James Goddings 3131147 LSBU Final Pr

School of Engineering
BEng(Hons) Project in Mechanical Engineering
Final Project Report
The Testing and Development of Cardboard
Tubes as a Structural Material with the Intended
Application being the Construction of a Bicycle
James Goddings
2015/16
Project Supervisor: Dr. Geoff Goss
Mechanical Engineering BEng(Hons)
Project (ENG_6_424_1516)
Part Time

School of Engineering
BEng(Hons) Project in Mechanical Engineering
The Testing and Development of Cardboard
Tubes as a Structural Material with the Intended
Application being the Construction of a Bicycle
James Goddings
Student No: 3131147
Submission Date: 30/04/16
Project Supervisor: Dr. Geoff Goss
Module: Project (ENG_6_424_1516)
Part Time
This report has been submitted for assessment towards a Bachelor of Engineering
Degree in Mechanical Engineering in the Department of Engineering and Design,
London South Bank University. The report is written in the author’s own words and
all sources have been properly cited.
Author’s Signature:
Date:

Table of Contents
Abstract................................................................................................................................i
Glossary.............................................................................................................................. ii
1. Introduction.................................................................................................................1
1.1 The History of the Cardboard Bicycle.....................................................................1
1.2 Cardboard Forms......................................................................................................2
1.3 The Bicycle as an Mechanical Engineering Application.......................................3
2. Project Aim..................................................................................................................4
3. Objectives.....................................................................................................................4
4. Deliverables.................................................................................................................6
5. Technical Background ................................................................................................6
5.1 Bicycle Frame Materials..........................................................................................6
5.2 The Advantage of Larger Diameter Tubes.............................................................8
5.3 Why Build a Bicycle from Cardboard?..................................................................10
5.4 Is Cardboard Suited to Building A Bicycle?........................................................11
Printable ....................................................................................................................11
Reusable and Recyclable...........................................................................................11
Inexpensive to Manufacture.....................................................................................11
Mechanical Strength.................................................................................................12
Low Density...............................................................................................................13
5.5 Cardboard’s Limitations ........................................................................................13
Moisture.....................................................................................................................13
Fatigue .......................................................................................................................13
Manufacturing Defects.............................................................................................13
6. Technical Approach...................................................................................................14
6.1 Laboratory Testing of Cardboard Tubes...............................................................14
Apparatus..................................................................................................................14
Experimental Procedure...........................................................................................14
Results........................................................................................................................16
Discussion..................................................................................................................16
6.2 Frame Design..........................................................................................................18
Existing Frame Designs ...........................................................................................18
Geometry....................................................................................................................19

6.3 Finite Element Analysis ........................................................................................20
6.4 Tube Development.................................................................................................22
6.5 Joint Development.................................................................................................25
6.6 Construction of the Front Triangle......................................................................26
6.7 Re-Design and Construction of Rear Triangle....................................................27
6.8 Construction of Forks and Prototype Front Wheel.........................................28
6.9 Waterproofing....................................................................................................28
6.10 Prototype Testing...............................................................................................28
7. Results and Discussion.............................................................................................28
7.1 Evaluation of the Project ......................................................................................28
7.2 Evaluation of the materials developed ................................................................29
7.3 Evaluation of the design process..........................................................................30
7.4 Evaluation of the project management process..................................................31
7.5 Evaluation of the final product.........................................................................31
Conclusions.......................................................................................................................32
APPENDIX A...................................................................................................................A1
Laboratory Testing Results and Charts ....................................................................A1
APPENDIX B Finite Element Analysis.........................................................................B1
Analysis 1 Static Study - Seated Whilst Pedalling Right Pedal.............................B1
Analysis 2 Static Study - Seated Whilst Pedalling Left Pedal ...............................B2
Analysis 3 Static Study – Standing Whilst Pedalling Left Pedal..........................B3
Analysis 4 Static Study – Standing Whilst Pedalling Right Pedal.......................B4
Analysis 5 Static Study – “Hitting a Pothole” while Seated...................................B5
Analysis 6 Static Study – Braking while Standing ................................................B6
Analysis 7 Static Study – Falling Mass...................................................................B8
Analysis 8 Static Study – Falling Frame.................................................................B9
APPENDIX C Models and Build Photos........................................................................C1
APPENDIX D...................................................................................................................D1
Product Design Specification for a Cardboard Bicycle Frame and Forks...........D1
Prototype Bicycle Frame and Forks Costing for Project.......................................D1
Table of Bicycle Ancillary Donor Parts Used for Build.........................................D2
Dimensional Analysis of Prototype Frame and Forks..........................................D2
APPENDIX E Gantt Chart.............................................................................................E1
References........................................................................................................................... I

Figure References........................................................................................................ I
References.................................................................................................................... I
Bicycle Industry Testing Standards.........................................................................V
Other Standards.........................................................................................................V

i
Abstract
This project examines the mechanical properties of cardboard, focussing on
cardboard tubes and their development as a viable structural material. Few studies
have been made on the properties of cardboard tubes; however they are an abundant
resource and provide an inexpensive, sustainable alternative to current materials.
Axial compression tests are carried out on cardboard tubes to establish their
mechanical properties. This data is used in the development of enhanced forms with
the application being the design and manufacture of a prototype cardboard bicycle
frame and forks. Through the achievement of this objective, the project seeks to
prove the materials developed, and provide insight into the feasibility of the
cardboard bicycle as a product.

ii
Glossary
𝐼 = 𝑆𝑒𝑐𝑜𝑛𝑑 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐴𝑟𝑒𝑎 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐼𝑛𝑒𝑟𝑡𝑖𝑎⁄
𝑟𝑜 = 𝑂𝑢𝑡𝑒𝑟 𝐸𝑥𝑡𝑒𝑟𝑛𝑎𝑙⁄ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
𝑟𝑖 = 𝐼𝑛𝑛𝑒𝑟 𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙⁄ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
𝛿 = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝐷𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛⁄
𝐿 = 𝐿𝑒𝑛𝑔𝑡ℎ
𝐸 = 𝑌𝑜𝑢𝑛𝑔′ 𝑠 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 𝐸𝑙𝑎𝑠𝑡𝑖𝑐 𝑀𝑜𝑑𝑢𝑙𝑢𝑠⁄
𝜃 = 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝐷𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛⁄
𝑇 = 𝑇𝑜𝑟𝑞𝑢𝑒
𝐴 = 𝐴𝑟𝑒𝑎
𝑉 = 𝑉𝑜𝑙𝑢𝑚𝑒
𝛾 = 𝑆𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡, 𝑠𝑒𝑒 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 5.2.8
𝜑 = 𝑊𝑎𝑙𝑙 𝑅𝑎𝑡𝑖𝑜, 𝑠𝑒𝑒 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 5.2.9
𝜆 = 𝑊𝑎𝑙𝑙 𝑅𝑎𝑡𝑖𝑜, 𝑠𝑒𝑒 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 5.2.9
𝑅 = 𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐺𝑦𝑟𝑎𝑡𝑖𝑜𝑛
𝑚′ = 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ (𝑚𝑒𝑡𝑟𝑒)
Top Tube
Down Tube
Seat Tube
Head Tube
Seat Stays
Chain Stays
Front Forks
Rear Dropouts
Handlebars
Stem
Front Dropouts
Tube
Fork Legs
Fork Crown
Bottom BracketCranks
Bicycle Frame

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1. Introduction
The original title of this project was “Eco-bicycle”, the challenge being to design and build a
cardboard bicycle. After reassignment from the project’s proponent supervisor/assessor, and
discussion with the new supervisor/assessor, a decision was taken to change to the project
title to its current form.
The Testing and Development of Cardboard Tubes as a Structural Material with the
Intended Application being the Construction of a Bicycle
It is agreed that this presents more opportunity to approach the project from an analytical
engineering angle. The most important question to arise from this discussion is, “Why build a
cardboard bicycle?”
This project seeks to answer this question, and in the process establish, whether cardboard is
a viable structural material and if so, how to build a bicycle from it to prove this.
1.1 The History of the Cardboard Bicycle
There is precedent for the manufacture of a functional cardboard bicycle. Two well-publicised
attempts have been made previously:
Figure 1.1.1 Left - Phil Bridge’s honeycomb panel cardboard bicycle 2008, Right - Izhar
Gafni’s cardboard bicycle 2012
Whilst pursuing a Product Design degree from Sheffield Hallam University in 2008, Phil
Bridge built a cardboard bicycle from honeycomb cardboard panels produced for advertising
hoardings and the building industry. The final product is elegantly designed and received
publicity from local and national media; however it was a downscaled model that could not be
pedalled, and could only support 75kg statically. This demonstrates the concept, but does not
prove the mechanical viability of building a functional bicycle from cardboard.
In 2012 Izhar Gafni was successful in building a mechanically sound functional bicycle from
cardboard and launched a crowd-funding scheme on Indiegogo to raise $2 million to fund the
setup of Cardboard Technologies, a company for producing his cardboard bicycle. The
fundraiser fell short only raising $40,000, the schemes failure is attributed to the “lucky
owners” of the first bicycles being asked to pay in excess of $500 for a bicycle with a claimed
retail price of $20 to the third world. (www.Indiegogo.com, 2012)
Both Phil Bridge and Izhar Gafni cite the low cost and recyclability of cardboard as their
reasons for choosing cardboard as a material to build a bicycle. They also both claim they

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could supply a $20 retail product to the market, a claim discussed in Section 7.5.
1.2 Cardboard Forms
Figure 1.2.1 from Top Left to Bottom Right, Plain Card Stock, Corrugated Cardboard,
Honeycomb Cardboard and Cardboard Tube
Cardboard is manufactured in different forms, illustrated by Figure 1.2.1, and is currently
used in the building industry for the manufacture of honeycomb cored doors, stud wall panels
and lightweight countertops. The architect Shigeru Ban, who specialises in designing
buildings from sustainable materials has even designed and built large architectural
structures from cardboard tubes with metal joints.
Figure 1.2.2 Both Shigeru Ban designs - Left - The Japanese Pavilion Expo 2000 Hannover,
Germany, Right - Cardboard Tube Bridge with the Pont du Gard, France in background (A
2000-year-old Roman aqueduct)

3
Cardboard tubes are a widely available form of cardboard used as packing and packaging
products for transport and sale. They have a number of characteristics that make them well
suited to this:
 Printable
 Reusable and recyclable
 Inexpensive to manufacture
 Mechanically strong
 Low in density
This project will investigate the mechanical properties of cardboard tubes (see Section 6.1
and APPENDIX A) and their development as a feasible structural material for the design
and manufacture of a functional bicycle (see Sections 6.2-6.10 and APPENDICES C and D).
1.3 The Bicycle as an Mechanical Engineering Application
The modern bicycle experiences all modes of mechanical forces, both static and dynamic, see
Figures 1.3.1 and 1.3.2. As a result, the frame of a bicycle experiences all modes of structural
stresses at some point during its use; this makes it an excellent application for examining a
structural material.
Figure 1.3.1 and 1.3.2 show a model of a conventional double triangle truss frame and critical
force bearing components (see Section 6.2). The model has been developed for Finite Element
Analysis (see Section 6.3 and APPENDIX B), and is used in Figures 1.3.2-1.3.3 to illustrate
the modes of forces that a bicycle experiences during normal seated use.
When seated but exerting no propulsive pedalling force, the rider’s acceleration under gravity
causes their mass to exert a static downward force on the saddle, handlebars and pedals. As
a result, an equal upward force is generated from the ground on the tyre contact patch that is
translated through the bicycle. This places the truss members in either compression or
tension according to their position in the frame.
Figure 1.3.1Forces experienced by a bicycle when in a situation analogous to Newton’s First
Law with the rider seated
The forces illustrated in Figure 1.3.1 are always experienced when the rider is mounted
(unless airborne), and vary in their ratios between the components depending on the riding
situation and gradient. They have been excluded unless essential from Figure 1.3.2 for
clarity.
Normal ReactionForce
Force Exerted by
Rider

4
Figure 1.3.2 demonstrates pedalling considered statically at the point where the rider places
an unequal force on one pedal. A bending moment results about the bottom bracket. The
rider anchors this application of force by pulling upwards on the handle bar on the same side
whilst also pulling on both handlebars towards the saddle; this creates a torsion couple about
an axis through the frame. The force also creates tension in the chain (or belt) which
compresses the seat stay on the drive side of the rear of the bicycle and creates a bending
moment about the seat tube.
Figure 1.3.2 Forces, moments and couples experienced by a bicycle when the rider applies a
propulsive pedal force to the left pedal resulting in forward acceleration
The action of pedalling is cyclic, placing unequal forces on the pedals alternating from one
side to the other, this creates dynamic forces, bending moments and torsion couples within
the frame. These presents a considerable challenge for a bicycle designer as the stresses
generated can cause fatigue in the bicycle frame and components, leading to failures.
This analysis forms the basis of the design of the reinforced cardboard forms and their
construction into a prototype bicycle frame and forks (see Section 6.2-6.10 and APPENDICES
B and C), the ultimate goal of this project.
2. Project Aim
The aim of this project is to investigate an existing form of cardboard available on the
consumer market, by testing and developing it as a structural material; the intended
application being the construction of a prototype bicycle frame and forks.
3. Objectives
3.1. Quantify the mechanical properties of cardboard tubes through laboratory testing
and attempt to classify their modes of failure in order to qualify their suitability for
development as bicycle frame and forks construction materials.
Torsion
Bending Moment
Acceleration
Friction

5
Progress: Unconfined compressive strength tests have been performed on cardboard tubes,
results are shown in Section 6.1 and APPENDIX A.
3.2. Using structural reinforcing elements, improve the mechanical properties of
cardboard tubes in order to improve their suitability as a structural material for constructing
a prototype bicycle frame and forks.
• Design, Construction and Testing of Composite materials incorporating combinations
of cardboard forms, with cardboard tubes as the principal component
Progress: Reinforced cardboard forms have been designed and produced with improved
mechanical properties (see Section 6.4), tested (see Section 6.1 and APPENDIX A) and
applied to the construction of a prototype bicycle frame and forks (see Section 6.6-6.9 and
APPENDIX C).
3.3 Develop joints to connect the developed composite cardboard forms with sufficient
structural integrity to construct a prototype bicycle frame and forks.
Progress: Joints have been designed and manufactured, optimising their mechanical
properties for application being the construction of a prototype bicycle frame and forks (see
Section 6.5).
3.4 Design a prototype bicycle frame and forks using the materials and construction
techniques developed.
• Product Design Specification (P.D.S.) for a cardboard bicycle frame and forks.
• Finite Element Analysis (F.E.A.) of a bicycle model using generic data and BS EN
ISO 4210-6:2015 test requirements, to highlight areas exposed to higher stresses.
Progress: A P.D.S. has been produced, see APPENDIX D along with an F.E. model of a
bicycle frame with geometry matching that of the intended design, this has had Analysis
performed on it in line with generic data, and BS EN ISO 4210-6:2015 (see Section 6.3). From
these analyses a prototype bicycle frame and forks have been designed and manufactured.
3.5 Construct a prototype bicycle frame and forks using the materials and construction
techniques developed, in order that it may be tested to assess the frame’s integrity and the
suitability of cardboard as a bicycle frame material.
• Development of construction techniques specific the developed cardboard forms.
• Manufacture of a jig for construction, to control and evaluate the dimensions and
angles of the constructed frame.
• Health and Safety Risk Assessment for all construction processes and methods.
Progress: Construction techniques specific to using the developed cardboard forms have been
developed (see Section 6.4-6.9 and APPENDIX C).
A jig has been constructed, allowing the dimensions and angles of the frame to be controlled
during construction (see Section 6.6).
A prototype bicycle frame and forks have been manufactured using the materials and
construction techniques developed (see Section 6.4-6.9 and APPENDIX C).

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3.6 Analyse and test the completed prototype bicycle frame, and demonstrate its
performance in comparison to existing bicycle frames.
• Quality Assurance and Quality Control (Q.A.Q.C.) in the form of a dimensional
analysis of the final bicycle frame and an evaluation of the uniformity and applicability of the
final materials.
• Laboratory testing of the final bicycle frame in line with the industry standards.
• Final proof test to ride the bicycle.
Progress: The bicycle frame and forks have been dimensionally analysed (see APPENDIX
D)and the uniformity and applicability of the final materials evaluated.
Laboratory testing of the prototype bicycle frame has not been possible, discussed in Section
6.10 and Section 7.
The prototype bicycle has not been ridden due to schedule overruns, however it will be ready
prior to the presentation of this project on 13th June 2016, and providing it passes elementary
safety evaluation it will be ridden in a demonstration.
3.7 Evaluation of the project
• Evaluation of the materials developed their applicability to building a bicycle frame
and the possibility of use as structural products suitable for other parts and applications.
• Evaluation of the design process.
• Evaluation of the project management process.
• Evaluation of the final product
Progress: The project has been evaluated and the results are discussed in Section 7. and 8.
4. Deliverables
The deliverables for this project will be demonstrated at the presentation on 13thJune 2016 or
submitted prior in accordance with predetermined deadlines, they consist of the following
 Final Project Report
 Supervisor Meeting Record
 Health and Safety Risk Assessment
 Bicycle Frame Construction Jig
 Laboratory Testing Samples
 Cardboard Development Examples
 Prototype Bicycle Frame and Forks
5. Technical Background
5.1 Bicycle Frame Materials
Since the invention of the “Rover Safety Bicycle” by John Kemp Starley in 1885 metals have
been the optimum material choice of the bicycle frame designer. Metals have many

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advantageous characteristics for building a bicycle frame: High Tensile Strength, High
Young’s Modulus, High Malleability and Ductility, and the ability to be Brazed or Welded.
Bicycle frames and components undergo considerable forces, most significantly in the forms
of torsion and bending moments, which impart high stresses to localised areas of those
components (Dwyer F. et al. 2012). A material with a high tensile strength allows a safe,
strong structure to be realised capable of withstanding those stresses without failing.
Figure 5.1.1 Left, The Rover Safety Bicycle - Right, The Lu-Mi-Num
A high Young’s Modulus permits a stiff frame to be constructed that does not deform
excessively from loads the rider places on it, effecting efficient transfer of the rider input
forces and giving predictable handling traits.
Malleability, ductility and the ability of metals to be brazed or welded all facilitate the
manufacture of bicycle frames and components. Malleability and ductility enable metals to be
formed into useful shapes, especially the drawing or extrusion of tubing, which has been the
staple of bicycle manufacture since the 1880’s. Brazing and welding are exceptionally
efficient means by which to joint materials, and if realised properly can be as strong as the
principal material itself.
Today steel accounts for 85-90% (David Lundy, 1994) of bicycle frames, other materials
include titanium, carbon fibre and predominantly aluminium. Despite the first aluminium
bicycle frame being built in 1896, the Lu-Mi-Num, aluminium bicycle frame production did
not become more widespread until the 1980’s.
Prior to the 1980’s manufacturers who had tried to use the material had merely tried to
imitate the design of steel frames leading to overly compliant frames, which tended to fail
under the principle forces experienced due to fatigue. Aluminium is far less fatigue resistant
than steel as discussed by Dwyer F et al. (2012), having a proportionally lower fatigue
strength relative to other strength characteristics. Aluminium alloys generally harden with
age, a characteristic that is exploited by solution heat treatment. Solution heat treatment
improves the materials tensile strength, however it can also make the material more brittle
and prone to stress fracturing through fatigue. When exposed to the environmental elements
of variable temperature and humidity whilst being dynamically stressed, aluminium can
naturally age and harden.
During the late 1970’s Gary Klein an American chemical engineer developed a number of
techniques allowing aluminium to be applied proficiently as a bicycle frame material, one of
the most significant of which was making frames from larger diameter tubes.

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5.2 The Advantage of Larger Diameter Tubes
The Second Moment of Area or Moment of Inertia for a Tube: Equation 5.2.1
𝐼 =
𝜋𝑟𝑜
4
4
−
𝜋𝑟𝑖
4
4
When applied to the Bending of a Beam: Equation 5.2.2
𝛿 =
−𝑃𝐿3
48𝐸𝐼
The Polar Moment of Inertia: Equation 5.2.3
𝐽 =
𝜋𝑟𝑜
4
2
−
𝜋𝑟𝑖
4
2
When applied to the Torsional Deflection of a Shaft: Equation 5.2.4
𝜃 =
𝑇𝐿
𝐽
The Area for a tube: Equation 5.2.5
𝐴 = 𝜋𝑟𝑜
2
− 𝜋𝑟𝑖
2
When applied to the Compression or Extension of a Member: Equation 5.2.6
𝛿 =
−𝑃𝐿
𝐸𝐴
The Volume of a Tube Wall: Equation 5.2.7
𝑉 = ( 𝜋𝑟𝑜
2
− 𝜋𝑟𝑖
2) 𝐿
These formulae show that doubling the radius of a tube with constant length, whilst
maintaining the same volume of material in the wall will have no effect on the weight or
compressive strength of the tube, it will however quadruple the tubes ability to resist torsion
or bending moments. In a truss structure such as a bicycle frame, this increases the overall
stiffness of the structure, improving its resistance to displacement and deformation under
load.
Chart 5.2.10 uses Equations 5.2.1 to 5.2.8 to demonstrate a matched increase in stiffness of
6061 T6 aluminium and 4130 Cromoly steel tubes, with increasing tube outer diameter
between 25 and 38 mm.
Stiffness Coefficient used in Chart 5.2.10: Equation 5.2.8
𝑆𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 ( 𝛾) = 48𝐸𝐼
This data is normalised relative to the mass per unit length of 4130 Cromoly steel, with a
resulting mass per unit length for 6061 T6 aluminium until a wall ratio of 60:1 is reached for
steel.

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Wall Ratio and Slenderness Ratio Equation 5.2.9
𝑊𝑎𝑙𝑙 𝑅𝑎𝑡𝑖𝑜∗
(𝜑) =
𝑇𝑢𝑏𝑒 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠
=
𝑑
𝑡
=
2𝑟𝑜
(𝑟𝑜 − 𝑟𝑖 )
∗ 𝑇𝑒𝑟𝑚𝑒𝑑 𝑊𝑎𝑙𝑙 𝑅𝑎𝑡𝑖𝑜 𝑡𝑜 𝑎𝑣𝑜𝑖𝑑 𝑐𝑜𝑛𝑓𝑢𝑠𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝑆𝑙𝑒𝑛𝑑𝑒𝑟𝑛𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜
𝑆𝑙𝑒𝑛𝑑𝑒𝑟𝑛𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜( 𝜆) =
𝑇𝑢𝑏𝑒 𝐿𝑒𝑛𝑔𝑡ℎ
𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐺𝑦𝑟𝑎𝑡𝑖𝑜𝑛
=
𝐿
𝑅
=
𝐿
√ 𝐼/𝐴
A 60:1 wall ratio is considered critical in bicycle manufacture (Nichols S, 2015) and other
tubular structures. For example, El-Reedy M. (2012) in his textbook “Offshore Structures:
Design, Construction and Maintenance” cites 60:1 as the threshold design safety limit for
fixed tubular steel structures. Whereas, BS EN ISO 19902:2007 - Petroleum and natural gas
industries - Fixed steel offshore structures, 80:1 is considered the maximum safe limit;
however through experiment in “Uncertainty quantification and risk assessment of offshore
structures,” Obisesan A. (2012) showed that 50:1 is a more practical limit.
This 60:1 ratio appears to be independent of material properties (assuming material
homogeneity), as the finite element simulations of Pled F. et Al. (2007), and work carried out
by National Advisory Committee For Aeronautics (1947) and National Aeronautics and Space
Administration (1970) on Aluminium tubes demonstrates. Homogeneous materials appear to
converge at this ratio as the mode of buckling transitions from an axisymmetric concertina
mode for ratios <40:1 through a transitional 40:1>60:1 where mixed modes can occur, to
>60:1 beyond which Euler and Multi-nodal Shell, or Diamond buckling occur. Singer J. et Al.
(2012) confirm this experimentally.
Referring back to Chart 5.2.10 ,the trend for aluminium is continued beyond 38mm matching
the ultimate stiffness and maintaining tensile tube strength greater than or equal to that of
4130 steel at 38mm until the same 60:1 ratio is reached for aluminium. This shows that
aluminium tubes with larger diameters are capable of matching and even exceeding the
strength and stiffness of steel tubes, whilst saving considerable weight. To illustrate these
trends visually, scale models of aluminium and steel tubes, generated in SolidWorks, are
superimposed over the chart
This demonstration and Equations 5.2.1-5.2.7 have significance in the development of
cardboard as a structural material in Sections 6.4-6.9:
 Tensile and Compressive Strength of a structural member can only be increased by
increasing the axial surface area of the member.
 Resistance to Bending Moments and Torsion can be increased by increasing the
moment of inertia of a member.

A2
0
100
200
300
400
500
600
700
800
900
1,000
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
20 25 30 35 40 45 50 55
MassPerUnitLength[kg/m]
StiffnessCoeficient[Pam4]
Tube Outer Diameter [mm]
Steel Stiffness Coefficient [Pam^4] Aluminium Stiffness Coefficient [Pam^4]
Steel Mass per Unit Length [g/m] Aluminium Mass per Unit Length [g/m]
Steel Critical Buckling Ratio, Outer Diameter to Wall Thickness 60:1
6061 T6
Aluminium
4130
Cromoly
Steel
Chart 5.2.10 the relationshipbetween Stiffness and Mass per Unit Length for 4130 Steel and 6061 T6 Aluminium Tubes with increasing
outer diameters. All data sourced from Aerospace Specification Metals Inc

10
5.3 Why Build a Bicycle from Cardboard?
Cycling is a non-pollutant transport means that “offers people a route out of poverty and a
means to improve their lives, giving them opportunities to travel to work and school, giving
small scale farmers and traders the opportunity to reach customers further afield, or take
more produce to market” (Alexei Sayle, circa 2000).
Table 5.3.1 shows 3 environmental factors associated with the production of raw materials.
Steel and Aluminium production are extremely energy intensive and polluting compared to
Cardboard production. The water consumption figures include water usage figures in
brackets, these show metal production has become more efficient at treating and reusing
water than the paper and pulp industry.
It is notable that these figures are for the production of virgin material from its naturally
occurring state, and not recycled material. The gains in using recycled materials are similar
across the board, saving approximately 60% of the energy and CO2 production, as extracting
the raw material from its naturally occurring state accounts for much of these figures.
Global Steel
Production
Global
Aluminium
Production
Global Paper
and Board
Production
Energy Consumption
[kWh/tonne]
4500 14000 12
Water Consumption
[m3/tonne]
3 (28) 1 (26) 10(25)
CO2 and Equivalents
Production [tonne/tonne]
0.9 9.2 0.4
Table 5.3.1 Environmental Impact of Primary Cardboard versus Primary Metal
Production
Bicycles are produced using higher-grade alloys from virgin material. Cardboard is currently
produced using an average of 60% recycled material, and it is possible to create products with
up to 100% recycled material, although it is optimal to use approximately 15% virgin
material in order to maintain strength characteristics (IEA, 2007).
Table 5.3.1 does not tell the whole story of modern high-end bicycle frame production, where
the environmental impact of raw material production is compounded significantly using
further energy intensive manufacturing processes including welding and heat treatments.
Table 5.3.2 presents a manufacturer’s figures for the production of two high-end bicycle
frames. It is notable that these are figures per kilogram of frame production, with typical
frame mass of approximately 1 kilogram. The figures take into account the entire process
from raw materials in their naturally occurring state to final product.

11
Specialized
Roubaix
Carbon Fibre
Specialized
Allez
Aluminium
Energy Consumption
[kWh/kg]
420 1600
Water Consumption
[m3/kg]
2.2 1.5
CO2 and Equivalents
Production [kg/kg]
65 170
Table 5.3.2 Environmental Impact of Production of 2 High End Bicycle Frames
Assuming all 430 million bicycle owners in China (Brown, L., 2009) decided to upgrade to an
aluminium bike similar to the Specialized Allez it would consume 688 [TWh] of energy, 22
times China’s total annual electricity output for 2012 (IEA, 2013). The CO2 emissions for each
individual would be equivalent to driving a new car 1360 [km], 10% of the average Chinese
driver’s annual mileage (Huong Huo et Al. 2012).
Cardboard, or paperboard as it is more correctly termed, is a widely used consumer product
mainly used in the packing and shipping industry. It is widely available in all regions, can be
manufactured from a sustainable resource, trees, and is 100% recyclable. It is also
biodegradable, and can be burnt to create energy at the end of its lifecycle; in fact many
cardboard production facilities in Canada are now net Energy producers (IEA, 2007).
Producing bicycles from cardboard will utilise an existing inexpensive recycled product and
re-appropriate it for use in the construction of a new product that can then be implemented
as a non-pollutant transport means.
5.4 Is Cardboard Suited to Building A Bicycle?
As mentioned in Section 1, cardboard has a number of characteristics that make it well
suited to use as a packing and packaging material.
Printable
Whilst not a structural advantage, it may be a desirable attribute for the production of a
bicycle, enabling graphics and possibly advertising to be applied to a bicycle quickly and
inexpensively with existing equipment. An end user may even be able to customise their
bicycle at no extra cost.
Reusable and Recyclable
These are considered sustainability advantages, which make them desirable but non-critical
attributes for a structural material; however in many industries regulations governing
certain regions dictate that materials must achieve an certain level of sustainability.
Inexpensiveto Manufacture
Cardboard is mass produced from Pine trees, an inexpensive, sustainable raw material,
renewable through replanting, that is produced on equivalent scales to steel and aluminium..

12
Trees are felled and processed in a pulping mill into wood pulp, a fibrous material. The pulp
is processed in a rolling mill into Kraft paper rolls and further processes by various methods
into the different types of cardboard (see Figure 1.2.1)
Corrugated Cardboard is made by passing Kraft paper through a corrugating machine which
folds the paper into its rounded wave, or fluted form. Corrugated paper layers are then
layered up with flat liner layers and glued together with a corn starch adhesive (Kline J.
1991). This process is facilitated by high pressure steam.
Honeycomb Cardboard is made in a similar way to corrugated cardboard, Kraft paper is
passed through a continuous honeycomb core machine which cuts adheres and folds the
paper into an expandable hexagonal form. This honeycomb core layer is then laminated up
with flat liner layers on both sides, and glued together in a laminating machine.
Cardboard Tubes are produced in a continuous process using a tube laminating machine.
Multiple Kraft paper strips are passed through an adhesive bath and over tensioning rollers
before being wrapped under pressure by a Mobius belt over a mandrel. The continuous tube
passes through a series of cutters that move longitudinally along the tube as it is cut to the
required lengths without interrupting the process.
Mechanical Strength
Mechanical strength is an essential structural characteristic and vital in the manufacture of
a bicycle.
Equations 5.2.1-5.2.7 show Young’s Modulus E, to be a critical value for structural materials,
denoting its ability to resist stress whilst exhibiting elastic behaviour. A high Young’s
Modulus, high Ultimate Tensile Strength and high Yield Strength are all essential
characteristics of a good structural material.
Two groups, one based in Sweden and the other France have made a number of
investigations into the mechanical properties of Corrugated Cardboard. The French studies
of Allaoui S. and Aboura Z. (with collaborators in 2004, 2008 and 2009) result in data for
Young’s Modulus of Kraft paper of 8.5 [GPa] in the fibre biased direction, a feature
introduced by the rolling practice during manufacture with 3.5 [GPa] in the lateral direction.
The Ultimate Tensile Strength in the fibre biased direction is 40 [MPa], with a Yield at 28
[MPa]. The data agree with the Swedish studies of Nordstrand T. and Nyman U. (with
collaborators in 1997, 2000 and 2004), although they achieved Ultimate Tensile Strength as
high as 85 [MPa]. This makes raw Kraft paper approximately 25 times less stiff than 4130
Cromoly steel and 15 times weaker (10 times less stiff than 6061-T6 aluminium and 8 times
weaker).
Allaoui S. and Aboura Z. (with collaborators in 2004, 2008 and 2009) give values of 630 -850
[Mpa] for the Young’s Modulus of a single “C” fluted constructed board in the Machine
Direction (running along the flutes), and 430 – 550 [MPa] in the Cross Direction (across the
flutes). Tensile Strength results were obtained of 5 [MPa] and a Yield of 2.5 [MPa] of a single
“C” fluted constructed board in the Machine Direction, and a Tensile Strength of 2.9 [MPa]
and a Yield of 1.8 [MPa] in the Cross Direction.
There is very little data available on the mechanical properties of cardboard tubes, therefore
part of this project has been dedicated to investigating these properties, see Section 6.1.
These tests are limited in scope to obtain data for completing the objectives of this project,
however they could form the basis of further research.

13
Low Density
Kraft Paper’s density according to the Scandinavian Pulp, Paper and Board Testing
Committee 2001 is 790 [kg/m3] making it approximately 10 times less dense than 4130
Cromoly steel and 3.5 times less dense than 6061-T6 aluminium.
A high grade Kraft paper single “C” fluted constructed board has a quoted mass per unit area
of 300 [g/m2] (Teakcroft, 2016), with a thickness of 4.1mm (Allaoui S. et al., 2009) this
equates to a density of 73 [kg/m3] equating to 107 times less dense than 4130 Cromoly steel
and 37 less dense than 6061-T6 aluminium. Taking the data above, corrugated cardboard
has a strength to weight ratio on a par with steel 4130 Cromoly steel and 6061-T6
aluminium.
Given the favourable strength to weight ratio data, it should be possible to use cardboard to
create a structural material capable of making a bicycle frame and forks.
5.5 Cardboard’s Limitations
It is worth considering cardboard’s limitations that affect its suitability as a structural
material. These are all considerable issues when considering the manufacture of a prototype
bicycle frame and forks.
Moisture
Cardboard is susceptible to water (see Section 6.8), being a composite of fibres and a bonding
agent, starch. Untreated it will degrade and eventually dissolve if immersed in water.
Exposed to high humidity cardboards structural characteristics degrade. Allaoui S. et al.
(2009).
Fatigue
As non-homogeneous composites, cardboard forms are susceptible to anisotropic fatigue and
cyclic hysteresis where accumulative strain can cause degradation of the composites
structure, causing premature failure at a much lower stress than anticipated. (Chawla,
Krishan K. 2012 and Singer J. 2002)
ManufacturingDefects
Cardboard is an inexpensive mass produced material used in non-critical applications such
as packing boxes, with redundancy built into their structure. Whilst standards for QAQC
procedures and mechanical properties tolerances are implemented, they are not as stringent
as those employed during the manufacture of critical structural materials. Structural
materials undergo strict QAQC procedures, even to the point of CT scanning the materials
for defects at the molecular level.
Manufacturing defects could cause unexpected or premature failures despite good design
practices.

14
6. Technical Approach
6.1 Laboratory Testing of Cardboard Tubes
Figure 6.1.1 GDS Instruments 50 [kN] compressive load frame setup for a test with
cardboard tube aligned and checked.
Laboratory Testing Results and Charts
Apparatus
A 50 [kN] capacity, servo actuated ball screw, compressive load frame with spherical seat and
10 [kN] S-beam type load cell are used to apply axial loads to the cardboard samples. A GDS
logging interface and a PC equipped with GDS Lab software are used to control and record
the tests.
A calibrated steel ruler and Mitotoyu digital callipers are used to measure the sample
dimensions, and align the samples.
A calibrated engineer’s spirit level is used to check the load frame is level.
ExperimentalProcedure
The test window of the load frame is first adjusted to a suitable height for the samples under
test. The load frame is then aligned, levelled, and connected to the logging interface.
The load cell is attached with a spherical seat, a flat ground Perspex loading plate is
attached, and the cell wired up to the logging interface.
The logging interface is connected to the computer, and the correct calibration factors entered
into the control/logging software.
A test plan is prepared for each type of test:

15
For the initial test on each sample type, a series of 3 stress cycles within the elastic region
and then a ramp to failure are programmed as 7 separate ramp stages:
1. Ramp up within elastic region at 0.5 [kN/minute] and hold for 1 [minute] (normally
accounts for bedding in of the sample)
2. Ramp down 0.5 [kN/minute] and hold for 1 [minute]
3. Repeat 1. and 2.
5. Repeat 1. and 2.
7. Ramp to failure at 1 [kN/minute] (limited by load cell to 10 [kN]
Further repeat tests on each sample type, are ramped to failure in a single stage:
1. Ramp to failure at 1 [kN/minute] (limited by load cell to 10 [kN])
The tests are ended before total failure of the samples due to the angular deviation exceeding
a practicable limit of approximately 5°.
Notes:
Sample types A and E through F were all sourced from a single supplier (CT).
Sample types B through D are recycled architectural bond paper roll cores from another
supplier (HP).
Sample types C and D have been modified as outlined in Section 6.4 Tube Development, with
ribs and stringers. Both have four 5.2 [mm] thick stringers, C† has 5.2 [mm] thick radial ribs
at 20 [mm] spacing, whereas D†† has 5.2 [mm] thick ribs at 10 [mm] spacing. Table 5.1 forms
a summary of unconfined compression tests on cardboard tubes, charts can be found in
APPENDIX A relating to these results.
Sample types A and E through F were all sourced from a single supplier, Cores and Tubes
(CT), Croydon.
Sample types B through D are recycled Hewlett Packard (HP) architectural bond paper roll
cores.
Sample types C and D have been modified as outlined in Frame Construction with ribs and
stringers. Both have four 5.2 mm stringers, C† has 5.2mm ribs at 20mm spacing, whereas D††
has 5.2mm ribs at 10mm spacing.

16
Results
Sample
Number
Tube O.D.
[mm]*
Tube I.D.
[mm]*
Young’s
Modulus [GPa]
0.02% Yield
Stress [MPa]
Ultimate
Compressive
Stress [MPa]
A1 34 26 1.18 4.2 6.32
A2 34 26 NA 5.28 6.25
A 34 26 1.18 4.74 6.29
B1 55 51 1.56 5.90 8.46
B2 55 51 NA 6.80 9.27
B3 55 51 NA 4.15 5.50
B4 55 51 NA 7.30 10.63
B 55 51 1.56 6.04 8.47
C1† 55 51 1.54 5.96 9.88
D1† † 55 51 1.28 9.55 10.32
E1 50 45 1.38 4.72 6.22
E2 50 45 NA 4.65 6.50
E 50 45 1.38 4.69 6.36
F1 34 26 1.04 2.36 5.35
F2 34 26 NA 3.37 6.18
F 34 26 1.04 2.87 5.77
Table 6.1.2 Summary of results from unconfined compression tests on cardboard tubes
Table 6.1.2 forms a summary of unconfined compression tests on cardboard tubes. A
complete set of charts can also be found in APPENDIX A relating to these results, along with
photos of tested samples.
Discussion
Chart 6.1.3 illustrates the combination of modes of failure by which cardboard tubes fail
under axial compression throughout a 1 [kN/min] load ramp. All tested samples of types A-E
failed in the sequence indicated:
1. Yield caused by lateral delamination of the paper layers creating a larger effective
surface area, and stabilising the structure temporarily as load increases.
2. The sample shears at an embedded seam like spiral manufacturing flaw between the
helical windings.
3. The sheared section causes the tube to destabilise and the load deviates from acting
axially causing the tube to buckle inelastically, kneeling to one side.

A3
Chart with Figure 6.1.3 Typical Stress – Strain response of a spiral wound cardboard
tube to 1kN/min load ramp to failure
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02
Stressσ[MPa]
Strain ԑ
B2
0.2% Line
1
2
31
2
3

A4
Chart 6.1.4 Typical Stress – Strain response of a spiral wound cardboard tube to 0.5kN/min
elastic load ramp cycles on sample A1.
Chart 6.1.5 Comparison of Stress – Strain response of spiral wound cardboard tubes with
differing levels of reinforcement to 1kN/min load ramp
y = 1,172,857,758x - 627,996
R² = 1
y = 1,184,031,804x - 686,938
R² = 1
y = 1,192,005,217x - 730,087
R² = 1
0
0.2
0.4
0.6
0.8
1
1.2
0 0.0005 0.001 0.0015 0.002
Stressσ[MPa]
Strain ԑ
Stress V Strain
Linear (Stage 3
Ramp)
Linear (Stage 5
Ramp)
Linear (Stage 7
Ramp)
"Bedding
inof sample"
3 "Elastic"ramps
to ensure
repeatable
Young'sModulus
Trendline Equations
Hysteresis
A1
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02 0.025
Stressσ[MPa]
Strain ԑ
B2
0.2% Line
C1
0.2% Line
D1
0.2% Line

17
The only exception to this sequence were the type F samples which had a slenderness ratio
( 𝜆) of approximately 10:1, double any of the other tubes which all had a slenderness ratio
( 𝜆) of approximately 5:1, and a wall ratio (𝜑) of 6:1 versus 9:1 respectively. It was noted
during the F sample tests that the tubes began kneeling outward before yielding by local
delamination of the paper layer construction. This occured on the side of the end face toward
which the tube was kneeling as it came under increasingly bias load. There was very little
spiral winding seam shear.
Chart 6.1.4 demonstrates the typical response of a
spiral wound cardboard tube to the initial
0.5kN/min load cycles. The first cycle forms a
“bedding in” phase, where any irregularities in the
cardboard tubes cut edges at both ends are loaded
and the surfaces flattened. When the sample is
then unloaded and reloaded in the second cycle it
behaves in a more conventional elastic manner
forming a straight line Stress versus Strain
response. This process is repeated to enable a
repeatable mean value for Young’s Modulus to be
obtained. A small hysteresis and a slight
hardening of the sample is produced between
cycles, evident from the progressively increasing
gradient of trendlines; however this is an limited
effect of less than 1%.
Figure 6.1.6 Tested cardboard samples; Left to
Right - B2, C1, D1
A notable result is that not all cardboard tubes are
made equal, the HP tubes have superior mechanical properties to the CT tubes; they are
approximately 50% stiffer and stronger. The tubes intended for use in the construction of a
bicycle frame and forks are the CT tubes, CT is very kindly supplying the tubes free of charge
(FOC) in production line lengths, which are longer than cut down commercially available
lengths.
The CT tubes result in the following mechanical properties, which are used to develop the
bicycle frame and forks in Sections 6.2-6.7:
Young’s Modulus = 1.2 [GPa]
Yield Strength = 4.7 [MPa]
Ultimate Compressive Strength =6.3 [MPa]
Chart 6.1.5 compares the Stress versus Strain response of tube types B, C and D. Types C
and D have been modified as outlined in Section 6.4. As predicted, the small amount of axial
surface area added to the tubes cross section in samples C1 and D1 has increased the axial
mechanical properties. The Young’s Modulus has not changed significantly as the material
composition has not been altered; however a 60% increase in Yield Strength and a 20%
increase in Ultimate Compressive Strength have been achieved in the most reinforced D1
sample. Most interesting is the nature by which this appears to have occurred.

18
Studying the samples in Figure 6.1.6 it is evident that the less reinforced sample C1 failed in
the same manner as B2 delaminating and buckling at one end through an embedded spiral
flaw; D1 however failed by spirally delaminating along the entire length of the tube at every
seam. It can be concluded that rib and stringer reinforcements have stabilised the tube along
its length, preventing failure at an isolated weak point, most likely a manufacturing defect.
This allowed the full potential strength of the tube to be realised.
6.2 Frame Design
Existing Frame Designs
The earliest bicycle frames were of the simple beam design, which has become more popular
recently with the uptake of foldable bicycles for commuters. The Lotus bicycle that Chris
Boardman won an Olympic Gold Medal and broke many world records on is a Z or S-beam
variation of this design.
Ever since its perfection in the late 1880’s the double triangle or diamond truss design has
been the design of choice for bicycle manufacturers. This is due mostly to the sound
engineering of a triangle truss, where forces are transmitted in “straight lines” along the
tubes, which reinforce each other, spreading the load through the “incompressible” triangular
structure efficiently.
These 2 predominant design types are quite often combined, with a beam bridging the head
tube and seat tube, and a triangle truss connecting the rear wheel to the seat tube. The other
significant category in terms of numbers is the Monocoque. Most monocoques could be
classed as a variation on a beam structure; however they
are normally formed as a complex single element
designed in its entirety with radically varying material
thicknesses throughout.
Another interesting design, the Moulton Space Frame,
which formed the basis of one of the fastest bikes to have
been designed; and is now outlawed in competitive
cycling along with Z or S-beam designs.
Figure 6.2.1 Moulton Speed

19
Emphasis in this project is placed on designing a double triangle truss frame with cardboard
tubes. There are many reasons why the double triangle truss has been the staple of bicycle
designs for 140 years, including the fact that it is forced upon the designers of competitive
bicycles by the UCI, cycling’s governing body, however it remains a design classic and lends
itself well for static and dynamic analyses.
Geometry
There are a number of different factors to take into account when designing a bicycle. For
example, there are at least six different commercially available wheel sizes, 650c, 700c, 26”,
27.5”, 29”, not including folding or children’s bicycles. Due to budget constraints on this
project a selection of donor parts will be used, constraining the frame design. These are listed
in APPENDIX D.
There are a number of dimensions and angles formed by a bicycle frame and forks that
directly affect the handling and comfort of a bicycle, typical values are summarised in Table
6.2.3.
Figure 6.2.2 Critical frame dimensions affecting bicycle handling with the proposed values
for a cardboard frame.
1. Seat Tube Angle – A steeper seat tube angle shortens the top tube and opens the rider’s
hip angle. When incorporated with dropped handlebars, this places the rider in a more
forward position laid over the bicycle favoured by road and track cyclists. Conversely, a
shallower angle lengthens the top tube and closes the rider’s hip angle. This forces the
rider into an upright position favoured by mountain bikers and leisure cyclists, often
encouraged by a shorter stem and upward swept handlebars. Another effect of a shallower
seat tube angle is the shortening of the seat stays, this makes for a stiffer more responsive
rear end when pedalling and steering
2. Head Tube Angle – A steeper head tube angle creates more responsive steering that
requires a smaller input force to change the front wheel angle; racing road bikes often
have a very steep head tube angle, to make them feel light, agile and responsive.
Conversely, a shallower angle creates a heavier, slower, less edgy steering response
favoured by mountain bikers and leisure cyclists.
3. Trail – Has a more significant effect on steering response than head tube angle. A bicycle
can be leaned into a turn, moving mass over to one side of, and creating a radius between
the front and rear tyre contact patches. The bicycle will naturally follow this radius.
BBdrop
Trail
Seat Tube
Angle Head Tube
Angle

20
Trail is the term used for the offset between the tyre to ground contact patch and a line
projected along the head tube and forks to the ground. Less trail creates a lighter, more
nervous feel, whereas increased trail creates a more stable, but heavier feel that will tend
to self-centre the steering angle when the bicycle is upright and moving forward.
4. Bottom Bracket Drop –A lower bottom bracket places mass below the wheel axles creating
a more stable, “on rails” feeling when the bicycle is leant over while cornering. It takes
less effort to lean the bicycle creating a more agile, responsive feel. A higher bottom
bracket raises the overall centre of gravity, when cornering this requires more effort to
lean the bicycle into a corner, and creates a less stable feel.
Too low a bottom bracket restricts pedalling when cornering and the irregularity of
terrain over which the bicycle can be ridden.
Bicycle Type Seat Tube Angle
[°]
Head Tube
Angle [°]
Trail [mm] Bottom Bracket
Drop [mm]
Road Racing 72-76 70-74 40-70 50-70
City/Touring 70-74 70-72 60-80 50-80
Mountain Bike 70-74 66-72 60-100 10-50
Downhill
Mountain Bike
66-70 64-68 75-150 (-50)-25
Table 6.2.3 Typical ranges of critical bicycle geometry values
Ergonomics are the most important consideration in bicycle geometry, as the rider may have
to be seated and pedalling for prolonged periods. A number of different bicycle types have
been mentioned, all with different objectives. The riding position of any bicycle should be as
comfortable as possible taking into account these objectives. People range in a number of
metrics that effect bicycle design, height, leg length and arm length and foot size being
among the most important.
Before carrying out any structural analysis, a generic bicycle double triangle truss frame to
establish the geometry of the proposed design has been modelled in SolidWorks. (see Figure
6.2.4 APPENDIX C). The proposed geometry suits a rider 175 cm to 185 cm and places the
rider in a neutral position typical of that of a city hybrid bicycle or mountain bicycle.
6.3 Finite Element Analysis
A generic frame and forks assembly have been modelled in SolidWorks (see Figure 6.2.4
APPENDIX C). These form the basis of an FEA investigation involving a number of
simulations using input data from “Bicycle frame optimization by means of an advanced
gradient method algorithm” (L.Maestrelli, A. Falsini, 2008), data which is believed to
originate from “Forces applied to a bicycle during normal cycling”. Journal of Biomechanics
12, 527-541 (Soden, P. Adeyefa, B. 1979), although it is not clearly cited.
Further input data is calculated from the test parameters for evaluating bicycle frames and
forks in “BS EN ISO 4210-6:2015 Cycles — Safety requirements for bicycles - Part 6: Frame
and fork test methods”. The principle of conservation of energy has been applied, and the
Work-Energy method has been applied to the drop test requirements in the “Falling Mass
Test” and the “Falling Frame Test” to calculate forces for static analyses. A 25% rebound has
been assumed, based upon videos available online of a selection of these tests.
This section forms a summary of the findings, and has been used as a tool for highlighting
the areas of most concern in the design of a cardboard bicycle frame and forks. Loading

21
details and results for each test can be found in APPENDIX B. These analyses have been
important in understanding the nature of stresses placed on a bicycle.
Figure 6.3.5 Resultant Von Mises Stress - GenericFrame and Forks Assembly- 6061
T6 Aluminium -Analysis 1 - Static Study - Seated Whilst Pedalling Right Pedal
From the analyses six main areas of concern have been identified, these are illustrated in
Figure 6.3.5 and numbered in order of severity:
1. Downtube - In every simulation, the area at the top of the downtube, just behind the
head tube encounters high stresses. This is a well-documented (Dwyer F et al. 2012)
area for fatigue failures in aluminium bicycle frames. The downtube is frequently made
a larger diameter and wall thickness to compensate for these stresses and is often
reinforced by means of a welded, shaped metal plate called a Gusset.
2. Bottom Bracket - In all pedalling simulations the bottom bracket area confronts high
stresses. This is another well-documented (Callens A., Bignonnet A., 2012) area for
fatigue failures in aluminium bicycle frames. The area behind the chain stays is often
reinforced with a CNC machined yolk to increase strength and stiffness.
3. Handlebars – Due to their nature to act as a lever, the handlebars endure high stresses
at their base; this is a serious concern in this project, as handlebar failures can cause
serious accidents, with severe consequences to the rider. There is a separate section of
BS EN ISO 4210 specifically for handlebars that is more commonly enforced by
governments than other sections
4. Seat Stays and Top Tube– When the rider is seated, the top of the seat stays and the top
tube encounter high instantaneous stresses when bumps or drops are negotiated by the
rider.
5. Fork Crown – The fork crown forms a junction between the members supporting the
front wheel and the frame, therefore it must communicate any load transfer between the
1
2
3
4
56

22
front wheel and the rest of the bicycle. This places high stresses on this area, even
during simulations where the principle forces are pedalling.
6. Chain Stays- The chain stay area around the rear dropout experiences high stresses
during static pedalling simulations due to the chain tension from the transfer of power
to the rear wheel.
There is an obvious commonality between these areas of high stress, they all occur near
junctions between members. This places extra emphasis on the design of joints in Section 6.5,
as they will be essential to the success of a prototype frame and forks.
Figure 6.3.20 shows an early simulation performed as an experiment, using the mechanical
properties to make a preliminary assessment of cardboard as a bicycle frame material. The
image shows three identical frames, except they are made of different materials
4130 Cromoly Steel 6061-T6 Aluminium CT-Cardboard Tube
Figure 6.3.20 Displacement [mm] of a generic bicycle frame under an asymmetrical pedalling
load of 1000N, simulating a static the BS EN ISO 4210-6:2015 Pedal Spindle Fatigue Test for
3 materials.
6.4 Tube Development
Through the literature review and cardboard tube testing, the mechanical properties
established show cardboard to be comparable to metals in yield strength and ultimate
tensile/compressive strength on strength to weight ratio basis. Therefore adding more
material, by increasing the wall thickness of tubes it is possible to make cardboard tubes
strong enough to build a bicycle frame. The Young’s Modulus of cardboard is proportionally
inferior to metals on a strength to weight ratio basis, so the resulting frame would suffer
from being too compliant.
Referring back to Equations 5.2.1-5.2.8 it is evident that there are two properties of a tube
that effect its resistance to both bending and twisting, these are Young’s Modulus (E) and the
Moment of Inertia (I or J). Young’s Modulus is a property inherent to the material itself, and
in this case remains fixed, so a method must be found to increase the Moment of Inertia of
the tubes.

23
One method, as shown in Chart 5.2.10 (see APPENDIX A) is to increase the tubes outer
diameter. Another method is to increase the distance between the inner diameter and the
outer diameter. The simplest way to do this is adding material is to make the wall thickness
greater. For a bicycle, this becomes impractical with the thicknesses required, as the mass
becomes too great: Calculation 6.4.1 compares the bending of a typical Aluminium 6061-T6
tube with a stiffness matched cardboard tube. The following assumptions have been made:
 Aluminium 6061-T6 has a Young’s Modulus of 68.9 [GPa], 57 times stiffer than
Cardboard at 1.2 [MPa] see Section 6.1.
 An typical Aluminium tube wall thickness for a 38 [mm] down tube can be as thin as 1.0
[mm] between butts (most of its length) (Columbus, 2014).
 For an equal displacement ( 𝛿) from two different materials, the stiffness coefficient( 𝛾) =
48𝐸𝐼 must be equal.
Equation 5.2.1 → Calculation 6.4.1
𝐼 𝑎𝑙𝑢𝑚𝑖𝑛𝑖𝑢𝑚 =
𝜋19[𝑚𝑚]4
4
−
𝜋18[ 𝑚𝑚]4
4
= 1.99 × 104
[𝑚𝑚4
]
Equation 5.2.2, assuming (P) and (L) remain constant →
∴ 𝛾 𝑎𝑙𝑢𝑚𝑖𝑛𝑖𝑢 𝑚 = 48 × 68.9 [GPa] × 1.99 × 104 [ 𝑚𝑚4 ] = 6.58 × 104
[𝑁𝑚2
]
∴ 𝐼 𝑐𝑎𝑟𝑑𝑏𝑜𝑎𝑟𝑑 =
6.58 × 104[ 𝑁𝑚2]
48 × 1.2 [GPa]
= 1.14 × 106 [ 𝑚𝑚4]
Increasing the cardboard tube outer diameter to a reasonable size of 70 [mm], considering it
must fit between the rider’s legs:
𝑟𝑖 = {
4
𝜋
(
𝜋35[𝑚𝑚]4
4
− 1.14 × 106
[𝑚𝑚4
])}
1
4
= 14.6[𝑚𝑚]
Therefore, a cardboard tube with a 70 [mm] outer diameter and a 29.2 [mm] inner diameter
would have the same stiffness coefficient ( 𝛾) as a typical aluminium bicycle downtube.
The mass per metre of these tubes for comparison would be:
𝜇 𝑎𝑙𝑢𝑚𝑖𝑛𝑖𝑢𝑚 = 𝜌𝑎𝑙𝑢𝑚𝑖𝑛𝑖𝑢𝑚 𝑉 = 2700[ 𝑘𝑔 𝑚3⁄ ]( 𝜋(19 × 10−3)2[ 𝑚] − 𝜋(19 × 10−3)2[ 𝑚]) × 1𝑚
= 0.314[ 𝑘𝑔]
𝜇 𝑐𝑎𝑟𝑑𝑏𝑜𝑎𝑟𝑑 = 𝜌𝑐𝑎𝑟𝑑𝑏𝑜𝑎𝑟𝑑 𝑉 = 790[ 𝑘𝑔 𝑚3⁄ ]( 𝜋(35 × 10−3)2[ 𝑚] − 𝜋(14.6 × 10−3)2[ 𝑚]) × 1𝑚
= 2.51[ 𝑘𝑔]
This would make the cardboard bicycle frame very heavy. The solution is to borrow principles
implemented on existing structural members to increase the moment of inertia whilst
minimising weight from other structures. A good example is an I-beam, which places the
majority of the material in the flanges, as far from the centroid of the cross-section as
possible, whilst remaining joined by as narrow a web so the beam may act as a single
member. Consideration was made of a number of ideas:

24
Figure 6.4.2 Early Development Ideas
Different shaped tubes are fashionable in
modern bicycles. Often they gain moment of
inertia benefits in one plane however; they
will always make a compromise in another
plane.
The chosen objective is to develop circular
profile cardboard tubes, increasing their
moment of inertia by joining a tube within a
tube using a honeycomb structure between
the two tubes.
Honeycomb structures are already used in
cardboard products (see Section 1), and have
been used in the development of spacecraft
and racing car chassis to create strong, stiff, lightweight structures. The assembly will have
the effect of creating a tube with a small inner diameter and a large outer diameter with a
fraction of the mass, and allow optimisation of the corrugated cardboard reinforcements flute
and Kraft paper machine direction orientations.
Figure 6.4.3 (see APPENDIX C) illustrates the design and manufacturing process of the
reinforced cardboard tubes for use in the bicycle frame:
1. From development sketches, profile drawings were created in AutoCAD, these were
transferred to the laser cutter.
2. After developing a custom laser cutting profile for cutting corrugated cardboard, ribs and
stringers were laser cut.
3. A working prototype reinforced tube was constructed, shown with a cutaway to
demonstrate the internal structure.
4. The prototype was evaluated, and deemed too heavy, so a model was developed in
SolidWorks for lightweight reinforced tubes for laboratory testing. The model was
broken down into rib and stringer profiles and laser cut using the methods learnt in
steps 1. To 3.
5. The method developed for assembly of the tubes in step 3. was improved, a method that
is carried through the project:
.
Figure 6.4.4 Final Bicycle Frame Down Tube, before shaping of reinforcement core.

25
Laser cut ribs and stringers are assembled, bonded together, then the inner tube is slid in
and bonded into the assembly, and finally the outer tube is slid over and bonded to the inner
assembly.
The final image in Figure 6.4.3(see APPENDIX C) demonstrates the component parts of the
test compound tubes at different stages of construction, from right to left, Inner Tube, Inner
Tube inside Reinforcement Assembly, Reinforcement Assembly, Outer Tube, Fully
Assembled Reinforced Tube.
The final reinforced tube is better illustrated by Figure 6.4.4which shows the end one of the
final bicycle tubes constructed before final shaping of the reinforcement core to match the
coped outer tube (see Section 6.5).
6.5 Joint Development
One of the major obstacles to the design and construction of a circular profile tubular double
triangle truss frame is the joining of the component tubes. Two methods are used to joint
metal bicycle frames, welded butt joints and brazed tubes into lugs.
Welding is an excellent method for joining circular profile metal tubes, where effective
penetration and well formed fillet profile can be attained, however many materials, including
composites, cannot be welded.
Brazing tubes into lugs was the primary method of manufacture of bicycles until the 1970’s,
when welding techniques and material improvements enabled welding to become the
predominant method. Lugged jointing lends itself well to materials that cannot be welded
and has had a renaisance with the advent and proliferation of carbon fibre bicycles.
The lug forms an oversized junction of sleeves, that the main tubes are bonded into. The
main benefit of lugged construction for composite materials is the maximisation of bonding
area. There are a number of factors affecting the strength of a bonded joint as discussed in
Section 3 of “Design Requirements for Bonded and Bolted Composite Structures” (Broughton
et al. 2002), the most important factor being the maximisation of bonding area.
For this project, lugs formed by an oversized tube have been developed. The oversized tube is
pierced by the main frame tubes (top tube, down tube and seat tube) which are in turn
pierced by the bearing housing tube for the moving part (steerer tube, bottom bracket axle or
seat post). The assembly is filled with an integral matrix of bonded corrugated cardboard
which has a number of intended benefits versus a bonded or welded butt joint:
1. The inter-piercing of tubes provides a mechanical pin joint fixing. Once assembled and
bonded this increases the stiffness of the joint and prevents the main frame tubes from
being pulled out of the junction.
2. By combining both an internal butt joint and a long sleeve joint the bonding area is
maximised.
3. The corrugated cadboard matrix increases the contact surface area of the lug sleeves,
and also provides a support structure to spread static loads and dampen dynamic loads,
in the same manner as a spoked wheel.
In designing the lugs a number of challenges have been overcome; including designing coping
patterns for internally butted pierced tube joints, and creating complex, joined matrices of
laser cut cardboard profiles, see Figure 6.5.2.

26
Coping the tubes involved modelling the tubes in Solidworks and using the Sheet Metal
function to unroll the tubes into flat patterns. The patterns were precisely adhesive taped to
each tube, and the tubes cut with a sharp craft knife.
Figure 6.5.2 Final Head Tube Joint under construction, illustrating the principles of the
jointing system developed for this project.
6.6 Construction of the Front Triangle
Throughout the processes described in Section 6 a CAD model was being developed and
refined, culminating the final model displayed in Figure 6.6.1 (see APPENDIX C) was
realised. In addition to generating the production drawings, sections for laser-cutting and
coping patterns for the frame and fork components, this model was used to produce the jig
required to assemble them, see Figure 6.6.2.
A jig is an essential tool in achieving accurate and precise construction of a frame. The jig
holds the components in the correct position whilst the components are joined. In this
instance, the jig also aided construction by providing a guide for sanding the lug tubes to
achieve the correct angles and separation required for a well-bonded joint. This is critical
stage in construction, any sizing or alignment problems will cause excessive flexing and could
result in point loads at the joints, leading to fatigue and failure.
The frame was first assembled dry within the jig to check angles and dimensions, and to fine-
tune the fit within lugs. Then the tubes were disassembled, adhesive applied to the lugs and
tubes, reassembled, and finally clamped in the jig and left to dry for 24 hrs.
Tube Bonded to Matrix
Tube Butt
Jointed and
Bonded to
Head Tube
Main Frame
Tube Inserted
Bearing Housing Tube Inserted and Bonded to Matrix

27
Figure 6.6.2 Left, Section through model developed in SolidWorks of front triangle – Right,
Frame components in the process of assembly in the frame jig, more photos of construction
are included in APPENDIX C.
6.7 Re-Design and Construction of Rear Triangle
Initially the intention was to use cardboard tubes for the rear triangle of the bicycle, however
whilst modelling the design in CAD a number of problems were encountered and a different
solution had to be developed.
The first issue with using cardboard tubes for the rear triangle is that the diameter of tube
required to support the loads predicted would have to be so large that where they are jointed
to the front triangle, the joints would interfere with the rider’s legs when pedalling.
The other main issue is packaging the moving parts necessary to drive the rear wheel around
the tubes is not possible.
During research of cardboard forms and the search for material suppliers, contact was
established with a supplier willing to supply Tri-Wall cardboard at no cost. Tri-Wall is a
triple layered corrugated cardboard made of 3 C fluted layers interleafed with 5 paper liner
layers. It is claimed to be incredibly strong, a single layer can support 680 [kg/m2] during
transport (ULine 2016).
This led to the design of a tri-wall cardboard rear triangle incorporating a number of features
illustrated by Figure 6.7.1 (see APPENDIX C)
 A folded junction under the downtube running along the flute direction to maximise the
bonding area of the interface between the front and rear frame triangles
 Introduction of a third triangle to optimise the directionality of the Tri-Wall cardboard
rear triangle in the flute direction, maximising strength and stiffness
 Use of the existing front triangle lug joint tubes at the bottom bracket and top of the seat
tube to act as pins; spreading the load over as large an area as possible and acting as a
mechanical joint to prevent reliance on adhesive joints.
 Multiple layers of cardboard to increase strength and stiffness of the rear triangle, one of
which is removable to allow access to the drivetrain and brake parts for setup and
maintenance

28
6.8 Construction of Forks and Prototype Front Wheel
Using the lessons learnt, and methods developed in designing, manufacturing and
constructing the cardboard bicycle frame explained in Sections 6.2-6.7, forks and a prototype
front wheel have been produced. Models and photographs of the final products can be viewed
in APPENDIX C.
6.9 Waterproofing
Section 5.5 highlights the sensitivity of moisture to cardboard. This is a major limitation of
cardboard as a structural material. Cardboard tubes are produced in a waxed coated form,
which are claimed to be waterproof for shipping crucial architectural drawings and similar
items.
Through research a number of methods of waterproofing were explored. Most of the methods
encountered involved volatile organic chemicals and unsustainably produced resins. An
interesting Epoxy resin called Poly-Soy was discovered, a resin produced from 100% Soya
protein, a natural renewable resource, and the supplier was willing to supply a sample at no
cost, however there are shipping restrictions as they only manufacture the product in the
U.S.A.
The prototype frame and forks have been coated in two coats of diluted Polyvinyl Acetate
followed by two coats of Polyurethane Varnish. Similar to fatigue, waterproof coatings
require long-term evaluation, and could form the basis of further research work.
6.10 Prototype Testing
Prototype testing is an area of the project that has been neglected up to this juncture. The
ambition at the outset of the project was to test the prototype frame and forks using some or
all of the BS EN ISO 4210-6:2015 tests.
These tests are not a legal requirement in any state or country yet, but form the basis of good
practice for safety assurance in the bicycle industry. The standard for frames and forks
contains 14 tests.
Two quotes were obtained from a German testing centres for these tests one had a
breakdown of tests ranging from €150-€500 per test, the other quoted a discounted rate of
€5000 for a full suite of tests. These costs are beyond this projects budget; however the
development of testing apparatus would form a very good basis for future work. There is
currently only one recognised provider of these tests in the U.K., Bureau Veritas, this may
leave a gap in the market which forms an opportunity for an institution such as a University
to develop and offer such testing.
7. Results and Discussion
7.1 Evaluation of the Project
This project was ambitious from the outset; in essence it constitutes the marriage of two
projects in one; “The Testing and Development of Cardboard Tubes as a Structural Material”,
and “The Design and Construction of a Cardboard Bicycle.”
Through the testing and development of cardboard tubes as a structural material, interesting
insights have been made in an area where very little prior work exists. If engineers and

29
architects are to develop the use of cardboard as a structural material, this provides a solid
building block for future work. This work could be expanded and developed in a great many
directions:
 Testing of more samples from a variety of manufacturers, in differing dimension ratios,
both slenderness (λ) and wall thickness ( )
 Development of a means for analysing the material density and homogeneity for
cardboard tubes
 Bending moment and torsion testing
 Dynamic and long term fatigue testing
 Investigating environmental effects, such as humidity/moisture effects and ambient
temperature
Section 6.1 and APPENDIX A demonstrate a strong correlation of the nature by which spiral
wound cardboard tubes fail under axial compression. This could give insight to the
manufacturers of cardboard tubes as to the methods by which they could produce stronger
tubes and eliminate manufacturing defects.
Spiral wound structures are employed in ventilation ducts, pipelines and drill pipe. The
study of spiral-welded pipes is a well-documented field that has major implications in the Oil
and Gas Industry (Winston Revie R. 2015). Spiral wound pipes are inexpensive to produce
and can be made in a continuous process like cardboard tubes, however there are structural
consequences to this method of manufacture that in certain situations make them inferior to
drawn, extruded or straight seamed pipe.
The design and construction of a cardboard bicycle frame has been a much larger
undertaking than anticipated, (see Sections 6.2-6.9 and APPENDIX C). Ordinarily a small
team of engineers and designers would be employed to design and construct a bicycle frame
and forks from conventional materials. Compounding this with attempting to design and
build a frame using a novel composite material, whose properties are virtually undocumented
has been a considerable challenge for an individual. It has been a great achievement to
produce a prototype bicycle frame and forks from materials researched, tested and developed
in the course of this project.
The workload and underestimation of task duration has led to overruns on some of the later
scheduled tasks critical to evaluating the final product. This will not be overlooked and the
project remains ongoing until the presentation and submission of the hardware on the 13th
June 2016. Before this date, the outstanding tasks will be completed, and the author will
attempt to prove the bicycle during the presentation.
7.2 Evaluation of the materials developed
The reinforced cardboard tubes developed during the project proved to be stronger and stiffer
than their constituent parts during the compression testing completed in Section 6.1.
Combined with the further development made after this testing and improved construction
techniques a substantially stronger and stiffer material has been produced capable of
supporting more than the 1 [tonne] on a single 56 [mm] outer diameter tube, that the testing
samples sustained, see Chart 6.1.5.
These tubes are manufactured from a material that in this instance is made from at least
85% (potentially 100%) recycled raw material, and remains 100% recyclable at the end of its

30
lifespan. This could have implications for the use of cardboard tubes in structural situations
as a sustainable alternative to existing materials.
 Low cost sustainable buildings – i.e. temporary housing in disaster areas, temporary
classrooms for schools, temporary repair/support kits for structures awaiting final repair
 Low cost structural medical aids, temporary wheelchairs, crutches and prosthetic limbs,
or permanent ones for those who cannot afford current offerings
Manufacturing techniques would have to be improved and altered for scalability. The 56
[mm] outer diameter, 22 [mm] inner diameter tubes 800 [mm] long took 1 [hr] to laser cut
and 6 [hrs] of labour to construct, followed by 12 [hrs] adhesive curing time and waterproof
coat curing time. The laser cutting time could be slashed to a few seconds with investment in
the production of a single cutting die, such as those used to cut cardboard boxes from sheets
of corrugated cardboard, however labour time would still be considerable.
The best solution would be to develop a structural medium that could be produced in a
continuous process, similar to the fluted/corrugated layers used in corrugated cardboard
sheets, or the honeycomb filler used in honeycomb panels. This structural spacer could be
integrated into the production of tubes with the benefits gained from an increased moment of
inertia.
It remains to be evaluated whether the materials developed are truly suitable for
constructing bicycles. The real tests are long term, nearly all bicycle failures are due to
accumulated fatigue. It is well documented that composite materials, especially laminated
materials, often suffer from separation of the structural material and matrix material when
fatigued. No information is available on the ability of spiral wound cardboard tubes to resist
fatigue, so this project produce ongoing insights should the bicycle frame and forks last for
any duration, as the author intends to fatigue test it through use.
7.3 Evaluation of the design process
To maintain relevance to the pursuit of a BEng in Mechanical Engineering a theory and FEA
based design process has been emphasised. A fundamental Product Design Specification has
been included see APPENDIX D. Further use of design tools like Functional Decomposition,
SWOT Analysis and a Scoring Table would have been useful, however when only considering
an individual’s views these types of analyses can be biased and result in a constrained
outcome, even when the individual sets out to be objective. Consultation with other engineers
and designers or collaboration in a team would be a huge advantage in this type of project,
leading to a greater diversity of ideas and solutions.
The Finite Element Analysis represents a considerable amount of valuable work. Whilst
researching this project and requesting rudimentary data as a starting point for analysis, it
was discovered that mainstream companies are very protective over the data produced by
this type of work. An excellent academic exercise would be to use sensors and strain gauges
attached to a modern bicycle frame and perform tests to gather empirical data, and then use
that data as a basis for an FEA model. This type of analysis would have been very valuable
as the existing data in the public domain is dated.
For a thorough, more diverse design process, it would be advisable to have performed a
survey of potential customers. It may be that Izhar Gafni, see Section 1. has already provided
an answer to the customer appeal aspect of a cardboard bicycle in his products failure to raise

31
capital. This may be the restriction on the viability of a cardboard bicycle as a consumer
product, the lack of a market.
7.4 Evaluation of the project management process
Overall the project planning has been well executed, the Gantt Chart produced (see
APPENDIX E) has been very useful in guiding the project, and has allowed a good balance of
work progress and production quality. Unfortunately, some of the later tasks, which through
the design have become critical to the final product, were underestimated in complexity and
duration. Their complexity has led to the requirement of advice and assistance from
technicians, which has required alterations to the schedule and schedule synchronisation
considerations.
It has been exceptionally useful to develop a working relationship with most of the
Engineering Department technicians, all of whom have provided excellent guidance in the
use of the Universities engineering facilities; this has expedited the progress of the project.
7.5 Evaluation of the final product
Craig Calfee, one of the foremost custom bicycle builders in the world was contacted early on
when searching for FEA data in the conception of this project; his personal reply included a
short but poignant 2 points:
1. Consider the real world economics of the finished product, including labor.
Both Phil Bridge and Izhar Gafni claimed they could supply a $20 (£14) retail cardboard
product to the market and cited this as one of their primary reasons for designing a
cardboard bicycle. There are complete steel bicycles available in the UK for $120 (£84.99,
sportsdirect.com,.2016) Taking into account 20% VAT, and other taxes, rates and overheads;
this probably results in a cost to the retailer of $30-$40 (£20-£27) for a complete bicycle.
During this project the materials were donated free of charge. Comparison with retail sellers
in Table 7.1, see APPENDIX D show the material costs to be £35 ($50), adjusting for bulk
scaling could probably bring this down to $20-$30 (£14-£20), but this takes no labour into
consideration and does not allow for any of the components necessary to drive and stop a
bicycle. The labour and laser cutting costs, again donated free of charge on this project,
amount to £2115 ($3080), assuming market costs for the laser cutting and minimal labour
costs of the author at £15/hr, which when accounting for National Insurance and other
business rates would approximately represent the minimum wage.
2. Have fun with it and make it something you can be seen ridin g without embarrassing
yourself.
The project has been successful in producing a prototype cardboard bicycle frame, forks and
wheel. The dimensional tolerances achieved (see APPENDIX D) and aesthetic finish (see
APPENDIX C) exceed the author’s expectations.
Two questions are asked earlier in Section 5: “Why Build a Bicycle from Cardboard?”, and “Is
Cardboard Suited to Building a Bicycle?” This project, the data presented and the arguments
made all provide a case presenting cardboard in a favourable light, whilst addressing some of
its limitations. As a project, it has been informative, challenging and an excellent test of the
author’s mechanical engineering skills.

32
When regarding the feasibility of a cardboard bike as a consumer product the best question to
ask would be, “Would anyone buy a bicycle made from Cardboard?” The evidence does not
weigh heavily in favour of cardboard.
A possible means by which to successfully market a cardboard bicycle would be to develop a
kit that could be assembled with no adhesive or tools in an hour or two, similar to 3D printer
kits. It could be delivered in the cardboard tubes used for the build. The product could very
easily and inexpensively have customised graphics printed on it. If produced at a low enough
cost it may be a marketable corporate promotional/advertising product.
Conclusions
 This project is successful in fulfilling its aims, Section 3.
 Cardboard Tubes have been tested and developed as a structural material founded on
theoretical analysis and empirical testing.
 A prototype bicycle frame and forks have been designed and constructed.
 This project has delivered on all of its deliverables, Section 4.
 Evidence has been presented in Sections 5 and 6, proving cardboard is a practicable
structural material that has well established sustainability benefits over existing
materials.
 An elementary insight into the modes of failure of spiral wound cardboard tubes under
compression has been presented, in Section 6.1.
 It has been imparted and backed-up by theory and simulation that a bicycle frame is an
excellent structural exercise for comprehensive analysis of a structural material,
Sections 5 and 6.
 Strong evidence has been presented, and before the final submission stage of this project
a definitive answer will be obtained to prove it possible to build a structurally viable
bicycle frame and forks from the materials developed.
 Currently there is no viable market for a cardboard bicycle; it is therefore not a saleable
product, but formed an interesting mechanical engineering pursuit.
 .A number of future work opportunities have been identified, some of which may form
valuable research projects; others which could form a lucrative business opportunity.

A1
APPENDIX A
Laboratory Testing Results and Charts
Sample
Number
Tube O.D.
[mm]*
Tube I.D.
[mm]*
Young’s
Modulus [GPa]
0.02% Yield
Stress [MPa]
Ultimate
Compressive
Stress [MPa]
A1 34 26 1.18 4.2 6.32
A2 34 26 NA 5.28 6.25
A 34 26 1.18 4.74 6.29
B1 55 51 1.56 5.90 8.46
B2 55 51 NA 6.80 9.27
B3 55 51 NA 4.15 5.50
B4 55 51 NA 7.30 10.63
B 55 51 1.56 6.04 8.47
C1† 55 51 1.54 5.96 9.88
D1† † 55 51 1.28 9.55 10.32
E1 50 45 1.38 4.72 6.22
E2 50 45 NA 4.65 6.50
E 50 45 1.38 4.69 6.36
F1 34 26 1.04 2.36 5.35
F2 34 26 NA 3.37 6.18
F 34 26 1.04 2.87 5.77
Table 6.1.2 Summary of results from unconfined compression tests on cardboard tubes
Notes:
Sample types A and E through F were all sourced from a single supplier (CT).
Sample types B through D are recycled architectural bond paper roll cores from another
supplier (HP).
Sample types C and D have been modified as outlined in Section 6.4 Tube Development, with
ribs and stringers. Both have four 5.2 [mm] thick stringers, C† has 5.2 [mm] thick radial ribs
at 20 [mm] spacing, whereas D†† has 5.2 [mm] thick ribs at 10 [mm] spacing.

A2
0
100
200
300
400
500
600
700
800
900
1,000
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
20 25 30 35 40 45 50 55
MassPerUnitLength[kg/m]
StiffnessCoeficient[Pam4]
Tube Outer Diameter [mm]
Steel Stiffness Coefficient [Pam^4] Aluminium Stiffness Coefficient [Pam^4]
Steel Mass per Unit Length [g/m] Aluminium Mass per Unit Length [g/m]
Steel Critical Buckling Ratio, Outer Diameter to Wall Thickness 60:1
6061 T6
Aluminium
4130
Cromoly
Steel
Chart 5.2.10 the relationship between Stiffness and Mass per Unit Length for 4130 Steel and 6061 T6 Aluminium Tubes with
increasing outer diameters. All data sourced from Aerospace Specification Metals Inc.

A3
Chart with Figure 6.1.3 Typical Stress – Strain response of a spiral wound cardboard tube to
1kN/min load ramp to failure
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02
Stressσ[MPa]
Strain ԑ
B2
0.2% Line
1
2
31
2
3

A5
Chart 6.1.6 Comparison of Stress – Strain response of A-Type spiral wound cardboard tubes
1kN/min load ramp
Chart 6.1.7 Elastic Stress – Strain response of sample B1, spiral wound cardboard tube to
0.5kN/min elastic load ramp cycles.
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02
Stressσ[MPa]
Strain ԑ
A1
0.2% Line
A2
0.2% Line
y = 1,524,676,913x - 843,717
R² = 1
y = 1,596,197,772x - 1,004,625
R² = 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.0005 0.001 0.0015 0.002
Stressσ[MPa]
Strain ԑ
B1
Linear (Stage 3)
Linear (Stage 5)
Trendline Equations

A6
Chart 6.1.8 Comparison of Stress – Strain response of B-Type spiral wound cardboard tubes
1kN/min load ramp
Chart 6.1.9 Elastic Stress – Strain response of sample C1, spiral wound cardboard tube to
0.5kN/min elastic load ramp cycles
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02
Stressσ[MPa]
Strain ԑ
B4
0.2% Line
B3
0.2% Line
B2
0.2% Line
B1
0.2% Line
y = 1,508,952,063x - 1,291,397
R² = 1
y = 1,577,829,926x - 1,672,219
R² = 1
y = 1,681,839,190x - 2,028,605
R² = 1
0
0.5
1
1.5
2
2.5
3
3.5
0 0.001 0.002 0.003
Stressσ[MPa]
Strain ԑ
C1
Linear (Stage
3)
Linear (Stage
5)
Trendline Equations

A7
Chart 6.1.10 Elastic Stress – Strain response of sample D1, spiral wound cardboard tube to
Chart 6.1.11 Elastic Stress – Strain response of sample E1, spiral wound cardboard tube to
y = 1,171,982,448x + 316,648
R² = 1
y = 1,218,057,518x + 187,074
R² = 1
y = 1,459,637,687x - 124,855
R² = 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.0005 0.001 0.0015 0.002
Stressσ[MPa]
Strain ԑ
D1
Linear (Stage 3)
Linear (Stage 5)
Linear (Stage 7)
Trendline Equations
y = 1,364,121,936x + 260,459
R² = 1
y = 1,379,232,773x + 190,987
R² = 1
y = 1,407,175,091x + 121,690
R² = 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.0005 0.001 0.0015 0.002
Stressσ[Pa]
Strain ԑ
E1
Linear (Stage 3)
Linear (Stage 5)
Linear (Stage 7)
Trendline Equations

A8
Chart 6.1.12 Comparison of Stress – Strain response of E-Type spiral wound cardboard tubes
1kN/min load ramp
Chart 6.1.13 Elastic Stress – Strain response of sample F1, spiral wound cardboard tube to
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02
Stressσ[MPa]
Strain ԑ
E2
0.2% Line
E1
0.2% Line
y = 1,030,481,269x + 264,165
R² = 1
y = 1,040,415,623x + 243,140
R² = 1
y = 1,063,401,078x + 221,459
R² = 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.0002 0.0004 0.0006 0.0008 0.001
Stressσ[Pa]
Strain ԑ
F1
Linear (Stage 3)
Linear (Stage 5)
Linear (Stage 7)
Trendline Equations

A9
Chart 6.1.14 Comparison of Stress – Strain response of F-Type spiral wound cardboard tubes
1kN/min load ramp
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02
Stressσ[MPa]
Strain ԑ
F2
0.2% Line
F1
0.2% Line

B1
APPENDIX B Finite Element Analysis
Analysis 1 Static Study - Seated Whilst Pedalling Right Pedal
Figure 6.3.3 Forces Applied to Generic Frame and Forks Assembly- 6061 T6
Aluminium -Analysis 1
Figure 6.3.4 Resultant Von Mises Stress Generic Frame and Forks Assembly- 6061
T6 Aluminium -Analysis 1
115N
360N
30N
160N
480N
490N
Fixed
Fixed

B2
Analysis 2 Static Study - Seated Whilst Pedalling Left Pedal
Aluminium -Analysis 2
160N
360N
30N
115N
480N
490N
Fixed
Fixed

B3
Analysis 3 Static Study – Standing Whilst Pedalling Left Pedal
Figure 6.3.7Forces Applied to Generic Frame and Forks Assembly- 6061 T6
Aluminium-Analysis 3
50N
640N
150N
1200N
1660N
Fixed
Fixed
50N

B4
Analysis 4 Static Study – Standing Whilst Pedalling Right Pedal
50N
150N
640N
1200N
1660N
Fixed
Fixed
50N

B5
Analysis 5 Static Study – “Hitting a Pothole” while Seated
2400N

B6
T6 Aluminium -Analysis 5 - Close-up of reverse angle to equal scale as 6.3.13
Analysis 6 Static Study – Braking while Standing
400N
200N
200N
200N
200N
Fixed
Slider
400N

B7
Figure 6.3.15 Resultant Von Mises Stress -Generic Frame and Forks Assembly- 6061
Figure 6.3.16 Resultant Von Mises Stress - Generic Frame and Forks Assembly-
6061 T6 Aluminium –Analysis 6- Close-up of reverse angle

B8
Analysis 7 Static Study – Falling Mass
220N
220N
Slider
Fixed

B9
Analysis 8 Static Study – Falling Frame
870N
1400N
1260N
Fixed
Slider

C1
APPENDIX C Models and Build Photos
Figure 6.2.4 Generic bicycle frame generated in SolidWorks to establish proposed
geometry and dimensions for prototype cardboard bicycle frame.

C2
Figure 6.4.3 Design and manufacturing process for the compound cardboard tubes
developed for laboratory testing. This process has be refined and applied to the
manufacture of the actual frame tubes of the final prototype
Design Sketch
Prototype Tube
Laser Cutting
Machine
Reinforced Tubes for Materials
Testing, showing Constituent
Parts and Final Assembly
Drawing from Model
After Testing these Tubes
were Evaluated and
Redesigned for the Final
Bicycle Frame Tubes
Broken Down
into Profile
Drawings
1 2
3
4
5
6

C3
Figure 6.4.5Final Bicycle Frame Down Tube, after shaping of reinforcement core to
match coped outer tube
Figure 6.6.1SolidWorks Model of front triangle

C4
Figure 6.6.3 Frame jig production drawing
Figure 6.6.4 Complete front triangle jig prior to building front triangle

C5
Figure 6.6.5Front triangle assembled and bonding in jig
Figure 6.6.6 Front triangle during waterproofing and drying.

C6
Figure 6.7.1 Final render of completed bicycle model
Figure 6.7.2 1SolidWorks Model of rear triangle

C7
Figure 6.7.3 Rear triangle and front triangle mated and bonded to eachother, after
waterproofing.
Figure 6.8.1 1SolidWorks Model of front forks

C8
Figure 6.2.12 Front forks part way through construction.
Figure 6.2.13 Front wheel prototype after construction.

D1
APPENDIX D
ProductDesign Specification for a Cardboard BicycleFrame and
Forks
A bicycle is a form of transport
Function – To transport the rider (and cargo) from one location to another.
A bicycle frame and forks are the main structural elements of a bicycle
ESSENTIAL FUNCTIONS DESIGN CRITERIA
DESIRABLE
CRITERIA
Must Fulfil Should Fulfil
Connect the two wheels
together
Constructed with as high a
percentage of cardboard as
possible
Compliant enough to
provide a comfortable
ride
Support the riders weight
Comply with BS EN ISO 4210-
6:2015 Aesthetically
pleasing
Provide a stable platform to
transmit propulsion forces
to the driving wheel
Stiff enough to transmit power
efficiently to the driving wheel
and steering inputs to the steering
wheel.
Lightweight
transmit steering forces to
the steering wheel
Provide a suitable riding position
transmit braking forces to
the wheel brakes
Operate in all weathers
PrototypeBicycle Frameand Forks Costing for Project
Materials Quantity
Retail Cost
Per Unit
Project Source
Ø56mm Cardboard Tube 2 £2.74 Cores and Tubes (FOC)
Ø 96mm Cardboard Tube 1 £4.66 Cores and Tubes (FOC)
Tri-Wall Cardboard 1 £7.80 SAL Packing(FOC)
Materials Total £29.78
Services
Laser Cutting 27[hrs] £30 LSBU (FOC)
Labour 87[hrs] £15 Authors time
Services Total £2115.00

James Goddings 3131147 LSBU Final Pr

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