Shot Angle Velocity

207 Pages·2015·0.52 MB·English

THE RELATIONSHIP BETWEEN THE ANGLE OF RELEASE AND
THE VELOCITY OF RELEASE IN THE SHOT-PUT, AND THE
APPLICATION OF A THEORETICAL MODEL TO
ESTIMATE THE OPTIMUM ANGLE OF RELEASE

By

Andreas V. Maheras
B.A., University of Athens, 1986
M.A., Western Michigan University, 1990

Submitted to the Department of Health, Physical Education
and Recreation and the Faculty of the Graduate School of
the University of Kansas in partial fulfillment of the
requirements for the degree of Doctor of Philosophy.

Dissertation Committee:

Carole J. Zebas_____________
Chairperson

James D. LaPoint____________

Matthew Adeyanju____________

Thomas E. Mulinazzi_________

D. B. Tracy__________________

Dissertation defended: June 13, 1995
ABSTRACT
Given the relative importance of the angle of
release in the shot-put event, the estimation of the
optimum angle of release in a way that the distance
thrown is maximized, is sought. Theory has shown that
the optimum angle of release fluctuates between 41 and 43
degrees. Biomechanical analyses have indicated that
shot-putters release their shots at angles between 32 and
38 degrees, with few cases reported in the above 40
degree category. As a result, a discrepancy between
theory and practice has been observed. The purpose of
the study was to examine whether a thrower specific
dependency of the angle of release on the velocity of
release exists in the shot-put event. Such dependency
would probably make the theoretical model inapplicable to
real life shot-putting. The agreement between the real
life models and the theoretical model was also
investigated.
Five male, collegiate, shot-putters from four
universities in the state of Kansas were employed. Each
shot-putter threw under five different angles of release,
from a very low to a very high. Each thrower attempted
10 throws in each of these five angles for a total of 50
throws. High speed videography was used to record the
throwers’ attempts. A Peak Performance system analysis
along with a FORTRAN computer program were used to obtain

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the velocity, the angle, and the height of release for
each of the 250 throws filmed.
Correlational analyses were used to obtain the
relationship between the obtained parameters. Multiple
regression techniques were used to estimate the real life
angle of release.
For all five subjects there was a significant
relationship between the angle of release and the
velocity of release thus, showing dependency of the angle
of release on the velocity of release. For all five
subjects there was no agreement between the real life
angles and those estimated by the theoretical model.
It was concluded that at present, the theoretical
model is not applicable in the shot-put event. The
optimum release conditions other than velocity depend
crucially on how the maximum achievable release velocity
is functionally related to the other release conditions.

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ACKNOWLEDGMENTS
I would like to thank my advisor Dr. Carole Zebas
for her help and encouragement in doing this project, and
also for her leadership and guidance during the course of
my studies.
Thanks to my committee members Dr. Matthew Adeyanju
and Dr. James LaPoint, of the H.P.E.R department, Dr.
Dick Tracy of the E.P.R department, and Dr. Tom Mulinazzi
of the Engineering department, for their leadership.
Special thanks go to Dr. Jesus Dapena of Indiana
University, and Dr. Elvin Eltze of Fort Hays State
University, for sharing their valuable insights
pertaining to the present study. I also thank Dr.
Raymond McCoy of the college of William and Mary, Dr.
Francis Mirabelle of the United States Air Force
Ballistics department and, Dr. Charles Votaw of Fort Hays
State University, for their cooperation with this study.
To coaches Jim Krob of Fort Hays State University,
Laurie Trapp of the University of Kansas, Will Wabaunsee
of Emporia State University, and Tom Hays of Wichita
State University, thanks for their cooperation.
I would like to thank my brothers Panagiotis and
Manthos Maheras for sharing their knowledge with me over
the years.
I would also like to acknowledge Mr. Petros
Papageorgiou, coach, professor and mentor who first
introduced me to the “secrets” of the human movement.

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I must also acknowledge the authorities of the
Ministry of Culture of Greece for the opportunity they
gave me to study abroad.
Last, but not least, a big thanks goes to those who
participated in the study and made it possible.

Andreas Vassilios Maheras

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DEDICATION
I would like, here, to especially acknowledge Mrs.
Donna Fleischacker/Maheras, and also my parents Zoe and
Vassilios Maheras, for the abundance of support they have
provided me over the years. This study is dedicated to
them.

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TABLE OF CONTENTS

ABSTRACT................................ ii
ACKNOWLEDGMENTS......................... iv
DEDICATION.............................. vi
LIST OF TABLES.......................... xi
LIST OF FIGURES....................... xiii

Chapter 1. THE PROBLEM.............................. 1
Introduction........................... 1
The Relationship Between the Angle of
Release and Velocity of Release and
the Application of the Model......... 3
The Theoretical Model.................. 6
Statement of the Purpose .............. 10
Scope of the Study.................... 11
Assumptions........................... 14
Significance of the Study............. 15
Hypotheses............................ 19
Definition of Terms................... 19

Chapter 2. REVIEW OF RELATED LITERATURE............ 22
Introduction.......................... 22
Review of Literature Related to the
Shot-Put event with Emphasis on the
Basic Mechanics and also the Angle,
Velocity and Height of Release..... 22
Basic Mechanical and Other
Principles....................... 22
Methods of Estimating the Optimum
Angle of Release................. 29
The Geometrical Method........... 29
The Range and Height Equation.... 31
The General Range Equation....... 32
The Release Angle in Shot-Putting.. 33
Height of Release.................. 39
Velocity of the Shot During the
Final Effort and at Release...... 40
Review of Literature Related to
Projectile Motion.................. 46
Projectiles in General................ 46
Gravitational Force and Air
Resistance...................... 46

Table of Contents--Continued

The Shot as Projectile............. 47
Velocities and Resultant........... 48

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Complementary Angles............... 49
Path of a Projectile Released from
Ground Level.................... 51
Velocities and Resultant........ 52
Peak Height..................... 54
Total Time...................... 54
Range........................... 54
Path of a Projectile Released
from a Height (h)............... 55
Total Time...................... 56
Range........................... 56
Forces Affecting Projectiles.......... 56
Gravity............................ 57
Aerodynamical Forces............... 59
Drag Coefficient................... 60
Frontal Sectional Area............. 61
Fluid Density...................... 61
Velocity........................... 62
Relative Acceleration.............. 62
Drag Effect on Different Masses.... 63
Vector Representation in Projectile
Motion............................. 65
Resultant Vector................... 65
Vector Components.................. 66
Factors Affecting a Projectile’s
Maximum Horizontal Displacement.... 68
Point of Release at Ground Level... 69
Point of Release at a Height (h)
Above the Ground................. 69
Velocity of Release.............. 72
Angle of Release................. 72
Height of Release ............... 73
Optimum Angle of Release when Projectile
is Released from a Height (h).... 73
Summary................................ 75

Chapter 3. METHODOLOGY............................. 77
Research Design....................... 77

Table of Contents--Continued

The Relationship Between the Angle,
Velocity, and the Height
of Release.......................... 79
Preliminary Investigation............. 79
Subjects.............................. 81
Instrumentation....................... 83

viii
Collection of Data.................... 84
Filming Procedures.................. 84
Testing Procedures.................. 86
Analysis of Data...................... 89
Film Analysis....................... 89
Statistical Analysis................ 92
The Theoretical Model................. 94
Gravity............................ 94
Velocity and Position Vectors...... 95
The Range of a Projectile Released
from a Height (h).............. 100
The Model for the Optimum Angle of
Release........................ 102
Validation of the Model.............. 111
Comparison with the Range and
Height Equation.................. 112
Result for the 45 Degree Angle..... 114

Chapter 4. RESULTS................................ 116
Introduction......................... 116
Findings............................. 119
Relationships and Correlation
Coefficients..................... 120
Scattergrams....................... 121
The Real Life Regression Models
and the Significance of the
Regression Equations............. 124
The Assumptions of the Regression
Models......................... 125
Validity and Numerical Solution
of the Model..................... 131
The Real Life vs. The Theoretical
Angles of Release.............. 137
Obtained Ranges.................... 147

Table of Contents--Continued

Chapter 5. DISCUSSION............................. 153
The Relationship Between the Angle and
the Velocity of Release........... 153
Possible Causes for the Observed
Discrepancy and Suggested
Remedies.......................... 156
The Issue of Collinearity with the
Regression Models................. 158
The Optimum Angle Model.............. 161
The Assumptions of the Theoretical

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Model.......................... 161
Force due to Air Resistance....... 162
The Projectile is a Point Mass.... 163
The Earth is Non-rotating......... 163
The Gravitational Force is Constant
and Acts Perpendicularly to the
Earth’s Surface............... 164
Motion Occurs in a Plane.......... 164
The Construction of the Model........ 164
The Importance of the Angle of
Release........................ 165

Chapter 6. SUMMARY, CONCLUSIONS AND
RECOMMENDATIONS........................ 171
Summary.............................. 171
Conclusions.......................... 176
Recommendations...................... 178

References............................. 179
Appendix A............................. 188
Appendix B............................. 197
Appendix C............................. 199
Appendix D............................. 201

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