1. art and entertainment
2. visual art and design
3. design

The Eco-Core Snowboard
By SnowCore Innovations
Tom Santoro
Chris Grant
Curtis Franklin
December 12, 2006
APD2006-02
ABSTRACT
Natural fiber composites have been heavily investigated in recent years not only because they are
more environmentally friendly than other composite materials but also because of the apparent
high strength and low density of the fibers. The hemp plant in particular produces high quality
natural fibers exhibiting strong mechanical properties which are also inexpensive. Our research,
engineering analysis and material testing has led us to a material called FlexForm which exhibits
properties comparable to current core materials on the market, generally various types of woods
and foams. FlexForm is a composite made of jute, a derivative of the hemp plant, and its
implementation in a sustainable snowboard shows a feasible alternative to current core materials.
The purpose of this report is to present our product solution for a more environmentally friendly
snowboard aimed towards eco-friendly, counter-culture snowboarders.
TABLE OF CONTENTS
NOMENCLATURE.................................................................................................... 1
INTRODUCTION...................................................................................................... 2
Previous Designs............................................................................................. 2
Design Objectives........................................................................................... 4
PRODUCT DESCRIPTION..................................................................................... 5
Conceptual Solutions..................................................................................... 5
Concept Selection – Pugh Matrix................................................................. 6
Design Requirements – Quality Function Deployment.............................. 7
Quantifiable Design Requirements.............................................................. 9
Project Prototypes.......................................................................................... 9
ENGINEERING ANALYSIS.................................................................................... 13
Design Optimization ...................................................................................... 13
Material Testing............................................................................................. 16
AESTHETIC ANALYSIS......................................................................................... 18
INITIAL MICROECONOMIC ANALYSIS........................................................... 20
MARKETING ANALYSIS....................................................................................... 22
Modified Microeconomic Analysis............................................................... 24
PRODUCT DEVELOPMENT PROCESS .............................................................. 27
PRODUCT BROADER IMPACT............................................................................ 29
CONCLUSION........................................................................................................... 30
RESOURCES............................................................................................................. 32
APPENDIX A: INITIAL SURVEY RESULTS AND QUESTIONS................... A-1
APPENDIX B: PHOTOS OF BENCHMARKED SNOWBOARDS................... B-1
APPENDIX C: ENGINEERING ANALYSIS MODELS...................................... C-1
APPENDIX D: ENGINEERING ANALYSIS SPREADSHEETS....................... D-1
APPENDIX E: CHOICE BASED CONJOINT SURVEY QUESTIONS........... E-1
APPENDIX F: MODIFIED MICROECONOMIC CALCULATIONS.............. F-1
i
NOMENCLATURE
wc
tc
we
te
a
b
l
e
d
vi
Pj
W
Y
∏
Q
P
C
θ
λp
λd
∆α
VC
FC
λx
xb
Q1.05xb
Qb
Width of snowboard at center
Thickness of snowboard at center
Width of snowboard at end
Thickness of snowboard at end
End of snowboard to bindings
Distance between bindings
Length of contact with ground
Distance between contact surfaces
End of snowboard to contact surface
Snowboard deflection for load case i
Maximum allowable load for load case j
Weight
Engineering objective function
Profit
Quantity of boards sold per year
Price per board
Cost per year
Market size
Price sensitivity
Design sensitivity
Microeconomic constant
Variable costs per snowboard
Fixed costs of operating per year
Elasticity of design characteristic
Base design level of characteristic x
Market demand associated with an increase of 1.05 times xb
Market demand of base design
1
INTRODUCTION
The demand for environmentally sustainable products has skyrocketed within the last decade due
to increasing global sustainability concerns. The winter sports market is no exception and
demonstrates a significant population of people concerned with these environmental issues. Our
survey results show that the average snowboarder is concerned with global warming and is also a
frequent newspaper recycler (Appendix A, Survey Results). Based on these points, it is a worthy
endeavor to produce a more environmentally sustainable snowboard in order to target this
market.
Hemp, when compared to glass fibers, has shown an equivalent Young’s modulus, a much lower
density and costs roughly half the price [1]. The counter-culture mindset surrounding hemp is
also a very attractive proposition to many snowboarders. Our survey showed that 47% of people
who snowboard own a hemp product, whereas only 14% of non-snowboarders own something
produced with hemp. Jute is a plant derived from hemp and can be produced in composites at a
higher quality than that of hemp and at a cheaper price. Although 95% of the world’s jute fiber
comes from Bangladesh and India, it should be noted that the industrial growth of the plant is
legal in the United States, whereas hemp is not [2].
We feel that there is significant demand for a sustainable snowboard incorporating natural fibers
and thus we have decided to design and develop a snowboard concept from the viewpoint of a
small snowboard manufacturing company.
Previous Designs
The sport of snowboarding started in the 1960’s, with most of the credit given to a young surfer
named Sherman Poppen. Poppen joined two skis together for his daughter to “surf” down the
hill on snow. He called this creation a Snurfer (Figure 1 below), coming from the words “snow”
and “surf”.
Figure 1. Poppen’s early Snurfer
This spark led enthusiasts like Jake Burton, Tom Sims, and Demetrije Milovich to refine the
board shape and create what is known as the modern snowboard. Snowboarding began to pick
up momentum in the late-eighties, underwent rapid growth throughout the nineties and was the
2
fastest growing sport in the United States at the year 2000. According to the fourteenth annual
American Sports Data Superstudy of Sports Participation, the number of people snowboarding
increased 51 percent from 1999 to 2000, whereas skiing only increased by 6 percent. In just a
few short years, the number of snowboarders had grown to over 7.2 million participants, gaining
quickly on the 14.7 million skiers [4]. This rapid growth placed an extreme demand on the
snowboard manufacturing industry.
Snowboard technology has evolved drastically over its forty-year history. When Jake Burton
started creating snowboards in 1977, he attached water ski bindings to a wooden plank. The
evolution has led to rounded tails, hard boots, and plate bindings. Now you can purchase an
asymmetrical, twin-tip (shown in Figure 2 below), carving board, or other designs depending on
your own personal riding style.
Figure 2. K2 Zeppelin twin-tip snowboard
There are two types of snowboard construction. The first is the traditional sandwich construction,
in which the sidewall is flat and angled to the base. The second type is called ‘capped’, shown in
Figure 3 below. In this type of construction, the top sheet is pinched over the sides of the
snowboard to meet the steel edge. Both methods are very similar and only have a few different
steps. The seven most common ingredients in snowboards are the wood or foam core, fiberglass,
epoxy, base, topsheet, edges and binding inserts.
Topsheet
Core
Laminates
Plastic Base
Edge
Figure 3. Cross section of a capped-construction snowboard
The wood or foam core is the building block of the board and its shape and thickness are the
characteristics which affect the flex and weight. Wood is a good material choice because it
3
contains long fibers that transmit high-frequency vibrations along the board length, resulting in a
smooth ride. Foam is becoming more popular as technology advances, but does not have the
long fibers like wood and therefore these boards usually have more ride vibration, or feel
‘chatty.’ Bolt inserts are integrated in the core for the mounting of bindings and are typically
made of stainless steel to avoid rusting. The industry standard is a 4x4, 6mm bolt pattern to
make the adjustment, installation, and removal of bindings as simple as possible.
Construction of a snowboard begins by shaping the base. Next, steel edges are attached to the
perimeter of the base. These prevent slipping or sliding while on snow and ice and also assist in
turning and controlling speed. Next, fiberglass cloth is applied to the top and bottom of the core.
This provides the board with much needed torsional resistance and strength without adding
significant weight. The direction in which the fiberglass is positioned relative to the board length
varies from manufacturer to manufacturer. Next, an epoxy system is mixed thoroughly
(consisting of a resin and hardener) and applied to both sides of the core and covered in
fiberglass. The epoxy system saturates the fiberglass and serves as the binder to laminate the
whole board together. A top sheet is placed above the core for aesthetics and the base is placed
underneath. The board is then placed in a shaped press under extreme pressure to give it a
formed nose and tail and also to adhere all of the layers together. After the epoxy system cures,
the excess material is trimmed away, the edges sharpened and the snowboard is ready for
packing and shipping to the dealer.
Snowboards made using this construction technique range from approximately $250 to $950,
depending on the quality of materials used, with most falling in the $300 to $500 price range.
Depending on your demand for ride performance, numerous options allow for each user to
choose the specifications which will match his/her needs best. Even given multiple options, one
aspect is not currently a choice for the new snowboard investor - the use of more
environmentally friendly, sustainable materials. Fiberglass, the resin system, top sheet and base
are all manufactured from oil, while the wood core comes from trees. With a growing concern
and interest in resource conservation and environmentally friendly design, it is clear that the
rapidly growing snowboard market is yearning for a design that produces the same performance
but uses resources that are sustainable.
Design Objectives
The following are the key design requirements that we have identified for our snowboard design
concept:
-
-
-
Must be robust: This takes into account mechanical properties such as Young’s modulus,
yield strength and impact strength, as well as the overall durability of the board. Any
permanent deformation of the board after riding is unacceptable. This will be quantified with
the properties mentioned as well as the thickness.
Must provide good ride: The board must perform well on the slopes by providing superb
bump absorption, easy turning/carving, and adequate rider stability. While this depends on
several factors, we will again look at the mechanical properties, as well as tip radii and board
thickness.
Should be lightweight: A lighter board is easier to maneuver as well as transport. Weight
reduction should be accomplished with different materials.
4
-
-
Should have a competitive retail price: Reducing price is not our foremost concern, but we
would like to keep it on par with most other snowboards.
Must be more environmentally friendly: This is our major objective for the project. We
will quantify this by the percentage of sustainable materials by volume in the snowboard.
Hemp is preferred as a sustainable material due to its “counter-culture” appeal to
snowboarders.
Must have increased possibility for recycling: This is related to the amount of sustainable
materials. However, we must also devise a way to separate sustainable materials from the
other materials in the board, which is a challenge.
Sustainability should be obvious: From a marketing standpoint, we would like people to
know that our board is environmentally sustainable. This could be accomplished with a clear
or partially clear topsheet.
Must be aesthetically pleasing: Visual appeal is a major factor in customer preference of
snowboards, therefore ours must be able to catch the eye of riders.
Should be easy to maintain/transport: Snowboards generally require little maintenance,
and we would like ours to be no different.
Must be weatherproof: Given the outdoor nature of the sport, our snowboard must be able
to withstand freezing temperatures, snow, ice, and water without sacrificing performance.
Must include universal bolt pattern: In order to be compatible with the majority of
bindings, the bolt pattern on the board must be the universal 4x4.
Should be easy to ride fakie (both ways): Part of the freestyle element of snowboarding is
being able to switch which end of the snowboard is in front while riding. Riding with the
opposite foot from normal forward is called fakie, and can be done with a twin tip board
(with equal tip radii).
In addition to serving as measures of how successful the project will eventually be, these
objectives are used to determine the key engineering parameters of our snowboard design
concept, as accomplished with a Quality Functional Deployment (QFD). Also, concept selection
is achieved by rating how well each concept would meet these objectives with a Pugh matrix.
Both the Pugh matrix (Figure 6, page 7) and QFD (Figure 7, page 8) are discussed and shown in
the Product Description section.
PRODUCT DESCRIPTION
Conceptual Solutions
The two main aspects we examined when developing snowboard concepts were the material
construction and the shape, with materials taking precedence. The core of a snowboard is
generally composed of foam in lower quality boards and different types of wood in higher
quality boards. Poplar and ash are generally categorized as woods of medium quality and hard
sugar maple is generally used in top end boards. The natural fiber based materials shown in
Figure 4 on page 6 represent significant areas of improvement from the view of environmental
sustainability. The use of chopped natural fiber composites, hemp and jute in particular, as
replacement for the core as well as woven hemp composites as replacement for the laminates
(typically fiberglass) would dramatically increase the percentage of sustainable materials found
in a snowboard.
5
(a) FlexForm Natural Fiber Composite
(b) Woven Hemp
Figure 4. Proposed natural fiber materials for snowboard use
Material testing has been completed and is presented below in the Material Testing section on
page 16. Due to time constraints, we focused our investigation on the replacement of the core
since this represents the largest percent volume of a typical snowboard.
Our survey results have shown that the twin tip snowboard design is preferred to the powder
design (see Appendix A, Survey Results). The directional shape has virtually no demand
associated with it. These designs are shown in Figure 5 below. These results come from our
web survey which was completed by 74 people at the time the results were analyzed.
(A)
(B)
(C)
Figure 5. Twin tip (A), powder (B), and directional (C) snowboard shapes considered
The design concepts, which are listed in the Pugh matrix (Figure 6, page 7), are based on
different combinations of shapes, core materials and laminate materials.
Concept Selection – Pugh Matrix
After comparing several snowboard design concepts, we have found that the most promising
concept is a twin tip board with a hemp composite core and woven hemp laminate. This is
justified by our Pugh matrix analysis, as shown in Figure 6 on page 7. Time limitations have not
allowed us to investigate laminate replacements, therefore we have pursued only the replacement
the core material with a natural fiber composite.
6
Shape
Core
Design Criteria
Robust
Good ride
Lightweight
Competitive retail price
More environmentally friendly
Increased possibility of recycling
Sustainability is obvious
Aesthetically pleasing
Easy to maintain/transport
Weatherproof
Universal bolt pattern
Easy to ride fakie (both ways)
Weight
8
10
5
6
9
8
7
6
6
10
4
3
Laminate
+
0
Total
Snowboard Design Concepts
Twin tip
Twin tip
Twin tip
Twin tip
Fiber
Fiber
Foam
Foam
Wood
composite composite
Woven
Woven
Woven
Fiberglass Fiberglass
hemp
hemp
hemp
D
++
+
+
A
+
0
+
T
+
++
+
+
U
+
+
0
M
+
++
+
+
.
+
++
+
+
D
+
++
+
+
A
+
+
+
+
T
--U
0
M
0
0
0
0
.
0
0
0
0
0
61
78
41
53
82
17
7
7
13
0
12
22
34
22
0
49
56
7
31
Twin tip
Powder
Powder
Fiber
Fiber
composite composite
Woven
Fiberglass
hemp
++
+
+
0
+
++
+
+
++
+
++
+
++
-0
0
0
55
72
14
14
21
31
34
41
Figure 6. Pugh matrix indicates most promising design incorporates natural fibers in both core and laminate
In the Pugh matrix, we examined whether each of six design concepts would be better than (+),
worse than (-), or equivalent to (0) our datum snowboard at meeting each design criterion. The
datum was the Rossignol foam core twin tip board which we previously benchmarked. The basis
for the + and – marks in the chart was the research we have done in the last month on both
sustainable natural fiber materials (composite and woven) and how they compare to current
snowboard construction materials (foam, wood, fiberglass). Quantified details are discussed on
page 9. Overall, we were unsurprised to see that the concept with the highest score incorporated
both a natural fiber core and laminate in a twin tip design. Unfortunately, time has limited our
investigation into the woven fiber laminates and therefore our efforts have been solely on the
core material replacement. This decision was made based on the fact that the core material
represents a much larger percent volume within a snowboard.
Design Requirements – Quality Function Deployment
On page 4, the key design objectives for our snowboard concept were stated and summarized.
These objectives are key ingredients of the Quality Function Deployment (QFD) matrix, shown
in Figure 7 on the following page. The design parameters are listed along the top of the matrix,
and their contribution to the design objectives is quantified on a 1-3-9 scale. Totaling these
scores gives us an importance rating for each of the parameters, based on how well they help to
achieve the objectives. The most important parameters to focus on are the external finish of the
board, the percentage of sustainable materials, and the outside visibility of these sustainable
materials. The QFD also shows the tradeoffs between design parameters in the triangular
correlation matrix. The important tradeoffs we found were between the mechanical properties
(Young’s modulus and tensile strength) and the weight of the board. Ultimately, we would
prefer to have a strong, heavier board than a weak, lighter board. On the right side of the matrix,
our hemp snowboard concept is benchmarked against two existing boards (Appendix B) with
different material construction. We expect that our concept will be the best at meeting most of
the design objectives, although potentially sacrificing aspects such as price and maintenance.
These parameters will be used mainly for optimization of the design.
7
-
9
1
3
9
9
1
1
9
9
3
1
1
1
3
1
3
9
9
9
9
1
GPa
4
4
168
0.116
5.09
12
0.003
1
1
1
MPa Pa kg mm
$
%
% 1-10
40
2.9 11
50 75
9
6
6
8
5
9
2
3
1
108 108 75 127 64 186 162 315
0.07 0.07 0.05 0.09 0.04 0.13 0.11 0.22
45.9
2.59 11 150 52
10
0
12
0
3
9
11
0
0
4
1
1
1
3
9
9
mm
#
1/K
0
8
11 12 10
43 42 54
0.03 0.03 0.04
8
0
8
0
8
-
Rossignol Foam Core Snowboard
3
K2 Zeppelin Wood Core Snowboard
+
Hemp Composite Snowboard Concept
3
3
9
+
+
Coefficient of Thermal Expansion (-)
3
9
+
Number of Bolt Holes / Pattern (std)
-
Difference in Tip Radius (-)
1
++
+
External Finish (+)
1
+
Visible Sustainable Materials (+)
1
+
-
+
-
Sustainable Materials (+)
9
3
+
Production Cost (-)
9
3
+
-
Thickness (-)
9
9
+
-
Weight (-)
Impact Strength (+)
+
Tensile Strength (+)
Weight
Robust
8
Good ride
10
Lightweight
5
Competitive retail price
6
More environmentally friendly
9
Increased possibility of recycling
8
Sustainability is obvious
7
Aesthetically pleasing
6
Easy to maintain/transport
6
Weatherproof
10
Universal bolt pattern
4
Easy to ride fakie (both ways)
3
Measurement Unit
Target Value
Importance Rating
Total
Normalized
Hemp Composite Snowboard Concept
K2 Zeppelin Wood Core Snowboard
Rossignol Foam Core Snowboard
+
+
Young's Modulus (+)
+
+
+
+
-
4
4
5
4
5
4
4
5
4
3
5
5
5
5
3
2
2
2
3
5
4
4
5
5
3
3
4
5
1
1
1
2
4
4
5
5
Figure 7. Quality Function Deployment matrix assisting with parameter importance and benchmarking
8
Quantifiable Design Requirements
Examining our design requirements for parameters which can be quantified and eventually
optimized, we first looked at the main focus of our project, which is the sustainability of the
snowboard. We have decided to quantify the sustainability by the percentage of sustainable
materials by volume. This is an important quantity which we are targeting to be 50%. Greater
than 50% can be achieved, but this number represents a major improvement already over
existing snowboards.
As important as sustainability is to our design, we cannot sacrifice strength of the board and
quality of the ride. Therefore we must look at the key quantifiable mechanical properties,
including Young’s modulus, yield and impact strength, and potentially the coefficient of thermal
expansion.
Another quantity which we have optimized is the weight of the board, making it as light as
possible for easy maneuvering. Our target value is 2.9 kg for a board length of 156 cm, which is
on par with some of the lighter boards on the market. The weight will depend on quantities we
can change, such as board thickness and width, as well as the densities of the materials used. We
optimize these parameters by going through a series of core materials, which integrate set
densities into the solver program. The mechanical properties can also be set for each material
and are determined from research and testing; for example, we have determined through testing
(described on page 16) that the modulus of the FlexForm natural fiber composite is 5.09 GPa.
While price is not a technical quantity, it is heavily dependent on the values of engineering
parameters. Since our market research indicated that snowboarders are not willing to pay a
significant additional amount despite the sustainability of the board, we need to minimize price.
Price will be a function of the amount of each material used, which will have fixed costs on a
volumetric basis. Because we do not foresee the need for any new or more complicated
manufacturing methods in the fabrication of the natural fiber snowboard concept, the focus will
be placed on the materials. Issues dealing with price and cost, as well as potential profits, are
discussed in our Initial Microeconomic Analysis on page 20 and our Marketing Analysis on page
22.
The formulation of quantifiable design requirements helps to develop an engineering analysis in
which parameters are optimized. This analysis is described on page 13.
Project Prototypes
To help visualize and communicate possible solutions, we created a rapid mockup prototype,
shown in Figure 8 on page 10. The goal of this prototype was to ensure that each member of the
team understood the order of different layers that would be implemented (Figure 3 on page 3).
This prototype was made from scrap products such as different types of foam board and pieces of
cloth, but accomplished its goal, as anyone we showed it to was able to understand (with an
explanation) what different layers would compose our new design.
9
Topsheet
Laminates
Core
Base
Figure 8. Initial rapid prototype of snowboard cross section
Next, a CAD model of the cross-section was produced (Figure 9 below) to introduce material
proportions and overall dimensions.
Topsheet
Hemp Composite Core
Woven Hemp
Laminates
Plastic Base
Edge
Figure 9. Conceptual snowboard cross section with proposed materials
Then, knowing that our new concept would have the same edge, base and top sheet as most
existing snowboards, we decided to construct the next prototype (alpha) using a section of a
Rossignol foam core board, pictured in Figure 10 on the following page. The foam core was
removed by sawing and sanding, until only the fiberglass, base, edges, and top sheet remained.
A non-woven composite material made from a blend of jute fibers (a derivative of hemp) and
polypropylene, called FlexForm, was discovered and we hoped to use this material as the
replacement core. However, FlexForm is currently only available in 2mm thick sheets and we
had to epoxy three layers together to achieve the desired thickness for the core. For this
10
prototype we wanted to show what a cross-section of the new design would look like compared
to an existing one.
FlexForm composite
core
(replacement)
Foam core
(existing)
Figure 10. Alpha prototype depicting section of foam core board with FlexForm composite replacement
A three-dimensional model of the FlexForm core was created in AutoCAD modeling software
and was then exported to 3D Studio Max where our topsheet design was applied. Figure 11
below shows the 3D rendering of the beta prototype. This design work is particularly important
given that the external finish of the board was the top ranked design parameter on our Quality
Function Deployment model (Figure 7, page 8). The design below also incorporates visibility of
the sustainable core material, a design parameter which ranked third on our QFD.
Figure 11. Three dimensional rendering of the beta prototype
11
Our beta prototype was constructed from a 1600x300x6mm sheet of FlexForm. From this sheet,
the core was created by cutting out the shape and then tapering the thickness from one end to the
other. With the base material on the workshop table, the “lay up” of the snowboard was
completed in the following steps: application of epoxy to base, first layer of fiberglass, epoxy,
FlexForm core, epoxy, second layer of fiberglass, epoxy. It would be at this point in the
manufacturing process that the board would be placed in a press to shape the tip and tail of the
board and to squeeze excess epoxy out from between the layers. Our design team did not have
access to a press at the time of making the beta prototype, so there are no contours to our board
and contains excessive epoxy, making the board heavier than we anticipate for a production level
board. We also neglected edges and binding inserts in our prototype due to additional
manufacturing limitations. After allowing the epoxy sufficient time to set, a final topcoat of
epoxy was applied to enhance the glossiness and finish. The triaxial fiberglass, base material
and epoxies were purchased from a snowboard material supplier, SnowboardMaterials.com [10].
With the epoxies fully set, the excess fiberglass and base material were cut away and the
sidewalls sanded down. The lay up of our beta prototype is shown below in Figure 12.
Figure 12. Beta prototype lay up
A decal of our company logo was then applied to the center portion of the board. The completed
beta prototype is shown in Figure 13 on page 13.
12
Figure 13. Completed beta prototype
ENGINEERING ANALYSIS
Design Optimization
Once we decided on our final design concept of a twin tip board with a core made of sustainable
material and all other materials the same as current boards, the next step was to optimize the
design. For simplification given the allotted time, two main objectives were examined – the
robustness, or rigidity, of the board (desire to maximize), and the weight of the board (desire to
minimize). Intuitively, we realized that there is a tradeoff between these two objectives. Other
objectives were either unable to be optimized with engineering analysis, not as important to the
overall design, or too complex to analyze.
To complete the optimization, we needed to decide on the engineering parameters that we could
change to influence both the robustness of the board and the weight. This led us to look at
establishing several key dimensions as the variable parameters. The variable parameters are
listed in Table 1 and depicted in Figure 14, both on the following page.
13
Dimension
Width of board at center
Thickness of board at center
Width of board at end
Thickness of board at end
End of board to binding
Distance between bindings
Length of contact with ground
Distance between contact surfaces
End of board to contact surface
Designation
wc
tc
we
te
a
b
L
e
d
Table 1. Dimensions used as variable engineering parameters for design optimization
we
wc
te
d
we
tc
e
l
a
w
l
b
w
d
c=a
L
Figure 14. Illustration of board dimensions used in engineering analysis
The analysis models used to compute the objective and constraints in terms of these design
variables were broken up into two groups of functions – beam deflections/loads based on
equilibrium analyses, and a simplified weight calculation. For the equilibrium analyses, the
snowboard was treated as a beam and five load cases were applied, as listed in Table 2 below.
Load Case
1
2
3
4
5
Description
Rider standing on board, flat surface
Rider standing on board, upside down
Riding on rail, board longitudinal
Board cantilevered, point load on end
Board cantilevered, uniform distributed load
Result
Middle deflection, v(L/2)
Middle deflection, v(L/2)
End deflection, v(0)
Maximum load, Pmax
Maximum load, Pmax
Table 2. Load cases used in equilibrium beam analysis
14
This beam analysis was partly inspired by a similar (but more complex) snowboard structural
analysis conducted at the University of Rome in 2005 [7]. Complete derivations of the functions
for the results given in Table 2 can be found in Appendix C.1, along with more details on the
equilibrium analyses performed.
Weight of the board (specifically the core) can be calculated by multiplying the density we
determined for the core material by the volume of our core design in AutoCAD, however we
needed to formulate a model for the weight which depended on the variable parameters; this is
the simplified weight model. The simplified weight model is derived and explained in Appendix
C.2.
For the engineering optimization, we want to maximize robustness, which would be achieved by
minimizing the three deflections in Cases 1, 2, and 3 while maximizing the maximum allowable
loads from Cases 4 and 5 (see Appendix C.1 for load case descriptions). Note that absolute
values are needed for the deflections, since they are originally negative. We also want to
minimize weight, and in this case minimize the simplified weight. Based on these decisions, an
objective function was formulated as follows:
Y = [(v1/v1,orig) + (v2/v2,orig) + (v3/v3,orig) + (Ws/Ws,orig)] / [(P4/P4,orig) + (P5/P5,orig)]
Notice that each output value is normalized to its original value based on the averages of the
design variables collected from snowboard benchmarking.
This objective function Y, the design variables, and other key parameters and constants were
coded into Microsoft Excel for optimization. In addition, the variable dimensions were
constrained so that they must stay within +/- 5% of the original values, which were based on
benchmarking averages. The material properties that we determined for FlexForm (density,
Young’s modulus, tensile strength) were used in the spreadsheet for the calculations. The
spreadsheet also includes intermediate results such as maximum stresses in the snowboard so
that we can easily compare them to numbers such as the yield strength and observe how the
likelihood of failure changes. The original design spreadsheet can be found in Appendix D.1.
The Solver utility, minimizing the objective function, was run several times with different initial
values. The solutions that were generated confirmed the tradeoff between weight and
robustness, and while we were getting very small deflections and large allowable loads, the
weight was very high. Although this was actually somewhat desirable, since we are placing a
greater emphasis on the board being robust than lightweight, we ended up constraining the
weight to a maximum of 2.5% greater than the original. With this additional constraint, we
generated a solution that is optimized to our design preferences. The original and optimized
values for the variable parameters as well as engineering results (including the objective
function) are given on the following page in Tables 3 and 4, respectively. In addition, the
optimized spreadsheet can be found in Appendix D.2.
15
Dimension
wc
tc
we
te
a
b
L
e
d
Original Value (m)
0.24765
0.01
0.25087
0.005
0.46355
0.35985
0.127
1.052
0.127
Optimized Value (m)
0.23527
0.0105
0.25304
0.00525
0.47255
0.34186
0.13335
1.0266
0.13335
Table 3. Original and optimized snowboard dimensions
Result
Y
Ws
v1
v2
v3
P4
P5
Original Value
2
2.65190 kg
0.25681 m
0.45480 m
0.11523 m
19.387 N
37.774 N
Optimized Value
1.65332
2.71820 kg
0.23163 m
0.42023 m
0.09519 m
21.559 N
43.118 N
Table 4. Original and optimized engineering results (note deflections are absolute values)
It is important to note that as far as materials, this engineering analysis was performed
considering the core of the snowboard only. Because of this, the numbers for deflections and
loads do not reflect predicted values for the actual snowboard. For example, the addition of
fiberglass layers greatly enhances the Young’s modulus of the board, which will reduce the
deflections. In this engineering analysis, the deflections, maximum loads, and weights were used
simply to generate optimum values for the variable dimensions.
Also, since material properties such as density and Young’s modulus are discrete and depend on
the specific material used, these could not be varied continuously. However, we are able to
simply substitute in properties for a given material and observe how the results of the
optimization change from material to material, which ultimately will help us to verify our
material choice.
Material Testing
To determine the validity of our core choice, FlexForm, tensile testing was performed on four
different samples. This allowed us to quantify material properties for this composite.
First, we crafted tensile load testing samples of the FlexForm composite material. This was
achieved by drawing the “dog-bone” shaped samples (Figure 15 on page 17) in BobCAD, and
then cutting them using the laser cutter in the G.G. Brown machine shop.
16
Figure 15. Tensile load testing samples of FlexForm
Each of these samples was tested on the Instron 4206 at a rate of 0.1 inches/minute until failure.
The data was recorded and interpreted using Labview 7.0 and Microsoft Office Excel. The
loading force and microstrain were compared and used to produce the relationship between stress
and strain. This relationship was plotted as shown in Figure 16 below. Figure 16 displays the
data for sample ‘D,’ but all produced very similar plots and values for Young’s Modulus and the
ultimate tensile strength.
Stress (MPa)
Flexform Sample 'D' Stress-Strain Relationship
50
45
40
35
30
25
20
15
10
5
0
Ultimate Tensile
Strength = 45.9 MPa
Youngs Modulus = 5.09 GPa
0
0.005
0.01
0.015
0.02
Strain
Figure 16. Tensile testing results for FlexForm sample ‘D’
The testing showed that Young’s modulus was approximately 5.09 GPa, the ultimate tensile
strength was 45.9 MPa, and the density was 801 kg/m3, with the value for Young’s Modulus and
17
density being most pertinent to this project. The values obtained for the other samples were
within 5% of these stated values. The plot does not display a clear yield strength, which leads us
to believe that this material may be viscoelastic. However, due to high levels of equipment use
from ME 395/495, we were limited from doing additional tensile testing at different loading
rates.
To validate our testing results and give reason to believe that this material would function
acceptably as a snowboard core, we compared the material properties of FlexForm to existing
snowboard core materials (polyurethane microcellular foam, birch, ash, maple). This
comparison (Table 5 below) showed that FlexForm was on the high end for density, but still
within range. The Young’s Modulus of FlexForm was between the values for the foam and
wood, which leads us to believe that this material might give a performance between that of a
foam and wood core board. Although this does not mean that FlexForm will definitely work as a
core replacement, it does suggest that it is a possibility.
Core Material
FlexForm
Polyurethane Microcellular Foam
Birch
Ash
Maple
Density (kg/m3) Young’s Modulus (GPa)
801
5.09
700-750
0.0032-0.0036
620-740
14.7-17.9
490-600
10.9-13.3
640-780
12.5-15.3
Table 5. Core material comparison
FlexForm Technologies does not commercially produce a 6mm thick sheet of FlexForm, as we
desired. Our contact informed us that the only way to achieve this thickness was to layer three
2mm sheets, heat them until the polypropylene binder liquefied, and then let them cool under
pressure to form one sheet. FlexForm Technologies agreed to perform this service and shipped
us a 1600x300x6 mm sheet, which was then cut and shaped to our optimized design parameters.
Fiberglass, a base and two-part West Systems epoxy were used to complete the assembly.
Although we strongly desired to compare our prototype material properties to those of existing
snowboards, the time permitted for this project did not allow for this. Final labs occurring in ME
395/495 also severely limited the amount of testing equipment time we had available. However,
using a very rough, but practical estimate of flexing different snowboards including our beta
prototype by hand, our board seemed to have a reasonable rigidity. Should interest in this project
continue into the future, testing of the prototype’s Young’s modulus, torsional resistance,
binding insert strength and resistance to moisture absorption would be strongly desired.
AESTHETIC ANALYSIS
Our Quality Function Deployment matrix (Figure 7, page 8) shows the external finish of our
snowboard as the top ranked design parameter and the visibility of sustainable materials being
the third. The importance of these parameters is reflected by the aesthetic design work we have
completed. Firstly, we have developed a company logo which reflects our eco-friendly values as
18
a company. This logo, which incorporates an image of the world encompassed by a leaf, is
shown below in Figure 17.
Figure 17. Eco-Core company logo
In order to allow for high visibility of our sustainable core material, a clear topsheet will be
implemented in addition to the clear laminate layer above the core. This topsheet is represented
below in a 3D Studio Max model and is also shown on our beta prototype (Figure 13, page 13).
Our company logo will also be applied to the center portion of the topsheet.
Figure 18. Topsheet graphics
The shape of the snowboard was derived from our market surveys which showed the highest
demand for the twin tip board shape (Appendix A.1). Using Microsoft Excel coupled with a
proportionality macro, we were able to evaluate the dimensions of our CAD model based on
eleven different proportionalities. The overall proportionality percentage value for our model is
51.43%. The output of the Excel proportionality macro and the variable dimensions are shown
below in Table 6.
Dimension
Sidecut Length
Tail Width
Nose Width
Sidecut Radius
Nose Radius
Tail Radius
Body Extrusion
Value (mm)
1250
290
290
11000
146
146
7
Minimum (mm)
1245
285
285
11000
140
140
2
Maximum (mm)
1260
300
300
11005
150
150
12
Table 6. CAD model variable dimensions used for proportionality analysis
19
INITIAL MICROECONOMIC ANALYSIS
This section explains how we optimized the design using a postulated microeconomic analysis,
specifically by maximizing profit. Equations 1 and 2 give the profit function where Q is the
quantity of boards sold per year, P is the price per board and C is the cost per year.
Π = QP − C
Q = θ + λ P P + λ d Δα
(1,2)
In equation 2 above, theta (θ) was estimated by researching the current snowboard market. It is
estimated that there are 12 million people who currently snowboard [8], of which we
approximate that one-third will be interested in purchasing a new board this year. As the price of
our snowboard approaches zero, we are able to conclude that the interested population is about
1% of the total market, equal to 40,000 (θ).
By researching current and past designs from major snowboard manufacturers we were able to
conclude that the maximum price we would be able to charge for a board would be about $1000.
Using this information, combined with value of theta, we were able to determine the price
sensitivity (λp = -4000). Demand can increase with optimized parameters of the board, therefore
we can approximate a new demand curve based on our own design parameters. These
parameters would shift the curve outward without affecting the slope (λp). With our optimized
parameters, we estimated that no one would pay more than $1100 for a board, even with our
optimized parameters, and declared this the new maximum price. With the slope constant, λp =
-4000, we were able to determine the new value of theta (θn = 44,000). The quantity ( λ d Δα ) is
equal to the difference between θn and θ and found it to equal 4,000. This quantity represents the
relationship between our design parameters and change in price as well as product demand,
multiplied by a constant.
The three design characteristics we chose to evaluate in the microeconomic model are weight,
stiffness, and percent volume of sustainable materials. Our survey results showed that our
customers demand an increase in percentage of sustainable materials in snowboards. Lower
weight and a board with optimized stiffness are also demanded by our consumers. Table 7
below shows how each of these changes in design characteristics affect price.
Design Characteristic
Weight (Decrease by 10%)
Effect on Cost (per board)
+$15
Stiffness (Optimized)
+$10
Percent Volume of Sustainable Materials
(Increase by 50%)
+$15
Table 7. Consumer design characteristic optimization and effects on cost
The cost function (equations 3 and 4, page 21) was also difficult to determine and involved
significant estimation.
20
C = Q(VC) + FC
C = (θ + λ p P + λ d Δα ) * 250 + 100000
(3,4)
Where:
VC is the variable cost per board, estimated to equal $250
FC is the fixed cost of operating per year, estimated to equal $100,000
The variable cost per board was estimated using data supplied by our sponsor company. The
fixed cost of operating was a much rougher estimate, encompassing costs such as rent,
equipment, licenses, and insurance. This leads to an overall profit equation (5).
Π = (θ + λ p P + λ d Δα ) P − (θ − λ p P + λ d Δα ) * 250 + 100000
(5)
Demand and profit functions were plotted for both the current parameters and our optimized
parameters. This is shown in Figure 19 below.
4
6
Profit from Current Model
Demand from Current Model
Profit from Optimized Model
Demand from Optimized Model
Figure 19. Demand and profit functions for a board with current and optimized parameters
This model shows that when producing this product with current design characteristics, we
should be selling our boards at $625.00 to maximize profit. With the optimized parameters, our
21
selling price should be set at $675.00 to maximize profit. It is important to note that according to
this model, the new design parameters should lead to an increase of 2,000 more snowboards per
year and a profit increase of $260,000 of profit per year. According to FlexForm Technologies,
the increase of purchasing 2,000 more snowboard cores per year will not lead to a decreased cost
per unit. Similarly, our sponsor company stated that this increase would not decrease their
variable cost per board. Therefore, we should aim to sell the board with our design parameters at
a price of $675.00, hoping to achieve a yearly profit of $720,000. Uncertainty in this analysis is
affected most significantly by the estimated design sensitivity. Should this value be much lower
or higher than expected, the predicted profit may change.
MARKETING ANALYSIS
In order to develop a modified microeconomic model which better represents the demand for our
product, we re-examined our market size and conducted a choice based conjoint survey
incorporating different levels of price and design characteristics.
After re-evaluating the snowboard market landscape, we realized that the market is dominated by
large companies. The largest is Burton, which controls roughly 40% of the market, however
there are several second-tier companies such as K2, Forum and Gnu that each claim a good size
of the market as well (5-15%). These companies have all been around for at least a decade, and
their capital and resources greatly exceed that which our company would be able to obtain at
start-up. Therefore, of the 4 million people that are looking to buy a new snowboard each year,
we now estimate that we can capture a maximum of 10,000, or 0.25% of the total market size.
This would be a niche market of environmentally-conscious snowboarders, or simply
snowboarders looking for something unique in their board to be distinguished.
To determine customer preferences based on our snowboard’s key design characteristics, we
assembled a choice based conjoint survey. Three levels were assigned to each of the product
characteristics from the previous microeconomic analysis (weight, stiffness, and percentage of
sustainable materials) as well as price. The survey was administered to approximately 200
members of the Michigan Snowboard Club, and the results generated part-worth (beta) values
that gave an indication of utility, as shown in Table 8 below.
Level
Estimated Beta
Level
Estimated Beta
Level
Estimated Beta
Level
Estimated Beta
Weight
Light (2.35 kg)
Medium (2.55 kg)
0.23169
0.24820
Stiffness Factor
Low (65)
Medium (80)
-0.11127
0.19322
% Sustainable Materials
Low (10%)
Medium (35%)
-0.50767
-0.02791
Price
Low ($300)
Moderate ($450)
0.58615
0.19435
Heavy (2.75 kg)
-0.47989
High (95)
-0.08195
High (70%)
0.53558
High ($600)
-0.78050
Table 8. Choice based conjoint survey levels and results, indicating utility of characteristics
22
It is important to note that the survey was worded in qualitative terms rather than quantitative
terms, such that consumers could relate to their own snowboarding experience. Please see
Appendix E for examples of the choice based conjoint survey questions. It is also important to
note that in order to quantify the stiffness and link it to our design parameters for profit
maximization, we came up with a “stiffness factor”, described by equation 6 below:
StiffnessFactor =
P4 + P5
v1 + v 2 + v3
(6)
Where Pi is the maximum allowable load in load case i and vj is the deflection in load case j (see
Engineering Analysis on page 13). This way, a higher stiffness factor represents a stiffer board.
The results of the survey can be better interpreted in graphical form with a spline function
applied. These results are depicted in Figure 20 below.
Stiffness Factor
1
0.5
0.5
0
2.30
2.40
2.50
2.60
2.70
Part Worths
Part Worths
Weight
1
2.80
-0.5
0
0
20
60
80
100
-0.5
-1
-1
Price
% Sustainable Materials
1
1
0.5
0.5
Part Worths
Part Worths
40
0
0
20
40
60
80
-0.5
0
$-
$200
$400
$600
$800
-0.5
-1
-1
Figure 20. Part worth (beta) values for varying levels of design characteristics, indicating market utility
Clearly, a heavy snowboard is highly undesirable, while there is relative consumer indifference
between a light and mid-weight board. While medium stiffness is most desirable, the range of
beta values is small enough that stiffness is not a significant factor in the minds of consumers.
However, the percentage of sustainable materials is a major factor, with a high percentage (70%)
being most desirable. Also, price is a major factor in the purchase, as expected. Essentially, we
learned from these results that snowboard consumers are willing to sacrifice stiffness for a board
that is not heavy, has a high amount of sustainable materials, and can be sold at a moderate price.
23
To formulate a modified demand model with these beta values, we applied the logit model and
then linearized the demand function. Applying the logit model (with the spline function)
allowed us to generate theoretical part worth values for the design characteristics on a continuous
scale over the ranges specified in the survey. We were then able to linearize the demand
function for our snowboard by using a Taylor series expansion and quantifying the finite
differences associated with a small movement from a “base design” board. This base design,
which was generated from benchmarking current snowboards, had a weight of 2.65 kg, a
stiffness factor of 70.3, a medium percentage of sustainable materials (35%), and a price of $450.
The linear elasticities were then calculated with equation 7 as:
λx =
Q1.05 xb − Qb
1.05 xb − xb
(7)
Where λx is the elasticity of design characteristic (or price) x, xb is the base design level of
characteristic (or price) x, Q1.05xb is the market demand associated with an increase of 1.05 times
xb, and Qb is the market demand of the base design. The new linear elasticities are listed in
Table 9 below.
Product Characteristic
Weight
Stiffness
% Sustainable Materials
Price
Linear Elasticity of Demand
-10935.92 boards/kg
41.34 boards/sf
34.88 boards/percent
-16.06 boards/dollar
Table 9. New linear elasticities for snowboard characteristics, determined from survey results
The spreadsheet in which these elasticities were calculated can be found in Appendix F.1.
Modified Microeconomic Analysis
A modified demand model for the snowboard was generated from equation 2 on page 20 by
plugging in the new linear elasticities as well as our new market size (θ) of 10,000. The cost
model was also reformulated by examining the necessary resources for producing 10,000 boards
or less per year. The modified fixed cost per year came out to be $990,000, which included the
salaries for 17 employees (2 managers, 3 engineers, 2 marketing/sales reps, 2 maintenance
workers, and 8 production employees), the cost of snowboard manufacturing equipment [10], the
cost of renting a 15,000 square-foot facility in Colorado [11], and utilities [12], plus other minor
costs. The variable cost per board came out to be $15.50 per kg of core material [5] and $110 for
the remainder of the board [10].
With these modified demand and cost models in place, the design parameters of the snowboard
(dimensions from Engineering Analysis, page 13) as well as the price were optimized using
Microsoft Excel’s Solver to maximize profit while meeting the engineering constraints. Table 10
on page 25 shows how the design parameters changed from the original benchmarked values, to
the optimized values from the Engineering Analysis, to the final optimized values from the
Modified Microeconomic Analysis.
24
Dimension
Original Value (m)
wc
tc
we
te
a
b
L
e
d
0.24765
0.01
0.25087
0.005
0.46355
0.35985
0.127
1.052
0.127
Engineering
Optimized Value (m)
0.23527
0.0105
0.25304
0.00525
0.47255
0.34186
0.13335
1.0266
0.13335
Microeconomic
Optimized Value (m)
0.24764
0.00971
0.25086
0.00502
0.46355
0.35985
0.127
1.052
0.127
Table 10. Original and optimized snowboard dimensions (from both engineering and microeconomic standpoints)
The resulting design characteristics from these parameters are shown in Table 11 below. Note
that while weight and stiffness factor are functions of the design parameters, percentage of
sustainable materials is determined exogenously.
Characteristic
Original
Weight (kg)
Stiffness Factor
% Sustainable Materials
2.6519
70.3
35
Engineering
Optimized
2.7182
86.6
70
Microeconomic
Optimized
2.5906
65.0
70
Table 11. Original and optimized snowboard characteristics (from engineering and microeconomic standpoints)
With the design parameters optimized for maximum profit, the revenue, costs, and profit
associated with a range of prices were calculated and plotted, as shown in Figure 21 on page 26.
See Appendix F.2 for the base spreadsheet.
25
Eco-Core Snowboard Simple Profit Model
$3,000,000.00
$2,500,000.00
Value
$2,000,000.00
Revenue
Cost
Profit
$1,500,000.00
$1,000,000.00
$500,000.00
$0.00
$0.00
$200.00
$400.00
$600.00
$800.00
$1,000.00
Product Price
Figure 21. New microeconomic model with modified demand function depicting revenue, costs, and profit
The profit is maximized when the price is set to $440, which is the price at which we will sell
our snowboard. At this price, the modified microeconomic model predicts a profit of $344,000.
Note that this analysis is only for the first year of operation, and in future years we are assuming
a potential market growth of 5%, which will slightly change the optimum price (namely an
increase to $460 in the second year).
In the end, we have used consumer input to optimize our snowboard’s design parameters and
price in order to maximize profit. When we conducted our Engineering Analysis, we wanted to
maximize stiffness while keeping the weight from being extremely high. However, when the
optimized parameters from the Engineering Analysis are used in the modified microeconomic
model, the predicted profit is only $191,000, just more than half of the profit predicted with the
optimized parameters from the microeconomic analysis. The reason for this difference is
because we put too much focus on stiffness, as it turned out that it is not a major factor for
consumers. Our final optimized snowboard design has a low stiffness, but also a relatively low
weight, which is desirable. It is also interesting to note that if the percentage of sustainable
materials is set at 35%, the maximum profit is only $15,000 (which would be accomplished at a
price of $400). Therefore by increasing the percentage of sustainable materials to 70%, we can
earn roughly $330,000 more in profit.
As it turns out, replacing the core of the snowboard with the FlexForm natural fiber composite is
very appropriate. While the stiffness of FlexForm is relatively low compared to wood, the
weight can kept at a low-medium level, and most importantly, the percentage of sustainable
materials in the board by volume is increased to approximately 70% (based on the relative
volume of the core).
26
PRODUCT DEVELOPMENT PROCESS
The block diagram in Figure 22 below depicts the steps required to go from our original
identification of the demand for a sustainable snowboard to the potential fabrication of a working
natural fiber snowboard prototype. The design structure matrix (Figure 23, page 28) is similar to
the product development process chart but displays tasks in matrix form to identify straight and
iterative transitions (iterative to the right of the diagonal).
Beyond scope of this project
Figure 22. Product development process for snowboard
27
1
Identify problem
Recognize need and/or want
Research existing products
Brainstorm ideas to address need/want
Examine feasability of ideas
Research ideas
Discuss pros/cons of ideas
Market research
Select design conept
Illustrate concept (alpha prototype)
Identify target market
Identify customer requirements
Identify engineering requirements
Develop key design parameters
Determine market utility for design characteristics
Determine market size
Determine necessary capital/resources
Cost modeling
Develop design elasticities
Link to design parameters
Benchmark similar products in existence
Formulate target values for design parameters
Initial design of product
Virtual modeling
Design for emotion
Develop aesthetics
Design to meet engineering targets
Design for feasible manufacturing
Optimize design (max profit, meet eng. constraints)
Make financial projections
Construct prototype (beta)
Internal testing
Market testing
Review design
Develop manufacturing plan
Verify financial predictions call for success
Initial production runs
Identify/fix problems
Final product
2
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Figure 23. Design Structure Matrix tracking the product development process
There were essentially four main stages of the product development process that were completed.
The initial stage, which involved identifying the market demand for a sustainable snowboard,
recognizing the desire for a counter-culture board material such as hemp, and brainstorming
ways to incorporate hemp into a snowboard design was the first step taken. We came up with
several ways that hemp could be used, but after researching existing snowboard construction and
the construction of hemp composites and weaves, we narrowed our ideas down to a natural fiber
composite core and/or a woven natural fiber laminate.
The next stage, involved selecting the design concept and defining the parameters to start
focusing on. A Pugh matrix was used (Figure 6, page 7) to select the most promising design
concept from a host of material and shape combinations, which turned out to be a twin tip board
with a natural fiber composite core and woven natural fiber laminate. An alpha prototype
(Figure 10, page 11) has been constructed to illustrate our design concept. In conjunction with a
market research survey, a QFD (Figure 7, page 8) was used to translate customer requirements,
such as a competitive price and high content of sustainable materials, into design parameters.
Our decision to shift our design focus to the core alone (rather than the laminate layer) was also
part of this stage. Modifying both the core and the laminate layer would entail extensive
engineering analysis that would require additional education and far more time than was allotted
for this course, and was therefore out of the scope for this project.
28
#
The third stage involved optimizing the snowboard design concept from an engineering,
manufacturing, marketing, and financial perspective. We completed the engineering and
economic analyses as described on pages 13 and 20, respectively. Our first survey results, as
well as results from a revised survey, supplied us with marketing input that was used to enhance
the engineering and economic analyses. Specifically, the revised survey, in conjunction with
Sawtooth SSI Web software, provided “part-worth” values (an indication of utility) for each of
the design characteristics of weight, stiffness, price, and percent sustainable materials. This
enabled us to formulate a modified demand model for our product, which led to optimization of
the design parameters to maximize profit. These values, along with the QFD matrix, helped us
to conceptualize and build a prototype with the most desirable characteristics.
Construction of the beta prototype, a full-scale model, was the final stage of this project. This
required obtaining the necessary materials from online resources, stacking the layers, and
completing assembly by bonding with two-part epoxy. Ideally, a snowboard should be
assembled as previously described and then subjected to very high pressures in a snowboard
press and allowed to cure. Lacking this resource, we assembled the board without a press and
still achieved a very aesthetically appealing prototype.
Our final product development process model changed over the duration of this project. Each
team member created their own plan at the beginning of the project. Goals and the amount of
work spent on each phase differed slightly between members. As the project progressed, certain
limitations, specifically time, equipment, and extensive knowledge of advanced materials, helped
us to mold our individual plans into one model. We began to see that it was no longer feasible to
investigate the replacement of both the core and reinforcing layer. We also determined that
phases such as durability testing, completing a production run, or verifying financial predictions
by monitoring sales were advanced stages and were not in the scope of this project.
PRODUCT BROADER IMPACT
As previously described, snowboards have existed in different variations for over forty years,
gaining most popularity in the last fifteen. Our product is not a new invention but not all great
ideas are. Take the Apple computer corporation for example. Apples and PC’s were developed
around the same time and each had their own advantages. However, as time progressed, PC’s
started to dominate the market and Apple’s sales began to fade. In the late 1990’s, however,
Apple made changes that addressed the weaknesses of the PC, namely reliability and ease of use.
By creating computer and digital media players that were more intuitive, aesthetically appealing,
and overwhelmingly reliable, Apple regained a large portion of the market. The same
philosophy is true for our product. Our goal was not to produce the strongest or lightest
snowboard on the market. Rather we focused our efforts on a product that the user could connect
to emotionally, aesthetically, and even environmentally.
If we could produce a product that meets current snowboard standards while using materials that
place less stress on our environment, had an emotional appeal to the ‘counter-culture,’ and could
help to encourage others to be more eco-conscious, we would consider this concept a success. If
we found potential ways to reduce weight or achieve better material properties, that would be
29
even better but not essential. We feel that this product would be successful especially because of
its emotional and aesthetic appeal.
At the start of this project, our design team members came together with different viewpoints and
passions; each of which were accommodated for within the scope of this project. For example,
Chris has a passion for sporting goods and events whereas Curtis has an interest in the outdoor
sports industry and Tom has a borderline obsession with snowboarding. Collectively, all of us
are passionate about our planet and decreasing the amount of harm that is being inflicted upon it.
Bringing the three of us together provided a multi-dimensional work atmosphere with different
backgrounds and strengths, granting the team an exceptional opportunity to be successful with
the final product.
It is rewarding as a designer to work on a project that helps people to get outside and enjoy the
astounding beauty of the world that we live in. This feeling is so much more rewarding than
designing a product that encourages people to be inactive like a new video gaming system. Our
team shares the fundamental belief in staying healthy by remaining active, but doing so while
enjoying the experience. If we can design a product which the user has a positive emotional
connection to, that person will be more likely to want to get out, use it, and be active. We will
then have created a product that we deem successful.
CONCLUSION
The Eco-Core snowboard started out as an idea that would appeal to the counter-culture
snowboarder. We began by conceptualizing ways to modify the basic components, namely the
core, reinforcing layer, topsheet, base and edges. Of these we decided that the core composes the
largest percent volume of the snowboard and would be a significant modification. The
reinforcing layer, most commonly fiberglass, also posed interest. The team decided that the
remaining components either made up a small volume percentage of the board or were not
possible to make more eco-friendly.
Efforts during the first month of the project were focused on looking for alternative materials for
the core and reinforcing layer. We found multiple options for each, but came to the agreement
that with the given time, it was not feasible to work on replacing both components. Having
found more options for core replacement and more equipment available for testing than for the
reinforcing layer, it was decided to focus our future efforts solely on the core. Upon validation
testing, a material called FlexForm was chosen as the best natural fiber replacement. The
material properties were between those of wood and foam, materials currently used as
snowboard cores. FlexForm Technologies supplied us with a full-size sheet, which we cut to
form and modified the taper to match our design. Originally, we had hoped that our sponsor
company would be able to use our core and their pressing equipment to assemble our prototype,
complete with tip curvature, edges, and binding inserts. However, due to internal complications,
the company informed us that this would not be possible. Therefore, we decided to do the next
best option: purchase the supplies and make the prototype in a workshop without the aide of a
press. The prototype turned out exceptionally well despite lacking a press but is heavier than
30
normal due to the excess epoxy that would normally have squeezed out under the pressing
operation.
We are extremely excited about the outcome of this project but know that future work and testing
is required before production can begin. Before a snowboard model can be sold, all
manufacturers insist that boards meet certain torsional resistance and binding mounting strength
specifications, neither of which have been tested yet. Also, a series of prototype boards would
have to be ridden extensively for a period of time to determine if this core’s material properties
change over a period of time. Even if all testing was completed and showed promising results,
our team has decided that this is not an idea we would like to pursue. Current snowboard
manufacturers, especially the large companies, are extremely powerful and control such large
portions of the market. We feel it would be very difficult to form a start-up company and be
successful with only this idea. Had we developed this concept 10 years ago, when snowboarding
was much newer, we might feel differently. The team has decided that the best future for this
concept and us would be to sell the intellectual property to an existing snowboard company and
have them integrate the idea as another option in their line.
As a team, we would like to thank Dr. Panos Papalambros, the class assistants, Bart
Frischknecht, Katie Kerfoot, Erin MacDonald and especially Jarod Kelly for his efforts in the
concept development. The enthusiasm and encouragement given was extremely helpful and
inspiring.
31
RESOURCES
[1] A REEDF Project: “Manufacturing Process Development for Natural Fiber Reinforced
Thermoplastics for High Stiffness Applications.” Professor Pankaj Mallick, University of
Michigan-Dearborn, 2006.
[2] Food and Agriculture Organization of the United Nations: “Agricultural Commodities:
Profiles and Relevant WTO Negotiating Issues,” October 31, 2006,
http://www.fao.org/docrep/006/Y4343E/y4343e00.htm.
[3] Dewey & Merrill: “Bulletin #404.” U.S. Department of Agriculture, 1916.
[4] Arnold, Brandon: “History of Snowboarding,” About.com, October 3, 2006,
http://snowboarding.about.com/cs/basics1/a/history.htm.
[5] FlexForm Technologies: “Products,” October 30, 2006,
http://www.flexformtech.com/prod/prod.html.
[6] FlexForm Technologies: “Molding the Future with Natural Fiber Composites,” 2006.
[7] Biancolini, M.E., Reccia, L., and Zanini, A.: “Structural Analysis of a Snowboard,”
University of Rome “Tor Vergata”. Rome, Italy, September 2005.
[8] Healthlink, Medical College of Wisconsin: “Preventing Snowboarding Injuries,”
November 1, 2006, http://healthlink.mcw.edu/article/976736567.html.
[9] K2 Snowboards: “K2 Snowboarding Technology,” September 26, 2006,
http://www.k2snowboards.com/tech.
[10] SnowboardMaterials.com: “Materials,” November 22, 2006,
http://www.snowboardmaterials.com/pages/materials2.htm.
[11] CityFeet, Commercial Real Estate Listings & News, November 27, 2006,
http://www.cityfeet.com/searchspace/detailedlisting.asp?ListingID=1158547
[12] ACHE Energy & Utilities Report: “Utilities cost per square foot,” 2005,
http://www.southalabama.edu/instres/pdf/phys_fac/table6.4.pdf
32
APPENDIX A: INITIAL SURVEY RESULTS AND QUESTIONS
A.1: Survey Results
This initial survey was sent to fellow classmates as well as members and officers of the Michigan
Snowboard Club. At the time the data for this report was gathered, 71 people had completed the
survey, 57 of which were snowboarders.
Market Demand for Snowboard Attributes
1.5
1
$275 Retail Price
0.5
Beta Value
Twin Tip
Board Shape
$350 Retail Price
70% Sustainable Materials
35% Sustainable Materials
0
-0.5
Directional
Board Shape
Powder
Board Shape
No Sustainable Materials
-1
$425 Retail Price
-1.5
Figure 24. Market favors cheaper, twin tip snowboards with a high percentage of sustainable materials
A-1
Total Number of Respondents
Average Age
Max Age
Min Age
Average Snowboard Experience
Average Recycling Habits
Average Board Maintenance Habit
% of people that own a hemp product
Average Concern for Global Warming
71
20.8
35.0
17.0
2.9
5.3
4.2
39.4
5.3
Materials Questions
% of people that thought a board
contained:
Wood
Plexiglass
Hair
Steel
Fiberglass
Plastics
Wax
Baby Squirrels
Glass
Carbon Fiber
Rubber
Foam
Hemp
Gold
Aluminum
Cotton
47.9
43.7
0.0
29.6
87.3
87.3
52.1
5.6
5.6
78.9
11.3
16.9
2.8
0.0
31.0
1.4
Table 12. Survey data
A-2
A.2: Survey Questions
The questions on the following page were asked in random order. Six of the questions (2 of
which are shown below) were generated using a random combination of three of our snowboard
attributes: retail price, board shape and percentage of sustainable materials. The results from
these questions generated market demand for each attribute as shown in Figure 13 on page A-1.
A-3
A-4
A-5
APPENDIX B: PHOTOS OF BENCHMARKED SNOWBOARDS
Figure 25. K2 Zeppelin snowboard with twin tip shape, wood core, and fiberglass laminate
Figure 26. Rossignol snowboard with twin tip shape, foam core, and fiberglass laminate
B-1
APPENDIX C: ENGINEERING ANALYSIS MODELS
C.1: Equilibrium Analysis (Snowboard as a Beam)
Using singularity
V = internal shear force, M = internal bending moment, v = vertical deflection, P = load
Note (dV/dx) = -q(x), (dM/dx) = -V(x), EI(d2v/dx2) = M(x)
Cross Sections
y
For center of board Æ Ic = (1/12)wctc3
tc
z
wc
y
For end of board Æ Ie =
(1/12)wete3
te
z
we
Case 1: Rider standing on board, flat surface, find middle deflection
W/2w
W/2l
d
W/2w
W/2l
e
l
a
w
l
b
w
d
c=a
L
(note that the board is shaped so that there is a gap between the middle and the ground)
Max bending moment at middle of board, so use Ic
q(x) = (W/2l)<x-d>0 – (W/2l)<x-(d+l)>0 – (W/2w)<x-a>0 + (W/2w)<x-(a+w)>0 – (W/2w)<x(a+b+w)>0 + (W/2w)<x-(a+b+2w)>0 + (W/2l)<x-(d+e+l)>0 –
(W/2l)<x-(d+e+2l)>0
C-1
dV/dx = -(W/2l)<x-d>0 + (W/2l)<x-(d+l)>0 + (W/2w)<x-a>0 – (W/2w)<x-(a+w)>0 +
(W/2w)<x-(a+b+w)>0 – (W/2w)<x-(a+b+2w)>0 – (W/2l)<x-(d+e+l)>0 +
(W/2l)<x-(d+e+2l)>0
V(x) = -(W/2l)<x-d>1 + (W/2l)<x-(d+l)>1 + (W/2w)<x-a>1 – (W/2w)<x-(a+w)>1 + (W/2w)<x(a+b+w)>1 – (W/2w)<x-(a+b+2w)>1 – (W/2l)<x-(d+e+l)>1 +
(W/2l)<x-(d+e+2l)>1 + C1 Æ C1=0 (V(0)=0)
dM/dx = (W/2l)<x-d>1 – (W/2l)<x-(d+l)>1 – (W/2w)<x-a>1 + (W/2w)<x-(a+w)>1 – (W/2w)<x(a+b+w)>1 + (W/2w)<x-(a+b+2w)>1 + (W/2l)<x-(d+e+l)>1 –
(W/2l)<x-(d+e+2l)>1
M(x) = (W/4l)<x-d>2 – (W/4l)<x-(d+l)>2 – (W/4w)<x-a>2 + (W/4w)<x-(a+w)>2 – (W/4w)<x(a+b+w)>2 + (W/4w)<x-(a+b+2w)>2 + (W/4l)<x-(d+e+l)>2 –
(W/4l)<x-(d+e+2l)2 + C2 Æ C2=0 (M(0)=0)
EI (dv/dx) = (W/12l)<x-d>3 – (W/12l)<x-(d+l)>3 – (W/12w)<x-a>3 + (W/12w)<x-(a+w)>3 –
(W/12w)<x-(a+b+w)>3 + (W/12w)<x-(a+b+2w)>3 + (W/12l)<x-(d+e+l)>3 – (W/12l)<x(d+e+2l)>3 + C3 Æ C3≠0 (dv/dx(L/2)=0)
Æ C3 = (W/12) {[-(L/2-d)3+(L/2-(d+l))3]/l + [(L/2-a)3-(L/2-(a+w))3]/w}
EI v(x) = (W/48l)<x-d>4 – (W/48l)<x-(d+l)>4 – (W/48w)<x-a>4 + (W/48w)<x-(a+w)>4 –
(W/48w)<x-(a+b+w)>4 + (W/48w)<x-(a+b+2w)>4 + (W/48l)<x-(d+e+l)>4 – (W/48l)<x(d+e+2l)>4 + C3 x+ C4 Æ C4=0 (v(d)=0)
v(L/2) = (W/48EI) {[(L/2-d)4-(L/2-(d+l))4]/l+[-(L/2-a)4+ (L/2-(a+w))4]/w} + (C3L)/(2EI)
(note that deflection will be negative, indicating down towards the ground)
Case 2: Rider standing on board, upside down, find middle deflection
W/2
W/2w
W/2w
d
W/2
e
l
a
w
l
b
w
L
C-2
c=a
d
Max bending moment at middle of board, so use Ic
q(x) = (W/2)<x-0>-1 – (W/2w)<x-a>0 + (W/2w)<x-(a+w)>0 – (W/2w)<x-(a+b+w)>0 +
(W/2w)<x-(a+b+2w)>0 + (W/2)<x-L>-1
(Select steps are listed below, otherwise v(x) is found similar to Case 1)
EI (dv/dx) = (W/4)<x-0>2 – (W/12w)<x-a>3 + (W/12w)<x-(a+w)>3 –
(W/12w)<x-(a+b+w)>3 + (W/12w)<x-(a+b+2w)>3 + (W/4)<x-L>2 + C3
Æ C3≠0 (dv/dx(L/2)=0)
Æ C3 = (W/12) {-3(L/2)2 + [(L/2-a)3-(L/2-(a+w))3]/w}
v(L/2) = (W/48EI) {4(L/2)3 + [-(L/2-a)4+ (L/2-(a+w))4]/w} + (C3L)/(2EI)
(note that deflection will be negative, indicating down towards the ground)
Case 3: Riding on rail, board longitudinal (board slide), find end deflection
d
W/2w
W
W/2w
e
l
a
w
l
b
w
d
c=a
L
Note max bending moment at middle of board, so use Ic
q(x) = -(W/2w)<x-a>0 + (W/2w)<x-(a+w)>0 + W<x-L/2>-1 – (W/2w)<x-(a+b+w)>0 +
(W/2w)<x-(a+b+2w)>0
(Select steps are listed below, otherwise v(x) is found similar to Case 1)
EI (dv/dx) = -(W/12w)<x-a>3 + (W/12w)<x-(a+w)>3 + (W/2)<x-L/2>2 –
(W/12w)<x-(a+b+w)>3 + (W/12w)<x-(a+b+2w)>3 + C3 Æ C3≠0 (dv/dx(L/2)=0)
C-3
Æ C3 = (W/12w) [(L/2-a)3-(L/2-(a+w))3]
EI v(x) = -(W/48w)<x-a>4 + (W/48w)<x-(a+w)>4 + (W/6)<x-L/2>3 –
(W/48w)<x-(a+b+w)>4 + (W/48w)<x-(a+b+2w)>4 + C3 x + C4 Æ C4≠0 (v(L/2)=0)
Æ C4 = (W/48w) [(L/2-a)4-(L/2-(a+w))4] – C3(L/2)
v(0) = C4/(EI)
(note that deflection will be negative, indicating down towards the ground)
Case 4: Board cantilevered, find maximum load on end
P
L
Note max bending moment at end of board, so use Ie
For cantilevered beam with point contact load on free end,
v(L) = (PL)3/(3EI)
Mmax = PL (at x=0)
σ = (My)/I Æ M = (σI)/y and Mmax = [(σy/S)I]/y
(with y = t/2, and note safety factor S)
Æ Pmax = Mmax/L = [(σy/S)I]/[L(t/2)] (use yield strength determined from testing)
(note Pmax is the maximum load the board can take under these conditions before yielding, with
safety factor included)
C-4
Case 5: Board cantilevered, find maximum load if distributed
P/L
L
Note max bending moment at end of board, so use Ie
For cantilevered beam with uniform distributed load,
v(L) = (PL)3/(8EI)
Mmax = PL/2 (at x=0)
σ = (My)/I Æ M = (σI)/y and Mmax = [(σy/S)I]/y
(with y = t/2, and note safety factor S)
Æ Pmax = 2Mmax/L = [2(σy/S)I]/[L(t/2)] (use yield strength determined from testing)
(note Pmax is the maximum load the board can take under these conditions before yielding, with
safety factor included)
C-5
C.2: Simplified Weight Calculation
Weight can be calculated by multiplying the density we determine for the core material by the
volume of our core design in AutoCAD, however we needed to formulate a model for the weight
which depended on the variable parameters; this is the simplified weight model.
Simplified view from side of board
tc
te
a
w + b/2
L/2
L
Simplified side area = As = 2[(1/2)a(tc-te) + (w+b/2)(tc-te) + (L/2)(te)]
For width, average value used Æ wavg = (wc+we)/2
Then simplified volume = Vs = Aswavg
And simplified weight = Ws = ρVs
C-6
APPENDIX D: ENGINEERING ANALYSIS SPREADSHEET
D.1: Snowboard Design Spreadsheet with Original Values
The EcoCore Snowboard Design
Chris Grant, Tom Santoro, Curtis Franklin - APD Fall '06
Objective Functions
Actual weight, W a
1.551017974 kg
Simplified weight, W s
Objective Function, Y
Case 1 middle deflection, v1
2.651897642 kg
2
0.256808232 m
ρV
ρV s
*MINIMIZE*
(see equil. analysis)
Case 2 middle deflection, v2
0.45479827 m
(see equil. analysis)
Case 3 end deflection, v3
0.115225764 m
Case 4 max load, P4
Case 5 max load, P5
19.38703348 N
(see equil. analysis)
M 4 /L
M 5 /L
Design Variables
Center width, wc
Center thickness, tc
End width, we
End thickness, te
Rear to binding, a
Between bindings, b
Contact length, l
Contact to contact, e
F/R to contact, d
Constraints
Board length (a, b)
Board length (l, d)
W s max
wc min
wc max
38.77406695 N
Fixed Values
Density, ρ
Volume, V
Binding width, w
Board length, L
Young's modulus, E
Tensile yield strength, σt
0.25087 m
0.46355
0.35985
0.127
1.052
0.127
avg
1.56 m
1.56 m
2.718195083 kg
2.651897642
0.2352675 m
0.24765
*from testing
(165 lbs)
4
2.06E-08 m
4
2.61E-09 m
0.46355 m
2
0.013282 m
2
0.003311 m
394.4549
95567507
464.3684
1.13E+08
178.1084
43151637
30.24377
2.89E+07
N-m
Pa
N-m
Pa
N-m
Pa
N-m
Pa
Case 5 max moment
30.24377 N-m
Case 5 max stress
2.89E+07 Pa
0.2600325 m
0.24765
tc min
0.0095 m
0.01
tc max
0.0105 m
0.01
we min
0.2383265 m
0.25087
we max
0.2634135 m
0.25087
Y
v1
0.256808 m
te min
0.00475 m
0.005
v2
0.454798 m
te max
0.00525 m
0.005
v3
0.115226 m
a min
0.4403725 m
0.46355
19.38703 N
a max
b min
b max
l min
l max
e min
e max
d min
d max
0.4867275
0.3418575
0.3778425
0.12065
0.13335
0.9994
1.1046
0.12065
0.13335
0.46355
0.35985
0.35985
0.127
0.127
1.052
1.052
0.127
0.127
P4
P5
m
m
m
m
m
m
m
m
m
Original Values (before optimization)
Ws
2.651898 kg
D-1
*from AutoCAD
*from benchmarking
*from testing
1.5
Simplified volume, Vs
Case 1 max moment
Case 1 max stress
Case 2 max moment
Case 2 max stress
Case 3 max moment
Case 3 max stress
Case 4 max moment
Case 4 max stress
m
m
m
m
m
*from Curtis
4.34E+07 Pa
Safety factor, S
Front to binding, c
Simplified area from side, As
0.005 m
3
5.09E+09 Pa
734 N
End moment of intertia, Ie
0.01 m
0.136525 m
1.56 m
Weight of rider, W
Intermediate Results
Center moment of inertia, Ic
0.24765 m
801 kg/m
3
0.001936 m
2
38.77407 N
(1/12)w c t c
3
(1/12)w e t e
3
a (twin tip)
(see weight calc.)
(see weight calc.)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
σ*I/y
σ t /S
σ*I/y
σ t /S
D.2: Snowboard Design Spreadsheet with Optimized Values (after running Solver)
The EcoCore Snowboard Design - OPTIMIZED
Chris Grant, Tom Santoro, Curtis Franklin - APD Fall '06
Objective Functions
Actual weight, W a
1.551017974 kg
Simplified weight, W s
Objective Function, Y
Case 1 middle deflection, v1
2.718195081 kg
1.653319478
0.23163278 m
ρV
ρV s
*MINIMIZE*
(see equil. analysis)
Case 2 middle deflection, v2
0.42022958 m
(see equil. analysis)
Case 3 end deflection, v3
0.09518749 m
(see equil. analysis)
M 4 /L
M 5 /L
Case 4 max load, P4
Case 5 max load, P5
Design Variables
Center width, wc
Center thickness, tc
End width, we
End thickness, te
Rear to binding, a
Between bindings, b
Contact length, l
Contact to contact, e
F/R to contact, d
Constraints
Board length (a, b)
Board length (l, d)
W s max
wc min
wc max
21.55880379 N
43.11760759 N
Fixed Values
Density, ρ
Volume, V
Binding width, w
Board length, L
Young's modulus, E
Tensile yield strength, σt
0.0105 m
0.253036651 m
0.00525 m
0.47254625
0.3418575
0.13335
1.0266
0.13335
m
m
m
m
m
avg
1.56 m
1.56 m
2.718195083 kg
2.651897642
0.2352675 m
0.24765
5.09E+09 Pa
4.34E+07 Pa
734 N
Safety factor, S
1.5
4
End moment of intertia, Ie
Front to binding, c
Simplified area from side, As
0.472546 m
2
0.013899 m
Simplified volume, Vs
Case 1 max moment
Case 1 max stress
Case 2 max moment
Case 2 max stress
Case 3 max moment
Case 3 max stress
Case 4 max moment
Case 4 max stress
0.003394
379.1728
87709750
452.582
1.05E+08
166.322
38473377
33.63173
2.89E+07
m
2
N-m
Pa
N-m
Pa
N-m
Pa
N-m
Pa
Case 5 max moment
33.63173 N-m
Case 5 max stress
2.89E+07 Pa
0.2600325 m
0.24765
0.0095 m
0.01
tc max
0.0105 m
0.01
we min
0.2383265 m
0.25087
we max
0.2634135 m
0.25087
Y
v1
0.256808 m
te min
0.00475 m
0.005
v2
0.454798 m
te max
0.00525 m
0.005
v3
0.115226 m
a min
0.4403725 m
0.46355
19.38703 N
a max
b min
b max
l min
l max
e min
e max
d min
d max
0.4867275
0.3418575
0.3778425
0.12065
0.13335
0.9994
1.1046
0.12065
0.13335
0.46355
0.35985
0.35985
0.127
0.127
1.052
1.052
0.127
0.127
P4
P5
Original Values (before optimization)
Ws
2.651898 kg
D-2
*from Curtis
*from AutoCAD
2
38.77407 N
*from testing
*from testing
(165 lbs)
2.27E-08 m
4
3.05E-09 m
tc min
m
m
m
m
m
m
m
m
m
3
0.136525 m
1.56 m
Weight of rider, W
Intermediate Results
Center moment of inertia, Ic
0.2352675 m
801 kg/m
3
0.001936 m
(1/12)w c t c
3
(1/12)w e t e
3
a (twin tip)
(see weight calc.)
(see weight calc.)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
σ*I/y
σ t /S
σ*I/y
σ t /S
APPENDIX E: CHOICE BASED CONJOINT SURVEY QUESTIONS
Below are two examples of the choice based conjoint surveys questions from our second
marketing survey. A total of 12 questions of this style were asked of the respondent.
E-1
APPENDIX F: MODIFIED MICROECONOMIC CALCULATIONS
F.1: Modified Linear Elasticities of Demand
Attribute Information from Conjoint Survey
Weight (kg)
Level
2.35
Est. Beta
0.23169
Stiffness factor
Level
Est. Beta
Specification
65
-0.11127
2.55
0.2482
2.75
-0.47989
80
0.19322
95
-0.08195
Weight
Stiffness
% Sustainable
Price
2.65
70.3
35.0
560
450
"v"
Our Product
No Choice
% Sustainable Materials
Level
Est. Beta
Price
Level
Est. Beta
Our Final Product
10
-0.50767
$
35
-0.02791
-0.46
-1.45
Part Worth Spline Functions
-0.029712
0.06363
-0.02791
-0.463531
% of Market that Chooses Our Product
73%
27%
70
0.53558
300.00 $ 450.00 $ 600.00
0.58615 0.19435
-0.7805
Market Size
Total Consumers
Qm
10,000
7297
Here we have determined the finite differences associated with a small movement from the "base
design" as used in in the Refined MicroEconomic Model. This allows us to calculate the
associated linear elasticities in a much more accurate way than previously. The elasticities (shown
at right beneath the arrow) can then be used in a New MicroEconomic Formulation.
Engineering Model
Objective Functions
Actual weight, W a
1.551017974 kg
Simplified weight, W s
Objective Function, Y
Case 1 middle deflection, v1
2.651897642 kg
2
0.256808232 m
ρV
ρV s
*MINIMIZE*
(see equil. analysis)
Case 2 middle deflection, v2
0.45479827 m
(see equil. analysis)
Case 3 end deflection, v3
0.115225764 m
Case 4 max load, P4
Case 5 max load, P5
19.38703348 N
(see equil. analysis)
M 4 /L
M 5 /L
Design Variables
Center width, wc
Center thickness, tc
End width, we
End thickness, te
Rear to binding, a
Between bindings, b
Contact length, l
Contact to contact, e
F/R to contact, d
Constraints
Board length (a, b)
Board length (l, d)
W s max
wc min
wc max
38.77406695 N
801 kg/m
3
0.001936352 m
Volume, V
Binding width, w
Board length, L
Young's modulus, E
Tensile yield strength, σt
0.01 m
m
m
m
m
m
avg
1.56 m
1.56 m
2.718195083 kg
2.651898
0.2352675 m
0.24765
*from testing
1.5
(165 lbs)
4
2.06375E-08 m
4
2.61323E-09 m
0.46355 m
2
0.01328225 m
2
0.003310734 m
Simplified volume, Vs
Case 1 max moment
Case 1 max stress
Case 2 max moment
Case 2 max stress
Case 3 max moment
Case 3 max stress
Case 4 max moment
Case 4 max stress
394.4548837
95567506.66
464.3683837
112505968.2
178.1083837
43151637.49
30.24377222
2.89E+07
Case 5 max moment
30.24377222 N-m
Case 5 max stress
N-m
Pa
N-m
Pa
N-m
Pa
N-m
Pa
2.89E+07 Pa
0.2600325 m
0.24765
tc min
0.0095 m
0.01
tc max
0.0105 m
0.01
we min
0.2383265 m
0.25087
we max
0.2634135 m
0.25087
Y
v1
te min
0.00475 m
0.005
v2
0.45479827 m
te max
0.00525 m
0.005
v3
0.115225764 m
a min
0.4403725 m
0.46355
0.4867275
0.3418575
0.3778425
0.12065
0.13335
0.9994
1.1046
0.12065
0.13335
0.46355
0.35985
0.35985
0.127
0.127
1.052
1.052
0.127
0.127
P4
P5
19.38703348 N
a max
b min
b max
l min
l max
e min
e max
d min
d max
m
m
m
m
m
m
m
m
m
*from AutoCAD
*from testing
Safety factor, S
Front to binding, c
Simplified area from side, As
0.005 m
*from Curtis
4.34E+07 Pa
734 N
Original Values (before optimization)
Ws
2.651897642 kg
2
0.256808232 m
38.77406695 N
70.34207879
stiffness
F-1
(1/12)w c t c
3
(1/12)w e t e 3
a (twin tip)
(see weight calc.)
(see weight calc.)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
(see equil. analysis)
σ*I/y
σ t /S
σ*I/y
σ t /S
Qm
5847.00433
7442.43202
7358.09176
6847.31523
Q = θ − λ p P + λTd Δα
5.09E+09 Pa
Weight of rider, W
End moment of intertia, Ie
0.25087 m
3
Linearized Elasticities
Var
"v"
% of Market
Weight
-1.11
58%
Stiffness
-0.38
74%
% Sustainable
-0.43
74%
Price
-0.68
68%
0.136525 m
1.56 m
Intermediate Results
Center moment of inertia, Ic
0.24765 m
0.46355
0.35985
0.127
1.052
0.127
Fixed Values
Density, ρ
Finite Differencing
Specification Part Worth Spline Fns
2.784492524 -0.6807396
73.85918273 0.13864333
36.75 0.00326182
588 -0.6810558
dQm/dVar
-10935.92
41.33519
34.87994
-16.06202
F.2: Modified Microeconomic Model
Price
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
$180.00
$200.00
$220.00
$240.00
$260.00
$280.00
$300.00
$320.00
$340.00
$360.00
$380.00
$400.00
$420.00
$440.00
$460.00
$480.00
$500.00
$520.00
$540.00
$560.00
$580.00
$600.00
$620.00
$640.00
$660.00
$680.00
$700.00
$720.00
$740.00
$760.00
$780.00
$800.00
$820.00
$840.00
$860.00
Quantity
11669.82487
11348.58441
11027.34396
10706.1035
10384.86305
10063.62259
9742.382139
9421.141685
9099.90123
8778.660776
8457.420321
8136.179867
7814.939413
7493.698958
7172.458504
6851.218049
6529.977595
6208.737141
5887.496686
5566.256232
5245.015778
4923.775323
4602.534869
4281.294414
3960.05396
3638.813506
3317.573051
2996.332597
2675.092142
2353.851688
2032.611234
1711.370779
1390.130325
1068.88987
747.6494161
426.4089617
105.1685073
-216.0719471
-537.3124015
-858.5528559
-1179.79331
-1501.033765
-1822.274219
-2143.514673
Revenue
$0.00
$226,971.69
$441,093.76
$642,366.21
$830,789.04
$1,006,362.26
$1,169,085.86
$1,318,959.84
$1,455,984.20
$1,580,158.94
$1,691,484.06
$1,789,959.57
$1,875,585.46
$1,948,361.73
$2,008,288.38
$2,055,365.41
$2,089,592.83
$2,110,970.63
$2,119,498.81
$2,115,177.37
$2,098,006.31
$2,067,985.64
$2,025,115.34
$1,969,395.43
$1,900,825.90
$1,819,406.75
$1,725,137.99
$1,618,019.60
$1,498,051.60
$1,365,233.98
$1,219,566.74
$1,061,049.88
$889,683.41
$705,467.31
$508,401.60
$298,486.27
$75,721.33
($159,893.24)
($408,357.43)
($669,671.23)
($943,834.65)
($1,230,847.69)
($1,530,710.34)
($1,843,422.62)
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
Costs
2,742,282.71
2,694,046.85
2,645,810.98
2,597,575.12
2,549,339.25
2,501,103.39
2,452,867.52
2,404,631.66
2,356,395.79
2,308,159.93
2,259,924.06
2,211,688.20
2,163,452.33
2,115,216.47
2,066,980.61
2,018,744.74
1,970,508.88
1,922,273.01
1,874,037.15
1,825,801.28
1,777,565.42
1,729,329.55
1,681,093.69
1,632,857.82
1,584,621.96
1,536,386.09
1,488,150.23
1,439,914.36
1,391,678.50
1,343,442.63
1,295,206.77
1,246,970.90
1,198,735.04
1,150,499.17
1,102,263.31
1,054,027.44
1,005,791.58
957,555.71
909,319.85
861,083.98
812,848.12
764,612.25
716,376.39
668,140.52
Profit
($2,742,282.71)
($2,467,075.16)
($2,204,717.23)
($1,955,208.91)
($1,718,550.21)
($1,494,741.13)
($1,283,781.67)
($1,085,671.82)
($900,411.60)
($728,000.99)
($568,440.00)
($421,728.63)
($287,866.88)
($166,854.74)
($58,692.22)
$36,620.67
$119,083.95 Optimization
Weight
Stiffness % Sustainable
Profit
$188,697.62 Price
$245,461.66 $
438.35 2.590646
65
70 $ 344,065.31
$289,376.09
$320,440.89
$338,656.08
$344,021.66
$336,537.61
$316,203.94
$283,020.66
$236,987.76
$178,105.24
$106,373.10
$21,791.35
($75,640.03)
($185,921.02)
($309,051.63)
($445,031.86)
($593,861.71)
($755,541.17)
($930,070.25)
($1,117,448.95)
($1,317,677.27)
($1,530,755.21)
($1,756,682.77)
($1,995,459.94)
($2,247,086.73)
($2,511,563.14)
(Engineering Model with parameters to be optimized is below but not shown here)
F-2