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Analytical Product Design

Final Report

Title: Redesign of Drinking Water Fountain

Member of group APD07-05: Mobeen Shaukat Rafael Ramos Adrien Yee Yi Ren

Instructor: Panos Y. Papalambros

Team consultant:

Erin MacDonald

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Contents

1. Introduction ..................................................................................................................... 4 1.1 Problem statement ..................................................................................................... 5

1.2 Preliminary market research ..................................................................................... 5 1.3 Laws and Regulations ............................................................................................... 6 2. Previous Designs ............................................................................................................. 8

Current Patents .............................................................................................................. 10 3. Design Objectives ......................................................................................................... 11

4. Concept Generation ...................................................................................................... 12 4.1 Brainstorming ......................................................................................................... 12

4.2 Selection of concepts .............................................................................................. 12 4.2.1 Attributes.......................................................................................................... 12 4.2.2 Rejected concepts............................................................................................. 12 4.2.3 Concepts chosen for further consideration ...................................................... 13

4.3 Early sketches and prototypes ................................................................................. 13 4.3.1 Concept #1: Adjustable nozzle ........................................................................ 13

4.3.2 Concept #2: Shaped basin ................................................................................ 14 4.3.3 Concept #3: Leveled nozzle ............................................................................. 14 4.3.4 Concept #4: High pressure stream ................................................................... 15

4.4 Selection criteria and method.................................................................................. 16 4.5 Selected Product Concept ....................................................................................... 16

4.6 Product features ...................................................................................................... 17 5. Quantification of Design Concept ................................................................................ 20

6. The Engineering Design ............................................................................................... 22 6.1 Design Attributes .................................................................................................... 22 Ergonomic Consideration ......................................................................................... 22

Hygienic Consideration ............................................................................................ 22 Strength Consideration.............................................................................................. 23

6.2 Design with Mathematical Methods ....................................................................... 23 Ergonomic Optimization Model ............................................................................... 23 Basin Spine Design ................................................................................................... 26 Drain Radius Design ................................................................................................. 29 Strength Consideration.............................................................................................. 30

6.3 Design with Experimental Methods ........................................................................ 31 Beta prototype ........................................................................................................... 31

Basin Boundary and Depth Design ........................................................................... 32 6.4 CAD Model .............................................................. Error! Bookmark not defined. 6.5 Conclusion .............................................................................................................. 34

7. Choice Based Conjoint Analysis .................................................................................. 35 7.1 Logit model ............................................................................................................. 35

7.2 Composition of the utility and CBC results ............................................................ 35 8. The Microeconomic Model........................................................................................... 37

8.1 Market Size ............................................................................................................. 37

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8.2 Cost Estimates ......................................................................................................... 38

Costs independent from design variables ............................................................... 38 Costs dependent on design variables ...................................................................... 38 8.3 Market Share Estimates .......................................................................................... 39

8.3.1 Assumption ..................................................................................................... 39 8.3.2 Utilities from competitors and fE ................................................................... 39 8.4 Profit Model ............................................................................................................ 41

9. Future Work .................................................................................................................. 42 Modeling methods ........................................................................................................ 42

Concepts realization ...................................................................................................... 42 10. Design in the Designed World .................................................................................... 43

Appendix 1 – Business Plan ............................................................................................. 44 Appendix 2- Previous Designs Schematics ...................................................................... 51

Appendix 3 - Relevant Patents .......................................................................................... 53 Appendix 4 - ADA-compliance of the Drinking Fountain ............................................... 54

Appendix 5 - Brainstorming ideas .................................................................................... 55 Appendix 6 - QFD Chart................................................................................................... 57 Appendix 7 - Product Development Process .................................................................... 58

Appendix 8 - Pugh ............................................................................................................ 59 Appendix 9 - Gantt Chart .................................................................................................. 60

Appendix 10 - Survey 1 .................................................................................................... 61 Summary of Survey 1 Results................................................................... 63 Appendix 11 - Survey 2 .................................................................................................... 64

Appendix 12 - Finite element analysis (FEA) used in progress report ............................. 67

Fountain body ........................................................................................... 67 Basin shape ............................................................................................... 68

Appendix 13 - Product architecture .................................................................................. 69

Appendix 14 – Matlab codes ............................................................................................ 72

Figure 1 Drinking fountain ADA requirements .................................................................. 7

Figure 2 Adjustable nozzle concept .................................................................................. 14

Figure 3 Shaped basin concept ......................................................................................... 14

Figure 4 Leveled nozzle concept ...................................................................................... 15

Figure 5 High pressure stream concept ............................................................................. 16

Figure 6 Detailed CAD of product features and user posture ........................................... 17

Figure 7 Water consumption - Nozzle diameter2 diagram ............................................... 18

Figure 8 Clam shell ........................................................................................................... 19

Figure 9 Expanded view of fE .......................................................................................... 19

Figure 10 Determine users satisfactory by bending angle ................................................ 24

Figure 11 ADA requirements for bottle filling ................................................................. 27

Figure 12 The contact angle α........................................................................................... 27

Figure 13 Design with different nozzle position............................................................... 28

Figure 14 Design with different shooting angle ............................................................... 28

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Figure 15 Final design characteristics............................................................................... 29

Figure 16 Block diagram of beta prototype ...................................................................... 31

Figure 17 Beta prototype top view.................................................................................... 32

Figure 18 Beta prototype side view .................................................................................. 32

Figure 19 Beta prototype fixture ....................................................................................... 33

Figure 20 Design flow ...................................................................................................... 34

Figure 21 Beta values for bending angles ......................................................................... 36

Figure 22 Beta values for colors ....................................................................................... 36

Figure 23 Beta values for filling times ............................................................................. 36

Figure 24 Beta values for prices ....................................................................................... 36

Figure 25 Microeconomic model ...................................................................................... 37

Figure 26 Market size estimation ...................................................................................... 37

Figure 27 Business Plan: Drinking water fountain shipments .......................................... 44

Figure 28 Business Plan: Breakeven timeline .................................................................. 49

Figure 29 Stress analysis of fountain body thickness = 2.108 .......................................... 67

Figure 30 Stress analysis of fountain body thickness = 3.048 .......................................... 68

Figure 31 Stress analysis of initial basin design ............................................................... 69

Figure 32 Stress Analysis of modified basin shape .......................................................... 69

Table 1 Design objectives for Ergo Water Fountain ...................................................... 11

Table 2 Design Variables ................................................................................................ 20

Table 3 Nomenclature for Ergo Design .......................................................................... 24

Table 4 Optimization Results for Nozzle Height ............................................................ 25

Table 5 Nomenclature for Ergo Water Fountain ............................................................ 26

Table 6 Strength Analysis Var./Para. .............................................................................. 30

Table 7 Design Methods for Experiments ...................................................................... 33

Table 8 Beta values ......................................................................................................... 35

Table 9 Components cost ................................................................................................ 38

Table 10 Utility for fE....................................................................................................... 40

Table 11 Utilities for competitors ..................................................................................... 40

Table 12 Final optimization results................................................................................... 41

Table 13 Business Plan: Advantages of fE ....................................................................... 47

Table 14 Business Plan: Cost estimation .......................................................................... 48

Table 15 Business Plan: Net present value ....................................................................... 48

Table 16 FEA Results of fountain body ........................................................................... 67

Table 17 FEA Results of basin shape ............................................................................... 68

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1. Introduction

1.1 Problem statement

Drinking water fountain design is over one hundred year old. Observation of drinking

fountain use at the University campus indicated that there is room for improving the

design of these fountains. More specifically, ergonomics, aesthetics, and hygiene of

drinking fountains can be improved through a better design. Along the same lines, more

features can be added to drinking water fountains that will enhance the end user

experience. This project presents the design effort to improve the ergonomics, aesthetics,

and hygiene of drinking water fountains.

1.2 Preliminary market research

A customer survey was distributed to University of Michigan students based on the

problem statement to identify their concerns of using drinking water fountains in the

campus. The survey can be found in Appendix 5 of this report. The survey had 45

respondents, mainly university students.

At the beginning of the survey, a question determines if the respondent is qualified to

take survey by asking if they use the drinking water fountain. This question qualified 42

respondents who use drinking fountain. In the following question, it is found that 81% of

these respondents use the drinking water fountain at least once a day. The responses to

both questions show that the drinking fountain is one of the sources of drinking water for

the majority of students when they are in the university campus and hence any issues

associated with the drinking fountain will most likely have a significant impact.

A quick search on the internet will tell one that one of the main issues of using the

drinking fountain is the quality of the water. Based on initial findings of our team, some

drinking fountains are not frequently examined for their water quality. In some cases, the

level of contaminants (e.g. arsenic, lead, etc) in the drinking fountains goes above the

safety standards undetected until a complaint is made. Among the respondents who are

concerned with the hygiene of using the drinking fountain, 31% of the respondents are

either moderately or extremely concerned. Based on their feedback, they are doubtful of

the water quality as well as the cleanliness of the drinking fountain itself due to heavy

public usage. Besides, 50% of the fountain users are bothered by the splash of water from

the fountain.

In general, not many know how drinking water is processed in the existing drinking

fountains. This is strongly supported by the survey which shown that 88% of the users

cannot identify the type of filtering process in a drinking fountain. This may be one of

factors that deter some respondents from drinking as much as they would from a trusted

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water source such as bottled water. Provision of information such as periodical water

quality, type of filter and its life span may reassure the user and therefore further establish

drinking fountain as main source of drinking water in university buildings.

The ergonomics of using water fountain deals with the posture while operating the

fountain and properties of the water consumed (e.g. temperature, flavor, etc). Only 26%

of the respondents felt uncomfortable with the posture and 14% did not like the taste of

the water. Survey analysis on the limited number of respondents could not identify

relationship between user height and discomfort level. The respondents who felt

uncomfortable with the posture chose back (73%), neck (36%), and hair (27%) as the

causes of discomfort. In order to attain optimum ergonomic posture for fountain users,

the team needs to find the optimum fountain height based on the survey‟s average height

of around 172 cm.

Other than drinking directly from the fountain, the users also use it to fill up bottles. Most

the drinking fountains in the university do not provide separate water dispensing

mechanism for filling bottle. From the survey, it is found that 71% of the respondents are

using fountain for this purpose in which 43% of them had difficulty to do so. Through

observing fountain users, they typically spend an average of 30 seconds to fill up a 500-

800ml water bottle. A more efficient water dispensing mechanism may be to cut filling

time to and possibly reduce wastage of water.

While the design of a drinking fountain is mainly to provide drinking water, the

aesthetics aspect of it, especially in a building, can be used not only to give an

extraordinary drinking experience but even provide a good atmosphere for learning

experience in the university. Although only 24% of the survey respondents thought that

the drinking fountain was not aesthetically pleasing, the drinking fountain may still be

added with cost-effective artistic features to become a highly desirable designer piece.

1.3 Laws and Regulations

Water

Based on our research, the water dispensed through the drinking fountain is regulated for

its quality and its temperature. The Safe Drinking Water Act (SDWA) regulates the

quality and safety of drinking water to protect public health. It regulates 90 contaminants

to their allowable levels as set by Environmental Protection Agency (EPA) and

specifically controls lead contamination through several provisions. EPA recommends

drinking fountain to be taken out of service if lead level reaches 20 ppb. In simplifying

our product design, our team assumes that the quality of the water supply to the drinking

fountain meets the standards and no contaminants are added to the water within the

system. On the other hand, refrigerated drinking water fountain is required to deliver

water temperature between 40˚F to 50˚F by the American National Standard Institute.

Our drinking water fountain will incorporate simple temperature control mechanism to

conform to this requirement.

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Physical Dimensions

The American with Disabilities Act (ADA) placed several constraints on the physical

dimensions of an ADA-compliant drinking fountain to ensure accessibility for disabled

people. Dimensions relevant to our drinking fountain are the distance between the wall to

the front edge of the unit (430-485 mm), max height of nozzle from the ground (915 mm)

and min height of lower edge of the unit to the ground (685 mm). In addition, the nozzle

must be within 75 mm from the front edge of the unit and shall direct the water flow in a

trajectory that is parallel or nearly parallel to the front of the unit. The nozzle shall

provide water stream of at least 4 in (100 mm) high to accommodate insertion of a cup or

glass under the flow of water. As for the unit controls, it shall be front mounted or side

mounted near the front edge.1

Figure 1 Drinking fountain ADA requirements

1 http://www.access-board.gov/adaag/html/adaag.htm#4.15

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2. Previous Designs

There are many different types of drinking water fountains currently available. Among

the biggest manufacturers there are Haws, Elkay, Halsey Taylor. Here is some examples

representative of each of the major categories of water fountains. Detailed engineering

schematics are in Appendix 1.

Category1: Indoors

Wall mounted

Haws 1001FR Wall Mounted Drinking Fountains

Model 1001 is a barrier free, stainless steel drinking

fountain with round sculpted bowl. Bubbler, waste

strainer and push button are polished chrome plated

brass. Model includes vandal resistant bottom plate,

special mounting plate and 1-1/4" O.D. waste arm. It

is manufactured in 18 gauges, Type 304, No. 4 satin

finish stainless steel for easy maintenance and

provides the perfect finishing touch for any project.

Recessed

Haws 2405 Recessed Wall Mounted Drinking Fountains.

Model 2405 is a barrier free, fully recessed, stainless steel drinking

fountain in a 18 gauge, type 304, no. 4 satin finish. It is designed to be

installed above a wheel chair access area. It features front mounted push

button valve and vandal resistant, polished chrome plated brass bubbler

head and waste strainer. The mounting consists of furnished hanging

brackets and screws. 1-1/4" O.D. waste arm. Provision for trap (not

included) must be made in or behind wall. Model 2405 meets all current

Federal Regulations for the disabled, including those in the Americans

with Disabilities Act. Haws manufactures drinking fountains, electric

water coolers and electric drinking fountains to be lead free by all

known definitions including ANSI/NSF Standard 61, Section 9, California Proposition 65

and the Federal Safe Drinking Water Act.

1 Pictures and data collected from www. Doctordrinkingfountain.com

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Pedestal mounted

Haws 3377 Pedestal Mounted Drinking Fountains

Model 3377 is ideal for pedestrian and wheelchair access.

This pedestal drinking fountain may be installed indoors or

outdoors. It features sculpted bowl, front push button,

polished chrome plated brass bubbler head and waste

strainer, hose bib access hole, no. 4 satin finish stainless

steel receptor and bracket, heavy gauge galvanized steel

pedestal with green powder coated finish with top access

plate and vandal resistant screws, push button valve with

automatic stream regulation, vandal resistant bottom plate

on fountain and 1/2" NPT screwdriver stop. Fountain

contains a 12" square integral mounting base with four bolt holes. Anchor bolts are

furnished. Model 3377 meets all current Federal Regulations for the disabled including

those in the Americans with Disabilities Act.

Category: Outdoors

Pedestal mounted

Haws 3060 Pedestal Mounted Drinking Fountains.

Model 3060 is a durable and vandal resistant circular, vibracast-reinforced

concrete pedestal drinking fountain with exposed aggregate finish that is a

perfect complement to all outdoor environments. Vandal resistant features

include bubbler hooded by an extension of the precast pedestal to deter bubbler

damage. It is manufactured with the highest quality cement, select aggregates

and sand. Model 3060 includes push button valve with automatic stream

regulation, concrete guard for polished chrome plated brass bubbler head,

stainless steel access plates with vandal resistant screws and 1/2" NPT

screwdriver stop. Standard color is Portland Gray cement with exposed

aggregate finish. Pedestal is reinforced with 3/16" galvanized wire. The mounting

consists of three furnished integral mounting brackets plus anchor bolts. Matching stone

plugs conceal mountings.

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Current Patents

Some patents for existing drinking water fountains include:

Patent No.: US D545, 109 S – “FOUNTAIN”

Patent No.: US D547, 104 S – “DRINKING FOUNTAIN”

Patent No.: Des 343,330 – “DRINKING FOUNTAIN”

See Appendix 3 – Current Patents for patent details.

These patents provided us with a preliminary understanding of how certain materials (like

aluminum) are used often to help standardize elements like the basin, in order to achieve

a minimum level of hygiene. This also facilitates cleaning with standard cleaning

products.

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3. Design Objectives

The overall objective of current design activity is to enhance the experience of water

fountain user by improving the form and function of water fountain. After observing

users, analyzing survey data, and reviewing the current products available, design

objectives given in Table 1 were selected for the project.

Table 1 Design objectives for Ergo Water Fountain

Design Objective Quantitative Measurement

Ease of use Comfortable posture – back angle

Effort to activate the fountain

Height of fountain

Ease of filling bottle Effort required to fill the bottle

Time required to fill the bottle

Improved Hygiene Surface area of basin

Drain rate of water

Information availability Information display for ads, news etc.

Water quality display

Improved visual appeal Color appeal on scale of 1 – 5

Shape appeal on scale of 1-5

Material appeal on scale of 1- 5

Competitive pricing Price equal to current water fountain

Overall user satisfaction User satisfaction on scale of 1 -7

These objectives fall into three categories: function, form, and business. The function of

the current water fountain will be enhanced by improving the ergonomics of the fountain

and at the same time by providing extra features that are currently not available, like

information display.

Initial survey indicated that there is room for improving aesthetics of water fountain.

Aesthetics is very subjective and difficult to measure. However, subjective rating will be

used to compare the improved design versus the current design. Shape, color, and

material will be varied to improve the aesthetics of the fountain. The goal of the project

will be to make water fountain a sculpture piece that at the same time serves the purpose

of quenching thirst.

Since the user group and buyer for this product are different, it is difficult to develop a

business objective. Users selected for the study are students whereas buyer is the

construction firm or the University. Nevertheless, the goal of the project will be to

provide added functionality and visual appeal at a comparable price of a current water

fountain.

These objectives were used to construct the QFD that is given in Appendix 6. Also

several concepts were evaluated using these objectives. This concept selection process is

explained in the next section.

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4. Concept Generation

In this chapter the solution concepts are developed and addressed in the effort of finding

the most promising solution for further analysis. This is done by using brainstorming to

develop the concepts, followed by a careful categorization of concepts and a systematic

decision making process. Finally, the design requirements that can be quantified for

engineering analysis are chosen.

4.1 Brainstorming

With existing observation, survey analysis and design requirements, the team came up

with 24 concepts by brainstorming, each of which aimed at some of the requirements.

These ideas were further filtered through group discussion and voting, ended up with 4

favorite choices. Pugh chart was then applied with the guidance of weighted design

requirements, and a final decision was made. Other concepts were also reviewed as

substitutes. The list in Appendix 4 shows the results of the brainstorming.

4.2 Selection of concepts

An initial selection of the most reasonable concepts was made starting from the original

brainstorming. Some of the original concepts where considered too extravagant or likely

to be prohibitively expensive. We also noted that some concepts have similar function,

and are more like attributes that can be added to other ones (listed in 4.2.1).

4.2.1 Attributes

Numbers 1-7 are identified as attributes, which fall in the following categories:

*Trigger improvement: 1, 2, 4 and 7

*Hygienic devices: 3

*Bottle filling facility: 5 and 6

4.2.2 Rejected concepts

Number 13 and 16 are already on the market so these ideas are not relevant in the further

development of a new product.

Number 14 is obviously not cost-effective and unfriendly to users. Number 15 is

applicable but not appealing to manufacturers as well as maintenance, and it‟s also

expensive to build.

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Ideal ergonomic targets will be met by applying number 17 and 20; however, these

concepts obviously neglect hygiene concerns, which are in fact, one of the most

important considerations in our design.

Number 19, 21 and 22 are scrapped simply because we have similar ideas of these.

Number 18, where users with different height can easily approach the fountain without

adjusting their posture, is also discarded. An obvious reason for discarding this idea is the

possible unpleasant water splash. Other obstacles with this concept include its drainage

system and its coordination with surroundings.

Number 24 is space demanding and is somewhat redundant in its function. Number 12 is

also canceled because it involves too much material which our team need to avoid.

Moreover, we have no idea how to convince our manufacturers to produce an instant

product with little profit.

Number 23 is scrapped as well because there might be too much work to accomplish, and

since none of our team members have EE background, this idea is not practical.

4.2.3 Concepts chosen for further consideration

Concepts 8, 9, 10 and 11 are considered as possible solutions. They are all capable of

fulfilling the design objectives in some way. Furthermore, the team considered the

manufacturability of these four options and it is concluded that these concepts are both

feasible to realize and cost-efficient to meet demands. A more comprehensive analysis of

the concepts is thus given below.

4.3 Early sketches and prototypes

Brief hand sketches and CAD models were built to visually understand and evaluate

concepts. This is done to facilitate team discussion over whether and how these concepts

meet the requirements and to explore possible questions in the concepts.

4.3.1 Concept #1: Adjustable nozzle

The concept shown in Figure 2 consists of an adjustable nozzle, both in-plane position

and its height, which allows the user to drink with left and right neck rotation

(conventionally, people use drinking fountain by rotating their necks to the right). Further

development in this direction will involve design decisions like: the number of nozzles

needed, the rotation angle of the nozzle, a appropriate rotation force and the physical

dimension of the basin. A disadvantage of this concept is that bottle filling facility is not

included.

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Figure 2 Adjustable nozzle concept

4.3.2 Concept #2: Shaped basin

This solution shown in Figure 3 is developed to eliminate remained water in basin. Also,

the curved basin shape was supposed to help avoid water splash on the use. By adapting

this concept, several things needed to discuss further: 1. What contour of the basin we

need to meet our desirable result, that is, both eliminate remained water and reduce water

splash; 2. What nozzle position and stream pressure we need to cooperate with the basin

contour to meet our goals; 3. What materials to apply to the basin so that from

manufacturer perspective, this design is cost effective to produce; 4. Again, the basic

physical dimensions will need to be discussed.

Figure 3 Shaped basin concept

4.3.3 Concept #3: Leveled nozzle

This solution is a straight answer to our design objectives. Both leveled nozzles and

bottle filler are included. The bottle filler suppose to acquire range or force sensor so

button is omitted. By installing leveled nozzles, our goal is to reduce bending motion of

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users, thus in turn increase their satisfaction of drinking posture. One significant problem

with this concept is that higher nozzle increase the possibility of water splash, which

could only be eliminated by either increasing the basin radius or reducing the stream

pressure. However, neither amendment has positive effect on user satisfaction. So, the

main objective of this concept realization is to optimize its function by appropriate design

of the elements mentioned above.

Figure 4 Leveled nozzle concept

4.3.4 Concept #4: High pressure stream

A water station is an extension of the previous concept with higher stream pressure.

Water shoots from left side to right side so people can approach water directly. This idea

is somewhat fancy and a major problem is whether people can afford this high water

pressure. Further research of water property will be needed if we go this way.

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Figure 5 High pressure stream concept

4.4 Selection criteria and method

The four concepts have been illustrated and one primary concept is going to be chosen.

Pugh chart is introduced to rank these concepts. Specific criteria are imported from QFD

shell and weights are given based on team discussion. For each criterion, concepts are

evaluated from -3 to +3 by members‟ knowledge and experience. As can be seen in the

chart, the result yields one positive score (Concept #2) and three negative ones. The gaps

among scores are significant. This is because weighting coefficients for design objectives

are relatively high. We all consider the result valid and Concept #2 is finally chosen.

4.5 Selected Product Concept

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Figure 6 Detailed CAD of product features and user posture

Figure 6 shows a compilation of views of detailed CAD of product features including the

view of a potential user.

4.6 Product features

Hygiene

The hygiene of aspect of the drinking fountain is improved with an innovative basin

design. It is designed to reduce water splash to the user by making the contact point

between the water droplets and basin surface 37 degrees more parallel. The water splash

is significantly reduced compared to a flat basin design. As presence of water promotes

growth of germs, the shape of the basin surface is also designed to closely resembles a

brachistochrone curve i.e. curve of fastest descent to minimize water containment on the

basin. This shape will considerably reduce the water left on the basin than a flatter

design.

Water consumption

Info display

Automatic sensing

Bottle filler

Nozzle

Splash

reducer

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In determining the diameter of the nozzle, results from an experiment done by K.

Coetzee, and C. Bennett in 19781 are analyzed. This experiment studies the effect of

nozzle diameter on drinking time, water utilization, water consumption and power used

per user within a range of 3mm to 9mm. A 6mm nozzle diameter is chosen for highest

water consumption of 60 cm3 per person while compromising 15% lower water

utilization and 10% higher power used per user.

Figure 7 Water consumption - Nozzle diameter2 diagram

Accessibility

Using the drinking fountain is effortless with automatic sensing controls placed at easily

accessible location. With this control mechanism, the user can use the drinking fountain

without having to touch it, hence eliminating hygienic concern. For filling bottles, a

simple yet effective feature, with a small basin and automated filler, is added to make the

process quick and easy. The drinking fountain will also comply with the ADA

requirements for disabled users (Appendix - ADA Requirements).

Information display

With the information display screen, various types of information will be shown to the

users. If the information displayed is attractive to the user, it should encourage more users

to drink from the fountain. Real-time information such as weather and time, Mbus

arrivals, news and events, etc can be easily acquired and shown. In addition, the “health”

status of the drinking fountain will also be available to the user by simply stating the filter

change due date.

Emotional Design

1 K. Coetzee, and C. Bennett , The efficiency of a drinking fountain, Applied Ergonomics 1978, 9.2, 97-100

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The drinking fountain incorporates emotional design to inflict a sense of hygiene and

purity in the mind of the users with shiny finishing on the stainless steel fountain body

and basin. The clam shell shaped basin will also improve the ambience in a building and

contribute to people feeling positive about the surroundings.

Figure 8 Clam shell

Modularity

By integrating modularity the product architecture, the drinking fountain can be easily

customized to address specific user needs. The bottle filler and information display

screen can be optionally packaged with the basic drinking fountain. Besides, the basin

shape can be tailor-made to different shapes to match its environment. For instance, it can

be shaped like an opened book to be placed in a library.

Figure 9 Expanded view of fE

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5. Quantification of Design Concept

This part is initialized in our proposal report and during the design process we gradually

refined our variables, parameters, constraints and objectives in the model. The final

quantification of our design concept is presented here before the detailed analysis as a

preview of our optimization model. More detailed descriptions and connections can be

found in the Chapter 6 and 7.

Variables, Parameters1, Constraints and Objectives:

Table 2 Design Variables

Variable/Parameter Description

*Basin

Shape: Basin spine characteristic length a, angle φ:

These values define the Brachistochrone

spine;

Parameter

Width: w: Basin widths are essential variables for

splash design. We conducted experiments

using our beta prototype to decide these

widths.

Variable

Thickness: t: It refers to the thickness of the basin Variable

*Nozzle

Position: hn : It refers to the height of the nozzle from

the basin bottom; Variable

Shooting angle: β: It refers to the shooting angle of the stream; Variable

Trajectory: u, v are local coordinates of the stream

trajectory;

Parameter

*Drain

Radius: Rd : It controls the drain rate and is

determined by the flow rate;

Parameter

*Installation

Fountain height: h : Different fountain height will have

different ergonomic score according to our

survey analysis and ergo model;

Variable

*Economic

Price: P : Price influents the market share as well as

engineering attributes, thus is also involved; Variable

%Market: Pr : Market share is determined using logit

model where user utilities are inputs;

Parameter

Revenue: R : The total income throughout 5 years‟

business plan;

Parameter

Total cost: C: Based on the fixed investment, unit cost

and estimated market share of our product.

Parameter

1 Here “Parameter” means all the intermediate values calculated during the design process.

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Constraint Related to: Description

*Mechanical Const.

ADA requirements: Fountain height h (in our

design, this constraint is

relaxed, see economic model

for details);

Supporting pipe length L;

Nozzle position from the far

end of the supporting pipe Dn;

See Appendix for

detailed requirements.

Basin bending stress: max (shape_basin a, φ,

width_basin w, test load) y

(mat)

Here y is chosen as

the stress limitation of

stainless steel.

*Ergonomic Const.

Distance between user

head and basin surface:

Derg(Stream trajectory u, v,

shape_basin a, φ) 50mm;

From common

knowledge, people will

feel uncomfortable if

the basin surface is too

near. This value is set

as 50mm in our design.

User back bending

angle: (fountain height h, Stream

trajectory max{v}, user stature)

erg;

erg is an ergonomic

recommended interval

of back bending angle,

we assume erg =[0,

90].

*Hygienic Con.

Drain rate: rate_drain(drain radius Rd,

shape_basin a, φ, stream

trajectory u, v) Stream rate;

higher than stream rate

to achieve drain

effectiveness.

*Bottle Filling Con.

Height of the filler hf hbottle The average bottle

height hbottle

Radius of the filler

basin

Rf Rbottle The average bottle

height Rbottle

Objective Description

Sergo+Ssplash: This objective is used in the engineering design

optimization phase where Sergo and Ssplash are scores for

ergonomic and splash performance of our design (see

Chapter 6 for more information). This objective is further

introduced in to the logit model where we estimate our

market share in the economic optimization.

Profit P: Profit is our ultimate objective of the economic

optimization based on all the analysis, surveys and

assumptions we made. (see Chapter 7 for more

information)

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6. The Engineering Design

All pieces of engineering design discussions are presented here: An optimization method

is first used to find the best height for the fountain; then both a mathematical model and a

beta prototype is built to search for the best basin shape in terms of splash reduction and

drain rate improvement; finally, we exam the drain efficiency by determining the drain

radius. During this process, assumptions are made based on both online database and

common sense.

6.1 Design Attributes

Ergonomic Consideration

The performance of a drinking water fountain is highly related to its interaction with

users. From our survey analysis as well as own experience, current designs lack credits to

prove itself as an ergonomically pleasing interface. Unfortunately, as we found out in our

project, designing a fountain in a more ergonomic way somehow conflicts with ADA

requirement, which is an essential attribute in design and market though not mandatory.

Current designs treat this dilemma in two ways. One, adjust the basin to a lower position

to meet ADA requirement of fountain height. The cost of this compromise will be high if

the fountain is installed at some place with rare ADA access like gym. The other way is

to make modulus products, usually two fountain sets with different height to both meet

the needs of ADA requirements and achieve better ergo performance. The team also

discussed the possibility of making the fountain vertically adjustable, and we agreed that

there will be much more trivial things to take care about if we go this way, and moreover,

since adjustable basin involves the new problem of increasing user time consumption, we

don‟t think it is wise to bring ourselves this problem.

Thus, in our design, we mainly focused on improving the fountain ergo performance by

determine the best basin height for both male and female users. An optimization model

on this issue is later built and calculation carried out. In the model, we defined a scoring

mechanism based on user bending angle, and the target is written as a weighted sum

value of total score.

Hygienic Consideration

This part contains two goals: increasing drain rate and minimizing splash.

Splash

Splash is annoying and it always exits with drinking water fountain. Two ideas correlated

in this issue and will help us to move forward are ‟How to efficiently reduce splash with

a given basin size?‟ and „What is the minimum basin boundary to hold the splash?‟

Intuitively, adding beads at appropriate places in the basin will tackle the first problem

and with a given stream rate and basin depth, it is easy to define a basin by bounding it

23

with maximum splash radius. Since none of the team member is expertise in fluid, we

used experiments to iteratively find the solution for these two problems and the derived

the converged result.

Drain Rate

A major concern about drinking water fountain is its hygiene. Two problems exist:

firstly, lead contamination occurs in public fountain; secondly, the basin surface was

reported to have significant amount of germs. We decided not to include the former one

in our design since it involves piping system. The latter problem is treated as equal to

minimize the droplet remain on the basin surface after use. This design target then helps

us to form the main spine of the basin.

A covered bubbler is also used (like current designs) to prevent lips or flow of water from

mouth to splash on the spout itself.

Strength Consideration

Besides the above, we also build an approximated model to calculate the basin bending

stress by using theoretical analysis and making assumptions to simplify our problem.

This model is further used as a nonlinear constraint in the optimization model.

Please understand that we did not use Catia FEA model in our final optimization model.

However, a separated FEA model can be found in the progress report. Commercial

software will be used to link Catia FEA model with our profit model (See Chapter 8) in

our future work. (See Chapter 10)

6.2 Design with Mathematical Methods

Ergonomic Optimization Model

The basic idea is to use back bending angles as an indicator of user satisfaction. A survey

analysis with the help from Dr. Erin Macdonald helped us to quantify user preference on

the bending angle. The result is shown below:

24

Figure 10 Determine users satisfactory by bending angle

It is arguable whether we need more angles on human body besides back bending angle

to better interpret user experience, however, it is reasonable to identify back bending

angle as the major indicator of user satisfaction.

A detailed list of variables, parameters, constants and objectives is shown below:

Table 3 Nomenclature for Ergo Design

Name Description

H = Stature height of the user, 5% -95% for both male and female Constant

h = Basin height, or more precisely, the nozzle height Variable

hw = Maximum stream height: max{v} Linking variable

U = The distance from mouth to the top Parameter

r = golden ratio (0.62) Constant

θ = User bending angle Parameter

S(θ) = Score for a certain θ Parameter

SE = Total ergonomic score Objective

SM = Score for male user Parameter

SF = Score for female user Parameter

µM = Mean value for male stature height distribution Constant

µF = Mean value for female stature height distribution Constant

бM = Standard deviation for male stature height distribution Constant

бF = Standard deviation for female stature height distribution Constant

PM(H) = Probability density of stature height H for male users Parameter

PF(H) = Probability density of stature height H for female users Parameter

25

With the assumption that people drink water from the highest point of the stream

(max{v}) and the bending point divides upper and lower body with golden ratio, the

bending angle is given by:

θ = acos(hw + h − Hr

H(1 − r))

Based on the regression of the conjoint analysis result, score (utility) of this certain angle

is:

S θ = −0.072θ2 + 0.541θ − 0.232

And the weighted score is:

Si = Pi(H)S(θ)dH Where i = F, M.

And thus the total score is given by:

S = 1

2 Pi(H)S(θ)dH

H i95

H i5i=M,F

Constants and parameters are given values based on database and assumptions:

Data Source

U =200mm Assumption

HF95= 1736mm, HF5= 1521mm Anthropometric Reference Data for

Children and Aults: U.S. Population,

1999-20021

HM95= 1895mm, HF5= 1628mm

µF = 1628mm, µM = 1767mm

бF = 99.68mm, бM = 78.03mm

A MATLAB toolbox is then used to find the optimal solution for this program, and the

results are given below:

Table 4 Optimization Results for Nozzle Height

Optimization Results:

h (the nozzle height) = 133.2 cm

SE (Total ergonomic score) = 0.52

1 Here we use data for U.S. citizens in the range between 20 – 29 years old. By keeping

the same methodology, the program can be easily modified for other user groups.

26

Basin Spine Design

In this part we try to minimize the droplet remained on the basin surface. Although there

are other ways to achieve this goal, e.g. changing the material to increase water

repellence, we focus on the basic physical method to maximize the usage of gravity. The

existing Brachistochrone solution helps us to “find the shape of the curve down which a

bead sliding from rest and accelerated by gravity will slip from one point to another in the

least time”. Although it is arguable since fluid behavior is different from that of solid

bead, however, this method is still applicable because it meets our goal to maximize the

usage of gravity.

The Brachistochrone curve is actually the equations of an inverse cycloid, as shown

below:

x = a(θ − sin(θ))

y = −a(1 − cos(θ))

This equation set assumes zero friction, which is not the fact in our case. We will resort

to the equation set which enables dynamic friction after we decide the basin surface

material.

In the similar fashion as we did in the ergonomic model, a detailed list of variables,

parameters, constants, constraints and objectives is shown below:

Table 5 Nomenclature for Ergo Water Fountain

hn = Nozzle height from drain Variable

ln = Nozzle distance from drain Parameter

v = Stream velocity Parameter

β = Nozzle shooting angle Variable

α = Contact angle between stream and basin surface Objective

a = Character value for basin spine Parameter

φ = π , Character angle for spine at the drain Constant

R = 3.5‟, Radius of the supporting pipe Constant

Derg50mm, Distance between user head and basin surface Constraint

Lb= πa, Basin length limitation Constraint

ADA = The distance for ADA requirement Constraint

Explanation of the nomenclature is given below:

1. From common knowledge, people will feel uncomfortable is the basin surface is too

near when they are drinking. This value is set as 50mm in our design.

27

2. Basin length limitation: From the point of material cost, the idea length will be

exactly long enough to cover the stream trajectory. With the given design function of

basin spine and the assumption of stream rate and angle, visual experiments are

carried out to find the best spine length.

3. ADA requirement on stream trajectory height: This height should be more than 4

inches from the basin to enable bottle insertion.

Figure 11 ADA requirements for bottle filling

4. The lower end of the basin spine should have a descent direction to ensure drain is

effective. For our equation set, this indicates θ ∈ [0, π]. Here we fix θd = π for θ at

the drain.

Figure 12 The contact angle α

5. The nozzle shooting angle β should not be zero, i.e. shooting directly upwards is not

allowed, according to the regulation. Here we set β ∈ 𝜋

6,𝜋

2 .

6. From our design concept, the nozzle is place on a pipe of 3.5 inches. Refer to

Engineering Analysis for details about this pipe.

7. The angle of the stream hitting the basin α (the contact angle) should be minimized to

reduce the splash. We found certain research report to prove our intuitive guess.

A mathematical model is then built in MATLAB to play with and optimize the contact

angle. The results are shown below.

28

Figure 13 Design with different nozzle position

Figure 14 Design with different shooting angle

Conclusions:

1. From our calculations, hn should be at least 60mm high from the bottom to meet the

ADA requirement;

2. With given stream velocity and angle, the minimum α is reached when the nozzle is

placed at the highest possible position.

3. The minimum α is reached at the lower boundary of β.

0 0.05 0.1 0.15 0.2

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

Nozzle at 1.5r

Nozzle at 2r

0 0.05 0.1 0.15 0.2

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04Shooting Angle = 30deg

Shooting Angle = 45deg

29

Figure 15 Final design characteristics

Drain Radius Design

Sufficient drain radius will ensure the whole system performance. Here we calculate the

radius based on the model we‟ve discussed above. Notice that this is only a first order

model where we treat droplets as solid rigid bodies and basin as ideally smooth surface;

while the stream pressure at the nozzle and drain are the same (we cut a hole in the drain

pipe to meet this goal). Thus the drain radius is given by the XXX:

𝑅𝑛2𝑣1 = 𝑅𝑑

2𝑣2

, where Rn is the radius of the nozzle, v1 and v2 are stream velocity at the nozzle and the

drain accordingly.

Notice that the stream lost part of its velocity when contacting the basin surface, and

there is a height gap between the nozzle and the drain. Based on the optimized design, the

relationship between v1 and v2 is then given as:

1

2𝑣12 =

1

2𝑣32 + 𝑔(2𝑎 − 𝒉𝒏)

𝑣1′ = 𝑣3cos(𝜶)

0 0.05 0.1 0.15 0.2 0.25-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

x/m

y/m

Nozzle

Shooting angle = 30deg

Stream velocity = 1.6m/s

Nozzle position from drain:

hn = 3.5 inches

ln = 0

Contact angle = 37.0deg

Basin spine design:

Total length: 200.9mm

Total Height: 127.9mm

30

1

2𝑣1′2 + 2𝑔𝑎 =

1

2𝑣22

Given values of v1(1.6m/s), a (64mm), hn (89mm) and 𝜶 (37deg) according to the design

results, the minimum value for Rd is calculated as 2.7mm.

However, we find out later in the test run that this radius is far from enough the produce

sufficient drain rate. The problem could be that the pressure at the drain is practically

higher than that of the nozzle, thus lead to the decrease of v2 and higher Rd.

Strength Consideration

The simplified strength analysis model is given below:

The dimensions of the basin cross-section at the bottom, the inertial moment, and the

main axis are determined by the results from “Experimental Methods” section (See

section 6.3); the length of the basin is determined by “Basin Spine Design”; the applied

load is set as 80kg and the safety coefficient as 1.5. All values are listed below:

Table 6 Strength Analysis Var./Para.

Var./Para. Description Value Units

Parameters

M Applied load 80 kg

mu Safety coefficient 1.5 /

g Gravity constant 9.8 m/s2

L Basin length Determined by Basin Spine

Design

mm

c Maximum distance from the

principal axis

Determined by Experiments mm

I Moment of inertia of the cross-

section

Determined by Experiments mm4

Variable

t Basin thickness / mm

31

The stress constraint is then given by:

𝜎 =𝑀𝑐

𝐼=

𝑚𝑔𝜇𝐿𝑐

𝐼(𝑡)≤ 𝜎𝑦

6.3 Design with Experimental Methods

We studied several reports on the topic of droplets‟ behaviors. However, formulas given

in those papers are not coherent with our experimental results. The problem might be the

difference between the Reynolds number/Weber number of fountain stream and that of

single droplets used in those papers. Thus, we conducted our design with experiments

based on our beta prototype.

Beta prototype

Due to the nature of the project, it was determined that a system that could help emulate

water flow into the basin shape would be of great value. This prototype aims at

demonstrating the design concept can be realized into an actual product. It is intended as

a first step to demonstrate that the architecture proposed can be built with real materials

at an appropriate cost, and that it is likely to meet most of the design requirements,

including functionality and user appeal.

Ideally it is portable, so it can be used for demonstration purposes as well.

Figure 16 Block diagram of beta prototype

As can be seen in Figure 16, there is a submersible water pump contained in a reservoir

that feeds through a “wall” into the basin. The water is collected and returned into the

container creating a closed loop.

32

Figure 17 Beta prototype top view

The basin shape of this prototype is built with copper rods as its skeleton and a

waterproof curtain as its surface. The side view of the skeleton is formed by previous

discussion on spine. The curtain is clipped to the skeleton at five fixed points. This

fixture helps us to easily reshape the basin by changing its length, width and depth.

Figure 18 Beta prototype side view

Basin Boundary and Depth Design

The idea here is to determine the basin boundary with the maximum splash radius along

the spine, and thus minimize the basin surface area. Besides, it is intuitively true that we

33

can reduce splash by using deeper basin, however, this method also increase the basin

surface area. Thus, our goal is to make the best compromise between splash and surface

area via experiments.

In detail, we separate the clips into two sets: the upper three (A, B and C as shown in the

figure below) and the lower two. By loosening or tightening these two sets of clips, we

can examine the different performance of splash and drain rate. The results are shown

below:

Figure 19 Beta prototype fixture

Table 7 Design Methods for Experiments

Method Observation

Case Tighten Loosen Splash/Drain Surface area

1 A B C D E Upper side splash 0

2 D E A B C Upper side splash

Water remains in the basin

+

3 All / Returning water goes out of

the basin

-

4 / All Good performance ++

Conclusions:

1. Both in case 1 and 2, upper side splash occurs because the stream almost hits the

upper boundary of the basin, which is true in the previous math model. So the basin

spine should be extended to hold this part of splash.

A

B C

D E

34

2. In case 2, water remains in the basin because the basin surface is almost flat thus the

drain is not efficient. So clip D E should be loosened appropriately to enhance drain

rate.

3. In case 3, water goes out of the basin because depth is not enough and thus enables

water to flow in other paths. From the point, we decide to add beads to create a

definite drain path. Also, when placed at proper positions, beads also help to reduce

splash.

4. In case 4, we obtain a fairly good performance by loosening all the clips, however,

this also increases the total surface and in turn the material cost.

Although there is no quantitative method available, iterative tries can help us to find a

qualified performance for both splash and drain rate. Both basin boundaries and depth are

decided by the experiment and used in the CAD model.

6.4 Conclusion

As a conclusion, the design flow chart is shown below. This is further used in the

microeconomic model where the whole picture is completed.

Figure 20 Design flow

35

7. Choice Based Conjoint Analysis

7.1 Logit model

Briefly, a logit model with CBC (choice-based conjoint) analysis serves to estimate the

probability of people choosing one product among the others, and further estimate the

market share of this product. This probability is given as:

𝑃𝑖𝑗 =𝑒𝑣𝑖𝑗

𝑒𝑣𝑖𝑗 ′𝑗 ′

, where i represents the ith

consumer, j represents the jth

product and vij is the utility value

of product j according to consumer i (here we assume that consumer preferences are

identical, so i can be omitted). In our model, the detailed form of %market is given

below:

%𝑚𝑎𝑟𝑘𝑒𝑡𝑓𝐸 =𝑒𝑣𝑓𝐸

𝑒𝑣𝑐𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑜𝑟𝑠 + 𝑒𝑣𝑁𝑜𝑛𝑒 + 𝑒𝑣𝑓𝐸

, where 𝑒𝑣𝑐𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑜𝑟𝑠 are utility values from other drinking fountain manufacturers 𝑒𝑣𝑁𝑜𝑛𝑒

is the utility value of choosing not to buy any product given.

7.2 Composition of the utility and CBC results

The utility values can be further decomposed into beta values which indicate people‟s

preferences on different design attributes. The beta values used in this model is listed

below:

Table 8 Beta values

Beta Description

Beta_color User preference on the fountain color

Beta_filler User preference on bottle filler efficiency

Beta_ergo The same as SE in Chapter 6

Beta_splash An alternative expression of contacting

angle α, it is defined as:

(-200tan(α)/pi+50)/50

Beta_price User preference on the price

The values of these betas are obtained by conducting a CBC survey. The survey results

with regression curves are shown below:

36

Figure 21 Beta values for bending angles

Figure 22 Beta values for colors

Figure 23 Beta values for filling times

Figure 24 Beta values for prices

37

8. The Microeconomic Model

Economic analysis for fE consists of estimating the annual US market size of drinking

water fountain, estimating fixed and variable costs for producing water fountain,

estimating market share via logit model and then maximizing profits using optimization.

The complete model is show below while methods used in brackets. Details are discussed

in the following.

Figure 25 Microeconomic model

8.1 Market Size

The market size is given by an authenticate business report1. Here we use the number

from year 2007 as the total market size of drinking water fountain. And we assume that

the premium market our product will aim at is roughly 15% of the total market.

Figure 26 Market size estimation

1 SBI Market Profile: Plumbing Fixtures and Fittings – a market intelligence report,

Find/SVP published products, NY, 1998 (Note: 2007 estimate only)

4230041600457004230044400504005200057000

64000

1992 1993 1994 1995 1996 1997 1998 2003 2007

US Drinking Fountain Shipments

38

8.2 Cost Estimates

Since the product is similar to current products in the market, cost estimates were

obtained by comparing the prices of competitive products. Also, prices of various

replacement parts were obtained that helped to calculate the variable cost of the product.

One thing needs to mention is that the basin price is based on its volume, thus the unit

cost is not a constant. The following table shows the variable costs of components.

Costs independent from design variables

Table 9 Components cost

Variable costs

Component Price

Bubbler 20

Trigger 18

Bottle filler 120

Chiller 440

Supporting 225

LCD screen 80

Basin **

Total 903+

Manufacturing costs

Labor 100

Packaging 25

Shipping 50

Total 175

Total Cost/Unit 1078+

Fixed Costs

Casting Mold 300000*

Assembly Eq 100000

Rent 25000

Salary 250000

Overhead 50000

Total 725000

* We use cast here because the basin shape we created is hard to stamp.

* *The basin price is based on its volume.

Costs dependent on design variables

The basin price is based on its volume and hence linked to basin spine, width and

thickness. An analytical model is built as follows:

39

𝑉𝑜𝑙𝑢𝑚𝑒 =𝒘𝟏 + 𝒘𝟐

2𝐿𝑠𝑝𝑖𝑛𝑒 𝒕

, where w1 and w2 are determined by experiments, t is the basin thickness and 𝐿𝑠𝑝𝑖𝑛𝑒 is

the total length of the spine curve, which is given by the following calculation:

𝐿𝑠𝑝𝑖𝑛𝑒 = 𝑑𝑥2 + 𝑑𝑦2𝜋

0

= 1 + (𝑑𝑦

𝑑𝑥)2

𝜋

0

𝑑𝑥

= 𝑎 (1 − 𝑐𝑜𝑠𝜃)2 + 𝑠𝑖𝑛2𝜃𝜋

0

𝑑𝜃 = 4𝑎

The unit cost for the basin is approximately $5/kg, and the density of the material is set at

7.8e-6kg/mm3. Thus the price for one basin is:

𝐶𝑏𝑎𝑠𝑖𝑛 =𝒘𝟏 + 𝒘𝟐

24𝑎𝒕 ∙ (7.8 ∙ 10−6

kg

mm3) ∙ $5/kg

8.3 Market Share Estimates

8.3.1 Assumption

Predicting market share is always challenging but still essential. In this part we introduce

the Logit model and CBC analysis results (from Chapter 7) to address this problem.

However, some critical assumptions should be highlighted at the first place:

1. The preference of drinking water fountains is coherent throughout consumers and

users. This might be the most arguable assumption we made. However, this

assumption helps us to simply the problem.

2. There are only a few competitors in the market and the products families of these

competitors are both limited in number and stable in design attribute.

3. Design attributes will not change, i.e. people only consider about certain attributes

we analyzed and will not turn to other ones.

8.3.2 Utilities from competitors and fE

Based on the conjoint analysis results in Chapter 7, we calculated utilities from our

product (𝒗𝒇𝑬) and our competitors‟. (𝒗𝒄𝒐𝒎𝒑𝒆𝒕𝒊𝒕𝒐𝒓𝒔)

*𝒗𝒇𝑬:

To address to the ADA requirement on fountain height, we resort to two installation

fixtures: one fountain installed at ADA height (80cm), or bi-leveled fountains with both

ADA height and optimized height. The utilities of both fixtures are listed below:

40

Table 10 Utility for fE

fE fixture 1 Exterior

color

Bottle

filling time

Bending

angle

(Ergo)

Contacting

angle

(Splash)

Price Utility

𝐵𝑒𝑡𝑎

Cooler N/A Chapter 6 Chapter 6 Variable

Beta_color Beta_filler Beta_ergo Beta_splash Beta_price

0.34 0.53 0.52 0.04 / /

fE fixture 2 Exterior

color

Bottle

filling time

Bending

angle

(Ergo)

Contacting

angle

(Splash)

Price Utility

𝐵𝑒𝑡𝑎

Cooler N/A Chapter 6 Chapter 6 Variable

Beta_color Beta_filler Beta_ergo Beta_splash Beta_price

0.34 0.53 0.52 0.04 / /

*𝒗𝒄𝒐𝒎𝒑𝒆𝒕𝒊𝒕𝒐𝒓𝒔:

Two premium market competitors‟ utilities are estimated by determining their beta

values. Both of these are from ELKAY Manufacturing Co., Competitor 1 has bi-leveled

fountains which is similar to our selling strategy; Competitor 2 bears some critical

characteristics that are identical to our design (recessed cooler, redesigned basin). Also,

we assume the ADA requirement is complied with in all cases. The resulting utilities are

shown below:

Table 11 Utilities for competitors

Competitor 1 Exterior

color

Bottle

filling time

Bending

angle

(Ergo)

Contacting

angle

(Splash)

Price Utility

𝐵𝑒𝑡𝑎

Natural N/A According

to ADA

requirement

Beta value

estimated

directly

$1962

Beta_color Beta_filler Beta_ergo Beta_splash Beta_price

-0.08 -0.57 -0.57 (h =

100cm)

-0.3 0.65 -0.87

Competitor 2 Exterior

color

Bottle

filling time

Bending

angle

(Ergo)

Contacting

angle

(Splash)

Price Utility

𝐵𝑒𝑡𝑎

Natural N/A According

to ADA

requirement

Beta value

estimated

directly

$1800

Beta_color Beta_filler Beta_ergo Beta_splash Beta_price

-0.08 -0.57 -1.87 (h =

80cm)

-0.3 0.97 -1.85

41

*𝒗𝑵𝒐𝒏𝒆:

𝑣𝑁𝑜𝑛𝑒 is given by CBC result as -0.74;

As a conclusion, the market share is estimated through the method discussed above.

However, as a “first order” analysis, this estimation may need further revision based on

the following issues: 1. Real consumers (facility managers) may not have the same

preference as survey takers; 2. Competitors may also have new designs with higher

utilities.

8.4 Profit Model

Based on the engineering analysis (Chapter 6), CBC analysis (Chapter 7) and market

estimates in this chapter, we are now able to optimize the profit by establishing the

microeconomic model. The Matlab Opimization Toolbox is used and the final results are

listed below, also, the complete implementation can be found in the appendix:

Table 12 Final optimization results

Var./Para. Description Maximal Solution Reference/Methods

*Basin

Width: w Variable 150mm at the bottom,

200mm at the top

Chapter 6/

Experiments

Thickness: t Variable 1.41mm (active const.*) Chapter 6/Optimized

*Nozzle

Position: hn Variable 88.9mm (active const.) Chapter 6/Optimized

Shooting angle: β Variable 30deg (active const.) Chapter 6/Optimized

*Installation

Fountain height: h Variable 1332mm Chapter 6/Optimized

*Economic

Price: P1 Variable $2184 Chapter 8/Optimized

P2 $3268 Chapter 8/Optimized

%Market: Pr1 Parameter 29%

Pr2 25%

Revenue: R Parameter $14.0m

Total cost: C Parameter $9.0m

Objective Description Maxima

Profit: P $5.0m

42

9. Future Work

Modeling methods

The current engineering and microeconomic models are analytical ones. Some parts still

need fine-tune to produce more convincing results: Catia will be used both in the stress

analysis and basin volume calculation, and further integrated other parts to get the

accurate value for thickness; the economic model can be revised by taking a close look at

our competitors and using more sophisticated logit model.

Concepts realization

It is a pity that we haven‟t realized all the conceptual ideas we bring out during the

brainstorm session, however, this is almost always the fact in design. Concepts like

connection between info display and fountain usage and sensor trigger are not fully

studied in this design but are interesting ideas to look at in the future.

43

10. Design in the Designed World

Is irrationality predictable? – Reflection on market-driven aesthetic design

This question is inspired by two guest lecturers, namely, Prof. Jan-Henrik Andersen and

Mr. Adam Cooper during the Analytical Product Design course. The question itself might

be too broad to talk about in this little space and with very limited knowledge from the

author. However, by questioning and thinking this way the author is offered great

experience and interesting perspective.

Designers have two phases: irrational minds and sensitivity towards the market. The

former one comes from the nature of their work – to create ideas; and the latter from the

objective of their work – to create profit. Somehow in many cases these two phases

conflict with each other and make the design process a run-and-debug loop. On the other

hand, it is commonly acknowledged that consumers nowadays also carry two phases:

unpredictable pursuit of fashion and nitpicky over quality.

Moreover, there still exists a bigger picture where policies are involved. These forces

always bound designers‟ freedom and at the same time reshape consumer‟s preference.

By stating these facts, it seems like demands are not predictable and designers can only

hit the target with luck. However, daily experience with successful brands tells us that

irrationality is predictable.

As an amateur in design field, the author had sufficient learning opportunities during the

project and is fascinated by the theoretical and practical methods used to control the

design. The result might not be professional, however, this learning process helps the

author to rethink „design‟ in a more sophisticated context where the intuitive aesthetic

pursuit of designers is constrained by profit, market, engineering requirements,

manufacturability, time and others. These constraints and objectives separate design apart

from fine art and applied new values to it. The ideas of „Sustainable design‟ and „Design

for society‟ are among them.

A further reflection as well as communication with insiders inspired even more thoughts.

By linking design attributes (in many cases these are engineering attributes), consumer

preference and policies together, we can push the boundary in the most effective fashion

and this leads to controlling the seemingly irrational market.

-- Ren, Yi

44

Appendix 1 – Business Plan

Business Objective

Our proposed business objective can be stated as follows:

To design, manufacture and market a premium drinking water fountain with enhanced

ergonomics, visual appeal, a modern information display and a bottle filler capability.

The traditional drinking fountain design is 100 years old, and our team believes that there

is much room to improve it, in particular in the following areas:

Ergonomics

Hygiene

Aesthetics

Provide additional features

The background research showed that there is a clear trend in the increase of shipments

for drinking fountains within the United States.

Figure 27 Business Plan: Drinking water fountain shipments1

This creates the natural expectation that there will be a well-defined market for a modern

drinking fountain.

1 Source: SBI Market Profile: Plumbing Fixtures and Fittings – a market intelligence

report, Find/SVP published products, NY, 1998 (Note: 2007 estimate only)

42300 4160045700

42300 4440050400 52000

5700064000

1992 1993 1994 1995 1996 1997 1998 2003 2007

US Drinking Fountain Shipments

45

Users The facilities that would have fE fountains are considered to be “high-end”, that

incorporate the fountain into an already modern and sophisticated environment. There is

a stylish and urban atmosphere that is inviting for people to have small groups of people

interacting in the comfort of a relax environment like a lounge area, or next to a lobby

that expects visitors often and that could be interested in having some water to quench

their thirst. At the same time, they get the opportunity to re-fill their standard water

bottle and while this is happening they get relevant information about the weather, local

news or announcements of events of interest to the user. The user also has the confidence

that this drinking fountain has been properly maintain and that it meets an understandable

standard of hygiene, since the station itself displays information about the quality of the

water, last time filters where replaced, etc.

Product Specifications

The beta prototype for the product is shown in the Figure .

Figure 28 Experimental prototype

46

Figure 29 Working prototype in the Design Expo

The key features of fE fountain are:

1. A supporting pipe that houses water supply, water drain, and trigger mechanism.

2. A basin with splash reduction shape

3. Bottle fill mechanism with sensor

4. Information display

The base pipe serves as the backbone of the product. It holds all the components of the

water fountain. Water supply pipe and water drain pipe runs inside the base pipe. The

drain is also the part of the base pipe and it is hidden from the user. That is one of the

major improvement over the current drinking fountains where drain is usually visible and

it collects water and debris.

Two further enhancements over the current water fountain are bottle filler and

information display. Bottle filler is attached to the base pipe and it is marketed as a

separate module. This means, that if a customer do not want a bottle filler then it can be

deleted from the final product. Bottle fill has an automatic sensing mechanism that senses

the bottle and dispenses water as required. Information display is also provided as a

separate module. Info display can be programmed to display customizable information,

weather, news, etc.

Overall, with all these features fE is a superior product as compared to any existing water

fountains.

Market Analysis Our research reveals that there are less than ten major manufacturers of drinking water

fountains. Some of them include Elkay, Halsey Taylor and Sunroc. Their prices range

from $400 to more than $2500 depending on the finishing, materials used and number of

basins per station.

47

Within the new buildings at the University of Michigan it has been found that the water

fountains installed are the higher end priced ones. We are making the business model

assumption that 15% of the target market is “premium”, meaning facilities or locations

that are new, or that present architectural and interior design elements that give the

visitors of the facility a sense of modern and progressive visual arrangements. With fE

the plan is to capture up to 50% of the total premium market within five years.

A summary of the advantages of fE over Existing Water Fountains is shown in the next

table.

Table 13 Business Plan: Advantages of fE

fE

Existing water fountains

Consumer Improved ergonomics

Less splash

Bottle fill

Information display

High back angle

Splash and stagnant water

Bottle fill only on limited

fountains

No information display

Customer Improved aesthetics

Customization

Revenues from ads

Old design

No/minimal customization

No revenues

Financial Data

Costs, Manufacturing and Pricing

Many things within the plan to reduce the overall cost of fE have to do with a broad

vision of the processes entailed to generate a product of this nature. For instance, due to

the exclusive architecture that characterizes the basin of the fE drinking water fountains it

is proposed that the casting of it be made in-house. Since the architecture of the design is

meant to be modular in the sub-assemblies, this allows for the basin to be constructed as

an independent entity. The remaining components can be commercial off the shelf

purchased from third parties. As far as personnel required it has been calculated that 2

engineers and 3 technicians in the assembly area would satisfy the requirements during

the first few years. For characteristic finishing of the products (for instance painting and

other special materials before shipping) there will be a list of suppliers with which there

would be a previous agreement of their rates and material costs. A summary of the costs

is shown in the next tables.

48

Table 14 Business Plan: Cost estimation

Variable costs

Component Price

Bubbler 20

Trigger 18

Bottle filler 120

Chiller 440

Supporting 225

LCD screen 80

Basin **

Total 903+

Manufacturing costs

Labor 100

Packaging 25

Shipping 50

Total 175

Total Cost/Unit 1078+

Fixed Costs

Casting Mold 300000*

Assembly Eq 100000

Rent 25000

Salary 250000

Overhead 50000

Total 725000

* We use cast here because the basin shape we created is hard to stamp.

* *The basin price is based on its volume.

Table 15 Business Plan: Net present value

Net Present Value

Year 0 1 2 3 4 5

Investment 400000 0 0 0 0 0

Fixed Costs 325000 325000 325000 325000 325000 325000

Unit Sales 0 480 1139.424 2045.341 3289.889 4992

COGS 0 778361.5 1847674.62 3316697 5334840 8094960

Revenue 0 1273246 3022431.72 5425463 8726747 13241760

Net Profit 0 169884.6 849757.1 1783766 3066907 4821800

Tax @ 35% 0 59459.62 297414.985 624318.1 1073418 1687630

Net Profit -725000 110425 552342.115 1159448 1993490 3134170

Net Present Value $3,646,028.23

49

By assuming that we will achieve the estimated market share in 5 years and with an

annual sales increase of 37%, the Net Present Value (NPV) is around $3.6m (See Table

15).

Figure 30 Business Plan: Breakeven timeline

By the second year according to your calculations we would breakeven, suggesting that

the fE business model is strong, complementing a good NPV and with the satisfaction

that a great product has been placed in high end locations within reach of the mainstream

users.

Business Assumptions

1. The preference of drinking water fountains is coherent throughout consumers and

users.

2. There are only a few competitors in the market and the products families of these

competitors are both limited in number and stable in design attribute.

3. Design attributes will not change, i.e. people only consider about certain attributes we

analyzed and will not turn to other ones.

4. We will be able to achieve the estimated market share in 5 years.

5. The premium market size of the drinking water fountain is 15% of the total market.

6. An initial market share of 5% of the premium market can be achieved in the first

year.

7. An annual increase of 37% of our market share can be achieved and maintained for

five year.

8. There will be no significant policies changing and water issues to influence this

market.

($10,000,000.00)

($5,000,000.00)

$0.00

$5,000,000.00

$10,000,000.00

$15,000,000.00

0 1 2 3 4 5

year

Chart Title

Net Profit

COGS

Revenue

50

Existing Patents and Products

United States Design Patent, Clark et. al. Patent No: US D545,109 S, June 26, 2007

United States Design Patent, Hong. Patent No: US D547,104 S, Jul 24, 2007

United States Design Patent, Windenburg et al. Patent No: 343,330, Jan 18, 1994

51

Appendix 2- Previous Designs Schematics

52

53

Appendix 3 - Relevant Patents

54

Appendix 4 - ADA-compliance of the Drinking Fountain

ADA-compliance of the Drinking Fountain

55

Appendix 5 - Brainstorming ideas1

1 Figures are numbered from left to right and top to bottom.

56

1. A pressure control feature added to the handle.

2. Foot triggered drinking fountain.

3. Auto-disinfectant spray added for hygiene concerns.

4. Range motion sensor used to trigger on stream.

5. Efficient bottle filler replacing the existing drinking fountain.

6. A hollow at calculated position in the basin to facilitate efficient bottle filling.

7. Innovative pressure triggered rubber handle.

8. Adjustable (rotatable) drinking fountain to meet demands of people with different

height.

9. Redesigned basin material and shape to improve drain rate.

10. Drinking fountain with three nozzles at different height and separated bottle filler.

11. Water station to meet multiple requirements.

12. Recyclable Paper-made basin to minimize bacteria level of the drinking fountain.

13. A traditional bended nozzle with long neck for bottle filling.

14. Water-fountain-like drinking fountain.

15. Cup-dispenser add-on to alleviate hygiene concerns.

16. Redesigned rotatable nozzle.

17. A snake like adjustable nozzle to achieve better user posture.

18. “Water bar” serving all thirsty creatures.

19. Rotatable and connected handle and nozzle for ergonomic considerations.

20. Direct nozzle with increased stream pressure.

21. Adjustable stream pressure and increased basin depth for better bottle filling

experience.

22. Separated bottle filler.

23. Use inkjet technology to direct water to the bottle or to the user as required

24. A set of three drinking fountains with different height.

57

Appendix 6 - QFD Chart

58

Appendix 7 - Product Development Process

59

Appendix 8 - Pugh

60

Appendix 9 - Gantt Chart

61

Appendix 10 - Survey 1

Drinking Water Fountain Survey

Age: Gender: M F Height:

Occupation: [Student] [Office dweller] or specify other:

Please tick answer in [ ].

1. Do you use a water fountain for drinking water? [ YES ]

[ NO ]

If NO, why not?

2. On average, how many times do you use a water fountain in a day?

[ Seldom ] [ 1 – 5 ] [ 6 – 10 ] [ 11+ ]

3. When do you use the water fountain the most? Please rank:

(1-most often; 4-least likely)

___ after eating ___ coming out of the restroom ___ after gym ___

after work ___ [ other ]

4. Are you concerned about the hygiene of using a water fountain?

[ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] 1 = Not at all, 2 = Slightly, 3 = Moderately, 4 =Highly, 5 = Extremely

Please specify your concern

______

5. Does the fountain do any of the following to the water:

1. Reverse osmosis

2. Charcoal filtering

3. UV filtering

4. I do not know

6. Is the water:

1. Very Cold

2. Cold

3. Neutral

4. Hot

5. Very Hot

7. Do you like the taste of the water?

[ YES ] [ NO ]

62

8. While using the water fountain, are you concerned about splashing water?

[ YES ] [ NO]

9. While using the water fountain, do you feel comfortable? [ YES ]

[ NO ]

If NO, what makes you uncomfortable?

[ Neck Rotation] [ Back Bending] [ Trigger Position ] [

Long Hair ]

10. Is the design of existing water fountain aesthetically pleasing? Please circle a

number:

Ugly 1 2 3 4 5 Pleasing

11. Do you use the fountain to fill up a water bottle? [ YES

] [ NO ]

If YES, is it easy to fill the bottle? 1 = Very Difficult, 7 = Very Easy

[ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ]

12. Do you use fountain for any other purpose than drinking? [ YES ]

[ NO ]

If YES, please specify

13. Would you like to have information displayed next to the fountain? [ YES ]

[ NO ]

If YES, then what sort of information would you like to see? You can select as many as you want.

[ News ] [ Weather ] [ Time ] [ Advertisement ]

Others

63

14. Do you find drinking water fountain noisy?

1. Strongly Agree 2. Agree 3. Neither Agree/Disagree 4. Disagree 5. Strongly

Disagree

15. How satisfied are you with the overall drinking experience from the fountain?

1 = Very Unsatisfied, 7 = Very Satisfied

[ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ]

Summary of Survey 1 Results

1. 93% use water fountain 2. 81% use it at least once a day 3. Most often after work 4. 90% concern about the hygiene 5. 88% has no knowledge of filter process in fountain 6. 79% think the water is cold 7. 86% thinks the taste is OK 8. 50% concerned with splash 9. 26% uncomfortable with using existing fountain

a. 36% neck b. 73% back c. 18% trigger position d. 27%hair

10. 24% thinks it’s not aesthetically pleasing 11. 71% fill bottle with water fountain 12. 43% thinks it’s not easy to fill up bottle 13. 10% use for other purpose than drinking/filling bottle 14. 38% wants to see information displayed next to fountain

a. 50% news b. 63% weather c. 63% time d. 19% ads

15. 26% finds it noisy 16. 17% unsatisfied with it

64

Appendix 11 - Survey 2

65

66

*CBC questions continue like this.

67

Appendix 12 - Finite element analysis (FEA) used in progress report

Static stress analysis is carried to determine the specifications of the fountain body and

basin. The cylindrically-shaped fountain body, which acts as the structure of the drinking

fountain, and the basin must withstand worst-scenario load case. Several industrial tube

sizes and various basin designs are analyzed to determine minimum specifications for the

designated load. The load is assumed to be the weight of a 99.99th

percentile American

male of 122.702kg. With safety factor of 2, the Von Mises stress from the FEA must not

exceed half of the yield strength of stainless steel (2.5 x 108 N/m

2). Through several case

studies, the fountain body and basin shape that meet the requirements are found. Variety

In conclusion, the fountain body will be made of a round tube with a nominal size of 3 in.

and wall thickness of 3.1 mm while basin shape B with a slightly thicker cross sectional

profile.

Fountain body

Table 16 FEA Results of fountain body

Nominal

Size

Outer

Diameter

(mm)

Wall

thickness

(mm)

Restraint Basin shape

Von Mises

stress

(N/m2)

3.0in 88.9 2.108 1 side A 1.29

3.0in 88.9 3.048 1 side A 1.03

Figure 31 Stress analysis of fountain body thickness = 2.108

68

Figure 32 Stress analysis of fountain body thickness = 3.048

Basin shape

Table 17 FEA Results of basin shape

Nominal

Size

Outer

Diameter

(mm)

Wall

thickness

(mm)

Restraint Basin shape

Von Mises

stress

(Nm2)

3.0in 88.9 3.048 2 sides A 1.36

3.0in 88.9 3.048 2 sides B 1.14

Restraint

Load

69

Figure 33 Stress analysis of initial basin design

Figure 34 Stress Analysis of modified basin shape

Appendix 13 - Product architecture

By integrating modularity into the product architecture, the drinking fountain can be

easily customized to address specific user needs. The surface finishing and basin shape

can be easily tailored to match its surroundings or convey specific emotion. The bottle

filler and information display screen can be optionally packaged with the basic drinking

fountain. With the modular design, we will be able to produce the parts at costs that do

not differ significantly from the cost of mass producing a single product design.

Restraint

Load

70

Main

1. Basin incl. nozzle

2. Fountain body

3. Water supply & drain pipe

4. Chiller & filter assembly

5. Touch-activated electrical system

6. Solenoid valve

7. Fasteners

8. Back-panel

Optional

9. Info display assembly

a. power supply unit

b. LCD screen

10. Bottler filler assembly

a. secondary basin

b. filler tube

c. water supply pipe

d. solenoid valve

e. pressure-activated electrical system

Product manufacturing

Majority of our drinking fountain system components that are standardized will be

outsourced. The customizable, non-standard components are main basin, fountain body,

secondary basin and filler tube, will be produced through investment casting. This casting

method is found to be most suitable for these parts to satisfy the following requirements

of our design:

- Excellent surface finish

71

- Light weight and thin wall

- Aesthetically pleasing contours

- Structural strength to withstand worst-case load

- Corrosion, abrasion and heat resistant

- Electrical characteristics for touch-activated mechanism

- Interior cavities & passageways for system components and fluid flow

- Small dimensional tolerance to ensure proper fit when joining two parts

- Appearance that can be plated or anodized to meet customized user needs

- Alloys that can be welded or brazed to allow further customization

In addition, investment casting method will also offer several financial and marketing

benefits. The single casting with integrated components (e.g. spout guard) minimizes

secondary processes such as welded fabrication, machining or bolted assembly, saving

time and costs. Additional cost saving is realized by keeping metal usage to a minimum

because castings can be designed and produced to net-shape configuration. Also, the

availability of prototyping and temporary tooling for cast components can be developed

quickly to prove out designs and respond to market demands.

Assembly

The assembly of our drinking fountain components will be primarily carried out on site at

customer‟s location to reduce manufacturing cost and hence, achieve our business goal of

competitive pricing. This is enabled by incorporating design for assembly into the

product with reduced number of part counts by integration as mentioned previously. The

assembly process can be broken down into three main sections:

1) Install and connect chiller and filter assembly systems in the designated wall-

recess

2) Insert and fasten piping and activation systems into basin and assemble to

fountain body

3) Fasten basin and fountain body assembly to back panel and close wall recess

area.

72

Appendix 14 – Matlab codes

The implementation consists three part. Profit.m is the main objective function;

profit_constraint.m is the non-linear constraint function called by fmincon and

Solver_profit.m is the main file where optimization is executed and results listed.

Profit.m

% APD

% Optimization Model

% for Max. Profit

% clear

function P=Profit(X,u,sigma,r1,v,r,sita,L,Q_max,Beta_color...

,Beta_filler,U2,U3,U_none,Cv_constant,Cf)

%------------------------------------------Variables

%-------------------Ergo-----------------------------

% h=85; %Basin height, NEED TO OPTIMIZE

h=X(1);price=X(2:3);

%-----------------------------------------------------

%-------------------Splash----------------------------

% hn=2*r; %Nozzle position from the drain, OPTIMIZED

hn=X(4);

%-----------------------------------------------------

%-------------------Structure-------------------------

t=X(5); %basin thickness, NEED TO OPTIMIZE

%-----------------------------------------------------

%-------------------Economic--------------------------

% price=[1500, 2500];

%-----------------------------------------------------

%------------------------------------------Parameters

%-------------------Splash----------------------------

%-------------------Inputs: v,sita,hn

%-------------------Outputs:S_splash

ln=(r^2-(r-hn)^2)^.5;

ada=(v*cos(sita))^2/2/9.8+hn; %this is hw in the ergo part.

hh=fsolve(@(hh)

v*cos(sita)/9.8*v*sin(sita)+(2*hh/9.8).^0.5*v*sin(sita)-pi*(ada-

hh)/2+ln, [0,0.15]);

hh=min(hh);

a=(ada-hh)/2;

n=1;

for phi=0:pi/100:pi

x(n)=a*(phi-sin(phi));

y(n)=-a*(1-cos(phi));

n=n+1;

end

Tmax=(max(x)-ln)/v/sin(sita);

i=1;

for T=0.00:Tmax/100:Tmax

xx(i)=pi*a-ln-v*sin(sita)*T;

yy(i)=-2*a+v*cos(sita)*T-1/2*9.8*T^2+hn;

73

i=i+1;

end

[Y,ii]=max(yy);

i=find(abs(x-xx(ii))<0.001);

% if yy(ii)-y(i)>4*25.4*0.001&&...

% ((x(length(x))-xx(ii))^2+(y(length(y))-yy(ii))^2)^.5-

100*0.001>=50*0.001

k=(xx(length(xx))-xx(length(xx)-1))/(yy(length(yy))-yy(length(yy)-

1));

S_splash=(-200/pi*k+50)/50;

% end

%-----------------------------------------------------

%-------------------Ergo------------------------------

%-------------------Inputs: u,sigma,h0

%-------------------Outputs: S_ergo

h=real(h);

sita0=37.6/180*pi; % From conjoint analysis

hw=ada; % will be replaced as a variable

hf_low=max(h+hw,132.1);

hm_low=max(h+hw,142.8);

hf=hf_low:(153.6-hf_low)/100:153.6;

hm=hm_low:(169.5-hm_low)/100:169.5;

sita=acos((hw+h-[hf;hm]*r1)./[hf+0.001;hm+0.001]/(1-r1));

S=-0.072*(sita/pi*18).^2+.541*(sita/pi*18)-.232; % coefficients from

conjoint analysis

w=[(153.6-hf_low)/100*normpdf(hf,u(1),sigma(1));...

(169.5-hm_low)/100*normpdf(hm,u(2),sigma(2))];

S_ergo=(S(1,:)*w(1,:)'+S(2,:)*w(2,:)')/2;

S_ergo=real(S_ergo);

%-----------------------------------------------------

%-------------------Structure-------------------------

Stress_basin=0; %Stress calculated at basin bottom

%-----------------------------------------------------

%-------------------Economic--------------------------

% Utilities

% Utilitiy for ergo

Beta_ergo=[-1.4946 S_ergo];

% Utilitiy for splash

Beta_splash=S_splash;

% Utility for price

Beta_price=-0.002*price+4.571;

Current_U=[exp(sum([Beta_ergo(1),Beta_splash,Beta_color,Beta_filler,Bet

a_price(1)])),...

exp(sum([Beta_ergo(2),Beta_splash,Beta_color,Beta_filler,Beta_price(2)]

))];

Total_U=Current_U(1)+Current_U(2)+exp(U2)+exp(U3)+exp(U_none);

Pr=Current_U/Total_U; %market proportion of our design

%Cost related:

%Basin_mat

74

Basin_mat_unit_price=5; %5 dollars per kg

%Basin_Vol

Basin_Vol=4*a*1000*t*(120+300)/2;

Pipe_Vol=r*1000*pi*t*L;

Vol=Basin_Vol+Pipe_Vol;

C_Basin=Vol*7.8/1e6*5;

Cv=C_Basin+Cv_constant;

Cv=[Cv,2*Cv];

%-----------------------------------------------------

%------------------------------------------Objective Function

%-------------------Economic--------------------------

P=-(Q_max*Pr*(price-Cv)'-Cf);

%-----------------------------------------------------

profit_constraint.m

function [C,Cq]=profit_constraint(X,v,r,sita)

%------------------------------------------Constraints

%-------------------Ergo------------------------------

% d_face=50; %the minimum distance between face and basin surface

%-----------------------------------------------------

%-------------------Splash----------------------------

% sita_nozzle_lower=pi/6; %met

%-----------------------------------------------------

%-------------------Structure-------------------------

%Stress

% Stress_Y=2.5e8;

80(mass)*9.8*1.5(coef)*L*20.5(c)/(1.37e4*t)(I)<=2.5e8;

% hn=X(4);

% t=X(5);

ln=(r^2-(r-X(4))^2)^.5;

ada=(v*cos(sita))^2/2/9.8+X(4); %this is hw in the ergo part.

hh=fsolve(@(hh)

v*cos(sita)/9.8*v*sin(sita)+(2*hh/9.8).^0.5*v*sin(sita)-pi*(ada-

hh)/2+ln, [0,0.15]);

hh=min(hh);

a=(ada-hh)/2;

n=1;

for phi=0:pi/100:pi

x(n)=a*(phi-sin(phi));

y(n)=-a*(1-cos(phi));

n=n+1;

end

Tmax=(max(x)-ln)/v/sin(sita);

i=1;

for T=0.00:Tmax/100:Tmax

xx(i)=pi*a-ln-v*sin(sita)*T;

75

yy(i)=-2*a+v*cos(sita)*T-1/2*9.8*T^2+X(4);

i=i+1;

end

[Y,ii]=max(yy);

i=find(abs(x-xx(ii))<0.001);

C=[a*pi/X(5)-.1421;

-yy(ii)+y(i)-4*25.4*0.001;

-((x(length(x))-xx(ii))^2+(y(length(y))-

yy(ii))^2)^.5+100*0.001+50*0.001];

%Dimension

% Basin_width_uppper=6*25.4;

% Pipe_radius_upper=4*25.4;

% Pipe_radius_lower=3*25.4;

% L_upper=19*25.4;

% L_lower=17*25.4;

Cq=0;

%-----------------------------------------------------

%-------------------Economic--------------------------

%-----------------------------------------------------

Solver_profit.m %------------------------------------------Constants

%-------------------Ergo-----------------------------

u=[162.8,176.7]-[20,20];

sigma=[9.96831981830439,7.80310194730275];%20-29 US citizens F/M

r1=(-1+5^.5)/2; % golden ratio

%-----------------------------------------------------

%-------------------Splash----------------------------

v=1.6;%stream veloctiy (m/s)

r=3.5/2*25.4*0.001; % Pipe radius

sita=pi/6; %Nozzle shooting angle, OPTIMIZED

%-----------------------------------------------------

%-------------------Structure-------------------------

L=17*25.4; %Pipe length

%-----------------------------------------------------

%-------------------Economic--------------------------

Q_max=64000*.15; %total market size for Premium Drinking Foutain

% Utilitiy for color

Beta_color=0.33929;

% Utilitiy for filler time

Beta_filler=0.5275;

% Competitors

% U1=1.09-1/2; %from spread sheet

U2=-0.87;

U3=-1.85;

U_none=-0.74;

%Unit Costs

76

%Bubble part

C_bubble=20;

%Trigger

C_trigger=18;

%Bottle filler part

C_fill=120;

%Chiller

C_chiller=665;

%Sliding

C_LCD=80;

%Labour

C_assembly=100;

C_ship=50;

C_package=25;

Cv_constant=sum([C_bubble C_trigger C_fill C_chiller...

C_LCD C_assembly C_ship C_package]);

%Fixed Costs

%Stamping Mold

C_CM=300000;

C_Assembly_Eq=100000;

C_Rent=25000;

C_Salary=250000;

C_overhead=50000;

Cf=sum([C_CM,C_Assembly_Eq,C_Rent,C_Salary,C_overhead]);

%-----------------------------------------------------

%------------------------------------------Optimization

% X=[basin_height, price_one, price_two, nozzle_height, thickness];

[X,fval]=fmincon(@(X)Profit(X,u,sigma,r1,v,r,sita,L,Q_max,Beta_color,..

.

Beta_filler,U2,U3,U_none,Cv_constant,Cf),[130,2200,3500, 2*r,

3],[],[],[],[],...

[85,1000,2000,r,1],[160,3500,4000,2*r,4],@(X)profit_constraint(X,v,r,si

ta));

%------------------------------------------Results

h=X(1);price(1)=X(2);price(2)=X(3);hn=X(4);t=X(5);

ln=(r^2-(r-hn)^2)^.5;

ada=(v*cos(sita))^2/2/9.8+hn; %this is hw in the ergo part.

hh=fsolve(@(hh)

v*cos(sita)/9.8*v*sin(sita)+(2*hh/9.8).^0.5*v*sin(sita)-pi*(ada-

hh)/2+ln, [0,0.15]);

hh=min(hh);

a=(ada-hh)/2;

n=1;

for phi=0:pi/100:pi

x(n)=a*(phi-sin(phi));

y(n)=-a*(1-cos(phi));

n=n+1;

end

Tmax=(max(x)-ln)/v/sin(sita);

77

i=1;

for T=0.00:Tmax/100:Tmax

xx(i)=pi*a-ln-v*sin(sita)*T;

yy(i)=-2*a+v*cos(sita)*T-1/2*9.8*T^2+hn;

i=i+1;

end

[Y,ii]=max(yy);

i=find(abs(x-xx(ii))<0.001);

if yy(ii)-y(i)>4*25.4*0.001&&...

((x(length(x))-xx(ii))^2+(y(length(y))-yy(ii))^2)^.5-

100*0.001>=50*0.001

k=(xx(length(xx))-xx(length(xx)-1))/(yy(length(yy))-yy(length(yy)-

1));

S_splash=(-200/pi*k+50)/50;

end

%-----------------------------------------------------

%-------------------Ergo------------------------------

%-------------------Inputs: u,sigma,h0

%-------------------Outputs: S_ergo

h=real(h);

sita0=37.6/180*pi; % From conjoint analysis

hw=ada; % will be replaced as a variable

hf_low=max(h+hw,132.1);

hm_low=max(h+hw,142.8);

hf=hf_low:(153.6-hf_low)/100:153.6;

hm=hm_low:(169.5-hm_low)/100:169.5;

sita1=acos((hw+h-[hf;hm]*r1)./[hf+0.001;hm+0.001]/(1-r1));

S=-0.072*(sita1/pi*18).^2+.541*(sita1/pi*18)-.232; % coefficients from

conjoint analysis

w=[(153.6-hf_low)/100*normpdf(hf,u(1),sigma(1));...

(169.5-hm_low)/100*normpdf(hm,u(2),sigma(2))];

S_ergo=(S(1,:)*w(1,:)'+S(2,:)*w(2,:)')/2;

S_ergo=real(S_ergo);

%-----------------------------------------------------

%-------------------Structure-------------------------

Stress_basin=0; %Stress calculated at basin bottom

%-----------------------------------------------------

%-------------------Economic--------------------------

% Utilities

% Utilitiy for ergo

Beta_ergo=[-1.4946 S_ergo];

% Utilitiy for splash

Beta_splash=S_splash;

% Utility for price

Beta_price=-0.002*price+4.571;

Current_U=[exp(sum([Beta_ergo(1),Beta_splash,Beta_color,Beta_filler,Bet

a_price(1)])),...

exp(sum([Beta_ergo(2),Beta_splash,Beta_color,Beta_filler,Beta_price(2)]

))];

Total_U=Current_U(1)+Current_U(2)+exp(U2)+exp(U3)+exp(U_none);

Pr=Current_U/Total_U; %market proportion of our design

78

%Cost related:

%Basin_mat

Basin_mat_unit_price=5; %5 dollars per kg

%Basin_Vol

Basin_Vol=4*a*1000*t*(120+300)/2;

Pipe_Vol=r*1000*pi*t*L;

Vol=Basin_Vol+Pipe_Vol;

C_Basin=Vol*7.8/1e6*5;

Cv=C_Basin+Cv_constant;

Cv=[Cv,2*Cv];

Result={'Basin Height:',X(1)*10;

'Nozzle Position: (H/L)',X(4)*1000;...

'Basin Thickness:',X(5);...

'Price_one:',X(2);...

'Price_two:',X(3);...

'%Market_one:',Pr(1);...

'%Market_two:',Pr(2);...

'Revenue:',Q_max*Pr*price';...

'Cost:',(Q_max*Pr*(-Cv)'-Cf);...

'Profit',-fval}