning the absorption of water.

Recent research has shown that working with paper with small and thin fibres and via new chemical processes has great potential in industries such as the automobile or medical industries.

starch

dye and pigments

coal

clay

lime

sulfur

water

50 kg wood

94

Quantity and list of ingredients necessary to produce one ton of paper. Paper is primarily composed of wooden fibres, but some unexpected ingredients such as clay or pigments may also enter in its constitution or in its fabrication process.

4. MATERIAL

Each additive lends special characteristics to paper and acts as support over a long period of time. Surface sizing is used to modify the absorption performance of paper. This helps the ink stay at the surface of the paper. Bleaching agents make paper whiter.

Additives to enhance paper properties:

Sulfur

Lime

Clay

Starch

Bleaching agent.

Dissolving non-cellulose wood elements. Bleaching agent. Flocculating, neutralising and clarifying agent for residual water.

Surface sizing. Improves printing or writing.

Surface sizing. Retention and de-watering aid. Acts as adhesive or binder to bind the pigment particles to each other and to the paper.

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SWEATING PAPER ARCHITECTURE

Section and surface of a paper sheet being processed:

Microscopic observation of a section of a paper sheet.

Surface of the paper at a microscopic scale.

Uncoated paper

Coated paper

This microscopic observation of paper illustrates how paper gains its qualities and characteristics through layering and adjustment of different additives, and results in a smooth, homogeneous surface.

4. MATERIAL

Material

Classification

Compressive modulus

Paper pulp

Pure

40 GPa pulping

Paperclay

Composite

Paper + Polymer

Composite

Paper + Strong fibres

Composite

Various sizes of fibres

Pure

Paper + Cement

Composite

Microfibril cellulose

Pure

70 GPa hydroliysis fallowed by mechanical disintegration.

A list of existing and potential materials was created. Depending on the feasibility or on the tools required, certain combinations of materials were targeted.

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SWEATING PAPER ARCHITECTURE

Institute

Cellulose science

Paper science

Field advice

Mix different fibre lengths, manufacturing processes.

Mechanical properties of fibres, organization of fibres, bonding solution.

Choice of adhesive Science of polymeric materials

Wood chemistry

Building material

(silicone paper, teflon, polybinol, 5% polymeric MDI, isocyanate)

Choice of fibres, composite material.

Composite material, mechanical test.

To elaborate upon the performative elements of the material, various institutes at The University of Tokyo were consulted regarding proper solutions and advice for creation of the targeted waterabsorbing material.

4. MATERIAL

Manufacturing techniques This section investigates different manufacturing processes that contributed to the expansion of structural, water absorbing components. These processes were directly inspired by the paper industry, which has developed particularly efficient techniques, systems, and processes for manipulating paper. The use of approaches similar to those used in the industry allows for efficient control of patch sizes, sizes of fibres, pulp appearance, and the color of the paper. Some processes utilize mechanical forces which are somewhat energy-consuming; others feature chemical processes which have the ability to treat and modify the quality of the paper via the simple interaction of molecules.

99

100 SWEATING PAPER ARCHITECTURE

0s

1min 0s

2min 0s

3min 0s

4min 0s

5min 0s

6min 0s

7min 0s

8min 0s

9min 0s

10min 0s

Boiling fibres caused them to partially separate, and created a consistent paper paste. Although the process caused the paper sheets to divide, large patches of paper remained.

4. MATERIAL 101

0s

6s

12s

18s

22s

26s

30s

34s

38s

42s

46s

50s

Dry blinding the paper to de-fiber proved very effective. The paper was immediately reduced to smaller sizes. In this process, the paper tended to form thin particles, like a powder. At the end of the process, the paper was dry and highly decomposed.

102 SWEATING PAPER ARCHITECTURE

Paper and fibres were cut to divide them. Microscopic observations provided information concerning the behaviour of the fibres when reduced to smaller sizes. When the fibres were made very small, they tended to create an ultra smooth and dense layer.

34 s

50 s

Assumed microscopic observation of the division of the fibres.

180 s

4. MATERIAL 103

0s

6s

12s

18s

22s

26s

30s

34s

38s

42s

46s

50s

The wet blending process was also very effective in terms of efficiency in reducing the size of the fibres. This system produced very short fibres from large patches of paper. The size of the fibres was easily controlled. When the paper was blended for a very long period of time, it formed a very thin layer of accumulated fibres that retained the flow of water (a water-retaining layer).

104 SWEATING PAPER ARCHITECTURE

Main original direction of the fibres in a paper sheet.

Cutting fibres during the shredding process.

The shredding process created long fibres (shreds) in the same direction as the oriented microscopic fibres in the paper sheet. The shreds were highly structural in tension due to the semi-anisotropy of the composing fibres.

4. MATERIAL 105

The bleaching process induced the whitening of the paper sheet. The process cleaned the paper sheet of pigments and other chemical solutions. In doing so, the paper became more practical for the de-fibering process.

1

2

3

4

5

6

Pure paper 7

This investigation sought to create a material with pure paper or cellulose fibres. The research team aimed to understand processes most appropriate for revealing specific properties from cellulose fibres. Through examination of current research in the material sciences and the invention of new processes for manipulating fibres in the paper industry, our research team found that the use of pure cellulose demonstrated new high performance.

The recently invented microbril cellulose material showed new properties with the use of only cellulose fibres. The material can be translucid and strong under certain conditions. Our focus was to learn which process would enhance the absorption of water in the material.

Absorption is correlated to the space between fibres and the capacity of cellulose fibres to attract water. Knowing this, a series of experiments were conducted to create a material capable of absorbing a considerable amount of water without deteriorating.

106 SWEATING PAPER ARCHITECTURE

Pure cellulose - Powder

Pressed pure cellulose Experiment 1. Very thin cellulose was pressed. The pure material has interesting qualities; when dry, it occupies a large volume of space. This quality accommodated the pressing and the geometrical mass-customization of the components with the developed manufacturing process. After pressing, the material exhibited structural performance and was capable of efficiently absorbing water.

4. MATERIAL 107

This paper paste was collected after wet blending 7 sheets of recycled paper. The initial weight of the paper was 29 g (in a dried state).

Medium size fibres in water

Tiny fibres in water

Medium size fibres after mixing in ashes

Tiny fibres after mixing, ashless

Mixing and shaking fibres in water after the wet blending process determines the size of the fibres extracted.

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With the help of different manufacturing processes and drying methods, the research team was able to produce paper with different properties and appearances. The paper easiest to manipulate was paper which occupied a large volume of space relative to its own weight. This knowledge allowed differentiated geometries to be produced through pressing of the paper while the paper.

Treatments for producing ashless paper and paper powder were not determined and or experimented upon, but these types of papers present great opportunities.

volume due to water clinging to fibers.

volume due to fibre stacking.

?

paper pulp

dried tiny paper fibres

ashless paper

paper powder

After four days of bleaching, the paper resembles a building material and has has excellent absorbing properties.

4. MATERIAL 109

+

=

30% - 50%

50% - 70%

Long shreds

Thin cellulose

Mix of short and long fibres

Fallowing a discussion with Professor Saito from the Global Plant Material Science Laboratory at the agriculture campus, a combination of different sizes of paper were tested. The hypothesis was that each paper size brings its own structural abilities within its scale.

110 SWEATING PAPER ARCHITECTURE

Experiment 2. The same experiment was completed with the aim of creating a paper plate.

Very tiny fibres

Tiny fibres

Combination of different fibre sizes

Very tiny fibres

Shreds

4. MATERIAL 111

experiment 1 ingredients

experiment 2

thin cellulose

thin cellulose

middle size cellulose

1-2 mm paper shreds

100% 53 g

40% - 60% 4 sheets of paper 18 g

10% 3 sheets of paper 13 g

30% - 50% 5 sheets of paper 22 g

1 hour bleach- 1 hour diping process ping in water

total weight in dried state

53 g

adhesive or water

1/16 glue + 15/16 water

1/16 glue + 15/16 water

total weight after pressing

121 g

129 g

result

53 g

112 SWEATING PAPER ARCHITECTURE

In this experiment, paper towel manufacturing methods and the material’s capacity to absorb water were used as references. Paper towels were structurally reinforced with designated with geometrical dotted patterns. The sizes of the dots and the distances between the dots were specific to the desired performance. The dots acted as anchors for puncturing layers of paper together, and the spaces between dots improved the capillarity of the paper. For a high absorption coefficient, the fibres were carefully selected and their organization was highly controlled.

Pressing pattern.

Creation of capillary spaces (paper towel).

Structural dots.

Amplification of the watercontaining pattern.

4. MATERIAL 113

This experiment demonstrated the potential inherent in modifying manufacturing methods or tools to interfere with paper properties. The separating sheets placed between two layers of paper were remodeled. Instead of using simple separators, the sheets brought differentiation to the plate. Holes (or “footprints�) were created, depending on the dimensions of the dots.

The result of pressing with a customized pressing sheet was a plate with variegated footprints. Macroscopically, spaces in between fibres were rearranged. When holes were created, a multiple plate layering system was appropriate.

The first layer (with its holes) controlled the amount of water which flowed to the next layer.

114 SWEATING PAPER ARCHITECTURE

The absorptive capacity of a paper plate was modified via control of the pattern. When a dense pattern composed of large half-spheres was used, the structural qualities of the produced plate were emphasized, but the absorptive properties were not strong. When a sparse pattern of small half-spheres was used, structural qualities were maintained, and the material exhibited a high capacity for absorption.

absorptive capabilities

density

size

structurality

4. MATERIAL 115

1.

Drilled holes Rope

To create the most appropriate pattern for a given plate, the connections on the plate were used as a basis. In this experiment, were paper plates were regarded as having no structural properties in the overall geometry.

2.

A mapping of the area indicating locations requiring reinforcement was drawn. Red areas required a large amount of pressing while blue areas required partial pressing.

116 SWEATING PAPER ARCHITECTURE

3.

Once reinforcement areas were determined, different sizes of circles were designed. The separating sheets during the manufacturing process were generated with this precise influencing pattern.

4.

The result was a plate with an optimized pattern. To create this plate, special fibres were selected before the production process, and microscopic spaces were controlled.

4. MATERIAL 117

5.

These steps produced a plate with an optimized rate of absorption.

The connection points were very stable, and the central part of the plate was capable of absorbing a greater capacity of water. The plate was designed as a container.

118 SWEATING PAPER ARCHITECTURE

Composite with paper Wood can be understood as a composite material. Wood is very strong because the cellulose fibres in the material are embedded in a lignin matrix. The previous study indicated that shredding paper and sealing it in a wooden glue matrix could create a material that is structurally very similar to wood. Material composites with paper, such as paper clay (in the field of art) and papercrete (in the building industry) already exist.

This section of the document will explore experiments with other materials. The experiments include materials which are homogeneous overall, or materials made of multiple layers with different properties and functions for each layer. The paper was processed with techniques which optimized water absorption, but other materials tended to optimize the structural performance of the material overall. Experiments aimed to find the best combination of materials for the design of a water-absorbing paper plate, or a structural plate made of paper.

Experiment number four in the figure on the right indicates optimum characteristics for water absorption. The spaces in between fibres were large, and a strong cohesion existed in the material overall. Experiment number nine indicates characteristics for the production of paper-based structural component. The sample was very light and strong. Four days were required for the sample to dry instead of the regular two days. This suggested that the evaporation rate of the component was low, and consequently the absorption rate of the component was also low.

4. MATERIAL 119

Experiment 3: 7 sheets long time boiling 800 ml of glue 100 ml of water

Experiment 6: 5 sheets short time boiling 42 g of castille soap (oil) 28 g of wax 800 ml of glue 100 ml of water

Experiment 9: 5 sheets short time boiling 4 tablespoons of flour 28 g of wax 800 ml of glue 100 ml of water

Experiment 4: 7 sheets grinding 800 ml of glue 100 ml of water

Experiment 7: 5 sheets long time boiling 28 g of wax 800 ml of glue 100 ml of water

Experiment 5: 7 sheets long time boiling and grinding 800 ml of glue 100 ml of water waxed with a brush

Experiment 8: 7 sheets short time boiling flour 800 ml of glue 100 ml of water

120 SWEATING PAPER ARCHITECTURE

The below image illustrates a potential method of improving the rate of absorption of a plate. It utilizes multiple coatings of mass-produced paper, a surface layer which absorbs water, and an internal layer made of cellulose fibres (used as a structure).

Coated paper

Uncoated paper

4. MATERIAL 121

Plaster 75 g Water 43 ml

Plaster powder 48 g

=

+

+

=

Thin paper fibres Paper+Plaster 78 g 12 g

Plaster and wet blended paper were mixed together. When 12 g of wet paper was mixed with 48 g of plaster, the final volume was double the volume of the dried plaster. In this case, the paper acted as a structural and lightweight binder.

The liquid appearance of the mixture was not appropriate for the manufacturing method, (except in cases where the mixture was used as a filling for porous support).

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Paper sheets

For ex. : bleaching process Paper treatment

Paper cement plate

The system is upgraded using cement with thin cellulose to produce a paper cement paste that could be pressed.

4. MATERIAL 123

Wet blending Cement

Drying

Thin cellulose

80% 48 g

20% 12 g

Water

Pressing Paper cement paste

124 SWEATING PAPER ARCHITECTURE

After drying, the cement and paper plate tended to shrink considerably. In the conducted experiment, the plate reduced by approximately 7 mm on each side. To avoid this shrinkage, some parameters can be controlled, such as moisture content, size of paper ashes, and drying time.

7 mm

120 mm

Final size Initial size

Plate made of a mixture of cement and paper paste.

4. MATERIAL 125

Thin cellulose

Cement

Long fibres (sisal)

53% 35 g

3% 2g

44% 29 g 7 sheets of paper

Ingredients with the addition of sisal fibres.

The shrinkage parameters of cement were better controlled for this test. The plates did not shrink.

The addition of long fibres improved the overall strength of the material.

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Ingredients

Weight in dried state

Experiment 10 Thin paper fibres 50% 30 g

Adhesive or water

Weight after pressing

60 g

19.5 cl

239 g

60 g

4.3 cl

60 g

2.0 cl

54 g

12.4 cl

178 g

83 g

14.1 cl

224 g

59 g

19.0 cl

254 g

66 g

12.4 cl

180 g

Plaster 50% 30 g

Mixed separately Experiment 11 Thin paper fibres 20% 12 g

Plaster 80% 48 g

Experiment 12 Cement 80% 48 g

Paper 20% 12 g Experiment 13

Cement 50% 28 g

Paper 50% 26 g

Paper paste was dried before mixing with cement Experiment 14 Cement 60% 50 g

Paper 40% 33 g Experiment 15

Cement 50% 30 g

Paper 50% 29 g Experiment 16 Long fibres (sisal) 3% 2g

Paper

Cement

44%

53%

29 g

35 g

Result

4. MATERIAL 127

The resulting data indicated that the most appropriate plate for absorbing water was the plate from experiment 10. The plate which exhibited the best structural capabilities was the plate from experiment 13. Further experiments were executed with white cement, but additional experiments are required (with porous support) to differentiate the components geometrically).

128 SWEATING PAPER ARCHITECTURE

Summary Different manufacturing processes were explored and special treatments for the paper were tested to optimize the absorptive properties and/or the structural properties of paper. Blending the paper or wet blending the paper tended to enhance the absorptive properties of the paper in pure or composite materials.

Our research team hypothesized that the structurally performative components could be created as a composite material made of concrete (white) and a low amount of a paper filling (used as a supporting material). Water performative components could be produced with a mixture of paper and glue poured in a similar and flexible support. During the fabrication process, a layer can be applied to control the internal moisture content of the elements via the customization of the separating sheets.

Pure material

Pure paper

Experiment 1

Experiment 2

Customized optimization

4. MATERIAL 129

Water performative material Structurally performative material

Composite material

Reinforced fibres

Matrix material

Experiment 10

Experiment 12

Experiment 4

Experiment 9

Sandwich structure

130 SWEATING PAPER ARCHITECTURE

5. EVAPORATION 131

5

Evaporation Evaporation studies aimed to create a comfortable environment for humans during hot summer days in the immediate vicinity of the sweating paper infrastructure. “Sweating” descriptively explains the term “evaporation” in the context of the developed material’s intelligence. By containing water, the paper plates perform evaporation and lower the temperature of the air in the local environment based on principles of thermal convection.

The focus of these studies was an elaboration upon manufacturing potentials and the potential impact of the structure on the microclimate.

Additionally, the studies considered how to evaluate these effects. Temperature, humidity, and wind velocity were the primary factors manipulated by our design to keep the heat index within the bounds of comfort.

132 SWEATING PAPER ARCHITECTURE

5. EVAPORATION 133

In the past, paper was typically used only because of its “eco-friendly� reputation; however, the treatments it underwent to gain desirable structural performance killed its natural properties. This could be understood as paper misuse.

Additionally, paper was primarily used for aesthetic purposes wherein the full potential of the properties of paper was neglected.

The research at hand aimed to utilize the true, natural properties of paper to maximize its material intelligence.

134 SWEATING PAPER ARCHITECTURE

Urban Integration Research illustrated many of the pre-existing properties of paper, including the ability to absorb liquid water, absorb moisture content from the air, transport water (via the capillary effect), be both hard and light or soft and heavy, possess structural properties, absorb sound, and be both dissolvable and burnable. The next step was to find a set of urban problems for which these properties (or some of them) could be used in a positive way. Our aim was to generate an environmental infrastructure as part of an urban system.

Absorbing liquid water

Absorbing water from air

Transporting water

Absorbing sound

Heat isolation

Hard and light when dry

Soft and heavy when wet

Structural

Dissolvable

Burnable

In a search for how the newly proposed paper infrastructure could contribute to the city, an interesting issue was identified; due to urbanization, an annual relative humdity drop of 20% and an annual mean temperature increase of 30C have been recorded in highly urbanized areas over the last 120 years.

Just as in other highly urbanized cities, a lack of soft surfaces in downtown areas could be a potential cause for such occurrence (due to the relationship between soft surfaces and the water cycle). During the day, temperatures in highly urbanized areas rise 3 degrees higher than rural areas.

Additionally, more than 80% of runoff water following rain is unable to join the natural water loop, making urban areas even hotter.

5. EVAPORATION 135 Annual relative humidty (%)

14 13

80 Annual mean temperature departure from average (째C)

12

3.0

11 75

10

2.5 2.0

9 8

70

7

1.5 1.0

Inhabitants (millions)

6 65

5 4

0.5

3

60

2

0.0

1 -0.5

55 1880

1900

1920

1940

1960

1980

2000

0

Urban expansion:

Graph showing increasing temperature and decreasing humidity levels in Tokyo, along with increasing population and urban development 1880-2000

330 320 310 300

100 mm

Diagram of typical urban-heat island profile

17 mm

URBAN

RESIDENTIAL

INDUSTRIAL

87 mm

SUBURBAN

RURAL

100 mm

136 SWEATING PAPER ARCHITECTURE

It was interesting to note that there are potential water sources in the city which are currently mostly considered "waste", however, these could be linked to the city in a different way in order to contribute to the environment.

Research considered these sources "Urban Water Sources".

Rain water

Urban leakage

Urban Water Source

Domestic water

5. EVAPORATION 137

Instead of sending Urban Water Sources directly to the sewage system, we proposed use of the water source for interaction with our paper plates. After this use (and the resulting evaporation process), the water condenses in the atmosphere and loops back into the city.

Water condensation

Pressed plates

Urban water source

Sewage

138 SWEATING PAPER ARCHITECTURE

The first approach to the prototype was to refer to forest structure ecosystems. The research aimed to produce effects similar to those produced by tree canopies, which regulate their understory micro-climates.

This was an effective analogy for the project because the evaporative paper plates behaved much in the same way tree leaves do. Additionally, since the project also sought to scatter, reflect, and reduce solar energy before it reached ground levels (to generate milder temperatures), use of different algorithmic organizations was examined to achieve this with the paper plates. Our research team decided to explore this system more in the future because the primary concern was understanding how the water absorbing paper plates would behave under simple geometric setups.

5-15% (20%) of the energy is reected

Leaves can absorb moisture from the air, and water is lost by transpiration The canopy absorbs most of the incoming energy

The solar radiation & light that reaches the ground has been ďŹ ltered and scattered by the canopy

MORE HUMID MILDER TEMPERATURE

Forest environments are characterized by a more pleasant temperature during hot weather conditions.

Paper properties in relation to water were the focus of the experiments. The experiments sought to replicate the evaporation process to lower the temperature of the immediate environment, thus making the environment more comfortable. Such a system could help decrease usage of active air conditioning systems, decrease usage of electricity, and, on a larger scale, have an impact on the heat island effect of highly urbanized areas.

5. EVAPORATION 139

Paper properties in relation to water: capable of absorbing, containing, transporting, and evaporating

Micro-climate impacts: ∙ reduces temperature ∙ creates comfortable environment

Mapping of over-heated areas in Tokyo. The red squares indicate the areas in the central parts of the city that are most affected by the heat island effect.

140 SWEATING PAPER ARCHITECTURE

System Principles This sub-chapter, examines the developed cooling model and optimization of cooling performance. Once the water absorbing paper plates have been adequately soaked, they will start to perform evaporation, given the right conditions (high temperature and low/medium levels of humidity). In accordance with the thermal convection physics laws, the adjusted air is cooled by over-heating the aerated water, removing the heat, and lifting it to the atmosphere. Cool air travels down, making a more comfortable environment for people nearby. This secondary system should perform very much like the uchimizu tradition of sprinkling secondary used water on pavement to produce temperature decreases.

environmental paper plates [water absorbing paper plates]

5. EVAPORATION 141

The traditional custom of "uchimizu" in Japan is based on the idea that water can be used for its evaporative purposes and can be effective in cooling immediate environments.

This research aimed to produce the same effect with the water evaporating from our structure. Additionally, we also aimed to create a basis for social interaction, and to use the uchimizu system as a water delivery system for our absorbent plates, thus resulting in cooler, more comfortable environments during hot summer days.

Because most water flows away from wet vertical surfaces, we sought to encourage evaporation from vertical surfaces with our structure. By containing water longer in our vertical, soft surfaces, we could prolong and increase evaporative effects.

Street environment

Architecture Environment

142 SWEATING PAPER ARCHITECTURE

HARD VERTICAL SURFACES, WATER RUN OFF

SOFT VERTICAL SURFACES, WATER RETENTION

5. EVAPORATION 143

Some existing materials indicate efficiency in performing evaporation and cooling in their immediate environments, like terra cotta (applied to Sony's Osaki New Building project). Image Source: Retrieved 25 July 2014 from http:// inhabitat.com/nikken-sekkeis-evaporative-cooling-bioskinbuilding-wins-production-energy-and-recycling-award-atworld-architecture-festival/

Paper is a material resource readily available in the city network.

Due to the temporary nature of our proposal, paper is both structurally and environmentally suited to the aims of the project.

144 SWEATING PAPER ARCHITECTURE

Absorption Experiments We performed water absorption and water transportation tests on our paper plates. An 18 x 18 cm paper plate can absorb up to .25 liters of water.

Another conclusion we reached was that water cannot bridge the gap between two paper plates if the type of connection is a screw, but it can be bridged using fabric or rope (which is why we proceeded with the rope-type joint).

Vertical absorption, Vertical absorption, flat plate, angled plate, paper type A paper type A

1h

24 h

24 h

Vertical absorption, flat plate, paper type B

Vertical absorption, angled plate, paper type B

5. EVAPORATION 145

Horizontal absorption, angled plate, paper type A

Vertical absorption, metal screw joint, paper type A

Vertical absorption, fabric node joint, paper type A

0h

2h

24 h

3h

24 h

146 SWEATING PAPER ARCHITECTURE

Evaporation experiment Very important for the chapter ‘thermodynamic calculus‘ is this experiment, upon which physical and mathematical calculations was based. The experiment simply shows that one paper plate, after being soaked and placed into a 50 l box with starting conditions of 30 degrees C and humidity of 48%, decreased the surrounding temperature by 7 degrees C and increased humidity to 86% after approximately one hour.

Following is the proportion according to which mass of water within 1 m2 of wall (10 mm thick) was calculated in relation to the performed experiment:

1 đ?‘šđ?‘š2 âˆś đ?‘Ľđ?‘Ľ = 0.0324 đ?‘šđ?‘š2 âˆś 0.225 đ?‘™đ?‘™ đ?‘Ľđ?‘Ľ =

0.225 = 6.94444 �� 0.0324

361 g 0.225 L water absorbed

136g

50 L box

60 min Initial conditions: Temperature 29.50 C Humidity 48%

Final conditions: Temperature 22.60 C Humidity 86%

5. EVAPORATION 147

Housing Cooling Models In our research on how people in the past worked to make their environments more comfortable, we investigated books describing energy technologies in Japanese traditional houses. In particular, we referred to the following two models.

People relied on two different principles based on the type of dwelling. In rural areas, wind flow was utilized for both ventilation and cooling. In urban areas, however, people created inner gardens to take advantage of transpiration for cooling inner spaces. We aimed to combine both principles. In street conditions, we could rely on wind flow.

COOL ENVIRONMENT

1. Rural house type wind flow, cooling effect

COOL ENVIRONMENT

2. Urban house type

tree transpiration, cooling effect

148 SWEATING PAPER ARCHITECTURE

Thermodynamic Calculus The physical model that will be presented as the core of this chapter deals with calculations of volume, time, and amounts of water needed for effective evaporation, with and without wind intensity. To affect the desired volume of air, i.e., the targeted volume we want to cool down, we relied on the thermal physics law of thermal convection.

To test the efficiency of our future system and evaluate its effects, we started with experiments of absorption and evaporation. Data gained included the maximum amount of water soaking, temperature drop, and humidity increases in the defined air volume. Having a background for the experiment, we proceeded with the thermal dynamic equation principles, heat amount equation, and Saint-Vennant’s energy equation for evaluating the effects.

In our system, we relied on basic logic of hot and cold air movement, humidity movements according to pressure differences, and wind flow activities for evaporation effectiveness increases. The conclusion was that more enclosed geometries are adequately effective, but not as effective as semi-opened geometries with wind flow. paper wall overheated aerated water

paper wall overheated aerated water

surrounding moist air

surrounding moist air

t2

t2 t1

q

t1

q+qw

δ

l

δ

l

λ1

λ2

λ1

λ2

Physical model scheme 1

Physical model scheme 2

5. EVAPORATION 149

Model Description Two cases were examined for cooling of spaces via water evaporation: Model 1: When enclosed spaces are cooled down via evaporation from paper surfaces, a mixture of steam and heated air is created which we call "moist air."

Model 2: This model is based upon cases where semi-enclosed spaces are cooled by temperature changes produced via factors like air flow (wind), which mixes with steam that evaporates from the surfaces.

In both cases, we must describe a thermodynamic analysis of the behaviour of most air, and in the wind flow model, Saint-Vennant’s energy equation and the continuity equation must be applied.

Both cases were described in detail with some initial conditions that must be met in order for the moist air cooling process to be effective. a) Moist air cooling of an enclosed space Task: For the prevailing conditions in the enclosed space, execute a thermodynamic analysis of water vapor mixing with the paper surfaces (soaked with water) and dry air.

The space is cooled within a temperature range of 22 degrees to 30 degrees.

A schematic representation of the imagined enclosed space is shown in the figure below. For wet air circulation to take place uninterrupted, the following conditions must be met.

150 SWEATING PAPER ARCHITECTURE

flow of heated moist air

heat produced by solar radiation

Water soaked wall

Evaporation from wall Figure 1. Moist air cooling enclosed space scheme

Physical qualities interpretation: - p1, moist air pressure in section 1-1; - p2, moist air pressure in section 2-2; - t1, moist air temperature in section 1-1; - t2, moist air temperature in section 2-2; - v1, moist air velocity in section 1-1; - v2, moist air velocity in section 2-2; - A1, surface area in section 1-1; - A2, surface area in section 2-2; - q, amount of heat warming the paper surface.

5. EVAPORATION 151

1. Thermodynamics process analysis From the moist air of state 1 (p1 = 1 bar, t1 = 300C, x = 0.0117, according to table 1 and diagram 1) the heat should be taken away to affect the temperature drop of the moist air after heat dissipation, within the temperature range given in table 1.

According to performed calculations the values in Table 1 are adequate; therefore, specific moist air enthalpy for the range of temperatures from 22 degrees C to 30 degrees C could be adopted for 60 KJ/Kg. Explanation: Moist air is a mixture of dry air and water vapor. Water vapor is humid air which has been overheated and is under relatively low pressure. Vapor can be considered an ideal gas. Characteristics of moist air in relation to temperature and degree of saturation (0.48 to 0.86 - according to experiments, p. 218) are given in the table below: Table 1 Temperature t (ËšC)

Moist x (Kg/Kg)

Partial pressure of water vapor in moist air pv

22

0.01492

0,02343

23

0.01443

0,02267

24

0.01394

0,02192

25

0.01375

0,02163

26

0.01343

0,02114

27

0.01287

0,01996

28

0.0124

0,01955

29

0.01199

0,01891

30

0.01177

0,01857

Table 1

đ?‘?đ?‘?đ?‘Łđ?‘Ł =

đ?‘Ľđ?‘Ľ ∙ đ?‘?đ?‘? (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) đ?‘Ľđ?‘Ľ + 0,622

đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?)

đ?‘„đ?‘„ = đ?‘žđ?‘ž ∙ đ??´đ??´ = 160 ∙ 1 = 160 (đ?‘Šđ?‘Š) ∆đ?‘Ľđ?‘Ľ = đ?‘Ľđ?‘Ľ2 − đ?‘Ľđ?‘Ľ1

)

�������� ��. ��.

152 SWEATING PAPER ARCHITECTURE

Table 1 Temperature t (ËšC)

Moist x (Kg/Kg)

Partial pressure of water vapor in moist air pv

22

0.01492

0,02343

23

0.01443

0,02267

24

0.01394

0,02192

25

0.01375

0,02163

26

0.01343

0,02114

27

0.01287

0,01996

Diagram air 28 1. Diagram of moist 0.0124

0,01955

29

0.01199

0,01891

0,01857 Partial30pressure (pv) of0.01177 water vapor in a given section of moist air is calculated according to a model as follows. Each value of humidity is shown in the table (Table 1) so that: đ?‘?đ?‘?đ?‘Łđ?‘Ł =

đ?‘Ľđ?‘Ľ ∙ đ?‘?đ?‘? (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) đ?‘Ľđ?‘Ľ + 0,622

đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?)

Since the vapor pressure in the air is very low, the following đ?‘„đ?‘„ = đ?‘žđ?‘ž ∙ đ??´đ??´ = 160 ∙ 1 = 160 (đ?‘Šđ?‘Š) criteria were applied: 1. All calculus is computed for a surface of 1 m2; ∆đ?‘Ľđ?‘Ľ = đ?‘Ľđ?‘Ľ − đ?‘Ľđ?‘Ľ 2. All calculus is computed for21 kg1of dry air (d.a.); 3. Ambient (atmospheric) pressure can be adopted so that p = 1 bar = const; Tablethat 2 1m2 of paper at 10 mm 4. Exact measurements show thick can absorb about 6.9 kg of water (this result obtained 1 2 3 4 5 6 7 from experiments, p. 218); 0,00022 0,00063 0,00166flux 0,00198 5. The mean value0,0011 of the thermal at Tokyo's0,00217 latitude at0,00266 the time of the summer solstice is approximately 160 W/ m2 .

8 0,00315

25

0.01375

26

0,02163

0.01343 Table 1

27

0,02114

5. EVAPORATION 153

0.01287

0,01996

28

0.0124 0,01955 Partial pressure of Temperature Moist water vapor in moist Table 1 29 0.01199 0,01891 t (ËšC) x (Kg/Kg) The date of the summer solstice obtained from the air pwas v 30 0.01177 0,01857 of Partialof pressure Japan Meteorological Agency the latitude Tokyo from 22 0.01492 0,02343 Temperature Moist for water vapor in moist t (ËšC) x this (Kg/Kg) 1890 to 2012.

Within range, it is possible to air pv read the 23 0.01443 0,02267

mean22thermal (table following p.0,02343 240 and 241).

0.01492 0.01394flux monthly 0,02192 The heat (Q) that is available depends on the mean heat 23 0.01375 0.01443đ?‘Ľđ?‘Ľ ∙ đ?‘?đ?‘?0,02163 0,02267 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) đ?‘?đ?‘?đ?‘Łđ?‘Ł = đ?‘Ľđ?‘Ľ + 0,622(taken from the table of flux (q) per one square meter 24 0.01343 0.01394 0,02192 0,02114 measured solar radiation at Tokyo’s latitude).

The amount đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?)

25 0.01287 0.01375 0,02163 0,01996 of heat Q is obtained as follows: 26 0.0124 0.01343 0,01955 0,02114

24 25 26 27 28

27 0.01199

29

0.01287 0,01891 0,01996 đ?‘„đ?‘„ = đ?‘žđ?‘ž ∙ đ??´đ??´ = 160 ∙ 1 = 160 (đ?‘Šđ?‘Š) 0.0124 0,01857 0,01955

28 0.01177

30

Where: 29 30

0.01199

0,01891

0.01177 ∆đ?‘Ľđ?‘Ľ = đ?‘Ľđ?‘Ľ2 − đ?‘Ľđ?‘Ľ1

0,01857

q = 160 (W/m2) - The mean value of the thermal flux through đ?‘Ľđ?‘Ľ ∙ đ?‘?đ?‘? a square (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) đ?‘?đ?‘?đ?‘Łđ?‘Ł =meter; đ?‘Ľđ?‘Ľ + 0,622 2 A = 1 (m ) - surface.

∆đ?‘Ľđ?‘Ľ

đ?‘Ľđ?‘ĽTable ∙ đ?‘?đ?‘? 2 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) đ?‘Ľđ?‘Ľ + 0,622 1 Because the by paper (6.9 kg/ 7 2 amount3of water 4absorbed 5 6 đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) m2) with a thickness of 10 mm is known, we can calculate đ?‘„đ?‘„ = đ?‘žđ?‘ž ∙ đ??´đ??´ = 160 ∙ 1 = 160 (đ?‘Šđ?‘Š) 0,00022 0,00063 0,0011 0,00166 0,00198 0,00217 0,00266 đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) đ?‘?đ?‘?đ?‘Łđ?‘Ł =

đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤ đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘‘đ?‘‘. đ?‘Žđ?‘Ž.

the amount of water vapor or moist air mass that can evaporate into đ?‘„đ?‘„space 2 (higher temperature = đ?‘žđ?‘ž ∙ đ??´đ??´from = 160 state ∙ 1 = 160 (đ?‘Šđ?‘Š) ∆đ?‘Ľđ?‘Ľ = đ?‘Ľđ?‘Ľ − đ?‘Ľđ?‘Ľ 1 areas) to state 12 (lower temperature areas), (Δx): ∆đ?‘Ľđ?‘Ľ = đ?‘Ľđ?‘Ľ2 − đ?‘Ľđ?‘Ľ1

Table 2 đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤ ∆đ?‘Ľđ?‘Ľ đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘‘đ?‘‘. đ?‘Žđ?‘Ž.

1

2

0,00022

0,00063

Table 2

∆đ?‘Ľđ?‘Ľ

đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤ đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘‘đ?‘‘. đ?‘Žđ?‘Ž.

3

1

0,0011

0,00022

4 2

5 Table 2

0,00166 3

0,00063

0

0,00198 4

0,0011

6

7

8

0,00217 5

0,00266 6

0,00315 7

0,00166

0,00198

0,00217

0,00266

In Diagram 2, the cooling process from state 2 to state 1 is schematically presented depending on the relative humidity curve for moist air, as outlined in Diagram 1. The diagram also indicates relative humidity curves obtained through experimentation.

Mass of vapor (mp), in relation to the available mass of moist air, which is necessary in order to lower the temperature in the surrounding area, is calculated according to the following formula: đ?‘šđ?‘šđ?‘?đ?‘? =

đ?‘šđ?‘šđ?‘Łđ?‘Ł ∙ ∆đ?‘Ľđ?‘Ľ (1 + đ?‘Ľđ?‘Ľ1 ) ∙ đ?œ?đ?œ?

đ?‘?đ?‘?đ?‘ đ?‘ đ?‘ đ?‘ = đ?‘?đ?‘? − đ?‘?đ?‘?đ?‘Łđ?‘Ł

đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘–đ?‘–đ?‘–đ?‘–: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?)

0,

154 SWEATING PAPER ARCHITECTURE TOKYO

Year 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951

Station No:47662 Lat 35o41.4'N Lon 139o45.6'E

Jan

Feb

× 233.9 170.6 171.4 167.7 205.5 232.0 162.6 141.7 224.1 160.1 163.4 241.7 156.9 200.7 178.8 216.8 136.4 194.7 148.2 111.7 166.1 219.2 205.7 223.7 169.2 194.1 213.9 219.2 147.5 223.5 202.0 194.1 183.7 201.6 184.1 191.2 188.7 163.8 201.2 174.2 149.5 192.8 141.9 213.1 193.7 212.6 142.2 198.1 199.9 226.1 199.3 217.3 220.4 172.2 204.9 193.1 152.3 191.1 183.5 175.8 183.1

× 173.6 177.6 159.0 212.1 235.0 177.8 166.1 194.6 176.0 174.9 208.8 201.0 176.6 156.7 207.8 147.2 192.6 187.9 194.5 206.5 169.3 174.6 153.1 165.6 130.8 155.4 202.3 168.1 159.5 148.7 207.1 157.6 118.5 177.7 157.9 167.7 153.9 202.4 208.9 150.8 88.9 187.9 172.6 199.2 143.7 158.5 132.7 206.6 184.4 188.5 185.9 139.5 203.4 188.0 193.0 164.1 199.1 178.7 135.9 138.5 155.5

Mar 126.9 154.4 167.7 206.3 152.2 163.8 181.3 153.8 117.6 217.4 171.5 230.1 184.4 146.4 144.2 184.9 205.0 152.0 150.9 136.9 184.5 152.3 166.5 216.5 148.4 217.8 178.6 187.4 202.1 190.3 157.1 209.1 236.7 189.2 220.0 229.2 195.8 167.6 199.7 211.3 143.1 212.5 212.8 127.6 202.8 193.4 201.3 168.2 134.6 217.1 228.6 166.3 177.1 191.0 162.4 189.1 163.0 176.5 149.9 171.0 178.7 156.3

Apr 131.4 157.5 183.1 206.1 159.4 232.1 184.2 174.7 175.3 189.7 135.3 192.6 194.2 145.1 151.5 151.8 211.5 189.4 173.1 215.5 197.3 211.2 216.8 158.5 209.4 134.2 157.3 210.9 168.9 214.2 191.2 174.8 209.0 155.1 165.1 167.3 220.9 194.8 218.8 187.7 166.1 179.9 189.3 104.3 166.0 182.1 154.1 189.7 213.0 186.4 219.2 185.1 208.6 208.4 170.7 210.7 210.1 246.2 183.2 215.5 147.5 146.1

May 109.9 270.2 174.7 180.0 214.1 222.9 171.7 224.9 209.3 220.7 219.0 191.4 181.7 184.7 159.2 177.2 231.9 236.0 217.6 208.3 171.0 222.1 210.6 224.8 186.7 212.8 188.6 238.3 207.9 224.4 162.4 180.0 186.9 127.5 212.6 180.9 168.8 221.9 184.7 146.3 186.7 244.5 233.1 219.6 226.8 200.0 156.2 200.4 180.2 211.6 269.5 190.6 200.9 193.9 183.6 184.0 141.6 187.2 146.1 195.3 163.1 198.7

Jun 176.2 138.8 83.9 179.1 256.1 203.8 167.2 157.7 144.1 162.6 223.6 145.7 181.4 192.1 196.4 89.9 127.8 154.9 168.8 103.8 127.3 130.8 162.8 156.0 172.7 169.9 201.6 152.0 119.3 151.4 134.6 109.1 230.8 121.0 125.9 143.7 196.1 183.9 105.4 189.6 147.5 181.7 111.2 185.6 186.7 189.0 202.3 156.2 130.1 184.9 233.4 118.7 139.5 122.4 191.5 129.5 232.4 89.8 145.3 115.5 125.9 168.0

(h)

Jul 172.7 135.7 197.2 267.0 270.4 122.3 175.8 156.7 304.5 131.9 137.5 122.5 130.6 154.3 211.2 154.9 133.8 187.7 146.1 197.8 110.3 172.0 172.7 156.0 218.7 221.3 160.4 240.7 270.0 189.2 269.1 201.1 177.4 139.0 258.6 195.7 202.2 203.7 144.4 226.8 162.6 106.5 187.1 215.1 105.0 181.3 218.0 227.6 170.4 246.3 267.2 122.9 215.4 213.3 195.2 149.9 214.0 242.0 177.0 227.6 249.4 162.0

Tokyo Station No: 47662 Lat 35041.4'N Lon 139045.6'E (h)

Aug 155.7 217.7 231.9 213.2 243.4 193.8 222.5 165.8 211.9 235.4 272.0 230.4 123.1 259.3 269.0 113.9 179.0 196.4 227.0 212.2 139.3 201.7 223.7 211.2 263.2 138.5 163.4 186.8 243.4 214.0 207.3 211.0 263.6 232.3 213.4 196.1 201.0 224.4 115.0 240.2 211.0 267.2 205.3 218.4 184.3 172.4 208.8 284.9 181.9 226.8 198.7 146.6 210.7 235.2 242.0 248.1 230.6 277.9 151.2 197.4 178.6 218.2

Sep 191.5 165.2 157.9 151.9 125.7 169.2 167.0 122.6 157.7 106.5 165.7 169.5 126.9 127.5 176.2 167.2 84.2 159.9 118.8 130.9 107.7 146.5 78.4 138.1 169.9 132.7 170.9 85.3 185.3 165.7 153.8 118.4 185.0 133.2 140.1 160.8 140.6 124.8 187.2 109.1 193.6 118.3 110.5 206.7 74.4 100.1 170.4 171.5 138.1 160.9 158.6 104.5 158.0 125.0 161.5 122.8 167.0 130.3 174.2 144.3 172.6 99.7

Oct 137.2 192.1 93.6 133.0 131.4 147.4 137.7 183.1 154.3 184.3 165.2 128.6 154.8 119.6 126.4 159.2 146.4 202.4 153.8 149.0 108.6 136.5 140.2 120.1 210.3 126.4 87.5 112.2 105.4 140.6 168.7 138.9 197.7 147.2 127.1 132.6 173.8 150.2 115.6 110.5 144.0 137.3 131.3 147.9 112.2 163.0 123.3 132.3 142.6 136.5 160.5 193.6 184.5 131.9 112.8 127.6 166.9 141.8 129.4 113.9 120.7 126.2

Nov 179.1 179.3 165.7 195.0 184.8 166.5 199.0 165.7 143.4 201.8 148.4 191.8 160.1 163.3 217.3 170.1 153.4 124.9 218.1 178.8 189.4 173.8 128.5 152.1 152.6 147.9 134.5 184.9 159.2 101.6 169.7 232.2 159.9 150.9 201.8 155.5 195.8 171.0 128.6 103.1 170.1 132.8 123.6 148.0 156.1 146.2 136.6 137.9 183.4 136.7 118.1 98.2 178.6 162.0 144.7 186.4 123.7 173.4 143.6 105.4 120.7 165.9

Dec Annual 158.3 1538.9 ] 179.6 2198.0 178.2 1982.1 234.1 2296.1 218.5 2335.8 206.7 2269.0 197.6 2213.8 212.7 2046.4 186.3 2140.7 173.3 2223.7 209.2 2182.4 215.1 2189.9 154.5 2034.4 207.9 2033.7 185.4 2194.2 133.7 1889.4 191.9 2028.9 207.1 2139.7 195.9 2152.7 209.0 2084.9 194.0 1847.6 172.9 2055.2 133.3 2027.3 201.7 2093.8 193.7 2314.9 206.3 2007.8 157.5 1949.8 231.0 2245.7 158.2 2207.0 194.6 2093.0 185.5 2171.6 185.5 2169.2 224.4 2423.1 156.1 1853.7 165.5 2209.4 199.0 2102.8 159.7 2213.6 160.3 2145.2 146.7 1912.3 2052.0 117.3 2000.1 150.4 135.8 1954.9 148.4 2033.3 193.3 2081.0 131.2 1957.8 141.0 2005.9 143.9 2086.0 222.1 2165.7 167.7 2046.7 173.0 2264.5 174.4 2442.8 145.6 1857.3 188.2 2218.3 170.1 2177.0 189.7 2114.3 220.7 2166.7 182.7 2189.2 157.7 2174.2 136.4 1906.1 153.5 1958.8 165.9 1937.4 173.9 1953.6

5. EVAPORATION 155

Year Jan Feb Mar 1952 177.7 107.4 152.2 1953 183.3 158.4 159.3 1954 129.2 176.8 178.7 1955 215.9 174.6 101.2 1956 185.5 173.4 143.0 1957 161.2 128.3 216.3 1958 190.7 180.3 158.6 1959 170.0 118.5 179.4 1960 208.9 207.3 209.0 1961 183.6 197.9 181.1 210.7 195.0 189.8 1962 1963 231.1 199.9 198.8 1964 124.6 151.0 199.0 1965 175.4 193.4 252.4 1966 195.8 149.6 150.4 1967 194.4 162.6 180.8 1968 219.2 205.8 157.9 1969 148.4 97.1 179.3 1970 182.0 160.1 195.8 1971 181.6 148.9 203.3 1972 156.4 112.6 207.7 1973 177.6 162.9 207.5 1974 229.5 134.8 183.7 1975 182.7 176.4 182.3 1976 225.2 137.3 148.2 1977 161.5 188.6 141.9 1978 160.0 157.7 193.1 1979 179.5 164.6 190.2 1980 182.0 206.1 157.5 1981 233.4 157.3 192.6 1982 194.0 168.0 177.8 1983 205.0 202.9 176.0 1984 208.8 182.5 205.7 1985 200.9 153.2 74.0 185.7 181.6 161.5 1986 1987 181.4 159.2 149.1 1988 197.0 178.3 129.8 1989 152.6 135.5 176.4 1990 179.3 81.6 200.4 1991 210.6 199.3 115.8 1992 183.2 166.4 98.8 1993 130.0 195.7 187.7 1994 173.6 206.2 158.1 1995 224.2 179.3 134.4 1996 197.8 186.8 162.5 1997 236.6 ) 191.6 181.9 1998 162.5 150.4 191.5 1999 217.0 200.9 119.0 2000 153.8 207.7 207.9 2001 178.8 153.0 180.1 2002 201.9 163.5 191.3 2003 208.0 154.0 203.8 2004 203.6 218.3 170.9 2005 200.0 148.9 175.1 2006 169.9 128.5 176.2 175.6 193.6 195.0 2007 2008 164.8 214.8 187.2 2009 174.7 131.2 162.9 2010 221.9 118.3 ) 139.8 2011 243.9 148.9 214.8 2012 183.0 148.6 149.7 2013 212.5 173.7 113.6 ]

Apr 165.5 197.8 146.3 143.1 170.2 151.7 161.4 191.3 154.6 205.8 202.6 193.6 128.4 178.4 132.6 172.0 192.1 178.5 130.2 164.5 181.4 163.3 202.8 152.4 120.2 182.1 163.9 161.3 156.6 207.5 177.5 176.6 168.2 183.8 175.2 199.4 183.3 218.4 155.4 150.7 172.5 183.0 209.5 158.5 204.8 184.3 108.8 146.3 174.9 219.5 164.2 162.6 235.4 216.1 147.0 151.0 150.0 226.7 139.9 204.0 162.4

May 228.5 186.4 158.9 173.1 133.5 191.9 205.1 194.2 186.9 191.2 177.0 102.9 209.5 189.1 232.6 258.3 182.6 200.4 194.1 168.9 207.1 205.1 231.5 213.1 174.5 225.0 167.2 230.6 204.2 182.6 243.7 241.5 172.2 201.8 194.2 172.6 178.3 131.6 174.6 204.0 162.4 192.2 194.6 147.6 183.7 162.7 132.5 184.0 184.0 160.6 153.0 145.6 139.9 172.3 136.7 226.4 136.9 154.6 198.8 146.3 195.4

Jun Jul Aug 134.6 158.5 203.1 84.2 127.0 116.4 82.6 105.4 199.4 148.2 246.6 189.8 142.4 134.7 164.5 104.1 91.9 190.3 174.9 129.3 161.0 113.9 157.5 180.5 155.4 181.3 218.5 166.4 217.2 172.2 111.8 135.9 270.5 119.4 151.9 166.2 125.2 153.6 184.3 148.5 102.2 232.2 137.3 112.6 204.3 182.7 143.5 160.5 152.9 127.4 130.5 156.4 138.1 148.6 90.5 137.0 187.8 106.0 161.1 203.1 155.7 167.0 242.0 96.3 225.8 226.4 137.0 108.9 198.3 82.9 189.7 250.8 83.9 178.8 156.6 99.5 204.3 100.8 192.6 217.1 255.6 217.9 143.1 156.0 146.7 95.0 105.3 83.2 181.3 190.7 152.6 102.3 170.1 162.7 119.4 163.7 113.2 180.1 252.3 104.3 194.8 257.8 158.1 109.1 199.8 193.3 177.6 159.2 122.6 61.8 143.7 134.6 118.6 191.5 133.4 143.8 230.2 127.7 136.4 138.4 113.0 153.6 184.7 110.9 75.2 102.2 136.2 202.9 239.9 62.6 137.1 248.7 117.8 199.6 149.1 160.6 191.9 176.1 73.1 113.6 91.7 135.8 169.0 ) 204.0 ) 129.8 210.2 185.7 107.8 259.2 94.0 123.3 189.5 231.0 103.6 48.2 130.3 170.6 232.2 177.8 119.3 103.9 159.9 79.5 59.2 160.6 187.2 80.6 227.9 106.9 168.4 130.0 98.8 103.5 136.1 162.5 182.7 222.6 105.1 186.2 168.9 125.3 181.3 ) 236.0

Sep 107.2 106.4 159.3 129.1 132.4 76.8 132.6 121.9 147.9 181.1 168.7 123.1 89.0 128.6 122.9 98.4 133.9 122.4 92.9 77.5 171.1 154.2 132.5 192.7 128.6 133.0 102.2 119.1 125.2 140.0 104.3 92.8 146.9 101.9 113.9 104.1 39.2 115.1 140.2 85.6 161.7 90.8 131.8 149.0 139.0 91.7 83.8 130.3 128.9 109.4 117.3 160.2 140.0 154.2 103.5 121.3 124.1 136.5 165.3 165.8 164.4

Oct Nov 128.3 121.9 167.3 169.6 116.2 168.4 117.6 184.1 84.7 133.4 141.2 164.1 119.5 117.6 124.1 117.2 134.4 134.1 82.3 161.0 135.9 117.6 135.3 164.2 143.9 170.6 199.4 150.2 175.7 132.8 131.5 114.1 101.6 197.8 140.4 129.0 131.5 156.3 121.1 154.7 149.4 159.7 151.1 196.5 99.6 154.5 100.5 124.0 141.5 132.6 173.9 136.5 132.9 160.2 149.3 102.9 160.0 149.6 161.2 130.6 171.6 118.8 141.6 181.8 145.9 148.7 149.4 173.5 155.9 126.0 145.3 122.5 152.1 205.8 134.3 145.2 137.6 166.9 74.8 145.8 115.6 146.6 143.5 147.5 76.5 167.0 148.0 203.4 139.9 115.4 192.6 140.8 117.2 157.9 158.4 157.1 97.7 109.7 154.6 169.6 183.4 140.9 87.9 137.6 116.8 160.9 108.3 194.6 147.5 137.8 119.8 148.8 141.0 142.9 153.3 124.0 81.4 158.9 141.3 143.4 156.6 153.3 )

Dec 152.5 130.4 150.3 194.8 217.0 163.0 187.7 159.9 183.9 202.6 175.8 184.6 164.1 153.5 162.2 187.8 137.2 199.3 132.5 172.4 161.6 229.0 151.2 171.4 173.3 177.4 154.7 186.2 213.2 206.6 156.1 217.1 163.3 202.9 163.8 166.7 213.8 178.9 197.3 143.9 164.9 153.2 167.3 235.3 187.8 153.1 152.4 186.3 172.2 189.9 130.7 181.4 166.3 212.4 141.4

Annual 1837.4 1786.5 1771.5 2018.1 1814.7 1780.8 1918.7 1828.4 2122.2 2142.4 2091.3 1971.0 1843.2 2103.3 1908.8 1986.6 1938.9 1837.9 1790.7 1863.1 2071.7 2195.7 1964.3 2018.9 1800.7 1924.5 2057.2 2000.7 1901.4 2067.0 1936.8 2081.1 2087.8 1998.3 1924.8 1930.4 1805.7 1832.7 1940.7 1733.0 1823.4 1711.9 2063.6 2028.1 1984.2 2063.9 1535.4 2008.1 1962.5 1976.5 1990.0 1723.2 2132.7 1965.0 1587.8

168.8 190.8 181.0 194.9 187.6 166.9

1996.0 1857.8 1783.3 1987.0 2056.2 2022.9 499.8 ]

156 SWEATING PAPER ARCHITECTURE

Wherein: mv, amount of water that will (under certain conditions) evaporate, mp, available amount (mass) of vapor, t, evaporation time. x1, humidity at the saturation limit.

Diagram 2. Movement scheme from state 2 to state 1

To be able to calculate the total mass of water (mw) needed to generate adequate amounts of vapor, firstly the mass of vapor (mp) must be calculated for the given conditions defined by the task. Therefore, the (calculated) dry air partial pressure of moist air must be determined. In Table 1 partial pressure of water vapor in moist air has already been defined, so by applying a model for the calculation of dry air partial pressure we get the following:

5. EVAPORATION 157

đ?‘šđ?‘šđ?‘Łđ?‘Ł ∙ ∆đ?‘Ľđ?‘Ľ đ?‘šđ?‘šđ?‘?đ?‘? = (1 + đ?‘Ľđ?‘Ľ1 ) ∙ đ?œ?đ?œ? đ?‘?đ?‘?đ?‘ đ?‘ đ?‘ đ?‘ = đ?‘?đ?‘? − đ?‘?đ?‘?đ?‘Łđ?‘Ł

đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘–đ?‘–đ?‘–đ?‘–: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?)

Table đ?‘šđ?‘šđ?‘Łđ?‘Ł ∙ ∆đ?‘Ľđ?‘Ľ Based on 3the above equation, the partial pressure of dry air, đ?‘šđ?‘šđ?‘?đ?‘? = ) (1 ∙ đ?œ?đ?œ? constant pressure, and the thermal + đ?‘Ľđ?‘Ľ 1 volume at Partial pressure of the specific Specific Thermal conductivity volume dry air in mosit air coeffiecient conductivity are presented in Table 3. It should 3 ,, coefficient psv (bar) Îť (W/mK) đ?’—đ?’— (m /Kg) be noted that the partial pressure has been mathematically 0,97657 51,612 0,02529 đ?‘?đ?‘?đ?‘ đ?‘ đ?‘ đ?‘ = đ?‘?đ?‘? − đ?‘?đ?‘?đ?‘Łđ?‘Ł calculated.

The values for volume at constant pressure and 0,97733 48,714 0,02533 đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘–đ?‘–đ?‘–đ?‘–: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?) the thermal conductivity coefficient are taken from the 0,97808 45,98 đ?‘šđ?‘šđ?‘Łđ?‘Ł ∙ ∆đ?‘Ľđ?‘Ľ 0,02537 đ?‘šđ?‘šđ?‘?đ?‘? = manual of thermodynamics.

(1 + đ?‘Ľđ?‘Ľ1 ) ∙ đ?œ?đ?œ?

Temperature t (ËšC) 22 23 24 25

0,97837

26 27

43,40 Table 3 40,98

0,97886

28

Temperature t (ËšC)

29

22

0,98004Partial pressure of dry air in mosit air 0,9803 psv (bar) 0,981 0,97657

30

23

0,9814

24 25 26 27 28 29 30

Table 3

0,97733

0,02540 0,02544

38,73

0,02547 Specific Thermal conductivity đ?‘?đ?‘?đ?‘ đ?‘ đ?‘ đ?‘ = đ?‘?đ?‘? − đ?‘?đ?‘?đ?‘Łđ?‘Ł volume coeffiecient 0,02550 3 ,, Îť (W/mK) đ?’—đ?’— (m /Kg) đ?‘Šđ?‘Šâ„Žđ?‘’đ?‘’đ?‘’đ?‘’đ?‘’đ?‘’ đ?‘–đ?‘–đ?‘–đ?‘–: đ?‘?đ?‘? = 1 (đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?đ?‘?)

34,70 0,02553 51,612 0,02529 36,63

32,93

0,02556

48,714

45,98Table 3

0,97808 0,97837 Partial pressure of Temperature air in mosit air 0,97886 1dryđ??žđ??žđ??žđ??ž t (ËšC) đ?œŒđ?œŒđ?‘?đ?‘? = đ?‘Łđ?‘Ł,, (đ?‘šđ?‘š3p)sv (bar) 0,98004 22 0,97657 0,9803 23 0,97733 0,981 24 0,97808 0,9814 25 0,97837

43,40

0,02533 0,02537

Specific 0,02540Thermal conductiv volume coeffiecient 0,02544 3 Îť (W/mK) đ?’—đ?’—,, (m /Kg) 0,02547 51,612 0,02529 0,02550 48,714 0,02533 0,02553 45,98 0,02537 0,02556 43,40 0,02540

40,98 38,73 36,63 34,70 32,93

26

0,97886

40,98

0,02544

27

0,98004

38,73

0,02547

28 29 30

Next we must calculate saturated vapor (pp)0,02550 1 đ??žđ??žđ??žđ??ž the density of 0,9803 36,63 đ?œŒđ?œŒđ?‘?đ?‘? = đ?‘Łđ?‘Ł,, (đ?‘šđ?‘š3 ) that is inversely proportional to the specific volume. It is0,02553 0,981 34,70 calculated by0,9814 the following formula and the results will be0,02556 32,93 presented in Table 4:

1

đ??žđ??žđ??žđ??ž

đ?œŒđ?œŒđ?‘?đ?‘? = đ?‘Łđ?‘Ł,, (đ?‘šđ?‘š3 )

158 SWEATING PAPER ARCHITECTURE Table 4

22

Specific volume 3 đ?’—đ?’—,, (m /Kg)

Density of saturated vapor 3 đ??†đ??†đ?’‘đ?’‘ (Kg/m )

23

48,714 Table 4

0,02053

24

45,98

Temperature t (ËšC)

51,612

Table 4

0,01938

0,02175 Density Specific Temperature 25 0,02304 of saturated vapor volume 43,40 t (ËšC) Table 4 3 3 đ??†đ??†đ?’‘đ?’‘ (Kg/m ) đ?’—đ?’—,, (m /Kg) 26 40,98 0,02440 22 51,612 0,01938 Density Specific 27 38,73 0,02581 Temperature of saturated vapor volume t (ËšC) 48,714 3 3 23 0,02053 đ??†đ??†đ?’‘đ?’‘ (Kg/m ) đ?’—đ?’—,, (m /Kg) 28 36,63 0,02730 24 45,98 0,02175 51,612 0,01938 29 22 34,70 0,02882 25 43,40 0,02304 48,714 0,02053 30 23 32,93 0,02303 26 40,98 0,02440 24 45,98 0,02175 27

38,73

0,02581

0,02304 đ?‘?đ?‘?đ?‘ đ?‘ đ?‘ đ?‘ đ??žđ??žđ??žđ??žfrom the thermal The density of25dry air (psv) is 43,40 calculated đ?œŒđ?œŒđ?‘ đ?‘ đ?‘ đ?‘ = đ?‘…đ?‘…∙đ?‘‡đ?‘‡ (đ?‘šđ?‘š0,02730 3) 28 36,63 26 0,02440 equation for ideal gas (dry air 40,98 behaves as an ideal gas).

The 29 34,70 0,02882 38,73 0,02581 formula that 27 calculates dry air follows, and the results are 30 32,93 0,02303 28 36,63 0,02730 displayed in Table 5: Table 5 29 Temperature t (K)

Where: 295

30

34,70 Partial pressure đ?‘?đ?‘?đ?‘ đ?‘ đ?‘ đ?‘ đ??žđ??žđ??žđ??žof 32,93 đ?œŒđ?œŒ = ( air) dry airđ?‘ đ?‘ đ?‘ đ?‘ in mosit đ?‘…đ?‘…∙đ?‘‡đ?‘‡ đ?‘šđ?‘š3 psv (bar) 0,97657

đ?œŒđ?œŒ =

0,02882

đ?‘?đ?‘?đ?‘ đ?‘ đ?‘ đ?‘

(

đ??žđ??žđ??žđ??ž

đ?‘ đ?‘ đ?‘ đ?‘ 3 296 (J/KgK) - gas constant 0,97733 Table R = 287 of5dry air;đ?‘…đ?‘…∙đ?‘‡đ?‘‡ đ?‘šđ?‘š

)

Density of dry air 0,02303 3 đ??†đ??†đ?’”đ?’”đ?’”đ?’” (Kg/m ) 1,1535

1,1504

297 1,1474 T - temperature in pressure Kelvin.0,97808 Partial of Density of dry air Temperature298 0,97837 dry air in mosit air 31,1433 t (K) Table 5 đ??†đ??†đ?’”đ?’”đ?’”đ?’” (Kg/m ) psv (bar) 299 0,97886 1,141 295 0,97657Partial pressure of 1,1535 300 0,98004 1,1383 of dry air Density Temperature dry air in mosit air 3 t (K) đ??†đ??†đ?’”đ?’”đ?’”đ?’” (Kg/m ) 296 0,97733 1,1504 psv (bar) 301 0,9803 1,1348 297 0,97808 1,1474 0,97657 1,1535 302 295 0,981 1,1318 298 0,97837 1,1433 0,97733 1,1504 303 296 0,9814 1,1285 299 0,97886 1,141 297 0,97808 1,1474 300

298

0,98004

301

299

0,9803

302

300

0,981

303

301

0,9814

0,97837

1,1383

0,97886

1,1348

1,141

0,98004

1,1318

1,1383

0,9803

1,1285

1,1348

đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł = đ?œŒđ?œŒđ?‘?đ?‘? + đ?œŒđ?œŒđ?‘ đ?‘ đ?‘ đ?‘

1,1433

302

0,981

1,1318

303

đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł = đ?œŒđ?œŒđ?‘?đ?‘? +0,9814 đ?œŒđ?œŒđ?‘ đ?‘ đ?‘ đ?‘

1,1285

Based on the previous calculations possible to đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł = đ?œŒđ?œŒđ?‘?đ?‘?it +isđ?œŒđ?œŒnow đ?‘ đ?‘ đ?‘ đ?‘ calculate the density of moist air (pvv) that represents the sum of densities of saturated vapor and dry air. All data is shown in Table 6. The equation is:

Table 5

301

0,9803

302

0,981

303

0,9814

1,1348

159 1,1318 5. EVAPORATION 1,1285

đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł = đ?œŒđ?œŒđ?‘?đ?‘? + đ?œŒđ?œŒđ?‘ đ?‘ đ?‘ đ?‘

Table 6

Table 6

22

Density of moist air 3 đ??†đ??†đ?’—đ?’—đ?’—đ?’— (Kg/m )

23

1,17093

Temperature t (ËšC)

1,17288

24

Table 6

25

1,1692 1,16634

Density of moist air 1,1654 3 đ??†đ??†đ?’—đ?’—đ?’—đ?’— (Kg/m ) 1,16411 1,17288 1,1621 1,17093 1,16062 1,1692 1,15153 1,16634

Temperature 26 t (ËšC) 27 22 28 23 29 24 30 25 26

1,1654

27

1,16411

28 (mp) of moist đ?‘šđ?‘š 1,1621 The mass of vapor air from the available đ?‘Łđ?‘Ł ∙ ∆đ?‘Ľđ?‘Ľ đ?‘šđ?‘šđ?‘?đ?‘? = (1 + đ?‘Ľđ?‘Ľ1 ) ∙ đ?œ?đ?œ? is necessary in 29 square meter,1,16062 mass of water per which 30 temperature of 1,15153 order to lower the the surrounding area, is calculated according to the following formula:

∆đ?‘Ľđ?‘Ľ

đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤ đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘‘đ?‘‘. đ?‘Žđ?‘Ž.

mp (Kg/s)

∆đ?‘Ľđ?‘Ľ

đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤ đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘‘đ?‘‘. đ?‘Žđ?‘Ž.

mp (Kg/s)

0,00022

0,00063

0,001502 Where:

0,00435

đ?‘šđ?‘šđ?‘?đ?‘? =

đ?‘šđ?‘šđ?‘Łđ?‘Ł ∙ ∆đ?‘Ľđ?‘Ľ Table 7 (1 + đ?‘Ľđ?‘Ľ1 ) ∙ đ?œ?đ?œ?

0,0011

0,00166

0,00198

0,00217

0,00

0,0075

0.0113

0,0135

0,0148

0,0

đ?‘šđ?‘šđ?‘?đ?‘?one m2 of paper wall, mv = 6.91 (Kg); the amount of water đ?‘‰đ?‘‰ = in ∙ đ?œ?đ?œ?

Table đ?œŒđ?œŒ7đ?‘Łđ?‘Łđ?‘Łđ?‘Ł mp, mass of vapor, t = 1s, 0,00063 0,00022 0,0011 0,00166 0,00198 0,00217 x1, humidity at the saturation limit. đ?‘šđ?‘šđ?‘¤đ?‘¤ = đ?‘šđ?‘šđ?‘?đ?‘? ∙0,0135 đ?œ?đ?œ?

0,001502 0,00435 0,0075 0.0113 0,0148 �� =

đ?‘šđ?‘šđ?‘?đ?‘? ∙ đ?œ?đ?œ? đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł

đ?‘šđ?‘šđ?‘¤đ?‘¤ = đ?‘šđ?‘šđ?‘?đ?‘? ∙ đ?œ?đ?œ?

0,00266 0,0176

Table 6 1,1621

28

29 ARCHITECTURE 1,16062 Density of moist air Temperature 160 SWEATING PAPER 3 t (ËšC) 30 22

đ??†đ??†đ?’—đ?’—đ?’—đ?’— (Kg/m ) 1,15153 1,17288

đ?‘šđ?‘šđ?‘?đ?‘? =

đ?‘šđ?‘šđ?‘Łđ?‘Ł ∙ ∆đ?‘Ľđ?‘Ľ (1 + đ?‘Ľđ?‘Ľ1 ) ∙ đ?œ?đ?œ?

23 1,17093 Table 7 displays mass of vapor (mp) per second from the 24 1,1692 available mass of water (6.91 kg per square meter) at a wall ∙ ∆đ?‘Ľđ?‘Ľ thickness of2510 mm:đ?‘šđ?‘šđ?‘?đ?‘? = đ?‘šđ?‘šđ?‘Łđ?‘Ł 1,16634 (1 + đ?‘Ľđ?‘Ľ1 ) ∙ đ?œ?đ?œ?

1,1654

26 27

đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤đ?‘¤28 đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘‘đ?‘‘. đ?‘Žđ?‘Ž. 29

∆đ?‘Ľđ?‘Ľ

1,1621 0,00063 0,0011 1,16062 0,00435 1,15153 0,0075

0,00022

mp (Kg/s) 30 0,001502

0,00022

Table 7

1,16411

0,00063

0,0011

0,00166

0,00198

0,00217

0,00266

0,00315

0.0113

0,0135

0,0148

0,0176

0.02144

0,00266

0,00315

Table 7

0,00166

đ?‘šđ?‘šđ?‘?đ?‘? ∙ đ?œ?đ?œ?

0,00198 đ?‘‰đ?‘‰ =0,00217 đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł

Table 7

The calculation of the affected cooling volume is shown in 0,00435 0,0075 đ?‘šđ?‘šđ?‘Łđ?‘Ł0.0113 0,0135 0,0148 0,0176 ∙ ∆đ?‘Ľđ?‘Ľ đ?‘šđ?‘šđ?‘?đ?‘? = Table 8, and was calculated to the model: ) ∙ đ?œ?đ?œ?

(1 + đ?‘Ľđ?‘Ľaccording

0,001502

1

đ?‘šđ?‘šđ?‘¤đ?‘¤ = đ?‘šđ?‘šđ?‘?đ?‘? ∙ đ?œ?đ?œ?

đ?‘šđ?‘šđ?‘?đ?‘? đ?‘‰đ?‘‰ = ∙ đ?œ?đ?œ? đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł

Once the necessary amount of moist air vapor had been đ?‘šđ?‘šđ?‘¤đ?‘¤ = đ?‘šđ?‘šhow đ?‘?đ?‘? ∙ đ?œ?đ?œ? much water would be calculated, we calculated Table 7 available during a period of one hour with relation to wall 0,00063 0,0011 0,00166 0,00198 0,00217 0,00266 thickness.

0,00022 0,001502

0,00435

0,0075

0.0113

0.02144

0,0135

0,0148

0,0176

The time in which the available mass of water (mw) was turned into moist air vapor đ?‘šđ?‘šđ?‘?đ?‘? is presented in table 8 and was đ?‘‰đ?‘‰ = ∙ đ?œ?đ?œ? calculated according to the đ?œŒđ?œŒđ?‘Łđ?‘Łđ?‘Łđ?‘Ł following model:

0,00315 0.02144

đ?‘šđ?‘šđ?‘¤đ?‘¤ = đ?‘šđ?‘šđ?‘?đ?‘? ∙ đ?œ?đ?œ?

(All values were calculated for a wall surface area of 81m2) Table đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

1

2

3

4

5

6

7

8

mp (Kg/s)

0,001502

0,00435

0,0075

0.0113

0,0135

0,0148

0,0176

0.02144

�� (����)

7,83

22,66

39

58,87

70,33

77,1

91,7

111,7

đ?œ?đ?œ?(đ?‘ đ?‘ )

3600

3600

3600

3600

3600

3600

3600

V(m )

4,7

13,5

23,23

35

41,7

45,7

54,3

65,9

đ?‘šđ?‘šđ?‘¤đ?‘¤ (đ??žđ??žđ??žđ??ž)

5,41

15,66

27

40,68

48,6

53,28

63,36

77,2

3

Proportion for determining wall thickness based on previously conducted experiment (p. 219):

đ?‘Ľđ?‘Ľ âˆś 5,41 đ?‘˜đ?‘˜đ?‘˜đ?‘˜ = 10 đ?‘šđ?‘šđ?‘šđ?‘š âˆś 6.91 đ?‘˜đ?‘˜đ?‘˜đ?‘˜ đ?‘Ľđ?‘Ľ =

54.1 = 7,83 6.91

đ?‘„đ?‘„ = đ?‘šđ?‘šđ?‘?đ?‘? đ??śđ??śđ?‘?đ?‘? (đ?‘Ąđ?‘Ą2 − đ?‘Ąđ?‘Ą1 ) (W)

3600

Table 8

3

V(m )

4,7

13,5

23,23

35

41,7

đ?‘šđ?‘šđ?‘¤đ?‘¤ (đ??žđ??žđ??žđ??ž)

5,41

15,66

27

40,68

48,65.

45,7

54,3

53,28 63,36 161 EVAPORATION

đ?‘Ľđ?‘Ľ âˆś 5,41 đ?‘˜đ?‘˜đ?‘˜đ?‘˜ = 10 đ?‘šđ?‘šđ?‘šđ?‘š âˆś 6.91 đ?‘˜đ?‘˜đ?‘˜đ?‘˜

NOTES ABOUT TABLE 8

đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

mp (Kg/s) đ??śđ??śđ?‘?đ?‘? (đ??žđ??žđ??žđ??ž/đ??žđ??žđ??žđ??žđ??žđ??ž) Required heat Qs (W)

đ?‘Ľđ?‘Ľ =

54.1 = 7,83 6.91

In Table 8, logical resultsđ?‘„đ?‘„ are order to lower the = đ?‘šđ?‘šobtained.

(W) đ?‘?đ?‘? đ??śđ??śđ?‘?đ?‘? (đ?‘Ąđ?‘Ą2 − đ?‘Ąđ?‘Ą1 )In temperature of the space being cooled (reference volume is 1m3), more water is required Tabela 9 in the wall. If, for example, the desired temperature decrease is 8°C, the required 1 amount of2 water in 3the paper4wall (again, 5 compared 6 to the 7 2 reference volume, an area of 1m ), calculated for the same 0,001502 0,00435 0,0075 0.0113 0,0135 0,0148 0,0176 time interval, is 77.2 liters per hour.

1,0545

1,0509

1,0482

1,0455

1,0437

1,0407

1,038

1,584 This

9,143 47,26 70,45of heat 92,414 result means23,58 if there is an amount affecting127,88 the outside wall (with a thickness of 111.7mm) which can absorb 77.2 liters of water, the wall will be able to generate enough moist air in the space to cool the temperature of đ?‘„đ?‘„by 8 degrees in one hour. the surrounding environment Đ„ = đ?‘ đ?‘

đ?‘„đ?‘„đ?‘ đ?‘

b) Heat transfer thermodynamic calculus

The physical model of heat transfer through the paper wall soaked with water to the area of moist air is shown in the Physical Model Scheme at the beginning of the chapter. The picture shows the amount of heat (q), which is received from solar radiation and transferred to the paper wall, which then heats the water and evaporates it into the space. The evaporated water mixes with the dry air, resulting in a mixture we call "moist air."

The given equation of heat amount (Q) is directly proportional to and a function of vapor mass, the specific heat of the moist air (measured values from the thermodynamic tables) and the temperature difference.

0.

1

Table 8

162 SWEATING PAPER ARCHITECTURE

1

2

3

4

5

6

7

8

0,00435

0,0075

0.0113

0,0135

0,0148

0,0176

0.02144

,83

22,66

39

58,87

70,33

77,1

91,7

111,7

600

3600

3600

3600

3600

3600

3600

13,5

23,23

35

41,7

45,7

54,3

01502

4,7

3600

The aim is to show how much heat is required to8pass Table 15,66 27 40,68 48,6 53,28 63,36 through the wet paper wall in order to achieve a certain đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž) 1 2 3 5 temperature drop over a specific volume area. 4

,41

mp (Kg/s)

0,001502

0,00435

0,0075

0.0113

0,0135

Because we aređ?‘Ľđ?‘Ľ âˆśfamiliar the temperature outside of =with 10 đ?‘šđ?‘šđ?‘šđ?‘š âˆś 6.91 7,83 5,41 đ?‘˜đ?‘˜đ?‘˜đ?‘˜22,66 39 đ?‘˜đ?‘˜đ?‘˜đ?‘˜ 58,87 70,33 the wall (30°C) and the temperature inside the wall, the 54.1 đ?œ?đ?œ?(đ?‘ đ?‘ ) 3600 3600 3600 = 7,833600 using the đ?‘Ľđ?‘Ľ =3600 amount of heat required is calculated following 6.91 3 4,7 13,5 23,23 35 41,7 Vformula: (m ) đ?›żđ?›ż (đ?‘šđ?‘šđ?‘šđ?‘š)

đ?‘šđ?‘šđ?‘¤đ?‘¤ (đ??žđ??žđ??žđ??ž)

5,41

15,66

40,68

1,584

6

7

8

0,0148

0,0176

0.02144

77,1

91,7

111,7

3600

3600

45,7

54,3

65,9

53,28

63,36

77,2

3600

đ?‘Ľđ?‘Ľ âˆś 5,41 đ?‘˜đ?‘˜đ?‘˜đ?‘˜ = 10 đ?‘šđ?‘šđ?‘šđ?‘š âˆś 6.91 đ?‘˜đ?‘˜đ?‘˜đ?‘˜

Tabela 9

2 3 mp - mass of vapor;

4

54.1 đ?‘Ľđ?‘Ľ = = 7,83 6 6.91 7

5

0,001502t1 - temperature 0,00435 0,0075 on the 0.0113 inner side 0,0135 of the wall;0,0148 1,0545

48,6

77,2

đ?‘„đ?‘„ = đ?‘šđ?‘šđ?‘?đ?‘? đ??śđ??śđ?‘?đ?‘? (đ?‘Ąđ?‘Ą2 − đ?‘Ąđ?‘Ą1 ) (W)

Where: 1

27

65,9

8

0,0176

t2 =1,0509 300 C – temperature in the environment; 1,0482 1,0455 1,0437 1,0407 1,038 Cp (KJ/KgK) - Specific heat of moist air (Cp) đ?‘„đ?‘„ =at đ?‘šđ?‘šđ?‘?đ?‘?constant đ??śđ??śđ?‘?đ?‘? (đ?‘Ąđ?‘Ą2 − đ?‘Ąđ?‘Ą1 ) (W) 9,143 23,58 47,26 70,45 92,414 127,88 pressure

0.02144 1,036 177,7

Tabela 9 đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

mp (Kg/s) đ??śđ??śđ?‘?đ?‘? (đ??žđ??žđ??žđ??ž/đ??žđ??žđ??žđ??žđ??žđ??ž) Required heat Qs (W)

1 2 đ?‘„đ?‘„ Đ„đ?‘ đ?‘ = đ?‘„đ?‘„đ?‘ đ?‘ 0,00435 0,001502

3

4

5

6

7

8

0,0075

0.0113

0,0135

0,0148

0,0176

0.02144

1,0545

1,0509

1,0482

1,0455

1,0437

1,0407

1,038

1,036

1,584

9,143

23,58

47,26

70,45

92,414

127,88

177,7

Table 9

The results in Table 9 are relevant because theyđ?‘„đ?‘„indicate Đ„đ?‘ đ?‘ = there is not enough available energy (the portionđ?‘„đ?‘„đ?‘ đ?‘ marked with a red line) to reduce the temperature by 8 degrees in the corresponding volume area (65.9 m3).

If we look at the measured solar radiation levels in Tokyo between 1890 and 2012, all the parameters listed in Table 9 are met during the months of July and August as the average temperature (i.e., heat amount) is greater than 160 (W).

đ?‘„đ?‘„ = đ?‘šđ?‘šđ?‘?đ?‘? đ??śđ??śđ?‘?đ?‘? (đ?‘Ąđ?‘Ą2 − đ?‘Ąđ?‘Ą1 ) (W)

5. EVAPORATION 163

Tabela 9

Based on the results in Table 9, we can calculate the thermal stage defines between 1 2 (Đ„s), which 3 4 the relationship 5 6 7 the available heat (i.e., between average heat available 0,001502 0,00435 0,0075 0.0113 0,0135 0,0148 0,0176 at the latitude Tokyo) and the required for the 1,038 1,0545 1,0509 of 1,0482 1,0455 1,0437 heat 1,0407 corresponding amounts of temperature reduction.

đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

mp (Kg/s) đ??śđ??śđ?‘?đ?‘? (đ??žđ??žđ??žđ??ž/đ??žđ??žđ??žđ??žđ??žđ??ž) Required heat Qs (W)

1,584

9,143

23,58

�� (����)

Mean heat amount Q (W) Required heat Qs (W) System efficency (Đ„s)

70,45

92,414

127,88

The formula for calculating the thermal stage (Đ„s) is indicated below, and the results are shown in Table 10: Đ„đ?‘ đ?‘ =

Table 10.

đ?œ&#x;đ?œ&#x;đ?œ&#x;đ?œ&#x;(đ?‘˛đ?‘˛)

47,26

đ?‘„đ?‘„ đ?‘„đ?‘„đ?‘ đ?‘

1

2

3

4

5

6

7

8

7,83

22,66

39

58,87

70,33

77,1

91,7

111,7

160 1,584

9,143

23,58

47,26

70,45

92,414

127,88

177,7

99

17,5

6,8

3,385

2,27

1,731

1,25

0,9

Table 10 đ?‘„đ?‘„ ∙ đ?œ?đ?œ? = đ??śđ??śđ?‘?đ?‘? đ?‘‡đ?‘‡ +

Space temperature đ?‘‡đ?‘‡(đ??žđ??ž) Wind velocity v (m/s) đ??śđ??śđ?‘?đ?‘? (đ??žđ??žđ??žđ??ž/đ??žđ??žđ??žđ??žđ??žđ??ž) Heat amount Qs (W)

302 0,5 1,0545 88,46

302 1 1,0545 88,46

đ?‘Łđ?‘Ł 2 2

Based on the results in Table 10, we can conclude it takes 99 times less heat from the amount of heat available for đ?‘Łđ?‘Ł 2 occur in order to result in a temperature 2đ??śđ??śđ?‘?đ?‘? đ?‘‡đ?‘‡ + to evaporation đ?‘„đ?‘„ = 2đ?œ?đ?œ? drop of 1 degrees C in the immediate environment. It is clear that a reduction in the thermal stage results in a need for more Table energy.

11 If the thermal stage falls below 1, there is not enough energy to create the desired temperature drop.

In302 these cases, is regarded as 302 the system 295 295inefficient.

295 295 1,5practical 2,5 application 2,5 0,5 of the1 thermal1,5 The stage is interesting 1,0545 1,036 1,036 1,036 1,036 we are familiar with the average or the exact heat 88,461 required 88,461 to84,9 84,9 amount calculate84,9 the water84,9 vapor amount and mass of water for the desired wall thickness.

1,0545 when

164 SWEATING PAPER ARCHITECTURE

For instance, if we task a certain value for (Đ„s) and if we are familiar with the exact heat amount available, according to Table 10 and the equations for heat amount, we can calculate the corresponding wall thickness, the amount of water within the wall, and the corresponding mass of vapor. The calculation can be performed backwards very quickly and can also be applied to other water-absorbing materials.

Table 10 shows that the efficiency of the system is satisfactory except in cases where the desired temperature reduction is 8°C. For the system to be effective and to achieve the desired change in temperature, additional heat is required to bring the (Єs) above 1.

Table 10.

đ?œ&#x;đ?œ&#x;đ?œ&#x;đ?œ&#x;(đ?‘˛đ?‘˛)

b) Calculation of moist air flow in a semi-enclosed space in cases where there is an additional air flow (wind) out of the semi-enclosed space

1

2

3

4

Tablesystem 10. is in an open atmosphere, it is Because the entire �� (����) essential to find 7,83connections 22,66 39outer flow58,87 between the of air,

5

6

7

70,33

77,1

91,7

which affects the temperature change in the semi-enclosed

heat amount 3 temperature 4 change within 5 the same area 6 160 Q (W) 2space, and the Required (due to evaporation).

39 58,87 70,33 77,1 heat 22,66 1,584 9,143 23,58 47,26 Qs (W) In our case, based on the Law of Conservation of Energy, em efficency we can apply Saint Vennant's 160 energy equation for fluid 99 17,5 6,8 3,385 (Đ„s) flows. The results of the following equation are displayed in Table 11.

9,143 23,58

17,5

pace perature

47,26

đ?‘Łđ?‘Ł đ??śđ??śđ?‘?đ?‘? đ?‘‡đ?‘‡ + 3,385 đ?‘„đ?‘„ ∙ đ?œ?đ?œ? =2,27 2 1,731

đ?‘„đ?‘„ ∙ đ?œ?đ?œ? = đ??śđ??śđ?‘?đ?‘? đ?‘‡đ?‘‡ +

đ?‘Łđ?‘Ł 2 2

2đ??śđ??śđ?‘?đ?‘? đ?‘‡đ?‘‡ + đ?‘Łđ?‘Ł 2 2đ?œ?đ?œ?

302

92,414 2

6,8

đ?‘„đ?‘„ =

70,45

302

đ?‘„đ?‘„ =

7

8

91,7 70,45

111,7 92,414

127,88

2,27

1,731

1,25

127,88

177,7

1,25

0,9

2đ??śđ??śđ?‘?đ?‘? đ?‘‡đ?‘‡ + đ?‘Łđ?‘Ł 2 2đ?œ?đ?œ?

Table 11

302

302

295

295

295

295

đ?œ&#x;đ?œ&#x;đ?œ&#x;đ?œ&#x;(đ?‘˛đ?‘˛)

�� (����)

Mean heat amount Q (W) Required heat Qs (W) System efficency (Đ„s)

1

2

3

4

5

6

7,83

22,66

39

58,87

70,33

7

77,1 91,7 165 111,7 5. EVAPORATION

160 1,584 Where: 9,143 99

23,58

47,26

70,45

92,414

127,88

17,5 6,8 2,27 1,731 1,25 Q – heat amount (W); 3,385 Cp (KJ/KgK) - specific heat of moist air (Cp) at constant pressure; đ?‘Łđ?‘Ł 2 đ?‘„đ?‘„ ∙ đ?œ?đ?œ? = đ??śđ??śđ?‘?đ?‘? đ?‘‡đ?‘‡ + 2 Ď„ = 3600 sec, time; Ď… – wind velocity in range from 0.5 to 2.5 m/s (mean values for urban đ?‘‡đ?‘‡ + đ?‘Łđ?‘Ł 2in Tokyo estimated with simulation 2đ??śđ??śđ?‘?đ?‘?areas đ?‘„đ?‘„ = software) 2đ?œ?đ?œ?

Table 11

Space temperature đ?‘‡đ?‘‡(đ??žđ??ž) Wind velocity v (m/s) đ??śđ??śđ?‘?đ?‘? (đ??žđ??žđ??žđ??ž/đ??žđ??žđ??žđ??žđ??žđ??ž) Heat amount Qs (W)

8

302 0,5 1,0545 88,46

302 1

302 1,5

1,0545

1,0545

88,46

88,461

302 2,5 1,0545 88,461

295 0,5 1,036 84,9

295

295

295

1

1,5

2,5

1,036

1,036

1,036

84,9

84,9

84,9

Table 11

From Table 11 it is apparent that with additional wind flow ranging from 0.5 to 2.5 m/s the effect is greater than in cases where there is no wind activity. It is obvious that for decreases in temperature from 30°C to 22°C less than half of the available energy is consumed.

These results indicate that our system with additional air flow is almost two times more effective than a system without any air flow activity. This proves the system will be more effective when performing with additional air flow (wind) from the environment. For our design, this result is of particular importance because we will proceed with a chapter focused upon the enhancement of wind flow activity and its utilization for increases in system efficiency.

In our conclusion, we will present a comparison of the two systems - systems with wind activity, and systems without wind activity.

177,7 0,9

166 SWEATING PAPER ARCHITECTURE

Steady State - No Wind Activity The calculation is completed for each wall thickness with full power solar radiation (160 W), precisely the amount of energy available on the site location in Ginza.

đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

1

2

3

4

5

6

7

8

�� (����)

7,83

22,66

39

58,87

70,33

77,1

91,7

111,7

đ??śđ??śđ?‘?đ?‘? (đ??žđ??žđ??žđ??ž/đ??žđ??žđ??žđ??žđ??žđ??ž)

1,0545

1,0509

1,0482

1,0455

1,0437

1,0407

1,038

1,036

đ??źđ??ź (wall wetting interval)

Every 35,65 seconds

Every 3,43 minutes

Every 8,84 minutes

Every 17,7 minutes

Every 26,42 minutes

Every 34,65 minutes

Every 47,91 minutes

Every 1h&6 minutes

���� (Kg)

5,41

15,66

27

40,68

48,6

53,28

63,36

77,2

546 l

274 l

183,2 l

139,3 l

110,5 l

92,2 l

79,3 l

69,5 l

V (m )

4,7

13,5

23,23

35

41,7

45,7

54,3

65,9

mp (Kg/s)

0,15173

0,0761

0,0509

0,0383

0,0307

0,02562

0,02202

0,0193

đ?‘„đ?‘„(đ?‘Šđ?‘Š)

���� (mass of water required over 1h) 3

Table 12

160

5. EVAPORATION 167

Dynamic State - Wind Activity and Energy Received from the Sun The calculation is completed for cases where walls are exposed to solar radiation at full power (160 W) and additional energy (air flow). The total amount of energy affecting the wet paper wall is 248 W if we utilize the result obtained in Table 11 - the extra energy is 88 W. The results shown in Table 13 indicate that when a water soaked paper wall is under the influence of a permanent amount of heat delivered by insolation and additional energy is obtained from air flow, a greater amount of water vapor is produced.

1

2

3

4

5

6

7

8

�� (����)

7,83

22,66

39

58,87

70,33

77,1

91,7

111,7

đ?‘„đ?‘„(đ?‘Šđ?‘Š)

đ??śđ??śđ?‘?đ?‘? (đ??žđ??žđ??žđ??ž/đ??žđ??žđ??žđ??žđ??žđ??ž)

1,0545

1,0509

1,0482

1,0455

1,0437

1,0407

1,038

1,036

đ??źđ??ź

Every 23 seconds

Every 2,212 minutes

Every 5,71 minutes

Every 11,433 minutes

Every 17,04 minutes

Every 22,36 minutes

Every 31 minutes

Every 43 minutes

����

5,41

15,66

27

40,68

48,6

53,28

63,36

77,2

847 l

425 l

284 l

213,5 l

171,1 l

143 l

122,6 l

108 l

4,7

13,5

23,23

35

41,7

45,7

54,3

65,9

0,0475

0,0397

đ?›Ľđ?›Ľđ?›Ľđ?›Ľ(đ??žđ??ž)

(wall wetting interval)

���� (mass of water required over 1h) 3

V (m ) mp (Kg/s)

Table 13

248

0,2352

0,118

0,0789

0,0593

0,03413

0,02992

168 SWEATING PAPER ARCHITECTURE

Notes on Tables 12 and 13 Tables 12 and 13 suggest an increase in wall thickness reduces the rate of evaporation (as seen in the amount of water required for evaporation; thicker walls require less water than thinner walls) and therefore systems with greater wall thicknesses are less efficient than systems with thinner walls.

Tables 12 and 13 indicate the faster the evaporation process, the faster the reduction of temperature. The lower wall thickness is reduced, and the evaporation process occurs more quickly, thus decreasing the surrounding temperature more quickly. Thinner walls will therefore provide better results.

Heat loss throughout the thinner walls is less than heat loss observed in the thicker wall, as defined in Table 9. A lower rate of heat loss is required to speed up the evaporation process. In Table 9 we can see that the lowest rate of heat drop is observed in the thinnest paper wall. This therefore suggests the cooling system is better realized through the use of thinner walls.

For this theoretical model to be verified, measurements must be performed under the specified conditions; a constant rate of enthalpy and humidity variable x.

There is great potential in our system. This potential lies in our ability to maximize the surface area, which serves both to decrease the amount of time required for the evaporative effect to occur, and to increase the volume of affected air.

5. EVAPORATION 169

5m

30째

5m

29째

10 mm

28째

1m

27째

Wall 1

1m Section 1

20 mm

Wall 2 Section 2

30 mm

Wall 3

Section 3

To visualize the equations in another sense, an area of 1 m2 affects approximately 5 m3 of air volume.

When the thickness of the paper plates is increased, more space for water to be absorbed is created.

170 SWEATING PAPER ARCHITECTURE

30 0

29 0

Water containing 7.0 l

27

(C )

30

30

29

29

28

28

27

27

0

0

28 0

0

(C )

WALL 1

0

Water containing 14.0 l

0

(min)

(C )

30

30

30

29

29

29

28

28

28

27

27

27

0

WALL 2 0

0.25

(C )

0.5

0

30

0.5

1

(min)

1.5

(min)

(C ) 0

Water containing 21.0 l

30

29

29

28

28

27

27

WALL 30

0

0

(min)

0

(min)

0.5

(C )

(C )

0.5

0.25

0.5

1

(min)

0

0.5

1

Then we can understand how the paper ‘wall 3’, with the grater reserves of water, can maintain the effect for a longer period of time - where paper ‘wall 1’ would have to be moistened an additional two times to result in the same performance.

0

5. EVAPORATION 171

≈ 10 m

≈ 10 m

1 m2 WALL 1 = 7.0 l

2 m2 WALL 2 = 14.0 l

a = 10 mm n = surface distance

a

a n a

section 1

section 2

≈ 15 m

≈ 15 m a n an a 3 m2 WALL 3 = 21.0 l section 3

In regard to maximization of the surface area, we can see its relationship to how the affected area will grow. More surfaces simply have more capacity to produce a greater amount of water vapor which will therefore occupy a greater volume. As well, the starting amount of 5 m3 of volume will be cooled quicker.

172 SWEATING PAPER ARCHITECTURE

Geometry evaluation process We tested a range of geometries (ranging from most compact to most stretched), analysing a series of deformations and a variety of different levels of porosity.

Finally, we evaluated our geometries according to overall efficiency. Again, we compared geometries with different amounts of airflow and without airflow activity.

Next to each geometry is its individual statistics. If we define time scale then we can evaluate them as indicated below.

GCode 00 00 00 150 150 50 150 150 150 300 G01

CONDITIONS: 2

Q = 160 W/m + Wind (E) T = 30 0C

G01a

G01b

G01c

GCode 0 0 5 0 10 0 150 150 5 150 150 210 310

GCode 0 0 15 0 25 0 165 160 20 155 220 215 370

GCode 5 0 15 0 15 0

170 155 100 170

cooling efficiency test

50% wet surface

V = 5 m3 T = 10 min.

W = 0.61 t E = 1.07 l/s

50%

V = 6 m3 T = 7 min.

W = 0.74 t E = 1.87 l/s

65%

V = 7.2 m 3 T = 6.6 min.

W = 0.83 l E = 2.08 l/s

67%

V = 7.5 m 3 T = 6.4 min.

W = 0.87 l E = 2.21 l/s

68%

5. EVAPORATION 173

V - geometry volume T - total time needed W - total amount of water needed E - evaporation speed

20 min.

0 min.

0%

100%

G01Z GCode 00 00 00 195 195 100 195 260 195 390

0 260 210 340

G01d

G01e

G01f

GCode 0 0 0 0 20 0 150 160 20 260 170 210 340

GCode 0 0 0 0 -20 0 150 165 30 192 100 150 355

GCode 00 00 00 195 197 10 165 355 150 390

V = 9.5 m 3 T = 6.3 min.

W = 0.87 l E = 2.31 l/s

69%

V = 10 m 3 T = 5.4 min.

W = 0.79 l E = 2.45 l/s

73%

V = 11.6 m 3 T = 4.8 min.

W = 0.81 l E = 2.81 l/s

76%

V = 11.6 m 3 T = 4.8 min.

W = 0.81 l E = 2.81 l/s

76%

174 SWEATING PAPER ARCHITECTURE

Wind Patterns Because we are aiming to encourage wind flow through our chosen geometries, in this sub chapter, we will examine different wind behaviours within our design in addition to how wind influences our geometries. This implies that our final design is not solely determined or justified by structural or special factors, but environmental factors as well.

Software “Project Vasari Beta 2� was used to simulate wind behaviour.

This image represents a desirable orientation. Multiple openings directly face wind flow, thus enabling wind branching and activity in the inner areas.

Cluster plan

5. EVAPORATION 175

176 SWEATING PAPER ARCHITECTURE

Wind steering T

T1

T2

T3

T4

T

T1 a

T2 a

T3 a

T4 a

cluster T6

T5

T5 a

T6

T6 a

cluster T

Preferable types T4

T5

T6

T4 a

T5 a

T6 a

5. EVAPORATION 177

Geometry plan

Unit addition

To steer the wind through our targeted areas, we note the relationship between the curvatures and the wind pattern. At the bottom we see preferable geometry types regarding wind steering.

178 SWEATING PAPER ARCHITECTURE

Möbius Strip geometry evaluation Wind & Evaporation 0 m/s n/a

8h 0%

0 m/s 10% wet area time: 6 h -2° C

25%

0 m/s 30% wet area time: 2 h -2° C

75%

2.5 m/s 30% wet area time: 1 h 20 min -2° C

83%

2.5 m/s 50% wet area time: 46 min -2° C

90%

2.5 m/s 70% wet area time: 32 min -2° C

93%

2.5 m/s 90% wet area time: 26 min -2° C

94% 0 min.

100%

5. EVAPORATION 179

At the conclusion of our analysis, we observed 7 identical mobius strip geometries. For some, we introduced a wind flow; for some, we did not. For some, we introduced an evaporative effect with different evaporative amounts in order to determine the time required for the desired effect to take place. In comparison to units solely acting as shade providers, we found our geometries were able to better increase comfort levels by regulating and accurately estimating evaporative effects with the precise computational methodology we developed.

Daily active sunshine scale for Tokyo (August) 00:00

09:00

37째 C

Plan

17:00

30째 C

Shade section

37째 C

28째 C

Environmental section

24:00

180 SWEATING PAPER ARCHITECTURE

6. STRUCTURE 181

6. Structure The local conditions of the surface are not homogenous.

Some areas demand more tensile or compressive strength, and others demand more wetness. Our aim is for the material composition and local geometry and reinforcement to respond to and visualize this heterogenity as it does in a monocoque shell structure.

A typical example of a monocoque is the shell of a car. It has a homogeneous and continuous appearance. Upon closer look, however, its joints and materials vary.

Extruded Aluminium Stamped Aluminium Cast Aluminium

Composition of the monocoque shell of a Jaguar XK. Image source: Retrieved July 25, 2014, from: https://www.i-car.com/graphics/about_icar/current_events/advantage/2008/Advantage_ online_0519/full_size/fig_05.jpg

182 SWEATING PAPER ARCHITECTURE

Structural Simulation In order to map the differences of the structural performance of the geometry – and in order to make sure that it withstands gravity – we make a structural simulation. Since the paper plate and connection have unique properties that are not listed in standard simulation programs, we empirically measure the performance with deflection tests. The experiment setup consists of a section of assembled plates spanning two points. Weights are hung in the middle and the deflection is measured. From this experiment it is possible to know when it breaks and how much it bends under various pressures, from which data it is possible to calculate Young’s Modulus, the most critical value for structural simulation.

Load (kg)

The collected data is plotted in a deflection graph.

The steeper the curve is, the more the joint resists deflection. With this graph, geometrical calculations of the components, and measurements of the surface density, it is possible to simulate the structure with accuracy.

Type 1 Type 2 Type 3

20

Type 4 Type 5 Young’s modulus E1 = 0.893 tonf/cm2

10

E2 = 0.644 tonf/cm2 E3 = 1.118 tonf/cm2 E4 = 1.494 tonf/cm2 E5 = 0.354 tonf/cm2

0 0

50

100

150

200

Deflection (mm)

Deflection graphs of various joints and water weights.

Reference values ESteel = 2 000 tonf/cm2 ERubber = 0.5 tonf/cm2

6. STRUCTURE 183 0 kg

2 kg

4 kg

0 mm

0 mm

5 mm

6 kg

8 kg

10 kg

7 mm

9 mm

14 mm

12 kg

14 kg

16 kg

20 mm

23 mm

33 mm

18 kg

20 kg

22 kg

38 mm

49 mm

59 mm

24 kg

26 kg

28 kg

69 mm

78 mm

94 mm

30 kg

32 kg

34 kg

99 mm

108 mm

124 mm

36 kg

38 kg

42 kg

129 mm

142 mm Critical breaking point

184 SWEATING PAPER ARCHITECTURE .lst-file

90 mm

180 mm 540 mm

Mu :

ultimate bending moment

Zp :

plastic section factor

σu :

ultimate stress

1 1 Paper plate: Mu = 4 *load*span = 4 *20 kg*50 cm = 250.0 kg*cm Wood plate: σu ≈ 300 kg/cm2

Dense mesh, 0.5 plate per line

Medium mesh, 1 plates per line

Sparse mesh, 3 plates per line

u 250.0 kg*cm 3 Zp = M σu = (no of plates in section)* 300 kg/cm2 = (no of plates in section)*0.8333 cm

B*D2 = 4*Zp = 4*(no of plates in section)*0.8333 cm3 = (no of plates in section)*3.333 cm3 "INPUT DATA"

3 B = (no of plates in section)* 3.333 2cm D

(no of plates in section) = 1, B = (no of plates in section)* (no of plates in section) = 2,

D = 1.5 cm 3.333 cm3 D2

=

3 1* 3.333 cm2 (1.5cm)

= 1.481

D = 1.5 cm

3 3 B = (no of plates in section)* 3.333 2cm = 2* 3.333 cm2 = 2.963 D (1.5cm)

(no of plates in section) = 6,

D = 1.5 cm

3 3 B = (no of plates in section)* 3.333 2cm = 6* 3.333 cm2 = 8.889 D (1.5cm)

1 Sandwiched paper plate: Mu ≈ 4 *42 kg*50 cm = 525 kg*cm Zp = (no of plates in section)* 525 kg*cm2 = (no of plates in section)*1.75 cm3 300 kg/cm 4*Zp = 4*(no of plates in section)*1.75 cm3 = (no of plates in section)*7.00 cm3 3 B = (no of plates in section)* 7.00 cm D2

(no of plates in section) = 1,

D = 4.0 cm

3 3 B = (no of plates in section)* 7.00 2cm = 1* 7.00 cm 2 = 0.438 D (4.0cm)

(no of plates in section) = 2,

"dense mesh 90" "approximation of paper plate using wood" "ingorable" "ignorable" "medium mesh 180" "approximation of paper plate using wood" "ingorable" "ignorable" "sparse mesh 540" "approximation of paper plate using wood" "ingorable" "ignorable" "dense mesh 90-sandwich" "approximation of paper plate using wood" "ingorable" "ignorable" "medium mesh 180-sandwich" "approximation of paper plate using wood" "ingorable" "ignorable" "sparse mesh 540-sandwich" "approximation of paper plate using wood" "ingorable" "ignorable" "tension string" "approximation of string plate using steel"

Steel SN400 : 4.0 0.1 = 0.025 cm2 4.0

.inp-file PROPERTIES "CREATED ORGAN FRAME." NNODE 3059 NELEM 5777 NPROP 8 NSECT 7

Structure weight: 1 dry plate = 134 g 1 moist plate = 164 g 1 soaked plate = 234 g With additional weight of 1 kgf/m2 for wind, weather and other forces 3

B(lst-file) = (no of plates in section)* 3.333 2cm D mesh_dim(m)=0.90m*(no of plates in section)

=

1.5 cm

Minimum D = 1.5 cm

Sandwiched surface of paper plates 4.0 cm

Minimum D = 4.5 cm

Tension weave string

Approximation of string dimensions with pre-programmed material of steel brace.

D = 4.0 cm

3 3 B = (no of plates in section)* 7.00 cm = 6* 7.00 cm 2 = 2.625 D2 (4.0cm)

F(ton/m2) =

One-layered surface of paper plates

D = 4.0 cm

3 3 B = (no of plates in section)* 7.00 cm = 2* 7.00 cm 2 = 0.875 D2 (4.0cm)

(no of plates in section) = 6,

Approximation of paper plate dimensions with pre-programmed material of wood.

CODE 201 WOOD COLUMN PLATE 1.5 1.481 SUGI XFACE 0.0 0.0 YFACE 0.0 0.0 CODE 202 WOOD COLUMN PLATE 1.5 2.963 SUGI XFACE 0.0 0.0 YFACE 0.0 0.0 CODE 203 WOOD COLUMN PLATE 1.5 8.889 SUGI XFACE 0.0 0.0 YFACE 0.0 0.0 CODE 204 WOOD COLUMN PLATE 4.0 0.438 SUGI XFACE 0.0 0.0 YFACE 0.0 0.0 CODE 205 WOOD COLUMN PLATE 4.0 0.875 SUGI XFACE 0.0 0.0 YFACE 0.0 0.0 CODE 206 WOOD COLUMN PLATE 4.0 2.625 SUGI XFACE 0.0 0.0 YFACE 0.0 0.0 CODE 601 S BRACE SAREA 0.025 SN400

2 layers*plate_weight(kg) + additional_weight(kg/m2) = plate_width(m)*plate_height(m)

BASE 0.200 LOCATE 1.000 TFACT 0.030 GPERIOD 0.600 GFACT 1.0 FOCUS 0.0 0.0 0.0 ANGLE 30.0 120.0 DISTS 1000.0 50000.0

2*plate_weight(kg) + 1kg/m2 = 61.7284/m2 *plate_weight(kg)+1kg/m2 0.18m*0.18m

F(ton/m2)*mesh_dim(m)*mesh_dim(m) 0.5*F(ton/m2)*mesh_dim(m) 2*mesh_dim(m) HUJI = = = D*B(lst-file) D*B(lst-file) 0.5*(61.7284*plate_weight(kg)+1)*10-3 ton/m2*0.090m*(no of plates in section) = = -6m3 D*(no of plates in section)* 3.333*10 D2

HUJI(single layer) = D(m)*(833.417*plate_weight(kg)+13.501) ton/m2 HUJI(dry) = 0.015*(833.417*0.134+13.501) ton/m2 = 1.88 ton/m2 HUJI(moist) = 0.015*(833.417*0.164+13.501) ton/m2 = 2.25 ton/m2 HUJI(soaked) = 0.015*(833.417*0.234+13.501) ton/m2 = 3.13 ton/m2

HUJI(double layer) = D(m)*(793.651*plate_weight(kg)+6.429) ton/m2 HUJI(dry+dry) = 0.04*(793.651*0.134*2+6.429) ton/m2 = 8.765 ton/m2 HUJI(dry+moist) = 0.04*(793.651*(0.134+0.164)+6.429) ton/m2 = 9.717ton/m2 HUJI(dry+soaked) = 0.04*(793.651*(0.134+0.234)+6.429) ton/m2 = 11.940 ton/m2

Neglectable

Young’s modulus (ton/m2) from physical test

PROP 101 PNAME PAPERLPLATE_dry_no_tension HIJU 1.880 E 8930.000 Dry POI 6.5 Approximation by wood PCOLOR 255 0 255 PROP 102 PNAME PAPERLPLATE_dry_local_tension HIJU 1.880 From physical test E 14940.000 Dry POI 6.5 Local tension PCOLOR 150 150 255 PROP 103 PNAME PAPERLPLATE_moist_3cl_water_in_one_plate HIJU 2.250 From physical test E 3040.000 Moist POI 6.5 PCOLOR 255 0 255 PROP 104 PNAME PAPERLPLATE_soaked HIJU 3.130 E 1520.000 Approximation: Soaked POI 6.5 0.5x value of moist plate PCOLOR 255 0 255 PROP 105 PNAME PAPERLPLATE_CONNECTION_dry_and_dry_sandwich HIJU 8.765 E 26790.000 Approximation: 3x value of Dry+dry POI 6.5 single layered dry plate PCOLOR 255 0 255 PROP 106 PNAME PAPERLPLATE_CONNECTION_dry_and_moist_sandwich HIJU 9.717 E 11970.000 Approximation: value of Dry+moist POI 6.5 single layered dry plate+moist plate PCOLOR 255 0 255 PROP 107 PNAME PAPERLPLATE_CONNECTION_dry_and_soaked_sandwich HIJU 11.940 E 10470.000 Approximation: value of Dry+soaked POI 6.5 single layered dry plate+soaked plate PCOLOR 255 0 255 PROP 501 PNAME TENSION_STRING HIJU 0.001 String E 0.02 Approximation 200 000 ton/m2 *10-7 POI 0.3 Approximation PCOLOR 255 0 255

SECT 201 SNAME PAPERLPLATE_dense_mesh_90 NFIG 1 A = plates_per_line*B*D = 0.5*0.18m*0.015m = FIG 1 FPROP 102 = 0.00135m2 AREA 0.0009 IXX 0.00000003 IXX = plates_per_line*(1/12)*B*D3 = IYY 0.00000365 =0.5*(1/12)*0.18m*(0.015m)3 = 0.00000003m4 VEN 0.00000003 IYY = plates_per_line*(1/12)*B3*D = EXP 1.500 =0.5*(1/12)*(0.18m)3*0.015m = 0.00000365m4 NZMAX 1.000 NZMIN -1.000 QXMAX 1.000 QXMIN -1.000 VEN ≈ IXX ≈ 0.0000003m4 QYMAX 1.000 QYMIN -1.000 MZMAX 1.000 MZMIN -1.000 MXMAX 1.000 MXMIN -1.000 MYMAX 1.000 MYMIN -1.000 COLOR 0 50 250 SECT 202 SNAME PAPERLPLATE_medium_mesh_180 NFIG 1 FIG 1 FPROP 102 A = 1*0.18m*0.015m = 0.00270m2 AREA 0.0027 IXX 0.00000005 IXX = 1*(1/12)*0.18m*(0.015m)3 = 0.00000005m4 IYY 0.00000729 IYY = 1*(1/12)*(0.18m)3*0.015m = 0.00000729m4 VEN 0.00000005 VEN ≈ IXX ≈ 0.0000005m4 EXP 1.500 NZMAX 1.000 NZMIN -1.000 QXMAX 1.000 QXMIN -1.000 QYMAX 1.000 QYMIN -1.000 MZMAX 1.000 MZMIN -1.000 MXMAX 1.000 MXMIN -1.000 MYMAX 1.000 MYMIN -1.000 COLOR 0 50 250 SECT 203 SNAME PAPERLPLATE_sparse_mesh_540 NFIG 1 FIG 1 FPROP 102 AREA 0.00810 A = 3*0.18m*0.015m = 0.00810m2 IXX 0.00000015 IXX = 3*(1/12)*0.18m*(0.015m)3 = 0.00000015m4 IYY 0.00002187 IYY = 3*(1/12)*(0.18m)3*0.015m = 0.00000729m4 VEN 0.00000015 VEN ≈ IXX ≈ 0.0000015m4 EXP 1.500 NZMAX 1.000 NZMIN -1.000 QXMAX 1.000 QXMIN -1.000 QYMAX 1.000 QYMIN -1.000 MZMAX 1.000 MZMIN -1.000 MXMAX 1.000 MXMIN -1.000 MYMAX 1.000 MYMIN -1.000 COLOR 0 50 250 SECT 204 SNAME PAPERLPLATE_dense_mesh_90_sandwich NFIG 1 FIG 1 FPROP 105 A = 0.5*0.18m*0.040m = 0.0036m2 AREA 0.00405 IXX 0.00000048 IXX = 0.5*(1/12)*0.18m*(0.04m)3 = 0.00000048m4 IYY 0.00000972 IYY = 0.5*(1/12)*(0.18m)3*0.04m = 0.00000972m4 VEN 0.00000048 VEN ≈ IXX ≈ 0.0000048m4 EXP 1.500 NZMAX 1.000 NZMIN -1.000 QXMAX 1.000 QXMIN -1.000 QYMAX 1.000 QYMIN -1.000 MZMAX 1.000 MZMIN -1.000 MXMAX 1.000 MXMIN -1.000 MYMAX 1.000 MYMIN -1.000 COLOR 0 50 250

.inp-file SECTIONS

NODE NODE NODE NODE NODE NODE NODE

101 102 103 104 105 106 107

CORD CORD CORD CORD CORD CORD CORD

0.800 0.781 0.760 0.748 0.767 0.735 0.708

-3.551 1.513 ICON 0 0 0 0 0 0 VCON -3.547 1.641 ICON 0 0 0 0 0 0 VCON -3.548 1.770 ICON 0 0 0 0 0 0 VCON -3.414 1.754 ICON 0 0 0 0 0 0 VCON -3.414 1.626 ICON 0 0 0 0 0 0 VCON -3.549 1.897 ICON 0 0 0 0 0 0 VCON -3.551...

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

SECT 205 SNAME PAPERLPLATE_medium_mesh_180_sandwich NFIG 1 AREA = Cross section area (m2) FIG 1 FPROP 105 AREA 0.00720 A = 1*0.18m*0.04m = 0.0072m2 IXX = Moment of intertia, x-direction (m4) IXX 0.00000096 IXX = 1*(1/12)*0.18m*(0.04m)3 = 0.00000096m4 IYY 0.00001944 IYY = 1*(1/12)*(0.18m)3*0.04m = 0.00001944m4 VEN 0.00000072 VEN ≈ IXX ≈ 0.0000072m4 EXP 1.500 NZMAX 1.000 NZMIN -1.000 QXMAX 1.000 QXMIN -1.000 QYMAX 1.000 QYMIN -1.000 IYY = Moment of intertia, y-direction (m4) MZMAX 1.000 MZMIN -1.000 MXMAX 1.000 MXMIN -1.000 MYMAX 1.000 MYMIN -1.000 COLOR 0 50 250 SECT 206 SNAME PAPERLPLATE_sparse_mesh_540_sandwich NFIG 1 FIG 1 FPROP 105 A = 3*0.18m*0.04m = 0.02160m2 AREA 0.02160 IXX 0.00000280 IXX = 3*(1/12)*0.18m*(0.04m)3 = 0.00000280m4 IYY = 3*(1/12)*(0.18m)3*0.04m = 0.00005832m4 IYY 0.00005832 VEN = St Venant’s torsion ≈ IXX VEN 0.00000280 VEN ≈ IXX ≈ 0.00000280m4 EXP 1.500 NZMAX 1.000 NZMIN -1.000 QXMAX 1.000 QXMIN -1.000 QYMAX 1.000 QYMIN -1.000 MZMAX 1.000 MZMIN -1.000 MXMAX 1.000 MXMIN -1.000 MYMAX 1.000 MYMIN -1.000 COLOR 0 50 250 SECT 601 SNAME TENSION_STRING NFIG 1 2 mm FIG 1 FPROP 501 AREA 31.416 Area *107 = PI*r(m)2 = PI*0.0012*107 = PI*10-6*107 = PI*10 = 31.416 IXX 0.00000785 PI PI *(2*10-3*)4*107 = PI *16*10-12*107 = Circular section --> IXX = IYY = VEN = *D4*107 = IYY 0.00000785 64 64 64 VEN 0.00000785 = PI *10-5 = 0.00000785 4 EXP 1.500 NZMAX 1.000 NZMIN -1.000 QXMAX 1.000 QXMIN -1.000 QYMAX 1.000 QYMIN -1.000 MZMAX 1.000 MZMIN -1.000 MXMAX 1.000 MXMIN -1.000 MYMAX 1.000 MYMIN -1.000 COLOR 0 250 0

6. STRUCTURE 185

Results of structural tests and geometric calculations inputted to the Hogan structural simulation software, created by Professor Jun Sato.

186 SWEATING PAPER ARCHITECTURE

8m

3m

3m

5m

4m

6m

How far can an arch made of paper plates span? The result of the simulation shows an arch composed of hydrophobic plates can span up to 8 meters.

4m

7m

6. STRUCTURE 187

Structural pasta geometries. Source: George L. Legendre, Pasta by design.

Non-carbonated plastic water bottles.

188 SWEATING PAPER ARCHITECTURE

Composing the Hydrotectonic Monocoque Shell Structure In the first step in the design process, the surface is simulated with hydrophobic plates. The surface condition of the initial target geometry is then altered in several ways. First, the local shape is updated with a ripple in the direction of the force lines in order to strengthen the structure by increasing the moment of inertia. This strategy is inspired by pasta and non-carbonated water bottles.

By rippling, bending, and curling the edges, pasta gains sufficient structural strength despite being a weak material.

Similarly, plastic bottles containing non-carbonated water are waved.

Next, the surface is further reinforced. An abundant number of tension strings are attached over the ripples.

A structural analysis determines which tension strings are not tense. These are eliminated and the necessary ones are kept – visualizing the variety of local tension forces of the shell.

In areas that are still failing due to compression loads, the surface is reinforced by doubling or tripling the layers of the assembly. In order to introduce wetness, the hydrophobic plates are substituted with weaker, but more waterabsorbent plates in low-stress areas. To include even more wetness, additional layers of hydrophilic plates are added at the base, where additional weight stabilizes the structure.

The result is a monocoque shell with a differentiated local shape in form of the ripple, a pattern of tension strings, areas of multiple layer reinforcement, and a range of hydrophilic paper properties.

6. STRUCTURE 189

Tension strings

Soaked layers

Dry plates

Moist plates

Reinforcement layers

190 SWEATING PAPER ARCHITECTURE

7. APPLICATION 191

7

7. Application

192 SWEATING PAPER ARCHITECTURE

Strip Aggregation The next step was to aggregate the Mobius strips in a modular system. The strips can be twisted in two directions; either clockwise or counter-clockwise. Two strips of the same direction do not align well, but two strips of opposing directions curve parallel to each other along the connecting edge. Thus, the strips can be aggregated by alternating twist directions to form larger spans of roofed interiors and connections between the modules.

When the aggregation is expanded, we observe that it forms a hexagonal grid with inaccessible voids. This pattern is laid out on the site and deformed to create differentiation in scale and to enable the wind from the cross streets to enter. Next, some units are omitted to open up the clusters, thus eliminating the inaccessible courtyards. Finally, the Mobius strips populate the street according to the pattern - connecting to one another.

Low part/floor

Low part/floor Low part/floor

High part/roof

High part/roof High part/roof

7. APPLICATION 193

194 SWEATING PAPER ARCHITECTURE

7. APPLICATION 195

196 SWEATING PAPER ARCHITECTURE

1. Hexagonal pattern of clockwise and counter-clockwise triple twisted mobius strips laid out on the site.

2. Deformation for differentiation in scale.

7. APPLICATION 197

3. Elimination of units along a central passageway in order to open up the inaccessible voids.

4. Population with mobius strips according to pattern.

198 SWEATING PAPER ARCHITECTURE

Chuo Dori Ginza Late August 30 degrees Celsius 50% humidity Uchimizu wetting at a regular interval

Small scale, high intensity evaporation unit Wind 2.5 m/s

Cools down 1 degree in 30 minutes A wind simulation shows the intensified wind activity in the crossings, and how it branches through the small units. During a summer day in Ginza, with the assumption that the structures are moistened by people bringing secondary use water - a smaller, high intensity, unit cools down the air volume that it contains for 1 degree in 30 minutes, and the larger one in 1 hour.

7. APPLICATION 199

Large scale, low-intensity evaporation unit Wind 0.5 m/s

Cools down 1 degree in 1 hour

Program: Rhino/Grashopper/Python

200 SWEATING PAPER ARCHITECTURE

7. APPLICATION 201

202 SWEATING PAPER ARCHITECTURE

8. CONCLUSION 203

6

Conclusions We have explored the possibility of fabricating a curvilinear geometry using a mass-production process while aiming to integrate the existing material flow of the city, and to maximize the effect of the reactive properties of paper.

This production process may have been possible 100 years ago, but the computational power of today’s machines provides us with new opportunities to use feedback from various simulations in the design process and to organize the geometrical and material information to define a recipe for production and construction.