THE EFFECTS OF VARYING

TENNIS RACKET DIMENSIONS

ON STROKE PERFORMANCE

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy In the Graduate School of the Ohio State University

By

HOWARD G. KNUTTGEN, B.S., M. S.

* * * « *

The Ohio State University 1959

Approved by:

Department of Physloel Education ACKNOWLEDGEMENTS

I wish to express my appreciation to my committee,

Dr. Delbert Oberteuffer, Dr* Lewis A. Hess, end Dr*

Donald K* Mathews, for their guidance and help* I also wish to thank Dr* Elena Sllepcsvlch of the Women's Divi­ sion of Physical Education, Dr* John Hendrix of the

Men's Division of Physical Education, and Dr* Ransom

Whitney of the Statistics Laboratory for their advice and their contributions to the successful outcome of the study* .

This Investigation would not have been possible without the cooperation of A* 0* Spalding and Brothers, of Chicopee, Massachusetts, and Victor Sports, Inc*, of

Chicago, Illinois* Spalding contributed the nine rack­ ets that were employed in the study, six of which were specially constructed* Victor donated all of the stringing material used in the study*

Finally, sincere appreciation must be extended to the eighteen test subjects who voluntarily donated their time end efforts so the necessary data could be obtained*

11 TABLE OF CONTENTS f CHAPTER PACE

I. INTRODUCTION ...... 1

Statement of the problem...... 4 Limitations of the study • • • ...... 4

II• SURVEY OF RELATED LITERATURE...... 7

Literature related to the history of racket development ...... 7 Literature related to the investigation of methods and techniques of the performance of tennis skills . . • • 16

III* PROCEDURE ...... 24

Testing the variables of racket length and w e i g h t ...... 24 Selection of rackets used in testing the effects of varying length and w e i g h t ...... 2V Testing the variables of stringing ma­ terial and tension ••*•«•«•• 50 Tests employed In the st u d y ...... 31 Accuracy T e s t ...... 31 Velocity Test ...... 33 Skill T e s t ...... 37 The testing sequence ...... 37 Personal data ...... 38 Treatment of the d a t a ...... 44

IV. ANALYSIS OF THE DATA ...... 48

Tables relating to the analysis of the d a t a ...... 48 Variations due to racket length and weight In the advanced player group • 49 Variations due to racket length and racket weight In the beginning player group ...... 54 List of significant variables and in­ teractions ...... 57

ill iv

CHAPTER PACE

Variations due to stringing material and stringing tension ...... 59 The relationship among personal mea­ surements and statistically sig­ nificant Interactions ...... 63

V. SUMMARY, CONCLUSIONS AND REC(EMENDATIONS . . . 66

Conclusions and their imnlications • . . . 68 Recommendations for further study .... 72 ATPENDIX

A. Test Scores ...... 73

B. Personal Data ...... 78

BIBLIOGRAPHY...... 80 LIST OP TABLES

TABLE PAGE

1# Rackets Employed In the Tests for Factors of Length and W e i g h t ...... 29

2* Testing Program for Factors of Racket Length and Racket '"eight...... 39

3* Effects of Length and Weieht on Accuracy Test Scores of Advanced Group ...... •••80

4m Effects of Length and Weight on Skill Test Scores of Advanced Group ...... 52

5* Effects of Length and Weight on Velocity Test Scores of Advanced G r o u p ...... 53

6m Effects of Length and Weight on Accuracy Test Scores of Beginning Group ...... 56

7* Effects of Length and Weight on Skill Test Scores of Beginning Group ...... 56

8. Effects of Length and Weight on Velocity Test Scores of Beginning Group ...... 68

9. Effects of Stringing Materials and Tensions on Accuracy Test Scores ...... 60

10« Effects of Stringing Materials and Tensions on Skill Test S c o r e s ...... 61

11* Effects of Stringing Materials and Tensions on Velocity Test S c o r e s ...... 62

12* Correlation Coefficients for Significant In­ teractions and Personal Data ••••••• 64

13* Accuracy Test Scores ...... * 7 4

14* Skill Test Scores ...... ••••76

15* Velocity Test Scores ...... 76 Vi

TABLg FflCHS

16* Test Scores with Stringing Materiel and Stringing Tension Varied ...... 77

17• Personal Data ...... 79 LIST OP DIAGRAMS

DIAGRAM PAGE

!• Testing Arrangement for the Accuracy Test • • • 34 2* Testing Arrangement for the Skill Test • • • • 33

Til CHAPTER I

INTRODUCTION

Lawn tennis, by reason of lta International pop­ ularity, ean truly take its plaee among the world's most important recreational and athletle activities.

It is played in virtually every country in the world and, like some other sport activities, has opened its list of participants in the last fifty years to include people from every socio-economic level as well as just about every age level.

Because of the extensive participation in tennis among athletes of different nations, the rules of Pl»y are International in nature. The rules of tennis, as with those of any sport activity, cover the various aspects of play — the dimensions of the court, the method of initiating play, the method of scoring, the restrictions placed upon the various articles of equip­ ment, etc. However, upon examining the rules of the

International Lawn Tennis Federation, It is surprising to find that, with the exception of the use of the term "racket'1 when discussing the player's contact with the ball, there is no rule that specifically de­ scribes this piece of equipment. The rules are very 2 specific in setting up the dimensions of the court and net and of describing what constitutes a legal ball, but there is no mention of any limitations on the

"racket" nor, aotually, any description of whst con­ stitutes a "racket."

The history of the present-day game of lawn ten­ nis trsces back to such games as le .1eus de longue paume. royal tennis, rackets, and fives. All were games involving the hitting of a ball. Le jeus de longue paume is a game that is mentioned aa having been played in France around the time of the Crusades

(eleventh and twelfth centuries, A. D.). It was orig­ inally a game in which the ball was hit with the bare hand.

Many tennla-type games were originally played with the bare hand until a heavy glove was adopted for the sake of protection. The next development was the fastening of eords and tendons around the hand in such a fashion that the player could give additional velo­ city to the ball. Later, panels or boards were used, first without and then with handles. The Implements with handles that were used for court tennis or royal tennis were called battolral

^Maloolm 0. Whitman, Tennis Origins and Myster­ ies. p. 37. Since the development of the battoir, the else and shape of the implements used in striking the ball have undergone many changes. Despite the great varle ty of battolrs, or rackets, that have been used down through the ages, present-day players employ rackets

* of nearly Identical dimensions. This situation has come about in spite of an absence of scientific lnves tigstion concerning the relationships of the various racket dimensions to the effectiveness of the racket to the player.

Hendrix has made the following comments concern­ ing this situation:

An absence of official regulation with regard to size, weight or shape Introduces an Interesting facet in the evolution of tennis rackets. Almost from the origin of lawn tennis, rackets have been twenty-seven Inches long and, since the turn of the cen­ tury, practically all have been nine inches wide* Manufacturers do not deviate from these dimensions (except in the junior rack­ ets for children) despite their contention that such a size does not necessarily pro­ vide an optimum swing, balance, or weight. It would, however, appear more than coinci­ dental that the sum of the length and width of the rackets totaling thirty-six Inches is the height of the net at the center. In fact, players routinely check the net for regulation height by using the length and width as a gauge. This fact causes much speculation as to whether no more logical basis than ease of measuring the net has de­ termined the dimensions of the tennis racket. Considerable research falls to Illuminate this point, but, none the less, despite the absence of any limitations, tennis rackets 4

rigidly conform to a pattern twenty-seven Inches long and nine lnohes wide.2

If the absence of reports of scientific Investi­

gation concerning the design of tennis rackets Is any

indication, It appears that we can take for granted

that the present design Is a product of "trial and er­

ror." This would refer to the process in which vrhat-

ever designs worked well were given further use* The

Imagination of sporting equipment designers and manu­

facturers probably played an important part, as well

as the personal preferences of the players.

The lack of any scientific data raises the ques­

tion: Is the present design of tennis racket the most

effective for the tennis player's use? In an effort

to determine an answer to this question, the present

Investigation was undertaken.

Statement of the problem. The purpose of this

study Is, therefore, to Investigate the changes brought about In the effectiveness of stroking In tennis by varying certain selected racket dimensions.

Limitations of the study. In order to measure possible changes in stroking effectiveness, the test­ ing vras done with the players employing a forehand

2John w. Hendrix, "Factors Influencing Playing Styles in Tennis," p. 84. Unpublished Doctoral disser­ tation of Teachers College, Coluadbla fhiversity, 1955. groundstroke* This stroke was chosen as being an im­ portant and representative phase of the over-all play of the game of tennis*

The racket variables that were Investigated were

(1) racket weight, (2) racket length, (3) stringing material, and (4) stringing tension. These factors were chosen because of their suspected importance to stroking effectiveness and the feasibility of varying them*

An investigation of the literature pertaining to tennis skills testing showed that the various studies

In this area emphasized two factors In stroke effec­ tiveness — speed (or velocity) and accuracy* There­ fore, these two faotora were given greatest considera­ tion as determinants of stroking effectiveness.

The number of testing subjects was limited to eighteen. All of the subjects were male and college- aged or older* Because of the length and number of the testing sessions, no attempt was made to oontrol the consistency of the time of day in testing, prox­ imity to meal tiTes, etc*

The experience of the players, especially in the advanced group, with the standard length rackets con­ stituted a factor of which the importance could not be evaluated* An attempt was made to counteract any 6 effects this experience might hsve on the testing re­ sults by allowing the subjects an unlimited warm-up period with each and every racket employed. CITAPTFR II

SURVEY OP RELATED LITERATURE

The literature related to this study has been di­ vided into two sections, literature related to the history of racket development and literature related to the investigation of methods and techniques of the performance of tennis skills* The investigation of the historical literature was undertaken for two prin­ cipal purposes: (1) to determine how the present de­ sign for tennis rackets evolved and (2) to determine the dimensions that have undergone variation and the reasons, if any, for the changes*

Literature related to the hi story of racket de-? velopment. Noel attributes the invention of the fore­ runner of all modern rackets to the Italians and quotea

Antonio Soalno's description of the racket, written in

1555, as follows:

It was of the shape of a guitar, one and a half feet in length and eleven Inches at the widest part* The strings were to be fine and short so that the ball might rebound instantly from them* These rackets were curved at the end for returning balls out of corners* This did not apparently mean that the head was "inclined" as it became in la­ ter days for there is no suggestion of it in Soalno's representation* The racket is as

7 e

straight as a lawn tennis racket today but is strung diagonally.1

The heads of the battoirs were later hollowed out

and cowered with parchment# Later, stringing took the place of parchment and, in this way, the racket In tennis was evolved* Examples are also found of rack­

ets strung in both a diagonal fashion and a "horizon­

tal and perpendicular" fashion*

Myers reports in the year 1880 that the lawn ten­ nis racket In use at this time wee designed after the fashion of the royal tennis racket and was grotesquely curved in the head* One of the earliest rackets of all had a playing surfaoe about half the slse of the area of present-day rackets and a handle covered with white leather that was proportionately thinner*

When the limitations of the royal ten­ nis stroke with its horizontal movement were realized and the game developed in other di­ rections, mainly in the employment of the vertical stroke, the face of the racket si­ multaneously broadened and become more uni­ form#®

Games resembling lawn tennis had been played for many years before 1873, but it was in this year that

1Evan Balllle Noel, "The Origin and Early Devel­ opment of Lawn Tennis," The National Review. No* 475 (September, 1922), pp* lol-llo, and No. i'rf (November, 1922), pp. 451-459*

2A# Wallis Myers, The Complete Lawn Tennis Player* p • 15# 9

Major '//alter Clopton Yingfield codified the laws and specified the shape and size of a court for a game he celled Sphalrlstike* Hendrix has stated that:

the enibryonic stage In the development of lean tennis playing styles extends from the publishing of the original rules of Sphair­ istike in 1873 until 1881 when the newly formed United States Lawn Tennis Association wielded myriad conflicting rule patterns in­ to a semblance of the present game*

The rules thus organised furnished the basis for the presently accepted regulations of play of lawn tennis* It is interesting to note that these rules codified in 1881, and all subsequent sets of rules ac­ cepted by the United States Lawn Tennis Association and the International Lawn Tennis Federation, have never made any attempt to describe the racket, which is mentioned in the rules as the playing implement with which the player hits the ball* As Myers puts it:

One may note that there is not and nev­ er has been any rule limiting the size or weight of the racket* Today if any daring spirit went into court at an open meeting armed with an original racket or with an im­ plement twice the orthodox dimensions, none could say him nay*4

Walter Wingfield's rules for the game of Sphair­ istike make no mention of what constitutes a raoket*

^Hendrix, op* olt*. p* 26*

*Myers, loc* clt* 10

The rules for ths new game of tennis In the jeer 1876 as adopted bj the Tennis Committee of the Marylebone

Club® make no rule regarding the racket* This set of rules never mentioned with what you hit the ball* In the 1885 Lawn Tennis rules, as adopted by the United

States National Lawn Tennis Association and published by V/rlght and Lltson,® there is no mention of what constitutes a racket* The same is true for the rules published In 1888*

Recommendations in the lawn tennis literature re­ garding the sixe and shape of rackets vary a great deal* In a letter appearing in "The Field" concerning lawn tennis, a writer reports thats

The racket should be similar in shape to a tennis raoket, 1* e., with an oblique head, which shape enables the striker to put on a heavier out than can be Imparted with an ordinary racket*7

In Jefferies1 Modern Pules of Lawn Tennis and Badmin­ ton. published In 1878, we find the advice thatt

The rackets are small tennis raoquets* We make them specially so that they can be

®Rules for the New Oames of Tennis and Badminton* Tennis Committee' ot The MaryleFone Clut>, 1876•

A Lawn Tennis Rales, as Adopted by the United States*Tawn Tennis Association* Wright and THTson, l O O D e

7Tha Field (November 14, 1874) from R* W. Hender­ son, Matoriels Relating to the Origin of Lawn Tennis* 11

easily handled and for the best length we recommend bats from twenty-seven to thirty Inches.8

Julian Marshall reports In 1879 that, "The best racket

• • • should weigh thirteen or fourteen ounces." For a lady he advises the weight to be only twelve ounoes but that a racket of fourteen ounces in weight is not too heavy for an able bodied youth.®

"Cavendish"10 reported in 1883 that lawn tennis rackets should be similar in shape to the racket used in the game of court tennis, only lighter and approxi­ mately twenty-seven inches in length. Beathcote11 re­ ports, In the 1890 publication of The Badminton Library of Sports and Pastimes, that the racket In use at that time was as nearly perfect as possible. He further states that!

Its early perfection has been said by some players to have caused deterioration of the game of tennis which has become so fast that the balance between activity and skill is less evenly adjusted than it was in the past.

®Jefferies/ Modern Rules of Lawn Tennis and Bad­ minton. p. 4.

®Julian Marshall, Lawn Tennis, p. 14.

10"Cavendish," The Came of Lawn Tennis and Bad­ minton. p. 9.

^John H. Heathcote, The Badminton Library of Sports and Pastimes, p. 55. 12

He also describes s new departure that was made around the year 1857* Before that time the cross strings were looped around the main strings* It was found, however, that when they were threaded through them the racket so strung would drive the ball much faster*

Although the smoother face prevented accurate and pre- else placing, It was found that a racket so strung would Impart It quite as severe as those of the former type* He goes on to state:

There is far more scope for individual taste In the selection of a racket. The es­ sential points are -- a good hoop free from knots with a well marked and continuous grain; a plain wooden handle, round or slight­ ly octagonal, fitting the hand of the player and attached to the middle piece without any perceptible interval; and good strong gut • . • The thickness of the hoop is to some extent a matter of taste • • • It is possi­ ble to string too tightly though this is a defect which a few days' play will generally modify and the degree of tightness desirable varies with the style and taste of the play­ er* Within limits weight means increased power; lightness, greater resource* Taking, therefore, fifteen ounces as the maximum and fourteen and one-quarter ounces as the mini­ mum to be recommended, there la considerable room for oholoe* The shape of the raoket is of less consequence* The curve borrowed from tennis was valuable so long as most strokes were made with a horizontal racket* Now that most of our strokes are made with the racket nearly vertical the curve has be­ come less desirable or even injurious and tending to increase the difficulty of striking 13

the ball with the middle of the racket.*^

It has been said that It was not until 1883 that

the first rackets were made of symmetrical f o r m ,

that is to say, without the lop-sided head common to

other tennis games* In an excellent description of

the racket commonly used almost ten years after this date, we find a great deal of similarity to the pres­ ently used racket* The description by "Cavendish'1 is as follows:

It should be about twenty-seven inches long and should weigh about fourteen and one-half ounces • • • The frame should be of well- seasoned ash; the stringing, of good catgut* The face, in other words the part of the head which le strung, should be about eleven inches long (or including the center piece down to the neck, thirteen inches long) and about eight and three-quarters inches at its widest part outside measurement • • • The balance should be about half way along the length of the racket, thirteen and one-half inches in from either extremity*

S. Powell Blaekmore, in a book published in 1921, presents one of the most complete sections on the choloe of tennis rackets to be found in the literature and, therefore, the following exoerpts are quoted:

Decide at once to have nothing but a

1glbld.* pp. 201-202*

Paraly Paret, Lawn Tennis* Its Past* Pres­ ent. and Future, p* 78*

^"Cavendish," The Oame of Lawn Tennis, p* 19* 14 very tightly strung racket, giving the high­ est clear note when the strings ere struck with the hand* The player who expects a racket to give a full season's play must make some compromise In choice in regard to the stoutness of the gut* The thinnest gut Is the best, but naturally Its life Is a short one • * . It should be strung so tightly that the greatest pressure with the fingers In the centre of the stringing can make but the slightest impression*

The consensus of advice hitherto has laid stress upon getting a racket preferably weighing fourteen and one-half ounces with the weight in the head and a handle of five and one-half inches in circumference * • •

Just as the slse of the hand should de­ termine the circumference of the handle so should the weight of the racket depend upon the physical build, the muscular power and the strength in the wrist of the player con­ cerned* There are numbers of medical elec­ trical establishments In London that reap a rich annual harvest from "tennis elbows" and "tennis arms*" These troubles are generally the direct result of playing with handles too big and rackets too heavy; moreover, they are very obstinate troubles to curs • • • Obviously, the heavier the racket the slower must the player be in repartees of fast vol­ leying at the net* Net play demands a much more finely balanced racket than base-line slogging • • • Except for the player of un­ usual physique • • , I suggest a thirteen and one-ha If ounoe or thirteen and three- fourtha ounoe racket for the first season or two • • • A young girl might advantageously start with a thirteen ounce racket * . •

I strongly recommend an evenly balanced racket — too much weight in the head slo^s up the quick movements In volleying and to the medium wrist is an undue strain • • • An even balance can be tested by halving the length of the racket exactly, and then test­ ing the weight from that ascertained point • 15

To the player who can comfortably wield a fourteen and one-half ounce racket my ad­ vice would be -- then get ItI Obviously there must be more punch behind the heavier racket If it can be as efficiently wielded without strain*U

It Is extremely unusual for a person writing on

tennis, especially the performance aspects of the

game, to devote so much space to recommendations con­

cerning the racket. In addition to evaluating racket

dimensions In light of such factors as tradition (the

most common In other texts) and durability, Mr*

Blaokmore gives considerable emphasis to the relation­

ship with the physical make-up of player, the strate­

gical use of the racket, and, therefore, Its efficien­

cy of use to the player. While he very often attempts

to reason why he makes a recommendation, the absence

of scientific Investigation Is quite apparent* This

absence is even more apparent in the recommendations

of other writers and, interestingly enough, even with outstanding personages In tennis who wrote ten, twenty,

and thirty years after the publication date of Black-

m ore^ book* Por example, Beasley has presented the

following typical set of recommendations, apparently

U s * Powell Blaokmore. Lawn Tennis Up-To-Date. pp. 2-6. 16

without reason:

1* For women and children* Handle - - 4 6/8 Inches In circumference Weight — 12 1/2 to 13 ounces Balance — slightly light in the head

2* For men: Handle — 4 7/8 inches in circumference Weight — 13 1/2 ounces Balance — slightly light in the heed*6

Literature related to the investigation of meth­

ods and techniques of the performance of tennis skills*

The various efforts employed to investigate possible previous work in the area under Investigation failed

to produce any studies which dealt directly with the

design of tennis rackets* One study was found in which

the effect of stringing tension on accuracy was inves­ tigated*

A pamphlet, published by Victor Sports, Inc., entitled "How Tight Should My Backet Be Strung?,"^ describes a series of tests that were designed to mea­

sure the effects of varying the tension of gut string­ ing* Tests were given to a group of professional and amateur tennis players of varying degrees of ability

In whloh they hit various shots to different marked-off sections on a tennis court on balls hit from various

l^ereer Beasley, How to Flay Tennis, p* 3*

^ 11 How Tight Should My Tennis Backet Be Strung?,n Victor Sports, Inc., 1966* 17 angles and distances by a tennis robot. The shots were then recorded as hits or misses. While there Is no way of determining the limits of the Class A, B, and C players that are referred to, the following are the conclusions drawn:

1. There Is a marked drop-off In shot con­ trol when string tension gets beyond a certain point. This Is true for all players with every degree of ability.

2. Better players can benefit from higher string tension more than those with less tennis skill. Class A players hit the peak of accuracy with string tensions between 60 and 65 lbs. Class B players did best at about 55 lbs. Class C players hit their peak around 50 lbs.

5. Extremely high string tension causes unduly rapid wear on strings and frame. Even the finest gut strings tend to fray and break sooner. Frames lose their shape. What*s more, on ordinary frames which do not have the reinforce­ ment of oross-graln laminations, ex­ tremely tight stringing tends to out through the wood, so that the frames will stand up for fewer restrlngings.

Unfortunately, the person who conducted this study is deceased and the Victor Company had neither a re­ port on the research techniques, the data, and the re­ lated Information, nor any Idea as to what became of this Information. No mention Is made In the pamphlet of any attempts to establish validity, reliability, or objectivity. 18

Photographloal methods have been employed in two

research projects bearing some relationship to this

study* Lockhart*® studied the validity of two timing devices, a one-hundredth-second stopwatch and a gravi- t©meter, used in measuring the velocity of tennis serves* She took readings of the services of three subjects and correlated the readings obtained by the two devices with the measurements taken by photograph­ ing the services through cinematography with an elec­ tric clock included in the picture* She reported that the one-hundredth-seoond stopwatch was found to be a satisfactory timing device for use in determining time in short Intervals, as in the tennis serve*

Edgerton and Killian*® did extensive work in pho­ tographing various sport activities with the use of stroboscopic lighting equipment* The method used was to open the lens of a camera long enough to capture an entire movement (e. g., a forehand tennis stroke), the

Illumination of the subject coming from a stroboscopic unit giving off repeated flashes of a very high frequency*

18Jeanne Aileene Lockhart, nA Study of the Valid­ ity of Two Timing Devices Used to Measure the Speed of a Tennis Serve," Unpublished Master's thesis. Univer­ sity of Wisconsin, 1937*

l®Harold 8* Edgerton and James R* Killian, FlashI Seeing the Unseen by Ultra High-Speed Hiotography* 19

This method results in a nicture containing numerous

images of the subject during the various phases of the

total movement* It is one possible method of calcu­

lating the velocity of strokes*

Swart studied the essential skills in tennis and devised methods for measuring these skills* He deter­ mined the essential skills through the observation of play, the analysis of stroking methods and technloues, and skill testing* Of the conclusions drawn, the one that hod a relationship to the present study was that the ''proficiency of service is In direct ratio to the speed of service,"**) the faster serves being the more successful. pi Johnsan* did an analytical study of the tennis serve of advanced women players* She investigated (1) the relationship between speed and accuracy of the slloe serve, (2) the serving movements of the players,

(3) the relationships between speed, accuracy, and player movements, and (4) the possibility of devising a target-type test for serving. With regard to the importance of her findings to the present study, she

^Harry A. Swart, "Tennis Technique Measurement," p. 24* Unpublished Master*s thesis. University of Southern California.

21Joan Johnson, "Tennis Serve of Advanced Women Players," Research Quarterly* Vol. XXVIII, No* 2 (May, 1957), pp. 123-131* 20

concluded that speed and accuracy were Independent

factors and that no relationship existed between them*

She also proposed that a circular target be devised

for measuring service accuracy*

Condon22 compiled a list of as many factors as

were thought to enter Into success in competition from

the tennis literature* On the basis of his findings

he attempted to make an analysis of playing ability*

After conducting tests Involving batteries of tests

very similar to the Dyer Backboard Test, he ran a fac­

tor analysis and concluded that, while many different

factors entered in, basically and fundamentally the

accomplished player must have speed In hitting the

ball and accuracy of placement*

Dyer2® constructed a test that was employed in a

modified form in the present study* The test consists

essentially of a person rallying a ball against a back­ board and above a line three feet from the floor as many times as he can within three thirty-second per­

iods* The total of the soores, or number of hits, of

22Carltan J* Condon, "The Development and Evolu­ tion of a Battery of Tennis Skills as an Index to Abil­ ity in Tennis," Unpublished Master*s thesis, Spring­ field College, 1941* 0 5 Joanna T* Dyer, "Revision of the Backboard Test of Tennis Ability," Research Quarterly. Vol* IX, No. 1 (March, 1958), pp* 25-51* Pi

the three periods results In the players test score.

Dyer reports reliability coefficients of .86, .87, and

•92 and a validity coefficient of .92. The latter was obtained by correlating res\’lts obtained by players on the test with resultant rank in a round-robin tourna­ ment.

Broer and Miller®* constructed a skill test for classifying and grading tennis students. They divided the total test into two seotions, one for forehand and one for backhand, in an attest to evaluate more than just general skill as in the Dyer Test. The test con­ sists of the player standing on the baseline, bouncing a ball, and hitting it into the back nine feet of the extreme opposite end of the court. The player hits fourteen forehand and fourteen beokhand strokes. Balls landing outside the aforementioned area are vraded down as are balls hit over a rope stretched foot feet above the net. They used an intermediate group and a beginning group and obtained reliability ooefflclents of .80 for both groups and validity coefficients of

^^Marion R. Broer and Donna Mae Miller, "Achieve­ ment Tests for Beginning and Intermediate Tennis," Be- ^eargh Quarterly. Vol. 21, No. 3 (October, 1950), pp. 22

•85 and .61, respectively. Slassow2® determined that

In this test It Is possible for strokes Imparting a

velocity of 56.6 feet per second to result In a score

Identical with those Imparting a velocity of 98.5 feet

per second.

In the various tests and Investigations regarding

tennis ability, the emphasis cm the player is quite

obvious* Therefore, when considering them as attempts

to Increase the over-all caliber of tennis play, the

players are definitely being forced to adapt them­

selves to the equipment. No evidence was found In the

literature of any effort to determine if players would be more efficient if outfitted with different equip­ ment* In other words, equipment Is not specifically designed to meet the playing needs of the players*

It Is evident that the literature contains very little material bearing direct relationships to the present study* Analyses have been made of the game of tennis to determine the essential elements; tests have been devised to measure general ability and ability In specific skills; and studies have been made of the re­

lationship between ability in specific skills and suo- cess in competition. With the exception of the study

^^Unpublished material received from R. B. 0lassow, University of Wisconsin. 23

concerning the tension of racket stringing, no studies

were found that bore dlreot relationships to the prob­

lem being Investigated In this study*

in the determination of the procedures to be em­

ployed In the present study, three recommendations were

drawn from the results of the studies described In

this chapter* First of all, results of Condon's®®

study served as a major factor in determining that, In

order to study effectiveness of stroking, velocity and

accuracy must reoelve highest consideration. Secondly,

on the basis of Lockhart's2^ success in measuring velocity with a one-hundredth-second stopwatch, a one- hundredth-second electrical timing devioe was obtained

for measuring stroke velocity In the present study.

Thirdly, with Johnson's®® recommendation In mind, a

clroular target was developed for measuring the accur­ acy of strokes.

®®Condon, op. clt. 27 Lockhart, op. clt.

Johnson, op. clt. CHAPTER III

PROCEDURE

The testing program of this study was divided In­ to two phsses: (1) the testing of the effeots of varying racket length and racket weight and (2) the testing of the effects of varying stringing material and string tension*

Testing the variables of racket length and weight*

The first, and major phase of the testing program was designed to determine the effects of varying the fao- tora of racket length and raoket weight on forehand stroke effectiveness* Eighteen subjects were employed, nine constituting the "advanced" group and nine con­ stituting a "beginning” group*

In obtaining the nine advanoed players, a con­ certed effort was made to obtain the nine best players, from the standpoint of competitive experience and suc­ cess, on the campus of the Ohio State University* The resultant group was composed of two faculty members, both of whom had played Intercollegiate varsity ten­ nis, and seven members of the University varsity team*

The nine players who participated In this study as the

84 25 advanced group are listed below along with their ten­ nis histories:

John Archer: nine years of tennis participation

4 years -- high school team

1 year -- 0. 3. TJ# freshman team

Runner-up and champion of a considerable

number of Ohio sectional singles and

doubles tournaments

Larry Blederman: eight years of tennis partici­

pation

4 years — high school team

1 year -- 0* S. U, freshman team

3 years -- 0. S. IT* varsity team

Extensive participation In summer amateur

tournaments with severe1 Ohio sectional

tournament championships

Fritz Fonts: six years of tennis participation

2 years — Junior high school team

3 years -- high sohool team

Several local end Ohio sectional champion­

ships

Member of Junior Davis Cup Team

Christie Geankoplls: twenty-five years of tennis

participation

3 years -- high school team 26

3 years •- University of Minnesota team

Extensive amateur play including many local

and state sectional championships

Arthur Gianakopoulos: eight years of tennis par­

ticipation

4 years -- high school teem

1 year -- 0. 3. U* freshman team

2 years — 0. S. TT* varsity team

Participation in various summer tournaments

Jacob Schlosser: five years of tennis narticipa-

tlon

2 years — high school team

1 year -- 0. S. U. freshman team

2 years -- 0. 3. F. varsity team

3 years -- Junior Davis Cup team

Volney Taylor: seven years of tennis narticipa-

tion

4 years -- high school team

1 year — 0* 3* F* freshman team

Various amateur tournaments, including sev­

eral local and Ohio sectional champion­

ships

Frank Watanabe: fifteen years of tennis partici­ pation 27

3 years -- University of ‘ashlngton varsity

team

Considerable number of local, state section­

al, and state ohamolonahlns in singles

and doubles

Daniel Winters: five years of tennis participa­

tion

1 year — high school team

1 year — 0. S. U. freshman team

2 years — 0. S. U. varsity team

The nine beginning players were obtained from

Physical Education 412, a freshman activities oourse

for male students in the Teacher Education Division of

Physical Education at the Ohio State University. One

phase of this oourse is a two-week seotlon of ninety- minute olasses (ten classes in all) designed to teaoh

the fundamental strokes of tennis* The nine subjects

were picked at random from a group of approximately

one hundred and twenty, the major factors in selection

being (1) absolutely no previous tennis experience and

(2) availability for four testing sessions*

Selection of rackets used In testing the effects

of varying length and weight. In the selection of the

rackets to be used in the evaluation of the importance 28

of length and weight, It was decided to start with

three "standard" rackets* The rackets were standard

In that they represented the rackets being used by to­

d a y ^ tennis players. Therefore, these three rackets

were twenty-seven inches In length and designated as

light, medium and heavy (or twelve and five-eighths

ounces, thirteen and one-eighth ounces, and thirteen

and five-eighths ounces, respectively). With the con­

currence of Hendrix^ and Fitz,2 it was decided to fol­

low along with the present variability standards in

weight and to alter the length factor two Inches plus

and minus. Since lamb gut is generally considered to be the best stringing material for tennis play, all

rackets were strung with this material at fifty-eight

pounds tension. The latter figure was chosen because

it represented the average tension that better tennis

players used as evaluated by Hendrix and by the writer

in his position as Tennis Professional at The Country

Club, Cleveland, Ohio. All other factors were kept

^Dr. John Hendrix Is varsity tennis coach at the Ohio State University and tennis professional at the Cleveland Skating Club.

®Dr. Paul Fits, formerly of the Department of Aviation Psychology at the Ohio State University, has done extensive researoh In related problems of design­ ing equipment to suit the needs of users. His work Involved airplane control design. 29 constant and represented the highest quality racket manufactured by A. 0, Spalding Brothers*

Therefore, the nine rackets emnloyed In the first phase of the testing can be described as follows: nine Spalding (Fancho Gonzales model) tennis rackets

-- four and flve-elghths Inch grins, balanced at their respective m5d-polnts, and strung with Victor Commander gut at fifty-eight pounds tension*

TABLE 1

RACKETS EMPLOYED IN THE TESTS FOR

FACTORS OF LENGTH AND "/EIGHT

Code Length Weight

AL.. <

AM • •...... 25” .....

AH...

BL. •...... 27”......

BM*..

BH.

CL...... 29”.....

CM...... 29"......

CH... 30

Testing the variables of stringing materiel and

tension* Three players from the advanced group par­

ticipated in this phase of the testing, Christie Gean-

koplis, Arthur Glanakopoulos, and Jacob Schlosser*

Each of the three players who participated -ere sent

through this phase of the testing program with only

one racket* In the first phase of testing, each of

these players did particularly well with a specific

racket, each racket, In turn, being of different

length* Therefore, the rackets used by these players

In the second testing phase were: Oeankoplls - CR,

Glanakopoulos - AH, and Schlosser - BL*

The variables were stringing materials and ten­

sion* The materials used were Victor Commander gut

and Victor Red Twist 15-gauge nylon* Since the play­ ers had already been tested with their particular rackets strung with gut at fifty-eight pounds, the two variables were rotated so as to obtain the following order of testing:

1* Gut at fifty-four pounds tension.

2* Nylon at fifty-four pounds tension*

3* Nylon at fifty-eight pounds tension.

4* Gut at slxty-two pounds tension*

5. Nylon at slxty-two pounds tension. 31

The saune three tests. Accuracy, Velocity, and

Skill, were employed In exactly the same manner as In

the first phase of testing*

Tests employed In the study* Three tests were

selected to evaluate the effectiveness of each racket*

Two tests were designed to meet the needs of the study,

one testing the factor of accuracy and the other test­

ing the factor of velocity* The third test, an adapta­

tion of the Dyer Tennis Test, was Included because (1)

the Dyer Test was the only standardised and popularly

used test of tennis ability available and (2) It seemed

to place emphasis on both of the factors considered to be most important in stroke production -- accuracy and

velocity*

All testing was done on the clay tennis court lo­

cated in the French Practice Shed of the Ohio State

University Athletlo Department* The principal purpose

for this was the ease in keeping so many factors, such

as light, wind, and court conditions, as constant as possible and completely ruling out the complications

that would have been caused by Inclement weather*

Accuracy Test t The test of accuracy involved the

ability of the player to hit a ball served to him by a

Ball-Boy Tennis Robot to a target located on the opposite side of the net. The Ball-Boy machine was

set at "Hard Hit”® and located one and one-hplf feet

in from the singles court side line and with its front

wheels straddling the right service court service line

on the opposite side of the net from the subject. It

was aimed to serve the bells so they would land in line

with an imaginary extension of the center court line

on the subjects side of the net. The target was lo­

cated on the same side of the net as the machine and

had its center sixty inches back from the service line

and eighty Inches from the left side line. The target

was composed of a circular section made of white cloth

with a radius of two and one-half feet. The remainder

of the target consisted of four concentric circles etched

into the clay court, each circle increasing In size of

radius by two and one-half feet.

The player was served a total of forty balls for

each racket. The forty balls were divided into two

testing rounds of twenty balls each. The player at­

tempted to return each ball to the center of the target

®Ball-Boy Tennis Robots have two settings, Hard Hit and Soft Hit. The Hard-Hit setting causes the ball to be hit out of the machine to an average dis­ tance of fifty-four feet before striking the ground. 33

with a score of five points swarded to each bn11 mak­

ing its initial contact with the center section* For balls landing in the next circular area a score of

four was assigned, then three, two and one to the cir­

cular areas in ord^r away from the center* A score of

zero was assigned to balls hitting outside of the tar­

get area and to balls hitting the net*

Reliability coefficients of .85 and .74 were ob­

tained for the advanced group and beginning group, re­

spectively. The coefficients were Obtained by corre­

lating the totals of the odd and even scores for the various rackets. A diagram of the testing set-up is presented on page 34•

Velocity Test! The test of velocity also emrloyed the Ball-Boy machine. The machine was set up this time along and at the furthest extremity from the net of the center court line. It was set on Soft Fit and alm»d to serve balls over the net to a snot mid-way between the service line and the base line and one- third of the distance from an imaginary extension of the center court line to the singles side line. The player returned the balls to a target set up nine in­ ches from the net on the same side of the net as the machine that measured three feet by three feet (surface DIATRAY 1

TESTING ARRANGEMENT FOR THE ACCHRACY

-'•NMlS

e v - >V.AV«* 35

all above the net)* A Hale Reaction-T'erfor-nance Tim-

was used to measure the time Interval between the

Instant of racket-ball contact and the Instant of

ball-target contact* The Hale Timer Is an electrical

timing device employing two Standard Kleetric timing

clocks, each measuring to one one-hundredth of a sec­

ond. It was necessary to use only one of the clocks

in this study. The clock was started and stopped by a manual method of closing and opening a circuit by hav­

ing one lead wire securely looped around the left

thumb and the other around the left Index finger of

the tester. The clock could then be onerated by mere­

ly closing and opening the fingers. Six readings were made for each subject using each racket.

Reliability coefficients of .9? and .64 were ob­ tained for the advanced group and beginning group, re­ spectively. The coefficients were obtained by correla­ ting the totals of the odd and even scores for the various rackets. A diagram of the testing set-up la presented on page 36.

*The Hale Reaction-Ferformance Timer was designed by Dr. Creighton Hale, Director of Research for Little League Baseball, Inc., of Williamsport, Pennsylvania. DIAGRAM 2 3e

TESTING ARPANOFVF»tT FOP TPF, SFILT, TEST

HBBT T

n M W + -«IT

MMMNl Q » - M P U H B Skill Tests The third teat employed was an adap­ tation of the Dyer Backboard Test of Tennis Ability

(revised form).® The Dyer Teat was designed to mea­ sure general tennis ability without analyzing the var­ ious strokes and elements that make up the game of tennis* Because of the fact that the present study was delimited to the forehand groundstroke, the only revision In the Dyer Test directions was that only the forehand groundstroke could be used In the play of the ball* The substitution of the adapted Dyer Teat, henceforth referred to as the Skill Test, was substan­ tiated by a correlation coefficient of *90 obtained by administering the original and adapted forms to thirty students In a tennis class for physical education ma­ jors at the Ohio State University*

The testing sequence* The subjects were tested

In four separate sessions* Each of the first three sessions was devoted to the administration of the Ac­ curacy Test and the Skill Test for three rackets of the same length* Bach subject went through the vari­ ous tests with a different order of use of the rackets from the other subjects In his particular group* This was done to counteract the effeots of learning, fatigue, 38 and any other factors that might have entered in. The order system that was used Is presented in Table 2 on page 39 with the code numbers of the subjects in the advanced group and the beginning group indicated in the first column* The fourth session Involved the ve­ locity testing for all nine rackets* The same order for testing was employed as is indicated in Table 8*

In all of the testing* the subjects were urged to take as much time to ''warm up" and get accustomed to each racket as they desired* They were permitted to employ any activities they desired in accomplishing this* It was felt that this approach was psychologi­ cally more sound than the use of a prescribed warm-up period*

In order to keep the factor of ball response con­ stant * the tennis balls employed In the testing were changed periodically* After a set of twenty-four balls had been used for twelve testing sessions* they were discarded and new balls were put in their place* The balls used in the study were specially selected by A*

0. Spalding Brothers Co. for uniformity in size* weight* and bounce*

Personal data* Eaeh person being tested filled out a short information sheet. Along with certain data obtained from this sheet* various measurements were 39

TABLE 2

TESTING PROGRAM FOR FACTORS OF

RACKET LENGTH AND RACKET •'.'EIGHT

Players (18) Session Order within Sessions

1 2 3

Ad-1 & Bg-1 1 A-- L A—M A-- H 2 B-- V B—H B—L 3 C— -H C-- L C-- M

Ad-2 ft Bg-2 1 A-- M A-—H A—L 2 B-- H B---L B— ——¥ 3 C—L C-- MC-- H

Ad-3 k Bg-3 1 A -- H A-- LA-- ¥ 2 B—L B—M B---H 3 C-- M C— -H C---L

Ad-4 k Bg-4 1 B---LB-- M B—H 2 C-- M C—HC---L 3 A---H A—L A-- M

Ad-5 3: Bg-5 1 B-—V B—H B—L 2 C---H C-—L C-- ¥ 3 A— -L A—M A-- H

Ad-6 ft Bg-6 1 B—H B---L B---K 2 C—L C-- ¥ C---H 3 A-- V A---H A—L

Ad-7 ft Bg-7 1 C-—L C-— ¥ C---H 2 A-- M A — -H A-—L 3 B---H B—L B—M

Ad-8 ft Bg-8 1 C-- W C---H C-- L 2 A—H A---L A-- ¥ 3 B—LB -- ¥ B-- H

Ad-9 ft Bg-v 1 C-- H C-—L C---K 2 A— -L A— -K A— H 3 B---M B—H B-- L 40

obtained through brief teste e dir ini stored in coordina­

tion with the main testing nrogmm. These personal

data are found in Table 17 on page 79 in Appendix B.

The data included were obtained as follows:

1. Height -- Information sheet*

2 * v;eight -- Information sheet*

3. Hand Size -- The distance betv-een the tips

of the thumb and the fifth fincrer on the

nlaying hand were taken with the hand fully

extended along a line on a mimeopraohed form

drawn u p for the study* The thumb tip was

aligned with a perpendicular at one end of

the line* A pencil mark was made at the end

of the fifth finger and the distance between

these two marks was measured to a sixteenth

of an inch*

4* Arm Length -- A firm wooden yardstick was

employed to measure the distance between the

top portion of the coracoid process to the

extreme portion of the middle finger of the

playing arm. The yardstick was first placed

In a vertical position close to a wall and

the uoper edge (0 ") was aligned with the up­ per edge of the coracoid process of the subject ss he stood next to the yardstick*

Vhen a successful alignment had been made, the subject was instructed to -^ake sure that his a m , hand, end middle finger ran straight down the yardstick and, then, to lean against the stick and, thus, the ’"all. The roint reached by the tin of the middle finger "-as then recorded to the nearest eighth of an inch* A reliability coefficient of * 8 8 was obtained for this method through the test- retest method emrloying a class of thirty- five physical education students*

Forehand Strength — In an attempt to deter­ mine the amount of force a player could ex­ ert in executing a forehand stroke, a simple static test was devised. First of all, It was decided that the simplest method of de­ termining "forehand strength" in a static fashion would be to record the tension on a cable that attached the racket to a fixed object* The subject would assume the posi­ tion reached at tne instant of racket-ball contact in a forehand stroke and exert as much forward pressure as possible in the 42

direction of an imaginary stroke* A reli­

ability coefficient of .83 was obtained for

this method by the same procedure as men­

tioned in the above item.

The most logical point of attachment of the

cable to the racket was decided upon as be­

ing the center of percussion of the racket.

Therefore, the center of percussion was cal­

culated for each of the medium weight rack­

ets. This was done by a simple experiment

that was perforated as follows:

a. Let “O'* represent the pivot point of

the racket, or the point around which

the racket rotates during the execution

of a stroke. b. Let "o* m." represent the center of

mass as the rackets were constructed to

balance at this mid-point when strung. c. Let "c. p*" represent the center of

percussion, the location of which is

one of the unknowns. d. Let "ljj" represent the distance between

the pivot point and the center of per­ cussion. 43 e. Let the racket oscillate like a pendu­

lum ♦ 1 0 ° and determine its period of

free oscillation with respect to pivot

point "0 .” This is accomplished by at­

taching a simple, home-made device that

causes two knife edges theoretically to

"pass through" pivot point "0 ," the

knife edges being directed toward the

major portion of the racket. The knife

edges are then oaused to rest in two

clean pipes, approximately 2 " in diame­

ter and stabilized. The racket is then

caused to oscillate + 1 0 ° and the num­

ber of conplete oscillations is record­

ed for a three-minute period of time.

Substituting the appropriate data in

the two formulae shown, the following

results were obtained for the medium

weight rackets:

a number of seconds______number of complete oscllla- tlons in the above time in­ terval 18 = (8 8 6 . 0 4tr* 44

15 Of AM « 18.26"

13 Of BM - 19.23"

I3 Of CM ■ 20.80"

As the weight constituted an Insignifi­

cant factor In this particular test,

only the results for the three medium

rackets were used, thus employing only

the variable of length.

The center of percussion for the three med-

lum-welght rackets being thus computed, each

subject was tested employing each racket. A

cable attached to the net post was attached

to the center of percussion of the particular

racket. The subject then assumed an "in­

stant of contact" stance and the cable was

adjusted for height on the net post so as to

make the cable horizontal. The subject was

then constructed to excert pressure forward

until he attained maximum effort. A tenslom-

eter was employed to record the tensions on

the cable. The tensions thus obtained for

each of the three rackets were then totaled

and recorded as Forehand Strength (FS). Treatment of the data. The scores obtained by each player for a particular set of racket variables 46 were totaled for each of the three tests* In the Ac on- racy Test, the player's score represented a total of the forty readings taken In the individual testing situa­ tion* In the Skill Test, the score renresented a total of the scores of the three thirty-second trial periods aa prescribed by Dyer. 6 The score in the Velocity Test represented a total of the six readings taken in one one-hur.dredths of a second. These "total scorbs" are found in Tables 13 through 16 on pages 73 through 76.

In each of the two test phases there were actu­ ally three variables: the factors of length and weight in phase number one, the factors of stringing material and tension in phase number two, and the factor of personnel making up the third factor in each of these two phases. Because of the nature of the data, the statistical method chosen to analyse the data was that of "Analysis of Variance*" This technique is designed to measure the existent variability within an entire testing situation, within subgroups of variables, and among these subgroups. The advantages of the use of this technique have been pointed out by VcNemar7 ae being t

®Dyer, lo£. oit.

7Quinn MoHemar, Psychological Statistics, pp. 288- 283. 1. It provide* an over-ell test of the signifi­

cance of the differences between two or more

means*

2 * It leads to a definitely imnroved estimate

of sampling error when double* triple* or

higher-order classification is involved by

allowing for variation due to one or more

variables*

5* It provides a means of testing whether the

Influence of one Independent variable on the

dependent variable is similar for subgroups

formed on the basis of a second independent

variable•

4* It provides a means for measuring possible

interactions among variables. This refers

to the possibility of one variable having a

certain "total effect11 but* when placed in

combination with another variable* having

the resultant effect changed in varying de­

grees*

Thus* in phase one of the testing* the effects of tne variables of player personnel* length of racket* and weight of racket were computed both separately and in combination. In the second phase of testing* the same treatment was employed to evaluate the factors of 47 player personnel, stringing material, and stringing tension*

In an attemut to determine if the various personal data had significant relationships with ability to usi certain rackets, correlations were run among various sets of measurements and success with a particular di­ mension of racket* This success was measured by the interaction between players and test variables* There­ fore, rank difference correlations were run among the personal measurements of height, weight, hand size, arm length, and forehand strength of (1 ) the advanced players and the interaction between length and players in both the Accuracy Test and the Skill Test and (2) the beginning players and the interaction between length and players in the Accuracy Test* The reason for the selection of these particular interactions was that they were the only ones that were statistically significant* CHAPTER IV

ANALYSIS OP THE DATA

Tablea ralating to the analyala of the data. The

scores of all the tests included In this study are

found in Tables 12 through 15 in Appendix A* These

tables are organised on the basis of the tests given

to the various subjects* The results of the prelimi­

nary treatment of the data Involved In the analysis of

variance are found In Tables 16 through 25* The treat­

ment Involved follows the standard procedures for this

technique as found In Snedecor*^

Tables 5 through 6 on pages 50 through 58 contain

the final computations for the data Involved In the

analysis of racket length and racket weight on success

In the three tests* The variables, the factors Inves­

tigated plus player personnel, are listed In the ex­

treme left column* The factors are listed separately, under "Main Effeots," and In Interaction with each oth­

er. The extreme right oolunn contains nP," or ratio between the mean square of the faotor and the mean

Vleorge w* Snedeoor, Statistical Methods Applied to Measurements In Agriculture and Biology.

46 49

square o? error, which la used in determining the sta­

tistical significance of the variation in scores in the

particular category* Tables 9, 1 0 , and 11 on pages 60,

61, and 62 contain similar data for the analysis of

variance due to stringing material and stringing ten­

sion* It should be pointed out that no analyses of in­

teractions have been Included for the Investigation of

stringing material and tension because of the small number of scores obtained* The reason for the small number of scores is attributable to the fact that three players participated in this second testing rhase*

Variations due to racket length and weight In the advanced plever group* The variation in scores due to personnel, or "players," was found to be statistically significant at the one per cent level of confidence in

each of the three tests. Accuracy, Skill, and Velocity*

Thi s variation was expected since the group, while constituting a good selection of the best tennis play­ ers at the University, represented a relatively wide range of skill*

In the Accuraoy Test (Table 3), the factor of

racket weight proved significant at the five per cent

level of confidence* The advanced player group exper­

ienced best results with the heavy weight racket* The 50

TABLE 3

EFFECTS OF LENGTH AND WEIGHT ON ACCURACY TEST SCORES

OF ADVANCED GROUP

Degrees Sums of of Mean Variables Sauares Freedom Souares F

Main Effects

Length: 151*41 2 7 5 . 7 0 5 1.067

Weight: 70 2 . 3 0 2 351*150 4. 9 5 0 *

Players: 9 0 2 0 . 4 5 8 1127.556 1 5 . 9 8 5 * *

Interactions

Length* Weight: 466.96 4 1 16.740 1.646

.Yeight- Players: 1139*47 16 71.217 1.004

Length* Players: 3954.36 16 247*148 3.484**

Error: 2 2 6 9 . 9 4 32 7 0 . 9 3 6

Total: 1 7 7 0 4 . 8 9 80

*Signlfleant at 5< level of confidence*

**Slgnlficent at 1% level of confidence* 51

variation In scores due to racket length was not sig­

nificant, The variation in scores due to the Interac­

tion between length and players was significant at the

one per cent level of confidence* Interaction refers

to the effect that two factors have when they act in

combination upon a particular outcome which, in this

case, is in terms of test scores* The interactions between length and weight and between weight and play­

ers were not found to be significant*

In addition to the factor of nlayera in the Skill

Test (Table 4), the variation due to length was found

to be statistically significant at the one per cent

level of confidence* Best results were obtained with

the short racket and poorest results with the long racket* Variation due to weight was not found to be significant* With regard to the interactions among the three factors, only the interaction between racket length and players proved to be significant* This in­ teraction proved significant at the one per cent level*

The variation due to the interactions between length and weight and between weight and players were not significant*

The variation due to players was the only one that proved significant In the Velocity Tost (Table 5)* The factors of length and weight did not. None of the 52

TABLE 4

EFFECTS OF LENGTH AHJ "/EICtHT ON SKILL T^ST SCOFFS

OF ADVANCED CFO IT

Degrees Sums of of Mean Variables Sauares Freedom Squares F

Main Effects

Length t 342*54 2 171.270 7.920*#

Weight t 40.77 2 20.385 • 943

Players: 3117.73 8 389.716 18.021**

Interactions

Length- Weight: 62.86 4 15.715 .727

Welght- Players: 209.67 16 13.104 • 606

Length- Players: 1475.24 16 92.203 4.264**

Error: 6 92.03 32 21.626

Total: 6940.84 80

**31gnifleant at 1% level of confidence 53

TABLE 5

EFFECTS OF LENGTH AND ’'EIGHT ON VELOCITY TEST SCOPES

OF ADVANCED GHCUF

Decrees Sums of of Mean Variables Squares Free!om Squares F

Main Effects

Length: 5 3 6 . 2 2 2 268.110 2.682

.Velght: 277.63 2 138 . 8 1 5 1 . 3 8 9

Players s 5 8111.56 8 7 2 6 3 . 9 4 5 7 2 . 6 3 3 * *

Interactions

Length- v/eight: 8 2 . 3 7 4 2 0.593 • 206

Welght- Players: 1543.70 16 9 6 . 4 8 1 • 965

Length- • a * a* Players * 2 3 1 0 . 4 4 16 1 4 4 . 4 0 3 1 . 4 4 4

Error: 3198.97 32 9 9 . 9 6 8

Total: 6 6 0 6 0 . 8 9 80

•♦Significant at 1% level of confidence 54 variations in scores due to Interactions among the var­ iables proved significant.

Variations due to racket length and racket weight

In the beginning player group. As was the case with tte advanced player group in the first phase of test­ ing, the factor of players proved to be significant at the one per cent level in each of the three tests.

This araln points out that the grours were relatively heterogeneous and that this heterogeneity definitely was the cause of considerable variation In the scores attained.

In addition to the factor of players, length was also found to be statistically significant at the one per cent level of confidence in the Accuracy Test

(Table 6 ). The standard length proved best with the long length next best. The factor of weight was not found to be significant. The interactions between length and weight, and weight and players were not found to be significant, but the variation In scores due to the Interaction between length and players was significant at the one per oent level.

The factor of length was also significant at the one per cent level in the Skill Test (Table 7). The beet results were obtained with the short rackets and 55

TABLE 6

EFFECTS OF LENGTH AND WEIGHT ON A C C m C Y TEST SCOPES

OF BEGINNING GROUP

Degrees Sums of of Mean Variable* Sou are s Freedom 3an ares F

Main Effects

Length: 1 461*41 2 730.705 6 . 1 5 6 * *

Weight: 353*41 2 176.705 1.489

Players: 372 7 . 7 8 8 465.973 3.927**

Interactions Length- Weight: 165.40 4 41.350 • 348

Weight- Players: 1162*81 16 72.676 •612

Length- Players: 857 6 * 1 4 16 556*009 4.517**

Error: 3797.05 32 118*658

Total: 19244.00 80

♦♦Significant at X% level of confidence* 56

TABLE 7

EFFECTS OF LENGTH AND WEIGHT ON SKILL TEST SCOPES

OF BEGINNING GROUP

Degrees Sum of of Mean Varlab lee Sauares Freedom Squares F

Main Effects

Length: 2 0 1 * 6 6 2 100.850 7 * 1 4 5 * *

Weight: 1*95 2 .975 •069

Pleyere: 4 664*05 8 5 7 0 . 5 0 4 4 0 . 4 2 7 * *

Interactions

Lenirth- Weight: 50*42 4 7*605 *539

Weight- Players: 178*71 16 11*169 •791

Length- P 1 ayers: 289*00 16 18.065 1 * 2 8 0

Error: 4 5 1*69 52 14*112

Total: 6717.56 80

**Signifleant at 1% level of confidence* 57 the poorest results with the long rackets* The varia­ tion in scores due to weight res not found to be sig­ nificant in this test* None of the interactions, length-weight, weipht-players, and length-players, were significant*

Only the variation in scores due to players was significant in the Velocity Test (Table 8 )* The vari­ ation because of the factors of length and weight were not significant. The interactions of length-weight and weight-playere were not significant, but the vari­ ation due to the interaction of length and players was significant at the one per cent level of confidence*

List of significant variables and interactions*

The following is a list of the variables or interactions of variables that had a significant effect (either at the five or one per cent levels of confidence) on the scoring in the three tests in the phase of this study that dealt with racket length and weight: Advanced Oroun

Accuracy Test: Weight

Players

Length with Players

Skill Test: Length

Players

Length with Players 58

TABLE 8

EFFECTS OF LENGTH AND ’//EIGHT ON VELOCITY TEST SCOPES

OF BEGINNING GROUP

Degrees Sum of of Mean Variables Squares Freedom Squares F

Wain Effects

Length: 393*81 2 196 . 6 0 5 1.155-

Weight: 677*80 2 3 3 8 * 9 0 0 1*991

Players: 4 9 5 7 5 * 4 3 8 6196*929 3 6 * 4 0 8 * *

Interactions

Length- Welpht : 83*75 4 2 0 * 9 3 8 • 123

Welght- Players * 4 1 9 8 * 4 2 16 262*401 1.542

Length- Players* 9798*34 16 612*396 3. 5 9 8 * *

Error s 5 4 4 6 * 7 0 32 1 7 0 . 2 0 9

Total: 7 0 1 7 3 . 6 5 80

♦♦Significant at level of confidence 59

Velocity Teet: Player#

Beginning Group

Accuracy Teet: Length

Playera

Length with Players

Skill Teatx Length

Players

Velocity Test: Length with Players

Players

Variations due to stringing material and string­ ing tension* In two of the tests. Velocity (Table 11) and Skill (Table 10), the factor of player nersonnel was significant at the one per cent level of confidence*

The Accuraoy Test (Table 9) in this phase of the study was the only test in the entire atudy In which this factor did not prove to be significant at either the one or five per cent levels* The variation in scores due to stringing tension and stringing material were not significant in the Accuracy Test, either*

In the Skill Teat (Table 10) the factor of string­ ing material proved to be significant at the one per cent level of confidence* Out material proved to be better in the performance of this test than did nylon*

The variation due to stringing tension was not signif­ icant* 60

TABLE 9

EFFECTS OF STRINGING FATERIAT.S AND TENSIONS

ON ACCURACY TEST SCORES

Degrees Sums of Of Meen Variable* Sauares Freedom Sauares F

Tension: 40.11 2 20.065 • 150

Material: 296.06 1 296.060 2.213

Flayers: 6 0 7 . 4 4 2 263.720 1.897

Error: 1606.34 1 2 133.778

Total: 2 448.94 17 61

TABLE 10

EFFECTS OF STRINOI^O VAT-PIALS AND T ^ TSIO^S

ON SKILL T T:ST SCOPES

Degrees Sums of of Mean Variables Squares Freedom Squares F

Tensions 8.45 2 4.225 •815

Material: 55.59 1 55.59 10.2 9 5 * *

Playerss 448.11 2 224.055 45.204**

Errors 62 .25 1 2 5.186

Totals 572.28 17

**Signifleant at \% level of oonfldenoe 62

TABLE 11

EFFECTS OF STRINGING VATEFIALS AND TENSIONS

ON VELOCITY TEST SCOPES

Degrees Sums of of Mean Variables Squares Freedom Sauares P

Tension: 154 4 * 7 7 2 672*585 5 . 2 5 1 *

Material! 215*55 1 2 15.550 1 * 6 6 8

Players s 4 6 2 1 * 4 4 2 24 1 0 . 7 2 1 8 * 8 2 5 * *

Error: 1 5 5 6 * 6 8 1 2 1 2 8 * 0 5 7

Total: 7 9 1 6 * 4 4 17

•Significant at 5 % level of confidence* •♦Significant at l£ level of confidence* 63

In the Velocity Teat (Table 11), the factor of stringing tension was significant, with the heat ten­ sion being sixty-two pounds and the poorest being fifty-eight pounds. This factor was significant at the five per cent level of confidence. The factor of material was not significant In this test.

As was stated previously, the interactions a^ong variables were not computed because of the small num­ ber of scores.

The relationship among personal measurements and statistically significant interactions. The results of the rank-difference correlations computed among the personal measurements and the significant interactions in the first phase of testing yielded information of no great use. The only correlations that proved sta­ tistically significant «rere positive correlations be­ tween scores of advanced players in the Accuracy Test using twenty-five inch (short) rackets and the measure­ ments of height, hand size, arm length, and "forehand strength." The results of the correlations computed are found in Table 12. 64

TABLE 12

CORRELATION COEFFICIENTS FOR

SIGNIFICANTCANT INTERACTIONS AND PERSONAL DATA

Coefficients of

Acouracy Test (advanced group)s

A-Length Rackets - Height *91 A-Length Rackets - Weight .48 A-Length Rackets - Hand Size *60 A-Length Rackets - Arm Length *74 A-Length Rackets - Forehand Strength -.01

B-Length Rackets - Height -.38 B-Length Rackets - Weight .21 B-Length Rackets - Hand Size -.48 B-Length Rackets - Arm Length -.26 B-Length Rackets - Forehand Strength *10

C-Length Rackets - Height -.40 C-Length Rackets - Weight -.10 C-Length Rackets - Hand Size -.03 C-Length Rackets - Arm Length -.10 C-Length Rackets - Forehand Strength -.40

Accuracy Teat (beginning group):

A-Length Rackets - Height -.50 A-Length Rackets - Weight -.25 A-Length Rackets - Hand Size -*22 A-Length Rackets - Am Length -.18 A-Length Rackets - Forehand Strength -.10

B-Length Rackets - Height *27 B-Length Rackets - Weight -*20 65

TABLE 12 (oontlnued)

CORRELATION COEFFICIENTS FOR

SIGNIFICANT INTERACTIONS AND PERSONAL DATA

Coefficients of Factors Correlation

B-Length Rackets - Hand Size —•45 B-Length Rackets - Arm Length -•56 B-Length Rackets - ForehBnd Strength -.30

C-Length Rackets • Height -.05 C-Length Raokets m Weight • 34 C-Length Rackets - Hand Size • 42 C-Length Rackets m Arm Length .55 C-Length Rackets - Forehand Strength -.02

Skill Test (advanced group):

A-Length Rackets • Height .10 A-Length Raokets - Weight • 30 A-Length Rackets - Hand Size -.45 A-Length Rackets - A m Length • 40 A-Length Rackets - Forehand Strength • 35

B-Length Rackets Helght -.05 B-Length Rackets - Weight -•07 B-Length Rackets - Hand Size • 50 B-Length Raokets - A m Length .04 B-Length Rackets - Forehand Strength -.42 C-Length Raokets Height • 18 C-Length Rackets - Weight •09 C-Length Rackets - Hand Size • 42 C-Length Rackets - Arm Length •04 C-Length Rackets - Forehand Strength •08 CHAPTER V

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

Because of the world-wide popularity of lawn ten­

nis, it is governed by an internationally aoeepted

code of rules* In spite of the fact that the rules

cover the various aspects of the play of the game it Is

surprising to find that the playing Implement used in

tennis, the racket, is not defined or limited in di­

mensions in any way*

Because of this interesting omission In the rules,

the Interest of the writer was aroused with regard to

the question of whether or not the presently accepted

dimensions of a "tennis racket" gave optimum effective­

ness to the tennis player*

It was deoided that the factors to be investigated

would be (1) racket length, (2) racket weight, (3)

stringing material, and (4) stringing tension* Eighteen players were used as subjects, nine beginning players

and nine advanced players* The total group of eighteen

was tested for the first two fastore, length and

weight, by means of three tests, an Aocuraoy Test, a

Velocity Test, and a test of total Tennis Skill* Three

66 fl7 advanced players participated in the second phase of testing involving the factors of stringing material and tension* They were put through the very same tests that were employed in the first phase* In every case, the forehand groundstroke was the only tennis skill used to measure the proficiency of the player in the various tests*

Scores were, therefore, obtained in terms of three tests for each player for every racket of different di­ mensions* Since there were three variations of each of two factors inoluded in the first phase of testing, this meant that two hundred and forty-three totals of scores were obtained in the three tests* In phase two, there were three variations of each of two factors with three players tested, thus obtaining fifty-four totals of scores in the three tests*

The scores obtained were treated according to the analysis of variance method* This made possible the evaluation of the effect of changing the variables in­ cluded In the testing » racket length, raoket weight, stringing material, stringing tension, and player per­ sonnel* Also, the interactions that proved to be sig­ nificant in the two groups for the first phase of test­ ing were correlated with the personal dimensions of the 68

advanced and beginning players by means of the rank-

difference method.

No Interactions were computed for the variables

in the second phase of the testing because of the re­

latively small number of data.

Conclusions and their implications. If the con­

clusions of this study are evaluated in light of their

meaning to the play of the actual game of tennis, cer­

tain implications can be drawn. The Involvement of

the human element, however. Immediately demands that

cautions be exercised In these evaluations as, only

too often, the interactions of factors and the ability

of the player to make adjustments can negate their sig­

nificance. With due regard for this caution, the con­

clusions based on the analysis of the data are hereby presented with their accompanying implications:

Conclusion #1: Advanced players, as a group, are more accurate with "heavy11 rackets (thirteen and five- eighths ounces). The implication here is that, as long as the weight does not Interfere with other phases of their game, advanced players should exercise increased preference for heavier rackets. The fact that weight was not significant to the advanced group in the Skill

Test, whioh required extremely rapid movements and ad­

justments, would indicate that heavy rackets should 69 not prove detrimental to volleying end half-volleying.

In light of the conditions in which accuracy was mea- s\ red, it would seem logical to give Increased e^ha- sis to the recommendations for heavier rackets when the player is involved in competition in which he is hitting a high number of groundstrokes from the base­ line area.

Conclusion #2: The factor of length is of impor­ tance to the accuracy and general play of advanced players in that there is an optimum length for each player. This conclusion Is drawn on the basis of the statistically significant interaction between advanced players and length. If there were a variety of lengths from which to choosef the recommendation would be made to the player to seek out the length giving him opti­ mum effectiveness. However, rackets are not available

In a variety of lengths at this time and, if they were, there would be no way of determining proper length be­ sides use in competition.

Conclusion #3: The faetor of length is Important to the accuracy of beginning players. Vlhen hitting groundstrokea from back court, the beginning group should use the standard length raoket (twenty-seven inches) or slightly longer. They should never use 70 shorter rackets or shorten their grip bv choking up on the handle* Th^se recommendations are made because of the poor results obtained with the shorter rackets and* also* with due consideration for the tyne of stroking

Involved in the Accuracy Test.

Conclusion #4: The factor of length is of impor­ tance to advanced and beginning players alike vhen they are called upon to make rapid movements and adjustments

In playing the ball* This conclusion is drawn on the basis of the scores obtained by both groups In the Skill

Test* which Involved hitting the ball rapidly against a wall a short distance from the player. This immedi­ ately brings to mind the type of play required when a player has advanced to the net* As long as the player finds that he does not lose the reach necessary for playing passing shots* the implication here would be for the player to shorten his grip, or choke up, on the racket when playing the net*

Conclusion #5s For the performance of the gener­ al skills of tennis, gut stringing gives better results than does nylon stringing* This conclusion is made on the basis of the Skill Teat scores of the three advanced players* Therefore, the implication would be for ad­ vanced players to exercise a preference for gut string­ ing* something the vast majority of them do already 71

because of the success experienced In actual uley.

This reconmendatlon would not be made for beginning

players becuase of the lack of experimental evidence

and, also, the suitability of nylon stringing for these

players because (1 ) it gives good results in play, (2 )

it is less expensive than gut, and (3) it is more dur­ able than gut*

Conclusion #6 t When attempting to regulate velo­ city of stroking, there is an optimum length for every beginning player* Because of the lack of need for ve­ locity on this level of play and the needless complexity of determining optimum lengths, no implications or rec­ ommendations are set forth*

Conclusion #7: A higher tension of racket string­ ing will give better results in velocity of stroking to advanced players* As this factor did not effect performance in the other tests, the implication would be for the advanced player desiring greater velocity to have his racket strung at increased tension*

Conclusion #8 r The relationships between the per­ sonal measurements taken and the significant interac­ tions were such as to warrant little further consider­ ation*

Conclusion #9: Individual differences constitute a tremendously important factor in the ability of a 78

player to perform the forehand groundstroke In tennis*

This conclusion re-affirms the point of emphasis that

the teacher of skills must recognize thet each person

has his own potentials, methods of performance, and

levels of success*

Recommendations for further study* On the basis

of the data obtained in this study and the experiences

involved In the experimental work, the following areas

are set forth as worthy of investigation*

1* Similar testing for other strokes, such as

the backhand groundstroke, forehand and backhand vol­

ley, and serve*

2 * Similar testing for different age and sex

groups and, possibly, for groups set up be a more rigid

control over either tennis or general athletic ability*

3* A thorough investigation of the total design and construction of tennis rackets in terms of their purposes In the play and strategy of the game*

4* A more thorough Investigation on the inter­ relationships among racket dimensions and sizes, and the strengths and abilities of players, employing large groups of subjects*

5* Investigations of the effects of varying oth­ er dimensions of the presently accepted model tennis racket* APPENDIX A

TEST SCORES

73 74

TABLE 13

ACCURACY TEST SCORES

ADVANCED GROUP Rackets: Players: AL AM AH BL BM BH CL CM CH

Ad - 1 154 143 167 157 172 153 144 136 137

Ad - 2 127 149 142 144 154 157 164 158 161

Ad - 3 125 105 118 137 130 142 1 1 1 123 1 2 1

Ad - 4 139 159 158 149 143 158 152 154 162

Ad - 5 138 136 158 129 147 159 163 130 145

Ad - 6 159 145 155 160 140 156 151 150 147

Ad - 7 153 144 160 119 134 152 146 151 166

Ad - 8 142 137 138 153 160 161 148 139 147

Ad - 9 133 131 146 114 127 125 129 113 1 1 0

BEGINNING GROUP Rackets: Players: AL AM AH BL B T " " BH CL CM CH

Bg - 1 95 1 0 0 74 1 1 1 125 113 1 2 0 125 1 2 2

Bg - 2 77 1 0 0 90 96 1 0 1 85 71 84 69

Bg - 3 84 89 90 92 97 103 1 0 1 103 96

Bg - 4 99 113 1 1 2 98 97 89 106 105 1 2 2

Bg - 5 84 1 0 0 1 1 1 92 84 78 107 95 96

Bg - 6 55 87 49 113 114 139 104 1 0 2 90

Bg - 7 1 0 0 87 81 98 83 73 87 1 0 1 94

Bg - 8 98 8 6 81 95 116 104 108 96 106

Bg . 9 81 97 1 2 1 1 0 1 1 0 1 107 79 93 76 75

TABLE 14

SKILL TEST SCOPES

ADVANCED CROUP Rackets * Players: AL /LM AHBL tiW tin CL CM CH

Ad - 1 246 271 251 268 260 272 257 259 246

Ad - 2 265 277 279 264 266 272 278 274 2 8 0

Ad - 3 307 283 303 273 270 296 270 292 280

Ad - 4 314 298 294 293 303 297 310 300 311

Ad - 5 252 236 250 249 243 242 262 243 259

Ad m 6 231 234 249 241 245 229 242 242 231

Ad - 7 257 255 249 257 244 250 261 245 247

Ad mm 8 236 213 248 227 219 195 208 192 217

Ad - 0 315 307 298 302 293 289 300 299 260

BEGINNING GROUP Raoketss Players* AL AM AH BL BM BH CL CM CH

Bg - 1 295 313 283 308 327 293 298 311 291

Bg - 2 352 346 323 336 348 377 382 394 395

Bg m 3 366 348 343 352 344 343 363 347 360

Bg - 4 310 321 324 331 364 322 317 328 306

Bg - 6 330 321 324 315 322 314 360 341 303

Bg - 6 297 299 308 303 290 304 254 265 280

Bg - 7 309 316 307 320 322 319 330 332 303

Bg - 8 361 341 319 368 365 359 343 347 333

Bg • 9 294 295 326 318 271 281 278 281 290 76

TABLE 15

VELOCITY TEST SCORES

ADVANCED CROUP Rackets: Players: AL AM AH BL fiM b h CL CV CH

Ad - 1 245 271 251 268 260 272 257 259 246

Ad - 2 265 277 279 264 265 272 278 274 280

Ad - 3 307 283 303 273 270 296 270 292 280

Ad - 4 314 298 294 293 303 297 310 300 311

Ad - 5 252 236 250 249 243 242 262 243 259

Ad - 6 231 234 249 241 245 229 242 242 231

Ad - 7 257 255 249 257 244 250 261 245 247

Ad - 8 236 213 248 227 219 195 208 192 217

Ad - 9 315 307 298 302 293 289 300 299 280

BEGINNING GROTJP Racketss Playerst AL AM AH BL BM &H CL CM CH

Bg - 1 295 313 283 308 327 293 298 311 291

Bg - 2 352 346 323 336 348 377 382 394 395

Bg - 3 366 348 343 352 344 343 363 347 360 Bg - 4 310 321 324 331 364 322 317 328 306

Bg - 5 330 321 324 315 322 314 360 341 303

Bg - 6 297 299 308 303 290 304 254 265 280

Bg - 7 309 316 307 320 322 319 330 332 303

Bg - e 361 341 319 368 366 359 343 347 333

Bg - 9 294 295 326 318 271 281 278 281 290 77

TABLE 16

TEST SCOPES VTTH STRINGING MATERIAL

AND STRINGING TENSION VARIED

Accuraey Scores

Players * N4 04 N8 08 R 2 0 2

Ad - 4 146 169 150 162 162 161 1 Q- Oi 160 141 119 158 137 127

Ad - 6 136 146 139 160 147 165

Velocity Scores

Players t N4 04 N8 08 N 2 0 2

Ad - 4 282 278 280 311 271 262

Ad - 5 271 264 265 250 261 240

Ad - 6 263 237 262 241 2 2 1 231

Skill Test Scores

Players t N4 04 N8 08 N2 0 2

Ad - 4 80 82 81 85 82 8 6

Ad - 5 69 74 71 75 71 73

Ad - 6 73 71 6 8 79 70 71

KeTi N4 -- Nylon at 64 lbs* tension 04 -- Out at 64 lbs* tension N8 — Nylon at 6 8 lbs* tension 08 — Out at 58 lbs* tension N2 -- Nylon at 62 lbs* tension 02 — Out at 62 lbs* tension APPENDIX B

PERSONAL DATA

78 79

TABLE 17

PERSONAL DATA

Hand Arm Forehand Player Height Weight Si*# Length Strength

Ad - 1 72 " 167 9.63" 31.13" 9.75

Ad - 2 69 " 160 8.94" 27.75" 9.25

Ad - 3 71*" 186 8.81" 30.50" 25.00

Ad - 4 70 n 145 10.06" 28.63" 6.75

Ad - 5 71 " 135 8.63" 30.50" 1 0 . 0 0

Ad - 6 73 " 165 8 .8 8 " 31.50" 8.50

Ad - 7 72 " 155 9.13" 32.00" 15.25

Ad - 8 67*" 145 7.81" 29.50" 10.50

Ad - 9 73 " 2 0 0 9.31" 31.50" 18.25

Bg - 1 72*" 178 9.44" 31.63" 1 2 . 0 0

Bg - 2 67 " 150 7.81" 28.25" 6.25

Bg - 3 6 6 " 140 8.31" 28.13" 8.50

Bg - 4 65 " 800 10.69" 34.00" 18.00

Bg - 5 72 " 178 9.19" 31.00" 15.00

Bg - 6 74 " 195 9.44" 31.50" 17.50

Bg - 7 74 " 174 9.63" 31.63" 20.50 CD CQ W 1 72 " 190 9.88" 31.00" 24*25

Bg - 9 71*" 166 8.94" 30.38" 16.50 BIBLIOGRAPHY

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. The Valor1 s Came of L a m Tennis. London : Karrlson and Sons,’”15757 AUTOBIOGRAPHY

I, Howard O, Knuttgen, was bora in Yonkers, New

York, on Way 5, 1931* My family moved shortly there­

after to Livingston, New Jersey, and it was In Living­

ston that I grew up* I attended the elementary and

junior high schools of the public school system of

Livingston and* In 1948, graduated from Caldwell, New

Jersey, High School*

I attended Springfield College where I received

the degree Bachelor of Science In June, 1952* I re­

ceived the degree Master of Science in June, 1953, from

the Pennsylvania State University. While there I held

a graduate asslstantshir in the School of T'hysical Ed­

ucation and Athletics*

I held the position of Assistant Director of Ath­

letics and Instructor of American History at Shady Side

Academy In Pittsburgh, Pennsylvania, during the aca­

demic year 1953-54* While in Pittsburgh I attended the

University of Pittsburgh In a part-time capacity study­

ing physical education and guidance*

In the autumn of 19 5 4 I came to the Ohio State

University as Instructor of Physical Education and

85 Coach of Intercollegiate Soccer and Lacrosse* I began rork on the degree Doctor of Philoaorhy in the Summer

Quarter of 1955 rdth physical education as my major field and guidance as my minor field*