THE EFFECTS OF VARIOUS POLE LENGTHS ON CROSS-COUNTRY SKIING POLING MECHANICS

David L. Borgemoen Abstract BORGEMOEN, David L. The effects of various pole lengths on cross-country skiing poling mechanics. M.S. in Physical Education-Human Performance., 1988.- 112 D. (Dr. William Floyd, PhD)

This study observed the diagonal stride of cross-country skiing cinematogrephically, to compare the effects of five different pole lengths on the mechanics of the kick, glide and pole implantation phases, The "preferred" pole length was 35 cm. less than subjects (g)body height; the other four pole lengths were 10 cm. longer, five cm. longer, five cm. shorter and 10 cm. shorter than the "preferred" pole length. A11 Ss used the same brand of ski equipment. Thirteen male and female ranged in age from 20-36 yrs., and skied each of the five trials with a different pole length. All trials were filmed at 150 frames per second and analyzed against nine variables. A Single Factor Analysis of Variance (ANOVA) with Repeated Measures followed by a Bonferroni T test was used to analyze the following variables: velocity, stride length, stride rate, trunk flexion, trunk extension, angular displacement from trunk flexion to trunk extension, lower leg angle at legs' parallel position, pole plant displacement, and pole angle at implantation. Significant differences (P<.05) created by the various pole lengths were found in the absolute angle of trunk flexion, the absolute trunk angle at trunk extension, the horizontal displacement of the pole plant in relation to the support foot, and the absolute pole angle at pole implantation. No significant differences (P>.05) were found in velocity, stride length, stride rate, angular displacement from trunk flexion to trunk extension, or the lower leg angle at legs parallel position. It was concluded that specific pole lengths do have an effect on various poling mechanics of the diagonal stride of cross-country skiing. THE EFFECTS OF VARIOUS POLE LENGTHS ON CROSS-COUNTRY SKIING POLING MECHANICS

A Thesis Presented to The Graduate Faculty University of Wisconin-La Crosse

In Partial Fulfillment of the Requirements for the Master of Science Degree

by David L. Borgernoen May, 1988 UNIVERSITY OF WISCONSIN-LA CROSSE School of Health, Physical Education, Recreation and Dance La Crosse, Wisconsin 54601

Candidate: David L. Borgemoen We recommend acceptance of this thesis in partial. fulfillment of this candidate's requirements for the degree: Master of Science - Physical Education-Human Performance. The candidate has completed his oral report.

Thesis Committee Chairpers6nb .da t e

L7 )jqLLLl lC/z8 Thesis Committee Member ;[?A te

This thesis is approved for the College of Health, Physical Education, Recreation and Dance.

ca C.&&.A~ %dt3: /9"/ ~dnlofGraduate Studies Date ACKNOWLEDGEMENTS This writer would like to extend thanks to his thesis cheirperson, Dr. William Floyd, for providing his anatomical exL2rtise and encouragement to push forward to complete this stt.3~;to committee member Dr. Dennis O'Brien, for his st tistical knowledge and help; and a special thanks to cornrnittee member Dr. Keith French for his biomechanical expertise, multiple readings, an open door whenever help was needed, his time, guidance, and support. Thanks to Mr. Marty Hall, Canadian Olympic Cross- Country Ski Coach, for his suggestion on "never going anywhere without the proper poles"; it made this writer think about what the "proper" poles were; to Dr. Charles J. Dillman, PhD. Director of Sports Sciences at the United States Olympic Training Center in Colorado Springs, Colorado, for the invitation, and making his library of cross-country skiing literature available for this study; to Dr. Dale Kendrick, of the University of Wisconsin-La Crasse Art Department, for his artistic and literary advice;

to Mr. Joel Worra, of the University of Wisconsin-La Crosse Computer Center, for his help with the computers used in this study; to Mike, Kim, and Tom, for helping with the filming of this project; to Gary for taking the still shots;

to Kathi and Deb for typing; and to Darrell for proof iii reading this project. Finally, to my wife, Susan, a very special thanks for providing me the opportunity to pursue this goal with her support, understanding, and encouragement throughout this entire project. TABLE OF CONTENTS

CHAPTER Page

I . INTRODUCTION ...... 1 Staternent of the Problem ...... 3 Purpose of the Study ...... 3 Need for the Study ...... 4 Null Hypothesis ...... 5 Assumptions ...... 5 Delimitations ...... 5 Limitations ...... 6 Definitions of Terms ...... 6 REVIEW OF RELATED LITERATURE

Diagonal Stride .Biomechanical Comparison of Techniques Used By Elite and Average Skiers .... 11 Kick Phase ...... 13 Glide Phase ...... 15 Pole Implantation Phase ...... 16 Arm Joint Angles During Poling Phase ...... 17

Problems.. Associated With Incorrect Pole Lengths ...... 18 General Rules and Methods for Determining Pole Lengths ...... 19 Related Biomechanical Studies of the Diagonal Stride ...... 20 I11 . METHODS ...... 22 Survey ...... 22 Pilot Study ...... 28 Preliminary Procedures ...... 32 Solection of Subjects ...... 32 Ski Equipment ...... 33 Instrumentation ...... 34 Height and Weight Measurements ...... 34 Equipment Calculation for Subjects ...... 35 Pole Assignment ...... 35 Criterion for Filming Subjects ...... 36 Model ...... 37 Cinematography ...... 40 CIIAPTER Subject Participation ...... 42 Warm-up Procedures ...... 42 Filming Procedures ...... 43 Kinematic Film Analysis ...... 44 Data Analysis Equipment ...... 44 Temporal Analysis of Films ...... 44 Frame Selection ...... 45 Digitizing Procedures ...... 45 Kinematic Analysis ...... 46 Statistical Analysis of Data ...... 48 IV. RESULTS AND DISCUSSION ...... 50 Subjects ...... 51 Velocity ...... 51 Stride Length ...... 53 Stride Rate ...... 55 Trunk Flexion ...... 56 Trunk Extension ...... 59 Angular Displacement from Trunk Flexion to Trunk Extension ...... 61 Lower Leg Angle at the Legs Parall.el. Position 64 Pole Angle At Implantation ...... 66 Pole Plant Displacement ...... 69 V . CONCLUSIONS ...... 72. Summary ...... 72 Findings ...... 73 Conclusions ...... 75 Recommendations ...... 75 REFERENCES ...... 77 APPENDIX A . Ski Pole Questionnaire For Cross Country Skiing 81 B. Survey Results ...... 84 C . Descriptive Characteristics of Skiers and Their Equipment ...... 86 D . Randomly Assigned Pole Lengths for Subjects .... 88 E . Model of Mechanics and Movement Patterns of the "Glide Phase" ...... 90 F . Model of Mec'snics and Movement Patterns of the "Kick Phase" ...... 92 APPENDIX PAGE

Model of Mechanics and Movement Patterns of the "Pole Implantation Phase" ...... 94 Analysis of Variance: Velocity ...... 96 Analysis of Variance: Stride Length ...... 98 Analysis of Variance: Stride Rate ...... 100 Analysis of Variance: Trunk Flexion ...... 102 Analysis of Variance: Trunk Extension ...... 104 Analysis of Variance: Angular Displacement From Trunk Flexion To Trunk Extension ...... 106 Analysis of Variance: Lower Leg Angle At Legs Parallel Position ...... 108 Analysis of Variance: Pole Plant Displacement . 110 Analysis of Variance: Pole Angle At Implantation ...... 112 LIST OF FIGURES r'g'1 ure Page

1 . Ski pole survey results ...... 24 2 . Deterministic model for the diagonal stride of cross-country skiing ...... 38 3 . The three phases of the diagonal stride ...... 39 4 . Photographic and timing equipment ...... 40 5 . Filming set-up ...... 41 6 . Testing site ...... 42 7 . Slcier assuming the body position at the beginning of the kick phase ...... 57 8. Skier assuming the body position at the termination of the kick phase ...... 60 9 . Slcier assuming the body position at the initation of the pole implantation phase ...... 66 10. Model of mechanics and movement patterns of the "Glide Phase" ...... 90 11 . Model of mechanics and movement patterns of the "Kick Phase" ...... 92 12. Model of mechanics and movement patterns of the "Pole Implantation Phase" ...... 94

viii LIST OF TABLES

Table Page 1. Descriptive Characteristics of the Skiers Presented in Mean and Standard Deviation Values .. 51 2. Mean Velocities of the Skiers for Each Pole Length ...... 52 3. Mean Stride Length of the Skiers for Each Pole Length ...... 54 4. Mean Stide Rate of the Skiers for Each Pole Length ...... 56 5. Mean Absolute Angle at Trunk Flexion (Degrees) and F Values for Skiers at Each Pole Length ...... 58 6. Mean Absolute Angle at Trunk Extension (Degrees) and F Values for Skiers at Each Pole Length ...... 61 7. Mean Absolute Angular Displacement from Trunk Flexion to Trunk Extension ...... 63 8. Mean Absolute Lower Leg Angle At the Legs Together Position of the Kick Phase ...... 64 9. Mean Absolute Angle of the Ski ~olkat Implantation and F Values for Each Pole Length ...... 67 10. Mean Horizontal Displacement of the Ski Pole in Reiation to the Support Foot at Pole Implantation 70 11. Survey Results ...... 84 12. Descriptive Characteristics of the Skiers and Their Equipment ...... 86 13. Randomly Assigned Pole Lengths for Subjects ...... 88 CHAPTER I INTRODUCTION

\!ithin the past five to ten years, a physical fitness awareness boom has developed in the United States. People from all walks of life have become more involved in a variety of fitness-related activities. The reasons for getting involved in physical activities vary from person to person. Many activities have expanded from the "ideal" weather conditions of spring, summer and fall to include fitness activities that are found in the inclement weather of the winter season. In the past few years physical activities such as ice skating, ice hockey, downhill skiing and cross-country skiing have aided the popularity boom of winter sports for individuals. Cross-country skiing is gaining in acceptance as a viable winter sport. Cross-country skiing has grown in popularity because of an increased public interest in the sport, the innovation and advancement of equipment, and the development of accessible, well-groomed trail systems, both public and private. Cross-country skiing is an individual physical activity that allows one to participate by moving across the snow either at his leisure or as rapidly as possible (Brady, 1979). The basic kinematic movements of cross-country skiing are similar to the mechanics used in walking and running. The basic maneuver to move across the snow while skiing is called the diagonal stride. The diagonal ~Lrlde is the simplest way of natural and effortless skiing (Arady, 1979). Skiing effortlessly requires that all body motions be applied at the proFer time, in correct sequence and merged into the individual's skiing form. The diagonal stride has been identified as having three phases: "(1) the kick, (2) the glide, and (3) ihe pole implantation" (Dillmari, India, & Martin, 1979, p. 40). Being able to physically perform each of the three phases in one fluid motion and getting the best performance out of the equipment car\ be a major problem. If a skier can physically perform the diagonal skride but has equipment unsuited for his ability, attempts to develop an effortless skiing form can be frustrating. Therefore, effortless skiing can hopefully be achieved if the skier starts with skiing equipment that will encourage the best performance possible, and if the equipment matches ones skiing ability. As the ability Level of the skier increases, so should his awareness of the importance of proper ski equipment, The intent of this study was to investigate possible significant effects and changes of selected kinematic parameters of the skier's body while performing the diagonal stride using ski poles of different lengths. Statement of the Problem The problem involved in this study was to examine the effects of varying lengths of ski poles on the poling technique u2ed in the diagonal stride while skiing.

Purpose of the Study Currently, there are many different methods for obtaining the proper pole length for a skier. (One method is a random choice of poles according to anatomical reference points; and another involves body height, and a third merely seeks a comfortable "fit" for an individual.) Another method is to hold the pole in an upright position and place it under the axilla, while another method suggests to invert the pole so that the handle touches the floor and the bottom of the pole's basket nearest the tip of the pole touches the axilla. Yet another method for obtaining an individual's "preferred" pole length recommends that thirty- five inches be subtracted from the skier's body height with the remainder being equivalent to a skier's "preferred" pole length. None of the methods listed above appears to be backed by research. The purposed study was to look at the significant effects and changes of selected kinematic parameters of the skier's body while performing the diagonal stride using ski poles of different lengths. Need for the Study At the time of this study, published literature concerning the "preferred" length of ski poles that were best suited for an individual skier was limited. There apparently were no standardizations or recommendations for determining the proper pole length for a skier. Much of the literature was in a popular layman's form and lacked statistical analysis. There was, however, a limited amount of biomechanical research available that had possible implications pertaining to ski pole length and had been identified by a limited number of individuals. Some of the findings of these studies have been published, and these researchers: Dillman et al. (1979), Ekstrom (1981), Martin (1979), Soliman (1977), and Waser (1976) have made their findings available. These particular studies were pioneering efforts that encompassed the techniques and importance of the poling kinematics of the diagonal stride used in cross-country skiing. A study by Haberli (1977) on the diagonal stride performed on an incline plane makes reference to the possible importance of the pole length. Kolhonen (1980) studied arm motions of cross-country skiers with mechanical devices but did not deal with the length of the pole. There appeared to this researcher a need for more biomechanical research related to cross-country skiing in terms of pole length. Such research could provide skiers with information that would be supported by significant scientific data. The main thrust of the research could possibly identify from statistical data a standardized method for determining the "preferred" pole length for optimum performance by cross-country skiers.

Null Hypothesis Pole length has no effect on selected kinematic parameters of the skier's body during the diagonal stride of "non-elite" cross-country skiers.

Assumptions The following assuptions were recognized for this study: 1. It was assumed that all subjects skied to the best of their abilities during the filming of this study. 2. It was assumed that all mechanical equipment used in this study could be calibrated correctly for each test.

Delimitations The fcllowing delimitations were recognized for this study : 1. The subjects used in this study were male and female volunteers from the University of Wisconsin-La Crosse who were pretested to determin if they could do the diagonal stride. Any individual not able to do the diagonal stride was not selected for this study. 2. The testing was performed on level ground. 3. A11 subjects used the same brand and model. of equipment which included poles, bindings, and skis. 4. All testing was performed on the same track. 5, All testing was performed on the same day.

Limitations The following limitations were recognized for this study: 1. Data obtained from the cinematographical film was a two-dimensional filmi.ng from a lateral view. 2. The subjects in this study were a non-random sample who had different ability levels of skiing. 3. The snow conditions changed from the beginning to the end of the testing session which had an effce:t on the subject's performance.

Definition of Terms The following terms were used in this study and are defined as follows: Angular Displacement - The angular distance through which a body moves in one direction from a beginning position to a final position (Hay, 1978). Angular Velocity - The total angular distance a body moves in a specific time (Hay, 1978). Biomechanics - "Biomechanics is the science that examins the internal and external forces acting on a human body and the effects produced by these forces" (Hay, 1978, p* 3). Cinematography - The investigation of athletic related activity which analyzes the activity through the use of high speed motion-picture films (Northrip, Logan and McKinney,

1983). Diagonal Stride - A basic form of locomotion when skiing on snow which is comprised of three phases: "(1) the kick, (2) the glide, and (3) the pole implantation phase"

(Dillman et al. 1979, p. 40). Free Glide Phase - The phase of the diagonal stride when the ski is moving down the track with the least amount of friction on the ski and the skier gets a rest (Hall,

1981). Kick Phase - The phase of the diagonal stride where the skier gaines the greatest amount of his forward momentum by forcibly extending the support leg downward and backward. Legs Together - A mechanical criterion used in the kinematic atlalysis of the skiers in this study. This position was achieved when both legs of the skier were parallel to each other when viewing the body from a lateral aspect. Non-Elite Skiers - Any skier who is not a member of a national ski team. Pole Implantation Phase - The phase of the diagonal stride occurring the moment that pole enters the snow and continues until the pole is removed from the snow. "Pole In to Pole In" - A method of quantifying a skier's stride length (Dillman et al. 1979). Pole Plant - A mechanical criterion used in tlie kinematic analysis of the skiers in this study. This action occurs the moment the tip of the pole makes contact with the surface of the snow. Preferred Pole Length - That pole length that best matches the skier's ability level and anatomical structure. Shoulder Flexion - A mechanical criterion used in the kinematic analysis of the skiers in this study. The position is achieved when the highest point at which the distal end of the hand has been obtained prior to the decreasing of the hand's height. Stride Length - The total distance a skier moves along a track using all three phases of the diagonal stride from "pole in to pole in" illma man et al. 1979). Stride Rate - The time it takes to complete one stride length (Dillman et al. 1979). Toe Off - A mechanical criterion used in the kinematic analysis of the skiers in this study. The position is obtained when the top of the non-support foot breaks contact with the ground. Trunk Extension - A mechanical criterion used in the kinematic analysis of the skiers in this study. Trunk extension is the angular position of the skier's trunk at "Toe Off" which terminates the kick phase. Trunk Flexion - A mechanical criterion used in the kinematic analysis of the skiers in this study. Trunk flexion is the angular position of the skier's trunk at "Legs Together" which is the initiation of the kick phase. Velocity - The stride length multiplied by the stride rate. The longer the stride and/or the faster the stride, the farther a skier will move in a shorter period of time (Dillman et al. 1979). CHAPTER I1 REVIEW OF RELATED LITERATURE

The primary method used by cross-country skiers to move across a level snow-covered surface efficiently is the diagonal stride as reported by Brady, (1979); Caldwell,

(1977) ; Caldwell & Brady, (1982) ; Crawford-Currie, (1982) ; Ekstrom, (1981); Gillette, (1979); Mendez, (1979); Sheahan,

(1984); Tokle & Luray, (1977) and Woodard, (1983). In order to achieve the desired outcome of the diagonal stride, all three phases must be performed as one fluid movement (Hall, 1981). If even one of these phases was omitted, the skill could not be performed properly. A comparison of each phase of the diagonal stride will be reviewed. If an individual's optimum pole length could be established by some method previously described, (Bauer,

1977; Brady, 1979; Caldwell, 1977; Crawford-Currie, 1982;

Gillette, 1979; Hall, 1981; Sheahan, 1984; Tokle & Luray, 1977; Woodard, 1983) it would insure that the optimum kinematics could be achieved by skiers, The more favorable anatomical positions would help increase the performance level of skiers. Presently, there is a paucity of research-related literature about the kinematics of the arm, hip and leg actions used in the diagonal stride of cross-country skiing. The first issue to be discussed will be a comparison of the biomechanical techniques of the diagonal stride that separate the elite skiers from the average skiers. All three phases of the diagonal stride will be reviewed: the kick phase, the glide phase and the pole implantation phase, which will receive the main emphasis.

Diagonal Stride - Biomechanical Comparison of Techniques Used By Elite and Average Skiers In terms of a skier's performance objective, the velocity that a skier can maintain from one stride to the next is the key element for successful locomotion on snow (Dillman et al. 1979). Work by Dillman et al. (1979), and Hall (1981) have defined velocity as the skier's stride length multiplied by the skier's stride rate. One study has clarified stride length as the measured distance from "pole in to pole in" illma man et al. 1979, p. 39). The diagonal stride is a cyclic form of locomotion on snow (Dillman et al. 1979). In order for a skier to increase velocity, the stride length and/or stride rate must be increased. The striae length and/or stride rate can be changed by the amount of force that is transferred from the skier to the ski to the snow (Dillman et al. 1979; Hall, 1981). The diagonal stride, "sometimes referred to as the 'single stride' "(Caldwell, 1979, p. 65), starts with the pole implantation slightly ahead of the opposite foot, at a pole angle almost vertical to the ground. One diagonal stride ends when the opposite pole is implanted into the snow (Dillman et al. 1979; Hall, 1981). The efficiency of the diagonal stride can only be accomplished if the skier is able to properly transfer the force from the arms and legs to the ground (Ekstrom, 1981; Hall, 1981). The length of the stride as reported by Dillman et al. (1979) is the horizontal distance traveled by the skier from one pole plant to the beginning of the next pole plant. For an elite skier, this distance was 2.88 meters and was traveled in .620 seconds. Dillman et al. (1979) stated: Thus, in one second, this skier would complete 1.G1 strides. This latter figure can be considered the stride rate - 1.61 strides/second or 97 strides per minute. The velocity of the skier (...) can now be caluculated by the following V = S.L. x S.R. V = 2.88m gr 1.61 stridesls V = 4.64mIs or 10.4 mileslhour The average stride velocity for this skier is 4.64 m/s or 10.4 miles/hour which is a typical speed in the diagonal stride for a skilled skier. This indicates that if this skier would continue at this pace, he would cover 4.64 m or 15.3 ft. of ground for every second of skiing (p. 39). Dillman et al. (1979) indicate the distance covered by the length of the stride is the main factor behind the elite skier being the faster skier, In other words, both skiers perform the same skill, but the elite skier goes farther each time the cycle is performed. The stride rate for the elite and average skier is very similar, as noted by Dillman et al. (1979).

Kick Phase The "kick" portion of the diagonal stride generates most of the force that propels a skier down the track (Caldwell, 1979). Generally speaking, the elite skier's trunk has more forward lean. The position of the trunk should be at an angle of about 45 degrees to the skiing surface (Dillman et al. 1979). Dillman et al. (1979) suggest that the elite skier's lower leg forms a 60 degree angle to the ski at the beginning of the kick phase when both thighs are together. According to Soliman (19771, the best angle for the lower leg is an angle approaching 70 degrees with a range of 58 to 80 degrees. According to Dillman et al. (1979), a 90 degree angle is generally found in a skiec of lesser ability. Both of the above studies indicated that the objective of the forward position is to get the center of gravity over the lead foot to facilitate an efficient transfer of weight from one ski to the other, which results in a quicker kick (Dillman et al. 1979; Hanson, 1983). The better the skier, the greater the force that is exerted downward (Dillman et al. 1979). Ekstrom (1981) credits a small amount of the skier's body weight and the power of the muscles as factors in the creation of friction between the snow surface and the ski. Greater friction allows for better ground reaction, which results in a more efficient Iciclc. Brady (1982), Caldwell (1979), and Hanson (1983) are in agreement with the

preceding statement. The amount of time that a skier has to perform the kick is extremely short, Dillman et al. (1979) state:

The objective of the kick is 7 create a relatively small horizontal force (parallel to the track) to maintain and slightly increase the velocity of the body as it rotates over the stationary supporting ski. However, to create this effect, the ski must be p:essed into the snow. It is this latter action which requires a larger amount of force. (p. 41). The vertical downward force that the elite skier exerts in the kick is approximately two to three times the skier's weight, whereas the average skier exerts 1.2 to 1.8 times his body weight (Ekstrom, 1981). The vertical force will be somewhat greater for the better skier and less for the less experienced skier, "depending on the hardness of the

track" (Ekstrom, 1981, p. 73). The greater force created by the better skier "is produced by the vigorous upward acceleration of all body segments involved in the kick motion" (Dillman et al. 1979, p. 41). When all body segments work together, the kick is more effective (Brady, 1983; Caldwell, 1977; Dillman et al. 1579; Ekstrom, 1981; Hall, 1981). When a skier's trunk is extended from a 45 to 55 degree angle, the skier's arms move upward (one in front and the other in back of the skier), and the kick leg forces the ski downward. The downward vertical force on the ski increases, which, in turn increases the ground reaction between the snow and the ski and creates a more efficient kick (Dillman et al. 1979).

Glide Phase As soon as the kick has been completed, the skier glides on the foot opposi.te of the kicking foot (Dillman et al. 1979; Hall, 1981). In the free glide, the arms prepare to initiate the next pole plant. This occurs while the center of gravity rises to reduce friction on the ski in contact with the snow and allows for a better glide (Hall, 1981). The better the kick, the farther the glide. The glide phase is the rest period for the skier; therefore, it is the objective of a skier to kick forcefully in order to glide as far as possible (Dillman et al. 1979). There appears to be disagreement in the percentage of distance that can be obtained from the glide phase. Soliman (1977) reports that the glide comprises 60 percent or more of the entire phase. Dillman et al. (1979) state: "For a good skier, this phase can account for 25 percent and more of the total stride distance" (p. 41). Dillman et al. (1979) stress the irnporcance of good balance to eliminate unnecessary upper body movement. The non-support ski of the more highly skilled skier is back farther than it is for a skier of lesser talent which helps shift the body weight back toward the heel, allowing the skier a better gliding potential. The greater the forces that are produced in the kick and poling motions, the more efficcnt the skier's stride will be (Hall, 1981).

Pole Implantation Phase The glide phase ends when the ski pole is planted to the basket (Brady, 1983). The arms and shoulders produce the force that projects the slcier down the track. As soon as the skier's support ski becomes stationary, and the skier gsts ready to initiate th2 kick, the implantation phase of the pole ends (Dillman et al. 1979). The pole implantation phase is a major contributing factor to the overall success of the diagonal stride. With an efficient poling phase the elite skier can increase the total distance traveled in one diagonal stride by as much as 60 percent over the average skier. This distance can account for approximately 40 centimeters, or about 16 inches every 1.6 seconds (Dillman et a1 1979). Brady (1982) suggested that the slcier insert the pole about even with the lead foot, while Dillman et al. (1979), Hall (1981), and Haberli (1977) propose that the elite skiers piznt their poles 15 to 25 centimeters, or five to 10 inches ahead of the lead foot, with the angle of insertion approaching 90 degrees. Suggestions by Brady (1982), Dillman et al. (1979), and Hall (1982) also proposed the reason this is possible is because the trunk angle is at a 45 degree angle to the snow, and the elbow is flexed, Soliman (1977) found a smaller elbow angle at the moment of pole implantation as being indicative of a better skier. A skier of lesser skill had a tendancy to pole with straight arms (Brady, 1982; Gillette, 1979). The elite skier has more fluid upper body and arm actions than the non-elite skier. It should be mentioned that the legs are a part of the fluid motion (Brady, 1979; Ekstrom, 1981; Hall, 1981). Once the pole is planted into the snow, the slightly bent arm should pull on the pole in a pendulum fashion, which causes the arm to pass close to the body (Brady, 1982). Information from Brady

(1979), Caldwell & Brady (1982), and Sheahan (1984) state that 10 to 25 percent of the skier's forward momentum comes from this phase.

Arm Joint Angles During the Poling Phase An analysis by Kolhonen (1980) revealed some angular displacements and angular velocities of the elbow and shoulder joints for the six skiers in her study. She reported findings of 147.6 degrees for the mean angular displacements and 246.3 degrees per second for the mean angular velocity of the shoulder. Her findings for the mean angular displacement of the elbow were 33.7 degrees with a mean angular velocity of 121.7 degrees per second. Supposedly, Kolhonen's (1980) study was dealing with skilled skiers. The skiing in Kolhonents (1980) study was performed under laboratory conditions. Due to the lack of significant research-related material, it is difficult to determine what the angular displacements and velocities of the shoulder and elbow joints should approximate for non-elite and elite skier s.

Problems Associated With Incorrect Pole Lengths Biomechanical work conducted by Dr. Charles J. Dillman at Lake Placid, New Yorlc, suggest that poles that are too long cause exaggerated up and down movements. A top American skier had this particular problem and shortened his poles to reduce vertical movement. If the pole plant is out in front of the skier too far and the handle of the pole is forced upward as the body moves toward the pole, a braking effect is created which decreases momentum. Brady (1983) recommends trying poles one or two inches shorter than the individuals preferred pole length. In addition, if a skier leaves the pole planted too long trying to receive the most momentum out of each push, or the hands do not come up in front of the skiers body quickly enough, the poles may be too short. Hall (1981) wrote: When selecting poles, length must be a prime consideration. The latest trend has been to go to long poles, but I think many racers have gone too far and created a major barrier in accomplishing good technique. A longer pole will give you a stronger push, but too long a pole will keep you upright, which means your poling action is less efficient because you end up pushing less off the pole and having an improper swing trajectory (p. 125). Hall (1981) indicates that the elite skiers have a variety of different length poles. Shorter poles are used for courses that are hilly, and poles that are longer are used for courses that are flatter in nature. For summer training, Hall (1982) recommends the use of poles five to seven centimeters shorter than the poles a skier uses in the winter.

General Rules and Methods for Determining Pole Length Numerous ways are suggested for determining the proper length of ski poles. Bauer (1977) states, "Select poles of the proper length by standing erect, feet together, and with one arm stretched straight out from the body. The pole should measure as far as the distance from the ground to a point between your elbow and armpit (p. 12)." The method recommended by Bauer (1977) would indicate that the lengths be between 13 and 15 inches or 33 to 39 centimeters shorter than the skier's height. Tokle and Luray (1977) suggest two methods for poie selection: (1) determine ones body height and subtract 13 inches which equals about 33 centimeters, or (2) turn the pole upside down, put it on the floor, and the basket should touch the axilla. The pole should reach from the ground to the axilla (Caldwell, 1979; Gillette, 1979; and Sheahan, 1984). Lind (cited in Ekstrom, 1981) recognizes the entire body as being important in making a pole selection. Factors that are relevant when attempting to determine the "preferred" pole length for a skier are the skier's height, his ability and his arm strength. Lind concludes that the length should be 35 centimeters less than the body height of the individual. Brady (1979) also recoaln~ertds the 35 centimeters less than the skier's body height, or to abduct the arm to the horizontal and place the pole vertical to the ground so it extends from the ground to the palm of the hand. Brady (1979) is in agreement with Lind (cited in Ekstrom, 1981) and adds that two skiers may be of the same height, but one skier with shorter arms than the other may use a longer pole than the skier with longer arms. Racing poles differ in structure and, therefore, the pole manufacturers have differing suggestions for selecting the proper pole length. The pole length of 33 centimeters less than the body height is recommended by a Finnish pole maker; the Norwegian pole makers are recommending the 35 centimeter rule. Hall (1981) is also in agreement with the 35 centimeters less than the body height.

-Related Biomechanical Studies of the Diagonal Stride There is a paucity of literature in this area of biomechanical related material for non-elite skiers that specifically pertains to poling mechanics and how pole lengths can change those mechanics. This study was a pioneering effort that investigated the mechanics of poling and the changes that occurred when poles of different lengths were used. CHAPTER ITS METHODS

The purpose of this study was to examine the effects of varying lengths of slci poles on the poling technique used in the diagonal stride while cross-country skiing. An underlying problem was to identify the various methods used for fitting skiers with poles. A survey was conducted prior to the testing, which attempted to identify factors that could create problems when fitting skiers with poles. A questionnaire (see Appendix A) was created in an attempt to isolate possible problems associated with pole length selection for skiers. This chapter describes the methods used to carry out this study and analyze the data. The chapter will be divided into the following categories: (1) survey; (2) pilot study; (3) preliminary procedures; (4) instrumentation; (5) subject participation; (6) filming procedures; (7) kinematic film analysis; and (8) analysis of data.

Survey A listing of 147 cross-country skiing businesses and their addresses were obtained from the Yellow Pages of all Wisconsin telephone directories located in Murphy Library on 22 the University of Wisconsin-La Crosse campus. The survey was sent to the 147 cross-country ski retailers and rental shops in Wisconsin. The initial mailing did not elicit an acceptable response, and a second mailing was conducted. The survey was remailed to those businesses who had not responded to the initial mailing. The return percentages of the survey can be found in

Appendix B, The results of this survey give some indication as to the complexity of properly fitting a skier with his "preferred" pole length, Figure 1 summarizes the renting and selling tendencies of the survey population, the percentage of businesses that handle multiple brands of ski poles, the percentages of the top four pole brands, the most common pole types and the most common pole increment for each pole type. As ranked by Wisconsin Ski Dealers, the percentages sold or rented to beginner skiers were 26%, intermediate skiers 23%, advanced skiers IS%, citizen racers 12%, and certified racers 6%. Another 18% of the businesses did not attempt to rank the ability level of the skiers. RETAIL MULTIPLE BRANDS & POLE TYPES & MOST TENDANCIES TOP FOUR BRANDS % COMMON INCREMENTS CATEGORIES Figure 1. Ski Pole Survey Results. This survey group was also asked to indicate whether or not they custom fitted their customers with ski poles. A total of 73% reported that they did not custom fit poles to skiers and 27% reported they did. Of those who did not custom fit skiers with poles, 58% of the replies indicated that the dealers used the upright pole position, putting the pole tip on the floor and the handle under the skier's axilla. This method of measurement uses the entire length of the pole in the calculation of the skier's pole length. Another 8% of the businesses used the inverted pole method which places the pole handle on the floor and the pole basket touches the axilla. This method of measurement does not take into account the portion of the pole from the bottom of the basket to the tip of the pole when calculating a skier's pole length. Another 13% of this survey group used ten other methods for fitting skiers with poles: (a) the handle of the pole is placed under the elbow of the arm which is extended horizontally to the ground; (b) some retailers use the chart sent by the pole manufacturer; (c) racers should have poles that touch the top of their shoulders; (d) pole length entirely depends upon the skier's experience and physique; (e) pole length depends upon the type of terrain the slcier will be skiing on; (f) the skier should extend the arm and invert the pole to the hand; (g) the pole length should be whatever is comfortable to the skier; (h) advanced skiers should use long poles; (i) the pole should fit under the skier's axilla when his shoulders are raised; and

(j) the dealer should obtain the skier's height in

inches, multiply that number by 2.03 and that should equal the skier's pole length. Twenty-one percent of the survey group did not respond to this question.

Of the 27% who reported custom fitting skiers with poles, 13 methods were reported being used to obtain the "preferred" pole length. The following is a list of the thirteen different measuring methods used by dealers in this survey to obtain the "preferred" pole length to which the poles will be cut when custom fitting a skier with poles: (a) with the skier in street shoes, the pole handle should extend to mid-shoulder;

(b) the arms should be at a 90 degree angle to the body and the arms should rest on top of the poles;

(c) slightly longer poles should be used by stronger and more experienced skiers; (dl measure the floor to the axilla in centimeters and cut the poles according to the total measurement: obtained; (e) pole length can vary between the axilla and the top of the shoulder, a skier with longer arms should get a longer set of poles; (f) pole length is a matter of personal preference; (g) a racer's pole should measure to the top of his shoulder; (h) the pole length is the distance to the skier's axilla when the shoulders are raised; (i) for track skiing add two inches to the pole length; (j) pole length should be 35 centimeters less than the skier's body height; (k) with the skier in ski boots, measure from the flour to the axilla, if the pole length is between sizes, give the skier the shorter pole; (1) with the skier in ski boots, measure from the floor to the axilla, if the pole length is between sizes, give the skier the longer pole; and (m) pole length can be plus or minus two centimeters of the axilla. When asked to make comments that pertain to factors that might be "significant" in determining a skiers "preferred" pole length, the survey population suggested the following: (a) strap fit; (b) skill level of the skier; (c) type of skiing to be done; (d) sex of skier; (e) snow condition; (f) arm length of the skier; (g) strength of the skier; and (h) the basket design. The information obtained from this survey indicated to this investigator that there are many different ways of measuring skiers for poles. Of the many methods that were reportedly being used by this survey group, few methods accounted for an identical pole length. Because of the survey results of multiple measuring techniques that obtained varying pole lengths, the survey indicated a possible need for additional investigation.

Pilot Study Preliminary studies were conducted one month prior to the filming of the actual project, The studies were used to aid this investigator in the development of procedures essential to the study. The first preliminary investigation involved two males who were cross-country skiers. Prior to going to the filming location, the subjects were weighed and measured for total body height. The body height would be used as the basis for determining ski and pole lengths. Their body weight would be necessary data for analysis of the film by the computer program. At the testing site both subjects were allowed to warm-up and then asked to perform the diagonal stride on a man-made track that was fifty yards long. Each subject skied two sets of five trials. In the first set of trials both subjeces used the same brand of no- wax skis. Both subjects .-!ere assigned poles of different lengths which were not randomly assi~ned. In the second set of trials both subjects used personal skis, boots, bindings, and wax. Both subjects applied wax to their skis to be compatible with the current snow conditions. The pole assignment was identical to the method used in the first set of trials. The investigator of this study observed the subjects to determine if they could perform the three phases of the

diagonal stride as described by Dillman et al. (197'). The proper progression of the three phases of the diagonal stride using different pole lengths is essential to this study. The following suggestions were made as a result of these observations: (a) all subjects must be able to perform the three phases of the diagonal stride in order to be selected for participation in this study; (b) because of the skier's unfamiliarity with the altered pole lengths, caution should be recommended prior to the initiation of the trials;

(c) a distance of thirty feet would be necessary to insure that one stride length is performed in the filming plane; (dl all subjects would have to use the same brand of no-wax skis; and (el the poles must be ramdomly assigned to the subjects without them having knowledge of the length they were using. In the second preliminary investigation, a Cine 8 Super 8 motion picture camera equipped with sn internal light

emitting diode (LED) which was attached to a timing light

generator and an Anginieux F 12-120 millimeter zoom lens was mounted on a tripod. (The tripod was used to immobilize the camera and lens at a specific height and distance Prom the activity to be filmed.) The film speed was set at 100

frames per second for both sets of five trials. Because of the natural outdoor lighting, f-stops varied to meet the changes in intensity of available light. The shutter factor was set at 120 degrees and Kodalc Elctachrome (ASA 160) type G color motion picture film was the selected film for this investigation. A sweep second hand clock and numeric subject and trial indicators were placed in the filming plane for timing and identification purposes. The following suggestions were made as a result of this study: (a) the cinematographic equipment must be positioned ninety feet from and perpendicular to the center of the level filming plane;

(5) the height at the center of the lens would have to be set at three feet to obtain the approximate center of all subjects heights; (c) a light meter reading would have to be taken every five trials to assure sufficient f-stop settings; (d) a distance of sixty feet would be riecessary for the subjects to attempt to obtain their maximum skiing velocity prior to entering the filming plane;

(2) a distance of sixty feet would be a sufficient length for the skiers to safely decelerate after leaving the filming plane; and (f) a camera operator, data recorder and an equipment person would be necessary to administer the tests. In the final preliminary investigation, the processed film was analyzed to make the following suggestions: (a) camera placement was adequate; (b) lens height was adequate;

(c) the film speed should be increased to 150 frames per second;

(d) the shutter factor would have to be changed to 160 degrees to let in more light with the increased film speed; (el film analysis procedures would have to be modified to obtain selected kinematic data; (f) the positive direction in which the skiers moved should remain the same; and (g) there is no need for a sweep second hand clock for the calculation of film speed because of the timing light generator (LED) that places timing marks on the film. Following the suggestions of these preliminary studies, further studies were warranted.

Preliminary Procedures The format followed for the implementation of this study was as follows: (a) selection of subjects; (b) ski equipment,

Selection of Subjects All individuals who volunteered to participate in this study had some type of an affiliation with the University of Wisconsin-La Crosse. The volunteers were members of the University Ski Club, students enrolled in cross-country skiing classes and other individuals who were cross-country skiers at the University. Permission was granted by the cross-country ski instructors at the University and the Ski Club President to inform any class or club members of the need for subjects in this study. All individuals who were aware of this study were asked to inform any other cross-country skiers (who were affiliated with the University) of the need for subjects in this study. Any other individuals who were interested in being a subject were informed to contact this writer by telephone, at which time he would be given the necessary details. Eleven male and seven female cross-country skiers with various levels of skiing ability volunteered to be subjects for this study. Before any evaluation began, all eighteen volunteers met with this investigator and were asked to follow along as the consent form was read aloud to them. They were allowed to ask questions about any of the material that may have been confusing to them, and then asked to sign the consent form if they wished to be subjects in this study. Due to extenuating circumstances, only eight males and five females (n=13) were analyzed as subjects of this study. Data pertaining to the subjects can be seen in Appendix C.

Ski Equipment Because of different types of ski equipment used by the two subjects in the pilot study, and their ability to wax skies so they would produce the same results when skiing, a need for indentical equipment was forseen. The slci equipment used in this study was obtained from the University of Wisconsin-La Crosse Physical. Education and Recreation and Parks Departments, The skis used in this study were the Trak no-wax model. The selection of skis ranged from 195 to 215 centimeters with five centimeter increments, Rottefella 75 millimeter Nordic Norm Bindings were mounted on all of the skis. Exel

E Sport model poles were used for this study. The pole selection ranged from 115 to 160 centimeters with five centimeter increments.

Instrumentation This section explains the instrumentation used for this study. Included in this section are (a) height and weight measurements; (b) equipment calculation for subjects; (c) pole assignment; (dl criterion for filming subjects; (e) model; and (f) cinematography.

Height and Weight Measurements Upon signing a consent form, each subject was weighed on a balance scale to the nearest quarter of a pound. Each subject's height was measured to the nearest one- quarter of an inch and converted to centimeters. The body height was necessary for calculating ski and "preferred" pole lengths for each subject. The information obtained from these two measurements were recorded for each individual along with other data pertinent to this study. A list of all subject heights and weights can be seen in Appendix C.

Equipment Calculation for Subjects

The method suggested by Brady (1979) and Hall (1981) was used for this study. To calculate the ski. 1engt.h to be used by each subject, 35 centimeters were added to the skier's body height. The sum of those two figures was averaged LO the nearest ski length available. When calculating a skier's "preferred" pole length, 35 centimeters were subtracted from the body height, The differences of those two numbers were rounded to the nearest pole length available. The remainder of the pole lengths were calculated by adding five and 10 centimeters to, and subtracting five and 10 centimeters from the "preferred" pole length. The data pertaining to the ski length and "preferred" pole length can also be found in Appendix C.

Pole Assign= Prior to the actual filming, all five pole sizes were calculated for all of the skiers. The five different increments were assigned a number from one to five. Number one indicated the "preferred" pole length. Number two signified a pole that was 10 centimeters longer than the 3 6

"preferred" pole, three signified a pole five centimeters longer than the "preferred" pole, four signified a pole live centimeters shorter than the "preferred" pole, and five signified a pole 10 centimeters shorter than the "preferred" length. All five numbers were randomly selected, and the list of the pole lengths were recorded for each skier (Appendix D). On the day of the filming, skiers received the random selection of poles in the order they appear in Appendix D. The intention was to issue the poles to the subjects without their knowledge of pole length. Without such knowledge, trial performances were hopefully unaffected by the pyschological factors.

Criterion for Filming Subjects On the day of the filming, individuals were allowed to warm up using the pole lengths they normally skied with prior to their filming session. While individuals were warming up, each individual's ability to perform the diagonal stride was assessed. If the individual could perform the three phases of the diagonal stride with sufficient proficiency, he would be filmed as a subject for this study; if not, he would ski the trials without being filmed. Model A mechanical model of the diagonal stride was developed in an attempt to identify the mechanical properties of the skill. The intention of the model development was to help gain a better understanding of the mechanical principles involved in the poling phase of the diagonal stride (see Figure 2). Knowledge of the mechanical principles, along with the ability to perform the three phases of the diagonal stride as described by Dillman et al. (1979), would aid in the selection of acceptable subjects for this study. The mechanics of these models are patterned after "The Development of Deterministic Models for Qualitative Analysis" (Hay, 1984, p. 71). Movement patterns of the "Kick", "Glide", and "Pole Implantation Phases" of the Diagonal Stride were obtained from the study by Dillman et al. (1979, pp. 40-42) and can be seen in Appendices E, F, and G. Figure 3 is an illustration of the three phases of stride length. FREQUENCY

AVERAGE STRIDE TIME

Figure 2. Deterministic model for the diagonal stride of cross-country skiing.

Cinematography

A high speed motion picture camera, the Cine-8 Super-8, with an Angenieux F 12-120 millimeter zoom lens was used to collect data for analysis. The filming equipment set-up was identical to that used in the pilot study. Filming and timing equipment are shown in Figure 4.

Figu1:e 4. Photographic and timing equipment.

The camera equipment was leveled with a bubble level. The manual adjuster used to set the film speed on the camera was set at 150 frames per second. Subject identification and trial identification numbers were placed in view of the filming field for each subject and test. The reference measure was placed on top of the identification numbers for each trial. Figure 5 depicts the placement of the equipment and set-up of the filming site. Figure 6 is a photograph of the testing site. Because of a thaw, the direction that the subjects skied was changed. All of the data was convsrted to read as though the subjects were skiing from left to right. This was done so the figures of this study could be compared to the findings of Dillman et al. (1979). The location of the filming was at Memorial Field softball diamond, adjacent to Mitchell Hall at the University of Wisconsin-La Crosse.

Warm-up Area Reference Measure xx-xx Subject & Trial Markers Finish Film Plane Start X X X X Track x 60 ' x 30' x 60 ' x

9: J: t ft ;: Poles +: A * 9: +: Skis J-,. JI,* II_., &,. .(_.. Shoes

90 '

Timing Light X-X Camera x Electricity Figure 5. Filming set-up. Figure 6. Testing site.

Subject Participation All subjects were allowed to ski as much as they desired on a daily basis, using their own ski equipment. Subjects were asked to refrain from skiing prior to the filming on the testing day. The subjects wore University ski equipment for the study.

Warm-Up Procedures Each subject was encouraged to do static stretching, easy skiing, or both prior to testing. The warm-up area was adjacent to the testing track (see Figure 5). As one subject began the testing protocol, the next subject was allowed to begin warming up. Filming Procedures All of the filming was conducted at Memorial Field on the same day. Upon arriving at the filming location, the subjects were informed what slci lengths they would wear, and given the correct pole lengths for each trial. The pole lengths were randomly selected for each subject. Appendix D is the randomized list of pole lengths used in this study. A horizontal and a vertical reference measure was taken at the beginning of each roll of film. A light meter reading was also taken to identify the proper exposure time of the film. And, for the purpose of identification, subject and trial numbers were used. The subjects received a predetermined, randomly selected pole length (Appendix D), were given ample time to adjust the straps, and began the trial when the photographer gave the indication. Prior to being tested, each subject was given the directions of the procedures of the test, The zones of the testing site were marked with orange pylons, and identifyed for each subject: the starting point; the filming plane; the deceleration zone; and, the return point. Each subject was instructed to ski as fast as possible while performing the diagonal stride for each trial. The camera operator gave a hand signal to begin when the subject had the pole straps adjusted to his liking. Kinematic Film Analysis This section disc~isses the sequential format necessary to conduct a kinematic analysis of film data. Subtopics included in this section are (a) data analysis equipment; (b) temporal analysis of films; (c) frame selection; (d) digitizing procedures; and (e) kinematic analysis.

Data Analysis Equipment The data on the processed rolls of Kodak Super 8 movie film was projected onto a Lafayette Editor-Viewer Counsole (Model 45-016) with a Lafayette Super 8 Motion Analyzer (Model AAP-927). A Numonics Digitizer (Model 1224), which was connected to an IBM Personal Computer was used to obtain the kinematic data of this study. An Epson dot matrix printer was employed to print a permanent or "hard" copy of the data.

-Temporal Analysis of Films Temporal data were calculated for each role of film. By determining the actual speed of each film, the time between frames could be determined. The Timing Pulse Generator (Model 228B) that was attached to the Cine-8 Super-8 camera placed a timing mark on the film. By locating two timing marks on the film, that occupy the same relative position on both frames the frame rate can be determined. The actual number of frames between two timing marks with the same relative position is divided by the number of timing marks between those two frames, and the product equals the actual film speed in frames per second. The reciprical of the film :peed, or the time interval between two frames can be -alculated. By multiplying any predetermined number of frames, the elapsed time for the action taking place can be calculated.

Frame Selection Films were reviewed for the purpose of selecting the desired frames to be analyzed. Upon locating the desired movements, the actual frame numbers were recorded and labled.

Digitizing Procedures After all of the ski phases were located, the digitizing process for each frame was initiated. Twenty segmental endpoints were located for each frame, with nine frames being analyzed for each trial. Single digitizings were performed on all of the frames analyzed in this study. In studies performed by Roberts (1971), Barlow (1973), Ward (1973), Davis (1974), and French

(19811, intraclass correlations of = -91 to r = .99 were reported, which suggests that the locating of data points by an individual is extremely reliable. Therefore, it was assumed that the measurements of all trials in this study were equally consistent. The data obtained from the segmental endpoints were entered into an IBM Personal Computer. The storage system utilized a program that calculates kinematic data.

Kinematic Analysis Kinematic analysis of cross-country skiers is limited at present. To date, the majority of research of this activity has focussed on the elite skier. The poling mechanics of the cross-country skier is one factor that separates the elite skier from the average skier (Dillman et al., 1979). Because poling mechanics can affect a skier's velocity, this study focuses on how different pole lengths affect the skier's stride length, stride rate, pole plant distance in relation to the support foot, the angle of the pole at implant, the angle of the lower leg at legs together of the kick phase, the angle of the trunk flexion at legs together during the kick phase, the angle of trunk extension at toe off, and the initiation of the glide phase, all of which affect velocity. A skier's velocity is calculated by multiplying the stride length by the stride rate. The average velocity of the center of gravity was determined for each trial by multiplying the stride length by the stride frequency. Selected frames were chosen to determine horizontal displacement of each subject. The displacements were read directly from the kinematic data output. Calculation of the horizontal displacement was achieved by subtracting the x coordinate, of frame two (right toe off) from the value of the x coordinate of frame six (left toe off). The remainder equalled the horizontal displacement, which was reported in meters. Calculation of the stride frequency was determined by subtracting the actual frame number of the right toe off from the actual frame number of the left toe off. The remainder equals the actual number of frames from right toe off to left toe off. This remainder is then multiplied by the time per frame which equals the time per stride and is recorded in seconds. By dividing the time per stride, the number of strides per second can be obtained. This figure in turn is multiplied by 60 to compute the number of strides per minute obtained by each skier. Therefore, when the meters per stride are multiplied by the strides per second, the average velocity or meters per second can be determined for each subject. The Point-To-Point Length Measurement mode on the Numonics Digitizer (Model 1224) was used to obtzin the distance that the various pole lengths were planted in relation to the support foot. The prle plant was the initial point located with the pointer and the next point was the skier's support foot. The figure taken directly from the digitizer was converted to centimeters. The angle of the pole at implant was obtained by employing the digitizer's Angle Measurement mode. The angle of the lower leg, when both legs were parallel in the kick phase, was obtained from the absolute angular output. The absolute angle reads the left side from the distal (medial malleolus) to the proximal (center of the knee). The trunk flexion and extension absolute angles read the left side of the body starting from the midpoint of the trochanters to the top of the sternum. As stated earlier, the segments on the left side must be established from the proximal to the distal segment. To determine these two angles, the numbers are read clockwise. The angular displacement from trunk flexion to trunk extension is read directly from the data output, as is the angular velocity.

Statistical Analysis of Data Results of all trials were analyzed to identify significant and non-significant changes in cross-country skiing mechanics which resulted when using different length ski poles. Statistical comparisons were developed using a Single Factor Analysis of Variance (ANOVA) with Repeated Measures (Kirk, 1968; Tuckman, 1978). The .05 confidence level was used to test the hypothesis of this study for significance.

Whenever the F ratio for the ANOVA was significant, the

Bonferroni T statistic (Kirk, 1968) was employed. A family of confidence intervals (Kirk, 1968) were constructed to identify where the difference occurred within the group. Standard descriptive statistics (~itte,1980) were used to compare findings of this study to findings by Dillman et al, (1979). CHAPTER IV RESULTS AND DISCUSSION

The purpose of this chapter was to present the results of the data obtained from the five trials slcied by each subject in this study. The method employed to statistically analyze the nine variables was a Single Factor Analysis of Variance with Repeated Measures (Kirk, 1968; Tuclcman, 1978). A confidence level of .05 was used as the critical statistical value for accepting or rejecting the null hypothesis. A computer program (BMDPBV) performed the initial analysis, and the Bonferroni-T statistic (Kirk, 1968) was employed to isolate where the significance actually occurred. Thirteen cross-country sltiers were aslced to ski as fast as possible for each of the five trials, and for each trial they were to use a pair of ski poles that differed in length. All subjects were filmed and analyzed for differences in velocity, stride length, stride frequency, trunk flexion phase, trunk extension phase, angular displacement from trunk flexion to trunk extension, lower leg angle at legs together phase, pole angle at implantation, and the pole plant displacement in relation to the support foot. The results and a discussion of the findings for each variable will be a presented within this chapter,

Subjects Descriptive characteristics of the 13 cross-country skiers who were subjects in this study can be found in Table 1. All 13 individuals were screened for their ability to perform the diagonal stride. The entire population was affiliated with the University of Wisconsin-La Crosse at the time of this study,

Table 1 Descriptive Characteristics of the Skiers Presented in Mean and Standard Deviation Values

Age Weight Height Skiers (yrs) (lbs (cm)

Mean s.d.

-Velocity Velocity is the performance objective of cross-country skiing according to Dillman et al, (1979); it is a resalt of the skier's stride length and stride frequency (Dillman et al., 1979; Hay, 1984). The mean velocities (meters per second and miles per hour) of the skiers using the five different pole lengths are reported in Table 2. The pole length that was identified as being five centimeters longer than the "preferred" pole length recorded the fastest mean velocity for the five conditions. A trend developed for 69% of the subjects. They obtained their fastest velocity with that pole length. However, the analysis of variance

(Appendix H) showed no significant differences (p > .05) between the five pole lengths at the .05 level, F (4, 48) = 0.92, 2 > .05.

Table 2 Mean Velocities of the Skiers for each Pole Length

Pole Length +10 cm +5 cm "Preferred" -5 cm -10 cm

- x Velocity 8.624 8.906 8.632 8.661 8.612 s.d. .921 .939 .922 .989 .962

The "average" skiers in this study skied at mean velocities ranging from 3.850 to 3.982 meters per second. These velocities were higher than the velocities of "average" skiers (3.51 mlsec) in a study by Dillman et al. (1979) but were not as fast as the "skilled" skiers (4.64 inlsec) in that same study. This possibly occurred as a result of the testing method used in this study. After each trial, the subjects in this study were able to recover for a short period of time. The recovery period was provided to allow each subject sufficient rest so he could ski as fast as possible for each of the five trials.

Stride Length The mean stride length (meters and feet) of the skiers for the five conditions, are reported in Table 3. The pole length that was identified as being five centimeters longer than the "Preferred" pole length produced the longest mean stride length of the five conditions. The analysis of variance (Appendix I) showed no significant differences between the five pole lengths at the .05 level, F (4, 48) = 1.46, > .05. Stride length is one of two performance factors of velocity (Dillman et al, 1979; Hay 1984) for the cyclic activity of the diagonal stride of cross-country skiing. According to Haberli (1977), a skier must have a large stride length in order to obtain a greater velocity. Stride length is the total displacement a ski.er travels in one cycle (Dillman et al., 1979). Studies by Dillman et al. (19791, Haberli (1977) and Waser (1976) have indicated that the skier who has a higher velocity will also have a greater stride length than the slower skier. Dillman et al. (1979) reported stride lengths of 2.22 meters for "average" skiers and 2.88 meters for "skilled" skiers. Again, the results of the skiers in this study fall between the results produced by the subjects of the study by Dillman et al. (1979). According to Dillman et al, (1979) and Soliman (1977), stride length is the more critical factor of the two performance factors of velocity. Even though the velocity and the stride length of this study did not produce significant findings, they did produce results that were in agreement with the previously identified authors. In this study the +5 centimeter pole length produced the longest stride length, which is the more important factor of velocity, and the same pole length also produced the fastest velocity.

Table 3 Mean Stride Length of the Skiers for Each Pole Length

Pole Lmgth +10 cm +5 cm "Preferred" -5 cm -10 cm

Meters x SL 2.363 2.455 2.360 2.345 2.440 s.d. ,377 .320 .339 .314 .378 Feet -xSL 7.75 8.05 7.74 7.70 7.82 -s,d. 1.24 1.05 1.11 1.03 1.16 Stride Rate The mean stride rate (strides per second and strides per minute) of the skiers, for the five conditions, is reported in Table 4. The pole length that is five centimeters ~horterthan the "Preferred" pole length recorded the greatest mean stride rate for the five conditions. The analysis of variance (Appendix J) showed no significant differences between the five pole lengths at the .05 level, (4, 48) = 0.44, Q > .05. Stride rate is the other performance factor of velocity (Dillman et al. 1979; Hay, 1984) for cross-country skiing. Stride rate is the time element for this cyclic activity (Dillman et al. 1979). The frequency of the stride has a positive effect on velocity; however, it is not as important as the length of the stride (Haberli, 1977). Dillman et al. (1979) reported stride rates of "1.57 strides per second" for "average" skiers and "1.61 strides per second" for "slcilled" skiers. The highest stride rates recorded in this study could have possibly been a result of the testing methods used. A study by Haberli (1977) showed thst skier's with high stride rates have a tendency to ski with their upper body in a more erect position, The erect body position causes the skier's stride length to shorten. Because of differences in strength, endurance and ability, each individual will have a different stride rate. Therefore, it is up to the individual to develop a cadence that enhances his stride length (Haberli, 1977).

Table 4 Mean Stride Rate of the Skiers for Each Pole Length

Pole Length t10 cm +5 cm "Preferred" -5 cm -10 cm

Strideslsec

Trunk Flexion At the initiation of the kick phase the trunk of the skier is in a flexed position, and both legs are parallel to one another (see Figure 7). The mean absolute angle at trunk flexion (Angle 2), of the skier's, for the five conditions are reported in Table 5. The analysis of variance (Appendix K) indicated a significant difference in the absolute angle (Angle 2) for trunk flexion at the .05 level, F (4, 48) = 5.34, < .05. The Bonferroni-T statistic identified where the significant differences occurred between the various pole lengths within the group (Table 5). In order to show a significant difference among the five means at the .05 level, a difference of 1.589 must be surpassed for these planned comparisons (Kirk, 1968).

Figure 7. Skier assuming the body position at the beginning of the kick phase.

According to Dillman et al. (1979) the most desirable trunk angle for this segment of the kick phase is approximately 45 degrees. This body position is more typical of the "highly skilled" skier. A skier who attains this position has his weight more forward than the "less skilled" skier and is also more flexed forward. Dillman et al. (1979) and Soliman (1977) agree that the smaller upper body angle is essential to skiing speed and is also necessary to initiate the motion that produces a sufficient transfer of force in a forward direction. A study by Haberli (1977) suggests that skiers with an erect upper body positi~nhave an increased cadence but decrease their stride length, which is the primary performance factor necessary to achieve a high skiing speed.

Table 5 Mean Absolute Angle at Trunk Flexion (Degrees) and I? Values for Skiers at Each Pole Length

Pole Length +10 cm +5 cm "Preferred" -5 cm -10 cm

TF Angle

Identification of Significant Differences Among the Means

Mean absolute angles at Trunk Flexion were significant and had values similar to those of "highly skilled" skiers. The +10 centimeter pole produced significant results as did the "preferred" pole length. Although these two pole lengths produced significant trunk flexion angles which are similar to the findings of the other studies, they did not produce the greatest velocity, This investigator can only surmise that the skiers in this study did not have a sufficient amount of strength or skiing efficiency to produce the highest velocity while achieving the desired trunk flexion angle.

Trunk Extension Additional body segments other than the legs can add to the effectiveness of the kick. The vigorous extension of the trunk is the largest body segment responsible for creating a reaction force between the ski and the snow

(Dillman et al., 1979 and Ekstrom, 1981). Upon extension of the trunk, the toe of the skier's nonsupport foot breaks contact with the ground (see Figure 8). These two actions terminate the kick phase of the diagonal stride. The mean absolute angle at trunk extension (Angle 3) of the skiers, for the five conditions are reported in Table 6. The analysis of variance (Appindix L) indicated a significant difference in the absolute angle (Angle 3) for trunk extension at the .05 level, (4, 48) = 3.01, 2 < .05. The Bonferroni-T statistic identified where the significant differences occurred between the various pole lengths within the group (Table 6). A level of 1.475 had to be exceeded in order to show a significant difference amoung the five means at the .05 confidence level for these planned comparisons (Kirk, 1968).

Figure 8. Skier assuming the body position at the termination of the kick phase.

The desired angle of trunk extension needed to develop the fastest skiing speed at the termination of the kick phase is 55 degrees according to Dillman et al. (1979) for "highly skilled" skiers. Waser (1976) found the fastest skiers in his study to have an optimum angle of 53 degrees.

Findings from this study were significant and similar to the desired results of the other studies already mentioned. The range of the five means in this study were 52.60 degrees to 54.51 degrees. Although the +10 centimeter pole length caused the skiers in this study to achieve the more desirable trunk extension angle, it did not produce the fastest skiing velocity. Again, this writer can only surmise that the subjects in this study lacked the necessary arm and shoulder strength and skiing efficiency (with the +10 centimeter pole) to produce the greatest velocity while achieving the desired trunk extension angle.

Table 6 Mean Absolute Angle at Trunk Extension (Degrees) and F Values for Skiers at Each Pole Length

Pole Length +10 cm t5 cm "Preferred" -5 cm -10 cm

TE Angle - x TE Angle 54.51 52.60 52.87 52.79 52.99 s.d. 5.80 6.74 5.92 5.50 5.98

Identification of Significant Difference Among the Means - - - - - x2 x4 x 3 x 5 xl

Angular Displacement from Trunk Flexion to Trunk Extension The mean angular displacement (degrees) from trunk flexion (Angle 1 of Figure 7) to trunk extension (Angle 3 of Figure 8) of the skier's, for the five conditions, are recorded in Table 7. The pole length labled -5 centimeters accounted for the largest angular displacement for the five conditions. The analysis of variance (Appendix M) showed no significant differences between the five pole lengths at the

.05 level, F (4, 48) = 1.79, p > .05. Ekstrom (1981) has reported that the 10 degree extension of the trunk during the kick phase is responsible for the amount of downward vertical force used to set the ski. He states that the upward extension that sets the ski into the track varies from 1.5 times the skier's weight for ski touring, to three times the skier's weight for the "highly skilled" skier during competition. Dillman et al. (1979) agree that the vigorous 10 degree extension "of the large mass of the trunk can add a significant amount to the reaction force between the ski and the snow" (p. 41). A study by Haberli (1977) referred to this segment of the kick phase in terms of "thrusting speed" (p. 35). "A high thrusting speed is critical for a high skiing speed whereby, above all, stride length is increased" (p. 35). It is essential that the thrust is short and vigorous; this type of a leg kick and trunk extension will increase the stride length, which will increase the skier's velocity. Waser (1976) and Soliman (1977) agree that skiers with a higher skill level have a shorter thrust phase than the less skilled skiers. Solimam (1977) depicts this portion of the kick phase as having a "relatively calm and motionless"

upper body (p. 13). Trunk flexion to trunk extension angles closest resembling the optimal angle reported by Dillman et al.

(1979) were obtained using the -5 and -10 centimeter poles, The thrusting speed was not calculated for this study.

Table 7 Mean Absolute Angular Displacement From Trunk Flexion to Trunk Extension

Pole Length +10 cm +5 cm "Preferred" -5 cm -10 cm

Degrees

Even though the two shortest poles in this study produced the greatest trunk flexion to trunk extension angle, they did not produce the greatest velocity or stride length. This is a contradiction to the results of the other aforementioned studies. This writer has no explanation why the results from this study were not similar. It is possible that the mechanics of the skiers in this study were not equal to the highly-developed mechanics of the skiers analyzed in other studies.

Lower Leg Angle at the Legs Parallel Position At the initiation of the kick phase, the skier's body is in a flexed position, and both legs are parallel to one another (see Figure 7). T!le mean absolute lower leg angle (degrees) at the legs together position (Angle 1) of the skier's, for the five conditions, is recorded in Table 8. The analysis of variance (Appendix N) indicated no significant difference in the absolute angle (Angle 1) for the lower leg at the .05 level, F (4, 48) = 1.50, ~>.05.

Table 8 Mean Absolute Lower Leg Angle At the Legs Together Position of the Kick Phase

Pole Length +I0 cm +5 cm "Preferred" -5 cm -10cm

Degrees - x ALL Angle 68.99 69.32 68.59 68.16 69.47 s.d. 3.87 4.38 4.54 5.00 4.59

The angles recorded in this study for the skier's lower leg angle at the legs together position of the kick phase are not significant. These same angles are 8.16 to 9.47 degrees greater than those reported by Dillman et al. (1979), and within .53 to 1.84 degrees of a study by Soliman (1977). According to Dillman et al. (1979), the lower leg angle at the legs together phase should approach 60 degrees for the "better skier"; Waser (1976) reports an angle of 63 degrees as being the optimal lower leg angle, while the best skiers in Soliman's (1977) study had an optimum angle of 70 degrees, and a range of 58 to 80 degrees. According to Dillman et al, (1979), the 60 degree angle of the lower leg helps create a body position which places the skier's center of gravity over his toes. This flexed body position enables the skier to apply a more rapid force in the direction of movement. All three studies agree that the stronger thrust is generated faster from a flexed body position with a range between 60 and 70 degrees. Waser (1976) concludes that if the lower leg ang1.e is too small, the skier's center of gravity displacement first moves upward, because of the upward motion the thrust is not totally directed along the track and is responsible for an ineffective kick. Dillman et al. (1979) identify a "less skilledt'skier in this position by having a lower leg angle approaching 90 degrees and skiing in a more erect position. A skier in this position distributes his weight over the entire foot. Thus, when the thrust of the kick is initiated, the skier must first move his center of gravity Eorward before applying a force that will eventually propel the skier in a forward direction. The more vertical lower leg angle takes a longer time to generate the kicking force and is responsible for the less effective kicking action.

Pole Angle At Implantation At the initiation of the pole implantation phase, the tip of the pole is inserted into the snow (see Figure 9).

Figure 9. Skier assuming the body position at the initiation of the pole implantation phase.

The pole angle at implantation is a result of the skier's trunk flexion, elbow flexion, pole length and spatial relationship of the pole plant to the anterior portion of the support foot. The mean absolute angle at pole implantation (Angle 4) of the skier's poles for the five conditions is reported in Table 9. The analysis of variance

(Appendix 0) indicated a significant difference in the absolute angle (Angle 4) of the ski poles for pole implantation at the .05 level, 1 (4, 48) = 6.22, E < .05. The Bonferroni-T statistic identified where the significant differences occurred between the various pole lengths within

the group (Table 9). In order to show a significant difference amoung the five means at the .05 level, a difference of 2.271 must be surpassed.

Table 9 )lean Absolute Angle of the Slci Pole at Implantation and F Values for Each Pole Length

Pole Length +10 cm +5 cm "Preferred" -5 cm -10 cm

Degrees - x AAPI 71.80 73.99 74.61 74.56 76.57 s.d. 6.08 6.57 5.33 4.83 5.09

Identification of Significant Differences Among the Means - - - - - xl x 2 x4 x3 x 5 - xl = 71.80 ----- 2.19 2.76" 2.81" 4.77" - x2 = 73.99 ----- .57 .42 2. 58iy - x4 = 74.56 ----- .05 2.01 - x3 = 74.61 ----- 1.96 - x5 = 76.57 --- - - The angle that the ski pole is planted into the snow during the pole plant phase of the diagonal. stride can enhance the amount of force generated by the various body segments (Dillman et al., 1979). Soliman (1977) identified the elbow angle and the pole length as being important factors for achieving the most effective pole implantation. He also mentioned that the smaller elbow angle is desirable at the moment of implantation but noted that skiers with insufficient arm and shoulder strength should not attempt to develop the smaller elbow angle. The skier with an insufficient amount of arm strength cannot produce sufficient force with his arms through the ski poles. Haberli (1977) reported that a greater pole angle at implantation is a result of a greater forward leaning position of the skier's trunk. This anatomical position is an important factor which fndicates an efficient transfer of force throughout the poling phase. No specific pole implantation angles were identified; however, Dillman et al. (1979) suggest that the better skiers plant their ski poles in a more vertical position. This study did not identify the elbow angle or the trunk angle of the skier's at the initiation of the pole implantation phase. In this study the subjects obtained greater pole implant angles with the "preferred" pole length and the two shorter pole lengths. This writer can only theorize that the subjects 'n this study obtained the greatest pole plant angle with the shortest pole because more time was allowed with the shorter pole for the forward swing prior to the pole plant.

Pole Plant Displacement It has been established that, at the beginning of the poling phase, the ski pole is planted at a specific angle to the skiing surface. The tip of the pole also has a spatial relationship to the anterior portion of the support foot (see Figure 9). This distance is a result of the trunk flexion and elbow flexion at the initiation of the pole plant, along with the length of the ski pole. The mean horizontal displacement of the skier's implant pole in relation to the anterior portion of the support foot (Displacement A to B) is reported in Table 10 for the five conditions. The analysis of variance (Appendix P) indicated a significant difference in the horizontal displacement isp placement A to B) of the ski pole for pole implantation

at the .05 level, F (4,48) = 8.73, 2 < .05. The Bonferroni- T statistic identified where the significant differences occurred between the various pole lengths within the group (Table 10). If a significant difference among the five means is to be indicated at the .05 level, a difference of 5,935 must be surpassed for these planned comparisons (Kirk, 1968). Table 10 Mean Horizontal Displacement of the Slci Pole in Relation to the Support Foot at Pole Implantation

Pole Length +10 cm +5 cm "Preferred" -5 cm -10 cm

Centimeters

Identification of Significant Differences Among the Means

Dillman et al. (1979) reported that during the implantation phase the pole is a greater distance ahead of the anterior portion of the support foot for better skiers along with a more vertical angle to the pole upon implantation. That same study suggests the distance of the pole plant in front of the support foot to be between 15 and 25 centimeters. Haberli (1977) states that the skier who plants his ski pole farther forward will have a longer stride length and a shorter free glide phase. This would propel the skier a greater distance with each stride. Since the study by Haberli (1977) was performed on an incline, the implantation of the pole in relation to the support foot was somewhat behind the support foot to the micldle of the support foot. Waser (1976) indicates that a pole which is implanted near the anterior portion of the support foot will result in a reduction of velocity. Soliman (1977) suggests that a greater distance between the support foot and the pole can be obtained by increasing the angle of the trailing pole and not by an increased elbow angle. By increasing the angle of the trailing pole, the skier will create greater forward flexion at the trunk which puts the skier's center of gravity in a more favorable position as opposed to increasing the elbow angle to obtain a greater pole distance from the support foot. "The greater the distance from pole to foot at the time of pole implantation for the greater the trailing pole angle then the greater will be the stride length" (Soliman, 1977, p. 21). As indicated, it is desirable for the pole to be planted ahead of the support foot. Therefore, the mechanics of the skiers in this study were more efficient with the "preferred" and the two shorter pole lengths. CHAPTER V CONCLUSIONS

Summary The purpose of this study was to compare the biomecl~anical information obtained from the different ski pole lengths to biomechanical data previously identified. The comparisons were studied in an attempt to determine whether or not a specific pole length was responsible for producing "ideal" poling mechanics. Such information would identify a standardized method for obtaining the "preferred" pole length for cross country skiers. The 13 subjects (eight males and five females) in this study were all affiliated with the University of Wisconsin-

La Crosse. The subject's ages ranged from 7,O to 36, years and all were able to perform the three phases of the diagonal stride, Each subject skied five trials performing the liagb-a1 stride and used randomly selected pole lengths for each trial. Filming of each subject was conducted on the same day to try to keep the conditions as similar as possible for all trials. Each subJect skied as fast as possible for each trial regardless of the pole length. A Single Factor Analysis of Variance with Repeated Measures was implemented to identify significant differences between skiing mechanics of the diagonal stride with poles of differnet lengths. The Bonferroni Family of Confidence intervals was employed whenever the F ratio for the Analysis of Variance was significant, it identified where the differences occurred within the group.

Findings Based on the statistical data obtained in this study, the following findings were identified: 1. There was no significant difference jn the skiers' velocity (E > .05) as a result of the different pole lengths. 2. There was no significant difference in the skiers' stride length (2 > .05j as a result of the different pole lengths. 3. There was no significant difference in the skiers'

stride rate (E > .05) as a result of different pole lengths. 4. There was a significant difference in the skiers' absolute angle at trunk flexion at the initiation

of the kick phase (2 < .05) as a result of the "preferred" and plus ten centimeter poles. 5. There was a significant difference in the skiers' absolute angle at trunk extension at the

termination of the kick phase (2 < .05) as a result of the plus ten centimeter pole length. 6. There was no significant difference in the skiers' absolute angular displacement from trunk flexion to trunk extension during the kick phase (E> .05) as a result of the different pole lengths. 7. There was no significant difference in the skiersf absolute lower leg angle during the legs together position of the kick phase (E > .05) as a result of the different pole lengths. 8. There was a significant difference in the skiers' absolute angle of the pole at the initiation of the pole implantation phase (2 < .05) as a result of the "nreferred", minus five and minus ten centmeter pole lengths. 9. There was a significant difference in the skiers' horizontal displacement of the ski pole at the initiation of the pole implantation phase (2 < .05) as a result of the "preferred", minus five and minus ten centimeter pole lengths.

10. Of the parameters that showed a significant difference, the "preferred" pole length was a factor 75 percent of the time; the plus ten, minus five and minus ten centimeter pole lengths were a factor 50 percent of the time, and the plus five centimeter pole length was never a factor in this study. Conclusions Based on the statistical findings of the data obtained, the following conclusions were formed: 1. Specific pole lengths do have an effect on various poling mechanics of the diagonal stride. 2. Of the parameters that showed a significant difference, the "preferred" pole length (rr~inus thirty five centimeters less than the skier's body height) would appear to be the best selection of ski pole length.

Recommendations The following recommendations are suggested for future related study: 1. A similar study using a larger sample size on a five and ten kilometer course, over a period of five days, should be conducted to determine what effect endurance has on the mechanics studied in this investigation. 2. A study using all male and/or all female subjects to identify possible mechanical differences between the two genders. 3. A si~~i-larstudy using performance skis, boots, bindings and poles should be conducted to determine how precision equipment effects skiing mechanics. 4. Further study needs to be conducted on ski technique over varying terrain to develop a larger data base for the mechanics of the diagonal stride. 5. Three-dimensional cinematography would possibly identify other important skiing mechanics. 6. More studies of the general skiing population need to be conducted to determine what type of skiing equipment will best meet their needs, so they obtain the greatest benifit from their energy expenditure. REFERENCES

Barlow, D. A., Kinematic and kinetic factors involved in pole vaulting, Unpublished doctoral dissertation, School. of HPER, Indiana University, Bloomington, 1973. Bauer, E. A. The cross-country ski.erlsbible. Garden City, N.Y. : Doubl.eday and Company, Inc., 1977. Brady, M, An easy start. Cross-Country Skiey, December 1982, pp. 56-58; 67. Brady, M. Cross-country ski gear. Seattle, WA.: The Mountaineers, 1979. Brady, M. Getting it together. Cross-Country Skiing, November 1983, 67-70. Brady, M. Nordic touring and cross country skiing. New York: Port City Press, Inc., 1979. Caldwell, J. Caldwell on competitive cross-country skiing. Brattleboro, VT.: The Stephen Green Press, 1977. Caldwell, J. Cross-country skiing today. Brattleboro, VT.: The Stephen Greene Press, 1977.

Caldwell, J., & Brady, M. Citizen racing. Seattle: The Mountaineers, 1982. Crawford-Currie, R. Cross-country skiing. New York: Van Nostrand Reinhold Company Inc., 1982. Davis, M. W., Quality of data collected by segmental analysis techniques Unpublished doctoral dissertation, School of HPER, Indiana University, Bloomingtan, 1974, p. 163.

Dillman, C. J,, India, D. M., & Martin, P. E. Biomechanical determinations of effective cross-country skiing techniques. Journal of the United States Ski coaches Association, 1979, 3 (11, 38-42; 48. Ekstrom, H. Force interplay in cross-country skiing. Scandanavian Journal-of Sports Scientist, 1981, 3 (2), 69-79, French, E. K. Validity and reliability of kinematic data from two dimensional cinematograp&, Unpublished doctoral disseration, School of HPER. Indiana Universitv. Bloomington, 1981, 142. J z Gillette, E. F. Cross-Country Skiing. Seattle, WA.: The Mountaineers, 1979.

Haberli, R. Cross-countrv skiing: A film analvsis- .- - - - - of- - the- - - - diagonal stride during*elevation. - unpublis6ed study, Swiss Federal Institute of Technolonv. Laboratorv of Biomechanics, Zurich, Switzerland, fGj7. Hall, B. The ski pole release. Cross Country Skier, November 1982, 20-21. Hall, M. Be specific! put a cutting edge on your training. Cross Country Skier, October 1982, 57-59. Hall, M. One stride ahead. Tulsa, OK.: Winchester Press, 1981. Hanson, W. Fine tuning track technique. Cross Country Slcier, February 1983, pp. 12; 14. Hay, J. G. The biomechanics of sports techniques (2nd ed.). Englewood Cliffs, N.J.: Prentice-Hall, Inc.; 1978. Hay, J. G. The development of deterministic models for quailitative analysis. In R. Shapiro and J. R. Murett (Eds,), Proceedings: second national symposium on teaching kinesiology and biomechanics in sports, U.S. Olympic Committee Sports Medicine Council b The Kinesiology ~cadem~-ofNASPE, January 1984.

Kirk, R. E. Experimental design: procedures for the behavioral sciences. Belmont, California: ~rook/'~ole Publishing Company, 1968. lhonen, M. J. A cinematographical a~lalysisof a cross- country skier's arm motion on snow, on the Nordic Track and on a treadmill equipped with the Nordic Track arm- pulley device. Unpublished master's thesis, University of Wisconsin-La Crosse, 1980. Martin, P. E. Multiple regression analysis of the diagonal stride of cross-country skiing on uphill terrain. M.S. Thesis, University of Illinois, Urbana, Illinois, 1979. Mendez, C. Beginning cross-country skiing. Denver: Prensa Publications, Inc., 1979.

Northrip, J .W., Logan, G. A., 6 McKinney, W. C. Analysis

Publishers, 1983. Roberts. E. M. Cinemato~ra~hvin Biomechanical ~nvesti~ations.In J: M: 6ooper (Ed.), Selected topics on biomechanics. The Athletic Institute, Chicago, pp. 41-50, 1971. Sheahan, C. Sports illustrated cross-country skiin%. New York: Harper & Row, Publishers, 1984. Soliman, A. T. Cross-country skiing: the diagonal stride in flat. Diploma in Biomechanics, Laboratory for Biomechanics, Swiss Federal Institute of Technolonv,-- . Zurich, ~ecember,1977.

Tokle, A., & Luray, M. The complete guide to cross-country skiing and touring. New York: Vintage Books, 1977. Tuclcman, B. W. Conducting educational research. New York: Harcort Brace Jovanovich, Inc., 1978. Ward, P. E. An analysis of kinetic and kinematic factors of the standup and the preferred crouch starting techniques with respect to sprinting performance. Unpublished doctoral disseration, School of HPER, Indiana University, Bloomington, 1973, pp. 245. Waser, J. Film analysis of biomechanical parameters -associated with cross-country skiing. Laboratory for Biomechanics, Swiss Institute of Technology, Zurich, paper presented at International Symposium, Biomechanik Des Schilaufs, Innsbruck, February,l976. Witte, R. S. Statistics. New York: Holt, Rinehart and Winston, Publishers, 1980. Woodward, B. The cross-country ski book. New York: Leisure Press, 1983. APPENDIX A SKI POLE QUESTIONNAIRE FOR CROSS COUNTRY SKIING Please complete all of the following material to the best of your knowledge. 1. Do you rent cross-country ski equipment? YES- NO- 2. Do you sell cross-country ski equipment? YESNO- 3, Do you rent and sell cross-country ski equipment? YES- NO- 4. Do you handle more thsn one brand of cross-country slci poles? YESNO- 5. Do you handle these types of ski poles? Tonkin (bamboo) YESNO- If yes, do they increase by 5cm-_, 10cmn-, other? Metal Shaft YESNO- If yes, do they increase by 5cm-, 10cm-, other? Fiberglass Shaft YESNO- If yes, do they increase by 5cm-, lOcm-, other? Carbon Fiber Shaft YESNO- If yes, do they increase by Scm-, 10cm-, other? 6. Please list the brand or brands of poles you handle. Also, please list the shortest and longest pole for that brandyand the increment that the pole length increases by.

POLE BRAND SHORTEST (cm) LONGEST (cm) INCREMENTS (em)

7. Do you use a stock length of pole to custom make and fit poles for skiers who desire that type of service? - - YESNO- If ycu answer yes to (7), how do you measure the skier for the preferred pole length? Please speculate the skiers' ability level, and rank in order, Number 5 being the pole most sold or rented by your business, and Number 1 being the least sold or rented. Beginning Skier (never skied to occasionally skis).

Intermediate Skier (has some skiing experience, 2-2 days per week over 2-3 years). Advanced Skier (has much slciing experience, 4 or more times per week over 5 years). Citizen Racer (races for the fun of competition). Certified Racer (belongs to USSA, an organized team, or other competitive racing group). How do you measure your customers to fit them with poles? Please check only one. a. In an upright position the pole should be able to fit under an individuals armpit and touch the floor to determine a skiers preferred pole length. b. Invert the pole with the handle on the floor and have the basket touch the armpit to determine the preferred pole length. c. Determine the individual's body height in centimeters (cm) and subtract 35 cm from that height to determine the preferred pole length. d. Do you use some other method to determine the length of pole you will sell to an individual? YES- NO- IF you answered yes to (d) would you please explain in detail?

Please list any other comments you may have that might be significant in determining a skiers "preferred" pole length for cross-country slciing? APPENDIX B TABLE 11. Survey Results

------Mailing Sent Returned Unanswered Percent Returned

Initial 14 7 Second 6 3

TOTAL APPENDIX C TABLE 12. Descriptive Characteristics Of the Skiers And Their Equipment

Subjects Age Weight Height "Preferred" Ski Length Pole Length (years) (lbs.) (cm) (cm)" (cm)**

1 20 104.5 158.75 125 195 2 2 8 162.5 186.69 150 215"",: 3 20 114.0 161.925 125 195 4 2 8 144.0 166.4 130 200 5 20 126.25 161.9 125 195 6 2 1 141.25 177.8 145 21 0 7 2 9 173.0 172.1 135 205 8 3 2 178.75 177.8 140 2 10 9 3 6 135.0 175.3 140 210 10 2 5 150.0 168.91 135 205 11 2 0 146.75 163.195 130 200 12 34 196.0 182.9 150 215 13 24 192.5 181.6 145 215 Mean 25.923 151.115 171.944 136.539 205.385 s.d. (25.484) (227.31) (28.721) (+8.855)- (+7.458)-

*"Preferredw pole length was calculated by subtracting 35 centimeters from the body height and then rounded to the closest pole length available.

**Ski length was calculated by adding 35 centimeters to the body height and then rounding off to the closest length available. ;k;k*This subject used skis 5 centimeters less than recommended because the recommended length was not an available size. APPENDIX D 8 8

TABLE 13. Randomly Assigned Pole Lengths For Subjects

Subjects Order the poles will be issued to the subjects. A B C D E

130 cm. 135 cm, 120 cm. 125 cm. 115 cm. 150 cm. 140 cm. 145 cm. 155 cm. 160 cm.

130 cm. 135 cm. 115 cm. 125 cm. 120 cm. 125 cm. 135 cm. 130 cm. 140 cm. 120 cm. 115 cm. 130 cm. 235 cm. 125 cm. 120 cm. 150 cm. 135 cm. 140 cm. 145 cm. 155 cm. 130 cm. 125 cm. 145 cm. 140 cm. 135 cm.

140 cm. 135 cm. 145 cm. 150 cm. 130 cm. 130 cm. 150 cm. 135 cm. 140 cm. 145 cm. 125 cm. 140 cm. 130 cm. 145 cm. 135 cm. 130 cm. 135 cm. 120 cm. 140 cm. 125 cm. 140 cm. 150 cm. 160 cm. 145 cm. 155 cm.

13 150 cm. 145 cm. 140 cm. 135 cm. 155 cm. APPENDIX E Figure 10. Model of mechanics and movement patterns of

the "Glide Phase"

STRTDE -s-nEQmNcyLENGTU A- I POLE KICK GLIDE STRTDE 1I.IPI.ANTATION PIIASE PHASIC TIME PHASE (Appendix F) (Appendix G)

KICK PtlASE PHASE TERI~IIIIATIOII DISTANCE I NJLL SUPPORT I POLE INSERTION PROPORTIONAL INTO TIIF. SIIOU TO EFFECTIVENESS POLE PLANT POLE OF KICK PHASE DISTANCE FROM ARIiLE AT :~IJPPOW~-FOUP ll~lP1,AN'l' I LlRAG I'CISI~~~UIIOP AI.!UGII~I* 01.. TRUNK -FLEXION ELBOW FLEXIOH SUPPORT I FREE OLIDE OPPOSITE SKI

FROM POSITION OF COEFFICIENT TIIE BODY ON TllE VELOCITY OF OF DRAG SUPPORT SKI CI.IDC PllASE I /'. GLIDING FRICTION VELCCITY CHANGE I GLIDE PIIASF. FR0I.I THE IN TIIE FRICTIOE! COEFFICIEIIT BODY POSITIOEI ICTCK PIIASE VELOCITY AS A WNCTIOtl OF CAMBER USED TO -.---', OPTII~IIZE t.lASS IMPULCE KICK FORGE I /\ SURFACE FRICTIOIJI RESULTIIIG GENERATED POSITIOll PROPOR'CIONAL 'TiI.IE FROM THE POSITION OF THE OF SKIER'S TO THE FORCE OF GLIDE IS BODY ON THE SUPPORT SKI WEIGHT ON GENERATED BY PROPORTIONAL AND TIE SKIER'S \+EIGHT TIIE KICK TO THE KICK EFFECTIVEIiESS

BODY POSITION OF STATIONARY WEIGHT BALANCE THE REAR SKI TRUNK AND BEHIND I OTHER 6ALL OF FURTllER SEGllENTS SUPPORT llACK IS 70nT DESI RABI,P APPENDIX F Figure 11. Model of mechanics and movement patterns of

the "Kick Phase"

VELOCITY _I ST111 UE F rtEQUENCY I CLYDE STRIDE PHASE IMPLNITATION (Appendix L) (Appendix G)

POLE PllASE KICK I IlASE TERMIIlATIOll

PULL Tfil? SUPPORT KICK PHASE EXTENSION SKI BEGTIIS THRES1IOI.D 01.' TIIRUST TO SPRTNG

STATIONARY SUPPORT

BODY ROTATES OVER POINT FNEE GLIDE

IIIITIATIO1I

OF DRAG LWS FORWARD PIlASF: II!TTIATIOII I STATIC AND GLIDING FRICTION I OF OF NDY UHILE PRICTIOll COEFFICIENT AS A POLE ROTATTIIC OVER FUNCTION OF CAI.IBER .. AND PIIASE STATIOIIAIIY TllE FRICTIOll COEFFICIEHT AS A SUPPORT SKI

LEO IN PRODUCED AtIOLE RELATION TIME BY THE TO THE DYNAMIC SUPPORT BODY SKI FORCE FORCE EXERTIOII POSTTIOH I I I 011 I'IIE 0I"PTI~IIII~l OPTIMUtl OPTIEIUI~I SI.IOIIT vr(;onou:: SKI I:OR A AlKl.E AIIGLE POSI1'1011 SPECIFIC 45 GO r.lnes ovsrt AEIOUNT DEG!lEES DEGREES TOES OF 01' I'IEIR OIIPPOIlT ARMS I)WIAl,l IC :;K I III'WAllll 'TI~IIIIK ACl~~~l,l~~llATlCJlt l

VELOCITY

01 A\ ::TIlIDI< F'I4EQUEllCY I KICK GLIDE POLE STRIDE PHASE PHASE IMPLANTATIOII TIEE (Appendix F) (Appendix E) PRASE (see Figure 2)

FREE GLIDE TERI,lINATIOII I PIIASE DISTANCE POLE PllA31.: POLE IIISERTION I TERI.IINATTOII INTO THE SllOW I I KICK PlIASE TIIRRSIIOLI: I DISTANCE FROM ANlil.l! AT I ZTATIONARY SUPPORT FOOT SUPPORT SKI I POSITIOEI OF UIOUNT OF BODY ROTATES TRUNK FLEXION ZLDDW FLEXION OVER POIIIT FRONTAL AREA \ OF SUPPORT D~I~MIC / BODY POSITlON \ COEFFICIEEIT RIDItIG 01 THE VELOCIT? OF THP OF SLIPPORT SKI I'OI,E PLANT PlfASE DRAG I CLIDINC'FRICTION FROMTHE VELOCITY 1 GI'ID!? P!!,\w,/\ TIlE FRICTIOli COEFFICIENT AS A PUIICTTON OF CAMnER .'-'-.t.lASS 1t.IPlILSE SURFACE SESTSTA~JCLS SURFACE IIESISTAIICE ORTAIIIE:~ OF ri~t~~nn'rr~~tOVR!~ RESULTIIIG PRO1.I THE RESULTING FR0l.I THE FROM TllE SKIER'S PllObl I,IIIICH DYNAMIC POSITIONS SKIER'S \EIGHT SHOULDER klEIOHT THE THE OF THE BODY Otl AllD ARMS ON THE COORDIIIATIOII FORCE T!IE SUPPORT SKI MUSCLES SUPPORT SI32I.IEtITAL IS SKI THRUST EXERTED

AMOUNT EXTENS1011 EXTEllSIOII OF TRWIK OF OF FLEXIOll UPPER ARE1 FOREARM AT AT SIIOULDER ELBOW APPENDIX H ANALYSIS OF VARIANCE: VELOCITY

Source Sums of d f Mean F Squares Squares

Mean 988.11733 1 988.11733 1240.17 Error 9.56112 12 0.79676 R 0.17325 4 0.04331 0 .9 2 Error 2.24851 4 8 0.04684 APPENDIX I ANALYSIS OF VARIANCE: STRIDE LENGTH

Source Sums of d f Mean F Squares Squares

Mean 371.98471 1 371.98471 667.44 Error 6.68800 12 0.55733

R 0.13539 4 0.03385 1.46+: Error 1.11627 4 8 0.02326 APPENDIX J ANALYSIS OF VARIANCE: STRIDE RATE

Source Sums of d f Mean F Squares Squares

Mean 176.73982 1 176.73982 1221.76 Error 1.73591 12 0,14466 APPENDIX K ANALYSIS OF VARIANCE: TRUNK FLEXION

Source Sums of d f Mean F Squares Squares

Mean 127182.48116 1 127182.48116 805.00 Error 1895.88883 12 157.99074 R 63.58423 4 15.89606 5.34" Error 142.92653 4 8 2.97764

*~<.05. APPENDIX L ANALYSIS OF VARIANCE: TRUNK EXTENSION

Source Sums of d f Mean Squares Square

Mean Error

R Error APPENDIX M ANALYSIS OF VARIANCE: ANGULAR DISPLACEMENT FROM TRUNK FLEXION TO TRUNK EXTENSION

Source Sums of d f Mean F Squares Squares

Mean 5167.44607 1 5167.44607 153.81 Error 403.14998 12 33.59583

R 23.21614 4 5.80403 1.79" Error 155.83908 4 8 3.24665 APPENDIX N ANALYSIS OF VARIANCE: LOWER LEG ANGLE AT LEGS PARALLEL POSITION

Source Sums of d f Mean F Squares Squares

Mean 308634.79170 1 308634.79170 3398.33 Error 1089.83494 12 90.81.958 R 14.95975 4 3.73994 1.50" Error 119.59404 4 8 2.49154 APPENDIX 0 ANALYSIS OF VARIANCE: POLE PLANT DISPLACEMENT

Source Sums of d f Mean P Squares Squares

Mean 3194.45699 1 3194.45699 1.83 Error 20937.61853 12 1744.80154 R 1450.56151 4 362.64038 8.73" Error 1993.11984 4 8 41.52333 APPENDIX P ANALYSIS OF VARIANCE: POLE ANGLE AT IMPLANTATION

Source Sums of d f Mean F Squares Squares

Mean 358901.69785 1 358901.69785 2689.35 Error 1601.43590 12 133,45299

R 151.30517 4 37.82629 6 .2 2;'; Error 291.75436 4 8 6.07822