A Performance Analysis System for the Sport of Bowling

The Pennsylvania State University
The Graduate School
Capital College
A PERFORMANCE ANALYSIS SYSTEM FOR
THE
SPORT OF BOWLING
A Master's Project and Paper in Computer Science
by
Donald J. Hake II
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
April 2002
©2002 Donald J. Hake II

ABSTRACT
Current technology offers precious little to the serious bowler in search of ways to
analyze and improve their 1 game. All existing methods acquire some type of "external"
view of the ball (from the bowler's perspective) as it rolls down the lane. The goal of
such systems is to quantify the various factors (release velocity, rotation rate, ball loft
distance, etc.) that contribute to the ball's reaction and, ultimately, to the bowler's
performance. However, not only are these externally-based methods time-consuming,
inconvenient, and/or expensive to install and use, but they each have their own inherent
limitations resulting from their external view of the ball.
This paper presents the results of research and preliminary development for a system that
is based on capturing an "internal" view (from the bowling ball's perspective) of the
velocity, spin, and loft imparted to the ball during the bowler's delivery, and the
subsequent reaction of the ball on its journey from the foul line to the pins.
The system described herein is comprised of several components: a small,
microprocessor-based sensor module that resides in the ball and collects and records
sensor data; an external wireless communication module for uploading the raw data from
the sensor module; and a PC or PDA-based software application that stores, analyzes, and
presents that data in a fashion useful to the bowler.
Such a personal bowling performance assessment and analysis system will help fill the
void that currently exists between the limited number of techniques available for
evaluating and improving the bowler's overall skill set, consistency of execution, and
ability to accurately assess lane conditions.
1 In the absence of a standard set of gender-neutral pronouns, the author uses "they", "them", and "their" as
the gender-neutral forms of "s/he", "him/her", and "his/her" throughout the document.

TABLE OF CONTENTS
Section I: Introduction, Background, and Motivation.................................................................1
1.1 Statement of the Problem ................................................................................................1
1.2 Introduction to the Physics of Bowling...........................................................................3
1.3 Scope of the Paper/Project ..............................................................................................4
1.3.1 Investigative Feasibility Phase ............................................................................4
1.3.2 Product Development Phase................................................................................5
1.4 Overview of the Feasibility Phase...................................................................................5
Section II: Collecting the Data - The SMARTDOT Module........................................................7
2.1 Design Basis....................................................................................................................7
2.2.1 Ease of Use..........................................................................................................9
2.2.2 Size, Weight, and Impact on the Balance of the Ball..........................................9
2.2.3 Cost....................................................................................................................10
2.2.4 Power Consumption ..........................................................................................10
2.2.5 Convenience of Installation and Removal.........................................................10
2.3 Sensing Requirements ...................................................................................................11
2.3.1 Sensing Rotation of the Ball (Angular Velocity) ..............................................11
2.3.2 Sensing Release, Lane Impact, and Pin Impact.................................................12
2.3.3 Measuring Time and Recording Data ...............................................................12
2.3.4 Communications................................................................................................14
2.4 Capabilities....................................................................................................................14
2.4.1 Ambient Light Sensor .......................................................................................15
2.4.2 Pressure/Impact Sensor .....................................................................................15
2.4.4 Clock .................................................................................................................15
2.5 Hardware Implementation.............................................................................................16
2.5.1 Hardware Configuration....................................................................................16
2.5.2 Hardware Operation Overview .........................................................................18
2.6 Hardware/Software Interaction Design Considerations................................................19
2.6.1 Microprocessor Clock Frequency .....................................................................19
2.6.2 Sampling Rate ...................................................................................................19
2.6.3 Baud Rate ..........................................................................................................21
2.7 Embedded Software Design and Operation ..................................................................21
2.7.1 Software Design Considerations .......................................................................21
2.7.2 Start-Up .............................................................................................................24
2.7.3 Pre-Sampling.....................................................................................................24
2.7.4 Waveform Discrimination and Validation ........................................................24
2.7.5 The Ball is Rolling ............................................................................................25
2.7.6 Sampling Modes................................................................................................25
2.7.7 Shutdown...........................................................................................................25
2.7.8 Communication with the COMM Wand ...........................................................26
2.7.9 Communication Protocol...................................................................................26
2.7.10 Commands.........................................................................................................27
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2.8 Performance...................................................................................................................28
2.8.1 Detecting Release..............................................................................................29
2.8.1 Detecting Release..............................................................................................29
2.8.2 Detecting Impacts..............................................................................................29
2.8.3 Waveform Discrimination and Validation ........................................................30
2.8.4 Waveform Shape ...............................................................................................32
2.8.5 Communications................................................................................................33
2.8.6 Battery Life........................................................................................................33
2.9 Future Work ..................................................................................................................34
2.9.1 Microprocessor..................................................................................................34
2.9.2 Communications................................................................................................35
2.9.3 Sample Memory and Multiple Waveforms.......................................................35
2.9.4 Data Compression .............................................................................................36
2.9.5 Module Training................................................................................................38
2.9.6 Adjustable Sampling Parameters.......................................................................38
2.10 Summary .......................................................................................................................39
Section III: Analyzing the Data - The MASTER Application ...................................................40
3.1 Raw Data Analysis ........................................................................................................40
3.1.1 The "Ideal" Waveform ......................................................................................40
3.1.2 The "Real" Waveform .......................................................................................41
3.2 Filtering the Raw Data ..................................................................................................44
3.3 Finding Revolutions and Angular Velocity...................................................................46
3.4 Linear Velocity, Distance, and Coefficient of Friction.................................................50
3.4.1 Finding the Linear Velocity of the Ball.............................................................52
3.4.2 Finding the Distance from the Foul Line ..........................................................53
3.4.3 Finding the Coefficient of Friction....................................................................54
3.5 Assumptions and Error Analysis...................................................................................55
3.5.1 Distance.............................................................................................................55
3.5.2 Time...................................................................................................................56
3.5.3 External Forces and Friction .............................................................................57
3.6 Implementation, Performance, and Accuracy ...............................................................58
3.6.1 Implementation and Performance .....................................................................59
3.6.2 Accuracy............................................................................................................61
3.6.2 Accuracy............................................................................................................62
3.6.3 The "Perfect" Game to Analyze ........................................................................63
3.7 Future Work ..................................................................................................................64
3.7.1 Algorithms.........................................................................................................64
3.7.2 End-User MASTER Software ............................................................................65
3.8 Summary - MASTER Analysis ......................................................................................66
Bibliography..............................................................................................................................67
Appendix A - SMARTDOT Module Embedded Software Flowcharts................................... A-1
Appendix B - SMARTDOT Module Source Code...................................................................B-1
Appendix C - SMARTDOT Module Command Timing Diagrams .........................................C-1
Appendix D - MASTER "Analysis" Calculations Source Code.............................................. D-1
Appendix E - 300 Game MASTER Screen Captures...............................................................E-1
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LIST OF FIGURES
Figure 2-1 SMARTDOT Module Cut-Away View .............................................................8
Figure 2-2a Lane Layout and Overhead Lighting ..............................................................13
Figure 2-2b Ambient Light Waveform...............................................................................13
Figure 2-3 SMARTDOT Module Block Diagram .............................................................17
Figure 2-4 SMARTDOT Module Software Architecture ..................................................22
Figure 2-5 EEPROM Memory Map ................................................................................23
Figure 2-6 MASTER "Raw Data" Screen Capture ...........................................................28
Figure 2-7 Raw Data Release Region (400 ms) ...............................................................29
Figure 2-8 Raw Data Impact Region (800 ms) ................................................................30
Figure 2-9 Raw Data Release Region (800 ms) ...............................................................31
Figure 2-10 10-Pin Shot, "Raw Data" Screen Capture ......................................................31
Figure 2-11 Waveform Shape, Impact Region (800 ms) ...................................................32
Figure 2-12 Data Compression Record Format..................................................................37
Figure 2-13 Data Compression Translation Table .............................................................38
Figure 3-1 MASTER "Raw Data" Screen Capture ...........................................................42
Figure 3-2 Raw Data Release Region (800 ms) ...............................................................43
Figure 3-3 Raw Data in Impact Region (800 ms).............................................................43
Figure 3-4 MASTER "Spectrum" Screen Capture ............................................................44
Figure 3-5 MASTER "Waveform" Screen Capture ...........................................................46
Figure 3-6 Maxima and Minima Location Interpolation .................................................48
Figure 3-7 MASTER "Analysis" Screen Capture ..............................................................49
Figure 3-8 MASTER Analysis Calculations Data Flow Diagram ....................................58
Figure 3-9 Effects of Roll Out, "Analysis" Screen Capture .............................................59
Figure 3-10 Pin Deck Phase Shift, Impact Region (800 ms) .............................................60
Figure 3-11 Effects of Phase Shift, "Analysis" Screen Captures .......................................61
Figure 3-12 300 Game Analysis Summary ........................................................................63
Figure A-1a Start-Up Task Flowchart ..............................................................................A-2
Figure A-1b Pre-Sampling Task Flowchart ......................................................................A-2
Figure A-2 Light Sample ISR Flowchart ........................................................................A-3
Figure A-3 Sampling Task Flowchart.............................................................................A-4
Figure A-4 Discrimination Task Flowchart ....................................................................A-5
Figure A-5 Communication Task Flowchart ..................................................................A-6
Figure A-6 Wand Detection ISR Flowchart ...................................................................A-7
Figure A-7 UART Receive Task Flowchart ...................................................................A-8
Figure A-8 Bit Sample ISR Flowchart............................................................................A-9
Figure A-9 Receive Time Out ISR Flowchart ................................................................A-9
Figure A-10 Shutdown Task Flowchart ..........................................................................A-10
Figure C-1 Upload Command Timing Diagram .............................................................C-2
Figure C-2 Mode Command Timing Diagram ...............................................................C-3
Figure C-3 Configuration Command Timing Diagram ..................................................C-4
Figure E-1 300 Game - "Raw Data" Screen Captures ....................................................E-2
Figure E-2 300 Game - "Spectrum" Screen Captures .....................................................E-4
Figure E-3 300 Game - "Analysis" Screen Captures.......................................................E-6
v

ACKNOWLEDGEMENTS
The idea for the SMARTDOT system evolved from a conversation I had with some fellow
teammates on the way back from the Pennsylvania State Bowling Championships in
Johnstown in May of 1988. I'd like to thank Mike Wolfrom and Dave Zelger for raising the
issue of how to accurately measure the rotational rate of a bowling ball. It has been through
seeking an answer to that seemingly simple question that this body of work has taken shape.
In 1988, the technology was simply not available to implement the various solutions that came
to mind. In the ensuing four years, the question stayed with me, and the technology
eventually caught up. I began developing the first SMARTDOT module prototype in May of
1992, and SMARTDOT captured its first waveform on April 11, 1993. I designed and built
that first prototype without prior knowledge of the nature of the waveform it was designed to
capture. Since then, numerous iterations of the module's hardware and embedded software
have been required to get the module to the point where it truly performs its function in a
"transparent" fashion.
Soon after the success of the initial prototype, I placed the project on the back burner as I
became engaged, and then married, and then purchased a house, and eventually assumed other
career obligations that kept me from returning to the pursuit of this research. It was with my
return to Penn State in June of 1998 in my quest for this Master's Degree in Computer Science
at Penn State Harrisburg that I decided to dust off SMARTDOT and get back to work on it.
I must thank Dr. Thang Bui, Dr. Timothy Wahls, and Dr. Linda Null for their collective
exuberance and enthusiasm in teaching. Without their obvious interest in the success and
welfare of their students, I would not have been drawn to Penn State Harrisburg, nor as driven
to achieve all that I have within their program. I have been a Penn State student, in one form
or another, at three different campuses, for more than a quarter of a century, and their
department is the finest that I have known.
Thanks again to Dr. Null for not only serving as my advisor and for appreciating my sense of
humor, but also for her willingness to step outside of her normal areas of expertise and into
"my" world of 8-bit embedded software. Thanks also to Dr. Seth Wolpert and Dr. Pavel
Naumov for reviewing this manuscript and serving on the thesis committee.
I must thank my friends and family for their collective support, understanding, and tolerance
throughout the years that I have been immersed in this Master's program and obsessed with
this project. I promise to them, in the near future, that I will emerge from my office and be
able to focus on issues other than SMARTDOT and the current status of my Master's degree.
Lastly, special praise must go to my wife Sandy, who has tolerated not only my obsession
with this project over the decade of its existence, but has also been consistently supportive of
my efforts towards its development. She has been there through every major milestone. In
addition, over the past four years, her support of my pursuit of this degree has been steadfast
and unwavering, even while I was taking six and nine credits a semester, and especially as I've
spent untold hours at my computer composing this paper. She has brought me breakfast,
lunch, and dinner at my desk so that I could continue working, and has never complained
about the time she has lost to this passion of mine. Without her support and her
encouragement, this project, this paper, and this degree would not have been possible.
vi

SECTION I: INTRODUCTION, BACKGROUND, AND MOTIVATION
1.1 STATEMENT OF THE PROBLEM
Bowling is often considered a game of accuracy, but it is actually a game of errors. The
goal of any experienced bowler is to find the optimal combination of style, equipment,
and lane adjustments that creates the widest margin of error while still allowing the
bowler to consistently deliver the ball to the pocket with sufficient force, angle, and
"action" to generate strikes. Success with this strategy requires a combination of factors:
the bowler's natural talent and ability, refined by a generous amount of coaching and
practice; experience with "reading" lane conditions and making adjustments to the
inevitable changes in those conditions; and the selection and use of the proper ball(s).
Bowling balls are available in a variety of weights, balances, hardnesses, and surfaces.
Those four variables combine to determine when and how much the ball hooks, and how
hard it hits the pins. The bowler selects a bowling ball based on his or her bowling style
and the current lane "condition", which is created by the distribution of oil on the lanes.
There is a great deal of friction generated between the ball and the lane surface as the ball
rolls down the lane, at a velocity that can approach 20 mph, with a rotational rate that
regularly exceeds 300 rpms. To protect the finish of the lane, special lane-dressing oil is
regularly applied to the first 30 to 40 feet of the lane. The oil can also be applied with a
varying density across and down the lane to affect the "playability" of the lane, making it
easier or more difficult for the ball to reach the strike pocket. The repeated action of
bowling balls rolling down the lane redistributes the oil over time, changing the oil
pattern as a bowling match progresses. The effects of that change can be quite
noticeable, sudden, and dramatic [13].
Of primary concern to all bowlers is quickly and correctly adjusting to the inevitable
changes in the oil pattern over the course of a bowling match. The bowling ball is the
bowler's "oil sensor" for determining where the lane oil is (and isn't), as well as where the
oil is "going". Based solely on observing the ball's reaction to the lane, the bowler
adjusts to the ever-changing lane condition by drawing upon past experience with the
results of various adjustments made under similar circumstances. These adjustments
usually involve lateral changes in the starting location on the approach and/or the target
on the lane, an increase or decrease in the speed of the ball, and/or a switch to a ball that
hooks more, or less, or sooner, or later, etc. The bowler may also opt to change the
amount of turn, lift, and/or spin they apply to the ball during release, with the intention of
changing the amount the ball hooks or curves as it rolls down the lane.
If the bowler does not release the ball with consistent amounts of speed, loft, lift, and turn
(the variables that directly affect the ball's reaction with the lane), it is particularly
difficult for them to accurately assess the condition of the lanes, let alone how that
condition is changing. It has always been difficult to accurately quantify a bowler's
relative level of consistency. It has been equally difficult to quantify and compare the
relative performance of different types of bowling balls.
1

Historically, the only technique readily available has been for the bowler to videotape
their delivery and the subsequent reaction and path of the ball, followed by a slow and
tedious frame-by-frame analysis to determine the release, hook, and roll characteristics of
the ball. However, videotape does not allow for the direct and accurate measurement of
ball speed, ball loft, rotation rate, and revolutions. Videotape also does not lend itself to
side-by-side, frame-by-frame comparison of multiple shots.
The ABC (American Bowling Congress) has recently deployed CATS (Computer Aided
Tracking System). CATS relies heavily on instrumenting the lane with numerous
position and velocity sensors in conjunction with high-speed video analysis. However,
this system is only available on a handful of lanes around the country (ABC headquarters
in Milwaukee and the National Bowling Stadium in Reno), along with several portable
installations [12].
Brunswick Corporation developed a patented system called BowlerVision ® , which is
capable of providing some of the same analyses as CATS, combining a system of built-in
sensors with high-speed video capture. However, BowlerVision ® is only available on a
limited basis around the country, is expensive to use, and is not portable [2,3].
There are several recent patents that describe various generic methods for detecting the
speed, spin, and/or curve of a projectile, missile, or ball. All of those patents, however,
involve one or more shortcomings in realizing truly practical and cost-effective
implementations as commercially viable products with regard to bowling.
US Patent 5,526,326 (June 11, 1996) details a "Speed Indicating Ball", which measures
the time of flight of a ball using a contact switch for release (throw) and a piezoelectric
switch for impact (catch). The device is designed for use in a baseball, and requires the
thrower to hold down a button until the ball is released. The device calculates release
velocity through time-of flight calculations over a predetermined distance (pitcher's
mound to home plate), and presents the results on a built-in display [4]. Due to the
method of release detection, the thrower must alter their normal grip when throwing the
ball. The weight of the device with respect to the ball affects the balance of the ball, thus
impacting the nature in which it curves. Also, due to the fragile nature of the built-in
display, the device cannot be used in actual competition (a baseball game).
US Patent 5,761,096 (June 2, 1998) describes a "Speed-sensing projectile" that uses an
interior mechanical inertial switch to detect release (requiring no external button), and the
same inertial switch to detect the cessation of movement. This device also has a built-in
display that presents the speed of the ball based on time-of-flight information over a fixed
distance, and was originally intended for use in a baseball [5]. This device has a similar
impact on the balance of the ball as the "Speed indicating Ball", and also is precluded
from use in actual competition.
US Patent 6,151,563 (November 21, 2000) presents the most comprehensive of devices
with regard to bowling. It describes a device that is capable of measuring the speed, spin
rate, and curve of a moving object, and specifically mentions applicability to both
baseball and bowling. The device uses magnetic field sensors to detect the rotation of the
ball within the earth's magnetic field. It supplements these readings with input from
multiple accelerometers that indicate the inertial forces acting on the ball. The device has
no direct display; instead it transmits the collected data in real-time to an external
2

eceiver that stores, processes, and displays the data for the user [6]. Although
comprehensive in nature, the device is expensive to implement and must be installed in
the center of the ball at the time of its manufacture.
As of this writing, no devices of the nature described in the patent literature have been
brought to market with regards to bowling. Between the inconvenience, expense, and
narrow availability of external (instrumented lane) solutions, and the dearth of internal
solutions, it remains particularly difficult for a bowler to accurately and adequately assess
the various impacts that changes in bowling style and bowling equipment have on their
game. Without such timely and consistent feedback on changes in wrist and hand
position, arm swing, stance, and grip, as well as changes in equipment (ball type, weight,
balance, and/or surface), the bowler generally participates in a guessing game when
assessing the effectiveness and usefulness of any of these considerations.
The information presented in this paper has been gathered with the intention of
developing an inexpensive, portable, user installable and replaceable performance
analysis system geared towards the individual bowler. The system captures, quantifies,
and analyzes the impetus the bowler applies to the ball, as well as the subsequent
interaction of the ball with the lane surface from the point of release to the point of
impact with the pins. This system is hereafter referred to as SMARTDOT.
The SMARTDOT system consists of the following components: an in-situ sensor module
(the SMARTDOT module) that resides in the ball and collects sensor data; a wireless
communication link (the COMM wand); and a PDA or PC-hosted MASTER software
application that uploads, archives, analyzes, and displays the data captured by the in-situ
sensor module.
1.2 INTRODUCTION TO THE PHYSICS OF BOWLING
The only force of any significance that acts upon a bowling ball after the ball is released
is the force due to friction generated between the ball and the lane (this force varies a
great deal due to the variations in oil distribution on the lane). A bowler invariably
releases a ball at an initial linear velocity greater than that which would result from the
ball's initial angular velocity. In other words, the distance the ball travels during one
complete revolution of the ball is greater than the circumference of the ball (the ball is
skidding or sliding). The bowler also imparts an axis of rotation to the ball that is tilted
or turned from normal, which is intended to make the ball hook towards the pocket. It is
the interaction of the linear and angular velocities with the frictional force acting between
the ball and the lane that causes the ball to hook.
As the ball travels down the lane, the frictional force also causes the ball to slow down.
As long as the ball is skidding, friction acts to transfer some of the ball's linear
momentum into angular momentum, decreasing the linear velocity while increasing the
angular velocity. A small (but not insignificant) percentage of the ball's linear
momentum is also lost due to the heat, noise, and vibration generated as the surfaces of
the ball and the lane rub against each other. If the linear and angular velocities resolve
themselves completely, the ball is no longer sliding (it has rolled out), and the frictional
force now causes both the angular and linear velocities of the ball to decrease in direct
proportion to each other [9,12,13].
3

By measuring the time between release and impact, and noting the duration of each
revolution of the bowling ball, it is possible to derive the angular velocity of the ball for
each revolution, and the energy necessary to induce this change in angular velocity. The
average linear velocity of the ball and the changes in the ball's angular velocity during the
course of the shot can then be combined with certain assumptions regarding energy
conservation and friction to derive the linear velocity and longitudinal location of the ball
at any instant. Using the same criteria, it is also possible to derive the varying frictional
force that acts between the ball and the lane. Section III gives a formal presentation of
the assumptions, physics, and mathematics that are used to extract this information from
the SMARTDOT sensor data.
1.3 SCOPE OF THE PAPER/PROJECT
The overall project development breaks down into two distinct phases: an investigative
feasibility phase and a product development phase. This paper presents the results of the
feasibility phase.
1.3.1 Investigative Feasibility Phase
The feasibility phase has focused on developing working prototypes of each component
of the system - the in-situ SMARTDOT sensor module, the wireless communications link,
and a PC-based data analysis tool, called the MASTER. The major tasks have been:
• Building a working prototype of the SMARTDOT module that conforms to all of
the physical constraints the in-situ sensor module is required to meet - these
constraints are presented in detail later in the paper. This task also determined the
extent to which adequate embedded software could be developed that fit within
the constraints of the embedded microprocessor's resources while still performing
all of the tasks essential to the success of the system. The working prototype
serves as proof-of-concept for the in-situ sensor module, while it simultaneously
has served as the data acquisition platform for characterizing the response of the
on-board sensors to the ambient conditions they sense.
• Building the COMM wand - a prototype wireless communications device that
serves as the physical link between the SMARTDOT module and the PC-hosted
MASTER software. A custom communications protocol also had to be
implemented in both the SMARTDOT module and the MASTER application so
that they could communicate via the COMM wand.
• Developing the MASTER program - a preliminary PC-based communications and
analysis software package that interacts with the prototype SMARTDOT module
through the COMM wand, uploads the acquired sensor data, and facilitates
analysis and graphical presentation of that data. This version of the MASTER
software is actually a tool geared toward cataloging the uploaded waveforms,
analyzing those waveforms, identifying appropriate data-analysis techniques, and
implementing those techniques to extract useful information from the data.
4

1.3.2 Product Development Phase
The product development phase will put to practice the discoveries from the feasibility
phase, both in refinement of the SMARTDOT module's capabilities, and in the
development of a PC-based (and possibly a PDA-based) GUI software application for the
end-user. The major tasks of the development phase will be to:
• Refine the operation of the SMARTDOT sensor module to generalize its design
and performance for a wide range of bowlers. Such refinements will be derived
from the analysis of data gathered in the feasibility phase of the development, as
well as from data collected during additional testing by other bowlers.
• Develop a GUI-based software application that interacts with the SMARTDOT
module, and uploads, catalogs, analyzes, and presents the data in a form useful to
the bowler. This application could take two forms: a full-featured, PC-hosted,
Windows ® -based application, and a compact PDA-based application.
1.4 OVERVIEW OF THE FEASIBILITY PHASE
The SMARTDOT system consists of a custom hardware module integrated with custom
embedded software that interacts with a PC-based user application through a (currently)
custom wireless communications device. The "intelligence" of the SMARTDOT system
is distributed across two portions of software: the SMARTDOT module embedded
software, and the PC-hosted MASTER application.
The SMARTDOT module is designed to collect sufficient data with a fine enough
granularity that the MASTER software can perform accurate and meaningful analysis of
that data. The paper discusses the design assumptions, constraints, capabilities, and
performance of the in-situ data collection module, and the underlying assumptions and
techniques used to analyze and present the data in the MASTER software, as well as the
conclusions drawn from the analysis of the data acquired in this phase of the project, and
suggestions for further development.
The key to the feasibility of the system was the initial development of the in-situ sensor
module. Without the means to gather sensor data from the perspective of the ball,
development of the remainder of the system would have been extraneous. Consequently,
the feasibility portion of the project encompassed these distinct stages:
• Designing and building a viable hardware platform for the in-situ SMARTDOT
sensor module and implementing the COMM wand hardware.
• Developing the embedded software for the SMARTDOT module, including the
communications protocol between the module and the MASTER application. This
portion of the feasibility phase is presented in Section II, "Collecting the Data -
The SMARTDOT Module".
• Analyzing the data the module collected in order to reveal the types of useful
information that could be extracted from that data. To that end, the MASTER
program was developed, which has served as the preliminary communications,
data analysis, and presentation application. Section III, "Analyzing the Data - The
MASTER Application", presents this portion of the feasibility phase in detail.
5

Prior to the start of this project (May 1992), there were no references in the literature or
the various patent databases to any previous attempts to develop this kind of internal
system. Brunswick Corporation has since developed a robot that can throw a bowling
ball with repeatable and precise amounts of speed, spin, and axis turn and tilt, but the
subsequent response of the ball is still measured with external sensors [9]. It is certainly
possible that one or more of the various bowling ball manufacturers may have developed
proprietary means for internally assessing the performance of their products. If that is the
case, they have chosen to retain that information in the form of trade secrets.
With no prior research to fall back on, it was necessary to design and build an initial
sensor module simply to establish that it was physically possible to construct such a
device within the extremely limited confines of its intended environment. A reliable and
inexpensive means for transferring data in a wireless (non-contact) fashion from the
module to a PC also had to be developed.
Those two tasks were completed as an initial part of the feasibility study. The paper
presents relevant background and details of the hardware that are essential to
understanding the design and development of the embedded software, and/or the analysis
of the raw data collected. However, an exhaustive presentation on the hardware is not
within the scope of this paper.
Since the waveform that SMARTDOT was attempting to capture had apparently never
before been seen, the first prototype module was also designed as a flexible data
collection device. That first module was intended to serve as both the bowling ball's eye
and its memory as it looked out through the finger hole and recorded what it saw while
the ball rolled down the lane. The basic assumptions and design for the embedded
software for the SMARTDOT module have been developed based on the analysis of that
captured data.
With the feasibility of the hardware established, the real problem at hand has been largely
one of software engineering. Although the module works as intended, this version has
been developed solely through the author's personal use and input. The development
phase of the project will involve a refinement of the sensor module, as described later in
the paper, followed by a limited beta test among a collection of bowlers with different
styles and capabilities. A subsequent refinement of the module's embedded software will
most likely follow to accommodate variations discovered during the beta test.
As for the PC-hosted MASTER software, the paper reports the results of, and the
conclusions drawn from, the various types of data analysis performed on the raw data
collected during this phase of development. The MASTER program was developed as a
custom data analysis and presentation application to facilitate review of sensor data under
a real-world scenario (i.e., during real practice sessions at a local bowling center), and to
apply the information extraction techniques presented in Section III of the paper. Based
on this preliminary analysis package, high-level design suggestions for the development
of the end-user application are included at the end of Section III.
6

SECTION II: COLLECTING THE DATA - THE SMARTDOT MODULE
This section presents, in detail, the initial development, current implementation, and
future considerations of the in-situ SMARTDOT sensor module. Discussions of the
design constraints, the hardware implementation, and the embedded software
implementation (including flowcharts, timing diagrams, and a memory map) are
included, along with an assessment of the prototype's performance. Suggestions for
future refinements to the module's hardware and software are also given.
2.1 DESIGN BASIS
The in-situ sensor module, at a minimum, must be a capable of detecting release of the
ball, rotation of the ball, and the ball's impact with the pins. It must also have an accurate
"clock" with which to time-stamp those occurrences. For the system to be economically
viable, a major premise behind the in-situ sensor module rests on the assumption that the
ball's rotation can be accurately inferred by observing the amount of ambient light
impinging on a particular point on the surface of the ball as the ball rolls down the lane,
and that an inexpensive device can be developed that fits unobtrusively into the ball for
the purpose of recording this data. Since all modern bowling centers have overhead
lighting of some type, a source of ambient light is always present (except for the novelty
of "moonlight" or "glow" bowling).
Figure 2-1 provides a cut-away view of the SMARTDOT sensor module installed in a
bowling ball. For the following reasons, the ideal place to install the module is under a
finger insert in an existing finger hole:
• To optimize the dynamic range of the ambient light incident on the sensor
module, the module should be placed so that it alternately rotates through the
shadow the ball casts on the lane, and then up towards the lighted ceiling. The
finger holes generally follow this line of rotation.
• If the module is installed in an existing finger hole, it is not necessary to drill an
additional hole, or modify the ball in any way.
• Finger insert holes have a standard diameter, allowing for a standard size
(diameter) module. The sensor module has been made small enough that minimal
additional material must be removed from the ball in order to install it,
simplifying the installation procedure. This location also allows for easy
replacement of the module's battery.
• Locating the module in close proximity to a finger hole facilitates detecting the
removal of the bowler's finger from that hole, which is necessary for accurately
detecting release of the ball during the bowler's delivery.
• Locating the module below the surface of the ball affords a good deal of
protection from the extreme forces that the surface of the ball experiences when
impacting the lane, the pins, the pit cushion, the gutter, and when being handled
by an automatic ball return.
7

SMARTDOT Module Cut-Away View
CL
1.375"
Finger
Insert
Piezoelectric
Film
Light Sensor
(TSL251)
Transmit
LED's
Crystal
(3.6864 MHz)
Printed Circuit
Board (PCB)
µProcessor
(87C752)
0.375"
6V Lithium
Battery
0.938"
0.969"
Figure 2-1: SMARTDOT Module Cut-Away View
8

2.2 Design Constraints
The feasibility of the SMARTDOT system rests on being able to create an in-situ sensor
module that is small, inexpensive, light-weight, convenient to install and remove, and
does not affect the balance of the ball nor interfere with the bowler's normal delivery or
release motions. These design constraints are interrelated and are discussed below.
2.2.1 Ease of Use
Ideally, the module must be "invisible" to the bowler. It should not alter the manner in
which the bowler grips or releases the ball, nor should the bowler be able to tactilely
detect the presence of the module. The operation of the module must have no impact on
the bowler's normal routine and, except for uploading data from the device for analysis,
there should be no interaction required from the bowler.
2.2.2 Size, Weight, and Impact on the Balance of the Ball
The module must be placed in a hole drilled in the ball, which can affect both the weight
and the balance of the ball. The module does have some intrinsic weight and placing the
module in the hole drilled for it offsets some of the weight removed from the ball, but the
density of the module will most likely differ from that of the ball. The closer the module
is placed to the surface of the ball (the shallower the hole is drilled), the greater any
difference in density affects the dynamic balance of the ball. However, a deeper hole
removes more material, also impacting the weight and balance. The location of the hole
relative to the finger holes also impacts the static and dynamic balance of the ball.
It is possible to minimize these effects by placing the module in one of the existing finger
holes. With the module sized and designed to perform its intended function while located
at the bottom of a finger hole, an additional hole is unnecessary. Also, the module has
less of an impact on the inertial balance of the ball if it can be located further below the
surface, especially if its overall weight offsets the weight of any extra material removed
from the finger hole.
The vast majority of bowlers of the caliber that would benefit from the SMARTDOT
system utilize replaceable plastic or rubber finger inserts. These inserts fit into a finger
hole with a standard diameter of 31 / 32 " (.969"). Allowing for tolerance and clearance, the
module must then fit on a circular printed circuit board (PCB) no more than 30 / 32 " (.938")
in diameter.
Finger holes are generally drilled only as deep as is necessary to fully accept the finger
insert. Inserts are 1 3 / 8 " (1.375") to 1 1 / 2 " (1.5") high, and require a similar depth hole. In
order to limit the depth to which the finger hole must be drilled to accommodate the
module, the module's height must be kept to a minimum.
The overall height of the SMARTDOT module prototype shown in Figure 2-1 is 0.375"
( 3 / 8 "). The volume of material that must be removed from the ball to accommodate the
module is:
(.969 / 2) 2 · π · 0.375 = .277 in 3 .
The specific gravity of the weight block material (the area where the finger holes are
normally drilled) is generally 1.5 to 2.0, thus the weight of the material to be removed
(assuming a density of 0.578 oz 3
/ in for a specific gravity of 1.0) is 0.24 oz to 0.32 oz (7-9
grams). The SMARTDOT module prototype weighs 7 grams, resulting in a net loss to the
9

all of 2 grams or less. Given that a simple plastic case enclosing the module will
contribute an additional 2-3 grams, the total weight of the module with case approximates
the weight of the material removed, resulting in an essentially neutral impact on the
weight and balance of the ball.
2.2.3 Cost
Good bowling balls now cost in excess of $150. A reasonable target retail price for the
SMARTDOT module is approximately one-quarter to one-third of that, or no more than
$50. Assuming normal margins and distribution channels places the target production
cost in the range of $12.50-$15.00. The target production cost determines the means and
methods that can be used to detect the action of the ball (the type and number of sensors),
as well as the technology used to implement the module, i.e., the type of microprocessor
and its on-board resources, the size and type of data memory, the means of
communicating with the outside world, and the costs associated with the battery, case
design, and assembly. The estimated production cost of the SMARTDOT module
prototype is currently $13.50.
2.2.4 Power Consumption
Although the module is readily accessible, battery life must be long enough that the
bowler is not frequently forced to replace the battery. Limiting the energy requirements
of the module extends the battery life, while also limiting the size (height) of the battery,
which is important, since the battery comprises a significant fraction of the height and
weight of the module.
Ideally, the module will spend most of its time in a micro-power standby state. It wakes
up as the bowler releases the ball, monitors and records the output of its sensors while the
ball is rolling down the lane, and then returns to standby mode soon after the ball hits the
pins. The only other time the module should wake up is to upload the sensor data it has
collected to the MASTER application.
Lithium coin cells are the most appropriate battery technology for the module. They are
round (as is the module), light, thin, inexpensive, readily available in standard sizes, and
have a high energy density and cell voltage (3-3.6 volts). The SMARTDOT module
prototype uses two 3-volt BR2016 lithium coin cells, which collectively weigh 3-4 grams
(a little over half of the module's total weight, and contribute a little over one-third
(0.13") to the overall height.
2.2.5 Convenience of Installation and Removal
Since the module has a user-replaceable battery, it must be convenient to install and
remove. By placing the module underneath a removable finger insert, the bowler has
ready access to the module, requiring no special equipment for installation or removal.
10

2.3 SENSING REQUIREMENTS
The module must be able to sense when the ball is released, when it hits the lane, when it
hits the pins, and the ball's angular velocity as it rolls down the lane. The module must
be able to accurately sense the passage of time, and to record time-stamped samples of
the light waveform and of the impacts the ball experiences. It also must be able to sense
the presence of the communication device and contain a transceiver of some type so that
the module can transfer information to/from the MASTER application.
The ease-of-use, size, cost, and power consumption criteria, combined with locating the
module underneath a finger insert, limit the types of sensors that the module can employ.
2.3.1 Sensing Rotation of the Ball (Angular Velocity)
Several methods have been considered to directly sense the rotation (angular velocity) of
the ball using passive techniques (measuring some response to ambient conditions):
• Sensing the changing orientation of the ball in the earth's magnetic field.
• Sensing the changing orientation of the ball in the earth's gravitational field.
• Measuring the angular acceleration directly with an accelerometer.
• Measuring the ambient light falling on a fixed point on the ball.
Honeywell makes an integrated two-axis magnetometer (HMC1052) that physically fits
the application, but the cost ($18) and peak current draw (~400 mAmps) are both
prohibitive [17]. Analog Devices makes a dual-axis tilt sensor/accelerometer
(ADXL202E) that also fits the application, both in size and power requirement, but its
cost (~$15 in 1000 piece quantities) makes it too expensive for this application, although
it could be used for a later upscale version of the module [15].
The main thrust of the research for this project centers on the fourth, albeit less obvious,
alternative. Besides presenting the feasibility of the in-situ sensor module, this paper
demonstrates that a photometric sensor placed at the bottom of a finger hole, underneath
a finger insert, can be used to accurately sense the angular velocity of the ball.
TAOS (Texas Advanced Optical Systems) makes a series of small, inexpensive, lowpower,
integrated visible light detectors (TSL25x) that suit the application [23]. In
addition, the same light sensor can also be used to detect the moment of release (indicated
by a sudden transition from dark-to-light), and serve as the receiver for an IR-based
wireless communications scheme. Refer to Figure 2-1 for the orientation of the light
sensor in relation to the finger insert.
An increasing light level is seen as the finger hole revolves up to face the ceiling, while a
decreasing light level is sensed as the finger hole revolves toward the lane. Peaks in the
light waveform occur at the top of each revolution (defined as the orientation of the ball
when the finger holes are facing toward the ceiling), and valleys occur at the bottom of
each revolution (defined as the orientation of the ball when the finger holes are closest to
the lane). In developing the light-sensor based module, it was the author's belief that the
ambient light level the sensor "sees" as the ball rotates would roughly transcribe a
sinusoidal shape, and that the sampled and digitized light waveform could be stored,
11

uploaded, processed, and analyzed in such a way as to yield results useful to the bowler.
See Figures 2-2a and 2-2b for an example of the module installed in the ball and rolling
down the lane. The dotted lines emanating from the finger hole indicate the module's
"viewing angle" for ambient light.
2.3.2 Sensing Release, Lane Impact, and Pin Impact
As previously presented, in order to limit the size of the battery, the module should
remain in an ultra-low power "sleep" state whenever the ball is not being held by the
bowler, or rolling down the lane. For the module to detect that the ball has been released,
it must have some means for identifying that the bowler has removed their fingers from
the ball. The light sensor could be used for this purpose, since the bottom of the finger
hole is dark while the bowler's finger is in the hole, and light(er) when the finger is
removed. However, to accomplish this task, the TSL251 must remain powered, even
while the module is asleep. This is not possible at the ultra-low standby current level (~1
µAmp) that is required for extended battery life.
The module also requires a means to detect impact with the pins (which also gives it the
capability of detecting impact with the lane). This "impact" sensor has been implemented
with a piezoelectric plastic film made from PVDF (polyvinylidene fluoride) [19]. This
film is inexpensive, durable, and requires no external power to generate a voltage signal
strong enough to wake up the module. Since it is piezoelectric, when pressure is applied
to the film, the film responds by producing a voltage proportional to the rate-of-change of
the pressure applied. With a piece of this film inserted between the outside of the finger
insert and the wall of the finger hole, it can sense not only the lane and pin impacts, but
also the bowler applying pressure to the insert. Since the film detects changes in
pressure, and not the applied static pressure, it can be placed between the insert and the
finger hole wall without concern that the static pressure of that placement might set off
the module. Refer to Figure 2-1 for the position of the piezoelectric film sensor.
Since the bowler must apply significant pressure to the insert during release, the impact
sensor also serves to wake up the module immediately before release. The light sensor is
then used to detect the moment of release by looking for a rapid increase in the light
level, from near or total darkness, to some higher level of light (or lesser level of
darkness).
2.3.3 Measuring Time and Recording Data
The microprocessor supplies the clock to measure time, and coordinates all of the various
activities required to make the module work. A stable time-source, currently a miniature
quartz crystal, serves as the basis for the microprocessor's clock. Additional external
non-volatile memory (EEPROM) is required for storing the sampled light waveform, the
impact data, and any configuration parameters that are required.
12

Pin Deck Light
Foul Line
Figure 2-2a: Lane Layout and Overhead Lighting
Release Point
(finger removed
from insert)
Sampled Light
Waveform
Foul Line
Impact with Lane
Pin Deck Light
Impact with Head Pin
Figure 2-2b: Ambient Light Waveform
13

2.3.4 Communications
The SMARTDOT module must transfer the data it collects to an external device for
archival, analysis, and display. The module must be able to detect the presence of the
external communications device, and both receive commands from it, and transmit data
to it. Communications occur in a non-contact (wireless) fashion, and a light-based
(infrared) communications scheme is used. The on-board transceiver consists of the
previously described light sensor and two visible red (660 nm) LEDs. An algorithm has
been developed that relies on the on-board transceiver to detect the presence of the
external communications device (COMM wand), and initiate communication.
2.4 CAPABILITIES
The module is intended to detect and record (at least some of) the major forces that the
ball experiences. A bowler attempts to exert various forces on a bowling ball during
delivery, to varying degrees, in a controlled manner. These forces are:
• Lift: Force applied to cause the ball to rotate about a primary axis relative to the
finger holes. The more lift that is applied to the ball at release, the faster the ball
rotates as it travels down the lane.
• Turn: The amount by which the axis of rotation of the ball is rotated away from
normal with respect to the length of the bowling lane. The more turn that is
applied at release, the more the ball has the potential to hook.
• Tilt: The amount by which the axis of rotation is tilted away from parallel with
the lane surface. The amount of tilt directly impacts how long the ball delays
(skids or slides) before starting to hook.
• Velocity: The speed and direction with which the ball leaves the bowler's hand.
The higher the velocity, the harder the ball hits the pins, but the less it hooks. The
velocity consists of a large x-coordinate component (towards the pins) and a small
(but not insignificant) y-component (towards either gutter). The x-component is
always positive, originating at the foul line and running towards the pins. The y-
component can be negative (toward the right gutter for a right-handed bowler) or
positive (toward the left gutter for a right-hander).
• Loft: The distance the ball travels (in the air) before it first makes contact with
the lane after release. A bowler can control the amount a ball hooks by altering
the distance the ball is lofted before it hits the pins. More loft generally means
less hook.
The basic premise behind the SMARTDOT module is that two sensors, an ambient light
sensor and a piezoelectric pressure/impact sensor, combined with an accurate time
source, are sufficient to accurately capture the amount of lift applied to the ball (the
angular velocity), the moment of release, and the various times of impact with the lane
and the pins. It was not expected that this combination of sensors would be capable of
reliably capturing the amount of turn, tilt, or the y-component of the ball's velocity.
14

2.4.1 Ambient Light Sensor
The ambient light sensor serves three purposes:
• It senses when the bowler has released the ball. A finger in the insert blocks
ambient light from reaching the module. When the ball is released, a sudden
increase in the ambient light level is detected.
• It detects the revolution of the ball as it rolls down the lane. The light sensor,
located on the top side of the SMARTDOT module PCB, "looks" out through the
finger insert and "sees" the ambient light as the ball rolls down the lane. It was
presumed that the ambient light level the sensor sees would be brighter when the
module faces upward (toward the ceiling), since the lights are located there, and
darker when the module faces downward (toward the lane surface).
It was further presumed that the light waveform the module sees would be
roughly sinusoidal in nature, exhibiting peaks when the module faces the ceiling,
and valleys when the module faces the lane. Counting these peaks and valleys
results in the total number of revolutions (to within ½ revolution) that the ball
underwent during its traversal of the lane. By measuring the time between peaks
(and/or valleys), it is then possible to calculate the angular velocity (rpms) of the
ball for any given revolution. Fractional revolutions (immediately following
release, and immediately before impact) can be extrapolated from the angular
velocity of the closest complete revolution, hopefully resulting in a resolution of
30° of rotation, or better than 0.1 revolution.
• It receives serial data from the communications module.
2.4.2 Pressure/Impact Sensor
The pressure/impact sensor serves these purposes:
• It wakes up the module when finger pressure is applied to the insert - indicating
that the bowler is holding the ball, and preparing for delivery and release.
• It senses the moment(s) of impact with the lane - ball loft distance.
• It senses the moment(s) of impact with the pins.
• It senses that the ball has rolled over a finger hole (the ball "hops" when it rolls
over one of the finger holes, since the hole acts like a flat spot on the ball).
2.4.4 Clock
The microprocessor's time-base serves the following purposes:
• It generates the ambient light sample timer.
• It provides a time-stamp for the impacts that the piezoelectric film sensor detects.
• It generates the baud rate(s) for the communications transceiver.
• It generates several precise time intervals and time out functions required for
coordination of the various microprocessor tasks.
15

2.5 HARDWARE IMPLEMENTATION.
The following is a summary of the SMARTDOT module's hardware configuration and an
overview of the hardware theory of operation. A working prototype of the SMARTDOT
sensor module (based on this hardware configuration) has been used under real-world
conditions (placed in a ball and rolled down the lane) for a total of about 500 frames (~50
games).
2.5.1 Hardware Configuration
A summary of the major hardware components and their respective features is given
below. See Figure 2-3 for a block diagram of the prototype SMARTDOT module.
Microprocessor - Phillips 87C752 [21]
• Intel 8051-based core.
• Crystal Frequency - 3.6864 MHz (3.26 µsec instruction cycle).
• 64 bytes on-board RAM (including general purpose registers and stack space).
• 2 Kbytes on-board program EPROM.
• 8-bit Analog-to-Digital Converter (130 µsec conversion time @ 3.6864 MHz).
• 16-bit auto reload timer.
• Additional fixed timer (300 Hz @ 3.6864 MHz).
• Interrupts (timers, external, ADC).
• Idle mode.
Light Sensor - TAOS TSL251 Light-to-Voltage Converter [23]
• Output: 60 mV/(µW/cm 2 ), 7.5 µsec rise/fall time.
Memory - Microchip 24C04 Serial I 2 C EEPROM (4096 bits, 512 x 8) [20]
• 8 byte page write.
• 10 msec maximum write time per page.
• 400 kHz maximum clock rate.
Amp Sensors Piezoelectric Film Sensor [19]
• Responds to changes in pressure.
Maxim MAX931 Ultra-Low Power Comparator [18]
• Current draw:

9
28
8
RST V CC
V CC
5
6
hyst 7
3
+
ref
V DD
MAX931 Out
4
-
GND
V-
2
1
8
1
2
7
PR V DD
D-FF Q
CLK
D Q
V SS CLR
4
6
8
5
3
23
20
19
87C752
SDA
SCL
P0.3 (SHUTDOWN_PIN)
INT0 (IMPACT_PIN)
AV CC
7
8
5
6
7
3
2
1
SDA
SCL
A 2
A 1
A 0
24C04
V SS
4
T1
SMARTDOT MODULE
BLOCK DIAGRAM
V+
Battery Ground
Microprocessor Ground
Light Sensor Ground
Signal Lines
2
V DD
TSL251
GND
1
Out
3
6
13
18
24
P0.2 (TRX_PIN)
ADC0 (LITE_INPUT_PIN)
AV SS
P0.4 (LITE_PWR_PIN)
X 2 X 1 V SS
10 11
12
Figure 2-3
17

2.5.2 Hardware Operation Overview
Figure 2-3 depicts a combination block diagram and pseudo-schematic detailing the
physical connectivity of the SMARTDOT module's hardware components. The following
discussion presents the theory of operation of the module's hardware, and refers to the
components shown in the block diagram.
The piezoelectric film sensor (T1) serves as both the "wake-up" sensor and impact
detector, and is connected to the negative input (-) of an ultra-low power comparator
(MAX931). Bias for the positive (+) input is provided by a voltage divider connected to
the MAX931's internal 1.18V reference, with hysteresis provided through connection to
the '931's "hyst" pin.
The MAX931's output is connected to the asynchronous preset of a single, low-power
CMOS D flip-flop (D-FF). Pressure applied to the insert is transferred to T1, generating
a voltage spike that triggers the comparator, forcing the state of the D-FF to a logical '1'.
The Q output of the D-FF transitions to the low (0) state, providing ground to the
remainder of the module, which causes the Philips 87C752 microprocessor to "wake-up"
and begin executing its program. The comparator output is also connected to an external
interrupt on the '752 (labeled IMPACT_PIN) so that the microprocessor can record any
subsequent activity (additional finger pressure, impact with the lane, impact with the
pins, etc.) sensed by T1.
With a 3.6864 MHz crystal, the 87C752 draws ~3 mAmps while running, but through use
of the '752's IDLE mode between light samples, the average current drawn is reduced to
less than 2 mAmps. When the '752 reaches the point where it is time to shutdown, it
clocks a logical '0' into the D-FF (the 'D' input is tied to ground and the CLK pin is
positive edge triggered), the Q output returns to the high (1) state, which removes ground
from the microprocessor portion of the circuit, putting the module back to "sleep". The
powered portion of the module (the comparator and the D-FF) draws less than 1 µA
while the module is in sleep mode.
The output of the TSL251 light-to-voltage converter is connected to the '752's on-board
ADC (at LITE_INPUT_PIN) and the '251's ground is controlled by the microprocessor
through LITE_PWR_PIN. The TSL251 draws about 800 µA when powered, and since
the light waveform is sampled, rather than continuously monitored, the '752 turns off
(removes ground from) the TSL251 between samples and then enters a power-reducing
IDLE mode until the next sample time.
The TSL251 also serves as the receiver portion of the IR communications transceiver.
The transmit portion of the IR transceiver is comprised of two LED's and a resistor that
limits the LED current to ~500 µA, driven by TRX_PIN. Since the transmit LEDs are
only lit during a '0' pulse, and there is generally an equal distribution of 0's and 1's in a
transmission, the average transmit current is ~250 µA.
The 24C04 serial EEPROM stores the configurable parameters and the collected sensor
data (impacts and light waveform samples) in nonvolatile memory. It draws
approximately 1 mA during a write operation, and ~300 µA during a read operation. The
24C04 draws negligible current while idle (not being accessed).
18

2.6 HARDWARE/SOFTWARE INTERACTION DESIGN CONSIDERATIONS
There are a number of areas where the design decisions for the hardware and the
embedded software are interdependent. These issues are presented next.
2.6.1 Microprocessor Clock Frequency
The clock frequency directly affects the current drawn by the microprocessor: the lower
the clock frequency, the less current the 87C752 draws from the battery. The lowest
standard oscillator frequency that supports the sample rate, the serial communications
baud rates, and the processing demands of the application is 3.6864 MHz. The internal
clock frequency for the 87C752 is 1 / 12 of the oscillator frequency, resulting in an
instruction time of 3.26 µsec (307,200 instructions per second) for a 3.6864 MHz crystal.
Quartz crystals and ceramic resonators are available in standard frequencies for
microprocessors. Crystals easily can maintain an accuracy (over their temperature range)
of 200 ppm (.03%), while ceramic resonators (cheaper and smaller) typically run in the 1-
2% range. During the feasibility phase, a crystal has been used to enhance the accuracy
of the sample clock, with the hope of switching to a ceramic resonator, in combination
with some clock calibration software, as part of the development phase.
2.6.2 Sampling Rate
The 87C752 microprocessor contains an 8-bit ADC with a conversion time of 130 µsec
(~7600 Hz) at the clock frequency of 3.6864 MHz. It is important to minimize the
sample rate, since the amount of data collected directly affects the amount of external
data memory required. Complicating matters, EEPROM technology has a fairly slow
write speed (5-10 msec per page write), thus presenting the possibility that the rate of
writing data to memory might not keep pace with the production of data to be written.
Also, it is desirable to run the microprocessor in IDLE mode as much as possible, since it
cuts the current draw in half, and the light sensor (TSL251) and the '752's on-board ADC
can be turned off between sample times. The higher the sample rate, the more time the
microprocessor must spend collecting and processing data, which shortens the life of the
battery.
Data must also be collected from the impact sensor, but this is a different process. An
impact can occur asynchronous to the time of a light sample, with a much shorter
duration than the sample period. Therefore, impact detection is interrupt driven. By
limiting the stored value of the light samples to the range 0-127 (0x00-0x7F), the impact
data for a sample can be stored in the high-order bit of the sample byte, thus associating
each impact with the light sample during which the impact occurred.
The primary factors in determining an appropriate sampling rate are the maximum
angular velocity (rpms), the minimum and maximum linear velocities (ball speed), and
the amount of memory available for the storage of captured data.
• Maximum RPMs: According to tests conducted by the ABC (American Bowling
Congress), the best bowlers, those that average greater than 210, generate an
average rotational rate of about 300 rpms (5 Hz) at release. In fact, the ABC
found a direct correlation between average score and angular velocity [12].
There is an upper bound on the number of revolutions the ball can make. If the
ball did not skid at all, it would travel 27 inches per revolution, while revolving
19

almost 27 times between the foul line and the head pin. The ball would also have
to be thrown at over 25 miles an hour for the rotational rate to reach 1000 rpms.
Those values are extreme, but they allow an upper limit of 1000 rpms (16.7 Hz) to
be set as the maximum angular velocity.
The vast majority of bowling establishments utilize fluorescent lighting.
Preliminary testing with the TSL251 revealed that the sensor is responsive enough
to detect the 120 Hz optical ripple of the overhead fluorescent lights. This ACinduced
ripple becomes part of the ambient light level, and could cause a
problem, since the pseudo-sinusoidal target waveform must be extracted from the
ambient light. However, the AC ripple is confined to a narrow band at 120 Hz,
while the desired fundamental waveform is of a much lower frequency.
Sampling the waveform at a frequency less than twice the 120 Hz ripple could
result in "aliasing" the 120 Hz content down into the frequencies of interest (< 20
Hz). And sampling at a frequency other than a harmonic multiple of 120 Hz
could introduce harmonic variations into the raw waveform that the module must
then deal with, since it certainly won't have the processing capabilities to digitally
filter the data. Sampling at a harmonic multiple of 120 Hz, such as 240 Hz, and
storing the average of two consecutive samples (yielding a net 120 Hz data rate),
averages out the AC ripple. The frequency of the AC ripple exceeds the target
waveform by at least a factor of 7 (in the extreme case), but is actually closer to a
factor of 15-20. Hence, the 120 Hz ripple should not interfere with data collection
as long as an appropriate sample frequency is chosen, allowing for a resolution of
at least 18°-24° of rotation.
• Ball Speed: The vast majority of bowlers, even at the 200+ average level,
generate an average ball speed of less than 20 mph (~30 fps). At 30 fps, it takes at
least 2 seconds for the ball to travel from the foul line to the head pin (60 feet).
For a ball speed of 30 fps and a net sampling frequency of 120 Hz, the ball travels
3" per sample period, good enough for 0.4% resolution over 60 feet. The vast
majority of bowlers generate ball speeds greater than 10 mph (15 fps), especially
those that average greater than 180. At 15 fps, it takes the ball 4 seconds to
completely traverse the lane, or 480 samples at 120 Hz.
• Data Memory: The hardware for the prototype SMARTDOT module was
originally specified in January of 1993. At that time, the highest serial memory
density readily available that was cheap enough to be practical was a 4096 bit
(512 x 8) chip. This size memory is only big enough to capture a single roll of the
ball. Affordable serial EEPROM memory density has increased dramatically
since the SMARTDOT module prototype was designed, and the "Sample Memory"
section details the implications of using a higher memory density.
For the prototype module, ambient light sample data is produced faster than it can
be consumed by single byte writes to the EEPROM. However, the EEPROM can
handle 8 samples at a time, with a 10 msec max write time. A sample is produced
every 8.333 msecs (120 Hz), and a circular sample buffer is used to accumulate 8
consecutive samples for writing to the EEPROM. The EEPROM performs the
actual write in the background, after the data has been input to its write buffer.
The 87C752 can continue collecting data in the circular buffer without having to
wait for the EEPROM to finish storing the data.
20

2.6.3 Baud Rate
The module communicates with the outside world through a serial IR interface using
standard baud rates. A software UART had to be implemented for the SMARTDOT
module, since the 87C752 does not have an on-board hardware UART. The 3.6864 MHz
crystal supports both the 240 Hz sampling rate, and running the software UART at all of
the standard baud rates up to 38400 baud.
The rise/fall time of the TSL251 limits the module's reception rate to 600 baud, which is
not a problem, since the module receives little information compared to what it must
transmit. On the transmit (upload) side, the entire contents of memory (512 bytes) must
be uploaded rapidly so as not to inconvenience the user. At the 38400 baud rate, the
entire contents of memory can be uploaded in less than a second.
2.7 EMBEDDED SOFTWARE DESIGN AND OPERATION
This section presents a detailed description of the SMARTDOT module's embedded
software operation. The module's software architecture is shown in Figure 2-4, which
diagrams the interrelation of the major software tasks, and their interaction with the
interrupt service routines (ISR's). The following software description and the
architecture diagram both make reference to flowcharts for the embedded tasks and
interrupt service routines, which are included in Appendix A. The actual assembly code
is thoroughly documented, and has been included in Appendix B.
2.7.1 Software Design Considerations
Due to the cost and physical size constraints of the application, the SMARTDOT module
relies on a relatively simple hardware design. The complexity of the module is contained
within its embedded software and the efficient use of the microprocessor's on-board
resources and peripherals. The 87C752 microcontroller has severe constraints on both its
on-board program EPROM (2048 bytes) and RAM (64 bytes). The RAM space also
includes the general-purpose registers, the bit addressable space, and any required stack
space.
Although 'C' compilers are available for the 87C752, they are notoriously spaceinefficient,
and 'C' makes heavy use of the stack. Due to the limited sizes of the code and
data spaces, the embedded software was implemented in Intel 51 assembly language,
with careful attention paid to the maximum depth of procedure calls, and with minimal
parameter passing via the stack. The required stack space has been held to 16 bytes,
allowing for a call depth of four (two-byte return addresses and two additional bytes
(usually ACC and PSW) PUSHed onto the stack for each call).
The application is both event and interrupt driven, with pre-emptive, round robin
multitasking used on a limited basis to implement task time-outs, sampling, and
discrimination between "valid" waveforms, attempts to communicate, and spurious
activations. Microprocessor interrupts are used for acquiring regular light waveform
samples, for impact detection, for implementation of the software UART, and for keeping
accurate track of time. Event driven (polled) tasks include detection of release and
detection of the COMM Wand. Semaphores are used for task synchronization.
21

SMARTDOT Module Software Architecture
SLEEP MODE
Wake Up on
Pressure Applied to
Insert
Not DARK enough
at start-up
START-UP TASK (Figure A-1A)
Initialize Module
Check Start-Up LITE Level
Enable Interrupts
Waited too long for
RELEASE
PRE-SAMPLING TASK (Figure A-1B)
Wait for Sample (IDLE)
Check for RELEASE
Select Active Scratch Pad
Write to EEPROM (8 pre-samples)
RELEASE
detected
RELEASE not detected
LIGHT SAMPLE ISR
(Figure A-2)
Reached END of
Sample Space
Scratch Pad END and
sampling disabled
SAMPLING TASK (Figure A-3)
Wait for Sample (IDLE)
Write to EEPROM (every 8 samples)
Check for END of Sample Space
Check for END of Scratch Pad
Check for Sampling Enabled
In TEST mode,
waveform VALID, and
sampling disabled
DISCRIMINATION TASK (Figure A-4)
Check for Valid Waveform
Check for Test Mode
Check for Sampling Enabled
Waveform invalid and
not in TEST mode
Waveform is still VALID
In TEST mode with
sampling enabled
COMMUNICATION TASK (Figure A-5)
Wait for DARK (IDLE)
Contact WAND
Wait for LITE (IDLE)
Acknowledge WAND
Get Command
(UART Receive Task - Figure A-7)
Process Command
(UART Receive Task - Figure A-7)
Check for Command Retry
Done trying
Continue trying
WAND DETECTION ISR
(Figure A-6)
BIT SAMPLE ISR
(Figure A-8)
RECEIVE TIME OUT ISR
(Figure A-9)
SHUTDOWN TASK (Figure A-10)
Done Sampling
Save Run Time
Back to Sleep
Figure 2-4
22

Configuration settings and the sampled light waveform are stored in the external serial
EEPROM. Sample memory is divided into three parts: two scratch pad areas, and a main
sample area. While the previously collected waveform is stored across one of the scratch
pads and the main sample memory, the other scratch pad is used to store potential
waveform data while the module decides whether the waveform is the result of a ball
rolling down the lane, or from some other activation (communications or spurious
impact). Each scratch pad holds 600 msecs (72 samples) of the waveform, including the
8 pre-samples taken immediately prior to release. The remainder of the waveform (up to
2933 msecs or 352 samples) is stored in main sample memory. Figure 2-5a shows the
logical layout of external memory.
SDM_DATE_CODE
[year]
000h
SDM_DATE_CODE
[week]
001h
SDM_SERIAL_NO
[HI byte]
002h
SDM_SERIAL_NO
[LO byte]
003h
SDM_CFG_BYTE
(see Figure 2-5b below)
004h
SDM_SAMPLE_END
(end of digitized waveform)
005h
SDM_RUN_TIME
[HI byte]
006h
SDM_RUN_TIME
[LO byte]
007h
SDM_ACTIVATION_CNT
[HI byte]
008h
SDM_ACTIVATION_CNT
[LO byte]
009h
SDM_BALL_CNT
[HI byte]
00Ah
SDM_BALL_CNT
[LO byte]
00Bh
SDM_AUTO_GROUPS
(Discrimination routine)
00Ch
SDM_GROUP_SIZE
(Discrimination routine)
00Dh
SDM_HYSTERESIS
(Discrimination routine)
00Eh
SDM_RELEASE_LEVEL
(light level for release)
00Fh
010h SDM_SCRATCH_PAD_0 Sample Scratch Pad 0 017h
(72 bytes - 600 msec Sample time)
• • •
• • •
050h
057h
058h SDM_SCRATCH_PAD_1 Sample Scratch Pad 1 05Fh
(72 bytes - 600 msec Sample time)
098h
• • •
• • •
09Fh
0A0h SDM_SAMPLE_BGN Main Sample Space 0A7h
(352 bytes - 2933 msecs Sample time)
1F8h
• • •
• • •
1FFh
Figure 2-5a: EEPROM Memory Map
7 6 5 4 3 2 1 0
Unused Auto Mode Sample Bit New Ball Bit Active Scratch Pad Overflow Test Mode Unused
0 - Single
1 - Auto
0 - Disabled
1 - Enabled
0 - Old Data
1 - New Data
SDM_CFG_BYTE
0 - Scratch Pad 0
1 - Scratch Pad 1
0 - No
1 - Yes
0 - No
1 - Yes
Figure 2-5b: SDM_CFG_BYTE Layout
23

2.7.2 Start-Up
The SMARTDOT module spends the vast majority of its time in an ultra-low power sleep
mode, which draws less than 1 µAmp. Finger pressure applied to the insert wakes the
module from its sleep. Since the bowler's finger must still be in the insert immediately
after start-up, if SMARTDOT detects too much light at start-up, the release is presumed to
be invalid (for instance, caused by another ball striking it on the ball return), and the
module shuts down (goes back to sleep).
If it is dark enough after start-up, SMARTDOT continues sampling the ambient light
level, waiting for the release of the ball (indicated by the measured light level exceeding a
configurable "release" level). The release process takes several seconds, while the
bowler picks up the ball from the ball return and subsequently delivers it to the lane
during their approach. If release is not detected within one second of activation, the
module shuts down. Since the bowler grips the inserts throughout their approach, the
module may experience several "false" start-ups before the actual release occurs. Refer
to Figure A-1a (Start-Up Task Flowchart) for the sequence of events at module start-up.
2.7.3 Pre-Sampling
As part of the actual release, the bowler applies significant pressure to the inserts
immediately before release. The module is again activated (several hundred milliseconds
before release), giving SMARTDOT sufficient time to see the ambient light release point.
Since the module detected a valid pre-release light level at start-up, it looks for the
release light level for up to one second. While waiting for release, the module stores the
pre-release light samples in an 8-byte circular buffer. This "pre-sampling" allows the
MASTER application to identify the precise moment of release. See Figure A-1b (Pre-
Sampling Task Flowchart) for the pre-sampling sequence of events.
The waveform is sampled at 240 Hz, but the sample data is collected and stored at a 120
Hz rate. In order to cancel the effects of the 120 Hz AC ripple superimposed on the
waveform by the overhead fluorescent lights, two consecutive 240 Hz samples are
averaged together to yield a single 120 Hz sample. The maximum stored sample value is
clipped to 127 (0x7F) so that the high-order bit of each sample is available for storing the
impact status for that sample. Refer to Figure A-2 (Light Sample ISR Flowchart).
2.7.4 Waveform Discrimination and Validation
The SMARTDOT module always runs in one of two major operational states: it samples,
validates, and stores the ambient light waveform; or it communicates with the COMM
wand. While the module samples and stores the waveform, it also executes a routine that
discriminates between waveforms that result from the ball rolling down the lane, the
MASTER attempting to make contact, and spurious activations.
After detecting the actual release of the ball, the module continues to sample the
waveform and collect data in its 8-byte RAM sample buffer (the same one used for
storing the pre-samples), transferring the buffer contents to the active scratch pad in
external EEPROM while scanning the sampled data for a pattern consistent with the ball
rolling down the lane. If the presence of a "valid" waveform (one that looks like the ball
is rolling) is not detected within 600 msecs (72 samples plus the 8 pre-samples) following
release, the module automatically switches from sampling the waveform to its
communication routines, and attempts to contact the COMM wand. Refer to Figure A-3
(Sampling Task Flowchart) and Figure A-4 (Discrimination Task Flowchart).
24

2.7.5 The Ball is Rolling
If the waveform is still valid after 600 msecs (when the active EEPROM scratch pad has
been filled) and sampling is enabled (see "Sampling Modes" below), the module begins
overwriting the previous waveform data stored in the main sample memory in EEPROM
with the data from the waveform it is currently sampling. The module continues to
sample, store, and validate the new waveform for up to 3.533 seconds (424 samples),
depending upon the sampling mode currently selected.
2.7.6 Sampling Modes
The SMARTDOT module can execute three different sampling modes: AUTO mode,
SINGLE mode, and TEST mode. Bits 1, 5, and 6 of SDM_CFG_BYTE, shown in
Figure 2-5b, are used to store the sampling mode. Also, refer again to Figure A-3
(Sampling Task Flowchart) and Figure A-4 (Discrimination Task Flowchart).
• AUTO mode enables the module to automatically capture every valid waveform it
detects. If the previously captured waveform is not uploaded to the COMM wand
before the next valid waveform is detected, the previous data is overwritten with
the new data. Since the module always stores the waveform of the most recent
ball rolled, this mode is useful when the bowler wants to upload the latest
waveform, based on the observation of an interesting or unusual ball reaction,
without having to interact with the module before every shot.
• SINGLE mode enables the module to store a new waveform only after the
previous waveform has been uploaded to the COMM wand. Uploading the
previous data automatically enables capture of the next valid waveform. If the
previous data has not been uploaded, the module will not capture a new
waveform. This mode is useful when the bowler wants to look at specific shots
(such as the first ball of each frame), but doesn't want to be required to upload the
data in the middle of a frame.
• TEST mode enables the module to capture a waveform only when it has been
expressly instructed to do so. On the first valid release following each receipt of
the TEST command, the module bypasses the waveform discrimination and
validation routine and unconditionally samples the resulting waveform for the
maximum 3.533 seconds. This mode is useful for recording events that fall
outside of the module's current definition for a valid waveform.
2.7.7 Shutdown
Rather than require the module to collect data for the full sample time of 3.533 seconds,
the discrimination and validation routine is used to limit the total run time of the module.
The module shuts down when the first of two shutdown conditions occurs: either the end
of the sample space is reached at 3.533 seconds, or the waveform discrimination routine
determines that the waveform has become invalid, signifying that the ball has stopped
rolling (entered the pit at the end of the lane). Once the module detects a shutdown, it
updates the total run time, the activation count, and the ball count, and goes back to sleep.
Refer to Figure A-10 (Shutdown Task Flowchart).
25

2.7.8 Communication with the COMM Wand
Communications with the module are conducted over a wireless, infrared (IR) interface,
using the TSL251 as the receiver, and two surface-mount LED's as the transmitter. Since
the 87C752 does not contain an on-board hardware UART, a software UART has been
implemented. The software UART conforms to several design constraints specific to the
SMARTDOT module hardware.
Baud Rates: Due to the limited response time of the TSL251, and the relatively
slow conversion rate of the '752's ADC at the module's clock frequency, reliable
reception is only possible up to 600 baud. The communication protocol between the
module and the COMM wand is designed such that the module normally receives
single character transmissions from the wand. Consequently, the 600 baud reception
rate does not create a communications bottle-neck. Since the COMM wand can
receive at a much higher baud rate than the SMARTDOT module, the module
transmits to the COMM wand at up to 38400 baud (another limitation imposed by the
module's clock frequency).
Data Frame: A 12-bit serial protocol is used on transmission: 1 START bit, 8 DATA
bits, 1 PARITY bit (EVEN), and 2 STOP bits. An 11-bit protocol (using a single
STOP bit) is used for reception. This imbalance in STOP bits guarantees a minimal
extra dead space between back-to-back characters, and allows for clock skew between
the module and the COMM wand.
Bit Sampling: The TSL251 and the 87C752's ADC are used for serial reception.
The light waveform is sampled at 4800 Hz (8 samples per bit time), and the middle
four samples of each bit determine the value (0 or 1) for that bit. Ignoring the first
two and last two bit samples allows for some clock skew between the transmit baud
rate of the COMM wand and the receive baud rate of the module. A count of two or
more DARK middle samples constitutes a logical '1', otherwise the bit is considered a
logical '0'. The bias is toward the DARK samples since the COMM wand's presence
over the finger insert creates a dark ambient condition. As long as the COMM wand
is held relatively close to the insert, the background remains dark enough for the
module to discriminate between the light pulses (0's), and the ambient background
level (1's). A noise margin is also built into the bit-sampling scheme. There is a gap
established between the DARK and LITE levels, with the transition point switched
between the two depending on the value of the last sample received, creating a digital
hysteresis function. Refer to Figure A-7 (UART Receive Task Flowchart) and Figure
A-8 (Bit Sample ISR Flowchart).
2.7.9 Communication Protocol
All communications with the module are initiated by pressing on the insert, and then
placing the COMM wand over the insert, covering the opening. The bowler has one
second to remove their finger from the insert, and another second following release to
cover the insert with the COMM wand. If either of these conditions is not met, the
module shuts down and must be reactivated.
Upon activation, the module waits for release to occur, as previously described. When it
identifies a release condition, it looks for a valid waveform. In the case of a COMM
wand transmission, the module discovers that the ball is not rolling within 600 msecs
(through the discrimination and validation routine), switches to the COMM wand
detection routine, and waits for up to one second for the insert to become dark (become
26

covered by the wand). When the module detects the appropriate level of darkness, it
assumes the COMM wand is in place, and transmits a specific "HI" character to the wand.
An ASCII 'U' (0x55 - 01010101b) is used as the "HI" character because it requires an
alternating light level of 38400 Hz to be detected, which is highly unlikely to occur under
ambient light conditions.
If the COMM wand is actually in place over the insert, it receives the "HI" character, and
responds with a NULL character at 600 baud. The NULL character (0x00) appears to the
module as a light pulse of a fairly precise length (~16.7 msec - 10 consecutive '0' bit
times, including the START bit and the EVEN parity bit) in an otherwise dark ambient
background, another condition that is unlikely to occur under ambient conditions. The
module waits for up to 200 msecs to receive the COMM wand's acknowledgment. If the
module does not receive a valid acknowledgement light pulse within this time, it
retransmits the "HI" character, and waits for the COMM wand's response. The module
tries to contact the COMM wand three times before assuming the wand is not present, at
which time it shuts down. Refer to Figures A-5 (Communication Task Flowchart), A-6
(Wand Detection ISR Flowchart), and A-9 (Receive Time Out ISR Flowchart).
If the module receives a valid light pulse, it transmits another "HI" character to the
COMM wand, at which point a "conversation" ensues between the SMARTDOT module
and the COMM wand. If the protocol fails at anytime, or a reception error is detected, the
module aborts the conversation and tries to reestablish communications with the COMM
wand from the beginning, for a total of three attempts, before finally shutting down.
2.7.10 Commands
The MASTER program can issue various commands through the COMM wand to the
module to retrieve data, to select the module's sampling mode, and to configure certain
module parameters shown in Figure 2-5a. Before the bowler can view the waveform the
SMARTDOT module has captured, the MASTER must upload that data from the module
by issuing the TRANSMIT command, which instructs the module to transmit the contents
of its data memory.
As an example, the protocol for uploading data from the module to the MASTER is:
MODULE: "HI" 'U' (0x55) @ 38400 baud - "Are you there?"
MASTER: NULL 0x00 @ 600 baud - "I'm Here"
MODULE: "HI" 'U' (0x55) @ 38400 baud - "Clear to Send"
MASTER: 'T' "Transmit" mnemonic @ 600 baud
MODULE: 'T' Echoed back to MASTER @ 38400 baud
MASTER: 'XON' 0x11 @ 600 baud, MASTER is ready to receive data
MODULE: EEPROM contents 512 bytes @ 38400 baud
To accommodate baud rate switching in the MASTER, the SMARTDOT module inserts a
delay between each reception from the MASTER and subsequent transmission to the
MASTER. Including the delays, the entire upload process still takes less than a second.
Appendix C includes timing diagrams for the individual command protocols: Figures C-1
(Upload Command), C-2 (Mode Command), and C-3 (Configuration Command).
27

2.8 PERFORMANCE
Approximately 500 frames (about 50 games) have been thrown with various versions of
the SMARTDOT module installed in several different bowling balls. To this point, the
author has been the sole user of the device and his bowling style has been the sole source
of input for developing the embedded software for the module. Although care has been
taken to generalize the module's embedded software, until wider range testing can be
performed, the embedded software must be considered as adapted to the author's style of
bowling and the specific parameters of his game.
The graph of a typical waveform captured by the SMARTDOT module prototype is
shown in Figure 2-6, which is a screen capture from the PC-based MASTER application
developed in concert with the SMARTDOT module.
The raw data points are shown in blue, the resulting waveform is shown in green, and the
impacts registered for this shot are shown in orange. The numerical results of the
analysis of the data are shown under the "RELEASE" and "IMPACT" headings. The
MASTER application is presented in Section III of the paper.
Figure 2-6: MASTER "Raw Data" Screen Capture
28

2.8.1 Detecting Release
Detecting the point of release by using a RELEASE light level has been quite effective.
Since the bowler must cover up the light sensor when placing their fingers in the ball, the
module sees a very low level of light (essentially 0) while the bowler is gripping the ball.
There are circumstances when, as part of a bowler's normal ritual, they insert and remove
their fingers in the ball several times before commencing their delivery. SMARTDOT
detects each of these as a release, assuming enough pressure has been applied to activate
the module, but the discrimination routine is intended to recognize, and ignore, such
behavior.
Pre-sampling of the waveform helps capture the moment of release - that point when the
light samples start to increase from their dark pre-release levels. Although the module
uses the configured RELEASE level to detect release (at which time it writes the eight
pre-samples to EEPROM), the MASTER program determines the exact moment of release
from those pre-sample values, which might differ from the time the module used by one
or two sample times. Referring to Figure 2-7, which zooms in on the first 400 msecs of
the waveform shown in Figure 2-6, the pre-sample light level is actually 0 (completely
dark) until the bowler starts to release the ball at -17 msecs. Release occurs between -8
msecs and 0 msecs, where a sharp increase in the light level is evident.
70
60
50
Impact with Lane
(ball loft)
Light Level
40
30
20
Release
Point
Finger Pressure
at Release
10
0
-50
0 50 100 150 200 250 300 350
Milliseconds (since Release)
Figure 2-7: Raw Data Release Region (400 ms)
2.8.2 Detecting Impacts
The piezoelectric film sensor and the comparator circuitry are more than adequate for
detecting the various impacts the ball experiences. Several impacts are shown in Figure
2-7, which presents the first few hundred milliseconds after release. At two consecutive
sample times, -8 msecs and 0 msecs, the sudden pressure that the bowler applied to the
finger insert while releasing the ball is indicated. At 183 msecs, the graph indicates the
ball contacting the lane. The module consistently records both the pressure applied at
release and the impact generated when the ball hits the lane.
At the other end of the lane, the module has no problem detecting multiple impacts with
the pins, as seen in Figure 2-8 (an expansion of the waveform in Figure 2-6). This
particular waveform is from a ball that hit the 1-3 pocket and resulted in a strike. A good
pocket hit generally results in the ball hitting four pins on its way through the rack, and
there are four impacts indicated on the graph. Throughout testing, solid pocket hits
tended to generate four impacts, while light pocket hits, and high hits resulted in three
29

impacts. By looking at the "signature" of the impacts, it might be possible for the
MASTER application to utilize the impact information at the pins to discern whether or
not the ball hit the pocket. It might also be possible to discriminate between the first and
second balls of a frame by looking at the impact signatures of consecutive waveforms.
Light Level
140
120
100
80
60
Impact
(Head Pin)
Impact
(5 Pin)
Impact
(3 Pin)
Impact
(9 Pin)
40
20
0
2450
2500 2550 2600 2650 2700 2750 2800 2850
Milliseconds (since Release)
Figure 2-8: Raw Data Impact Region (800 ms)
2.8.3 Waveform Discrimination and Validation
Correct operation of this function is critical for proper and convenient operation of the
module. The discrimination routine implemented in this version of the module is quite
simplistic, and is based on observations of waveforms from just a single individual. In
that regard, the routine served its purpose, but it does have some inherent limitations.
Figure 2-9 shows the first 800 msecs following release of the ball. The module must
determine, within the first 533 msecs after release, whether to continue recording the
waveform, or to switch to detecting the COMM wand. With the limited scratch pad space
available (72 samples worth) for the module to make this decision, it is possible for the
routine to "misfire". Since the author generates about 420 rpms (7 rps) at release, the
routine can detect three revolutions in the validation time of 533 msecs, causing it to
decide that the ball is, in fact, rolling down the lane.
However, when executing certain spare shots, many bowlers release the ball with as little
rotation as possible in order to "flatten" the ball's hook. In this case, the module reaches
the end of the scratch pad before the discrimination routine has determined that the ball
is, in fact, rolling down the lane. The discrimination routine decides that the waveform is
invalid, and switches to detecting the COMM wand.
The waveform in Figure 2-10 was captured using the module's TEST mode, and displays
a waveform from just such a spare conversion (10-pin). This waveform resulted from the
ball rolling down the lane, but the first 600 msecs do not conform to the current definition
for a "valid" waveform in the module's embedded software.
30

Light Level
100
90
80
70
60
50
40
30
20
1 st
complete
Revolution
2 nd
complete
Revolution
10
0
Release
Point
-50 0 100 200 300 400 500 600 700 800
Milliseconds (since Release)
Figure 2-9: Raw Data Release Region (800 ms)
Figure 2-10: 10-Pin Shot, "Raw Data" Screen Capture
31

Also, there have been instances in AUTO mode where the module recorded what
appeared to be the ball returning to and rolling on the ball return. SMARTDOT is
activated on every impact (as well as when the finger insert is pressed), and one of these
impacts can occur when the ball is hoisted from the subway up to the ball return. If the
module is facing downward after this impact (so that the release level is not detected at
start-up), and the ball rolls fast enough after start-up to satisfy the discrimination routine,
a "misfire" results.
If the module is in AUTO mode when this scenario occurs, the result is that the waveform
from the ball just rolled is lost, overwritten by the "misfire" generated at the ball return.
See the "Future Work" section for more information on revisions to the discrimination
routine.
An interesting observation from the waveform in Figure 2-9 is that the first complete
revolution of the ball occurred before the ball hit the lane. Thus, this revolution has not
yet been impacted by the interaction between the ball and the lane, and is truly
representative of the angular velocity of the ball at release.
2.8.4 Waveform Shape
The initial premise behind using a light sensor to detect revolution of the ball was that the
digitized light waveform would be roughly sinusoidal in nature. Looking at Figures 2-9
and 2-11, the actual waveform is much "rougher" than anticipated. Figure 2-10 shows
the first 800 msecs of a waveform, Figure 2-11 shows 800 msecs of the same waveform,
centered at the ball's initial impact with the pins.
140
120
100
Last complete
Revolution
Impact
(Head Pin)
Light Level
80
60
40
20
0
2000
2100 2200 2300 2400 2500 2600 2700 2800
Milliseconds (since Release)
Figure 2-11: Waveform Shape, Impact Region (800 ms)
Although the captured waveform is not exactly sinusoidal, it exhibits some basic
characteristics that are encouraging, such as a periodic oscillation, and a sinusoidal shape
in the "valleys" of the waveform. A sinusoidal envelope closely approximating the
digitized waveform is superimposed on the graphs, and the beginnings and endings of
each complete revolution of the ball, located by the peaks in the sine wave, are
demarcated in red. A digital filter applied to the captured data could extract the target
sine wave.
32

By filtering the data, and then counting the number of samples between the peaks, it is
possible to find the angular velocity (rpms) for each of the revolutions. In Figure 2-9,
there are between 16 and 17 samples in each of the revolutions, and the time between
samples is 8.333 msec (120 Hz sample rate), yielding an angular velocity of 424 to 450
rpms (7.06 - 7.50 Hz). In Figure 2-11, there are between 15 and 16 sample times,
yielding an angular velocity of 450 to 480 rpms (7.50 to 8.0 Hz).
One concern immediately apparent from the results just obtained is that by using the
method described (measuring time by counting samples), a difference of one sample time
resulted in a change of ~25-30 rpms over a range of 425-480 rpms (± 2.8%). A finer
resolution in the angular velocity calculations is probably required. Another concern is
developing a method for calculating appropriate cut-off frequencies for the digital filter.
Suggestions for dealing with these problems are presented in Section III.
2.8.5 Communications
The module's software UART has turned out to be quite reliable. In an infrared (IR)
wireless environment, the proximity of the communicating devices and ambient
background light infiltration are the two main concerns. The proximity of the devices is
fixed at about 1 3 / 8 " (1.375"), as long as the user does not remove the COMM wand during
communications.
Normally, an IR filter would be used to block visible light, but in this application,
detection of visible light is necessary. By having the module detect the presence of the
COMM wand (by looking for a very low light level), the module can assure that
background light infiltration has been reduced to an acceptable level before initiating
communications with the wand.
One recurring problem was encountered that will be fixed in a later version of the module
software. During the upload portion of the "Transmit" command, if the COMM wand
was moved such that light infiltrated during the wand's reception of the EEPROM
contents, the data file could be corrupted without detection by the MASTER program.
There is no handshaking going on during this portion of the exchange, and if the COMM
wand is positioned just right, it is possible for the 120 Hz fluorescent noise to simulate
repeated START bits. The wand continues to see START bits, and consequently continues
to receive data until it has counted 512 bytes, at which time it proceeds to process the
data.
Suggested improvements for the communication routines are discussed in the "Future
Work" section.
2.8.6 Battery Life
A major design goal was to limit the overall current drawn by the module. Lithium coin
cells are rated in milliamp-hours (the number of hours the battery can supply one
milliamp of current while maintaining its rated battery voltage). Several different
techniques were used to limit the current draw of the module. The TSL251 light sensor is
turned off when not in use, reducing current draw by 800 µAmps. While the module is
running, the 87C752's IDLE mode is used between sample times. This cuts the average
current draw of the module from 3.5 mAmps to under 2.0 mAmps. Extensive use of time
outs has also helped to limit the run time of the module. For any given shot, the average
current draw is 2.5 mAmps for 3-4 seconds, yielding 7.5-10 mAmp-seconds per shot.
33

However, testing revealed that there are also multiple "false" activations per shot, which
occur before release of the ball and from the ball return mechanism handling the ball.
These activations typically accumulate 10-15 seconds of additional run time, accounting
for another 25-35 mAmp-seconds per shot. Therefore, the actual battery usage works out
to be ~40 mAmp-seconds per ball. For a 200 mAmp-hour coin cell, this yields a battery
life of 18,000 shots (about 1000 games). The bowler could use the module up to 20
games a week for a year without having to replace the battery. A lower capacity battery
could also be specified, reducing the cost, weight, and height of the module.
2.9 FUTURE WORK
The prototype SMARTDOT module was developed to serve three functions: first, as a
proof-of-concept; second, as a data collection device to capture and characterize the
ambient light waveform that the module was being developed to record; and third, to
serve as the initial hardware platform upon which to develop and test the embedded
software for the commercial SMARTDOT module.
Recall that the nature of the light waveform was unknown at the start of this project.
Much knowledge has been gained since then from actually being able to observe and
analyze the captured data. This knowledge will be put to use in future iterations of the
module's embedded software.
Also, in the time since the design and construction of the SMARTDOT module prototype,
component technology has improved tremendously. Upgrading the module with these
advanced components will allow for significant improvements in the capabilities of both
the hardware and the embedded software, as well as in reductions in the cost, size, and
weight of the module.
2.9.1 Microprocessor
Microprocessor technology in the 8-bit arena has changed quite dramatically in the last
few years. Cygnal Integrated Products just recently introduced a true system-on-a-chip
8051-based microprocessor (C8051F300x). The 'F300x contains 8K bytes of on-board
flash memory (which can be used for both program and data), 256 bytes of RAM, an
advanced serial UART, advanced power-management functions, on-board ultra-low
power comparators, a low-power analog-to-digital converter (ADC), on-board
programmable oscillator, and reset circuitry, all in a package that measures 3mm by
3mm. With this microprocessor, the TSL25x light sensor, LED's and a small amount of
passive components, the module can be redesigned to be smaller, cheaper and more
powerful than the current design. It will even be possible to upgrade the module's
embedded software via the infrared interface while the module remains in the ball.
The 'F300x also makes certain software improvements possible. Since it contains both an
on-board comparator and a hardware UART, it will be possible to feed the TSL251
output to the comparator and then to the reception port of the UART. In addition, the
transmission port of the UART can directly drive the transmit LED's, allowing for much
higher transmit baud rates. This will be an issue with the much higher serial EEPROM
densities now available (see "Sample Memory" below). These improvements also
eliminate the software UART, freeing up a significant amount of code space.
34

The 'F300x can write to any portion of its flash memory "on the fly". Therefore, flash
memory that is not used for code space is available as sample memory. If the code can
be limited to 2K bytes, as it is in the prototype, 5.5K of on-board flash memory is
available for data space (the high-order 512 bytes are reserved for factory use). A
scheme for compressing the sample data is proposed in the "Data Compression" section
that allows for the recording of an entire game's worth of data (up to 21 shots) for most
bowlers. Using the excess on-board flash memory as the sample memory eliminates the
need for an external serial EEPROM chip, which results in cost savings and reductions in
PCB space and the overall weight of the module.
The 'F300x provides additional advantages. Where as the Philips 87C752 has an
instruction rate that is 1 / 12 of the clock frequency, the 'F300x's average instruction rate is
one-half that of the clock frequency, executing instructions at six times the rate of the
'752. Faster instruction execution means more time can be spent in the IDLE mode. The
'F300x also has an on-board ADC that samples at a rate 10 times faster than the '752,
again cutting down on time spent out of IDLE mode. In addition, the 'F300x has the
ability to switch its internal clock frequency, meaning that it can slow down when it's not
processing data, and speed up when it has work to do. Once again, this results in a
reduction in current draw. These additional power reductions could result in an average
current draw of one-eighth to one-quarter that of the current SMARTDOT prototype,
allowing the use of a smaller, cheaper, lighter-weight battery.
2.9.2 Communications
Since it is very easy to inject noise into an IR connection, the module should issue a
checksum after each grouping of bytes so that the MASTER program can verify the
contents of the data. The module should also send a fixed terminating character to
indicate that the transmission is complete. This character won't be unique to the
transmission since the data can take any of the 256 values, but it will be positioned at a
fixed location in the transmit stream. These were oversights in the current version of the
embedded software.
Ultimately, it would be beneficial to implement a limited IrDA (InfraRed Data
Association) protocol stack. Using one of the standard IrDA protocols would facilitate
communication with just about any PDA-type device, all of which utilize various IrDA
protocols to "beam" information back-and-forth. Unfortunately, implementing an IrDA
stack in an 8-bit device is a fairly complex task, which also consumes a fair amount of
code space. For now, it is something that will remain on the backburner.
2.9.3 Sample Memory and Multiple Waveforms
As the prototype is currently designed, the SMARTDOT module can only record one shot
at a time. This has proven to be highly inconvenient and time-consuming. Much more
desirable is the ability to record multiple shots, preferably at least an entire game's worth
of data, between uploads. In addition, the effectiveness of the waveform discrimination
and validation routine is severely impacted by the limited amount of scratch pad memory
in the prototype. If the module had more time (meaning more space) to record data while
deciding the source of a waveform, it could perform this task much more reliably.
In the time since the SMARTDOT module prototype was assembled, serial EEPROM
memory densities have increased dramatically. Using the assumptions previously
presented (a 4 second maximum sampling time at a 120 Hz sample rate), the amount of
data memory required to store the data for a single game can now be determined. It is
35

possible to roll up to 21 shots in one game of bowling. Allowing a maximum of 512
bytes per ball (500 samples, plus some additional header information), 10752 bytes are
required to store the "worst-case" game: 21 balls thrown at 10 mph.
Serial EEPROM is now available in 8Kx8 (64K bits), 16Kx8 (128Kk bits), and 32Kx8
(256K bits) chips, with 64Kx8 (512K bits) soon to be available. The 16Kx8 chip is
mandated using the above criteria. If a sample rate of 240 Hz is required, the 256Kb
module would have to be specified, with a commensurate increase in cost. At a 120Hz
data rate, the 256Kb chip will also accommodate three full games of bowling, which is
significant, since a league series usually consists of three games.
The above calculations are based on minimum ball speeds (maximum sample time per
ball). However, a greater number of shots can be captured for a given size memory if the
data is stored in variable length records. Such a record would consist of header
information (the ball count, the activation count, the run time, the length of the record, a
pointer to the previous record, a pointer to the next record, etc.) and the actual sample
data. The records would be stored as a doubly-linked list, and uploaded as a group,
probably at the end of each game, which would free up the memory for the next game.
2.9.4 Data Compression
Although serial EEPROM memory has increased in capacity while also becoming
cheaper, it is cost-effective to use the smallest memory space that will hold a game's
worth of data (21 balls maximum). The data collected so far might possess
characteristics that could be exploited by a data compression routine. Bearing in mind
that the collected waveforms are from a single bowler and a single bowling
establishment, it would be incorrect to assume that this data is representative of the entire
bowling population. However, it should be possible to draw some initial useful
conclusions that are worth further study.
It was originally assumed that the waveform the SMARTDOT module records would have
a roughly sinusoidal shape. Looking at just the lower half of the waveform, that
assumption is basically valid. However, the waveform exhibits striking directionality
when the module is facing the ceiling, as can be seen in Figure 2-10. By setting 0° to be
that point where the module is facing directly toward the ceiling, it is apparent that the
sample-to-sample values change rather rapidly (20 or more counts at a time) in the range
from 270° to 90°. This phenomenon results from the fluorescent ceiling lights acting as
point sources, rather than as a uniformly distributed light source, and from the module
being located below the surface of the ball.
However, the sample-to-sample values in the 180° of rotation between 90° and 270°
change relatively slowly (only a few counts at a time). This portion includes the valleys
of the waveform, which are produced when the module faces the lane surface, in the
shadow of the ball. The "interesting" portion of the waveform falls within the range 10-
50 (0x0A to 0x32), where the waveform exhibits a finer granularity. This information
can be used to advantage in contemplating appropriate data compression techniques.
A system needs to be established that can store two samples in one byte - 4 bits per
sample. If samples could be stored as a value relative to each other, or relative to some
known fixed value, this goal might be accomplished. It would be beneficial to maintain a
fine granularity around the inflection points of the valleys in the waveform, and loosen
that granularity as the sample values move further away from those inflection points.
36

One possibility is to use a transformation table to record the data. Each sample would be
compressed into four "value" bits, plus a fifth "range" bit. Two adjacent compressed
values would be stored together in a byte, while the "range" bits would be stored
consecutively in groups of eight comprising a "range" byte. The impact bits would also
need to be stored in separate bytes. In this fashion, six bytes would be required to store
eight samples: four dual sample bytes, one range byte, and one impact byte. Thus, a
compression of 25% has been achieved, allowing an 8-Kbyte external EEPROM to hold a
"worst-case" game's worth of sample data. The data for one waveform would be stored
as shown in Figures 2-12a and 2-12b.
(one header per waveform)
1 2 3 4 5-8
Ball
Count
Previous
Record
(address / 8)
Next
Record
(address / 8)
Pre-Samples
Impact Byte
(8 impact bits)
Pre-Sample Bytes
(no translation)
1 2 3 4 5 6 7 8
Figure 2-12a: Waveform Header
(repeated up to 60 times for 480 samples)
1 2 3-6
Impact Byte
(8 Impact bits)
Range Byte
(8 Range bits)
Sample Bytes
(translated values)
1 2 3 4 5 6 7 8
Figure 2-12b: Waveform Compressed Sample Record
An example translation table is shown in Figure 2-13. Notice that this table yields a nonlinear
translation, resulting in a hash function that converts 8-bit values into 5-bit values
(4 data bits plus the "range" bit). For example, using the translation table of Figure 2-13,
if eight consecutive samples contained the values 10, 12, 16, 38, 57, 75, 118, and 85 and
impacts were registered at the third (16) and fourth (38) samples, the compressed data
would appear as shown in Figure 2-12c.
1 2 3-6
Impact Byte
30h
(0011 0000)
Range Byte
1Fh
(0001 1111)
Sample Bytes
(translated values)
2 2 4 5 B C E D
Figure 2-12c: Compressed Samples Example
37

2.9.5 Module Training
Due to variations in bowler style and bowling
equipment, and with inherent variations in the
ambient background light levels at various bowling
establishments, it will probably be necessary to
"train" the module for a given bowler, and for a
given establishment. This can be easily
accommodated at the beginning of each session of
bowling.
The MASTER application would issue a command to
the module to take samples without data
compression. This data, collected from several
"training" shots would then be uploaded to the
MASTER program, which would scan the data and
come up with the best-fit translation table, and
download the table to the module. The module
would then use these values in its data compression
routines. If the module was not trained, it could use
the last translation table downloaded to it as a
default.
The MASTER program could also determine the
average ball speed of the bowler and use this
information to decide whether there was enough
room to store uncompressed data (since the amount
of space used is dependent on the waveform sample
time), or to use the data compression function.
Stored
Nibble
Value
Actual Sample Value
(0) Range
Bit
(1) Range
Bit
0x0 < 5 28-29
0x1 5-8 30-31
0x2 9-12 32-33
0x3 13-14 34-35
0x4 15-16 36-37
0x5 17 38-39
0x6 18 40-41
0x7 19 42-43
0x8 20 44-45
0x9 21 46-49
0xA 22 50-54
0xB 23 55-59
0xC 24 60-79
0xD 25 80-99
0xE 26 100-127
0xF 27 >127
Figure 2-13: Data Compression
Translation Table
2.9.6 Adjustable Sampling Parameters
Preliminary analysis of the data collected revealed that some type of digital filtering is
required in order to extract useful data from the captured waveform. However, the 120
Hz sampling rate may not be high enough to accurately achieve the desired resolution in
angular velocity (rpms). The 120 Hz rate is the minimum acceptable, but 240 Hz, or
even 480 Hz, may be required. Of course, higher sampling rates increase the data storage
requirements, and require faster EEPROM write times. Ramtron makes an appropriate
density ferroelectric serial EEPROM with a write time equivalent to the data bus speed
that fits the application, although the cost-per-bit is ∼50% higher than that for standard
serial EEPROMs [22].
The sampling rate could be adjusted based on the rate of rotation the bowler applies to the
ball and on the velocity that the bowler throws the ball. The higher the rate of rotation,
and/or the velocity, the higher the sampling rate should be. But with a higher ball speed,
less time is required to sample the full waveform, so there should be some offset between
the increased sample rate and the reduced sample time.
Another option is to interpolate between 120 Hz samples based on the rate of change of
the sample values surrounding the values to be interpolated. This interpolation would be
handled by the MASTER application.
38

2.10 SUMMARY
This portion of the research has shown that the in-situ sensor module is a viable concern,
although the current prototype has its limitations. The major limitation is that the module
is capable of capturing only one shot at a time. Given the advances in data storage
density and reductions in cost-per-bit, this limitation can be easily overcome.
Another major limitation is the effectiveness of the discrimination routine, but the routine
has been hampered by a lack of scratch pad memory space. This limitation is also solved
with an increase in the available storage space.
Now that the nature of the waveform is better understood, the next version of the module
will be more attuned to capturing the essence of the data. In addition, advances in
technology have made it possible to cut the weight and height of the module, as well as
the component cost, by at least a third. Those same advances also allow more
sophisticated techniques to be implemented within the module's embedded software, such
as data compression, variable sampling frequencies, better waveform discrimination, and
more advanced communication techniques.
The major concern to emerge during the SMARTDOT module's development is the
"rough" shape and the directionality of the captured ambient light waveform. Although it
is possible to visually count the revolutions of the ball directly from the waveform, it is
not at all evident that the angular velocity of the ball changes as the ball rolls down the
lane, nor is it possible to resolve the revolution count to better than about one-half
rotation.
Consequently, some level of digital signal processing is required in order to remove the
"noise" from the waveform before beginning to extract the useful information from that
waveform. The methods used to digitally filter the raw data and the assumptions and
methods used to extract the "interesting" information from the filtered waveform are
presented in the next section.
39

SECTION III: ANALYZING THE DATA - THE MASTER APPLICATION
This portion of the paper presents the data manipulations used to extract the waveform
from the raw data, the assumptions for analysis of the waveform, the mathematics and
physics behind those assumptions, and the possible information that can be derived from
the extracted waveform. Consideration is also given to future possibilities for analysis
and presentation of the data.
The SMARTDOT sensor module is intended solely as a data collection device, serving as
the sensing mechanism for the SMARTDOT system. The actual power of the system,
however, will reside in the MASTER application. For the purposes of this portion of the
project, it was necessary to develop a data-analysis program that was capable of
communicating with the module, and uploading, storing, and facilitating a quick analysis
and assessment of the data at the test site (a local bowling establishment) on a laptop
computer. As such, the current MASTER program is a research tool - the creation of a
user-friendly, GUI-based analysis and presentation package falls into the development
phase of the project.
3.1 RAW DATA ANALYSIS
The original premise behind the development of the SMARTDOT system was that the
light waveform the module captures would be sinusoidal in nature, and that information
relevant to the action of the ball could be extracted from that digitized waveform. Under
ideal circumstances, with truly uniform lighting, the data that SMARTDOT collects would
closely transcribe a sine wave. In actuality, the captured waveform is quite "rough" - it
does exhibit "peaks" and "valleys" like a sinusoid, and it also possesses a cyclic,
repetitive shape, but it only loosely resembles a simple sine wave.
It is possible to visually identify and count the revolutions of the ball from the raw data,
to a resolution of one-quarter to one-half revolution. The release and impact times are
captured with a fair amount of accuracy, and it is easy to use them to calculate the
average speed of the ball. However, the "rough" shape of the waveform makes it
impossible to reliably determine the starting and ending points of a particular revolution,
nor is it "easy" to determine the total number of revolutions to better than one-half
rotation. After the first look at the digitized waveform data in the early portions of the
research, it was obvious that the raw data would have to be digitally filtered before it
could be used in an automated analysis program.
3.1.1 The "Ideal" Waveform
Before developing a digital filter for the raw data, some understanding of what the
desired data should look like must be gained. Recall that the ball is released with a linear
velocity that is greater than the corresponding angular velocity will support - the ball is
skidding (traveling faster than it is revolving). Friction between the ball and the lane
works to resolve this discrepancy between the angular and linear velocities of the ball.
With no other force but friction acting on the ball from the moment of release until the
moment of impact with the pins, the ball experiences a monotonic increase in its angular
velocity (at any instant, the ball's angular velocity is greater than at any previous instant),
and a corresponding monotonic decrease in its linear velocity.
40

The ball's angular velocity increases until the discrepancy between the angular and linear
velocities is resolved (a condition called roll out). If the ball rolls out before reaching the
pins, it is no longer skidding, and the continuing decrease in its linear velocity due to
rolling friction also directly impacts the angular velocity (it begins to monotonically
decrease, as well). Under normal circumstances, the ball does not roll out before hitting
the pins, and therefore, the angular velocity generally increases until the ball hits the pins.
Given a uniform light distribution along the length of the lane, the light level seen by
SMARTDOT will be at its highest (brightest) when the module faces directly towards the
ceiling, and at its lowest (darkest) when the module faces directly towards the floor, with
a smooth transition occurring between those two points. Under these circumstances, a
graph of the light waveform appears as an increasing frequency "chirp". The peaks and
valleys of the sinusoid are spaced further apart near the release point, and get closer
together as the ball approaches the pins. Figure 3-5, which is a capture of the filtered
"Waveform" screen from the MASTER program, depicts this waveform.
If the ball rolls out, its angular velocity reaches a maximum at the roll out point, and then
begins decreasing. It is possible to use this information to detect whether or not roll out
has occurred by looking for a decrease in the angular velocity.
Recall also that friction-reducing lane oil is regularly applied to the first 30-40 feet of the
lane. Therefore, the ball is more prone to sliding on the upper half of the lane (nearer the
foul line), with the majority of the increase in angular velocity occurring on the lower
half of the lane (nearer the pins). Therefore, a graph of the angular velocity of the ball
versus time (or distance from the foul line) will have a hyperbolic or exponential shape,
assuming roll out has not occurred. The graph of the linear velocity will mirror that of
the angular velocity, starting high and falling off at the end. Figure 3-7, which is a
capture of the "Analysis" screen from the MASTER program, depicts these two graphs.
If the ball had rolled out, the graph of its angular velocity in Figure 3-7 would display an
inflection point at the point of roll out, decreasing after roll out, while the graph of its
linear velocity would continue to decrease. Figure 3-9 depicts a waveform that resulted
from the ball rolling out before hitting the pins.
3.1.2 The "Real" Waveform
The "jagged" appearance of the raw data waveform, as shown in Figure 3-1, indicates
that a good deal of high frequency "noise" has been captured along with the desired
waveform. Since the module filters out the 120 Hz flicker of the overhead fluorescent
lights while capturing the waveform, this noise must have another cause. In fact, the
noise could be the result of three additional sources: the non-homogenous nature of the
overhead lighting; the directionality of the light sensor that was introduced by placing the
SMARTDOT module at the bottom of a finger hole, 1 3 / 8 inches below the surface of the
ball; and from "aliasing" of frequencies greater than one-half the sampling frequency.
These higher frequencies might result from flash bulbs, reflections, etc. Other than these
transient sources, aliasing should have minimal impact, since there are no significant
sources of flickering light greater than 120 Hz in a bowling center.
41

Figure 3-1: MASTER "Raw Data" Screen Capture
The non-homogenous nature of the overhead lighting can be seen in Figure 3-2, which
zooms in on the first 800 msecs of Figure 3-1. Multiple local peaks are evident during
each revolution, with each of these "side lobes" occurring as a row of ceiling lights comes
into view of the light sensor. Looking closer, it is also evident that the side lobes grow
and recede as the ball travels further down the lane. Eventually they disappear
completely, as is evident in Figure 3-3, which zooms in on the last 800 msecs of the shot
in Figure 3-1.
The directionality of the module can be seen in the shape of Figure 3-3. The light level
rapidly approaches a peak value when the light sensor is pointing almost directly at the
light source, and just as rapidly retreats as the light sensor rotates away from the light.
Notice that the valleys of the waveform do not display this directional characteristic.
Drawing from Fourier analysis techniques, the cyclic waveform shown in Figure 3-1
must have a fundamental frequency close to that of its major peaks, which resulted from
each rotation of the ball. For a cyclic waveform to exhibit such sharp peaks, there must
also be a significant amount of high-frequency harmonic content. The multiple local
peaks present in each revolution, as shown in Figure 3-2, will be responsible for some
significant intermediate harmonic content, as well [7].
42

Light Level
100
90
80
70
60
50
40
30
20
10
0
Release
Point
-50 0 100 200 300 400 500 600 700 800
Milliseconds (since Release)
Figure 3-2: Raw Data Release Region (800 ms)
By considering the nature of the ideal waveform (an increasing frequency "chirp"), it is
possible to deduce the shape of the frequency spectrum of the raw data. Since the lane is
more heavily oiled near the foul line, the coefficient of friction is lower, and the ball will
slide more. This sliding prevents the ball's linear momentum from being transferred into
angular momentum, thus maintaining a fairly constant velocity for the first few
revolutions of the ball. Thus, a fundamental frequency is established that is close to the
initial angular velocity at release.
140
120
100
Impact
(Head Pin)
Light Level
80
60
40
20
0
2000
2100 2200 2300 2400 2500 2600 2700 2800
Milliseconds (since Release)
Figure 3-3: Raw Data Impact Region (800 ms)
As the ball continues down the lane, it eventually gains angular velocity, and this change
will be reflected in additional higher frequency content, albeit with a decreasing
magnitude, in the frequency bands immediately adjacent to the fundamental frequency.
Due to the harmonic content introduced by the sharp peaks and multiple local peaks,
there should be additional frequency content at integer multiples of the fundamental
frequency, appearing as an attenuated "echo" of the shape of the frequency content
around the fundamental. The characteristic frequency spectrum shape just described is
shown in Figure 3-4.
43

3.2 FILTERING THE RAW DATA
Figure 3-4 is a capture of the "Spectrum" screen from the MASTER program, and
demonstrates the use of digital signal processing (DSP) and, more specifically, the
application of the Fast Fourier Transform (FFT) to the raw data waveform shown in
Figure 3-1. By obtaining the frequency spectrum of the raw data, it is possible to identify
and retain the fundamental frequencies, while removing the harmonic content and other
noise. Applying the inverse FFT function (FFT -1 ) to the modified spectrum then yields
the filtered waveform of Figure 3-5, which closely resembles the ideal waveform that was
previously described [7,10].
Figure 3-4: MASTER "Spectrum" Screen Capture
The MASTER program must be able to perform this filtering automatically, without any
user input. Therefore, a reliable method for the MASTER to identify the fundamental
frequency, and the band of frequencies of interest, must be developed. For this
application, the fundamental frequency will be considered the component of the spectrum
with the greatest magnitude in excess of 2.0 Hz.
Looking at the spectrum of Figure 3-4, it is easy to identify the fundamental frequencies
centered at ~7.5 Hz (disregarding the low-frequency components located below 2.0 Hz),
with the first harmonic centered at twice the fundamental (~15 Hz). The magnitude of
44

the fundamental frequency has been normalized to 1.00, with the remainder of the
frequency components normalized relative to the fundamental frequency [7].
Extracting the desired waveform requires a bandpass filter that removes the unwanted
low and high frequencies while leaving the frequencies of interest unaltered. It is
important to note that the fundamental frequency will vary from bowler to bowler.
Consequently, a bandpass filter with fixed upper and lower bounds is not appropriate.
Instead, the MASTER must calculate the pass band dynamically for each bowler, and
possibly for each individual shot.
Several basic methods are appropriate for calculating the pass band limits. These limits
can be set based on:
• A percentage of the fundamental frequency.
• A percentage of the magnitude of the fundamental frequency.
• A combination of the first two.
There are two separate limits imposed on the upper band of the filter. First, the pass band
should not be allowed to extend into the harmonic portion of the spectrum, as this will
introduce components of the noise the filter is intended to remove. Second, the ball
reaches its highest angular velocity at the point of roll out, or at impact with the pins if it
doesn't roll out, and it can revolve, at most, 26.7 times in 60 feet (if it did not skid at all).
Combining that information with the time of transit of the ball, it is possible to apply an
upper bound to the maximum angular velocity of the ball and, therefore, the high side of
the bandpass filter.
The dashed orange line around the fundamental frequencies in Figure 3-4 represents the
adaptive bandpass filter for this spectrum. The MASTER program calculated these limits
automatically, using the third method listed above (through a combination of frequency
percentages and magnitudes). The MASTER identifies the fundamental frequency, and
then extends the pass band limits on either side of the fundamental until it finds an area of
"insignificant contribution". In this case, it finds a contiguous group of frequency
components with magnitudes less than 0.1 (10% of the fundamental).
The bandpass filter limits must also conform to minimum and maximum percentages of
the fundamental frequency. The spectrum shown is typical for the author's bowling style
and he has found that the minimum low cut-off frequency can be set relatively close to
the fundamental frequency (75% of the fundamental), while the high cut-off frequency
should be at least 125% of the fundamental, but no more than 175% of the fundamental.
Of course, these limits may differ for other bowlers.
With the pass band limits identified, a digital bandpass filter can now be applied to the
spectrum. The magnitudes of the frequency components within the pass band are
retained, while those outside the pass band are set to zero (0.00). Applying the inverse
FFT function (FFT -1 ) to the altered spectrum yields the waveform shown in Figure 3-5.
This filtered sinusoidal waveform describes the rotation of the finger hole that contained
the SMARTDOT module and, since the entire surface of the ball rotates at the same rate
as the finger hole, this waveform also describes the rotation of the ball. The 'C' source
code from the MASTER application for the adaptive bandpass filter implementation has
been included in Appendix D.
45

3.3 FINDING REVOLUTIONS AND ANGULAR VELOCITY
Due to the regular sinusoidal nature of the filtered waveform of Figure 3-5, it should be
possible to develop methods that enable the MASTER to automatically "count" the total
revolutions of the ball, find the period of each revolution, and calculate the angular
velocity (rpms) for each of those revolutions.
Figure 3-5: MASTER "Waveform" Screen Capture
Define a full revolution of the ball as starting at any local maximum or minimum of the
filtered waveform, and ending at the sample before the next local maximum or minimum,
i.e., two consecutive "peaks" or "valleys" define a revolution. The period of any
revolution can be found by counting the samples between the two peaks or valleys that
define that revolution, and dividing that count by the sampling frequency.
Let j i,0 and j i,n-1 be the indices of the starting and ending samples for revolution i, and f be
the sampling frequency (120 Hz in this case), then
t i = (i i,n-1 - i i,0 ) / f, where t i is the period, in seconds, for revolution i.
The angular velocity (ω i ) during revolution i is simply the inverse of the period.
ω i = 1 / t i .
46

Since the fundamental frequency and the minimum and maximum frequencies of the
waveform have already been found, and the manner in which the frequency changes over
time (monotonically increasing, with a possible inflection point, if roll out occurred) is
known, it is easy to develop a method to locate the local maxima and minima of the
filtered waveform.
This is accomplished by starting at the beginning of the filtered sample array (which
includes the pre-samples), and working through the array, looking for inflection points
(those points where the waveform changes direction). Each time an inflection point (a
local minimum or local maximum) is found, the index of the inflection point is recorded
in a separate array. Due to the monotonically increasing nature of the frequency of the
waveform, once the distance (the number of samples) between the first two inflection
points is found, that distance can be used to help estimate the location of the next
inflection point.
There are still two fractional revolutions that must be dealt with: from release until the
first peak, and from the last peak (or valley) to pin impact. Both of these fractional
values can be extrapolated from the angular velocity of the revolution immediate adjacent
to each fractional value.
Again let f be the sampling frequency (120 Hz), and j R be the index of the release sample,
j 1,0 be the index of the sample that begins the first full revolution, j F be the index of the
sample that ends the last full revolution, and j P be the index of the pin impact sample, and
ω 1 and ω F be the angular velocities during the first and last full revolutions of the ball,
respectively, then
R R = ((j 1,0 - j R ) / f) · ω 1 ,
and
R P = ((j P - j F ) / f) · ω F ,
where R R and R P are the fractional revolutions of the ball immediately after release and
immediately before pin impact, respectively.
The discussion in Section II established that there would be at least 15-20 samples per
revolution, allowing R R and R P to be resolved to at least 30° of rotation. Thus, it should
be possible to count the total revolutions of the ball to within 0.1 revolutions, yielding a
resolution of better than 1% for counts greater than 10 revolutions.
Even though a resolution of 1% has been obtained in counting the total revolutions, the
angular velocity can only be resolved to about 4% for a rotation rate of 300 rpms, using
the same technique. This discrepancy arises from the 120 Hz sampling frequency, which
yields a time resolution of 8.333 msecs. Although the waveform does not necessarily
capture the exact peaks and valleys of the waveform, it does at least capture a pair of
consecutive samples that form an 8.333 msec "window" around each true peak or valley.
It is possible to get around the sampling-induced resolution issue by interpolating
between each of those pairs of values to obtain very good approximations of the true
peaks and valleys of the waveform.
Figure 3-6 illustrates a simple interpolation technique for finding the "true" location of
the local maxima and minima of the filtered waveform. By finding the intersection point
of the slope lines of both sides of a peak or valley, the actual peaks and valleys can be
accurately located. Two sample values are used to find each slope line. These samples
47

are located on either side of the mid-point between the top and bottom of each side of a
peak or valley. Recall that the indices of the peak and valley samples were recorded
earlier. The intersection of the resulting two slope lines is considered as the true peak or
valley for subsequent calculations. Each adjacent peak-valley pair defines a halfrevolution
of the ball, and the lateral distance between them, measured in msecs, gives
the period of that half-rotation. The angular velocity for that half-revolution is simply the
inverse of the period.
140
120
Interpolated
Peaks
Half (180°)
Revolutions
Filtered Light Level
100
80
60
40
20
0
2200
Interpolated
Valley
2250 2300 2350 2400 2450 2500 2550 2600
Milliseconds (since Release)
Figure 3-6: Maxima and Minima Location Interpolation
Having obtained the angular velocity for each revolution of the ball, a graph of the
angular velocity of the ball with respect to time can be drawn, as shown in Figure 3-7.
The raw angular velocity values that were just found are shown in blue, with each entry
representing one-half revolution of the ball.
Obviously, something has gone awry. The angular velocity of the ball should be
monotonically increasing, yet the graph of the raw values exhibits a noticeable
oscillation, especially in the first two-thirds of the waveform. Since the angular velocity
of the ball can't actually be rising and falling as indicated by the raw angular velocity
graph in Figure 3-7, some other factor must be at work here.
By looking back at Figures 2-2a, 3-2, and 3-3, the cause of this oscillation can be
deduced. Figure 2-2a depicts the ball rolling down the lane under several rows of ceiling
lights. As stated before, these lights act as a point source, rather than as a uniformly
distributed source of light. As the SMARTDOT module rotates up towards the ceiling, the
light sensor faces backwards (toward the foul line) and "sees" the ceiling lights that it has
already passed under. These lights are detected earlier than they "should" be, i.e., before
the light sensor has rotated directly toward the ceiling. Consequently, the peak light level
for that revolution occurs earlier than it should.
As the ball continues down the lane, the module rotates toward the ceiling, and if it is not
directly under a light, the light level gets darker (rather than brighter), and a dip occurs
where the peak is expected to be. As the ball continues to rotate and travel down the
lane, the module eventually aligns with a different ceiling light and another local peak is
created. Figure 3-2 shows this phenomenon quite clearly. As the ball continues down
the lane, these point sources eventually combine to look like a single light source, hence
the lack of "side lobes" in Figure 3-3.
48

Figure 3-7: MASTER "Analysis" Screen Capture
Depending on the position of the ball relative to the ceiling lights, and the current
orientation of the module in relation to the ceiling, the directionality of the light sensor
can cause it to "see" a ceiling light too early, while at other times it must rotate longer
before encountering the next ceiling light. This action imposes a Doppler-like effect on
the waveform the module captures. The differences must average out, since the ball will
eventually transition from approaching a specific light source to moving away from that
same source, but the effects that this Doppler effect has imprinted on the filtered
waveform must still be dealt with.
Referring to Figure 3-7 again, the green line superimposed over the blue raw angular
velocity graph is a 5 th -order polynomial curve created by a generalized least squares
curve-fitting function, using the raw angular velocity data as input [10,11]. This line
yields the expected shape for the angular velocity curve. This is a "simple" fix that
presents a good approximation for the actual response of the angular velocity of the ball.
However, this method has its limitations. Unlike the actual monotonic response of the
ball, the polynomial curve-fitting scheme allows the angular velocity to initially dip
following release, and then recover as the ball travels down the lane.
The 'C' source code from the MASTER application for locating the revolutions and
finding the angular velocities has been included in Appendix D.
49

3.4 LINEAR VELOCITY, DISTANCE, AND COEFFICIENT OF FRICTION
If the manner in which the linear velocity of the ball changes over time can be
determined, it is then possible to determine the initial (release) velocity, which is one of
the major execution variables that a bowler must learn to control. The ball could then be
located (along with each revolution) on the lane relative to the foul line, rather than
relative to the time of release. This would allow the determination of the ball loft
distance (another major execution variable). Having found the conversion from time
(sample index) to distance, the coefficient of friction acting between the ball and the lane
can also be found, which can be used to infer the distribution of oil on the lane.
Since the length of the lane and the time that it took for the ball to travel from the foul
line to the pins are both known, it is easy to calculate the average speed (linear velocity)
of the ball. But this average value reveals little about the initial velocity that the bowler
applied to the ball at release, except that the release velocity must have been greater than
the average velocity (since the linear velocity of the ball is always decreasing).
Calculating the angular velocity of the ball was fairly straight forward, once the
waveform had been filtered. Even the Doppler effect created by the ball traveling
underneath multiple discrete light sources is fairly simple to deal with. However,
recovering the instantaneous linear velocity from the ball's average linear velocity and the
angular velocity of each revolution presents an interesting, challenging, and non-trivial
problem.
That task is currently the major focus of the ongoing research. One method that is based
on a simplistic form of energy conservation has already been developed. It relies on the
assumption that no energy is lost as friction works to transfer energy from the linear
momentum of the ball to the angular momentum of the ball. The same method can be
generalized to allow for a constant (but arbitrary) percentage of the energy transferred
from the linear momentum to be lost to friction.
To this point in the discussion, all of the MASTER screen captures, with the exception of
Figure 3-7, contained graphs with respect to time, rather than distance. Figure 3-7
contains graphs of both the angular and linear velocities of the ball with respect to
distance from the foul line, and represents the current state of the "Analysis" portion of
the MASTER program, which relies on the simplified version of the linear velocity
extraction function mentioned above.
Throughout the paper, it has been assumed that friction is the only force of any
significance acting on the ball. The results of the frictional force are apparent by
observing the angular velocity of the ball increase as friction acts to resolve the
discrepancy between the initial linear and angular velocities of the ball.
Assume, for the moment, that the ball loses no energy throughout the course of a shot
(the total kinetic energy and the total momentum of the ball remain constant). The
conclusion can then be drawn that all of the momentum the ball gains from the increase
in its angular velocity must have been transferred from the ball's linear momentum, i.e.,
any increase in angular momentum must be exactly offset by a decrease in linear
momentum.
Having assumed constant energy, the energy of the ball for each revolution of the shot
must remain the same. Since the angular velocity (and thus the angular momentum) for
each revolution of the ball has already been found, if the energy for that revolution is
50

known, the linear momentum (and thus the linear velocity) for that revolution can also be
found. Once the linear velocity for each revolution is known, the location of each
revolution of the ball and the ball loft distance, relative to the foul line, can be found.
Putting those assumptions and deductions into more formal terms, the assumption that the
ball does not lose energy over time means that the ball possesses constant energy
throughout its trip to the pins, and that its energy at any instant is equal to its energy at
any other instant [8].
The total energy of the ball (E) is the sum of its potential (P) and kinetic (K) energies:
E = P + K.
Since the ball rolls on a flat, level lane surface, there is no potential energy (P = 0), and
E = K.
Since it is assumed that the ball has constant energy from its release at the foul line to its
impact with the pins,
K R = K i = K P ,
where K i is the energy of the ball for each revolution i between release (K R ) and pin
impact (K P ).
The assumption of constant energy implies that energy losses due to vibration, heat, wind
resistance, and noise generation are negligible. Therefore the only components of the
energy of the ball are its angular momentum (K ω ) and its linear momentum (K v ), thus
K = K ω + K v .
The angular momentum of an object with angular velocity ω is given by
K ω = ½Iω 2 ,
where I is the moment of inertia of the rotating object.
The moment of inertia I of a bowling ball with mass m and radius R falls somewhere
between the moments of inertia of a solid sphere and a spherical shell, such that
2 / 5 mR 2 < I < 2 / 3 mR 2 .
The actual moment of inertia for a given ball will fall between these two values, but
closer to the first, since the density of a bowling ball in the 12-16 pound range is fairly
constant across the radius of the ball [8].
The 2 / 5 R 2 term is a constant, where R is the radius of the ball (nominally 4.3"), so if
k = 2 / 5 R 2 = 0.4 · (0.3583 ft) 2 = 0.05136 ft 2 ,
then
K ω = ½kmω 2 .
The linear momentum of an object with mass m and linear velocity v is
K v = ½mv 2 .
Therefore, the total kinetic energy K of the ball, under the assumptions, is given by
K = ½mv 2 + ½kmω 2
= ½m(v 2 + kω 2 ), where k = 0.05136 ft 2 .
51

3.4.1 Finding the Linear Velocity of the Ball
The following values have already either been measured or calculated:
1) The total distance D T the ball traveled from release to pin impact (nominally 60
feet from foul line to head pin).
2) The time T it took for the ball to travel D T feet.
3) The average linear velocity of the ball v ave = D T / T.
4) The number of revolutions R T that occurred in time T.
5) The period t i and angular velocity ω i = 1 / t i of each revolution i in R T .
Using these values, an equation can be developed that gives the linear velocity v i for each
revolution i of the ball.
Recalling the previous calculations for R R and R P (the fractional revolutions at release and
pin impact), D T can be represented as
D T = R R · (v 1 t 1 ) + v 1 t 1 + v 2 t 2 +....+ v n t n + R P · (v n t n )
= (1+ R R ) · v 1 t 1 + v 1 t 1 + v 2 t 2 +....+ v n t n + (1 + R P ) · v n t n .
By letting t 1 ' = (1 + R R ) · t 1 , t n ' = (1 + R P ) · t n , and t i ' = t i for 1 < i < n, the above equation
can be reduced to the summation
R T
D T = Σ (v i t i ').
i=1
Recall the assumption that the kinetic energy K of the ball remains constant from release
to pin impact, and let K i be the kinetic energy of the ball during revolution i. Then
K i = m / 2 (v i + kω 2 i ), where ω i = 1/t i '
and
K 1 = K i = K n , for 1 ≤ i ≤ n.
From the above,
m / 2 (v 2 1 + kω 2 1 ) = m / 2 (v 2 i + kω 2 i ),
and solving for v i in terms of v 1 ,
v i = (v 2 1 + k(ω 2 1 - ω 2 i )) ½ .
For constant energy, no energy is lost to friction, and the above equation reveals that
friction acts solely to transfer energy from linear momentum to angular momentum. An
expression can now be obtained for each velocity v i in terms of v 1 . Substituting that
expression into the previous summation yields
R T
D T = Σ (v 2 1 + k(ω 2 1 - ω 2 i )) ½ · t i '.
i=1
The value of D T is nominally 60 feet, and this summation can be used in developing a
converging iterative solution for v 1 . The remaining values for v i can be generated from
the value found for v 1 .
52

In order to find the value for v 1 , an initial "seed" value v is needed to start the iteration. A
good first guess for v is the average linear velocity v ave of the ball,
v ave = D T / T,
The actual value for v 1 (the initial velocity) is greater than v ave , since the ball is constantly
slowing down after release. Plugging v ave into the above summation will result in a value
D' that is less than D T . D' can be used to arrive at the next guess, as follows:
v' = v + (D T - D') / R T .
Iteration continues in this fashion (guess, calculate, adjust), until the difference between
D T and D' does not exceed a predefined threshold, at which point a value for v 1 has been
found. The velocities for the remaining revolutions are obtained by plugging v 1 and the
values for ω 1 and ω i into
v i = (v 2 1 + k(ω 2 1 - ω 2 i )) ½ .
3.4.2 Finding the Distance from the Foul Line
Using the values for v i from this equation, a method for converting time (sample index) to
distance for each sample in the waveform can be derived. With such a conversion, it is
possible to find the distance the ball has traveled at any time in the waveform, and also to
graph the linear and angular velocities of the ball with respect to distance. The location
of each revolution on the lane relative to the foul line, and the ball loft distance (the
distance the ball traveled before impacting the lane) can also be determined.
Recall that
R T
D T = Σ (v i t i ').
i=1
By performing the summation from i = 1 to R i-1 , such that
R i-1
D i = Σ (v i t i '),
i=1
D i then gives the distance from the foul line where revolution i started.
The value for each of the v i 's was found previously, and v i can now be assigned to each
sample of revolution i. Since the distance D i from the foul line to the start of each
revolution i has also been found, the distance for each sample in revolution i, relative to
the foul line can be calculated.
Define s i,0 to be the first sample of revolution i, so that s i,0 , s i,1 , …, s i,n-1 are the n samples
of revolution i and let d i,j be the corresponding distance for sample s i,j . A method for
finding the velocity v i and the distance D i for s i,0 has already been given. Assuming a
constant velocity during revolution i, the distances for the remaining samples of
revolution i can be generated from the equation
d i,j = D i + (j / f) · v i ,
where 0 ≤ j < n, and f is the sampling frequency (currently 120 Hz).
Thus, a conversion from time (sample index) to distance for each sample has been found,
and it is now possible to graph the linear and angular velocities of the ball with respect to
distance from the foul line, as well as indicate the location of each impact.
53

3.4.3 Finding the Coefficient of Friction
The coefficient of friction can be recovered from the previous calculations. Under the
assumptions, the only active force is the force due to friction acting between the ball and
the lane, and that force acts solely to transfer linear momentum to angular momentum.
Since the changes in angular and linear momentum for each sample are known, the
frictional force required to generate those changes can be found.
For any revolution i, the frictional force F µi acting during i is given by
Fµi = m / 2 · k(ω 2 i - ω 2 i-1 ) / (D i - D i-1 ) = m / 2 · (v 2 i - v 2 i-1 ) / (D i - D i-1 ).
The coefficient of friction µ i between the ball and the lane for revolution i is then
µ i = Fµi / mg, where g is the acceleration due to gravity.
Similarly, the frictional force for any sample j of revolution i can be found from
Fµi,j = m / 2 · k(ω 2 i,j - ω 2 i,j-1 ) / (d i,j - d i,j-1 ) = m / 2 · (v 2 i,j - v 2 i,j-1 ) / (d i,j - d i,j-1 ).
The coefficient of friction µ i,j between the ball and the lane for any sample j of revolution
i is then given by
µ i,j = Fµi,j / mg.
Using this result, there is now enough information to graph the coefficient of friction
between the ball and the lane with respect to the distance from the foul line.
54

3.5 ASSUMPTIONS AND ERROR ANALYSIS
The derivations behind the MASTER calculations presented in the previous discussion
rely heavily on several basic assumptions, some of which have already appeared in other
sections throughout the course of the paper. This section presents the analysis
assumptions in detail, along with an assessment of their possible error contributions.
3.5.1 Distance
Throughout the paper, it has been assumed that the ball travels 60 feet - the distance from
the foul line to the head pin. Under normal circumstances, release of the ball occurs close
to the foul line, and the first pin the ball encounters is the head pin (at least on the first
ball of any frame). It is time to take a closer look at what this assumption entails.
• The ball is released at the foul line: An error factor is introduced in the average
linear velocity calculation if the ball is released behind the foul line (the actual
velocity will be higher than calculated), or beyond the foul line (the actual
velocity will be lower than calculated). Generally, the bowler releases the ball at,
or just beyond, the foul line. For a legal delivery, no part of the bowler's body
may touch the lane beyond the foul line. This presents a physical limitation on
release beyond the foul line of approximately 12 inches.
Additional error is possible from behind the foul line, usually resulting from a
noticeable lapse in execution on the bowler's part (dropping the ball, releasing the
ball early, or stopping short of the foul line). Although the module can not detect
the absolute point of release, it does indicate when the ball hit the lane, in relation
to release. In addition, the bowler easily recognizes when these major lapses in
execution occur, and can take note of them.
The nominal margin of error at the point of release is estimated to be ±6", with the
vast majority of releases occurring within a ±3" range.
• The ball hits the head pin at a fixed location: At the other end of the lane, the
ball can hit the head pin in different spots - head on, or on the right or left side. A
pin is 4½" in diameter at the height at which the ball contacts it, and the center of
the pin is located 60' ±½" from the foul line. A ball is nominally 8½" in diameter.
Assuming the ball is released with its center over the foul line and it hits the head
pin dead center, it must travel 59' 5" to 59' 6" from the point of release. If the ball
barely grazes the right or left side of the head pin, the ball traveled at least 59'
11½" to 60' ½". A solid pocket hit (the goal of any potential strike delivery) falls
halfway between these two ranges, so the expected distance from the foul line that
the initial pin impact should occur is 59' 8¾". Therefore, the margin of error
introduced in hitting the head pin is ±3¾"
If the ball misses the head pin, it must travel at least an additional 10.4" to get to
the next pin, and the same error factors as for hitting the head pin come into play.
The bowler could take note of the first pin that was hit - the head pin, the 2/3 pins,
the 4/6 pins or the 7/10 pins, and the analysis software could again adjust for the
difference. Bowlers readily identify the location of the ball based on the board it
is on when it hits the pins. This information could be used to better locate the ball
at pin impact, along with the first pin hit, and this error could be reduced to
approximately ±1".
55

• The ball takes the shortest path from the foul line to the head pin: In
actuality, the ball is rarely thrown straight at the head pin from the center of the
foul line. Instead the ball is rolled with some amount of hook, and is released
from some place other than the center of the lane, and is initially directed
somewhat toward the right gutter (for a right-handed bowler). If the ball were
thrown from the outside edge of the right gutter in a straight line 45-50 feet down
the lane, and then suddenly hooked straight toward the pocket, it would travel an
extra 7 / 8 ". At the other extreme, if the ball were released at the left gutter, and
traced a regular arc to the right gutter at 30 feet, and then back to the head pin, it
would travel an extra 6". This is an extreme amount of hook, but will be factored
into the error budget as ±3".
• The ball and pins each have fixed diameters: The ABC maintains tight control
over the allowed dimensions of the ball and the pins. The ball has a nominal
diameter of 8.547 ±0.047", resulting in a nominal circumference of 26.853
±0.149". The diameter of the ball contributes a negligible error. However, the
circumference of the ball, which is used in later calculations to estimate the
amount of sliding and the coefficient of friction, could be multiplied by the total
number of revolutions the ball makes during a shot, which can total 20 or more.
In this case, the error contribution due to the ball's circumference could contribute
up to ±3".
At the height that the ball strikes a bowling pin (8.77"), the pin must have a
nominal diameter of 4.766 ±0.031". This is an insignificant contribution to the
error calculations.
Combining the three significant errors (at the foul line, at the pins, and the ball path),
yields a total of approximately ±12" of error in the distance the ball travels. For a
nominal distance of 60 feet, the total error works out to ±1.67%. For a ball thrown at 15
mph, this error will manifest itself in the velocity calculations as a difference of 0.25
mph.
This error could be reduced further by supplying the appropriate information to the
MASTER program. The bowler could input their normal release point as a configuration
parameter. Then, during normal play, they would indicate the approximate board where
the ball was released, the extreme right (or left) board that the ball crossed on its path to
the pins, and the first pin the ball hit, along with the type of hit (head on, right, left, graze,
etc.) and/or the board the ball was on at the time of impact. The analysis software would
utilize this information in its calculations. This type of input could reduce the margin of
error to less than 6", increasing the velocity resolution to 0.1 mph.
3.5.2 Time
Another assumption is that the microprocessor's clock is accurate. If the clock is based
on a quartz crystal, it will be accurate over temperature to at least ±200 ppm (0.02%), or
600 µsecs over a 3-second shot, which is an insignificant error contribution. If a ceramic
resonator is used (because it is much cheaper and much more durable), a ±2% error over
temperature is possible, which is ±60 msecs over a 3 second shot. This is not
insignificant, and would be additive to the distance error in any calculation of velocity.
However, this error could be calibrated out by measuring the actual clock rate with a
more precise clock and compensating for the difference in the MASTER software.
56

3.5.3 External Forces and Friction
The major assumption is that the frictional force between the ball and the lane is the only
force of any significance acting on the ball following release. Losses due to noise,
vibration, and aerodynamic drag are considered negligible. A further assumption is that
the force due to friction acts on the ball in such a way as to translate its linear momentum
to angular momentum.
The ball is released with an initial linear velocity that exceeds the ball's angular velocity.
That is, the ball travels further during one revolution of the ball than one circumference
of the ball. This difference causes the ball to skid (slide). Also, generally speaking, the
axis of rotation of the ball is neither parallel to the surface, nor is it normal to the
direction of the lane. The resolution of these differences as the ball traverses the lane
causes the ball to hook. The force due to friction causes the ball to resolve these
differences, slowing the ball down, while increasing its angular velocity. This resolution
occurs until such time as the ball is no longer skidding (rolled out), or the ball has
completely traversed the lane and entered the pit.
• The ball is always slowing down after it is released: The force due to friction
causes the ball to translate linear momentum to angular momentum, until such
time as the resolution (rollout) point is reached. If rollout is reached, both the
angular and linear velocities decrease. Therefore, the linear velocity is always
continuously and monotonically decreasing.
• The angular velocity is always increasing: The angular velocity of the ball will
continuously and monotonically increase until the rollout point is reached, at
which time the angular velocity also starts to decrease in a continuous and
monotonic fashion, along with the linear velocity. Roll out can be detected by
observing the angular velocity of the ball near the pins. The ball has rolled out if
the angular velocity has begun to decrease, in which case, the linear velocity of
the ball can be directly deduced, since it must travel 27" (one circumference of the
ball) for every revolution of the ball.
• Perfect transfer from linear momentum to angular momentum occurs:
Actually this is not the case, but the amount of transfer from linear to angular
momentum can be detected in the change in angular velocity between each
revolution of the ball. Since the force due to friction is the only force acting on
the ball, it will be directly related to the amount of change in the angular velocity.
The actual unaccounted for losses due to friction result from heating of the ball
and/or the lane, noise generation, vibration, and inelastic deformation of the ball
and lane.
If the ball rolls out, it is possible to directly observe the effects of friction, since the linear
velocity is directly related to the angular velocity, and the drop in kinetic energy of the
ball can then be measured. While the ball is skidding, the actual losses due to friction are
very probably some constant fraction (percentage) of the change in angular momentum,
i.e., 90% of the change in linear momentum is transferred to angular momentum, 10% is
given up as heat, noise, etc. The exact percentage is not yet known, and it probably
varies for each type of ball, but with additional research, it should be possible to place an
upper and lower bound on the frictional losses.
57

3.6 IMPLEMENTATION, PERFORMANCE, AND ACCURACY
The version of the MASTER application that was used to generate the screen captures for
this paper incorporates most of the derivations and methods given in Sections 3.1 to 3.4.
Figure 3-8 presents a data flow diagram of the various routines that generate the data for
the graphs displayed on the "Spectrum", "Waveform", and "Analysis" screens. Appendix
D contains the 'C' source code for those routines.
MASTER Analysis Calculations Data Flow Diagram
From:
Upload/Archive Routines
A
vCalcSpectrum (page D-3)
Initialize: RealData[ ] = RawData[ ]
Calc Spectrum: RealSpectrum[ ] = FFT (RealData[ ])
Calc Magnitudes: FFTMag[ ] = FFTMagnitude (RealSpectrum[ ])
Calc Frequencies: FFTFreq[ ] = FFTFrequency()
Find Fundamental: FundFreq = max (FFTMag[ ]), Freq > 2.0 Hz
Normalize:
FFTMag[ ] / FFTMag[FundFreq]
Find Pass Band Limits: LOFilterIndex, HIFilterIndex
vCalcVelocityData (page D-15)
Calc RPM Energies: RPMEnergy[i] = k * RPMData[i] 2
Calc RPM Ave Energy: RPMAveEnergy = Σ (RPMEnergy[ ]) /
(PinImpactIndex - ReleaseIndex)
Estimate Linear Energy: SpeedAveEnergy = ((LaneLength * SamplingFreq) /
(PinImpactIndex - ReleaseIndex)) 2
Calc Ball Ave Energy: BallAveEnergy =
(1+FrictionCoef) * RPMAveEnergy * SpeedAveEnergy
Calc Linear Velocities: VelocityData[i] =
(BallAveEnergy - ((1 + FrictionCoef) * RPMEnergy[i])) 1/2
Get Ball Loft Distance:
Get Release Velocity:
BallLoft = Σ ((VelocityData[i] * 12.0) / SamplingFreq),
ReleaseIndex ≤ i ≤ LaneImpactIndex
ReleaseVelocity = VelocityData[ReleaseIndex]
vCalcFilterData (page D-5)
Remove LO Freqs: RealData[i] = 0.0, i < LOFilterIndex
Remove HI Freqs: RealData[i] = 0.0, i > HIFilterIndex
Keep Pass Band Freqs: RealData[i] = RealSpectrum[i],
LOFilterIndex ≤ i ≤ HIFilterIndex
Get Impact Velocity:
ImpactVelocity = VelocityData[PinImpactIndex]
Get Ball Speed: BallSpeed = (LaneLength * SamplingFreq) /
(PinImpactIndex - ReleaseIndex)
Get Ball Time: BallTime = (PinImpactIndex - ReleaseIndex) /
SamplingFreq
Filter Data: RealData[ ] = FFT -1 (RealData[ ])
Remove DC Bias: RealData[ ] - Min (RealData[ ])
vCalcDistanceData (page D-16)
Calc Distance to Sample: Distance[i] = Σ ((VelocityData[j] * 12.0) / SamplingFreq),
0 ≤ j ≤ i
fAnalyzeData (page D-7)
Fill Distance Vectors: RPMDistance[ ], VelocityDistance[ ], RawRPMDistance[ ],
ImpactDistance[ ]
Find Rev Loc Indices: RevBGNLoc[ ], RevENDLoc[ ]
Interpolate:
RPMLoc[i] = Interpolate (RevENDLoc[i-1],
RevBGNLoc[i])
Calc Angular Velocities: CalcRPMs[i] = 1 / (RPMLoc[i] - RPMLoc[i-1])
Remove Doppler: RPMData[ ] = PolyCurveFit (CalcRPMs[ ])
Get Release RPMs: ReleaseRPMs = RPMData[ReleaseIndex]
Get Impact RPMs: ImpactRPMs = RPMData[PinImpactIndex]
Calc Rev Distance:
vCalcRevLocations (page D-17)
Fill Distance Vector: RevLocDistance[ ]
RevDistance[rev] = Σ ((VelocityData[i] * 12.0 ) / SamplingFreq),
0 ≤ i ≤ RPMLoc[rev]
A
Figure 3-8
To:
Graphing Routines
58

3.6.1 Implementation and Performance
There are several performance issues with the current version of the MASTER software
that are currently being addressed.
• The coefficient of friction calculations from Section 3.4.3 have not yet been
incorporated. Instead, a command-line argument specifies the percentage of the
change in angular momentum that is lost due to friction. For this paper, frictional
losses were set at 10%.
• A somewhat less accurate method for deriving the linear velocities than that
described in Section 3.3 is currently implemented. This method derives the
average linear momentum from the average linear velocity of the ball, and
calculates the average angular momentum from the angular velocities for each
revolution. Although this yields the proper shape for the waveform, it
misrepresents the magnitude of the linear velocities. See vCalcVelocityData in
Figure 3-8 for more detail.
• The current linear velocity extraction algorithm does not check for roll out of the
ball (that the angular velocity is decreasing). Therefore, under the constant
energy assumption, when the angular velocity begins to decrease, the calculated
linear velocity increases. The graph in Figure 3-9 demonstrates this phenomenon.
Figure 3-9: Effects of Roll Out, "Analysis" Screen Capture
59

• The angular velocity graph is highly sensitive to a "phase shift" that can occur in
the waveform when the ball crosses under the pin deck light. Referring back to
Figures 2-2a and 2-2b in Section II, the pin deck light is bright enough that it can
alter the duration of the last revolution significantly, depending on the orientation
of the light sensor as the ball approaches the pins. Consequently, the revolution
location algorithm detects a longer (or shorter) duration than actually occurred,
artificially inflating or deflating the final angular velocity of the ball. Figure 3-10
illustrates this phenomenon.
Light Level
140
120
100
80
60
Last complete
Revolution
Phase
Shift
Impact
(Head Pin)
40
20
0
2000
2100 2200 2300 2400 2500 2600 2700 2800
Milliseconds (since Release)
Figure 3-10: Pin Deck Phase Shift, Impact Region (800 ms)
Figures 3-11a and 3-11b indicate the adverse effects of this "phase shift" on the
analysis of the waveform. The analysis captured in Figure 3-11a was performed
on the waveform with the phase-shifted portion of the raw data included. The
angular velocity begins to roll off 10 feet in front of the pins. The same
waveform was used for the analysis captured in Figure 3-11b, but the phaseshifted
portion of the raw data was excluded from the calculations. As a
consequence, Figure 3-11b shows the angular velocity continuing to increase all
the way through impact with the pins.
The difference in the two raw data waveforms is only 50 msec (6 sample times),
but the difference in the resulting analysis is dramatic. The simplest method for
correcting the problem is to find the pin impact point in the waveform, and then
exclude from the spectrum calculation the 50-75 msecs (6-9 samples) that
immediately precede pin impact. After the raw data waveform has been filtered,
the time is reinserted by extrapolating the results of the angular velocity extraction
routine back into the excluded data.
The problem arises because the filtered waveform that is used for all of the
analysis calculations is reconstructed for time-independent frequency content.
Using an FFT function over the entire waveform at one time yields frequency
components of the data, but does not reveal when those frequencies were present
in the waveform. A more advanced technique would be to use wavelet methods
in the spectrum calculations to yield time-correlated frequency content.
60

Figure 3-11a: Effects of Phase Shift, Apparent Rollout
Figure 3-11b: Effects of Phase Shift, No Rollout
61

3.6.2 Accuracy
The question of accuracy has not yet been addressed. Just how accurately do the graphs
displayed in the "Analysis" screen of the MASTER program depict the actual response of
the ball? What accuracy can be claimed for the SMARTDOT system and, more
importantly, how can this accuracy be verified?
The SMARTDOT system is intended to serve the following functions: quantify the
consistency of a bowler's release; provide objective feedback with which to measure their
performance and improvement; and capture and measure the response of a bowling ball
over the course of a game or match, as well as capture its response to varying lane
conditions.
Therefore, it is more important that the system give consistent and repeatable results,
rather than absolutely accurate results. Ideally, if the bowler rolls the ball the same way
on two different shots, and the ball responds identically to that stimulus, then the results
that the MASTER reports should be the same. If the bowler releases one ball with a
velocity 10% higher than another ball, the MASTER should report a 10% difference in the
two release velocities.
There are several options available for accurately verifying SMARTDOT's performance:
• Take SMARTDOT to a CATS-instrumented facility and correlate the MASTER's
analysis results against the CATS findings [12] and/or contact Brunswick and
possibly obtain time on their "Throbot" machine, which can apply known
amounts of velocity, spin, and loft to the ball, and then correlate the MASTER's
findings against the release parameters of "Throbot" [9].
• Instrument a lane and perform external verification and validation. By fitting a
lane with a fast and accurate position/velocity sensing system, the actual response
of the ball from foul line to head pin could be captured. Since the linear velocity
and distance results are derived from the angular velocity data, if those results can
be externally quantified, it will be possible to determine the accuracy of the
assumptions and the calculations underlying the entire SMARTDOT system.
• Add a solid-state accelerometer/tilt-sensor to the module and correlate the actual
results of the accelerometer with the inferred angular velocity results from the
light sensor. This is a realistic possibility, using the ADXL202E accelerometer
from Analog Devices [15], although it requires a fair amount of additional
development effort on the sensor module.
To this point, the only practical (meaning cost-effective) assessment method has been to
use video analysis. With markers applied at known distances on the lane, and additional
markers applied to the ball each 30° of rotation, multiple shots have been simultaneously
captured with SMARTDOT and on videotape. Through this practice, the current MASTER
analysis techniques appear to be accurate to within 1/2 mph and 90° of rotation.
However, standard video is limited to 30 frames per second, yielding a resolution of 33
msecs per frame, which is insufficient for verifying accurate measurement to 0.1
revolution and 0.1 mph. It is also not possible, using this technique, to verify the angular
velocity measurements resulting from the filtered waveform, nor the actual locations of
each revolution. It will eventually be necessary to utilize one or more of the previously
mentioned techniques to reliably validate SMARTDOT.
62

3.6.3 The "Perfect" Game to Analyze
Several years ago, with an earlier prototype of the SMARTDOT sensor module installed
in the ball, the author had the extreme good fortune of rolling a perfect game while
testing the module. SMARTDOT successfully captured the waveforms for all 12 strikes
of that game. Figure 3-12 gives a tabular summary of the "Analysis" statistics and
Appendix E contains screen captures from the "Raw Data", "Spectrum", and "Analysis"
screens for the 12 frames of the 300 game.
Frame
Release
MPH RPMs
Impact
MPH RPMs
Loft
(in)
Time
(sec)
Average
MPH
Total
Revolutions
Average
RPMs
1 16.6 425 15.4 560 44 2.52 16.3 19.4 462
2 16.7 415 15.4 569 44 2.48 16.5 18.5 448
3 16.6 423 15.5 551 49 2.48 16.5 18.4 445
4 16.3 424 15.2 547 48 2.54 16.1 19.1 451
5 16.6 412 15.2 569 54 2.50 16.4 18.4 442
6 16.5 426 15.3 551 -- 2.50 16.4 18.2 437
7 16.8 426 15.7 548 54 2.48 16.5 19.2 465
8 16.3 422 15.1 553 -- 2.56 16.0 19.4 455
9 16.5 425 15.3 558 -- 2.52 16.3 19.2 457
10 16.8 434 15.8 551 -- 2.47 16.6 18.8 457
11 16.7 427 15.5 554 -- 2.48 16.5 18.6 450
12 16.6 426 15.6 542 -- 2.48 16.5 18.4 445
Min 16.3 412 15.1 542 44 2.47 16.0 18.2 437
Max 16.8 434 15.8 569 54 2.56 16.6 19.4 465
Median 16.6 425 15.4 552 49 2.49 16.5 18.7 451
Mean 16.6 424 15.4 554 49 2.50 16.4 18.8 451
Deviation ±1.5% ±2.5% ±2.3% ±2.4% ±5.0% ±2.0% ±1.8% ±3.2% ±3.1%
Figure 3-12: 300 Game Analysis Summary
This set of 12 waveforms possesses some interesting characteristics that could be used in
future versions of the MASTER analysis software, as well as to refine the embedded
software of the SMARTDOT module. First, the valleys of the waveforms exhibit a shape
much closer to that of a sinusoidal waveform than the peaks do. This suggests that much
of the impact of the Doppler effect and the directionality of the ceiling lights could be
eliminated by restricting the analysis to only the lower half of the waveform.
Also, the peak and average light levels increase dramatically when the ball crosses under
the pin deck light. The time interval between detection of the pin deck light and impact
with the pins could be used to determine whether or not the ball hit the head pin. The
"signature" of the pin impacts might also be useful.
Although the accuracy of the MASTER analysis algorithms requires a more rigorous
analysis, and has not yet been formally verified, the relative consistency of the results
from these twelve shots, all of which resulted in pocket hits, lends some credence to the
validity of the analysis methods.
It was also especially gratifying to the author to have thrown the first-ever 300 game
captured with the SMARTDOT system.
63

3.7 FUTURE WORK
The MASTER application, in its current incarnation, has served solely as a research tool.
It facilitates rapid assessment of the SMARTDOT module's performance, and enables the
review and archival of previously collected data. As the MASTER analysis algorithms
have been developed and modified, this version of the MASTER application has made it
possible to recall previous raw data waveforms and observe the effects of the changes to
the algorithms.
3.7.1 Algorithms
The analysis algorithms are still evolving. Various concerns and problems have been
presented over the course of the paper, and several of these stand out.
• Filtering the Raw Data Waveform: This is the most important step in the entire
analysis process. The basis for the analysis algorithms is that the waveform is
representative of the angular position of a single point on the ball. As the ball
rolls down the lane, that point transcribes a sinusoidal path that the SMARTDOT
module captures, and that the MASTER unit analyzes to recover the action of the
ball. If this waveform cannot be recovered "cleanly", the analysis will be flawed.
A simple FFT function was used to find the spectrum, and an adaptive filter was
used to filter the waveform. Although the spectrum of the waveform reveals a
great deal of information, the major focus of interest is the manner in which the
frequency changes over time, which an FFT does not reveal. Therefore, further
investigation needs to be performed into more advanced digital processing
techniques, more specifically into wavelet theory, which will allow the MASTER
algorithms to characterize the timing of the frequencies in the waveform.
• Curve Fitting: Due to the Doppler effect observed in the raw angular velocity
waveform, it has not been possible to directly recover the instantaneous angular
velocity of the ball from the raw data. Therefore, a least-squares curve-fitting
scheme was used to approximate the true shape of the angular velocity waveform.
However, this scheme does not include facts about the nature of the waveform
that are known to be true, i.e., that it is monotonically increasing, at least until
rollout occurs. A more refined method must be identified that takes into account
the specific nature of this problem.
• Friction: Throughout the analysis, an assumption has been maintained that no
energy is lost due to friction. Actually, the energy lost is relatively small, but not
negligible. Since the linear velocity is derived from the change in angular
momentum, any portion of the linear momentum that is not transferred to angular
momentum causes the resultant linear velocity calculation to be too low.
It appears to be possible to recover the actual frictional force or, at the very least,
to place upper and lower bounds upon it. Since the ball is always revolving
slower than it is traveling, and the number of revolutions of the ball is known, the
total distance the ball would have traveled had it not been skidding during those
revolutions can be calculated. This distance will always be less than the distance
the ball actually traveled (nominally 60 feet).
64

Since the change in angular velocity for each revolution of the ball is known, it
should be possible to distribute the discrepancy in the two distances in relation to
the changes in angular velocity. This process yields the distance the ball covered
for each revolution, and the linear velocity can be recovered using that distance
and the period of each revolution. The kinetic energy of the ball can then be
calculated for each revolution. Knowing the weight of the ball, and the energy
lost between revolutions, the coefficient of friction could be calculated for each
revolution.
3.7.2 End-User MASTER Software
The eventual development of the end-user version of the MASTER application is an entire
project in itself. The current version is merely a tool to aid in developing and assessing
the analysis algorithms, which are at the heart of the SMARTDOT system. Even though
further refinement of those algorithms is required, and formal verification of their
accuracy has yet to be performed, they have demonstrated the feasibility of the entire
system. Although some form of the algorithms will be part of the end-user version of the
MASTER software, the final implementation of the MASTER application will look and
feel nothing like its current incarnation.
There are two forms that the MASTER application will ultimately take. The first is as a
full-blown, PC-hosted, Windows ® -based GUI application, and the second is as a portable
PDA-based application. The two would tie together, resulting in real-time utility for the
bowler at the bowling center, while also allowing for in-depth analysis and performance
tracking and data archiving at home.
• PDA-based application: The PDA application would allow the bowler to upload
waveform information from the SMARTDOT module, and then save and review the
information during the course of a practice session or match. The application would
also accept user-input about the particular bowling session (bowling establishment,
lanes, ball used, etc.), and pertinent details for each frame thrown (release point, ball
path, impact location, result, etc).
The application would provide on-site feedback that pertains to the bowler's current
execution in relation to previously established norms. It could also provide trending
information regarding differences in ball response between the two lanes of a pair, or
from the beginning of a match to the end, or between several different bowling balls.
The bowler could also find out the manner in which their execution changes over the
course of a match: did their release velocity decrease/increase; did the release RPMs
drop-off or pick-up, etc.
• Windows ® application: The Windows ® MASTER application would have all of the
capabilities of the PDA application, but would also create and maintain a database of
past performances. The PDA would automatically upload the information it had
previously collected at the bowling alley to the MASTER application, which would
then archive that information in its database.
The primary function of the MASTER software would be to facilitate queries of this
database for various trends and relationships between scores, bowling balls, execution
parameters, etc. Ultimately, it would not only help correlate the bowler's execution
(release parameters) with their performance (score), it could also provide a correlation
between that information and the different equipment (bowling balls) that the bowler
uses.
65

3.8 SUMMARY - MASTER ANALYSIS
The SMARTDOT concept was predicated on the assumption that the action of a bowling
ball could be captured by sampling and recording the ambient light level at a single point
on the ball as the ball rolls down the lane. This concept was developed in two stages:
first, by building an in-situ sensor module that captures and uploads the waveform; and
second, by deriving and implementing a set of algorithms that filter, analyze, and display
the captured waveform.
It was assumed that the digitized waveform would be sinusoidal in nature, with the peaks
and valleys of the waveform occurring at 0° and 180° of rotation, respectively. In
actuality, the digitized waveform required some "massaging" through adaptive digital
filtering before the analysis process could be automated. Further, the discrete rows of
overhead fluorescent lights imprint a Doppler-like effect on the filtered waveform,
resulting in apparent oscillations in the angular velocity of the ball, especially on the first
half of the lane (closest to the foul line).
A polynomial curve-fitting scheme was used to smooth out the angular velocity
waveform, and the linear velocity of the ball was recovered through energy conservation
techniques, combined with certain assumptions about the effects of friction. From the
linear velocity, it was possible to find the distance the ball was lofted at release, and the
location of each revolution of the ball relative to the foul line. A method for finding the
coefficient of friction between the ball and the lane was also derived, although this
technique has not yet been implemented.
Another problem that arose from the analysis was that of "phase shift", where the pin
deck light overpowers the ceiling lights and imposes a sudden phase shift on the
waveform immediately before the ball hits the pins. This phase shift occurs in the last
revolution of the ball, and can drastically affect the resulting analysis. The effects of the
phase shift can be removed by excluding from the data passed to the digital filter the 50-
75 msecs (6-9 samples) of the waveform immediately preceding impact. Before
proceeding with the remainder of the analysis algorithms, the filtered waveform is
extrapolated back into the samples that were previously excluded.
It is important to note that all of the waveforms used for development of the MASTER
algorithms have originated from the author's use of the SMARTDOT system. As such,
testing of the SMARTDOT system with a wider range of users is mandated, and further
refinement of the algorithms will most likely result. Ultimately, the results of the
MASTER analysis algorithms must be verified and validated with formal testing. That
testing could also be used to reveal which algorithms are the most applicable to the
SMARTDOT system.
Admittedly, there is much development, verification, and validation yet to be done.
However, this phase of the project has shown that the SMARTDOT system, as described,
is a feasible and viable method for quantifying and assessing a bowler's level of
execution and performance.
66

BIBLIOGRAPHY
[1] United State Patent and Trademark Office, http://www.uspto.gov/, March 2002
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images of a moving object moving in an otherwise substantially static scene includes an image sensor
for generating video signals of the static scene and for generating video signals of the static scene
including the object moving therethrough. The video signals are generated over a plurality of frames.
A first memory stores the video signals of at least one of the plurality of frames from the static scene.
A second memory stores the video signals of the plurality of frames from the static scene including the
object moving therethrough. Structure is provided for comparing on a frame-by-frame basis the video
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[3] US Patent 5,118,105 (June 2, 1992) - Bowling Statistics Display System
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[4] US Patent 5,526,326 (June 11, 1996) - Speed Indicating Ball
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flight of the ball, and which corresponds to the relative velocity of the ball.
[5] US Patent 5,761,096 (June 2, 1998) - Speed-sensing projectile
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[6] US Patent 6,151,563 (November 21, 2000) -
Speed, spin rate, and curve measuring device using magnetic field sensors
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electronic processor circuit, magnetic field sensor circuit, and a radio transmitter. The other part of the
device, called the monitor unit, is held or worn by the user and serves as the user interface for the
device. The monitor unit has a radio receiver, a processor, an input keypad, and an output display that
shows the various measured motion characteristics of the movable object, such as the time of flight,
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the device.
67

[7] Bose, Nirmal K., Digital Filters - Theory and Applications, North-Holland, New
York, New York, 1985
[8] Halliday, David and Resnick, Robert, Physics - Parts 1 & 2, John Wiley and Sons,
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[11] Simmons, George F., Calculus with Analytic Geometry, McGraw Hill, New York,
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68

APPENDIX A - SMARTDOT MODULE EMBEDDED SOFTWARE
FLOWCHARTS
Figure A-1a Start-Up Task Flowchart ...............................................................................A-2
Figure A-1b Pre-Sampling Task Flowchart .......................................................................A-2
Figure A-2 Light Sample ISR Flowchart .........................................................................A-3
Figure A-3 Sampling Task Flowchart ..............................................................................A-4
Figure A-4 Discrimination Task Flowchart .....................................................................A-5
Figure A-5 Communication Task Flowchart ...................................................................A-6
Figure A-6 Wand Detection ISR Flowchart.....................................................................A-7
Figure A-7 UART Receive Task Flowchart .....................................................................A-8
Figure A-8 Bit Sample ISR Flowchart..............................................................................A-9
Figure A-9 Receive Time Out ISR Flowchart..................................................................A-9
Figure A-10 Shutdown Task Flowchart ...........................................................................A-10
A-1

Appendix A: SMARTDOT Module Embedded Software Flowcharts
START-UP TASK FLOWCHART
A
PRE-SAMPLING
TASK FLOWCHART
B
SLEEP MODE
Wait for
Pressure on Insert
IDLE MODE
Wait for
SAMPLE Interrupt (T0)
NO
Release
LITE
Level
Detected?
Initialize Module Resources
and Variables
YES
Get Start-Up LITE Sample
YES
Wait
too long
for
Release?
Select Active Scratch Pad
(0 or 1)
NO
Write Pre-Samples to EEPROM
(Sample Buffer - 8 bytes)
Is
Sample
DARK?
YES
NO
Impact
Detected
Since Last
Sample?
YES
Set Impact Bit for Sample
Advance to Next Page of
EEPROM (8 bytes)
Enable Interrupts
NO
Sample Timer (T0)
Impact Detection (EX0)
Time Out Timer (TI)
Move Sample to BUF[PTR]
PTR++
At End
of
Sample
Buffer?
YES
PTR = Buffer BGN
NO
Figure A-1a
A
To: SHUTDOWN
SAVE RUN TIME
B
Figure A-1b
To: SAMPLING
START
A-2

Appendix A: SMARTDOT Module Embedded Software Flowcharts
LIGHT SAMPLE ISR FLOWCHART
On:
Timer 0 (T0)
Overflow
A
B
C
Disable Interrupts
Push ACC
Push PSW
First Sample = TRUE
New Sample = TRUE
Turn ON TSL251
(start next ADC conversion)
First
Sample
Of
240 Hz
Pair?
YES
Sample = ADAT
(from previous conversion)
YES
Reached
Shutdown
Time?
NO
Is
Sample
=
Release
Level?
YES
NO
NO
Impact = FALSE
First Sample = FALSE
Is
Sample
Level below
Shutdown
Level?
NO
Reset Shutdown Count
for Release Time Out
Release = TRUE
Sample += ADAT
(from previous conversion)
NO
Is
Sum
>
255?
YES
B
Sample = 127
(clip to 127 for Impact Bit)
YES
Shutdown Count++
Has it
been
Dark
too Long?
NO
NO
Has
Release
Already
Occurred?
YES
Reset Shutdown Count
for Shutdown Time Out
Update Run Time
Turn Off TSL251
(waits for ADC to complete)
Pop PSW
Pop ACC
Enable Interrupts
Sample /= 2
(average out 240 Hz noise)
YES
Shutdown = TRUE
(reached Shutdown condition)
A
Figure A-2
C
RETURN FROM INTERRUPT
A-3

Appendix A: SMARTDOT Module Embedded Software Flowcharts
START
CONTINUE
A
SAMPLING TASK FLOWCHART
B
Is
Sampling
Enabled?
YES
Initialize GROUP Variables
Group Max = 0
Group Min = 255
Sample CNT = 0
Write BUF Contents to
EEPROM (8 bytes)
Advance to Next Page of
EEPROM (8 bytes)
NO
IDLE MODE
In
TEST
Mode?
YES
Wait for
SAMPLE Interrupt (T0)
Reached
End of
Sample
Space?
YES
Overflow = TRUE
NO
Impact
Detected?
YES
Set Impact Bit for Sample
NO
In
AUTO
Mode?
NO
NO
Move Sample to BUF[PTR]
PTR++
NO
Reached
End of
Scratch
Pad?
YES
YES
Ball Rolling = TRUE
Enable Sampling
Reached
End
of
BUF?
NO
Initialize AUTO Detection
PTR = BUF_BGN
Local Max = Sample
Local Min = Sample
Group CNT = 0
YES
PTR = Buffer BGN
YES
Is
Sampling
Enabled?
NO
A
B
Figure A-3
To: DISCRIMINATION
AUTO DETECTION
To: SHUTDOWN
SAVE RUN TIME
To: SHUTDOWN
DONE
SAMPLING
A-4

Appendix A: SMARTDOT Module Embedded Software Flowcharts
AUTO
DETECTION
A
DISCRIMINATION TASK FLOWCHART
B
Is
Sample
>
Group Max?
YES
Group Max = New Sample
NO
Did
Direction
Change?
(Change <
0)
YES
Is
Sampling
Enabled?
YES
In
TEST
Mode?
NO
YES
NO
NO
Is
Sample
<
Group Min?
NO
YES
Group Min = New Sample
Is
Change >
Hysteresis
?
NO
YES
Group Min = New Sample
Group Min = New Sample
NO
Is
Ball
Rolling?
YES
At
End of
Group?
NO
Group Min = New Sample
Group Min = New Sample
Group Min = New Sample
YES
Is
Waveform
Going
UP?
YES
Change =
Sample - Group Max
Reach
AUTO
Time
Out?
YES
NO
NO
Change =
Group Min - Sample
To: SAMPLING
CONTINUE
B
To: COMMUNICATION
SWITCH TO COMM
To: SHUTDOWN
DONE SAMPLING
A
Figure A-4
A-5

Appendix A: SMARTDOT Module Embedded Software Flowcharts
COMMUNICATION TASK FLOWCHART
SWITCH
TO COMM
A
B
C
Initialize Communications
Wait for Wand = TRUE
Wand Present = FALSE
Dark = FALSE
Level Count = 0
Shutdown Count = 0
Set Timer 0 (T0) for Wand Detection
Delay 40 msecs for Wand
to switch to 38400 baud
Retry Count = 3
Receive Time Out = 200 msecs
Did
Command
Terminate
Normally?
NO
YES
Transmit 'XON" @ 38400 baud
(acknowledge successful completion)
IDLE MODE
Transmit "HI" @ 38400 baud
to Wand ("Clear to Send")
Update Run Time Count
Wand Interrupt (T0)
(darkness for 125 msecs)
Receive Command Byte
from Wand @ 600 baud
Shutdown Count++
Transmit "HI" to Wand
@ 38400
Echo Command Byte
to Wand @ 38400 baud
IDLE MODE
Wand Interrupt (T0)
(receive NULL @ 600 baud)
Wait for Wand = FALSE
Wand Present = TRUE
Process Command
'A' - Set AUTO Mode
'S' - Set SINGLE Mode
'T' - Transmit Data
'X' - Set TEST Mode
0x0X - Set CFG Bytes X and X+1
Done
All
Retries?
NO
YES
B
C
A
To: SHUTDOWN
SAVE RUN TIME
Figure A-5
A-6

Appendix A: SMARTDOT Module Embedded Software Flowcharts
On:
Timer 0 (T0)
Overflow
A
WAND DETECTION ISR FLOWCHART
B
Disable Interrupts
Push ACC
Push PSW
Waiting
for
Dark?
NO
Is Sample
=
LITE
Level?
NO
Did
LITE
Pulse Just
End?
YES
Was
it the
Correct
Length?
YES
Dark = FALSE
Sample = ADAT
(from previous conversion)
YES
YES
NO
NO
Update Run Time
Turn ON TSL251
(start next ADC conversion)
Is
Sample
< Dark
Level?
NO
Reset Level Count
Level Count++
(counting LITE samples)
Turn OFF TSL251
(waits for ADC to finish)
A
YES
Level Count++
(counting DARK samples)
Pop PSW
Pop ACC
Enable Interrupts
Reached
Minimum
Dark
Time?
NO
Shutdown Count++
Was
Shutdown
Detected?
NO
YES
YES
Dark = TRUE
(Wand is in place)
Waited
Too
Long?
YES
Push SAVE RUN TIME
on to Stack
NO
Shutdown = TRUE
Figure A-6
B
RETURN FROM INTERRUPT
A-7

Appendix A: SMARTDOT Module Embedded Software Flowcharts
RECEIVE
BYTE
(from Wand)
A
UART RECEIVE TASK
FLOWCHART
B
C
Wait for Start Bit
Wait for Parity Bit
Reset Receive Time Out
Bit Sample Interrupt T0)
Bit Sample Interrupt (T0)
Turn ON TSL251
(starts ADC conversion)
New Bit = FALSE
NO
Is
PARITY
Bit
corrrect?
Halt Bit Sample Timer (T0)
Wait for Dark
Wand Interrupt (T0)
Valid
START
Bit?
NO
YES
New Bit = FALSE
Turn OFF TSL251
(ADC has already finished)
Set Bit Sample Timer (T0)
for 4800 Hz
YES
Wait for Stop Bit
Wait for 1 to 0 Transition
Wait for Data Bit
Bit Sample Interrupt (T0)
Wand Interrupt (T0)
Bit Sample Interrupt (T0)
New Bit = FALSE
Initialize Bit Sampling
New Bit = FALSE
Bit Dark Counter = 0
DARK Level = ZERO Level
Start Bit Sample Timer (T0)
Bit Count = 0
Bit Sample Count = 0
New Bit = FALSE
Shift Bit into RCV Byte
NO
Valid
STOP
Bit?
NO
Done
All 8
Data Bits?
Push NO RESPONSE
on to Stack
YES
New Bit = FALSE
YES
A
B
Figure A-7
C
RETURN
A-8

Appendix A: SMARTDOT Module Embedded Software Flowcharts
BIT SAMPLE ISR FLOWCHART
RECEIVE TIME OUT ISR FLOWCHART
On:
Timer 0 (T0)
Overflow
A
B
On:
Timer TI
Overflow
Disable Interrupts
Is this a
Middle
Bit
Sample?
NO
Take All
8 Bit
Samples?
NO
Disable Interrupts
Sample = ADAT
(from previous conversion)
YES
YES
NO
Reached
Time
Out?
Start ADC conversion
(TSL251 is already ON)
A
Is
Sample
< Dark
Level?
YES
NO
DARK
Samples
= 2?
YES
NO
YES
Halt Time Out Timer (TI)
Level Count++
(counting DARK samples)
Bit = 1 Bit = 0
Push NO RESPONSE
onto Stack
DARK Level = ZERO Level
(hysteresis between LITE and DARK)
DARK Level = ONE Level
(hysteresis between LITE and DARK)
Bit Sample Count++
Enable Interrupts
Enable Interrupts
B
RETURN FROM INTERRUPT
RETURN FROM INTERRUPT
Figure A-8
Figure A-9
A-9

Appendix A: SMARTDOT Module Embedded Software Flowcharts
SHUTDOWN TASK FLOWCHART
DONE
SAMPLING
A
SAVE
RUN TIME
BACK TO
SLEEP
Disable Interrupts
Update Run Time
in EEPROM
Switch Active
Scratch Pads
Update Ball Count
in EEPROM
Update Activation Count
in EEPROM
Sample
Overflow
?
NO
Write ZEROs to Unused
Sample Memory
Turn Off TSL251
Turn Off TRX LEDs
SHUTDOWN_PIN = 0 (D-FF CLK)
YES
Write CFG Byte, Sample
End to EEPROM
Run Shutdown Delay
Start Shutdown Time Out
SHUTDOWN_PIN = 1 (D-FF CLK)
(clocks '0' to D-FF on 0 to 1 edge)
SLEEP MODE
Shutdown Time Out or
Pressure on Insert
A
To:
START-UP
Figure A-10
A-10

APPENDIX B - SMARTDOT MODULE SOURCE CODE
SDM-DECL.R07 - Definitions and Declarations .................................................................B-2
SDM-REGS.H - Register bank 0 Definitions......................................................................B-11
SDM-MAIN.R07 - Start-Up, Sampling and Discrimination Routines, ISRs ..................B-12
SDM-MSTR.R07 - Communication Routines, Software UART, Commands, ISRs ......B-22
SDM-2404.R07 - I 2 C 24C04 EEPROM Routines ...............................................................B-36
B-1

APPENDIX C - SMARTDOT MODULE COMMAND TIMING DIAGRAMS
Upload Command Timing Diagram........................................................... C-2
Mode Command Timing Diagram.............................................................. C-3
Configuration Command Timing Diagram................................................ C-4
C-1

Appendix C: SMARTDOT Module Command Timing Diagrams
'U' - 0x55 'U' - 0x55 'T' EEPROM CONTENTS
512 Bytes
@ 38400 baud
200 msec time out
200 msec time out
200 msec time out
10 msec typical
"HI" character
@ 38400 baud
"HI" character
@ 38400 baud
Echo Command
@ 38400 baud
500 msec typical
to
1second max
160 msec nominal
C-2
500 msec typical
to
1 second max
125 msec
40 msec delay
40 msec delay
40 msec delay
TRANSMIT
1 Start
8 Data
EVEN Parity
2 Stop
0x00 'T' 0x11
uP START-UP
RELEASE
WAND IN PLACE
MODULE: "HI"
WAND: "I'M HERE"
MODULE: "CLEAR TO SEND"
WAND: "TRANSMIT"
MODULE: ECHO
WAND: "CLEAR TO SEND"
MODULE: UPLOADING DATA
uP SHUTDOWN
NULL character
@ 600 baud
Transmit Command
@ 600 baud
XON character
@ 600 baud
RECEIVE
1 Start
8 Data
EVEN Parity
1 Stop
Figure C-1
AMBIENT LIGHT
UPLOAD COMMAND TIMING DIAGRAM

Figure C-2
Appendix C: SMARTDOT Module Command Timing Diagrams
MODE COMMAND TIMING DIAGRAM
0x00 'A','S','X'
AMBIENT LIGHT
'U' - 0x55 'U' - 0x55 ECHO
200 msec time out
200 msec time out
"HI" character
@ 38400 baud
"HI" character
@ 38400 baud
Echo Command
@ 38400 baud
500 msec typical
to
1second max
C-3
500 msec typical
to
1 second max
125 msec
40 msec delay
40 msec delay
10 msec delay
NULL character
@ 600 baud
Set Mode CMD
@ 600 baud
RECEIVE
1 Start
8 Data
EVEN Parity
1 Stop
TRANSMIT
1 Start
8 Data
EVEN Parity
2 Stop
'A' - Auto Mode
'S' - Single Mode
'X' - Test Mode
uP START-UP
RELEASE
WAND IN PLACE
MODULE: "HI"
WAND: "I'M HERE"
MODULE: "CLEAR TO SEND"
WAND: "SET MODE"
MODULE: ECHO
uP SHUTDOWN

Figure C-3
Appendix C: SMARTDOT Module Command Timing Diagrams
CONFIGURATION COMMAND TIMING DIAGRAM
'U' - 0x55 'U' - 0x55 ECHO
200 msec time out
200 msec time out
200 msec time out
10 msec typical
"HI" character
@ 38400 baud
"HI" character
@ 38400 baud
Echo Command
@ 38400 baud
500 msec typical
to
1second max
0x00 0x00 - 0x0E 1 st BYTE
C-4
500 msec typical
to
1 second max
125 msec
40 msec delay
40 msec delay
NULL character
@ 600 baud
Configure CMD
@ 600 baud
Data Byte
@ 600 baud
RECEIVE
1 Start
8 Data
EVEN Parity
1 Stop
AMBIENT LIGHT
TRANSMIT
1 Start
8 Data
EVEN Parity
2 Stop
2 nd BYTE
ECHO
uP START-UP
RELEASE
WAND IN PLACE
MODULE: "HI"
WAND: "I'M HERE"
MODULE: "CLEAR TO SEND"
WAND: "CONFIGURE"
MODULE: ECHO
WAND: 1 st DATA BYTE
MODULE: ECHO
WAND: 2 nd DATA BYTE
MODULE: ECHO
uP SHUTDOWN
40 msec delay
200 msec time out
40 msec delay
Echo Byte
@ 38400 baud
Echo Byte
@ 38400 baud
Data Byte
@ 600 baud
ECHO

APPENDIX D - MASTER "ANALYSIS" CALCULATIONS SOURCE CODE
vCalcSpectrum ........................................................................................................................D-3
vCalcFilterData .......................................................................................................................D-5
fAnalyzeData ...........................................................................................................................D-7
vCalcReleaseImpactRPMs ...................................................................................................D-14
vCalcVelocity Data ...............................................................................................................D-15
vCalcDistanceData ................................................................................................................D-16
vCalcRevLocations ...............................................................................................................D-17
D-1

APPENDIX E - 300 GAME MASTER SCREEN CAPTURES
Frame
Release
MPH RPMs
Impact
MPH RPMs
Loft
(in)
Time
(sec)
Average
MPH
Total
Revolutions
Average
RPMs
1 16.6 425 15.4 560 44 2.52 16.3 19.4 462
2 16.7 415 15.4 569 44 2.48 16.5 18.5 448
3 16.6 423 15.5 551 49 2.48 16.5 18.4 445
4 16.3 424 15.2 547 48 2.54 16.1 19.1 451
5 16.6 412 15.2 569 54 2.50 16.4 18.4 442
6 16.5 426 15.3 551 -- 2.50 16.4 18.2 437
7 16.8 426 15.7 548 54 2.48 16.5 19.2 465
8 16.3 422 15.1 553 -- 2.56 16.0 19.4 455
9 16.5 425 15.3 558 -- 2.52 16.3 19.2 457
10 16.8 434 15.8 551 -- 2.47 16.6 18.8 457
11 16.7 427 15.5 554 -- 2.48 16.5 18.6 450
12 16.6 426 15.6 542 -- 2.48 16.5 18.4 445
Min 16.3 412 15.1 542 44 2.47 16.0 18.2 437
Max 16.8 434 15.8 569 54 2.56 16.6 19.4 465
Median 16.6 425 15.4 552 49 2.49 16.5 18.7 451
Mean 16.6 424 15.4 554 49 2.50 16.4 18.8 451
Deviation ±1.5% ±2.5% ±2.3% ±2.4% ±5.0% ±2.0% ±1.8% ±3.2% ±3.1%
Raw Data Screen Captures (Figure E-1) ..................................................................E-2
Spectrum Screen Captures (Figure E-2) .................................................................E-4
Analysis Screen Captures (Figures E-3) .................................................................E-6
E-1

Appendix E: 300 Game Analysis
Frame 1 Frame 2
Frame 3 Frame 4
Frame 5 Frame 6
Figure E-1a E-2

Appendix E: 300 Game Analysis
Frame 7 Frame 8
Frame 9
Frame 10, 1 st Ball
Frame 10, 2 nd Ball
Frame 10, 3 rd Ball
Figure E-1b E-3

Appendix E: 300 Game Analysis
Frame 1 Frame 2
Frame 3 Frame 4
Frame 5 Frame 6
Figure E-2a E-4

Appendix E: 300 Game Analysis
Frame 7 Frame 8
Frame 9
Frame 10, 1 st Ball
Frame 10, 2 nd Ball
Frame 10, 3 rd Ball
Figure E-2b E-5

Appendix E: 300 Game Analysis
Frame 1 Frame 2
Frame 3 Frame 4
Frame 5 Frame 6
Figure E-3a E-6

Appendix E: 300 Game Analysis
Frame 7 Frame 8
Frame 9
Frame 10, 1 st Ball
Frame 10, 2 nd Ball
Frame 10, 3 rd Ball
Figure E-3b E-7