J. Blomechanics Vol. 25, No. 6, pp. 609-625, 1992. Printed in Great Britain

0021-9290/92 $5.00+.00 © 1992 Pergamon Press Ltd

P R E D I C T I O N OF THE LOADING ALONG THE LEG D U R I N G SNOW SKIING T. P. QUINN and C. D. MOTE JR Department of Mechanical Engineering, University of California, Berkeley, CA 94.720, U.S.A. Abstract--The complete force and moment of each cross section of the leg between the ski boot top and the knee during normal skiing were predicted from measurements of the force and moment under the toe and heel of the boot and the flexion of the ankle. The force and moment components predicted at the base of the boot were significantly different from those predicted at sites of potential injury at the boot top and the knee. The maximum torsional and maximum varus-valgus moment~ predicted at the knee over all subjects tested were 70 Nm and 149 Nm, which are within the estimated range of the ultimate strength of the knee without support from contracted muscles crossing the knee. Regression analyses were used to find the force components at the base of the boot that best predict the bending and torsional moments at the boot top and knee. The torsional moments at the boot top and knee are best predicted by the medial-lateral force at the toe. The varus-valgus moment at the boot top and knee are best predicted by the resultant medial-lateral force component at the base of the boot. The set of best predictors of the anterior-posterior bending moments at the boot top and knee includes the vertical force at the toe, the vertical force at the heel and the component of the total vertical force directed perpendicular to the leg.

NOMENCLATURE

X o- Y o - Z o

slope, intercept, standard deviation, and correlation coefficient of the linear regression between independent variable Fj and dependent variable Me slopes, intercept, standard deviation, and sy, Pr overall correlation coefficient of the multiple regression between independent variables Fj and dependent variable Mrp ).~j and 2~o,/~, slopes, intercept, standard deviation, and overall correlation coefficient of the muls;, R~ tiple regression between independent variables Fj and (Fzo sin 0) and dependent variable M~ 6q uncertainty in variable q force and moment components where Fij, M o i = x, y, or z in X j- Y f Z j coordinates when j = t, h, or 0. When j is omitted the force and moment components refer to X - Y - Z M~, M~ Mx and My predicted at the knee when p = k, or at the boot top when p = b l distance from the center of rotation of the ankle joint to the origin of X-Y-Z; see Fig. 1 0 angle between the leg and the Zo axis i'n the Xo-Zo plane; see Fig. 1 Point O intersection of the Zo axis with the free surface on the bottom of the boot sole; see Fig. 1 X-Y-Z orthogonal coordinates with Z aligned with the long axis of the leg and Y parallel to Yo; see Fig. 1 x j- Yj-zj orthogonal coordinates with the origin on the free surface on the bottom of the boot sole under the toe when j = t and the heel when j = h . Xj are coincident with the centerline of the boot sole (ASTM, 1987a). Z 1 are perpendicular to the free surface on the bottom of the boot sole; see Fig. 1

a S, fl,~, a,~, r,~

Received in final form 27 June 1991.

Xh

Za

orthogonal coordinates with the origin on the free surface on the bottom of the sole, Xo is coincident with the centerline of the boot sole (ASTM, 1987a), and Z0 is perpendicular to the free surface on the bottom of the boot sole and passes through the center of rotation of the ankle joint; see Fig. 1 distance along X0 from point O to the origin of X t - Y t - Z t n e a r the center of the low-friction area of the boot sole (ASTM, 1987a); see Fig. 1 distance along Xo from point O to the origin of Xh--Yh--Zh about 2.5 cm from the end of the heel of the boot; see Fig. 1 distance from point O to the center of rotation of the ankle joint; see Fig. 1 INTRODUCTION

Over the past 15 years the rates of injury to the leg and knee during snow skiing have decreased, probably due to improvements in skiing equipment design, maintenance and standards. Johnson et al. (1989) report that the rate of injury to the lower extremity at a ski area in northern Vermont decreased from 2.9 injuries/1000 skier visits (SV) in 1972 to 1.2 injuries/1000 SV in 1987. Other estimates of lower extremity injury rates range from 2.1 injuries/1000 SV in Germany (Hawser, 1989) to 0.38 injuries/1000 SV in Norway (Ekeland et al., 1989). With approximately 50-100 million SV per year (Shealy, 1985), between 60,000 and 120,000 lower extremity injuries are expected each year in the U.S. Of all injuries to the lower extremity, Johnson et al. (1989) estimate that those to the knee account for 67%, fractures of the tibia 4%, and contusions of the leg at the boot top 8%. The most c o m m o n sites of injury to the lower extremity are on the leg near the

609

610

T.P. QUINNand C. D. MOTEJR

boot top and in the ligaments and other tissues crossing the knee joint. No field studies of the forces and moments applied to the leg while skiing have measured or predicted the loading at sites where injury normally occurs. In the first field study Outwater and Woodard (1966, 1968) predicted the torsion applied to the foot at a point directly below the ankle on the base of the boot (point O in Fig. 1). Asang et al. (1974) measured the maximum lateral and hold-down force at both the toe and heel of the boot (100 and 490 N, respectively), and the net downward force (1000 N), but no resultant forces or moments could be predicted. Later studies measured the complete force and moment under the ski boot and report the maximum torsional moment and maximum anterior-posterior bending moment at point O in Xo-Yo-Zo: M z o = 5 5 N m and Myo=415 Nm (Mote and Hull, 1978), 6 5 N m and 432 Nm (Hull and Mote, 1982), 60 N m and 580 Nm (Kuo et al., 1985). Current standards for ski-release binding adjustment (ASTM, 1987b) refer to anterior bending and torsional moments at point O. Maxwell and Hull (1989) assumed that the ski boot fixed the leg at 0 = 20°, and they predicted the force and moment at the knee using static equivalence to the force and moment measured at the base of the boot. The maximum average force and moment at the knee durng turning are 400, 120, and 450 N in Fx, Fy, and F, and 100, 190, and 25 N m in M~, M~, and M,. Because the ski boot allows ankle flexion of about 45 ° about the neutral angle near 0 = 200 (Walkhoff and Bauman, 1987), ankle flexion can significantly affect

Yh

Fig. 1. The coordinate systems. The bottom of the boot sole lies in the X f Y j plane, where j=t, h or O. Xo-¥o-Zo is fixed to the ski and X-Y-Z is fixed to the le8 and rotates in the Xo-Zo plane.

the prediction of the force and moment at sites along the tibia. In this study forces and moments along the leg from the boot top to the knee are predicted from measurements of the complete force and moment at the toe and heel and measurement of ankle flexion during skiing. The purposes of this study are: (i) to identify the differences between the force and moment predicted at point O and those predicted at the boot top and the knee, and (ii) to identify the binding force and moment components that best predict the moment components at the knee and boot top that are likely to be responsible for injury.

APPARATUS AND EXPERIMENTAL P R O C E D U R E

Snow skiing experiments were conducted during April 15-17, 1989 at Donner Ski Ranch, California. Six healthy male subjects (Table 1), who were average or skilled skiers ranging in age from 24 to 52 years, skied a slalom course approximately 50 m in length. It consisted of a straight run for about 20 m directed 30° to the left of the fall line, followed by a 60 ° right turn, a 10 m straight run, a 60 ° left turn, another 10 m straight run followed by an aggressive right turn to a stop. The grade of the slope was about 17%. The subjects executed Parallel or Stem Cristiania turns. The data recorded included the complete force and moment components under the toe and under the heel of the left boot and the flexion-extension rotation of the left ankle joint. Each test run was also recorded on a videotape. Recording of the binding release torque in clockwise self-release at the toe and self-release of the heel binding preceded each test run. The bindings were adjusted according to ASTM F-939, Selection of release torque values for Alpine ski bindings. The left ski was instrumented as shown in Fig. 2. An uncoupled six-degree-of-freedom dynamometer (Quinn and Mote, 1990) was positioned on the top of the ski under the toe [Fig. 2(a)]. A second, identical dynamometer was positioned under the heel [Fig. 2(b)]. The dynamometer resolutions were (1, 1, 4)N, (0.1, 0.5, 0.4)Nm for forces and moments along the axes (Xi, Yi, Zi) with i= t or h; see Fig. 1. The dynamic ranges of the force and moment measurements were (1.3, 1.2, 3.5) kN, (30, 25, 65) N m along (X~, Y~, Z~). The dynamometers were linear with correlation coefficients greater than 0.999 in all components. Hysteresis was less than 2% of full scale for all force and moment components with typical values substantially less than 2% (Levine and Mote, 1983). The minimum linear stiffness of the dynamometers was 64.1 kN mm-1 (Quinn and Mote, 1990). A spring mass model including the mass of the skier gave a natural frequency of the skier-dynamometer system of 140 Hz with an 83.9 kg skier. The dynamometers were 14 cm long, 9.5 cm wide, and 3.2 cm high and weighed approximately 17N each. The bindings on the uninstrumented ski were mounted

Fig. 2. The test ski. Two six-degree-of-freedom dynamometers are under the ski boot (a, b). The fixture (f) positions a potentiometer (c) over the axis of rotation of the ankle joint. A fiberglass wand (e) parallel to the long axis of the tibia extends from the potentiometer to the tibial tracking fixture (d).

611

Leg loading during snow skiing

613

Table l. Subject data

Subject

Mass (kg)

Height (cm)

No. of runs

Tibia length (cm)

I at boot top (cm)

Boot sole length (cm)

CR SF AC TD JW DM

79.4 69.0 65.8 67.0 74.8 83.9

189 179 173 177 182 185

5 5 4 3 6 6

43.5 40.8 36.4 39.2 41.2 41.2

16.0 15.7 17.1 17.6 16.6 16.5

31.9 31.0 31.0 31.0 31.9 31.9

3.2 cm over the ski so that the fight and left boots were at the same elevation. A potentiometer measured the flexion of the ankle [Fig. 2(c)]. A tibial tracking fixture, constructed from the lower half of a knee brace (Ecko II, Orthomedics, Brea, CA) with the hinge cut away [Fig. 2(d)], was strapped onto the tibia. A fiberglass wand extended from the potentiometer to the tibial tracking fixture approximately parallel to the axis of the tibia. The wand was attached with Velcro [Fig. 2(e)]. The rotation axis of the potentiometer was positioned approximately at the rotation axis of the ankle joint [Fig. 2(f)] by minimizing the translation of the wand along the tibia throughout the range of flexion in the experiments. The location of the potentiometer for each subject was repeatably located in independent mountings to within 3.2 mm along the Xo and Zo axes. The potentiometer resolution was 0.1 °, and the resistance was proportional to rotation with a correlation coefficient greater than 0.999 throughout a 1800 range. The distance from the axis of the potentiometer to the edge of the hard shell of the boot and to the tibial plateau were measured for each subject within _+1.6 mm. All subjects wore the same model ski boot (Salomon Model SX 91). The 12 dynamometer channels were sampled at 512s -1, and the potentiometer was sampled at 32 s-1. The data were multiplexed and telemetered from the subject to an indoor ground station as was done in Kuo et al. (1985) and recorded on an IBM PC-AT for on-site reduction.

Mx = Mxo cos 0 + Fyo(Za + I cos 0 ) - Mzo sin 0, (2a)

My=FzolsinO-Fxo(z, +l cosO)+ Myo,

(2b)

M,=Mxo sinO+z.Fyo sin 0+M~o cos0.

(2c)

M~ and My are linear in l; Fx, F , F~, and M~ are independent of I. The predictions assume that the forces of inertia are negligible and the varus-valgus rotations of the foot relative to the leg are negligible because of the constraint of the ski boot. The force and moment components at point O in Xo-Yo-Zo and at the boot top and knee in X - Y - Z were calculated for each test run. The maximum force and moment reported are averages of the data for 9.8 ms (5 sample) bracketing the peak value to filter high-amplitude, low-energy values. The uncertainties in the maximum forces and moments were estimated according to Taylor (1980) as shown in the Appendix. To test the equivalence of two paired variables (e.g. Fx and F~o), a two-tailed, paired, Student's t-test is used. Equivalence of more than twogrouped quantitires (e.g. Myo, My, and M~) is tested using a Student-Neumen-Keuls test. The null hypothesis that the means of the paired or grouped quantities are the same is rejected if the significance level is less than 0.05. The data recorded at the end of each test run for all subjects, where the maximum loading was measured, are pooled and used in the linear regression analyses.

RESULTS DATA A N A L Y ~ S

The X - Y - Z coordinate system in Fig. 1 is attached to the leg at point Z = l from the centerof rotation of the ankle joint. The force and moment reported in the Xo-Yo-Zo system are statically equivalent to the complete forces and moments measured by the heel and toe dynamometers. The forces and moments at sections of the leg between the boot top and the knee are predicted from equilibrium force and moment balances: Fx = F~o cos 0 - Fzo sin 0,

(la)

Fy = F,o,

(1b)

Fz = Fxo sin 0 + F,o cos O,

(lc)

Typical time histories of the forces, moments and ankle rotation predicted in the Xo-Yo-Zo and the X - Y - Z systems are shown in Figs 3, 4, and 5 for Run 5 of subject SF. Starting from the neutral positon 0=23 °, SF leaned backwards during the left turn [Fig. 3(d)], creating the large posterior (negative) bending moment [Figs 4(b) and 5(b)]. This was observed during the left turn in at least one test run of each subject. During the stopping maneuver at the etad of the run, the leg of each subject rotated forward [Fig. 3(d)], producing anterior (positive) bending moments [Figs 4(b) and 5(b)]. During the fight turn and during portions of the straight run SF shifted his weight from the left to the fight ski, causing periods of nearly zero F~o; this was observed with all subjects.

T.P. QUINNand C. D. MOTEJR

614 (a)

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800

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In X o - Y o - Z o : - -

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Left Turn

0

400 c X U.

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-1.50

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35

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25 15 I

5.4

7.9

10.4

12.9

15.4

Time (s) Fig. 3. The forces in the X-Y-Z and Xo-Yo-Zo systems and the ankle rotation during a typical test (Run 5 of subject SF).

The maximum magnitudes of the force and moment components predicted at the boot top and their uncertainties were Fx=1298 _ 22 N, F r = - 2 6 8 _ _ l N , F==-1778+6N, M~=82.2__0.9Nm, Mrb=237 + 6 N m and M== - 6 9 . 9 + 1.2 Nm (Table 2). The Fx, Fy, F=, and M~ in Table 2 are the maximum values along the leg from the boot top to the knee. The most negative values of F~, placing the anterior cruciate in tension, were - 2 4 2 N for TD, - 9 0 N for AC and smaller than - 4 9 N for the other four subjects. The maximum ankle flexion 0 measured was 46.5 ° for SF and DM (Table 2); the minimum was 0.5 ° for JW. The maximum range was 44.4 ° for DM. Mx and My depend linearly on l (Fig. 6). The maximum M~ magnitude over all subjects and the uncertainty is - 1 4 9 + 1 N m and the maximum magnitude M~ is -303___5Nm (Table3). The magnitude of

M~ exceeded 125 Nm for 70 ms. M~ did not exceed 190 N m for more than 60 ms. However, the events of maximum M= were of longer duration with several events exceeding 40 Nm longer than 100 ms. The maximum magnitudes of the force and moment components in Xo-Yo-Zo over all test subjects are Fxo=590___l N, Fyo=-268___1N, F = o = - 1 8 8 7 ___6N, Mxo=39.9+0.1 Nm, Myo=433___7Nm and M z o = - 7 0 . 8 + l . 2 N m (Table 4). The maximum Mro exceeded the adjusted release moment by more than 10% in 15 of the 29 test runs; Myo exceeded the adjusted release torque by more than 40% (100 Nm) in 9 of the 29 test runs. The force components with maximum magnitude from each test run in X - Y - Z are pooled and compared to the simultaneously occurring force component in Xo-Yo-Zo using a paired Student's t-test. The

Leg loading during snow skiing

(a)

In X-Y-Z at Boot Top: ~ StraightRun ~" z o

615

In Xo-Yo-Zo al Point O: : Right Turn

Left Turn

::::

Stop

8C

e.O x

I

-80

I

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(b) 200

o '~'

c -200

-400

(C) 4O A

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~

c

C

N

"20

-4C

I

5.4

7.9

Time

I

I

10.4

12.9

15.4

(s)

Fig. 4. The moments in the Xo-Yo-Zo system and the X-Y-Z system at the boot top during a typical test (Run 5 of subject SF).

results show that the force components in X - Y - Z are significantly different from the corresponding ones in Xo-Yo-Zo. The maximum Fx is significantly larger than the simultaneous Fxo [see Fig. 3(a)] by a mean 538% (630 N) over all test runs. The largest difference between the maximum Fx and the simultaneous Fxo is 1072 N in run 5 of DM. This difference between Fx and Fxo occurs because of ankle flexion in the range 0.5°~Fxo by as much as 1072 N. The maximum torsional and varus-valgus moment components predicted at the knee approximately equal the estimated ultimate strengths of the knee without muscle contraction. The maximum torsional moment in a cadaver knee without ligament damage is 35-80 Nm in torsion, and the ultimate strength in valgus bending is 125-210 Nm (Piziali et al., 1982). The maximum torsional moment supported by the knee predicted here was 7 0 N m in torsion and 149 Nm for the varus-valgus moment. Contraction of the muscles crossing the knee probably reduces the

622

T.P. QUlNN and C. D. MOTE JR

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Leg loading during snow skiing Table lO. Linear regression analysis relating the medial-lateral force at point 0 to the varus-valgus bending moment on the leg At boot top

At knee

Varus-valgus moment vs total lateral force at point O b__ b b M x - ~yo Fro + flxyO

Varus-valgus moment vs total lateral force at point O k Fro + flxyo k Mxk = ~yo

Subject

CR SF AC TD JW DM

~xbyO

flby0

rbxyO

O.x, Ob

OCx~ Ok

flkxyO

/~X,0

o'k,0

(m)

(Nm)

(-)

(Nm)

(m)

(Nm)

(-)

(Nm)

0.909

8.25

0.974

8.25

0.854

7.77

0.955

7.77

0.887

9.56

0.954

9.56

0.652

7.70

0.855

7.70

0.902

8.31

0.969

8.29

0.866

5.50

0.562 (0.002) 0.513 (0.oo2) 0.486 (0.002) 0.452 (0.005) 0.530 (0.001) 0.468 (0.002)

0.966

5.50

0.289 (0.002)* 0.262 (0.002) 0.294 (0.002) 0.235 (0.005) 0.285 (0.001) 0.217 (0.002)

11.3 (0.1) 7.74 (0.08) -0.8 (0.1) 9.0 (0.2) 12.01 (0.08) 16.6 (0.1)

11.3 (0.1) 7.74 (0.08) -0.8 (0.1) 9.0 (0.2) 12.01 (0.08) 16.6 (0.1)

*Standard deviations for the slope and intercept are shown in parentheses.

potential for injury. The stiffness of the knee has been shown to increase up to 400% in torsion (Louie and Mote, 1987) and 280% in varus-valgus rotation (Olmstead et al., 1986) under contraction of the muscles crossing the knee. If the stiffness increases, the resulting translations and rotations across the knee decrease for the same applied load, and the strain is reduced in the ligaments crossing the knee. The predicted anterior bending moments at the boot top approximately equaled the expected ultimate strength of the tibia (Asang, 1978). The mean ultimate strength of the tibia in anterior bending at the rates of loading measured here range from 228 to 312 Nm using the data summarized in Mote (1987) and Asang (1976). The maximum anterior bending moment predicted here was 237 N m for the relatively large subject CR. Note that the magnitude of the maximum posterior bending moment at the boot top was 196 Nm. Prediction of the force and moment components on the leg at the sites of injury requires the measurement of force and moment components at the base of the boot and the ankle flexion and then the application of equilibrium force and moment balances. If prediction of the moment components at sites of injury are to be made from selected force components, the regression analyses identify the best predictors of the moments at sections of the leg. The force component with the longest moment arm to the potential injury site is usually the best predictor of the moment at that site. Mz is best predicted by F , . A better prediction of My is made by Fzt , but M~ is better predicted by F,h. The values of the regression slopes and intercepts may depend on the skiing technique. The variation of

subject parameters from the means of the parameters over all subjects support this conclusion. For example, 2~z0 (Table 8) is an order of magnitude smaller for subject AC than for other subjects. The moment arm I for Fz sin 0 for subject AC is only 10% smaller than the mean value. Subject AC was the least-advanced test skier. CONCLUSIONS (1) Except for the force lateral to the ski, Fyo, the force and moment components in the ski binding coordinate system at the base of the boot (Xo-Yo-Zo) are significantly different from the corresponding force and moment components predicted at the boot top and knee in X - Y - Z . The force and moment components on the leg depend strongly on the ankle flexion angle, The varus-valgus and anterior-posterior moments depend additionally on the distance along the leg from the center of rotation of the ankle to the site of moment prediction. (2) The varus-valgus and torsional moments predicted at the knee from the measured forces and moments at the foot are often within the estimated ranges of the ultimate strengths of the tissues when the muscles crossing the knee are relaxed. The maximum torsional moment and the maximum varus-valgus moment predicted at the knee during these skiing experiments were 70 and 149 Nm, respectively. (3) The maximum posterior bending moments predicted from the data measured during skiing were 196 Nm at the boot top and 303 Nm at the knee. The maximum anterior bending moment at the boot top was 237 Nm.

624

T.P. QUINNand C. D. MOTEJR

Ekeland, A., Holtmoen, A. and Lystad, H. (1989) Skiing injuries in Alpine recreational skiers. In Skiing Trauma and Safety: Seventh International Symposium, ASTM STP 1022 (Edited by Johnson, R. J., Mote, C. D., Jr and Binet, M.-H.), pp. 41-50. American Society for Testing and Materials, Philadelphia. Hauser, W. (1989) Experimental prospective skiing injury study. In Skiing Trauma and Safety: Seventh International Symposium, ASTM STP 1022 (Edited by Johnson, R. J., Mote, C. D., Jr and Binet, M.-H.), pp. 18-24. American Society for Testing and Materials, Philadelphia. Hull, M. L. and Mote, C. D., Jr (1982) Computer analysis of leg loading in Alpine skiing. In Ski Trauma and Skiin# Safety III. pp. 58-63. Publication Series of TUV-Bayern, Munich. Johnson, R. H., Ettlinger, C. F. and Shealy,J. E. (1989) Skier injury trends. In Skiing Trauma and Safety: Seventh International Symposium, A S T M STP 1022 (Edited by Johnson, R. J., Mote, C. D., Jr and Binet, M-H.), pp. 25-31. American Societyfor Testing and Materials, Philadelphia. Kuo, C. Y., Louie, J. K. and Mote, C. D., Jr (1985)Control of torsion aRd bending of the lower extremity during skiing. In Skiing Trauma and Safety: Fifth International Symposium, ASTM STP 860 (Edited by Johnson, R. J. and Mote, C. D., Jr), pp. 91-110. American Society for Testing and Materials, Philadelphia. Levin,A. and Mote, C. D., Jr (1983) An uncoupled six degree of freedom dynamometer. University of California, Department of Mechanical Engineering Report. Louie, J. K. and Mote, C. D., Jr (1987) Contribution of the musculature to rotatory laxity and torsional stiffness at the knee. J. Biomechanics 20(3), 281-300. Maxwell, S. M. and Hull, M. L. (1989) Measurement of strength and loading variables on the knee during Alpine skiing. In Skiing Trauma and Safety: Seventh Interntional Symposium, ASTM STP 1022 (Edited by Johnson, R. J., Mote, C. D., Jr and Binet, M.-H.), pp. 231-251. American Society for Testing and Materials, Philadelphia. Mote, C. D., Jr and Hull, M. L. (1978) Laboratory and field research on ski bindings. In Skiing Safety II (Edited by Figueras, J. M.), International Series in Sports Sciences, Vol. 5, pp. 244-270. University Park Press, Baltimore. Mote, C. D., Jr (1987) The forces of skiing and their implication to injury. Int. J. Sports Biomechanics 3(4), 309-325. Olmstead, T. G., Wevers, H. W., Bryant, J. T. and Gouw, G. J. (1986) Effect of muscular activity on the valgus/varus laxity and stiffness of the knee. J. Biomechanics 19(8), 565-577. Outwater, J. O. and Woodard, M. S. (1966) Ski safety and tibial forces. ASME Paper No. 66-WA/BHF-14. Outwater, J. O. and Woodard, M. S. (1968)Skiing forces and fractures. JETS Journal, pp. 33-37. Piziali, R. L., Nagel, D. A., Koogle, T. and Whalen, R. (1982) Knee and tibia strength in snow skiing. In Ski Trauma and Skiin# Safety IV(Edited by Johnson R. J., Hauser, W. and REFERENCES Magi, M.), pp. 24-31. TUV Publication Series, Munich. Quinn, T. P. and Mote, C. D., Jr (1990) Optimal design of an uncoupled six degree of freedom dynamometer. ExperiAsang, E., Grimm, C., Krexa, H. and Wittmann, G. (1974) mental Mechanics 30(1), 40-48. Ski-telemetrie. IAS ScientificReport. Asang, E. (1976) Experimental biomechanics of the human Shealy,J. E. (1985)Overall analysis of NSAA/ASTMdata on skiing injuries for 1978 through 1981. In Skiing Trauma leg. Orthop. Clin. N. Am. 7, 63-73. and Safety: Fifth International Symposium. A S T M STP Asang, E. (1978) Injury thresholds of the leg: ten years of 860 (Edited by Johnson, R. J. and Mote, C. D., Jr), pp. research on safety in skiing. In Skiing Safety II (Edited by 302-313. American Society for Testing and Materials, Figueras, J. M.), International Series in Sports Sciences, Philadelphia. Vol. 5, pp. 103-129. University Park Press, Baltimore. ASTM (1987a) Boot sole dimensions of adult Alpine ski Taylor, J. R. (1980) An Introduction to Error Analysis. Mill Valley, California University Science Books. boots. In 1987 Annual Book of A S T M Standards Section 15. American Society for Testing and Materials, Philadel- Walkhoff, K. and Bauman, C. W. (1987) Alpine ski boot hysteresis characteristics interpreted for skier target phia, ASTM Standard F 944-85. groups within the current standards. In Skiing Trauma and ASTM (1987b) Selection of release torque values for Alpine Safety: Sixth International Symposium, A S T M STP 938 ski bindings. In 1987 Annual Book of A S T M Standards (Edited by Mote C. D., Jr and Johnson, R. J.), pp. 127-145. Section 15. American Society for Testing and Materials, American Societyfor Testing and Materials, Philadelphia. Philadelphia, ASTM Standard F939-85.

(4) Based on linear regression analyses during the final 3 s of each test run, the medial-lateral force at the toe is shown to be a good predictor of the torsional moment applied to the leg. The resultant medial-lateral force at the base of the boot is a good predictor of the varus-valgus moment on the leg, but the medial-lateral force components at the heel or the toe alone are not good predictors of the varus-valgus moment. Neither the vertical force under the toe nor the vertical force under the heel alone are satisfactory predictors of the anterior-posterior moment at the boot top and at the knee. The anterior-posterior bending moments at the boot top and knee are predicted with an overall correlation coefficient of 0.97 and 0.93, respectively, from the vertical force component under the toe, the vertical force component under the heel and the component of the resultant vertical force perpendicular to the leg. Prediction of the anterior-posterior bending moment at the boot top can be made with an overall correlation coefficient of 0.97 using the vertical force under the toe and the vertical force under the heel. (5) The slopes of the regression lines relating the torsional moment on the leg to the medial-lateral force on the toe and relating the varus-valgus moment on the leg to the resultant medial-lateral force on the foot are not significantly different from the moment arms for these forces at 20 ° of ankle flexion. When the anterior-posterior bending moment is predicted from the vertical force component under the toe, the vertical force component under the heel, and the component of the resultant vertical force perpendicular to the leg, there are significant differences between the slopes of the regression lines and the moment arms for the forces at 20° of ankle flexion. The regression slopes are 26-48% and 35-46% smaller than the length of the moment arms for the vertical force component under the toe and the component of the resultant vertical force perpendicular to the leg, respectively. The regression slope for the vertical force component under the heel is not significantly different from the length of the moment arm at 20°.

Leg loading during snow skiing Zatsiorsky, V. and Seluyanov, V. (1983)The mass and inertia characteristics of the main segments of the human body. In Biomechanics VIII-B (Edited by Matsui, H. and Kobayashi, K.), pp. 1152-1159. Human Kinetics, Champaign.

625

+ (Mxt + Mxh)sin 0] 2

+ 6F2 [ (z, + l)cos O- x, sin O]2 + 6F2h [(z a +/)cos 0-- Xh sin 0] 2 2 • "20 ÷ (6xt2F ,2 + 6x h2 Fy2h + 6Mzt2 + 6Mzh)Sln + [(622 + 612)(Fy t + Fyh)2 + tSM2 + 6M2h] cos 2 0} 1/2, (A3a)

APPENDIX 6My = {(6F 2 + 6Fffh) (z, + l cos 0)2 + 6F 2 (l sin 0 - xt )2 + 6F2h (l sin 0-- Xh)2 ..~602 r (Fxt+ Fxh)l sin 0

The uncertainty in a variable q, calculated from experi-

mental measurements xi, x2 . . . . . xn, is given by 6q = I/__~_l 6Xl/2 +/.~_2 6X2/2 + . .

/~q

+ (Fzt .4-Fzh)l cos 0] 2 + 612 [(F=t + F=h)sin 0-- (F~ + Fxh)COS0"]2

~2"]1/2

•+t~-7-~6xn) J(A1)

if the uncertainties ~xl, 6x2 . . . . . 6x, are independent and random (Taylor, 1980). The uncertainties in the force and moment components in X - Y - Z from equations (1) and (2) are"

2 2 2 2 + 6Xt Fzt + 6Xh Fzh

+67.2(Fxt+Fxh)2 + 6My2t + ¢~My2h }1/2,

+ 602 [(Fyh)Z~ COSO--(Fytx, + Fyhxh+ M~t + M:h) sin 0

+ (M,~ + Mxh)COS0] 2

6F=, = {602 [(Fx, + Fxh)sin 0 +(F:I + Fzh)COS0] 2 + (6F 2 + 6F2h)sin 2 0 + (6F2, + 6F2h)COS2 0} 1/2, 2 + 6Fy2h] 1/2, 6Fy = [6Fyt

+ (Fyt xl + Fyh xh + Mzt + Mzh)COS0

BN 25:6-E

2 ] sin - 20 + [6z,2(Fyt + Fyh)2 -'F6Mxt2 + 6Mxh 2 2 2 2 2 2 +(6X t Fyt+6XhFyh+6Mzt+6Mzh)COS 2 0} 1/2.

(A2a) (A2b)

6Fz = {602 [ (Fxt + Fxh)COS0-- (Fzt + Fzh)sin 0"l2 +(6F2t+~F2h)sin20+(6F2 +6F2h)COS20}l/2, (A2c) 6Mx = {602 I-(Fyt+ Fyh) (za +/)sin 0

(A3b)

6M~ = {6F2(z~ sin 0 + xt cos 0) 2 + 6F2h(z~sin 0 + Xh COS0)2

The

(A3c)

uncertainties in the measured quantities are 6Fxt = 6Fyt = 6Fxh = 6Fyh = 1.0 N, 6Fzt = 6Fzh = 4.0 N, 6M,~=6Mxh=O.1 Nm, 6Myt =6yh=0.5 Nm, 6M~t= 6Mzh=0.4 Nm, 6Xh=6X,"*6Za=3.2 mm, 6l= 1.6 mm, and 60 = 0.1 °. The values of the other variables (F,:t, F,t, etc.) are measured during the test runs.

Prediction of the loading along the leg during snow skiing.

The complete force and moment of each cross section of the leg between the ski boot top and the knee during normal skiing were predicted from measurem...
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