ABSTRACT
CANSLER, ETHAN ZACHARIAH. Identifying, Mapping, and Exploring Excess
Relationships in Engineered Systems Relevant to Service Phase Evolution. (Under the
direction of Dr. Scott Ferguson).
Engineers understand that attaining a full service life can add value to an engineered
system. Ensuring that this is possible requires that excess be embedded within the design phase
to enable system evolution when new or changed requirements are placed on it during the
service phase. However, since future needs are by definition unknown, knowing with certainty
which excesses to embed is impossible. This thesis addresses two research questions. The first
concerns how excess in component relationships can be mapped throughout a system in a
manner relatable to system stakeholder needs, thereby producing the set of excesses that affect
system evolvability. This is accomplished by considering and selectively combining elements
from existing techniques in the design literature for modeling systems and system change to
develop a quantified flow diagram method for mapping excess within a system. The method is
demonstrated using four case studies: a heat gun, a coffee maker, a toy dart gun, and a string
trimmer. The second research question addresses how knowledge made available by the
creation of a system excess map coupled with a set of potential future needs reveals if a design
possesses sufficient excess to respond to future needs, and if not, where the shortcomings are.
This approach is demonstrated using the toy dart gun. Results from the case studies show that
the excess mapping method can successfully identify excesses throughout a system relevant to
stakeholder needs, and that the stress test approach can successfully demonstrate the location
of potential shortcomings in a design.
© Copyright 2015 Ethan Zachariah Cansler
All Rights Reserved
Identifying, Mapping, and Exploring Excess Relationships in Engineered Systems
Relevant to Service Phase Evolution
by
Ethan Zachariah Cansler
A thesis submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirements for the degree of
Master of Science
Aerospace Engineering
Raleigh, North Carolina
2015
APPROVED BY:
_______________________________
Dr. Scott Ferguson
Committee Chair
________________________________
Dr. Gregory Buckner
________________________________
Dr. Andre Mazzoleni
i
BIOGRAPHY
Ethan Cansler graduated as valedictorian of Franklin High School in Franklin, NC in 2009. He
then studied at the University of Tennessee as a founding member of the Haslam Scholars
Program, and worked as a student engineer at Oak Ridge National Laboratory’s Spallation
Neutron Source, until graduating Magna cum Laude in 2013 with a Bachelor of Science in
Aerospace Engineering. In the fall of 2013 he began graduate studies at North Carolina State
University in the System Design Optimization Lab under Dr. Scott Ferguson.
ii
ACKNOWLEDGMENTS
I would like to thank my wife Sarah for her support through my two years of graduate school.
Additionally, I thank my advisor, Dr. Scott Ferguson, for his mentorship and inspiration, and
my past and current colleagues, Dr. Garrett Foster, Margaret Antonik, Beth May, Chris Miller,
Jaekwan Shin, Kayla Von Hagel, and Tyler Williams, for tolerating my rambling reflections
and offering their feedback and friendship.
iii
TABLE OF CONTENTS
LIST OF TABLES ...............................................................................................................
vi
LIST OF FIGURES ............................................................................................................. vii
Introduction ........................................................................................................
1
Evolvability................................................................................................................
1
Nature and Origins of Excess ....................................................................................
3
Motivation ..................................................................................................................
4
Background ........................................................................................................
8
System Evolvability and Excess ................................................................................
8
Change Relationships between Components .............................................................
9
Design Structure Matrices...................................................................................
9
Change Propagation ............................................................................................ 11
Functional Modeling .................................................................................................. 12
Real Options Theory .................................................................................................. 14
Conclusions from Literature Review ......................................................................... 14
Foundational Theory .......................................................................................... 16
Categorizing Excess ................................................................................................... 16
Excess Basis ............................................................................................................... 18
Resolution of Excess Flows ....................................................................................... 22
Developing a Mapping Approach for System Excess........................................ 23
Step 1: Collect Stakeholder Specifications ......................................................... 25
Step 2: Identify System Architecture and Relationships .................................... 26
Step 3: Assemble Excess Map ............................................................................ 38
Step 4: Identify State Parameters ........................................................................ 40
Evaluating System Level Excess ........................................................................ 41
Map Quality and Criteria for Update .................................................................. 43
Case Study 1 Conclusion: Heat Gun Evolution Examples ........................................ 43
Heat Gun Evolution 1: Replace Tri-Mode Switch with Variable Voltage
Switch .......................................................................................................................... 43
Heat Gun Evolution 2: Increase Output Temperature to 750 °C ........................ 44
Case Study 2: Coffee Maker ...................................................................................... 44
Coffee Maker Excess Map Creation ................................................................... 45
iv
Coffee Maker Evolution Examples..................................................................... 57
Scalability Case Study ............................................................................................... 59
Subsystem 1: Engine ........................................................................................... 61
Subsystem 2: Transmission................................................................................. 62
Subsystem 3: Cutting Attachment ...................................................................... 63
String Trimmer Excess Map ............................................................................... 64
Stress Test Approach.......................................................................................... 67
Stress Testing in Engineering .................................................................................... 67
Stress Test Approach Steps........................................................................................ 68
Step 1: Collect Future Needs and Specifications ................................................ 68
Step 2: Generate Solutions .................................................................................. 69
Step 3: Evaluate Impacts ..................................................................................... 70
Step 4: Judge Fitness/Review Excess Placement................................................ 71
Stress Test Case Study Preliminaries ......................................................................... 71
Toy Dart Gun Excess Map Creation ................................................................... 72
Stress Test Case Study ............................................................................................... 86
Step 1: Collect Future Needs and Specifications ................................................ 86
Steps 2 and 3: Generate Solutions and Evaluate Impacts ................................... 87
Step 3 Continued: Review Overlapping Future Needs ....................................... 97
Step 4: Judge Fitness/Review Excess Placement................................................ 99
Conclusions and Future Work ............................................................................ 103
Research Question 1: How can excesses pertinent to service phase evolution be
identified in a general system?......................................................................................... 103
Research Question 2: How can designers relate the identified excesses to the
system’s ability to meet future needs? ............................................................................. 104
Opportunities for Future Work .................................................................................. 105
REFERENCES .................................................................................................................... 106
APPENDIX .......................................................................................................................... 112
v
LIST OF TABLES
Table 3.1: Excess Basis........................................................................................................... 19
Table 3.2: Structural Excess Optional State Parameters ......................................................... 20
Table 4.1: Heat Gun Component Excesses ............................................................................. 39
Table 4.2: Coffee Maker Component Excesses ...................................................................... 55
Table 4.3: String Trimmer Needs and Specifications ............................................................. 60
Table 5.1: Dart Gun Component Measurements .................................................................... 72
Table 5.2: Dart Gun Component Excesses ............................................................................. 85
Table 5.3: Overlapping Future Needs ..................................................................................... 97
Table 5.4: Summary of Dart Gun Stress Test Results ............................................................ 99
vi
LIST OF FIGURES
Figure 2.1: Sample HD-DSM Faces for Heat Gun ................................................................. 11
Figure 2.2: Portion of Heat Gun Functional Diagram ............................................................ 13
Figure 3.1: Compatibility and Functional Flows .................................................................... 18
Figure 3.2: Naming Scheme for Excess Types ....................................................................... 19
Figure 4.1: Excess Mapping Procedure .................................................................................. 24
Figure 4.2: Heat Gun [42] ....................................................................................................... 24
Figure 4.3: Variable Level of Abstraction .............................................................................. 27
Figure 4.4: Excess Map Segment for General Architecture ................................................... 28
Figure 4.5: Disassembled Heat Gun ....................................................................................... 30
Figure 4.6: Heat Gun Case ...................................................................................................... 30
Figure 4.7: Case Excess Map Contribution ............................................................................ 32
Figure 4.8: Cord Excess Map Contribution ............................................................................ 32
Figure 4.9: Heat Gun Switch .................................................................................................. 33
Figure 4.10: Switch Excess Map Contribution ....................................................................... 34
Figure 4.11: Heat Gun Heating Coils ..................................................................................... 34
Figure 4.12: Heating Coils Excess Map Contribution ............................................................ 35
Figure 4.13: Heat Gun Fan...................................................................................................... 36
Figure 4.14: Fan Excess Map Contribution ............................................................................ 37
Figure 4.15: Heat Gun Nozzle ................................................................................................ 37
Figure 4.16: Nozzle Excess Map Contribution ....................................................................... 38
Figure 4.17: Heat Gun Excess Map ........................................................................................ 41
Figure 4.18: Coffee Maker [53] .............................................................................................. 45
Figure 4.19: Coffee Maker Body ............................................................................................ 47
Figure 4.20: Body Excess Map Contribution ......................................................................... 48
Figure 4.21: Cord Excess Map Contribution .......................................................................... 49
Figure 4.22: Coffee Maker Switch.......................................................................................... 49
Figure 4.23: Switch Excess Map Contribution ....................................................................... 49
Figure 4.24: Coffee Maker Heating Element .......................................................................... 50
Figure 4.25: Heating Element Excess Map Contribution ....................................................... 51
Figure 4.26: Coffee Maker Brew Basket ................................................................................ 52
Figure 4.27: Brew Basket Excess Map Contribution.............................................................. 52
Figure 4.28: Coffee Maker Hot Plate ...................................................................................... 53
Figure 4.29: Hot Plate Excess Map Contribution ................................................................... 53
Figure 4.30: Coffee Maker Carafe .......................................................................................... 54
Figure 4.31: Carafe Excess Map Contribution ....................................................................... 54
Figure 4.32: Coffee Maker Excess Map ................................................................................. 56
Figure 4.33: String Trimmer [57] ........................................................................................... 60
Figure 4.34: Engine Excess Map ............................................................................................ 62
Figure 4.35: Transmission Excess Map .................................................................................. 63
Figure 4.36: Cutting Attachment Excess Map ........................................................................ 64
Figure 4.37: String Trimmer Composite Excess Map ............................................................ 65
vii
Figure 5.1: Stress Test Approach Flowchart........................................................................... 68
Figure 5.2: Toy Dart Gun [62] ................................................................................................ 71
Figure 5.3: Dart Kinetic Energy Required vs. Distance for Level Fire at 1m ........................ 73
Figure 5.4: Dart Gun Body ..................................................................................................... 75
Figure 5.5: Dart Gun Component Layout ............................................................................... 75
Figure 5.6: Body Excess Map Contribution ........................................................................... 76
Figure 5.7: Dart Gun Slide Grip ............................................................................................. 76
Figure 5.8: Slide Grip Excess Map Contribution.................................................................... 77
Figure 5.9: Dart Gun Slide Pump ........................................................................................... 77
Figure 5.10: Slide Pump Excess Map Contribution................................................................ 78
Figure 5.11: Dart Gun Flex Tube ............................................................................................ 78
Figure 5.12: Flex Tube Excess Map Contribution .................................................................. 78
Figure 5.13: Dart Gun Check Valve/Release .......................................................................... 79
Figure 5.14: Check Valve/Release Excess Map Contribution ................................................ 79
Figure 5.15: Dart Gun Charge Pressure Vessel ...................................................................... 80
Figure 5.16: Charge Pressure Vessel Excess Map Contribution ............................................ 80
Figure 5.17: Dart Gun Floating Pressure Seal ........................................................................ 81
Figure 5.18: Floating Pressure Seal Excess Map Contribution .............................................. 82
Figure 5.19: Dart Gun Rotary Barrel ...................................................................................... 82
Figure 5.20: Rotary Barrel Excess Map Contribution ............................................................ 83
Figure 5.21: Dart Gun Trigger/Advance Assembly................................................................ 83
Figure 5.22: Trigger/Advance Assembly Excess Map Contribution ...................................... 84
Figure 5.23: Dart Gun Ratchet Shaft ...................................................................................... 84
Figure 5.24: Ratchet Shaft Excess Map Contribution ............................................................ 84
Figure 5.25: Toy Dart Gun Excess Map ................................................................................. 86
Figure 5.26: Dart Gun Stress Test Conclusions .................................................................... 100
viii
Introduction
Designs are created in response to market opportunities that are driven by the identification
of customer needs. As the design process advances, needs are mapped to numerical
specifications, which are in turn translated to a system architecture [1]. However, the
environment in which a system operates, and the needs that it is responsible for satisfying, may
change over the service life of the system. Changes to initial needs, or the identification of new
needs, after the design has been fielded are hereafter referred to as ‘future needs’.
Evolvability
The B-52 is one system that has successfully been able to respond to future needs.
Originally designed and deployed as a long-range nuclear strike bomber in 1955, it is expected
to serve until at least the 2040s [2]. Between its original introduction and now, the role of the
B-52 has shifted from a high altitude nuclear strike bomber, to a low altitude conventional
bomber, to a platform for standoff weapons [3]. The ability to take on these role changes were
enabled by the payload capacity associated with the airframe, the ability to expand the payload
volume via the ‘big belly’ modification, and reinforcing the interface structure between wings
and fuselage [4].
In contrast, the F/A-18 is a system that has failed to meet future needs. The F/A-18 was
originally introduced in 1983 as a joint attack and air superiority fighter. Over time the needs
that the system faced changed due to developing technologies. These needs included the ability
to return unused smart weapons to the carrier rather than dropping them at sea unused (thereby
placing additional load on the landing structures) and the requirement to accommodate a
greater volume of electronic warfare equipment. An updated version of the plane deployed in
1995 was redesigned so thoroughly that there is only 10% commonality between the original
and new airframes [5]. Such a drastic redesign indicates that the original system was not
capable of evolving to meet future needs due to factors including insufficient structural
capacity of the landing gear and insufficient volume available within the fuselage.
Ideally, all engineered systems would maintain value for system stakeholders by satisfying
future needs and ensuring continued system operation. In this research the ability to maintain
1
value when faced with future needs is made possible by service phase evolution – formally
defined as the ability of a system to physically transform from one configuration to a more
desirable configuration while in service. The motivation for evolvability research is based on
the belief that systems capable of service phase evolution possess greater value over their
lifespan than those that are not [6].
Other approaches in the literature to ensure that a system is capable of meeting future needs
include reconfigurability [7] and robustness [8]. However, these approaches have
shortcomings, particularly for systems that are expected to be in service for a significant
amount of time. Implementing reconfigurability is a choice made in the design phase that
explicitly allows aspects of the system to assume a range of configurations. These
configurations can be a set of fixed points or a bounded range on a continuum. Airfoils that
incorporate flaps and/or slats to change the wing’s flight characteristics is an example of
reconfigurable design.
Robust system design seeks to make a system insensitive to variations in its operating
environment, without any alteration to the system while in service – a valid approach, but one
that expends more resources than would be necessary if the system could be strategically
changed. However, achieving robustness is often accomplished by sacrificing system
performance. This is done by finding a location in the design space where the objective
function contours are relatively flat. Such a location in the design space is often not co-located
with the design that maximizes or minimizes system performance. Further, as the projected
system lifespan is increased, the envelope of uncertainty is also expanded, meaning that
applying robust design theory to a system with a long projected service life and completely
unknown future needs would result in a drastically over-built (or under-performing) system.
In contrast, evolvable design seeks to allow changes to a system that are not explicitly
prescribed in the design phase. Prior work [9] has demonstrated that one of the significant
contributing factors to evolvability is excess, defined as the surplus in a component or system
beyond what is currently required of it. This concept of excess in introduced in the next section.
2
Nature and Origins of Excess
Excess is defined as surplus in a system or component beyond what is currently required
of it [9]. These potential surpluses occur in inter-component relationships, or relationships
between components and the external environment. Much like enthalpy and entropy in
thermodynamics, there is no such thing as ‘absolute excess’. Rather, excess is a relative
measurement of the difference between the capabilities of the designed system and design
specifications. These relationships fall into one of three categories: flow (transmitted energy,
signal, or material), structural (stress or strain) or geometric (occupied length, area, or volume).
In practical engineering terms, excess occurs in situations such as:

wiring carrying only 7 A of current when rated with an ampacity of 10 A,

a pressure vessel operating at 200 MPa when it is certified for 400 MPa,

an equipment room holding 20 m3 of hardware when it can contain 35 m3.
The surplus embodied by the Factor of Safety (FoS) is generally considered to be
independent from the excesses used for system evolvability. As an example, consider a
structure made of material with a yield strength of 300 MPa. With a FoS of 3, the usable
material strength is 100 MPa. If subjected to a design load that produces stress of 70 MPa, the
excess within the structure is 30 MPa. The only situation where part of the FoS for a system
may be converted to usable excess occurs when the FoS has been revised downward due to
either overly conservative initial estimates or a less severe operating environment than
originally planned.
Intentional inclusion of excess in a system might enable future changes, or their presence
may be a side effect of other factors. A common example of the latter results from the
standardized sizing of commercial components such as fasteners, wiring, or externally sourced
components. Practically, it is inefficient to size each fastener exactly to the required load.
Rather, the smallest sufficient fastener from a list of standard sizes is chosen, creating some
quantity of excess. Another example comes from enforcing component commonality. The 2x4
lumber studs used extensively in residential construction are employed for both load-bearing
3
and non-load-bearing walls for the sake of easier construction, even though for the latter
application their full strength is unnecessary.
Since designers are incapable of knowing the future, the excess that is originally designed
into the system may not be constant over time. Rather, the excess present in a systems may
vary due to system evolutions or changes in system specifications while in service. When,
lower than anticipated service requirements are realized, excesses are created in the
components that are consequently underutilized.
Motivation
The formulation shown in Equation 1.1 was developed in [9] and refined in [10]. Here,
evolvability E is expressed as a function of excess X, evolvability gain per unit excess gx, and
the upper and lower bounds of usable excess xl and xu. Excess and its upper and lower usable
bounds have the unit of percent (%) of the normalized design quantity that is being measured,
while the gain per unit excess has units of reciprocal percent (1/%). Two classes of US Navy
aircraft carrier – the Nimitz class and the Ford class – were compared based on four parameters:
displacement, volume, stability, and electrical power. These parameters were sourced from the
decades of empirical design experience reflected in [11] [12]. It was found that the Nimitz class
aircraft carrier had an evolvability of 19.2 yr-%, while the Ford class carrier had an evolvability
of 257 yr-%. These units resulted from the fact that the US Navy measures aircraft carrier
evolvability in hypothetical years of extended service life. When using Equation 1.1, the
numbers that are produced have meaning when they are compared, as they represent the
relative evolvability of different design options for a single system. Hence, the Ford class was
demonstrated to be significantly more evolvable than the Nimitz class.

 = ∫  ∙  
( 1.1 )

Examining Equation 1.1 suggests that two main factors determine a system’s evolvability:
excesses and their associated gain factors. However, depending on the resolution of the system
analysis, a very large number of system excesses are possible, ranging from high-level
4
parameters such as power generation to low-level parameters such as tensile strength of the
screws affixing speakers to bulkheads. The demonstrative case study in [9], comparing two
classes of US Navy aircraft carrier, benefited from decades of empirical knowledge that told
designers which excesses were important to enable service phase evolvability. Practically
speaking, such knowledge allows designers to embed suitable quantities of these excesses in
the system. Clearly, a subset of the possible excesses that can be described for a system are
sufficient to describe a system’s evolvability; however, the question remains of how to identify
such excesses for general systems that do not necessarily benefit from prior experience.
Another consideration driving selection of excesses is that they must be of the correct type,
quantity, form, and location to be usable in bringing about system change [13]. This means
that for an evolution to occur, there must be the right kind of excess in every affected
component, there must be enough of it, it must be of the right form, and it must be accessible
to the component that requires it to undergo the evolution. As a simplified practical example,
an evolution to a building might require placing a new piece of equipment in a specific location.
However, the evolution may only proceed if there is sufficient volume, energy, and loadcarrying capacity at said location within the building, if these excesses are collocated with the
intended equipment placement, and if these excesses are of the correct form – i.e. the excess
volume is in a shape that can accept the new equipment, the energy is electrical and of the
correct voltage and/or frequency, and the load-carrying capacity of the structural members can
be interfaced with the new equipment.
Therefore, the question remains of how to identify excesses within general systems that are
relevant to system evolvability. This leads to the first research question explored in this thesis:
Research Question 1:
How can the presence and quantity of excess pertinent to
service phase evolution be identified?
Bearing in mind that excess can be described at different system resolutions, a strategy to
identify the excesses in a system most likely to influence its evolvability is needed. Continuing
with the aircraft carrier example, it is easy to accept that the total allowable displacement of
the ship is a useful parameter. On the other hand, the thickness of the steel rods used in the
5
deck railings is highly unlikely to have an impact on the ability of the ship to evolve. It is not
hard to categorize those two excesses as relevant and irrelevant, respectively, because they are
extreme examples. However, exactly where to draw the line between relevant and irrelevant
excesses is not clear.
Designers are incapable of knowing with certainty the future needs a system will face.
When considering system evolvability, a simplifying assumption used in [10] was that the top
level functions of a system remain fixed. In simple terms, this means that an aircraft carrier
will always transport and launch aircraft and a coffee maker will always brew coffee. This
assumption could be used to reduce the scope of excesses considered for their contribution to
evolvability to those that contribute to the current functions of the system, as future functions
would be related.
As excess is consumed to meet future needs, deliberate placement of excess in a system
must be a function of unknowable future needs. Blindly adding excess to components or
subsystems (even if they are the excesses identified as pertinent to system evolvability) adds
cost without guaranteed benefit, leading to decreased system value. These considerations lead
to the second research question:
Research Question 2:
How can designers relate the quantities of the identified excesses to the system’s ability
to meet future needs?
There is limited discussion in the literature regarding the inclusion of excess to meet future
needs. The available literature generally describes situations where designers draw on past
experience designing similar systems, as in [11] [12]. However, there is a lack of guidance for
systems without the benefit of empirical design knowledge.
Designers need a method to examine the evolvability of general systems. The outcome of
Research Question 1 includes the set of excesses that designers will be concerned with when
designing for evolvability and their present amounts. Yet, there is no insight provided into how
useful (or valuable) these amounts are. Portions of a design with excess quantities that
artificially limit the ability of a system to change, relative to the other available excess
6
quantities, diminish the evolvability of the design and reduce the utility of other excesses.
Therefore, the idea that a system design can be stress tested to find ‘bottlenecks’ for system
evolution is investigated. Beyond identifying locations in which excess should be added, the
similar idea of revealing excesses that are superfluous, i.e. those that support system changes
surpassing those enabled by the other excesses, is explored.
Chapter 2 of this thesis reviews works of the literature that pertain to system excess,
evolvability, system change, and methods of representing systems. Chapter 3 discusses the
underlying theory of this work’s contributions, while Chapters 4 and 5 address Research
Questions 1 and 2, respectively. Chapter 6 discusses conclusions from the products of the
preceding chapters and opportunities for continuing work.
7
Background
No analytical method exists in the literature with the ability to map or quantify excess for
an engineered system. Yet, it is recognized that system evolvability is intrinsically tied to
engineering change. Exploring how to manage change within an engineered system is a topic
that has received significant attention in the literature. This chapter discusses research
introducing the concept of excess, explores methods of modeling a system, and characterizes
how changes propagate.
System Evolvability and Excess
The last few years of evolvability-focused design research have seen a progression from
design guidelines to mathematical formulations. Work in [14] [15], for example, introduced
empirically-derived design guidelines to enable future evolvability. These guidelines are
centered around:

system modularity,

scalability,

reduction of unnecessary parts,

decoupling interfaces,

maintaining clearances and usable area,

designing tunable components,

and providing energy storage/importation capabilities in excess of the original
requirements.
Other work in the literature, such as [16], describes design margin as “the extent to which
a parameter exceeds what it needs to meet its functional requirements regardless of the
motivation for which the margin was included”. Thunnissen [17], on the other hand, describes
‘design margin’ as quantities of surplus placed to mitigate uncertainty in the design process.
These margins were probabilistically allocated to design parameters and organizational
parameters (schedule, cost and risk). This work, however, focused on how design margins
8
should be assigned to impact the successful completion of the original design rather than how
they might lead to system evolvability.
Moving toward a more mathematical framework, Tackett et al. [9] introduced excess as a
variable controlled by designers, meaning that they had control over the amount of surplus
present in each component of a system. Further work developed a mathematical formulation
of system evolvability as a function of excess [10] as was shown in Equation 1.1. This work
investigated excess in two classes of naval aircraft carriers, the older Nimitz class and the
upcoming Ford class. The Ford class was estimated to be more evolvable that the Nimitz class
when considering an upgrade from traditional steam catapults to electromagnetic catapults for
launching aircraft. A limitation of this work, however, was that it benefited from empirical
knowledge of naval design experts that defined the types of excess within a system and how
evolvability was tied into service life [11] [12].
Change Relationships between Components
Quantifying the excess within a system is necessary if it is to eventually be used as a
parameter when designing for evolvability. A specific target of the literature review was
strategies that integrate numerical information about components associated with change.
‘Engineering change’ has been defined as occurring while the system is still being designed,
and is defined as “an alteration to parts, drawings, or software that have already been released
during the product design process. The change can be of any size or type; the change can
involve any number of people and take any length of time.” [18]. Service phase evolution is
by definition different from engineering change, as it occurs after the system has been
constructed and deployed. However, system evolution requires redesign, and works exploring
engineering change may be applicable when predicting the ability of a system to evolve.
Design Structure Matrices
In its most basic form a Design Structure Matrix (DSM) is a square matrix diagrams where
each column and matching row correspond to a component or design task [19] [20]. They are
used to represent dependency relationships; the columns represent the originating component
9
or task while the rows represent the affected component or task. The information content of
DSMs has been expanded to include additional detail about component relationships. Pimmler
and Eppinger [21], for example, defined four classes of interaction: Spatial, Energy,
Information and Material. Sosa et al. [22] added a fifth class of interaction, Structural. With
these five classes, all relationships between components could be described. However, the
presence of five different interaction types on a two-dimensional plot led to challenges of
effectively conveying information.
In support of analyzing flexibility for future system evolvability, Tilstra et al. [23]
developed the High-Definition Design Structure Matrix (HD-DSM) methodology to account
for direct change propagation potential throughout a multi-domain engineered system. The
HD-DSM methodology maps changes to the domain to which they correspond, significantly
increasing resolution over the traditional DSM. It accomplishes this by making the DSM threedimensional, such that each face applies to a particular domain. The domains are collected in
an ‘Interaction Basis’ and are largely sourced from the functional basis defined by Hirtz et al.
[24] but also correspond to those used in [21] [22]. The HD-DSM process reveals an interesting
point: provided that two dimensions of the DSM structure correspond to originating and
receiving components, the DSM structure can be extended to any number of dimensions.
Importantly, this approach solves the information presentation issue experienced in prior
work while actually increasing resolution. Figure 2.1 shows sample HD-DSM faces for a heat
gun in the electrical energy, gas material, and thermal energy domains. Marked cells in a DSM
(grey in Figure 2.1) indicate a relationship or change dependency between components. Since
each component clearly affects itself, the diagonal of a DSM bears no useful information and
is marked out.
10
1
2
3
4
5
6
1
2
3
4
5
6
1
Case - 1
Case - 1
Case - 1
Controller - 2
Controller - 2
Controller - 2
Fan Motor - 3
Fan Motor - 3
Fan Motor - 3
Heat Coils - 4
Heat Coils - 4
Heat Coils - 4
Wire - 5
Wire - 5
Wire - 5
Fasteners - 6
Fasteners - 6
Fasteners - 6
2
3
4
5
6
Electrical Energy Domain
Gas Material Domain
Thermal Energy Domain
Figure 2.1: Sample HD-DSM Faces for Heat Gun
Change Propagation
A key segment of change research regards change propagation, which has been defined in
the literature as “the process by which a change to one part or element of an existing system
configuration or design results in one or more additional changes to the system, when those
changes would not otherwise have been required” [25]. Clearly, change propagation is not
desirable; ideally, a change to one component in a system design would never require change
in another. Change propagation analysis has received increased attention in engineering design
research because of the value associated with efficient change management in the system
design process.
Eckert et al. [26], recognizing that some components will have a greater effect on system
change than others, developed four classifications for components: constants, absorbers,
carriers, and multipliers. Constants are unaffected by change and have no relationship with
change whatsoever. Absorbers can absorb more changes than they cause and diminish change
complexity. Carriers cause and absorb changes in roughly equal measure, and do not affect
change complexity. Multipliers cause more changes than they absorb, and increase change
complexity.
Researchers exploring change propagation must employ some form of network to account
for the transmission of change from one node (whether component, designer, etc.) to another.
The most basic form of change propagation analysis simply includes the information that one
node changes another, without elaborating as to the nature or quantity of the change.
Researchers have developed ways to encode more information into change propagation
11
analysis, however. For example, Suh et al. [27] explored the use of quantified change
propagation analysis to strategically embed product flexibility. Some forms of change
propagation analysis target the overall risk to a design of change. Risk has been defined as the
likelihood of a change times its impact on redesign (i.e. how much work must be redone) [28].
Tools have been developed to quantitatively describe risk, including the Change Propagation
Method [29], RedesignIT [30], and a Matrix-Calculation-Based Algorithm [31].
Other researchers have sought to track changes over multiple domains; Pasqual and de
Weck [32] developed a change propagation network that included information from the
coupled product, change, and social domains. Over time, change propagation research has
incorporated both more domains and numerical information to increase the resolution of the
system change pathways being analyzed.
Change propagation analysis seeks to highlight sources of potential change to aid designers
in minimizing its propagation. However, design for service-phase evolution mandates specific
change(s) to specific component(s) and requires knowledge of physical component-specific
parameters that change propagation analysis is generally not equipped to offer. Further, the
presentation styles of change propagation analysis are typically not conducive to visualizing
the impacts of a specific change or evolution throughout a system. To that end, other techniques
from the literature were sought that are capable of representing an entire set of relationships
between subunits of a system within a single view. The most promising candidate was
functional modeling, as discussed next.
Functional Modeling
Functional models are a well-established method used to represent a system in terms of its
functions and flows, rather than by the properties of its components. Block diagrams are
created where the blocks represent the functions of the system (rather than individual
components or subsystems) and the arrows that pass between the blocks are labeled with the
functional flow they represent [33]. Of interest to this work is the concept of a functional chain,
as described in [34], which identifies the main sub-functions of a system. For a dart gun, some
of these function chains include converting human energy to kinetic energy of the dart,
12
transmitting air from the atmosphere to the base of the dart (as propellant), and converting the
aiming signal from the operator to a flight direction for the dart [33]. This approach allows a
designer to consider what the system is intended to do. In an effort to standardize the
nomenclature in a functional model, Hirtz et al. [24] developed a reconciled functional basis
that addressed both the functional flows between components and the functional vocabulary
pertaining to the individual components’ operations. The ability to abstract a system has
allowed functional modeling to be used for a variety of tasks that extend beyond pure
conceptual design. For example, Kalyanasundaram and Lewis [35] used the functional models
of two systems as the first phase in determining which functional flows would be shared in a
unified product. Kurtoglu and Tumer [36] have also employed a functional model as a tool for
evaluating functional-failure risk in systems in the conceptual design phase.
As a reference, a selected portion of a traditional functional diagram for a heat gun is shown
in Figure 2.2.
Hand
Import
Human
Signal
Import
Electricity
Hand
Actuate
Electricity
Energy
Signal
Material
Convert
Elec. To
Thermal
Figure 2.2: Portion of Heat Gun Functional Diagram
Similar to functional models are bond graphs, which are also simplified block
representations of systems. However, bond graphs are concerned solely with flows of energy
between components. Helms et al. [37] explored the use of computerized design catalogs in
design synthesis applications via a modified bond graph architecture. This represents a fusion
of block diagrams with equation-based physical effects. To be suitable for mapping excess,
however, this method would also have to accommodate geometric and structural attributes.
13
While functional modeling is excellent for visualizing how flows of energy, signal, and
mass travel through a system in terms of its functional blocks, there is no way to tell how these
flows interact with the physical components of the system, nor are the flows quantified.
Therefore, there are no provisions for the information that is needed when mapping excess – a
physical architecture based set of quantified excess relationships (that include more factors
than only flows of energy, signal, and mass).
Real Options Theory
Real options theory, originally used in the field of economics, has been adapted for use in
engineering as described in [38]. A real option is the right, but not the obligation, to undertake
a specific action. In the context of engineering, a real option is the ability to exercise a
predetermined change to a deployed system, or in other words, a designed-in future evolution.
Some works in the engineering literature [39] [40] have applied real options theory to the
problem of maximizing system value when a finite set of future evolutions is known. However,
the traditional formulation of real options analysis, reliant on a finite set of future needs, is
incapable of analyzing systems with unknowable future needs.
Conclusions from Literature Review
Considering that excess will often occur in terms of base flows (energy, mass, or signal), a
systematic treatment of excess must address the functional flows of a component. Therefore,
pertinent to this work is the set of functional flows described by Hirtz [24]. This is divided
between the three base types of flow—signal, energy, and mass—and sub-divided into specific
types such as control signal, electrical energy, thermal energy, liquid flow, etc. Absent are
geometric and structural parameters relevant to excess, but the involved flows are the same
and already standardized in design nomenclature. While excesses observed in a system do not
always belong to the energy, mass, or signal flow classes denoted in a functional diagram,
aspects of the functional diagram method’s approach to flows do hold value for this work.
Specifically, using arrows to map flows through a block-diagram based representation of a
system, coupled with numerical quantification, is considered applicable to modeling excess in
14
a system. It carries the additional benefit of being a visually accessible and intuitive means of
tracking component relationships throughout a system, unlike with HD-DSMs.
Regarding DSM-based methods, though their visual arrangement is not suitable to mapping
excesses in a system, aspects of their approaches are useful for mapping excess flows within a
system. HD-DSMs assimilate information from any necessary domain, while change
propagation approaches incorporate numerical information regarding component relationships.
Since excess can occur in any component relationship, an approach capable of interacting with
any domain is necessary. To standardize the domains of excess considered, a formal set of
excesses, similar to the HD-DSM interaction basis, is also needed.
From this review of the literature, it was concluded that a form of quantified block-based
flow diagram is a fusion of applicable characteristics from the published methods that satisfies
the requirements of excess mapping.
15
Foundational Theory
The preceding chapter detailed approaches in the literature pertaining to change and system
modeling and analysis. This section details the underlying theory particular to the nature and
treatment of excesses for enabling system change, and serves as the foundation of the work
developed in Chapters 4 and 5.
The approach presented in this thesis is based on the assumption that future needs placed
on a system are unknown, but bounded. Specifically, bounded means that the functional
purpose of a function chain does not change over time. Such an assumption is supported by
examples studied in the prior work of [10], wherein the demands placed on aircraft carriers
over time did not shift the core purpose (launching aircraft) but did change the means by which
that purpose was achieved (electromagnetic versus steam-driven catapults).
Categorizing Excess
Designers often deliberately include some quantity of excess for reasons discussed in the
four categories below. The first three categories - deterministic, epistemic, and aleatory - are
differentiated by their associated uncertainties, while the fourth category, consequent,
originates as a byproduct of other design decisions.

Deterministic excess is concerned with the excess that is expected to be consumed over
the course of the system’s lifetime based on original system requirements. A common
example is the thickness of sacrificial plating that is expected to corrode in the service
environment. Deterministic excess is assigned according to the environment that the
system is expected to face and its designed service life.

Epistemic excess is strategically placed within a design to address future needs that are
not yet realized, but could reasonably occur during the system’s lifetime. When placing
epistemic excess, designers might draw from sources such as institutional experience,
expected technological trends, expected market trends, etc.

Aleatory excess is the most difficult to allocate, as it is concerned with future needs
that are emergent and cannot be predicted by extrapolation or inference from available
sources of information. This is the excess that is utilized when a wholly unpredictable
16
future need emerges in the course of the system’s service life. No method exists to
guide the inclusion of aleatory excess.

Consequent excess occurs as a result of the presence of standardized components
within a design that exceed required capabilities. Examples include fasteners and
commercial off the shelf components that are chosen to accommodate standardized
sizing, commonality, or to minimize redesign. These excesses may not be of significant
quantity but can still be utilized to meet future needs.
If component relationships are considered, flows between components can be divided into
two categories (as shown in Figure 3.1):

Compatibility flows occur in the relationships required for a component to function,
and always are shown as input flows. For an electric motor, compatibility flows could
include the electrical current that the motor draws, the volume that the motor occupies,
the ability to withstand/convey the waste heat of the motor away, the reaction torque
from the motor, and the support reaction required for the weight of the motor.

Functional flows occur in the functional outputs of components. These either become
compatibility flows for other components or are system outputs across the control
volume. For an electric motor, functional flows could include the torque and/or power
that the motor develops, depending on which is important for the motor’s particular
application.
An implication of this classification scheme is that the indicated directionality of flow does
not necessarily match that of the associated physical parameters. Rather, flow is always shown
with the arrow pointing from the supplying component to the dependent component. An
example of this behavior occurs when a component must dissipate a waste flow to operate.
While the waste flow (of material, heat, etc.) is literally flowing away from the originating
component, the arrow points from the component that dissipates the flow to the originating
component. This is because the functionality of the originating component depends on the
component that dissipates the waste flow.
Compatibility and functional flows are often linked, especially for components that
transform input flow(s) of one type into output flow(s) of other type(s). As an example,
17
consider an electric motor. If additional torque is required from the motor (one of its functional
flows) it will require additional current (one of its compatibility flows). In contrast, as long as
the same motor is used, the volume required to accommodate it (another of its compatibility
flows) will not vary with the required torque. Critical to a system’s functionality is the ability
of each component to satisfy the requirements of any connected components. The presence of
sufficient excess in each contributing component permits change to the desired performance
characteristics of the system.
Compatibility
Flows
Component
Functional
Flows
Volume
Motor
Torque
Electrical Current
Figure 3.1: Compatibility and Functional Flows
Excess Basis
To effectively communicate in terms of excess, a unified vocabulary is necessary. This
work defines a standard ‘Excess Basis’ to account for all possible types of excess present in an
engineered system. To maintain consistency with the established literature, the reconciled
functional basis flow set developed in [24] is used as the core of the excess basis, shown on
the left side of Table 3.1. This basis is extended in this work to describe excesses that occur
only in the context of stored properties. Two ‘categorical’ extensions and six ‘type’ extensions
are needed, as shown on the right side of Table 3.1. The abbreviation scheme used in this thesis
is shown in Figure 3.2.
18
Table 3.1: Excess Basis
Class
Category
Signal
Material
Flow or
Storage
Energy
Type
Status
Control
Human
Gas
Liquid
Plasma
Mixture
Human
Acoustic
Biological
Chemical
Electrical
Electromagnetic
Hydraulic
Magnetic
Mechanical
Pneumatic
Radioactive
Thermal
Flow or Storage
Class
Abbr.
S-S
S-C
M-H
M-G
M-L
M-P
M-M
E-H
E-A
E-B
E-C
E-E
E-EM
E-Hy
E-Mag
E-M
E-P
E-R
E-T
Class
Storage
only
Category
Geometric
Structural
Energy, Signal,
Biological,
etc.
Length, etc.
Category
Type
Type
Length
Area
Volume
Stress
Strain
Abbr.
G-1
G-2
G-3
S-σ
S-ε
Figure 3.2: Naming Scheme for Excess Types
The first categorical extension is Geometric, with associated type entries of Length, Area,
and Volume. These extensions were necessary because there was no provision for geometric
characteristics in the existing flow set and they may not literally flow between components, as
is the case with the parameters described in the original basis. For example, mechanical energy
can flow through a shaft, material in gas form can flow through conduits, and control signals
can flow through wires. However, the ability to describe geometric properties is crucial for
characterizing certain excesses, and had been previously considered in work such as [21].
19
The second categorical extension is Structural, with associated type entries of stress (σ)
and strain (ε). Structural excess occurs when an artifact could withstand a greater stress or
strain than currently required. Component-level structural excesses may be consumed by other
components within a system or by conditions imposed by the operating environment.
When describing structural parameters of components, the true excesses that are being
consumed are stress and strain. However, designers may find it more convenient for certain
applications to define state parameters such as Load, Pressure, and Torque to describe the
structural excess relationships between components, with the understanding that such state
parameters ultimately map back to the stress and strain characteristics of the materials. In view
of these factors, the supplementary structural excess classification scheme shown in Table 3.2
is offered, and is used in the remainder of this thesis. As an example of why this ability is
important, consider an artifact made via injection molding that has multiple ribs comprising a
mounting interface for another component. While for a simple geometry such as a beam or
shaft relating the loading capacity back to the tolerable stresses verges on trivial, the load
tolerance of a more complex geometry cannot be so easily determined. Allowing designers to
calculate the maximum loading conditions for a particular artifact once will therefore ease the
use of the method by reducing the amount of required recalculations each time a differing load
is considered.
Table 3.2: Structural Excess Optional State Parameters
Category
Structural
Type
Load
Torque
Pressure
Abbr.
S-L
S-T
S-P
The Geometric and Structural categories comprise the set of excesses that may exist solely
within the Storage class, as none of the excesses described therein may flow between
components. Inversely, any excess that can be classified as a Flow may also exist as a Storage,
as anything that flows can also be stored. Since applied loading conditions cause strain energy
20
to develop within artifacts, the Structural category can be viewed as a storage of strain energy
[23].
Examples of all the signal, material, and energy flows described on the left side of Table
3.1 may be found in [34]. Each of these flows can also be stored and measured in some fashion.
Signals can be recorded, the means of which depend on whether the signal is auditory, visual,
electronic, etc. Material can be stored in an appropriate vessel; the units to use will depend on
the material in question. Uncompressed gas would likely be measured in volume, while
compressed gas would likely be measured in mass. Liquids and solids could be measured in
mass or volume depending on which is more useful for the situation at hand. Storage of the
varied energy types can always be measured in Joules or lbf. However, designers may find it
more useful to adopt a similar treatment as for the stress-strain structural relationships
described previously. In this way, stored thermal energy could be measured in Kelvin or
degrees Fahrenheit, stored hydraulic energy could be measured by its pressure head, and stored
pneumatic energy could be measured by its pressure, all with the understanding that the total
energy being stored in each case is ultimately measured in the base units of energy.
The associated units for the stored properties on the right side of Table 3.1 are self-evident
and depend only on whether the designer is working in the metric or imperial system and the
scale of the artifact being designed (i.e. cm3 would be appropriate for the volume of a small
pressure vessel while m3 would be appropriate for the volume of a room). However, which
geometric excess to use for a given situation may depend on the designer’s interpretation of
the particular case. Consider that all objects exist in three dimensional space, with
accompanying excess of volume. However, sometimes the pertinent excess in a design is the
length that a component can extend to, or the area that can be used for the mating of two friction
surfaces. Situations such as these mean that a three dimensional relationship can be distilled
by designers to a concise description of the pertinent geometry for the particular instance of
excess.
21
Resolution of Excess Flows
As stated in the motivation discussion of Chapter 1, excess can be described at ever
increasing levels of resolution. Yet to be useful in the design process, decisions about the
resolution at which to describe excess must be made. While some information and fidelity is
lost in a simplified model, this process is similar to using a Taylor Series Expansion (TSE) to
locally approximate system behavior with a reduced order function [41]. Stated another way,
a TSE neglects higher-order terms that add complexity to the model but offer little significant
information.
This work adopts this philosophy. As an example, consider an aircraft carrier. Top level
excesses such as displacement or power generation are unquestionably relevant to the overall
excess present in the system. However, the screws affixing speakers to bulkheads are irrelevant
in terms of system excess, as they do not directly contribute to the primary functions of the
system, are insignificant to replace if needed, and most importantly for this method, add
information that does not aid designers in their exploration of system evolvability.
The set of excesses found for a particular system are important because their presence and
their values will be a major factor in the ability of the system to evolve while in service, and
therefore to maintain value for stakeholders over time. In practice, the component excesses
considered will be a function of system architecture, customer needs and resulting system
specifications. Additionally, the desired representation of the architecture chosen (i.e. the
resolution for the overall system as well as for individual subsystems and components) will
play a role; a system might be represented using its five major subsystems, or three of the
subsystems might be further expanded while the other two remain black boxes because they
are externally sourced. These factors are further discussed in the next chapter.
22
Developing a Mapping Approach for System Excess
This chapter presents a method for constructing system maps of excess between
subsystems, while using a consumer heat gun, depicted in Figure 4.2, as a demonstrative
example. This method is intended to be used in parallel with the embodiment design of the
original system, so that designers may explore the effect of excesses on the ability of the system
to change as the original design progresses. As such, designers will have access to all of the
information associated with the system design, including stakeholder needs, specifications,
system architecture, and component parameters.
In this method, subsystems are abstracted as blocks with pertinent excess flows identified.
Therefore, the inner workings of the subsystem can be treated as a black box. This ability is
important for two main reasons. First, designers will often not need to analyze a system at the
lowest level of assembly (i.e. fasteners). Second, designers may be using externally sourced
components whose inner workings are not controllable by the designer. Here, each subsystem
will be referred to as a component in an excess map, even if the subsystem could be further
decomposed. The approach is detailed in the following sections. A flowchart giving an
overview of the steps to map excess relationships throughout a system is shown in Figure 4.1.
23
Step 1: Collect Stakeholder
Specifications
Step 2: Identify System
Architecture and Relationships
Step 3: Assemble Excess Map
Step 4: Identify State Parameters
Figure 4.1: Excess Mapping Procedure
Figure 4.2: Heat Gun [42]
The heat gun analyzed was a basic consumer model in the 1200 W power range with two
heat settings corresponding to 400 °C and 540 °C (Tout), based on the assumption of a 20 °C
operating environment (Tambient). The current draw of the device in operation was measured,
and a value of 10 A as advertised on the packaging was confirmed. A temperature-independent
24
specific heat of air at constant pressure (cp) of 1.0 J/(g-K) was assumed for all calculations in
this section.
Step 1: Collect Stakeholder Specifications
For component-level excesses to be meaningful and useful in the design process, they must
be relatable to specifications as defined by system stakeholders. This is because the
specifications are the quantified embodiment of stakeholder needs, and are what is expected to
change in response to future needs. Numbers chosen to complete the specifications should be
target values (the minimum that any design is expected to yield). These are available to
designers in the embodiment design phase. The product of this step is a requirements list of
quantified specifications in engineering language. These comprise the datums against which
system level excesses are measured.
Case study example
In the absence of direct customer needs information, it was assumed that the customer
needs were captured by the company producing the heat gun. Therefore, a subset of the
customer needs are:
•
Produce air sufficiently hot to melt plastic, desolder circuits, loosen floor tile adhesive,
etc.
•
Produce enough heated air flow to quickly accomplish tasks
•
Be lightweight enough to use with one hand
•
Be compatible with North American household electrical circuits
Based on the above customer needs, the following specifications were determined:
•
Maximum output temperature ≥ 540 °C
•
Total mass ≤ 500 g
•
Power ≥ 1.0 kW
•
Power ≤ 1.4 kW
The lower bound on the power draw was established to ensure a sufficient flow of energy
to the work piece. Consulting the available heat gun models on the market indicated that a
25
minimum bound for power is 1000 W. Assuming a mass flow rate of 2 g/s of air (the same as
the example heat gun consumes) a 1000 W input results in an output temperature of 743 K or
520 °C as given in Equations 4.1 and 4.2.
 =  +
∙
 ∙ ̇
J
1000 s
= 293 K +
= 793  = 520 °


1.0  ∙ 2 
( 4.1 )
( 4.2 )
In this equation, Tout is the output temperature of the heat gun, Tambient is the ambient air
temperature, I is the current feeding the heating coils, V is the main voltage, cp is the specific
heat of air at constant pressure, and ̇ is the mass flow rate of air.
The upper bound was established based on the assumption that the user will be powering
it from a household circuit with a 15A breaker, that the breaker’s maximum continuous load
is 80% of its rating per code [43], and that nothing else is operating on the circuit while the
heat gun is being used. Since the vast majority of the current drawn by the heat gun is a resistive
load, the assumption was made that
 = 15  ∙ 120  ∙ 80% = 1440
( 4.3 )
Step 2: Identify System Architecture and Relationships
The first decision made by the designer is the overall level of abstraction desired in the
system excess map, or in other words, the intended level of assembly to be mapped. This
decision is informed partly by the requirements list, which may pertain more to some
components/subsystems than others. A starting point is the highest level of abstraction that
separates the major components displaying modular behavior.
If subsystems exhibit enough complexity, further expansion may be required. However,
designers may externally source some components, placing a lower bound on the level of
26
abstraction of their representation [44]. Different subsystems may be described at different
levels of abstraction for these reasons. Figure 4.3 demonstrates how a component
representation can be expanded (or condensed) when needed in the course of mapping excess.
Compatibility
Flow
Subsystem
More
Detail
Compatibility
Flow
Functional
Flow
Less
Detail
Component
A
Component
B
Component
C
Functional Flow
Figure 4.3: Variable Level of Abstraction
This step determines the component blocks and flows that populate the excess map, as well
as the control volume that delineates the system from the external environment. Components,
indicated by primary blocks, are square-edged rectangles. The excesses produced by
components, shown in secondary blocks, are indicated by attached snipped-edge rectangles.
The excesses are categorized and labeled as shown in using the abbreviations denoted in the
left-most and right-most columns of Table 3.1. A visual example of a component block with
attached excess blocks is shown in Figure 4.4.
27
Functional Flows
Primary Block
Inbound
Type
Compatibility Type
Flows
Component
Type
Excess [Units]
(Total Capacity)
Type
Excess [Units]
(Total Capacity)
Type
Outbound
Functional
Flows
Type
Figure 4.4: Excess Map Segment for General Architecture
First, each component is considered individually and the types of compatibility (input) and
functional (output) flows are determined. This is done by consulting the original design
information for the purposes and requirements of each component. Then, the values associated
with these flows are quantified.
Some compatibility flows, such as an input of electrical energy that is converted by a
component to an output of heat energy, are a function of the required functional flow values
and will change if the functional requirements of the component are later altered. Other
compatibility flows that are static properties of components (typically Storage class excesses
such as loads or geometric requirements) are updated only if a different component is selected
as replacement. Some components will produce excesses that are linked; i.e. utilizing one of
the associated excesses will diminish another. This is indicated by drawing a double-ended
arrow between the two excess blocks.
Once the compatibility flow requirements of all components are satisfied by functional
flows from other components or the environment, the map’s set of excesses is provisionally
complete; all explicitly necessary excesses have been documented. However, it is possible that
some excesses have been implicitly assumed. The final activity in this step is to take each
28
component in turn and consider every possible excess from the Excess Basis. This forces the
designer to consider the task of identifying relationships from a different perspective, and
allows those that were not immediately clear to be captured. This activity reveals relationships
driven by inter-component requirements that may have remained implicit, such as the
requirement of a container to withstand the heat generated by internal components.
Case study example
The physical boundaries of the heat gun were used to define the control volume.
Specifically, any energy or signal passing into or out of the device, whether electrical energy
from the power grid, human energy from the operator, or heat from the nozzle, was viewed as
crossing the control volume. The components selected were the self-contained subsystems:
namely the case, controller, cord, fan, heating coils, and nozzle.
An important activity of this step is the selection of appropriate units for excess. The excess
basis intentionally does not assign units to excess types, since the most appropriate/useful way
to express a particular excess type is dependent on the situation at hand. In the case of a heat
gun, it would be valid to describe the thermal excess of the nozzle in terms of Watts of
dissipated energy. Most meaningful, however, is expressing the energy of the heated air in
terms of its temperature in degrees Kelvin. This avoids the intermediate calculations that would
be required to relate the thermal energy to a temperature threshold for the constituent materials
of the heat gun.
Next, the excess blocks and flows are quantified, demonstrating the method’s
incorporation of numerical information. Normally, these values are available directly from the
information of the embodiment design phase. For example, the internal volume of the case
would be available from CAD files and the amperage draw of the heating coils would be known
from the chosen component. Information regarding amperage input, ambient air temperature,
and output temperature is used with the relationship given in Equation 4.1 to calculate
thermodynamic properties of intermediate excess flows such as the mass of air which is heated.
Each component is discussed separately as follows. The overall assembly of the heat gun
is shown in Figure 4.5 below.
29
Figure 4.5: Disassembled Heat Gun
Case
Figure 4.6: Heat Gun Case
30
The case, shown in Figure 4.6, is made of plastic and disassembles to three pieces: two
mirrored grip/receiver pieces and a collar that locks onto the assembled grip. Assuming it is
made of ABS plastic, the maximum use temperature is 105 °C [45]. The grip section provides
volume for the switch to occupy and surface area for the switch to protrude through so that the
user can interact with it. The barrel section provides volume to the fan and nozzle and
withstands heat from the nozzle. Therefore, two distinct excess blocks for volume (Storage,
Geometric, Volume or S-G-3 per the abbreviations listed in Table 3.1) and two distinct excess
blocks for area (S-G-2) are shown since the spaces being occupied by the components are in
separate locations in the case.
Finally, a thermal energy excess block (Flow, Energy, Thermal or F-E-T) is shown due to
the dependence of the nozzle on the ability of the case to hold it at operating temperature. This
highlights an important aspect of the excess relationships: their directionality is based on
functional dependence, but this does not necessarily correspond to the direction of the involved
physical flows. The actual heat is flowing from the nozzle to the case, but the nozzle is
dependent on the ability of the case to withstand its steady-state operating temperature.
Therefore, the relationship is shown as a functional flow of the case (its ability to withstand
heat) satisfying a compatibility flow of the nozzle. The component and excess blocks for the
case are shown in Figure 4.7.
The first volume excess (S-G-3) supplies volume to the fan, which occupies 100 cm3 of the
available 240 cm3. The first area excess (S-G-2) supplies area to the nozzle, which occupies
11 cm2 of the available 16 cm2. The second volume and area excesses satisfy the needs of the
switch, which occupies 8 of the available 13 cm3 and the entirety (4 cm2) of the available area.
31
F-E-P
F-E-H
2 mm H20
Case
Support
S-G-3
140 [cm3]
(240)
100
F-E-T
60 [K]
(380)
320
S-G-2
5 [cm2]
(16)
11
S-G-3
5 [cm3]
(13)
8
S-G-2
0 [cm2]
(4)
4
Figure 4.7: Case Excess Map Contribution
Cord
The cord and internal wiring is three-wire (hot, neutral, and ground) 18 AWG and therefore
capable of carrying up to 14 A of current [43]. It requires electrical energy (F-E-E) from the
environment and supplies electrical energy to the switch. The component and excess blocks
for the cord are shown in Figure 4.8. The current passed on to the switch is 10 A, meaning that
4 A of excess current remains.
F-E-E
10A
Cord
F-E-E
4 [A]
(14)
10
Figure 4.8: Cord Excess Map Contribution
32
Switch
Figure 4.9: Heat Gun Switch
The switch, shown in Figure 4.9, is a three position sliding switch with positions
corresponding to sequential markings of Off, Low, and High. In the Off position, the circuit is
open. In the Low position, the circuit is fed by the current of the hot wire passed through a
diode, making the current half-wave rectified. Therefore, the root-mean-squared (RMS)
voltage fed to the heating coils and fan drops significantly; additionally, the diode itself drops
the voltage by 0.6-0.7V [46] but this is insignificant compared to the adjusted half-wave
rectified VRMS of
 =
 170 
=
= 85 
2
2
( 4.4 )
In the High position, the switch feeds the full voltage directly to the circuit of the heat gun.
The switch requires 8 cm3 of volume (S-G-3) from the case, 4 cm2 of area (S-G-2) from the
case, a control signal from the user (F-S-C), and 10 A of electrical energy from the cord (F-E-
33
E). The component and excess blocks for the switch are shown in Figure 4.10; their values are
based on the switch’s function in the High position.
S-G-3
S-G-2
F-S-C
F-E-E
8 cm 3
4 cm 2
Switch
Off/Low/High
F-E-E
3 [A]
(13)
10
10 A
Figure 4.10: Switch Excess Map Contribution
Heating Coils
Figure 4.11: Heat Gun Heating Coils
The resistive heating coils, shown in Figure 4.11, are made of nichrome alloy and wrapped
around a form made of mica sheets and ceramic supports. Not shown is the additional mica
sheet that wraps around the coil assembly and rests between the coils and the nozzle as a heat
shield. The melting temperature of nichrome is 1400 °C [47], that of the ceramic is at least
1000 °C [48], and the mica board can withstand 700 °C [49]. Therefore, the heating coils are
limited to a maximum operating temperature of 700 °C or 970 K. The heating coils also
function as a voltage divider for the fan, reducing the voltage to 11% of its input value (~12V
on the High setting) before it is fed to the fan. Altering the location of the fan’s tap into the
heating coils would change the division of current between the fan and heading coils; hence,
34
the excess of electrical flow that could be fed to the fan is correlated with the maximum air
temperature that the coils can yield.
The airflow values are calculated as shown in Equation 4.5. Based on these numbers, the
mass air flow through the heat gun at maximum temperature is approximately 2 g/s.
̇ =

 ∙ ( −  )
( 4.5 )
The heating coils require 75 cm3 of volume (S-G-3) from the nozzle, 2 g/s of airflow (FM-G) from the fan, and 10 A of electrical energy (F-E-E) from the switch. The component and
excess blocks for the heating coils are shown in Figure 4.12. They supply 810 K of thermal
energy (F-E-T) out of a maximum 970 K to the nozzle and 0.2 A of electrical energy (F-E-E)
out of a maximum 10 A to the fan.
S-G-3
F-M-G
F-E-E
75 cm 3
2 g/s
10 A
Heating
Coils
F-E-T
160 [K]
(970)
810
F-E-E
9.8 [A]
(10)
0.2
Figure 4.12: Heating Coils Excess Map Contribution
35
Fan
Figure 4.13: Heat Gun Fan
The fan, shown in Figure 4.13, is a 12V axial flow fan that delivers air from the case inlets
to the heating coils. The fan has an integrated rectifier, which allows the AC current received
from the coils to be converted to DC current. The fan, at its operating RPM, supplies
approximately 2 g/s of airflow (F-M-G) to the heating coils and overcomes an estimated 3 mm
H20 of static pressure (a relationship of F-E-P) imposed by the case and nozzle. The values of
estimated static pressure imposed by the case and nozzle were obtained by referencing the
static pressure that commercially available 12V fans are capable of overcoming and examining
the relative flow restrictions imposed by the case and nozzle. It is assumed that the rotational
speed of the fan motor can be as much as doubled by adjusting the voltage fed to the fan,
thereby creating excess in the two relationships. The fan affinity laws [50] for a constant
diameter fan, shown in Equations 4.6–4.7, demonstrate how these excesses are linked, i.e.
increasing airflow reduces the amount of additional static pressure that the motor can
overcome. Volume flow rate is denoted by q and pressure by p. This linkage is indicated by a
double-sided arrow between the excess blocks shown in Figure 4.14.
1 1
=
2 2
( 4.6 )
36
1
1 2
=(
)
2
2
( 4.7 )
The fan requires 0.2 A of electrical energy (F-E-E) from the heating coils and 100 cm3 of
volume (S-G-3) from the case. It supplies 1 mm H2O of pressure (F-E-P) to the nozzle and 2
mm H2O to the case out of a maximum of 12 mm H2O pressure. It supplies 2 g/s of airflow (FM-G) to the heating coils out of a maximum of 4 g/s. These two excesses are linked, meaning
that if one is utilized the available excess in the other will decrease. Therefore, a double sided
arrow is shown between the two excess blocks.
F-E-E
0.2 A
S-G-3
100 cm 3
F-E-P
9 [mm H 20]
(12)
1
2
Fan
F-M-G
2 [g/s]
(4)
2
Figure 4.14: Fan Excess Map Contribution
Nozzle
Figure 4.15: Heat Gun Nozzle
The nozzle, shown in Figure 4.15, is formed of a mildly magnetic stainless steel, likely
304. Therefore its melting point is approximately 1400 °C [51]. The nozzle does impose some
37
restriction on the airflow (F-E-P); however, its exit geometry is very similar to that of the
heating coils, so the impact is minimal. The static pressure imposed by the nozzle is assumed
to be 1 mm H2O. The nozzle also requires cross sectional area (S-G-3) from the case, the ability
for the case to withstand a temperature of 30 °C above the ambient due to heat flow from the
nozzle (F-E-T), and heated airflow (F-E-T) from the heating coils. The component and excess
blocks for the nozzle are shown in Figure 4.16.
The nozzle requires 1 mm H20 of pressure (F-E-P) from the fan, 320 K of thermal energy
(F-E-T) from the case, 11 cm2 of area (S-G-2) from the case, and 810 K of thermal energy (FE-T) from the heating coils. It supplies 810 K of thermal energy to the environment out of a
maximum of 1670 K, and 75 cm3 of volume (S-G-3) to the heating coils (the maximum
available).
F-E-P
F-E-T
S-G-2
F-E-T
1 mm H20
320 K
11 cm 2
F-E-T
860 [K]
(1670)
810
S-G-3
0 [cm3]
(75)
75
Nozzle
810 K
Figure 4.16: Nozzle Excess Map Contribution
Step 3: Assemble Excess Map
This step assembles the blocks and flows generated for each component in the previous
step into a full excess map, according to their input and output flows. Compatibility flows that
are not satisfied by other system components and consequently originate from outside the
system boundary are placed in an Environment block, and flows that discharge outside the
system boundary are labeled accordingly and cross the control volume. The Environment block
exists to summarize and denote the compatibility flows that originate from the system’s
operating environment, and may be split into multiple blocks if desired to minimize visual
complexity of the map. The equations relating output and input flows within and between
38
components are not shown on the map; they may be encoded in a computational environment
such as Simulink [52] or manually calculated.
Case study example
The process of assembling the excess map requires ensuring that the functional flows are
matched with the correct compatibility flows. Components are presented with their
summarized functional and compatibility flows in Table 4.1.
Table 4.1: Heat Gun Component Excesses
Component
Compatibility Flows
Functional Flows
Case
Flow-Material-Gas
Flow-Energy-Human
Flow-Energy-Thermal
Storage-Geometric-Volume (2)
Storage-Geometric-Area (2)
Switch
Cord
Fan
Heating
Coils
Nozzle
Flow-Signal-Control
Flow-Energy-Electrical
Storage-Geometric-Volume
Storage-Geometric-Area
Flow-Energy-Electrical
Storage-Geometric-Volume
Flow-Energy-Electrical
Flow-Material-Gas
Storage-Geometric-Volume
Flow-Energy-Electrical
Flow-Energy-Thermal (2)
Storage-Geometric-Area
Flow-Energy-Pneumatic
Flow-Energy-Electrical
Flow-Energy-Electrical
Flow-Material-Gas
Flow-Energy-Pneumatic
Flow-Energy-Thermal
Flow-Energy-Electrical
Flow-Energy-Thermal
Storage-Geometric-Volume
During this step the Environment block is also defined. For this system, the required
environmental flows are human energy (F-E-H) to support the heat gun, the control signal
provided by a human hand (F-S-C) to actuate the control switch, electrical energy (F-E-E) from
the power grid, and airflow (F-M-G). Finally, any outbound flows crossing the Control Volume
are identified. The only such flow in this case is a flow of thermal energy passing from the
nozzle to the environment.
39
Step 4: Identify State Parameters
Some of the datums created from system specifications will be relatable to single
component outputs, such as ‘10 MW of electrical power’ would be for a single-generator
system. However, the satisfaction of other specifications will be functions of multiple
components, as in the case of ‘total mass must be less than 5 kg’. To verify satisfaction, state
parameters (equations that are functions of multiple components’ characteristics) are defined.
These parameters are indicated in a block labeled ‘State Parameters’. Information is drawn
from component blocks and flows, but arrows are not required so that visual complexity of the
map is not increased. Component properties that do not interact with excess flows but are
relevant to state parameters are denoted within their respective block.
Case study example
Based on the system specifications, only two state parameters are required. The total
system mass is summed from all components excepting the cord, since much of its mass may
not be supported by the user. The amperage draw through the switch is summed and multiplied
by the line RMS voltage. The finished excess map is shown in Figure 4.17. A full size version
of the finished excess map is in the Appendix.
40
F-E-P
9 [mm H 20]
(12)
70 g
0.2 A
100 cm 3
1
State
Parameters
2
F-E-E
Fan
F-E-P
F-M-G
2 [g/s]
(4)
System Mass: 380 g
2
System Power: 1.2 kW
S-G-3
S-G-3
140 [cm3]
(240)
F-E-P
F-M-G
100
50 g
1 mm H20
Environment
F-S-C
[user]
F-E-T
60 [K]
(380)
320
S-G-2
5 [cm2]
(16)
11
F-E-T
S-G-2
320 K
11 cm 2
2 mm H20
F-E-H
[user]
Case
4N
S-G-3
7 [cm3]
(15)
F-E-H
S-G-2
0 [cm2]
(4)
F-E-E
F-S-C
810
S-G-3
0 [cm3]
(75)
75
F-E-T
160 [K]
(970)
810
F-E-E
9.8 [A]
(10)
0.2
To
Environment
Nozzle
810 K
160 g
F-E-E
[A]
F-E-T
860 [K]
(1670)
F-E-T
S-G-3
70 g
8
75 cm 3
2 g/s
10 A
Heating
Coils
S-G-3
4
F-E-E
10A
Cord
F-E-E
4 [A]
(14)
S-G-2
8 cm 3
30 g
1 cm 2
10
Switch
Off/Low/High
F-E-E
F-E-E
3 [A]
(13)
10
10 A
Figure 4.17: Heat Gun Excess Map
Evaluating System Level Excess
For a system excess map that incorporates equations relating component outputs and
inputs, it is possible to query the map and determine the extent that system specifications may
be exceeded; these values will be the system excesses. Additionally, for each top-level excess,
it is possible to determine which component is at an excess threshold and may limit
performance changes.
Case study example
Excess (X) in a specification is evaluated using the relationship in Equation 4.8.
 =  − Σ 
( 4.8 )
41
For the system in question, it was found that there exists 120 g excess in terms of allowable
mass, using Equation 4.8 along with Equation 4.9. For excesses driven by state parameters, the
‘available’ amount is considered to be the bound on the state parameter, in this case 500 g.
 =  +  +  + 
( 4.9 )
The maximum possible output temperature is 700 °C (an increase of 160K over the current
high output temperature), which is limited by the heating coil assembly. The switch, rated at
13 A, is the lowest-amperage component that feeds electrical energy into the system; therefore,
the electrical components also limit the heat gun to a maximum temperature of approximately
700 °C as detailed in Equations 4.10 and 4.11 below. Note that 12.8 A is used as the maximum
current value because roughly 0.2 A is consumed by the fan, thereby reducing the total current
that can be expended in the heating coils slightly.


12.8  ∙ 120
9.8  ∙ 120
=
−




1.0  ∙ 2.3  1.0  ∙ 2.3 
( 4.10 )


1540  1180 
=
−
= 160 K


2.3  2.3 
( 4.11 )
Though a higher temperature could also be achieved at the same amperage by lowering the
mass flow rate, an end user might not perceive any performance improvement if the total power
remained constant. Regarding the power specifications, the system might consume 200 W
more or less and still meet both. The power value for the system was determined from Equation
4.12, where I is the current passing through the switch.
 = 
( 4.12 )
Therefore, the limiting excesses for increasing the output temperature of the heat gun are
the amperage rating of the switch and the temperature rating of the heating coil assembly.
42
Map Quality and Criteria for Update
Two conditions can arise that require the excess map to be updated. Either the architecture
changes in a way that alters the presence and/or arrangement of components depicted in the
map, or system specifications have been added or removed. The addition or removal of
specifications could alter the map by affecting the components and/or relationships that must
be represented. However, an already present specification that is modified could change the
amount of excess indicated by the map, but will not require the map to be altered. Rather, a
modified need results in re-querying the map to determine how excesses are affected. The
following sections implement and demonstrate the steps of the excess mapping process.
Case Study 1 Conclusion: Heat Gun Evolution Examples
Two examples of potential evolutions for the heat gun are given here to demonstrate the
information made available to the designers by the excess map.
Heat Gun Evolution 1: Replace Tri-Mode Switch with Variable Voltage Switch
A possible future need for the heat gun is for the heat output to be made continuously
variable. This could be accomplished by replacing the original switch, capable only of
operating the heat gun in ‘low’ and ‘high’ temperature modes, with a dial switch that can vary
the voltage across the entire possible range (with the minimum voltage set so that the 12 V
nominal fan motor does not stall and thereby allow the heating coils to overheat and damage
the device).
The feasibility of such a modification can be investigated by consulting the Switch block
of Figure 4.17 and ensuring that a candidate replacement switch satisfies all existing functional
flow requirements and can operate within the compatibility flow limits imposed by the
supplying components to prevent change propagation. This means that a replacement switch
must be able to pass at least 10 A (the present design amperage), must fit within 13 cm3 inside
the case, and must occupy less than 4 cm2 of area on the case surface for the user to interface.
The ease of this process is one of the benefits of the excess mapping method; designers
considering a change to a system can quickly determine the pertinent excesses and constraints
43
for everything from a simple component exchange such as this to a more complicated alteration
that can affect multiple components, as discussed in the next evolution.
Heat Gun Evolution 2: Increase Output Temperature to 750 °C
Another potential future need for the system is for the output temperature to be increased
from 540 °C to 750 °C (1020 K) meaning a ΔT of 730 K. Consulting the system excess map
of Figure 4.17, it is apparent that the nozzle can tolerate the evolution. Additionally, assuming
that the ΔT between the case temperature and ambient air is linearly correlated with the ΔT
imparted to the airflow, the new case temperature will be 62°C, as shown in Equation 4.13.
This is still well within the maximum temperature of 105°C.
ΔTcase
30 K
 
= const =
=
ΔTairflow
520 K 730 K
( 4.13 )
However, the heating coils must be modified as their current maximum operating
temperature is 700 °C. Also, assuming that the airflow rate is to remain constant, the flows of
electrical energy must be considered. A ΔT of 730 K requires an energy input of 14 A.
Therefore, the switch (rated at 13 A) must be upgraded, but there is sufficient excess in the
cord.


̇ ∙  ∙ Δ 2.3  ∙ 1.0  ∙ 730
I=
=
= 12 

120
( 4.14 )
Upgrades to the switch and heating coils are governed by the available compatibility flows
(volume and area for the switch, and volume for the heating coils) if changes are not to
propagate to additional components in the design.
Case Study 2: Coffee Maker
The coffee maker used for the second demonstration was a 12-cup model as shown in
Figure 4.18.
44
Figure 4.18: Coffee Maker [53]
This particular model was an automatic drip brewer producing up to twelve 5 fl. oz. cups
of coffee using a basket filter. It was operated using an on-off switch without automatic shutoff
functionality. The carafe was heated from below, maintaining the coffee at brewing
temperature indefinitely.
Coffee Maker Excess Map Creation
Step 1: Collect Stakeholder Specifications
The coffee maker satisfied the following customer needs:
•
Brew coffee
•
Keep coffee hot after brewing
•
Brew enough coffee for a family
•
Brew coffee quickly
•
Be safe to use and operate
•
Operate from a standard household outlet
45
The corresponding specifications are:
•
Deliver water at ≥ 93°C to coffee
•
Maintain coffee at brewing temperature (93°C)
•
Brew at rate of ≥ 150 mL/min
•
Brew up to 1.8 L of coffee
•
Limit heating element temperature to ≤ 240 °C in emergency
•
Power ≤ 1.4 kW
The brewing rate specification translates to brewing an entire pot (1.8L, or twelve 5 fl. oz.
coffee cups) of coffee within 12 minutes. The power specification was set as in Equation 4.3.
Step 2: Identify Architecture, Appropriate Subassemblies, and Relationships
The system boundaries were determined based on the operation of the system between
when it is turned on and off. Therefore, it was assumed that water is already in the reservoir
when the system is turned on and that the system remains on until the last cup of coffee is
poured from the carafe. The components that display modular behavior are the body, cord,
brew basket, heating element, hot plate, and carafe. Pertinent to the following discussion is the
specific heat of water at constant pressure, cp = 4.19 J/(g-K), and the assumption that the tap
water placed in the reservoir is at 10°C while the brewing temperature of the coffee is 93°C.
The numerical values of the inter-component relationships were determined as follows for each
component.
46
Body
Figure 4.19: Coffee Maker Body
The body, shown in Figure 4.19, interacts directly with many of the other components, as
shown by the large number of excess blocks in Figure 4.20. The body cannot be readily
disassembled further; this consideration suggests that the system architecture is integral,
designed for a specific use case. The body supplies volume (S-G-3) in separate regions to the
carafe and brew basket. It also supplies area (S-G-2) and thermal tolerance (F-E-T) to the hot
plate in the base, storage of liquid water (S-M-L) for the carafe’s eventual receipt, a flow rate
of water (F-M-L) to the heater, and an area (S-G-2) to the operating switch. Stamped on the
components was an indication that the plastic material was polypropylene; hence its melting
47
temperature is 135°C [54]. The component and excess blocks for the body are shown in Figure
4.20.
Body
S-G-3
0 [L]
(1.9)
1.9
S-M-L
0.2 [L]
(2.0)
1.8
S-G-2
0 [cm2]
(110)
110
F-E-T
45 [K]
(408)
363
F-M-L
12.4 [mL/sec] 2.6
(15)
S-G-3
0 [cm3]
(860)
860
S-G-2
0 [cm2]
(2)
2
Figure 4.20: Body Excess Map Contribution
Cord
The cord is two-wire (hot and neutral) 18 AWG, and therefore capable of carrying 14 A of
electrical energy (F-E-E) per [43]. In use, it carries 7.5 A to satisfy the needs of the heater, the
only powered component. The component and excess blocks for the cord are shown in Figure
4.21.
48
F-E-E
7.5 A
Cord
F-E-E
6.5 [A]
(14)
7.5
Figure 4.21: Cord Excess Map Contribution
Switch
Figure 4.22: Coffee Maker Switch
The switch, shown from the inside of the coffee maker in Figure 4.22, is a simple on/off
rocker type, rated to 10 A, that governs the current flow from the cord to the heater. Its
associated component and excess blocks are shown in Figure 4.23.
S-G-2
F-E-E
2 cm 2
Switch
7.5 A
F-E-E
2.5 [A]
(10)
7.5
Figure 4.23: Switch Excess Map Contribution
49
Heater
Figure 4.24: Coffee Maker Heating Element
The heater consists of a resistive heating element sandwiched between a hollow tube for
heating brew water and a flat face that interfaces with the hot plate using thermal grease. The
heater has two functions: heat the water for brewing the coffee, and maintain the temperature
of the hot plate after the coffee has brewed. To accomplish the first, it draws water from the
cold reservoir in the body, heats it within the hollow horseshoe tube, and sends it up through
the body to be dispersed through the brew head over the brew basket. The movement of the
water is effected without a pump or any powered moving parts. Rather, there is a check valve
in the inlet tube from the reservoir that prevents water from flowing in reverse. The water
within the tube is locally heated to boiling, which converts some of it to steam, thereby
producing enough pressure to propel the heated water up to the brew head. More cold water is
then able to flow downward into the tube and the cycle repeats.
To accomplish the second purpose of maintaining the coffee at temperature after brewing
(supplying F-E-T) the interface side of the heater is coated with thermal grease and placed
against the underside of the hot plate. The maximum temperature value for the heating
assembly is dictated by the melting point of aluminum, 933 K [55]. The heater is stamped
900W on the side, which was confirmed by its measured resistance of 16 Ω. Therefore, it draws
50
7.5A of current. This power is sufficient to raise 2.6 mL/sec of water from tap to brewing
temperature, per Equation 5.5 (noting that 1 g of water is equal to 1 mL of water). This
relationship governs the F-M-L excess that the heater provides.
̇ =

 ∙ ( −  )
=

900 

4.19  ∙ (93 − 10)
= 2.6


( 4.15 )
Flow of electrical current to the heater is governed by a thermostat (shown on the right of
Figure 4.24) and two sequential thermal safety devices, stamped at 240°C. Replacing the
thermostat (or changing its set point) modifies the steady state temperature of the hot plate.
The thermal fuses satisfy the specification that temperature be limited to ≤ 240°C in an
emergency. However, their presence is not indicated anywhere on the excess map. This is
because no excess is reasonable to describe such a relationship; since coffee is made with
water, the maximum temperature that the brewing process could require anywhere on Earth (at
or above sea level) is at most 100°C. That is also the limiting value for maintaining the coffee
at temperature within the carafe. Therefore, no change to the thermal fuse cutout value should
ever be necessary for any modification to the coffee maker that is consistent with its top level
functional purpose of ‘brew coffee’.
The component and excess blocks for the heater are shown in Figure 4.25. That zero excess
is present in the liquid flow rate (F-M-L) is a consequence of how the gravity-fed heating
element operates; it will always heat the maximum possible mass flow rate of water that its
power output allows, unless the power is cycled on and off.
F-M-L
2.6 mL/sec
F-E-E
6.5 A
F-E-T
570 [K]
(933)
363
F-M-L
0 [mL/sec]
(2.6)
2.6
Heater
Figure 4.25: Heating Element Excess Map Contribution
51
Brew Basket
Figure 4.26: Coffee Maker Brew Basket
The brew basket, shown in Figure 4.26, sits in the top of the body under the brew head
(consuming S-G-3) and holds the coffee filter and grounds. Its purpose is to accept hot water
(F-M-L) and allow it to pass through the coffee grounds and filter before being drained to the
carafe below (F-M-L). Its maximum flow value was determined experimentally by measuring
the amount of water that passed through the basket orifice in thirty seconds. The component
and excess blocks for the brew basket are shown in Figure 4.27.
F-M-L
S-G-3
2.6 mL/sec
860 cm 3
Basket
F-M-L
14.1 [mL/sec] 2.6
(16.7)
Figure 4.27: Brew Basket Excess Map Contribution
52
Hot plate
Figure 4.28: Coffee Maker Hot Plate
Shown in Figure 4.28 is the underside of the hot plate with residual thermal grease. It
requires area (S-G-2) from the body, heat energy to maintain its operating temperature (F-ET) from the heater, and tolerance of its operating temperature (F-E-T) from the body. It supplies
heat energy (F-E-T) and area (S-G-2) to the carafe. Assuming that it is made of low-grade
steel, its melting point is 1813 K as given by [56]. Its component and excess blocks are shown
in Figure 4.29.
S-G-2
F-E-T
F-E-T
110 cm 2
XXX
363 K
363 K
Hot
Plate
F-E-T
1450 [K]
(1813)
363
S-G-2
0 [cm2]
(87)
87
Figure 4.29: Hot Plate Excess Map Contribution
53
Carafe
Figure 4.30: Coffee Maker Carafe
The carafe, shown in Figure 4.30, is the recipient of the brewed coffee from the brew
basket. It receives volume (S-G-3) and total liquid volume (S-M-L) from the body, and area
(S-G-2) and heat energy (F-E-T) from the hot plate. Its excess is a storage of liquid (S-M-L),
the final brewed coffee.
Note that flow rate is not considered as a compatibility flow for the carafe, as the rate at
which it can receive liquid is essentially unlimited compared to the rate that a 900 W (or even
2 kW) heater can produce. Also, the liquid storage excess is shown as coming from the body
since it is the total amount of water in the reservoir that dictates the final amount of brewed
coffee present in the carafe.
The component and excess blocks for the carafe are shown in Figure 4.31.
S-G-3
S-M-L
F-E-T
S-G-2
1.9 L
1.8 L
Carafe
363 K
S-M-L
0 [L]
(1.8)
1.8
87 cm 2
Figure 4.31: Carafe Excess Map Contribution
54
Step 3: Assemble Excess Map
The summarized compatibility and functional flows for the components of the coffee
maker are given in Table 4.2.
Table 4.2: Coffee Maker Component Excesses
Component
Compatibility Flows
Functional Flows
Body
N/A
Storage-Geometric-Volume (2)
Storage-Material-Liquid
Storage-Geometric-Area
Flow-Energy-Thermal
Flow-Material-Liquid
Cord
Flow-Energy-Electrical
Flow-Energy-Electrical
Switch
Flow-Energy-Electrical
Flow-Energy-Electrical
Flow-Energy-Electrical
Flow-Material-Liquid
Flow-Material-Liquid
Storage-Geometric-Volume
Storage-Geometric-Area
Flow-Energy-Thermal (2)
Storage-Geometric-Volume
Storage-Material-Liquid
Storage-Geometric-Area
Flow-Energy-Thermal
Flow-Energy-Thermal
Flow-Material-Liquid
Heater
Brew Basket
Hot Plate
Carafe
Flow-Material-Liquid
Storage-Geometric-Area
Flow-Energy-Thermal
Storage-Material-Liquid
For this system, the only required environmental flow in operation is electrical energy (FE-E). The outbound flows crossing the control volume (for purposes of satisfying the system
specifications) are the liquid storage (S-M-L) of the carafe and flow rate (F-M-L) from the
brew basket.
Step 4: Identify State Parameters
The only required state parameter for the coffee maker was the system power, derived as
in Equation 4.12, using the amperage passing through the cord for I. The finished excess map
is shown in Figure 4.32. A full size version of the finished excess map is in the Appendix.
55
S-G-3
0 [L]
(1.9)
S-G-3
1.9 L
1.9
S-M-L
0 [L]
(1.8)
1.8 L
S-M-L
Carafe
363 K
Body
1.8
S-G-2
0 [cm2]
(110)
110
S-G-2
F-E-T
110 cm 2
S-G-2
F-E-T
363
XXX K
363 K
F-E-E
[A]
S-G-3
0 [cm3]
(860)
S-G-2
0 [cm2]
(2)
F-E-T
1450 [K]
(1813)
Hot
Plate
S-G-2
0 [cm2]
(87)
363
F-M-L
12.4 [mL/sec] 2.6
(15)
Environment
To
Environment
87 cm 2
S-M-L
0.2 [L]
(2.0)
F-E-T
45 [K]
(408)
1.8
363
87
F-E-T
F-M-L
F-E-T
570 [K]
(933)
363
F-M-L
0 [mL/sec]
(2.6)
2.6
2.6 mL/sec
Heater
860
7.5 A
F-E-E
2
F-M-L
S-G-2
S-G-3
F-E-E
2.5 [A]
(10)
2 cm 2
F-E-E
Switch
7.5 A
F-E-E
5.5 [A]
(14)
Cord
860 cm 3
Basket
7.5
F-M-L
14.1 [mL/sec] 2.6
(16.7)
To
Environment
State
Parameters
F-E-E
7.5 A
2.6 mL/sec
7.5
System Power: 900 W
Figure 4.32: Coffee Maker Excess Map
Evaluating System Excesses
The coffee maker satisfies all of the specifications placed on it, but with minimal or no
excess in some cases. The power specification has the most excess (in terms of relative
increase) with 500 W additional power being permissible from the wall outlet. The brewing
rate of 2.6 mL/sec satisfies the required ≥ 2.0 mL/sec, but cannot be increased without
replacing the heater with a higher-wattage unit. Likewise, the carafe holds at maximum the
56
required 1.8L, but no more. If it was desired to replace the carafe, there is no excess volume in
the body to accommodate a larger carafe.
This general lack of excess points to a design that has been optimized for a narrow purpose
to minimize cost. For an inexpensive, mass-produced (and essentially disposable) product such
as the coffee maker in question, the term ‘excess’ as used in this paper becomes synonymous
with ‘excess’ in layman’s usage: superfluous and wasteful. Therefore, for this coffee maker,
the general lack of excess can be viewed as an example of good design for a product performing
a very deterministic task.
Coffee Maker Evolution Examples
Two possible evolutions are presented to demonstrate the use of information from the
excess map in system evolution.
Coffee Maker Evolution 1: Brew Full Pot in Two Thirds the Time
A possible future need for the system is to brew a full pot of coffee in less time than was
originally intended. Reducing the brew time to two thirds of the original would mean
increasing the flow rate by a factor of 1.5, thus the new flow rate would be 3.9 mL/sec. This
would affect the flow rate output of the brew basket, since that is what addresses the brewing
rate specification. Consulting Figure 4.32 shows that the brew basket can tolerate up to 16.7
mL/sec, while the body can tolerate up to 15 mL/sec. However, between the body and brew
basket is the heater, which is already producing its maximum flow rate of 2.6 mL/sec. Since,
in this case, flow rate is directly proportional to the input power to the heating element, the
new power required is 1350W as given by Equation 5.5.
 = 1.5  = 1350
( 4.16 )
This new value does not conflict with the power limit specification of 1.4 kW, and so all
that remains is to check each of the affected components. 1350W corresponds to 11.3A at
120VRMS, which can be tolerated by the cord but not the switch. Therefore, to reduce the brew
time to two thirds the original time, the heater and switch would have to be replaced.
57
Coffee Maker Evolution 2: Utilize Single-Serve Coffee Pods
A popular method of preparing coffee today involves single-portion coffee pods. A
possible future need for the coffee pot is to use these pods instead of the conventional filter
with loose grounds.
Evolving to meet such a need would result in a significant alteration to the system
architecture. Single serve coffee pods require a system that can deliver pressurized heated
water, as well as a receptacle for the pod itself that differs greatly from the conventional filter
basket. On the other hand, no carafe or hot plate is required since the coffee is brewed directly
into the serving vessel. For such an extreme evolution, use of the excess map in Figure 4.32
reduces to consulting the compatibility flow for the components that would be replaced to
effect the evolution. Such an evolution would be possible if:

The coffee pod holder could fit within the volume in the body currently occupied by
the brew basket (860 cm3).

The new control interface could fit within the area currently occupied by the switch, 2
cm2, assuming that the ability to select a coffee mug size is desired. Given that this is
unlikely to be possible, the body would have to be modified as well to allow the larger
control interface. However, if a single size coffee mug is assumed, it would be possible
to use the existing switch as a toggle to run the rest of the evolved system.

The requisite pump and whole-volume heater could fit somewhere within the body.
The volume occupied by the original heater was not indicated on the original map
because a more powerful conventional heater could have been added without requiring
more volume (i.e. a heater of the same geometry but greater resistance and therefore
greater power could have replaced the original). There is not sufficient volume in the
location of the original heater, and more volume would be required for the new
components. This is because single-serve coffee machines heat all of the brewing water
at once and then inject it at pressure into the coffee grounds, rather than boiling it
intermittently and relying on gravity to drip water through the grounds; heating all the
water at once naturally requires greater volume. However, the excess map does indicate
an excess of (S-M-L) for the cold water reservoir. Some of this could be occupied by
58
new hardware, since a single-serve brewing system does not require the same amount
of water in its reservoir as a conventional drip coffee maker. Logically, the volume
required for the full-size heater should not be significantly greater than the volume of
a single mug of coffee, meaning that there is definitely sufficient volume available in
the existing water reservoir. Likewise, a small pump that only needs to develop a head
on the order 30 cm should not be more than several cubic centimeters in volume, which
again could fit without issue in the existing cold water reservoir. The addition of both
these pieces of hardware to the portion of the body currently functioning as the cold
water reservoir would still leave enough water storage volume for multiple cups.

The electrical draw for the modified system is less than 14 A to remain compatible with
the existing cord.

The body is not exposed to temperatures exceeding 135°C by any of the modifications.
Scalability Case Study
Since excess maps are intended to be constructed during the embodiment phase of design,
they will logically be made by individual designers or design teams who are familiar with the
system in question. For more complex systems comprised of subsystems created by different
design teams, excess maps will be submitted/exchanged as part of the design documentation.
To demonstrate this process, a string trimmer as shown in Figure 4.33 was disassembled into
three subsystems: the Engine, Transmission, and Attachment. Three individuals created excess
maps for their respective assigned subsystems, and the results are detailed in the following
subsections. For this demonstration, no numerical values were collected since the object of the
exercise was to show how excess maps for subsystems can be joined.
59
Figure 4.33: String Trimmer [57]
A subset of the customer needs and corresponding specifications satisfied by the string
trimmer are summarized in Table 4.3.
Table 4.3: String Trimmer Needs and Specifications
Needs
Specifications
Cut weeds quickly
(1) Cutting swath in cm
Run for an adequate amount of time
(2) Fuel volume in mL
Be easy to carry
(3) Total mass in kg (state parameter)
Be sufficiently powerful
(4) Engine power in W
Cut moderately thick weeds
(5) String diameter in mm
Comfortable length
(6) Handle-to-end length in m (state parameter)
Carry extra line
(7) String storage volume in cm3
It was assumed that the interfaces between the components were mandated in advance for
all three designers/design teams for the components. Therefore, the geometry of the interfaces
was fixed for the overall design. The maximum power that it can transmit was treated as a state
parameter.
In keeping with the assumption that the design of subsystems is divided between multiple
design teams, the overall specifications for the system were split where necessary and assigned
to their corresponding subsystems. Therefore, the engine was responsible for
60

Specification 2

Specification 4

A portion of Specification 3 was allocated to the motor
The transmission was responsible for

Delivering the power from Specification 4

Supporting weight from Attachment

Providing length for mounting user interfaces

A portion of Specification 3 was allocated to the transmission

A portion of Specification 6 was allocated to the transmission
The cutting attachment was responsible for

Specification 1

Delivering the power from Specification 4

Specification 5

Specification 7

A portion of Specification 3 was allocated to the attachment

A portion of Specification 6 was allocated to the attachment
These specifications drove the excess maps created in the following subsections.
Subsystem 1: Engine
The engine was the most complicated subsystem, and its excess map was naturally the most
detailed based on the guidance of decomposing a system to the elements that display modular
behavior.
The engine requires length (S-G-1) from the transmission for the grip, human energy (FE-H) for the starter cord and grip, air flow (F-M-G) for the carburetor, and control signal (FS-C) for the trigger, carburetor, and stop switch. It produces mechanical energy (F-E-M) for
the transmission, and holds a quantity of fuel (S-M-L) to satisfy the corresponding system
specification. Its excess map, with internal component relationships, is shown in Figure 4.34.
Note that in this map there are two environmental blocks; the information is presented in this
way to minimize visual complexity.
61
F-E-T
State Parameters
Environment
S-G-1
F-E-H
F-S-C
F-E-H
System Mass
S-G-3
Case
S-G-3
S-G-3
S-G-2
F-E-T
S-G-2
S-G-2
S-G-3
S-G-2
F-E-H
F-E-M
To
Environment
F-E-M
S-G-3
Starter
Cord
Clutch
F-E-M
F-E-M
F-S-C
F-E-M
Motor
S-G-2
S-S-L
S-G-2
F-S-C
S-G-2
S-G-3
F-E-H
S-G-1
S-S-L
F-M-M
E-stop
S-M-L
S-S-L
F-S-C
S-G-2
Environment
S-S-L
F-S-C
Grip
F-M-L
F-M-G
Trigger
S-G-3
F-M-L
S-G-2
F-M-G
F-S-C
S-G-3
S-G-2
F-S-C
To
Environment
Fuel
Tank
F-S-C
F-S-C
F-S-C
Carburetor
F-M-M
S-G-2
Figure 4.34: Engine Excess Map
Subsystem 2: Transmission
In contrast to the engine, the transmission was the simplest of the three subsystems
considered, and its excess map reflects that fact. It requires human energy from the user for the
handle and mechanical energy from the engine for the shaft. It provides support (S-S-L) to the
cutting attachment, mechanical energy (F-E-M) to the attachment, and length (S-G-1) to the
engine’s grip. Its excess map is given in Figure 4.35.
62
Environment
F-E-H
F-E-M
State Parameters
System Mass
Overall Length
S-S-L
To
Environment
F-E-M
To
Environment
F-E-M
F-E-H
Handle
S-S-L
S-S-L
Shaft
S-G-1
S-G-1
To
Environment
Figure 4.35: Transmission Excess Map
Subsystem 3: Cutting Attachment
The cutting attachment requires mechanical energy (F-E-M) and support (S-S-L) from the
transmission. It provides a diameter of cutting swath (S-G-1), delivered mechanical power (FE-M), volume of the stored cutting string (S-G-3), and diameter of the cutting string (S-G-1)
to satisfy its specifications. The excess map for the cutting attachment is shown in Figure 4.36.
63
Environment
F-E-M
State Parameters
System Mass
S-S-L
Overall Length
S-G-1
F-E-M
Shield
S-G-1
To
Environment
S-S-L
S-G-1
Shaft
F-E-M
F-E-M
To
Environment
S-G-3
To
Environment
S-G-1
To
Environment
S-G-1
F-E-M
Head
Figure 4.36: Cutting Attachment Excess Map
String Trimmer Excess Map
Based on the results for the three individual subsystems, a composite excess map for the
string trimmer was created as shown in Figure 4.37. A full size version of the finished excess
map is in the Appendix. The environmental flows for each of the subsystems that are not
satisfied by another subsystem are displayed in the Environment block, while the excesses that
address system level specifications are shown as outputs to the environment. These excesses
combined with the state parameters address all of the system-level specifications placed on the
design.
64
Environment
F-E-H
F-S-C
F-S-C
F-E-H
F-S-C
F-M-G
F-E-H
State Parameters
System Mass
Interface Power
Overall Length
F-S-C
F-M-G
F-E-H
F-E-H
F-S-C
To
Environment
S-M-L
F-S-C
Engine
F-E-M
S-G-1
F-E-M
S-G-1
To
Environment
F-E-M
To
Environment
S-G-3
To
Environment
S-G-1
To
Environment
S-S-L
S-S-L
F-E-H
Transmission
F-E-M
F-E-M
Attachment
S-G-1
Figure 4.37: String Trimmer Composite Excess Map
This example demonstrates how the excess mapping method scales to more complex
systems that are designed by multiple individuals/teams. The separate excess maps created by
designers or teams for subsystems are condensed into individual component blocks, and the
excess flows that cross the control volume are mapped to other component blocks or to/from
the system environment.
This procedure can be applied to any system, provided that the excess maps for each
subsystem are created per the guidelines given in Section 4.1 and the system-level
specifications are divided clearly between the respective design teams. By building up maps
for complex systems in this way, it is possible to create multi-level maps, each one at a finer
level of detail. This is advantageous because it allows the designer to restrict their attention to
65
only the portion of interest within a system, at a desired level of granularity, without being
overwhelmed by all of the relationships between all of the components at the finest level of
detail.
The excess mapping method developed in this chapter delivers to designers the set of
excesses that affect a system’s ability to evolve to meet future needs. Excess maps incorporate
the quantities of available excess as well as the types, and therefore can be used to explore the
effect of a change to a system on the amount of excess that remains. However, knowing which
excesses are important for evolvability and their present designed amounts does not mean that
the ideal amount of excess to embed is clear. The next chapter develops an approach to aid
designers seeking to embed useful quantities of excess for evolvability.
66
Stress Test Approach
This chapter builds on the excess mapping method of Chapter 4 by coupling the excess
maps with future changes to explore the relationship between excess and evolutions to meet
future needs. Specifically, this approach helps to address the problem of allocating epistemic
excess when empirical design experience and ‘rules of thumb’ are unavailable.
Stress Testing in Engineering
Varying types of stress testing are encountered across different fields of engineering. The
most obvious is literal stress testing, performed on artifacts as a means of ensuring their quality
and safety, and/or of verifying analytical models, as described in [58]. The type that underpins
the approach taken by this paper, however, comes from software engineering. In general terms,
software stress testing exposes computer programs to conditions that could overwhelm their
ability to function [59], demanding “resources in abnormal quantity, frequency, or volume”
[60]. These tests go beyond the nominal operating conditions that the software was designed
for, in terms of either increased demands or reduced resources [61], to determine how the
system reacts to potential future needs. This process reveals bottlenecks within the software
that limit its ability to function under off-design conditions.
The steps are described in the following subsections, following the process shown in Figure
5.1, and assume that a system excess map has been created per the guidelines given in the
previous chapter.
67
Step 1: Collect Future Needs
Step 2: Generate Solutions
Step 3: Evaluate Impacts
Step 4: Judge Fitness/
Review Excess Placement
Figure 5.1: Stress Test Approach Flowchart
Stress Test Approach Steps
The following subsections detail the steps involved in stress testing a system.
Step 1: Collect Future Needs and Specifications
This step guides the application of the remainder of the stress test approach, and entails
acquiring the set of needs that the system will be tested against. Ideally, information about
possible future needs will be available from external sources such as marketing information or
historical changes similar systems have been required to undergo. However, such information
is not required. Designers may still apply this approach using only the original design
specifications as a base if necessary, since the primary functions of the system are believed to
remain the same over time and the original specifications embody the satisfaction of these
functions. At a minimum, designers should consider varied usage environments and the
possibility that stakeholders will desire increased performance as embodied in the system-level
specifications.
Information about future needs (if sourced externally) must be represented by new or
updated design specifications for the excesses in the system to be measured against. Where
possible and appropriate, each specification should be posited to have differing levels of
severity, three at minimum. This is meant to give a designer insight into how the system
68
responds to various degrees of required change. The values of the points to choose are subject
to designer discretion for each particular case – for a specification that is unlikely to change
significantly, alterations of +5%, +10%, and +20% could be appropriate. On the other hand,
for a specification with no clear reasonable upper bound, alterations of +20%, +50%, and
+150% could be justifiable. It is recommended that the spacing of these points is nonlinear so
that the design space can be more efficiently explored (relative to a linear set of points). Such
a nonlinear spacing allows designers to explore the results of a ‘minor’, ‘in between’, and
‘drastic’ change. However, designers may explore more than three points if they feel the
expenditure of effort is worthwhile.
Each future need will first be examined individually (i.e. as though only one occurs at a
time) in the following steps, so that the impacts of two different needs applied at the same time
are not confounded. In general, quantities of excesses consumed by one change cannot be
assumed to be usable to effect other changes as well – consider a wire that feeds current to a
system. If a change is made that requires an additional ampere of current, that excess cannot
be applied to a second change that also requires additional electrical energy to be conveyed by
the wire.
In general, the bounds of this step can be expanded depending on the circumstances of the
particular design. This decision is a function of many considerations such as available designer
effort, budget to embed excess, expected system lifetime, and anticipated volatility of service
environment. Therefore, the number and plausibility of future needs considered is left to the
designers of a particular system.
Step 2: Generate Solutions
For each posited future need, solution paths are determined using the excess map and
knowledge of the system’s design. Designers in the embodiment phase of system design will
be capable of altering the system design, using the existing design as a starting point, to satisfy
future needs. Multiple options should be found where possible; in general, the number of
solution paths will be proportional to system complexity. The solutions should be as
straightforward as possible so as to yield the most realistic options set. Ideally, all solutions for
a future need can be realized by modifying individual components or subsystems without
69
changing the system architecture. Realistically, many solutions will impact multiple
components by propagating changes from functional flows to compatibility flows, possibly
requiring some components to be replaced. There will naturally arise some scenarios where
only drastic solutions will suffice and major modification to the system architecture is required.
These cases indicate future needs that the system is ill-suited to respond to as presently
designed.
Step 3: Evaluate Impacts
In general, there are three possible outcomes when exploring solutions to meet future
needs:
•
All affected components possess enough excess to evolve the system; excess in the
components are reduced to either a positive or zero value by the solution.
•
One or more affected components have insufficient excess, indicating that for the
system to evolve, components would have to be upgraded or replaced.
•
Some portion of the system architecture does not support the solution; i.e. the
signal/mass/energy flows between multiple components cannot be adjusted in
magnitude or redirected in application to enable the evolution. A result of this type
raises important questions for the designer. If the posited future need is an outlier,
highly unlikely to actually occur, then the system design is likely acceptable. However,
if the posited future need is known to be a reasonable possibility, this result indicates
that the design might not be fit for purpose and should be carefully reevaluated.
Once all the impacts of the individual needs have been considered, a matrix, similar to a
DSM, is constructed to examine which potential needs could require the same excesses as other
potential needs. Each potential need receives a row and corresponding column so that its
interactions with other needs can be marked. These areas of overlap trigger a review so that
designers can examine the ability of the system to respond to simultaneous future needs that
require the same types of excess. The matrix is upper triangular since the interactions are nondirectional, and so filling out the entire matrix would only duplicate information.
70
Step 4: Judge Fitness/Review Excess Placement
After considering the results of all future needs scenarios, designers will be capable of
judging whether a design is likely capable of changing to meet future needs that are realized
once the system is deployed. Beyond this judgment, designers will have gained insight into the
relations between individual excesses and the system’s evolvability. Some components may
emerge as bottlenecks to system evolution because they possess no or limited excess. Others
may appear to so far outstrip other components that their excess is superfluous. Such cases
may result from oversights in the design process and present an opportunity to lower system
cost by eliminating some excess, or may be due to the factors discussed in Section 3.1
concerning excesses as side effects of other factors. These insights into component-level
excesses can be used to inform decisions of adding or subtracting excess from the system
design.
Stress Test Case Study Preliminaries
For the case study of this approach, a toy dart gun shown in Figure 5.2 was used, as it
offered a greater potential variety of future needs than the heat gun or coffee maker but could
still have all of its excess flows identified and quantified via reverse engineering. The details
of its excess map creation are given in this section.
Figure 5.2: Toy Dart Gun [62]
71
Toy Dart Gun Excess Map Creation
The plastic pieces that comprise the dart gun were assumed to be ABS plastic with a yield
strength of 40 MPa, and a Factor of Safety of 2 was assumed. This meant that yield strength
of the plastic was treated as 20 MPa with a corresponding shear strength of 10 MPa. The
pertinent measurements for calculations concerning components that contain and/or compress
air were measured and are given in Table 5.1.
Table 5.1: Dart Gun Component Measurements
Component
Flex tube
Slide pump
Charge PV
Barrel tube
Volume
(mL)
2.26
24.1
18.2
7.22
Radius
(mm)
Wall Thickness
(mm)
10
11
6.5
1.7
1.7
1.9
The compression of gas by the hand slide pump was assumed to be isothermal since it
occurs over a relatively long period of time. The expansion of gas when the dart is fired was
assumed to be adiabatic since it occurs very quickly.
For isothermal compression and expansion:
 = 
( 5.1 )
For adiabatic compression and expansion:
  =  = 
1−
 = 

( 5.2 )
1−
− 
1−
( 5.3 )
Where W is work, P is pressure, V is volume, Vf is final volume, Vi is initial volume, and γ
is the ratio of gas specific heats (1.4 for air).
Any figures involving dart flight distance assume level fire from a height of 1m. Therefore,
the time of flight (neglecting drag) for any dart is given as
72
ℎ
1
 = √
= √
= 0.45 
1
1


(9.8
)
2
2
2
( 5.4 )
Using the results of Equation 5.4, the elementary relation KE = ½ mv2 and the known 1.5g
mass of a dart, the plot shown in Figure 5.3 is created to show the required kinetic energy for
a dart as a function of flight distance.
Kinetic Energy Req (J)
2.5
2
1.5
1
0.5
0
0
5
10
15
Distance Req (m)
20
25
Figure 5.3: Dart Kinetic Energy Required vs. Distance for Level Fire at 1m
When analyzing cylindrical components that function as pressure vessels, the hoop stress
was considered to be the limiting loading scenario and was calculated by Equation 5.5, where
P is the pressure, r is the mean radius, and t is the thickness.
ℎ =


( 5.5 )
This can be rearranged into Equation 5.6 to give the maximum working pressure as a
function of the material yield strength (assumed 20 MPa for ABS plastic as earlier noted), the
wall thickness, and radius.
73
 = σ ∙


( 5.6 )
Step 1: Collect Stakeholder Specifications
A subset of specifications embodied in the design are:
•
Fire 1.5g foam suction-tipped darts
•
Operate in air at 1 atm pressure
•
Fire darts of dimensions 13mm OD x 6.4mm ID x 57mm long
•
Fire darts 6m (assuming level fire at height of 1m)
•
Hold 6 darts
•
Weigh less than 900 g
•
Trigger pull force less than 15N
Step 2: Identify Architecture, Appropriate Subassemblies, and Relationships
The components that display modular behavior are the body, slide grip, slide pump, flex
tube, check valve/release, charge pressure vessel, floating pressure seal, rotary barrel,
trigger/advance assembly, and ratchet shaft. Their contributions to the excess map are detailed
in the following subsections.
74
Body
Figure 5.4: Dart Gun Body
Figure 5.5: Dart Gun Component Layout
The body of the dart gun, shown in Figure 5.4, supplies volume (Storage, Geometric,
Volume or S-G-3) to the slide pump and charge pressure vessel, and mandates a radial distance
(Storage, Geometric, Length or S-G-1) from the axis of rotation for the dart pattern in the rotary
barrel.
75
The component and excess blocks for the body are given in Figure 5.6. The first volume
excess block supplies 26 mL of space out of a maximum 78 mL to the charge pressure vessel.
The length excess block supplies a 45 mm radial distance (from the axis of rotation to the dart
chamber) to the rotary barrel and has no excess remaining. The second volume excess supplies
all of the available 24 mL of space to the slide pump.
Body
S-G-3
52 [mL]
(78)
26
S-G-1
0 [mm]
(45)
45
S-G-3
0 [mL]
(24)
24
Figure 5.6: Body Excess Map Contribution
Slide Grip
Figure 5.7: Dart Gun Slide Grip
76
The slide grip, shown in Figure 5.7, is where the user’s hand grips the dart gun and operates
the slide pump. The screw posts on the right side nest together and interface with the slide
pump, transferring energy to compress the air, and can tolerate a maximum load as given in
the excess block in Figure 5.8 based on its dimensions and the properties of ABS plastic.
Assuming an isothermal compression, the relation in Equation 5.1 applies. Using an initial
pressure of 101 kPa (one atmosphere), an initial volume of 42 mL (the slide pump, flex tube,
and charge pressure vessel) and a final volume of 18 mL (the flex tube and charge pressure
vessel), the final gauge pressure in the charge pressure vessel is 135 kPa. Given that the inner
diameter of the slide pump is 19mm, with a corresponding area of 284E-6 m2, the resulting
force transmitted from the slide grip to the slide pump at the bottom of its stroke is 38N using
the elementary relation P=F/A. Given the cross-sectional area of the screw post that functions
as a structural member under shear load, 18mm2, along with the maximum shear load of 10
MPa, a maximum shear force of 180N can be applied. This is represented by a load excess
(Storage, Structural, Load or S-S-L).
F-E-H
38 N
Slide
Grip
S-S-L
142 [N]
(180)
38
Figure 5.8: Slide Grip Excess Map Contribution
Slide Pump
Figure 5.9: Dart Gun Slide Pump
77
The slide pump, shown in Figure 5.9, takes in atmospheric air and compresses it for use
elsewhere in the dart gun. It requires volume (Storage, Geometric, Volume or S-G-3) from the
body. Its radius and wall thickness, given in Table 5.1, yield a maximum working pressure of
3.4 MPa as shown in the excess block of Figure 5.10 using Equation 5.6.
S-G-3
24 mL
S-S-L
38 N
Slide
Pump
S-S-P
3265 [kPa] 135
(3400)
Figure 5.10: Slide Pump Excess Map Contribution
Flex Tube
Figure 5.11: Dart Gun Flex Tube
The flex tube, shown in Figure 5.11, conveys compressed air from the slide pump to the
check valve. It is made of vinyl tubing that is rated to 1 MPa based on its wall thickness (1
mm). This is represented by a pressure excess (Storage, Structural, Pressure or S-S-P).
S-S-P
135 kPa
Flex
Tube
S-S-P
865 [kPa]
(1000)
135
Figure 5.12: Flex Tube Excess Map Contribution
78
Check Valve/Release
Figure 5.13: Dart Gun Check Valve/Release
The check valve and release assembly, shown in Figure 5.13, allows unidirectional flow of
compressed air into the charge pressure vessel, and controls its release to the barrel by actuation
of the seal at the assembly’s base. Based on its measurable wall dimensions at its widest
cylindrical portion (the worst case stress scenario for hoop stress), its maximum working
pressure is estimated to be 1.4 MPa using Equation 5.6 with a wall thickness of 0.7 mm and a
radius of 10 mm. The component and excess blocks are shown in Figure 5.14.
S-S-P
135 kPa
Check
Valve/
Release
S-S-P
1265 [kPa] 135
(1400)
Figure 5.14: Check Valve/Release Excess Map Contribution
79
Charge Pressure Vessel
Figure 5.15: Dart Gun Charge Pressure Vessel
The charge pressure vessel, shown in Figure 5.15, contains the compressed air that powers
the flight of the darts. It requires volume (Storage, Geometric, Volume or S-G-3) from the
body. It is actuated by the check valve/release assembly, which attempts to release the pressure
in the charge pressure vessel through the check valve. This causes a piston to retract within the
charge pressure vessel, sealing the orifice to the check valve while opening the orifice to the
rotary barrel. The maximum working pressure is 5.8 MPa based on the dimensions of the
charge pressure vessel given in Table 5.1 and the results of Equation 5.6, as shown in Figure
5.16.
S-S-P
S-G-3
Charge
Pressure
26 mL
Vessel
135 kPa
S-S-P
5715 [kPa] 135
(5850)
Figure 5.16: Charge Pressure Vessel Excess Map Contribution
80
Floating Pressure Seal
Figure 5.17: Dart Gun Floating Pressure Seal
The floating pressure seal, shown in Figure 5.17, attempts to ensure that the full pressure
from the charge pressure vessel reaches the rotary barrel. It uses a spring to press a flat rubber
seal (hollow in the center to permit air flow) against the barrel. However, the spring is relatively
weak, and based on its measured spring constant (130 N/m), deflection at operating conditions
(9mm) and the dimensions of the rubber seal (13.5mm OD x 6mm ID), only 10 kPa of pressure
can be contained as shown in Equation 5.7.


130  ∙ 0.009

∙
=
=
=
= 10 
2 −  2 )
2 − .006 2 )

(
(.0135
4
4
( 5.7 )
Empirical flight testing results found that darts fired level from 1m above the ground
reached 6m. Consulting Figure 5.3 shows that the corresponding kinetic energy (and hence the
work done on the dart) must be approximately 0.12 J. Using Equation 5.3 with P = 10 kPa, Vi
= 15.6mL (the volume of the charge pressure vessel) and Vf = 22.8 mL (the volume of the
charge pressure vessel plus a dart chamber) results in an adiabatic work done on the dart of
0.05 J – clearly less than that actually imparted to the dart. This means that while the floating
pressure seal functions as a blowoff valve for any pressure above 10 kPa, back pressure causes
the delivered pressure to the dart to be higher than the cracking pressure of the floating pressure
seal.
81
Using the known work required for a flight of 6m (0.12 J) and back solving Equation 5.3
to find the original pressure results in 25 kPa, the pressure that is actually delivered to the dart
by the floating pressure seal. These considerations are represented by a pressure (Storage,
Structural, Pressure or S-S-P) excess block in Figure 5.18.
S-S-P
Float
Seal Assy
25 kPa
S-S-P
0 [kPa]
(25)
25
Figure 5.18: Floating Pressure Seal Excess Map Contribution
Rotary Barrel
Figure 5.19: Dart Gun Rotary Barrel
The rotary barrel, shown in Figure 5.19, requires a linear positioning (Storage, Geometric,
Length or S-G-1) of 45 mm between its dart pattern and its axis of rotation with respect to the
body, receives a positioning signal (Flow, Signal, Control or F-S-C) from the ratchet shaft, and
receives compressed air (Storage, Structural, Pressure or S-S-P) from the charge pressure
vessel/floating pressure seal. It can tolerate up to 5.8 MPa of pressure (S-S-P) based on the
82
dimensions of the individual chambers and contains six darts (Storage, Material, Solid or SM-S). Its component and excess blocks are shown in Figure 5.20.
S-S-P
S-G-1
F-S-C
25 kPa
45 mm
Signal
Rotary
Barrel
S-S-P
5775 [kPa]
(5800)
25
S-M-S
0 [darts]
(6)
6
Figure 5.20: Rotary Barrel Excess Map Contribution
Trigger/Advance Assembly
Figure 5.21: Dart Gun Trigger/Advance Assembly
The trigger/advance assembly, shown in Figure 5.21, receives human energy (Flow,
Energy, Human or F-E-H) as input to the trigger and translates it to a positioning signal (F-SC) to the ratchet shaft. The geometry of the assembly means that, depending on the geometry
of the ratchet shaft, any rotation from 40° to 180° can be commanded. The assembly also
actuates the release in the check valve/release to fire the gun; however, this is not modeled as
it is not reasonable to describe any excess in the binary relationship. The component and excess
blocks for the trigger/advance assembly are shown in Figure 5.22.
83
F-E-H
15 N
Trigger/
Advance
Assy
F-S-C
60
-20/+120 [deg]
(40-180)
Figure 5.22: Trigger/Advance Assembly Excess Map Contribution
Ratchet Shaft
Figure 5.23: Dart Gun Ratchet Shaft
The ratchet shaft, shown in Figure 5.23, translates the control signal (F-S-C) from the
trigger/advance assembly to a commanded rotational advance (F-S-C) of the rotary barrel.
While the trigger/advance assembly is not set to a fixed rotational amount, the ratchet shaft
may only rotate in set increments of 60° due to its construction. The black and white pieces are
keyed to one another and may only move in 60° increments with respect to one another;
changing this would require replacing both the black and white shaft pieces and therefore the
vast majority of the ratchet shaft assembly. The component and excess blocks for the ratchet
shaft are shown in Figure 5.24.
F-S-C
60°
Ratchet
Shaft
F-S-C
0 [deg]
(60±0)
60
Figure 5.24: Ratchet Shaft Excess Map Contribution
84
Step 3: Assemble Excess Map
The summarized compatibility and functional flows for the components of the dart gun are
given in Table 5.2. The environment block for this system consists of two human energy
relationships (Flow, Energy, Human or F-E-H); one to operate the pump and the other to pull
the trigger.
Table 5.2: Dart Gun Component Excesses
Component
Compatibility Flow
Functional Flow
Body
N/A
Storage-Geometric-Volume (2)
Storage-Geometric-Length
Slide Grip
Flow-Energy-Human
Storage-Structural-Load
Slide Pump
Storage-Geometric-Volume
Storage-Structural-Load
Storage-Structural-Pressure
Flex Tube
Storage-Structural-Pressure
Storage-Structural-Pressure
Check
Valve/Release
Charge Pressure
Vessel
Floating
Pressure Seal
Storage-Structural-Pressure
Storage-Structural-Pressure
Storage-Geometric-Volume
Storage-Structural-Pressure
Storage-Structural-Pressure
Storage-Structural-Pressure
Storage-Structural-Pressure
Rotary Barrel
Storage-Structural-Pressure
Storage-Geometric-Length
Flow-Signal-Control
Storage-Structural-Pressure
Storage-Material-Solid
Trigger/Advance
Assembly
Flow-Energy-Human
Flow-Signal-Control
Ratchet Shaft
Flow-Signal-Control
Flow-Signal-Control
Step 4: Identify State Parameters
There is only one necessary state parameter for the dart gun, total mass. The individual
component masses are indicated within the component blocks. The completed dart gun excess
map is shown in Figure 5.25. A full size version of the finished excess map is in the Appendix.
85
10 g
Charge
Pressure
26 mL
Vessel
S-S-P
5715 [kPa] 135
(5850)
135 kPa
State Parameters
System Mass: 420 g
S-G-3
S-S-P
S-S-P
Environment
F-E-H
[N]
1g
Check
135 kPa Valve/
Release
S-S-P
1265 [kPa] 135
(1400)
S-S-P
F-E-H
25 g
S-S-L
142 [N]
(180)
Slide
Grip
S-G-3
52 [mL]
(78)
26
S-G-1
0 [mm]
(45)
45
S-G-3
0 [mL]
(24)
135 kPa
Body
S-S-P
865 [kPa]
(1000)
Flex
Tube
24
135
F-E-H
S-S-P
S-G-1
S-S-P
S-G-3
50 g
20 g
24 mL
38 N
S-S-P
3265 [kPa] 135
(3400)
Slide
Pump
25 kPa
45 mm
Signal
Rotary
Barrel
F-S-C
15 g
15 N
Trigger/
Advance
Assy
25
270 g
38
5g
S-S-L
S-S-P
0 [kPa]
(25)
Float
25 kPa
Seal Assy
10 g
F-E-H
[N]
38 N
To
Environment
S-S-P
5775 [kPa]
(5800)
25
S-M-S
0 [darts]
(6)
6
To
Environment
To
Environment
15 g
F-S-C
60
-20/+120 [deg]
(40-180)
F-S-C
60°
Ratchet
Shaft
F-S-C
0 [deg]
(60±0)
60
Figure 5.25: Toy Dart Gun Excess Map
Stress Test Case Study
This sections details the use of the stress test approach on the toy dart gun.
Step 1: Collect Future Needs and Specifications
A list of potential future needs was generated, considering the initial performance
requirements placed on the gun and possible modifications, bearing in mind the constraint that
top-level functional behavior is fixed. For the dart gun the top-level function can be described
in the verb-noun nomenclature of functional modeling as ‘transmit darts’. The needs are listed
here:
86
•
Fire darts farther (+50%, +100%, +200%)
•
Fire heavier darts (+50%, +100%, +200%)
•
Increase dart accuracy
•
Hold more darts (+50%, +100%, +200%)
•
Fire underwater
•
Fire in vacuum
•
Self-powered (no pumping)
Steps 2 and 3: Generate Solutions and Evaluate Impacts
Steps 2 and 3 are discussed together for each of the examined future needs. This is done so
that the reader may see the solutions for and impacts of each posited future need together,
rather than having to remember the set of solutions for every need before discussion of the
solution impacts.
Fire Darts Farther
As originally designed, the gun fires darts to a distance of 6m. For the stress-test analysis,
three different evolutions were considered: fire darts 9m, 12m, and 18m (50%, 100% and 200%
increases, respectively).
Three approaches to boost the range of the darts were considered:
•
Replacing the spring in the floating pressure seal assembly (shown in Figure 5.17) to
increase pressure delivery to the barrel
•
Replacing the hand pump mechanism with a tank of compressed gas and a regulator
•
Adding a small propellant charge to the base of each dart
Approach 1
An analysis of the pressure energy flows through the dart gun combined with the
information in Figure 5.3 reveals that there is sufficient energy contained within the charge
pressure vessel to propel a dart 14m. This conclusion results from the following analysis:
87
•
•
The pressure delivered by a single pump is calculated as follows:
1 1 = (1 atm)(24.1 + 18.2 + 2.3 mL) = 2 2
( 5.8 )
2 = (18.2+2.3 mL) → 2 = 2.3 atm = 236 kPa = 135 kPa gauge
( 5.9 )
If the full 135 kPa is delivered to the dart according to Equation 5.9, it results in a work
of 0.7 J. This is sufficient, according to Figure 5.3 to propel the dart 14m.
However, this energy is delivered to the barrel via the floating pressure seal assembly. This
assembly uses a spring to press a flat rubber seal against the base of the rotary barrel. The
maximum air pressure that it can transmit is limited by the force with which the spring
compresses the seal against the barrel. As designed, the spring is relatively weak with a rate of
130 N/m. Given the dimensions of the rubber seal (13.5 mm OD x 6.0 mm ID), the floating
pressure seal assembly can only contain a pressure of 10 kPa from the relation P=F/A (given a
spring compression of 9mm). In essence, this assembly functions as a blowoff valve for any
pressure exceeding the cracking pressure of 10 kPa. However, as a blowoff valve, the assembly
has inadequate ventilation, resulting in significant back pressure that produces a pressure in
the barrel somewhere between the charge pressure and the cracking pressure.
Comparing empirical flight results and the thermodynamic and kinematic equations
suggest that, for a charge pressure of 135 kPa, the floating pressure seal assembly delivers
roughly 25 kPa to the barrel - about two and a half times its cracking pressure. This confirms
that there is back pressure that prevents the floating pressure seal from functioning as an ideal
blowoff valve. These considerations are condensed in the excess map of Figure 5.15 as a S-SP (storage, structural, pressure) excess of 25 kPa for the floating pressure seal.
For a dart to reach 9m, a pressure of at least 55 kPa is required. Information from the excess
map shows that if the floating pressure seal assembly’s ability to contain compressed air is
increased to 55 kPa, no other modifications to the system are required. This results from
consulting Figure 5.3 to find the required dart kinetic energy to reach 9m (0.3 J), solving
Equation 5.3 to find the corresponding initial pressure (55 kPa) and comparing that to the
pressure provided by a single pump (135 kPa). Since the required pressure is less than that
provided by a single pump, a single pump is sufficient. Consulting the S-S-P excesses within
88
Figure 5.25, attached to the slide pump, flex tube, check valve, charge pressure vessel, and
rotary barrel indicates that those components are capable of withstanding the 135 kPa
generated by a single pump, and therefore also the 55 kPa required for propelling a dart to 9m.
However, the floating pressure seal is only capable of transmitting 25 kPa of pressure, and
therefore must be upgraded. Similarly, increasing the range to 12m only requires that the
delivered pressure be increased to 95 kPa, still less than the pressure made available in the
charge pressure vessel by a single pump.
To reach the 18m goal the pressure supplied by a single pump is insufficient. However, the
presence of a check valve in the compressed air path means that the hand slide pump could be
cycled more than once to add air to the charge pressure vessel. With two pumps the dart gun
can produce a charge pressure of 270 kPa, and consequently can fire up to 20m. This was
concluded by using Equation 5.1 while doubling the volume of the slide pump and leaving the
flex tube and charge pressure volumes the same, since the flex tube volume functions as dead
space and the charge pressure vessel is behind the check valve. Using 270 kPa as the initial
pressure in Equation 5.3 yields a work of 1.5 J and a corresponding range of 20m. Consulting
the S-S-P blocks of Figure 5.25 determines that all components save the floating pressure seal
are capable of withstanding 270 kPa. Therefore, to increase the dart gun’s range to as much as
20m, only replacing the spring in the floating pressure seal is required.
An alternate approach to generating sufficient pressure to launch a dart 18m would be to
lengthen the region of the body that contains the hand slide pump so that a longer slide pump
could be added later. An increase of 55mm in the length allocated to the slide pump, resulting
in an additional volume of 13 mL, would allow a maximum pressure of 270 kPa from a single
pump. This would presumably increase customer satisfaction since range of up to 20m could
be produced from a single pump.
Approach 2:
Consumer paintball guns powered by carbon dioxide tanks demonstrate how a small
container of pressurized gas connected to a regulator can provide propellant energy. As a
primary energy source, the tank and regulator could replace the slide pump assembly within
the gun’s handle. As a secondary energy source (used to increase the charge pressure from that
89
provided by a single pump) portions of the propellant gas could be conserved. If a more
extreme range is desired, replacing the slide pump mechanism with a gas tank and regulator
would allow ranges of up to 38m (limited by the flex tube), provided that the compressed gas
tank could occupy a volume of 24 mL or less (the volume denoted by the S-G-3 excess in
Figure 5.25 consumed by the hand slide pump). Given that the orange hand slide would no
longer be required, its removal would expose openings in the body that could be used to refill
the gas canister with no further modification.
Approach 3:
The third approach considered was to add a consumable explosive charge to the barrel
along with each dart (much as bags of gunpowder were placed behind shells in artillery pieces).
However, a major obstacle to this strategy quickly became apparent. First, it is questionable
whether the use of consumable propellant agrees with the customer need of reusable
ammunition. Second, the darts themselves could become damaged by the heat of explosions.
This solution reveals a limitation of the excess mapping method. The excess map in Figure
5.25 is generated as a function of customer needs and the system architecture present in
embodiment design. Therefore, it is a product of the original solution determined by the
engineers, in which isothermally compressed atmospheric air is used as the propellant. As a
result, the temperature capabilities of the materials are not considered. When the solution
approach to a potential future need changes from that originally taken in embodiment design,
designers must be conscious of factors that were not originally included – in this case, the
temperature sensitivity of darts and system materials. Since the dart is assumed to be supplied
as a standardized external input to the system’s function, it was not included in Figure 5.25.
A cursory search reveals that the burning temperature of black powder is at least 550 °C
[63] while the melting temperature of polyethylene foam (which the darts are assumed to be
made of) is 265 °C [64]. Black powder is a relatively elementary explosive, and several more
powerful explosives have been developed. Any explosive powerful enough to give a significant
contribution to the darts’ muzzle velocity would likely produce at least localized burning of
the foam material, meaning that one of the key customer needs would be invalidated.
90
Therefore, only the first two approaches considered to address this need are valid based on the
customer needs given.
Conclusions:
If greater range is desired, the spring in the floating pressure seal will need to be replaced
with a stiffer version to increase the cracking pressure of the assembly. This alone is actually
sufficient to increase the range to over 20m, in conjunction with an additional pump from the
hand slide pump. If a greater increase in range is desired, the hand slide pump should be
replaced with a compressed gas tank and regulator that can deliver pressures that are limited
only by the weakest component in the gas flow path, the flex tube, which permits a 38m range.
Theoretically, the gun could be pumped up to a maximum pressure of 1 MPa (based on the
pressure that one pump would generate if the dead space of the flex tube was the final volume).
However, with such great pressure the simple model used for work done on the dart would
break down due to flow restrictions between the charge pressure vessel and the barrel.
Fire Heavier Darts
As originally designed, the dart gun fires standard darts with a mass of approximately 1.5g
a distance of 6m. For the analysis, three different evolutions were considered: fire 2.3g, 3.0g,
and 4.5g darts (an increase of 50%, 100%, and 200% respectively) the same distance. These
masses correlate to 0.20J, 0.27J, and 0.40J of required kinetic energy at the muzzle,
respectively. The assumption is made that the increase in mass of the dart is solely a function
of the density of the foam and/or tip mass (i.e. the darts are the same dimensions as the standard
darts).
Firing heavier darts, as in the previous scenario, reduces to a problem of imparting
additional kinetic energy to the dart. Therefore, two approaches were considered (bearing in
mind that adding an explosive charge is impractical): increasing the floating pressure seal
spring’s stiffness and replacing the hand slide pump with a compressed gas tank and regulator.
91
Approach 1:
A single pump can produce up to 0.74J of work delivered to a dart, far in excess of that
required for even a dart three times heavier than the standard, provided that the cracking
pressure of the floating pressure seal, denoted in the attached S-S-P block in Figure 5.25, is
increased to 135 kPa with a stiffer spring.
Approach 2:
Replacing the floating pressure seal spring is sufficient for up to an 8g dart to be propelled
6m. However, if for any reason an extremely heavy dart were desired, the pressure supplied by
a compressed gas tank could propel up to a 29g dart 6m, limited again by the maximum
pressure allowed by the check valve.
Conclusions:
Little challenge is presented by firing a heavier dart. A dart three times heavier than the
standard can be fired using a single pump if the spring in the floating pressure seal is replaced
as described in the previous scenario. Of note is that if a combination of increased range and
increased mass were desired, a compressed gas tank might become the most viable solution to
increase the energy delivered to the darts.
Fire in Vacuum
The dart gun as designed relies on the ready availability of air as propellant for the darts.
However, in a vacuum, any propellant would have to be supplied as well.
Approach 1:
Given that the darts are assumed to remain unchanged and therefore inert, the propellant
cannot be supplied by the hand slide pump as designed. The projectiles are foam and so cannot
be moved by alternate propulsive means such as electromagnetic fields. Given these
considerations, the only available solution enabling the dart gun to fire in a vacuum using gas
as a propellant is to replace the hand slide pump with a cylinder of compressed gas and a
regulator. Additionally, the spring in the floating pressure seal must be replaced with one that
produces a higher cracking pressure. The availability of paintball guns of similar size indicates
92
the feasibility of such a solution. This solution enables fire of up to 38m in Earth’s gravitational
field.
Approach 2:
Compressed gas is not the only possible means of propelling a dart. Another option is
mechanical propulsion, as in the case of the flywheel propulsion mechanism used by some dart
guns. Unfortunately, the geometry of a flywheel propulsion mechanism requires that there be
two opposing flywheels, and that the darts be fed individually, typically from a box rather than
drum magazine. Further, flywheel propulsion requires electrical energy to operate, meaning
that every component in the existing architecture that handles gas flow would be discarded.
Since the existing advance mechanisms (the trigger/advance assembly and the ratchet shaft)
are designed for a rotary barrel rather than a box magazine, they would have to be replaced as
well. Ultimately, for the dart gun architecture to be converted to a mechanical propulsion
scheme, every internal component and the rotary barrel would have to be discarded, and the
body would have to be significantly modified. Therefore, the only viable approach to
converting the dart gun to fire in a vacuum is the approach discussed previously.
Conclusions:
An external supply of compressed gas is the only reasonable solution to the need of firing
in a vacuum, and also to the potential future need of terrestrial self-powered fire. Additionally,
such a modification would allow semi-automatic fire since the gun as configured already
advances to a new chamber with each pull of the trigger.
Fire Underwater
This potential need presents the same limitations as the vacuum-firing case above. This is
because, though the gun would in this case be surrounded by a fluid that could be drawn into
the hand slide pump, the fluid is incompressible and therefore cannot be used as propellant in
the dart gun as configured. As a result, the immediate solution is the same as for the vacuum
case: replace the hand slide pump with a compressed gas cylinder and regulator. However, the
need to fire underwater presents another complication. In contrast to the nominal usage case in
which the working fluid is air, and drag on the dart is neglected in calculations, water as a flight
93
environment produces drag three orders of magnitude greater, which cannot be neglected.
Treating the dart as a flat-nosed cylinder and assuming a drag coefficient of 0.8, it is
functionally impossible for the dart to travel 6m before dropping 1m within Earth’s
gravitational field. Simulations were run to numerically integrate a dart’s position given initial
displacement and velocity, and it was found that even giving the dart a muzzle velocity of 2
km/s was insufficient to propel it beyond a meter. This is due to the relatively large crosssectional area to mass ratio, coupled with the immense drag that water exerts. Given that
imparting such a massive amount of kinetic energy (3 kJ, which is still insufficient) is clearly
impossible for the dart gun (as it would require a pressure of 700 MPa, far greater than any of
the S-S-P excesses denoted in Figure 5.25. Therefore, the only feasible solution is to modify
the darts so that they are in some way self-propelled. However, designing such a complicated
mechanism as a self-propelled underwater dart is beyond the scope of this paper. Realistically,
such a radical change in application would likely not benefit from the existing design,
optimized for firing darts in an atmosphere with negligible drag.
Increase Accuracy
Before the dart gun was disassembled, it was noted that successive shots fired from the
same position were not tightly grouped. While this is certainly a function of both the gun and
the individual darts, it is conceivable that a future need for the gun is for it to be made more
accurate. Historically, two approaches have been used to increase the accuracy of projectiles
fired from barrels: spin-stabilization provided by rifling and increased barrel length.
Approach 1:
The rifling approach has the benefit of allowing the existing rotary barrel to be modified,
thus requiring no new components. Consulting the S-S-P block attached to the rotary barrel in
the excess map of Figure 5.25 shows that the rotary barrel as designed has sufficient thickness
to contain 5.8 MPa of pressure, two orders of magnitude more than the pressure it is exposed
to as designed. Half of its 1.9mm thickness could be removed locally for rifling while still
leaving a maximum permissible pressure of 2.9 MPa, certainly adequate for any of the
scenarios discussed here.
94
However, this approach might have limited effectiveness for foam darts. This is because in
an actual firearm, the force of the explosion is sufficiently powerful to permanently deform the
relatively soft lead of the bullet in such a way that it conforms to the rifling in the barrel,
ensuring both a nearly gas-tight seal and a guaranteed interaction between the bullet and the
rifling (and a resulting spin-stabilization). In the case of a dart gun, foam darts would not be
sufficiently deformed by the relatively low pressures involved to mate well to the rifling. While
the limited frictional interaction could still be enough to make the darts spin, the larger issue
is that the propellant gas would very likely leak around the darts to some degree with a negative
effect on the dart’s range. Therefore, while possible, rifling the rotary barrel’s chambers would
likely not yield the desired results.
Approach 2:
Given the lack of promise of the first approach, lengthening the rotary barrel bears
exploration. A benefit of the current system design is that any rotary barrel with the same base
flange dimensions and chamber number/pattern may be swapped into the dart gun without
modification to any other components. Therefore, while lengthening the rotary barrel’s
chambers obviously requires a new rotary barrel, no other components would be affected. In
principle, the longer a barrel is, the more accurate the projectile becomes. Additionally, the
energy transfer from the charge pressure vessel to the dart is more complete with a longer
barrel as shown in Equation 4.16, due to the larger final volume. However, the work done by
friction on the projectile is also increased, and the air in the charge pressure vessel can only be
expanded so much before a negative pressure gradient is created relative to the atmosphere.
Therefore, experimental testing would need to be done with varying length barrels to determine
the optimal length. Regardless of the final length selected, this approach would work to both
increase accuracy and, to a lesser extent, range.
Conclusions:
If increased accuracy is desired, the only practical solution is to replace the rotary barrel
with one of increased length. The exact length would have to be determined by experimental
testing.
95
Hold More Darts
The dart gun as designed holds six darts in its rotary barrel. For this analysis, three different
evolutions were considered: holding 8, 12, and more than 12 darts. Two approaches were
considered: enlarging the rotary barrel and switching to a box magazine.
Approach 1:
The most direct solution to this need is to redesign the rotary barrel to accommodate more
darts. Examining the radius of the dart chamber pattern, denoted in the S-G-1 block attached
to the Body in Figure 5.25 and flowing to the rotary barrel (which is fixed for the barrel as a
function of the body geometry) reveals that a redesigned barrel could be created that holds 8
darts. The ratchet shaft would also have to be replaced, since it is keyed to a particular number
of darts by its number of positive stops, as shown by the F-S-C block in Figure 5.25. For 12
darts to be accommodated, the barrel, body, and ratchet shaft would have to be redesigned.
This would be non-trivial, since the body would have to be redesigned to diameter of the dart
chamber pattern, which entails repositioning the charge pressure vessel and floating pressure
seal with respect to the barrel’s axis of rotation. In principle, this could be done for an indefinite
number of darts. However, it is worth noting that the area and volume of the barrel are a
function of the square of the dart chamber pattern diameter, while the number of darts is
directly proportional to its diameter. This means that building a bigger barrel is a spatially
inefficient strategy to increase the number of darts held by the gun beyond small increases.
Approach 2:
A box magazine can hold any number of darts, limited only by the practicality of its
resulting size. Eight, twelve, or twenty darts could be held by such a magazine with the only
difference between the capacities being its resulting length. However, the question at hand is
whether the dart gun can be modified with a reasonable amount of effort to accept a box
magazine rather than a rotary barrel. Consulting the layout of the dart gun as shown in Figure
5.5, it becomes apparent that such a redesign could be performed by removing the barrel,
modifying the body to accept a box magazine horizontally, aligned with the floating pressure
seal, and building an additional assembly to fit between the existing ratchet advance shaft and
96
box magazine that translates the rotary motion of the ratchet advance shaft to a linear motion
of the box magazine. While a non-trivial modification, it could be done and would easily allow
a doubling, perhaps tripling of the number of darts held.
Conclusions:
Holding eight darts would require modification of only two components, the rotary barrel
and ratchet advance shaft. Converting the dart gun to use a box magazine is possible, but the
requisite effort suggests that it is only worthwhile if a substantial increase in dart capacity is
desired.
Step 3 Continued: Review Overlapping Future Needs
Based on the results of the preceding solutions for future needs, Table 5.3 shows the
possible interactions between various future needs. A bold X indicates a definite interaction,
and a regular X indicates a possible interaction. These are the areas that require review by
designers to further understand how multiple realized future needs could impact the system.
Farther
Heavier
Increase Accuracy
50% 100% 200% 50% 100% 200%
50%
X
X
X
X
100%
X
X
X
X
200%
X
X
X
X
50%
X
100%
X
200%
X
Hold more darts
50% 100% 200%
Vacuum/ Self
Powered
50%
100%
200%
Vacuum
/ Self
Power
Hold
more
Increase
Accuracy
Heavier Farther
Table 5.3: Overlapping Future Needs
97
The only two needs that are directly related, i.e. satisfying one will directly affect the ability
to satisfy the other, are firing darts farther and firing heavier darts. This is because both needs
relate to the amount of kinetic energy delivered to the darts, and therefore relate to the pressure
delivered to the dart. Examining the kinetic energy required for all of the possible combinations
of distance and mass increases, using the relationship KE = ½mv2, Figure 5.3, and Equation
5.3 reveals that if the spring in the floating pressure seal assembly is replaced to allow a
cracking pressure of 270 kPa (that provided by two pumps) the dart gun can evolve to fire
regular darts 200% farther (18m), 50% and 100% heavier darts 100% farther (12m), and 200%
heavier darts 50% farther (9m). If the slide pump is replaced with a compressed gas tank and
regulator and the spring is also replaced, 200% increases in both mass and range can be
achieved. Therefore, designers must consider how likely they believe it to be that both needs
will be realized, and if so, what levels of increase will be desired. A reasonable approach in
the design phase might be to replace the spring with a stiffer version that can contain up to 270
kPa, so that the dart gun only needs to be modified in service if significant increases in both
distance and dart mass are required.
A need for increased accuracy is noted to be possibly related to the ability to fire darts
farther and/or with greater mass because the best identified solution, increasing the length of
the barrel, could have side effects such as increased friction on the dart, thereby impacting the
amount of energy needed by the dart. However, without empirical testing data of a longer
barrel design it is impossible to know what impact this realized need could have on the system’s
ability to satisfy others, and so the possible interaction is left highlighted for designers to
consider if appropriate in the future.
On the other hand, the if the need to hold more darts is realized, it should not affect the
energy delivery systems within the dart gun because the modifications that it requires apply to
the geometry of the body and do not affect the components that deliver energy to the dart.
Likewise, altering the gun to fire in a vacuum (and consequently also to be self-powered) does
not negatively impact the ability to satisfy other future needs; indeed, adding a compressed gas
propellant system would allow 200% increases in both dart distance and mass by default, as
long as the floating pressure seal’s spring was also replaced.
98
Step 4: Judge Fitness/Review Excess Placement
Table 5.4: Summary of Dart Gun Stress Test Results
Need
Solution Strategy
Components
Replaced/Modified
Replace Spring
Floating pressure
assy spring
Comp Gas Tank
and Regulator
Floating pressure
assy spring, Hand
slide pump
Replace Spring
Floating pressure
assy spring
Fire Farther
Fire Heavier Darts
Fire in Vacuum/
Self Powered
Comp Gas Tank
and Regulator
Fire Underwater
N/A
Floating pressure
assy spring, Hand
slide pump
Floating pressure
assy spring, Hand
slide pump
N/A
Rifling
Rotary Barrel
Longer bore
Rotary barrel
Enlarge rotary
barrel
Rotary barrel
Box magazine
Rotary barrel,
Body
Comp Gas Tank
and Regulator
Increase Accuracy
Hold More Darts
Stress testing the dart gun revealed an unexpected conclusion: several potential future
needs can be partially or entirely addressed by replacing a single piece, the floating pressure
seal assembly’s spring, with a stiffer version. For an inexpensive consumer product, the dart
gun possesses substantial excess in all components that function as pressure vessels, and is
capable of responding to several varied potential future needs. The only need that presented an
insurmountable challenge was to fire underwater. However, this need is impossible to realize
for any consumer dart gun based on the results of the numerical simulations performed.
Component excesses in Figure 5.26 highlighted in red indicate where designers might
consider adding excess for the sake of future needs. Excesses highlighted in blue are possibly
99
superfluous based on the results of the stress test. These two sets of excesses are discussed in
the following subsections.
10 g
Charge
Pressure
26 mL
Vessel
S-S-P
5715 [kPa] 135
(5850)
135 kPa
State Parameters
System Mass: 420 g
S-G-3
S-S-P
S-S-P
Environment
F-E-H
[N]
1g
Float
25 kPa
Seal Assy
10 g
Check
135 kPa Valve/
Release
F-E-H
[N]
S-S-P
1265 [kPa] 135
(1400)
S-S-P
F-E-H
25 g
38 N
To
Environment
S-S-L
142 [N]
(180)
Slide
Grip
S-G-3
52 [mL]
(78)
26
S-G-1
0 [mm]
(45)
45
Body
135 kPa
S-S-P
865 [kPa]
(1000)
Flex
Tube
S-G-3
0 [mL]
(24)
24
135
F-E-H
S-S-P
S-G-1
S-S-P
S-G-3
50 g
20 g
24 mL
38 N
S-S-P
3265 [kPa] 135
(3400)
Slide
Pump
25 kPa
45 mm
Signal
Rotary
Barrel
F-S-C
15 g
15 N
Trigger/
Advance
Assy
25
270 g
38
5g
S-S-L
S-S-P
0 [kPa]
(25)
S-S-P
5775 [kPa]
(5800)
25
S-M-S
0 [darts]
(6)
6
To
Environment
To
Environment
15 g
F-S-C
60
-20/+120 [deg]
(40-180)
F-S-C
60°
Ratchet
Shaft
F-S-C
0 [deg]
(60±0)
60
Figure 5.26: Dart Gun Stress Test Conclusions
Potentially Inadequate Excesses
A clear result of the study is that the spring in the floating pressure seal should be replaced
with one with a stiffness of at least 1700 N/m (from the existing spring with stiffness 130 N/m).
The increased force between the seal and rotary barrel could potentially cause binding issues
due to increased static friction; however, the surfaces are already extremely smooth and a light,
100
long life lubricant or non-stick coating could be added to the base of the rotary barrel to address
any resulting problems from the added frictional force. This spring modification would allow
the gun to use all of the pressure generated by a single pump, and therefore to fire up to 14m
without any other modifications. Springs with higher compression rates could also be
considered, but at a minimum, embedding this excess would allow the gun to function to its
full potential in terms of range based on the current pump configuration.
Another change that could be made in the design phase is to increase the volume available
to the tube of the slide pump by 15 mL from the current 37 mL (indicated in the S-G-3 excess
block attached to the Body). This could be done by lengthening the area of the body allocated
to the hand slide pump, or by expanding its cross-sectional area. Embedding this excess would
allow for a higher charge pressure from a single pump if the hand slide pump were later
replaced with a larger version. This would presumably increase value to the customer by not
requiring multiple pumps of the slide to reach higher pressures when greater range or projectile
mass is desired.
These are the areas that adding epistemic excess should be considered by the designers to
reduce the possibility of bottlenecks. Whether or not these recommendations are actionable
depends on how likely the designer finds the realization of the particular future need scenarios
that drove them. This knowledge might come from various sources, such as past experience
with similar products, knowledge of aftermarket modification by customers, or by feedback
obtained directly from customers.
Potentially Superfluous Excesses
The pressure vessels present in the design – the slide pump, charge pressure vessel, and the
chambers of the rotary barrel – all possess excess an order of magnitude greater than what is
required of them. Initially, it might appear that these are inefficient design choices that might
benefit from paring back the available excess in these components. In context, the check valve
assembly limits the system pressure to about 0.5 MPa while the flex tubing can tolerate 1 MPa,
but the slide pump can contain 3.4 MPa safely and is the weakest pressure vessel. However, it
is likely that the presence of these excesses are side effects of other factors. Considering that
the plastic is not particularly thick (the chamber walls in the rotary barrel are thickest and still
101
less than 2mm) it is likely that manufacturability considerations were the primary driver behind
the wall thicknesses. Further, the fact that ABS plastic is an inexpensive material to
manufacture from means that any savings by removing some of the excess would be minimal
at best. Therefore, it is likely best to leave the design of the pressure vessels as-is because doing
so incurs little if any value penalty.
The stress test approach developed in this chapter assists designers in finding component
level excesses within a system that unduly limit the ability of the system to change, compared
to the limits imposed by the remainder of the component level excesses. Moreover, the results
of the approach suggest values of excess to embed to rectify these bottlenecks within the
system. The approach does not require any specific information regarding potential future
needs, but if it is available to designers the approach can make use of it to guide the changes
considered for the system, thereby improving the quality and applicability of the approach’s
results. The next chapter presents the conclusions of the works demonstrated in this thesis.
102
Conclusions and Future Work
This chapter returns the discussion to the original research questions. The works that
addressed them, the excess mapping method and stress test approach, are summarized and their
contributions are reviewed. Finally, opportunities for future work are considered.
Research Question 1: How can excesses pertinent to service phase evolution be identified
in a general system?
The work detailed in Chapter 4 defines a framework with which to map excess in an
engineered system via a combination of features sourced from existing methodologies: HDDSM’s, functional diagrams with their associated flow set, and flow diagrams. The process of
developing this map reveals the relationships between components in which excesses are
present that can affect the ability of the system to change. The fusion of techniques from the
methods in the literature allows the mapping of excess relationships between components in a
system based on customer needs information coupled with architectural knowledge from
embodiment design. These component level excesses are relatable to the top level system
needs, meaning that designers can see how component level excesses affect the ability of the
system as a whole to change. The produced method uses block diagrams coupled with
quantified flows, and defines two component-level flows: functional and compatibility.
Current system objectives and their consequent needs drive the selection of components for
inclusion. Inter-component relationships are labeled according to the excess basis that
identifies excesses based on their Class, Category, and Type. Overall, the excess basis
represents an extension to the extant functional modeling flow set to encompass all possible
types of excess relationships within a system. It accomplishes this by adding a Storage class,
which addresses that all flows may be stored in a system and that geometric and structural
excess considerations may also be treated as a form of storage. This basis may be further
extended in future if designers desire finer description of excesses.
As noted in Chapter 4, the excess mapping method’s application to complex systems would
differ only in that the map would be constructed in pieces, for each of the subsystems present
in each level of assembly, so that a multilevel excess map is the final product. Unlike dynamical
modeling methods which can scale poorly to complex systems due to un-modeled
103
relationships, the results of the excess mapping method are insensitive to scale. This is because
while dynamical models must make simplifying assumptions, disregarding smaller effects that
may amass to considerable error, excess relationships are well characterized and defined with
a high degree of confidence. This is largely because excess relationships are simpler,
concerning only the bounds on capabilities of a system at steady-state.
Using an excess map, system information available as part of the embodiment design phase
can be selectively transferred to a conceptual-phase design in terms of future evolutions. In
general, the maps generated by this method offer insight into both system excesses and the
governing flow relationships between system components, thereby allowing designers to
determine if a system is likely capable of responding to future needs. The excess mapping
method of Chapter 4 presents an improvement over other methods available in the design
literature because no other method presents, in a quantified manner, the properties of
components or subsystems (excesses) within a design that will enable it to meet future needs.
Research Question 2: How can designers relate the identified excesses to the system’s
ability to meet future needs?
The stress test approach presented in Chapter 5 aids the process of judging the fitness of a
design for potential future needs. An excess map is first generated for the system that distills
the system to its inter-component relationships critical to satisfying the customer needs-driven
requirements list. The excess map allows designers to rapidly determine the extent of system
changes that a particular evolution will require. Once the preliminary work of creating an
excess map is completed, the stress test approach generates a set of future need scenarios to
evaluate the system against. Ideally, external information sources, such as marketing data or
historical information concerning similar systems, are available to designers to guide the future
needs considered. However, if no such external information is available the approach can also
generate a set of future needs by considering increases to the high level specifications driving
the system. Further, multiple degrees of severity of future needs or change to specifications are
considered to increase understanding of the current bounds of system evolvability. Evolutions
to satisfy each future need are found using the designer’s knowledge of the system architecture,
using multiple paths if possible for each future need to increase the insight into the system’s
104
ability to evolve. Generally, each evolution requires either modification or replacement of
some component(s) in the system architecture. The extent of the changes depend on the
excesses present within the components, which can be quickly referenced by use of the excess
map. Once the set of evolutions in response to potential future needs is found, areas of overlap
are identified and the system’s response to simultaneous future needs is explored where
appropriate. Shortcomings that are identified in the available excess can then be used to direct
where epistemic excess is embedded within the system, thereby reducing bottlenecks within a
system that limit the ability to change. Further, potentially superfluous excess can be identified
which offers the opportunity to improve system value. Beyond showing where excesses can
be added to or removed from a system, the stress test approach ultimately aids in validating
the system against potential future stakeholder needs, which helps to ensure stakeholder value.
Opportunities for Future Work
A possible direction of future research is the development of metrics to analytically
describe the excess present in a system, and to relate excesses in individual components to
system objectives. It is expected that continued development of excess modeling will result in
the ultimate ability to determine the gains per unit excess required by the prior work of [5],
and hence the capacity to measure the evolvability of a system. Another application of the
method to systems of significant complexity is the development of a software-based GUI
which would allow for multiple-level representations of a system, i.e. where a primary block
representing a subsystem may be opened to reveal the constituent components with specifically
mapped excess relationships.
Other opportunities for future work include testing the effectiveness of the stress test
approach on a clean sheet design problem, and exploring how the approach scales to more
complex systems. Another possible avenue of research is to modify the excess mapping
method so that it is less dependent on the initial solution strategy embodied in the architecture,
and thereby capable of offering more useful information when considering solution strategies
that are a significant departure from the original.
105
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110
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111
APPENDIX
112
The following pages contain full-size excess maps for the heat gun, coffee maker, string
trimmer, and toy dart gun.
113
F-E-P
9 [mm H 20]
(12)
70 g
0.2 A
100 cm 3
1
State
Parameters
2
F-E-E
Fan
F-E-P
F-M-G
2 [g/s]
(4)
System Mass: 380 g
2
System Power: 1.2 kW
S-G-3
S-G-3
140 [cm3]
(240)
F-E-P
F-M-G
100
50 g
1 mm H20
Environment
F-S-C
[user]
F-E-T
60 [K]
(380)
320
S-G-2
5 [cm2]
(16)
11
F-E-T
S-G-2
320 K
11 cm 2
F-E-E
[A]
F-E-H
[user]
Case
4N
S-G-3
7 [cm3]
(15)
F-E-H
S-G-2
0 [cm2]
(4)
F-E-E
F-S-C
810
S-G-3
0 [cm3]
(75)
75
F-E-T
160 [K]
(970)
810
F-E-E
9.8 [A]
(10)
0.2
To
Environment
Nozzle
810 K
160 g
2 mm H20
F-E-T
860 [K]
(1670)
F-E-T
S-G-3
70 g
8
75 cm 3
2 g/s
10 A
Heating
Coils
S-G-3
4
F-E-E
10A
Cord
F-E-E
4 [A]
(14)
S-G-2
8 cm 3
30 g
1 cm 2
10
Switch
Off/Low/High
F-E-E
F-E-E
3 [A]
(13)
10
10 A
Heat Gun
114
S-G-3
0 [L]
(1.9)
S-G-3
1.9 L
1.9
S-M-L
0 [L]
(1.8)
1.8 L
S-M-L
Carafe
363 K
Body
1.8
S-G-2
0 [cm2]
(110)
110
S-G-2
F-E-T
110 cm 2
S-G-2
F-E-T
363
XXX K
363 K
F-E-E
[A]
S-G-3
0 [cm3]
(860)
S-G-2
0 [cm2]
(2)
F-E-T
1450 [K]
(1813)
Hot
Plate
S-G-2
0 [cm2]
(87)
363
F-M-L
12.4 [mL/sec] 2.6
(15)
Environment
To
Environment
87 cm 2
S-M-L
0.2 [L]
(2.0)
F-E-T
45 [K]
(408)
1.8
363
87
F-E-T
F-M-L
F-E-T
570 [K]
(933)
363
F-M-L
0 [mL/sec]
(2.6)
2.6
2.6 mL/sec
Heater
860
7.5 A
F-E-E
2
F-M-L
S-G-2
S-G-3
F-E-E
2.5 [A]
(10)
2 cm 2
F-E-E
Switch
7.5 A
7.5
2.6 mL/sec
860 cm
Cord
F-E-E
5.5 [A]
(14)
Basket
F-M-L
14.1 [mL/sec] 2.6
(16.7)
To
Environment
State
Parameters
F-E-E
7.5 A
3
7.5
System Power: 900 W
Coffee Maker
115
F-E-T
State Parameters
Environment
S-G-1
F-E-H
F-S-C
F-E-H
System Mass
S-G-3
Case
S-G-3
S-G-3
S-G-2
F-E-T
S-G-2
S-G-2
S-G-3
To
Environment
F-E-M
S-G-3
F-E-H
F-E-M
F-E-M
S-G-2
Starter
Cord
Clutch
F-E-M
F-S-C
F-E-M
Motor
S-G-2
S-S-L
S-G-2
F-S-C
S-G-2
S-G-3
F-E-H
S-G-1
S-S-L
F-M-M
E-stop
S-M-L
S-S-L
F-S-C
Fuel
Tank
S-G-2
Environment
S-S-L
F-S-C
Grip
F-M-L
F-M-G
F-M-G
Trigger
S-G-3
F-M-L
S-G-2
F-S-C
S-G-3
S-G-2
F-S-C
To
Environment
F-S-C
F-S-C
F-S-C
Carburetor
F-M-M
S-G-2
String Trimmer Engine
116
Environment
F-E-H
F-E-M
State Parameters
System Mass
Overall Length
S-S-L
To
Environment
F-E-M
To
Environment
F-E-M
F-E-H
Handle
S-S-L
S-S-L
Shaft
S-G-1
S-G-1
To
Environment
String Trimmer Transmission
117
Environment
F-E-M
State Parameters
System Mass
S-S-L
Overall Length
S-G-1
F-E-M
Shield
S-G-1
To
Environment
S-S-L
S-G-1
Shaft
F-E-M
F-E-M
To
Environment
S-G-3
To
Environment
S-G-1
To
Environment
S-G-1
F-E-M
Head
String Trimmer Attachment
118
Environment
F-E-H
F-S-C
F-S-C
F-E-H
F-S-C
F-M-G
F-E-H
State Parameters
System Mass
Interface Power
Overall Length
F-S-C
F-M-G
F-E-H
F-E-H
F-S-C
To
Environment
S-M-L
F-S-C
Engine
F-E-M
S-G-1
F-E-M
S-G-1
To
Environment
F-E-M
To
Environment
S-G-3
To
Environment
S-G-1
To
Environment
S-S-L
S-S-L
F-E-H
Transmission
F-E-M
F-E-M
Attachment
S-G-1
String Trimmer Composite
119
10 g
Charge
Pressure
26 mL
Vessel
S-S-P
5715 [kPa] 135
(5850)
135 kPa
State Parameters
System Mass: 420 g
S-G-3
S-S-P
S-S-P
Environment
F-E-H
[N]
1g
Float
Seal Assy
10 g
Check
135 kPa Valve/
Release
F-E-H
[N]
25 kPa
S-S-P
1265 [kPa] 135
(1400)
S-S-P
F-E-H
25 g
38 N
To
Environment
S-S-L
142 [N]
(180)
Slide
Grip
S-G-3
52 [mL]
(78)
26
S-G-1
0 [mm]
(45)
45
S-G-3
0 [mL]
(24)
Body
135 kPa
S-S-P
865 [kPa]
(1000)
Flex
Tube
24
135
F-E-H
S-S-P
S-G-1
S-S-P
S-G-3
50 g
20 g
24 mL
38 N
S-S-P
3265 [kPa] 135
(3400)
Slide
Pump
25 kPa
45 mm
Signal
Rotary
Barrel
F-S-C
15 g
15 N
Trigger/
Advance
Assy
25
270 g
38
5g
S-S-L
S-S-P
0 [kPa]
(25)
S-S-P
5775 [kPa]
(5800)
25
S-M-S
0 [darts]
(6)
6
To
Environment
To
Environment
15 g
F-S-C
60
-20/+120 [deg]
(40-180)
F-S-C
60°
Ratchet
Shaft
F-S-C
0 [deg]
(60±0)
60
Dart Gun
120
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