Tethered swimming forces in the crawl, breast and back strokes and their relationship to competitive performance

J Biomrchontrr

Vol.

14. No.

8. pp. 527

Primed inC&alBritain

CO21 9290/81/080527 cl 1981 Pcrgamon

537

II

$02.0~3,~ Prcrr L,,,

TETHERED SWIMMING FORCES IN THE CRAWL, BREAST AND BACK STROKES AND THEIR RELATIONSHIP TO COMPETITIVE PERFORMANCE* RACHEL A. YEATER~,R. BRUCE MARTIN:, MARY KAY WHITE? and KEVIN

H. GILSON?

tHuman Performance Laboratory, School of Physical Mucation and IOrthopedic Research Laboratory, Department of Orthopedic Surgery, West Virginia University, Morganstown, WV 26506, U.S.A. Abstract-Forces developed during fulIy tethered swimming by 18 male athletes were measured using a load call in the tether cable. Three competitive strokes were studied: crawl, breast and back. Arm and leg components of the crawl and breast stroke were observed separately. Attempts were made to correlate peak and mean tether forces with competitive velocities. A positive correlation was observed between mean tether force and velocity in the crawl, particularly among distance specialists. A negative correlation was found between crawl velocity and the peak/mean force ratio. The data aiso suggest that the kick contributes significant force in both thecrawl and breaststroke. In neither case, however, does the whole stroke produce as much force as the sum of the arm and leg components would indicate.

INTRODUCTION

In studying the biomechanics of swimming, a fundamental goal is to determine the propulsive force a swimmer must develop and its relationship to technique, performance, and musculoskeletal forces. An obvious way to measure propulsive force is to tether the athlete to the side of the pool and measure the tension in the tether cable while he swims. Variations of this method have been used by several investigators. The technique is simple but deceptive, since the swimmer is not moving relative to the water in the same sense that he is while swimming freely. Most investigators have recognized this and several have introduced experimental techniques designed to reveal the relationship between fully tethered swimming and free swimming. These relationships are further analyzed in the following article (Martin et al., 1981). The purpose of the present paper is to describe experiments relating fully tethered swimming measurements to competitive performance. These results may ultimately be used by coaches for improving the techniques of their swimmers and by theoreticians to develop models for elucidating the mechanics of swimming. Previous studies of tethered swimming have, for the most part, involved small numbers of subjects and variables. The earliest such studies were done by Cureton (1930), Tews (1941) and Cambell (1948), all of whom used fully tethered methods. This work was followed by the partially tethered experiments of Alley (1952) and Counsilman (195S), who measured tether force developed by the crawl stroke as a function of velocity. That is, the tether was payed out at a constant velocity, the subject was instructed to swim at maximum effort, and the resulting force in the tether was

measured. Taken together, the latter two studies examined a total offour male swimmers. They revealed the basic force patterns associated with freestyle swimming and measured mean fully tethered forces of approximately 1OON. T’hey showed relative forces produced by different crawl techniques. These experiments also showed that as velocity increased, tether force decreased to zcfo during free swimming. Alley’s paper discussed the relationship between tether force and actual propulsive force with particular insight. Another method of tethered swimming was instroduced by Magel (1970). In this case the swimmer was tethered to a constant horizontally acting weight and adjusted his stroke rate so as to remain at a fixed spot in the pool. In this fashion he measured fully tethered forces in all four competitive strokes using 26 male subjects. He discovered that the breast stroke and butterfly produce the largest peak forces of the four competitive strokes Craig and Boomer (1980) recently reported tethered swimming experiments using nine male and nine female subjects swimming the crawl. Like Counsilman and Alley (but using a different technique) they showed that decreasing tether force was associated with increasing velocity in an approximately linear fashion. In addition, they were the first to demonstrate a correlation between fully tethered force and free swimming speed. In order to confirm and extend the knowledge obtained by these earlier investigators, this study investigated fully tethered forces in three competitive swimming strokes (crawl, breast and back strokes) and also isolated the arm and leg components of the crawl and breast strokes. In addition, it sought to relate these forces to competitive velocities achieved by an entire collegiate swimming team. METHODS

l

Received

11 August

1980.

All subjects were male volunteers from the 1978-79

RACHELA. YEATER,R. BRUCE MARTIN, MARY KAY WHITE and KEVIN H. GILSON

528

asked to swim as he would during competition). Competitive velocities were determined from the mean of times recorded during meets in the 100 yard crawl, 100 yard back, 100 yard breast and the 500 yard crawl. In addition the following anatomical measurements were made on each subject: height; weight; sitting height; arm length; hand area; wrist, forearm and biceps circumferences ; and biceps, triceps, subscapular, and suprailiac skin folds. The swimmers were catagorized as sprinters (N = 7), middle distance (N = 4) or distance (N = 3) men according to their best events as determined by their coach (author KG). (Four men were tested in tethered swimming but did not swim competitively.) was

d cell

bridge amplif.

chart recorder

Fig. 1. Schematic diagram of the experimental apparatus, which was assembled in an outside lane of the West Virginia University Natatorium pool.

West Virginia University swimming team. This partiteam was of above average collegiate ability; it ranked third in the eastern U.S. at the close of the season. Three of the subjects qualified for one or more national championship competitions (NCAA, AAU, Olympic trials). Before testing began, a one inch thick foam pad (open cell) was placed around the waist of the subject to guard against injury or discomfort from the tethering belt. A nylon diving belt with a 1.6 mm diameter, flexible steel cable attached to the back, and a nylon rope attached to the front, served as the tethering system The rear cable was attached to a calibrated load ring secured to the backstroke handhold (about 30cm above the water) of a starting platform. The nylon rope on the front of the belt was attached to the opposite end of the pool using a pulley system so that line tension could be easily adjusted (see Fig. 1). The load sensitivity was checked before and after each subject test with a 13.6 kg weight. Signals from the load ring were amplified through a bridge circuit and recorded on a Houston Instruments Model 2000 XYT recorder. With the swimmer floating in the apparatus with the aid of a kick board, the initial line tension was set at approximately 50 N for each subject. cular

Determination of tether jorces ii‘ three competitive swimming strokes The 18 swimmers were asked to perform the following strokes: the crawl breathing on each stroke, the crawl with no breathing, the crawl using the arms only, the crawl using the legs only, the breast stroke, the breast stroke with arms only, the breast stroke with legs only, and the back stroke. Each stroke was performed slowly (about 50% of the swimmer’s maximum effort) and at maximum elTort (i.e. the swimmer

Determination of tether forces as a function of stroke rate These studies involved four of the above mentioned swimmers. The methods were similar except that only the crawl stroke was performed and the stroke rate was varied. The subjects were instructed to swim in time with a recorded metronome beat provided to them via a miniature ear phone. See Fig. 1. The actual stroke rate was determined from the tether force traces. Data analysis Six typical strokes (three left, three right) were selected for analysis of the front and back crawl; five breast strokes were used. Peak tether force (PKF) was determined by measuring the distance between the baseline (tether tension while floating) and the recorded peak force. Mean tether force (TF) was determined by measuring the area between the swimmer’s force trace and the baseline using a planimeter. This area was then divided by the time required for the measured strokes. Lean body weight was determined by summing the skinfold measurements and using tables from Dumin and Womersley (1974) to estimate percentage body fat. Additional anatomical measurements were utilized in an analytical model for the crawl stroke described in the following Paper.

RESULTS Typical tether force patterns for the three competitive strokes are shown in Fig. 2, and mean values for the tether forces of the male swimmers are shown in Table 1. There was considerable variation in the force patterns of different swimmers in each stroke, and these variations are reflected in the relatively large standard deviations for the force data. The breast stroke peak forces are significantly larger than those of the crawl, but the mean tether forces are very similar. Peak forces could not be determined in the back stroke due to the nature of the force pattern of some individuals. The mean tether force in the backstroke was significantly less than that of the breast and crawl strokes.

Swimming forces and their relationship to competitive performance

529

Table 2(a). Comparison of mean tether forcesofwhole stroke with that of arm and leg components* Whole stroke

Arms only

Legs only

Crawl

191*41 (N= IS)

97223 (N=18)

119rt35 (N = 18)

Breast stroke

188+_51 (N= 15)

126+_38 (N = 18)

138+_47 (N= 16)

*The means of mean tether forces are shown in Newtons.

e

300.

: = r

200.

Table 2(b). Two-tailed Student’s t-test p values for differences shown in Table 2(a) Arms< whole Legs
100.


co.OOo1 0.01

Arms < legs 0.04 0.43 -__

01 time,

sec.

Fig. 2. Typical force patterns are shown for each of the three competitive strokes studied.

Mean tether force values for the arm and leg components of the crawl and breast stokes are shown in Table 2. The arms only and legs only mean forces are significantly less than the whole stroke force in both the crawl and breast stroke. In the crawl stroke the mean tether force produced by the legs (flutter kick) was significantly greater (P = 0.04) than that produced by the arms. In the breast stroke the arms and legs (whip kick) produce similar mean and peak tether forces. The relationship between the mean tether force of the whole stroke (Fw) and the sum of the arm and leg tether forces (F, + FL) is shown in Fig. 3(a) for the crawl and Fig. 3(b) for the breast stroke. In both cases the whole stroke tether force is only about half the sum of its two components measured separately. Various possible correlations between forces measured during fully tethered swimming and competitive performance were studied (Table 3). Since both sprinters and distance swimmers were included in the

Table 1. Comparison of tether force by type of stroke* Mean tether force (N) Crawl (N = 18)

Back (N = 17) Breast (N= 15) Peak Tether Force N Crawl (N= 18)

Breast (N = 15)

384f77 693*231

p -0.001

l Values shown are team mean L- one standard deviation. values are for Student’s t-test.

p

their competitive crawl velocities were measured at the appropriate distance for their types: 100 yard mean competitive velocity for sprinters and 500 yard mean velocity for distance men. In the case of distance swimmers, competitive velocity versus mean tether force for the crawl stroke is shown in Fig. 4. A strong positive correlation (r = 0.86) was found between these variables in this type of swimmer. Normalizing the force data by either body weight or lean body weight did not improve the correlation. Among sprinters, on the other hand, only a slight negative correlation was seen between velocity and mean tether force (r = -0.086). When velocity was related to peak tether force, no appreciable correlations were seen in either type of swimmer. In order to assess the relationship between tethered swimming force and overall ability, the sum of the 100 and 500 yard velocities is shown versus mean tether force/lean body weight in Fig. 5. The overall correlation coefficient is only r = 0.52. Note, however, that for the distance/middle distance swimmers in the sampler = 0.89, whereas the sprinters actually show a negative correlation : r = 0.46. Correlations between mean tether force and velocity were not as great in the breast and back strokes; see Table 3. In examining the tethered force traces it was noted that some individuals maintained a steadier force than others. In order to study the effect of this characteristic on competitive performance, competive velocity was plotted as a function of peak tether force/mean tether force. Figure 6 shows that there is a strong negative correlation (r = -0.89) between these variables among distance swimmers. The relationshjp is less clear in the case of sprinters, however. In general the higher velocities of the sprinters arc -ted with higher peak/mean force ratios. Two m @ormed poorly even though th8 ratio w&uw+qmusrmbly due to other causes. When the sum of the Wo and MO sample,

RACHELA. YEATER,R. BRUCE MARTIN, MARY KAY WHITE and KEVIN H. GILSON

530

0A

FC-TF =

81.2792 + .506972 (FC-ML) CORRELRTIOW COEFFICIENT = .587

250

* *

. . . .

*t 8

200 FC-TF

* . . . .

N

l* t

* l

150

t

*

. . . .

*

* *

100 I. . . . . . . .

100

..!.........

I. . . . . . . . . . I. . . . . . . .

140

180

220

FC-A+L,

200

FB-TF n 100

0

I

300

0B

. . . 1 . . . . . . .

I

260

N

FB-IF = 38.6989 + .565418 (FB-A+L) CORRELATION COEFFICIENT = .789

300

..I..........

*

8, t *

*

*

**

*e

* *

l

t

1 I. . . . . . . . . t !. .. . . .. .. . .. . . . . . ...!...*..... ! .. . . . .. . . . I 400 BO 240 320 0 160 FB-ML,

R

Fig. 3. Mean tether force for whole stroke versus sum of arm and leg tether forces for the crawl (graph (a), FC-TF versus FC -A+ L) and breast stroke (graph (b), FB-TF versus FB - A + L).

yard competitive velocities was considered, the negative correlation remained (r = -0.70). The results of an independent t test showed distance swimmers had significantly lower peak to mean ratios in the crawl (P = 0.05) than did middle distance

swimmers or sprinters. Other differences between the different types of swimmers are seen in Table 3. Distance and middle distance men produced significantly more mean tether force/lean body weight in the crawl stroke than did sprinters (P = 0.05). In

Swimming

forces and their relationship

Table 3. Comparisons

between

sprinters

to competitive

and distance

performance

swimmers

531

in the crawl t-test P value

Middle Distance and distance

Sprinters

500 yard competitive velocity (m s-‘)

1.605+0.072 (N=7)

1.474+_0.054 (N=7)

0.002

100 yard competitive velocity (m s-‘)

1.860 f 0.075 (N=7)

I.847 kO.074 (N=7)

N.S.

Peak tether force (N)

420+44 (N=7)

397+69 (N=7)

N.S.

Mean tether force (N]

216+38 (N=7)

179+32 (N=7)

0.044

Mean tether force

0.26 t+_ 0.046 (N=6)

0.325+0.051 (N=7)

Lean body weight

comparing competitive times distance swimmers performed significantly better than sprinters in the 500 yard crawl (P = 0.05). There was no difference between those groups, however, in the 100 yard crawl. In a further attempt to determine how tethered swimming results relate to performance, the mean tether force of the five best swimmers was compared to that of the five worst swimmers in the 500 yard crawl (see Table 4). Tbe best swimmers had significantly higher (P = 0.03) mean forces than did the worst swimmers, however there was no difference in the peak forces. A similar comparison for the breast stroke showed significant differences between the five best

soot-v =

1.25721

CORRELATIOW

1.7

1.6

soot-u H/SEC 1.5

1.4

+

and five worst performers with regard to both mean (P = 0.02) and peak (P = 0.05) tether forces. In the case of the back stroke, there was no significant difference between the mean tether forces of the best and worst swimmers. In examining the force traces for the crawl stroke, it was observed that many individuals consistently produced greater peak forces with one arm or the other. When this asymmetry of stroke was quantified by dividing the right-left differences in peak force by mean peak force, no appreciable correlation was found between this variable and either mean tether force (r = -0.12) or competitive velocity (r = 0.55 for sprinters

l.S7095E-03

COEFFICIENT

0.053

(FC-TF)

= .942

. . .

l *

1 . . . 1 . . .

*

*

*

: t ... . .. . . . . I .. . . . .. . ..!.........!.........!......... 123 150 200 175 225 FC-TF, H

Fig. 4. Mean 500 yard competitive velocity middle distance

(SOOC-V)versus mean tether force f FC-TF) for distance and swimmers

in the crawl stroke.

lS0

RACHEL A.

532

R. BRUCE MARTIN, MARY KAY WHITE and KEVIN H. GILSON

YEATER,

VEL = 2.99264 + 1.36539 (FC-TF/LU) CORRELATION COEFFICIEIIT = .521

tot

3.6

El

.

Q Q

.

.

0

.

DD

0

3.4

0

TOT VEL

:68 . .

H/SEC 3.2

.

0

0

19 0

l

. . 3 I. . . . . . . . . .

I.

.2

.24

. . . . . .

..!......... .28

! . . . . . . . . . .I . . .32 .36

..I...

*.

I

.4

FC-ff/LU, Fig. 5. Sum of 100 and 500 yard mean competitive velocities (TOT VEL) in the crawl versus mean tether force/lean body weight (FC-TF/LW). Sprinters are denoted by circles; other team members are represented by squares.

0A

SOOC-V = 1.95822 - .177435 (PKf/tf) CORRELATIOK COEFFICIEKT = X-.891

1.7

* . .* . .

1.6

soot-v

. . . .

N/SEC

* * t

t

1.5

*

. . . . 1.4 I. . . . . . . . . . ! . . . . . . . ..!......... 2 1.75 1.5

PKf/Tf,

I. . . . . . . .

2.25

..!......... 2.5

! 2.7s

Swimming

forces and their relationship

to competitive

performance

533

0B

lOOC-V = 1.94501 .0524834 (PKF/TF) CORRELATIOW COEFFICIEWT = X-.261

2

. . . .

l*

1.9 lOOC-v

*

. . . .

H/SEC 1.8

. . . .

+

1.7 I. . . . . . . . . . I. . . . . . . .

1.75

2

..!.........!................... 2.25 2.5

I

! 3

2.75

PKF/TF, Fig. 6. Mean competitive velocity (SOOC-V or lOOC-V) versus peak/mean the crawl. (a) Distance and middle distance swimmers.

200

-

. . . . 150 Ml FORCE WEYTOWS 100

tether force ratio (PKF/TF) (b) Sprinters.

0 A

* *

. . .

*

: . .

*

I. . . . . . . . . . I. . . . . . . . . . I. . . . . . . . . . I. . . . . . . . . . I. . . . . . .

.2

for

.36

.J2

.68

STR RATE, l/SEC

.84

...! 1

RACHEL A. YEATER, R. BRUCE MARTIN, MARY KAY WHITEand KEVIN H. GILSON

534

.

200

0 B

*

*

150 HN FORCE

*

. . * .

NEMTONS 100

t . . . .

*

*

50 I. . . . . . . .

.2

..!.........!..................‘!.........! I .52 .68 .36 STR RATE,

.84

1

l/SEC

Fig. 7. Two examples of mean tether force versus actual stroke rate for the crawl. (a) Graph for a swimmer whose mean competitive time for the 100 yard freestyle event was 47.4 s. (b) Graph for a swimmer whose mean time in this event was 50.4s.

and r = -0.076 for distance swimmers). Theoretically, tethered swimming force and competitive velocity would be expected to depend on stroke rate (see the following paper). No such relationship was found, however, when these variables were correlated with the stroke rates used by the swimmers when asked for a maximum performance. In order to further test for such a relationship one may turn to the experiments in which stroke rate was controlled using a metronome. In the crawl stroke

250

. . .

200

1 . . .

150

1 . . .

HN FORCE HEUTONS

100

some of the swimmers showed a highly linear correlation between stroke rate and both mean and peak tether force (e.g. r = 0.98). In others, however the relationship was nonlinear; see Fig. 7. Similar results were obtained for the breast stroke, as shown in Fig. 8. In the crawl stroke mean tether force reached a maximum and then decreased with increasing stroke rate in 3 out of the four swimmers tested. The optimal stroke rate was typically 0.8-0.9 s - ’ ; see,for example, Fig. 7. This optimal stroke rate effect was also seen in

0A

*

*

1

*

: * I. . . . . . . . ..!...................!.........!.........! I .6 .8 1 8TR RATE,

1.2 l/WC

1.4

1.6

Swimming

forces and their relationship

to competitive

performance

0

200

B

*

150 NN

535

*

FORCE

* ‘I

t

t

NEUTOWS 100

50 I. . . . . . . .

.4

..!........ .6

. I. , . . . . . . . .

I. . . . . .

.8

1

STR RATE,

1/SEC

. . . . . ...!

.a..!.

1.2

1.4

Fig. 8. Two examples of mean tether force versus actual stroke rate for the breast stroke. (a) Graph for a swimmer whose mean competitive time for the 100 breast stroke event was 58.7 s. (b) Graph for a swimmer whose mean time in this event was 66.0 s.

the breast stroke, but to a lesser degree. DISCUSSION

The force patterns recorded in the three competitive swimming strokes are similar to those recorded by Magel (1970). Attempts were made to correlate peculiarities of stroke patterns with tether force and performance, but no useful correlations were found. The high peak forces seen in the breast stroke are not surprising since it is more pulsatile than the front or back crawl strokes. Mean tether forces are not significantly different in the breast and crawl strokes even though velocity in the breast stroke is much less. This implies that drag force in the breast stroke is much greater, as one would expect, given the duration and mechanics of the recovery phase. One of the most significant findings of this study was the fact that the flutter kick not only contributes signihcantly to tether force in the crawl stroke, but actually produces more mean tether force than the arms alone. Although opinions vary, many coaches feel that the flutter kick does not contribute significantly to propulsion, but merely reduces form drag by elevating the legs. If tethered swimming force is indicative of actual propulstive force, then the kick is at least as important as the arms in the crawl. In this regard it should be noted, however, that Alley (1952) found the actual propulsive force of the flutter kick fell to zero as the free swimming velocity was achieved. Since Alley only studied a single subject, this question needs further study before the true signilIcance of the kick in the crawl stroke can be known.

Attempts to compare the mean tether force of the whole stroke with that of the sum of the arm and leg

components in the crawl and breast strokes indicate that something is lost when the arm and leg components of either stroke are combined. This result extends similar observations by Alley (1952) for the crawl stroke as executed in various ways by a single subject. Several possible explanations for this come to mind. For example, it is possible that turbulence or flow from the arm stroke reduces the force of the leg stroke. Limitations of mental concentration or neuromuscular coordination may also reduce the effectivness of simultaneous arm and leg movements relative to each performed separately. Whatever the reasons, the fact that arm ‘and leg forces in fully tethered swimming do not simply add to give the whole stroke force is of considerable interest in terms of performance. Karpovich and Sinning (1971) has shown analytically that swimming velocity during the whole stroke (VW)should equal the square root of the sum of the component velocities (Us and or, respectively’ for arms only and legs only swimming. This result depends, however, on the’assumption that the propulsive force of the whole stroke (F,) equals that of the sum of that during arms only (F,,) and legs only (FL) free swimming. In that case, Fw = F* + FL

(1)

and assuming that Fw = kt& etc., where k is a drag coefficient,

one has kv$ = kv: + kv:.

This reduces to

(2)

RACHELA. YEATER.R. BRUCEMARTIS, MARYKAY WHITEand KEVIN H. GUON

536

Table 4. Comparisons of tether force in best and worst team members* Five best

Five Worst

P

Velocity (m s-‘) Mean tether force (N) Peak tether force (N)

1.636&0.044 229 & 19 417+34

1444~0.021 181+39 427k58

0.001 0.03 N.S.

100 yard breast stroke Velocity (m SK’) Mean tether force (N) Peak tether force (N)

1.477kO.059 231+37

1.292kO.076 158&44

0.002 0.02

809+ 191

566+ 169

500 yard

crawl

* ‘Best’ and ‘worst’ based on mean competitive

0,

If, however, equation

=

&I:

+ I$,.

(1) is replaced

(3)

(4)

where s is the slope of Fig. 3(a), (b) or a similar graph (ignoring the intercept for the sake of simplicity), then one obtains VW= Js J(vi

+ vi,.

(3

In the case of the breast stroke, s = 0.565 for the sample reported here. This gives vw = 0.152 J(vi

+ VE).

_

times.

by

FW = @A + FL)r

0.05

(6) This is exactly the result reported by MacDonald and Stearns (1969) for the breast stroke in another study. One should not take this agreement too literally because it overlooks the fact that forces measured during fully tethered swimming are not the same as free swimming propulsive forces. Nevertheless, it is encouraging that a measure of correspondence is found between two independent experimental studies, and the suggested modification of Karpovich’s theory is noted. The correlations between mean tether force and velocity for the crawl shown in Figs 4 and 5 are comparable to those by Craig and Boomer (1979) : r = 0.81 for males and r = 0.82 for females. The higher correlations obtained by Craig and Boomer may relate to the fact that their velocities were not based on competitive times and thus did not include the effects of starts and turns. In any events, it appears that fully tethered swimming force measurements may eventually provide a means of predicting competitive velocities. This is reinforced by the fact that (Table 4) the best swimmers had significantly higher mean forces than the worst swimmers in both the crawl and breast stroke. It is difficult to explain the lack of such a correlation in the case of the sprinters. Taken as a group the sprinters in the sample do not appear to be comparable in ability to the distance or middle distance swimmers since the latter groups did as well as the sprintis in the 100 yard crawl (I%is may be in part the result of tactical recruiting decisions by the coach.) Likewise a strong negative correlation between the ratio of peak to mean tether force and competitive

velocity may be useful in predicting performance among distance swimmers; again the lack of such a

correlation among the sprinters in this sample may or may not be meaningful. If indeed the sprinters in this sample are not typical, then the differences shown in Table 3 may be meaningless. In an attempt to improve the ability to predict performance from tethered swimming data, a multiple regression analysis was done between 500 yard competitive veIocity and both mean tether force and the peak-to-mean force ratio for the distance and middle distance swimmers. The coefficient of multiple correlation was 0.90, not significantly better than that for mean tether force alone (r = 0.89), however. The experiments in which tether force was measured as a function of stroke rate appear to be unique in the literature. The results, however, are in concert with the findings of Craig et al. (1979) with respect to velocity versus stroke rate in the crawl stroke. In both cases there appears to be an optimal stroke rate beyond which force and velocity decline. It is interesting that this effect seems to have been intuitively recognized by coaches long before these experiments were performed. The lack of such an effect in the breast stroke may be due to its slower arm velocity and shorter, simpler, stroke pattern. (It should also be noted that none of the subjects were exceptionally good breast strokers.) These experiments indicate that tethered swimming shows some promise of providing coaches with a means of predicting performance and diagnosing problems of technique. Tether force, however, is not the same as propulsive force during free swimming. The following paper (Martin et al., 1981) attempts to analyze the relationships between these two types of swimming force and performance. It is hoped that once these relationships are better understood, tethered swimming forces can be better interpreted to predict performance and analyze swimming technique.

Acknowledgement+The authors would like to thank the West Virginia University varsity swimming team and coaching staiT.Mr Roy Williamson, Dr Daryl Rowe, MS Suzanne Smith, MS R&I Rosenbag and MS Casandra Watkins for their help in completing this work.

Swimming

forces and their relationship

REFERENCES

Alley, L. E. (1952) An analysis of water resistance and propulsion in swimming the crawl stroke. Res. Quarferly 23, 253-270. Cambell, C. R. (1948) A study of the relationship of arm and shoulder strength and endurance in freestyle swimming. Unpublished Master’s Thesis, Iowa State University. Counsilman, J. (1955) Forces in swimming two types ofcrawl strokes. Res. Quarterly 26, 127- 139. Craig, A. B. and Boomer, W. F. (1980) Relationships between tethered and free swimming the front crawl stroke (abstract). 1. Biomechanics 13, 194. Craig, A. B.. Boomer, W. F. and Gibbons, J. F. (1979) Use of stroke rate, distance per stroke, and velocity relationships during training for competitive swimming. Swimming III. (Edited by Teruads, J. and Bedingfield, E. W.) University Park Press, Baltimore. Cureton, T. K. (1930) Mechanics and kinesiology of swimming the crawl flutter kick. Res. Quarterly 1, 97-98. Durnin, J. V. C. A. and Womersley, J. (1974) Body fat assessed from total body density and its estimation from skinfold thickness. Br. .I. Nutrition 32, 77-97. Karpovich, P. V. and Sinning, W. E. (1971) Physiology of Muscu/ur Actiuir~l. W. B. Saunders Company, Philadelphia. MacDonald, F. W. and Stearns. W. J. (1969) A mathematical

to competitive

performance

537

analysis of the dolphin-butterfly and breast strokes. Unpublished Master’s Thesis, Springfield College. Magel, J. R. (1970) Propelling force measured during tethered swimming in the four competitive slyles. Res. Quarterly 41, 68-74. Martin, R. B.. Yeater, R. A. and White, M. K. (198 1) A simple analytical model for the crawl stroke. J. Biomechanics. in press. Tews, R. W. J. (1941) The relationship of propulsive force and external resistance to speed in swimming. Unpublished Master’s Thesis, Iowa State University.

NOMENCLATURE F F:’

F, v, r* ;;’ s r

Mean tether force of the whole stroke Mean tether force for arms only swimming Mean tether force for legs only swimming Velocity for the whole stroke Velocity for arms only swimming Velocity for legs only swimming Drag coefficient for the body Slope of a F, versus (F, + FL) graph Linear regression analysis correlation coefficient