ALAN W. ARATA, Lt. Col., Ph.D.
Air Force Academy
Colorado Springs, Colorado USA
Results indicated that as BR velocity increased, 63% of the parameter values increased linearly. Intrinsic support length, ankle range of motion, knee angular velocity and impact peak time (as a percentage of stance time) did not change. Stance time, vertical oscillations, and resultant active peak time (as a percentage of stance time) decreased linearly. Seventy percent of the FRmax parameter values were greater than BRmax values, with the following exceptions: stride frequency, stance time, hip angular velocity at toe-off and resultant active peak time. In addition, trunk angle at ground contact and resultant active peak time (as a percentage of stance time) showed no significant differences. Equal velocity BR and FR were fairly evenly split between greater and lesser value parameters, with 21% of the comparisons indicating no significant differences. For all conditions, the Elite group averaged an 87% greater velocity than the Athletic group. Independent of velocity, the following parameters could explain the greater Elite group velocities: stride length, intrinsic support length, time to impact peak, loading rate, resultant active peak, time to resultant active peak and initial A-P peak.
With the advent of competition, humans have been looking for ways to enhance performance and increase chances of victory. Forward running (FR) has benefitted from a great deal of investigation because, as a form of locomotion, it is the basis for a number of competitive sports as well as health and fitness activities. With topics covering cardiovascular fitness to injury mechanisms to proper mechanics for fast running, an enormous amount of time has been poured into FR research. Backward running (BR), on the other hand, has not received this kind of attention. It has recently been investigated on motor control/motor learning and rehabilitation bases, but no investigations have been conducted with sports performance in mind. Only Bates, Morrison and Hamill (1986) have mentioned the importance of BR in sport, noting that it was done in quick bursts on athletic fields or courts. It is curious that BR has seen so little research, as it plays an important role in a number of highly competitive team sports, including football, basketball, soccer, lacrosse and other team competitions played in similar settings.
In football for example, a defensive back employing BR can keep both the receiver and the quarterback in his field of vision. Once the defensive back turns to run forward, he loses sight of one if not both of these players, placing him at a disadvantage since both the quarterback and the receiver know where the ball is supposed to go. Sports like soccer, basketball, and lacrosse, and other sports where a ball travels from one end of a field or court to another and in which running is the mode of transportation are all enhanced by BR. Superior speed at BR is an advantage for the above mentioned football defensive back or a player in any of these sports, because with greater speed they can keep their eyes on the ball, the player with the ball, and or other surrounding players longer, allowing them to better defend attacks.
Since high level performance in the sports listed above is lucrative business, one might think the BR aspect of sport would be thoroughly investigated so that athletes could reach their optimal BR performance. This has been done for FR in sport. But as stated above, there has been no BR research directed towards sports improvement. The topics of the limited BR research that do exist are, kinematics of BR movement at moderate velocities, and muscle force and joint moments. There has been no research aimed at improving BR performance in highly skilled athletes who use BR.
The reason for this lack of BR research may be that coaches do not separate backward running as a skill that is different from forward running. Jim Radcliff, University of Oregon Strength Coach and former National College Athletic Association (NCAA) defensive back says, "It's (BR) not something that everybody can just automatically be good at." He says that BR is important for three reasons: (a) the ability to move while looking down the field, (b) recovery/rehabilitation, and (c) movement efficiency and balance.
A question that needs study is whether FR and BR have similar gait characteristics at high speeds (maximum efforts). For example, the characteristic of maximum stride frequency may be limited by several factors, including length of limb, force production of the muscles, the task, the environmental conditions, the morphology of the individual, and a running motor program. In kinematically and kinetically comparing a maximum BR effort to a maximum FR effort, several of these factors can be controlled for and measured, helping to answer this question.
Winter, Pluck, and Yang (1989), in an investigation of the similarities and differences in forward and backward walking, concluded that backward walking was a 95% reversal of forward walking. This was true for joint movement patterns and joint powers. Conversely, Devita and Stribling (1991) in their investigation of lower extremity joint moment and joint muscle power with respect to BR found that BR was not simply a reversal of FR. Their results indicated the muscular structure supporting the ankle and knee reversed roles in FR and BR.
Backward running is a learned skill and one that seems to have its own motor program. The average individual does not spend a lot of time performing BR. This is quite different from FR, which is developed early in life. Lundberg (1979) studied locomotion in children and found that ninety percent could run (forward) at 18 months, though stiffly. Normal individuals have a strong motor program for forward running (FR). Currently, no study has been published recording when children learn the skill of BR.
Studying how a sedentary individual performs BR may have little value. These individuals may never perform BR throughout their lives. Though BR may find some uses as a balance control exercise, athletic individuals performing some activity mainly use it. These activities may be sports or rehabilitation related. Therefore, to better study the parameters of high speed BR, individuals who are highly experienced in BR (elite BR users) should be used as subjects. In choosing a control group for comparison, an athletic population of skilled movers should be used, since athletically unskilled individuals might have difficulty performing BR.
ANATOMICAL CONSTRAINTS OF FR AND BR
To comprehend the differences between BR and FR, one must understand the anatomical constraints of the hip, knee and ankle joints and how these constraints affect backward and forward running.
The hip joint is ultimately constrained in flexion by the physical contact of the quadriceps with the chest or musculo-tendonous units spanning the hip and the knee. In extension, the hip is constrained by the anterior musculo-tendonous units spanning the hip joint. There is no movement in either FR or BR that requires maximum flexion of the hip joint. However, both FR and BR can require full extension at the hip. In FR, the hip can reach full extension at or just after toe-off. In BR, the hip can reach full extension just prior to ground contact. Thus, the hip joint may constrain BR velocity by not allowing sufficient extension at ground contact. In FR, the hip joint may constrain velocity by not allowing sufficient extension at toe-off. In both directions, effective hip extension can be gained by increased trunk lean, which decreases hip angle.
The knee is constrained in flexion by the physical contact of the hamstrings muscle groups with the gastrocnemius. Extension of the knee is constrained by ligaments, posterior muscles and bone. Maximum velocity of forward running may be constrained slightly in knee flexion, however, it is unlikely that increased knee extension would increase running velocity. The knee does not constrain BR in flexion, but may in extension at or near toe-off. If the knee were able to hyperextend without injury, BR ground contact time could increase, which could potentially increase propulsive force. BR requires muscular work as the knee reaches full extension at toe-off. Knee joint proprioceptors sense joint extension and send neurological signals to activate antagonistic muscles. This action avoids damage to the knee joint structure, but the antagonistic muscular force is counterproductive to BR velocity.
The ankle is constrained in flexion and extension by bone, ligaments and musculo-tendonous units. It is unlikely that normal ankle ROM constrains FR (reduced plantarflexion may limit the ability to produce force). Like the knee, the ankle is not constructed for backward locomotion. From the standing position, ankle plantarflexion produces forward movement. BR is thus constrained during the stance phase. In addition, as the runner moves backward, the ankle angle increases as opposed to decreasing as in FR, lessening the amount of plantar flexion available and thus limiting propulsive potential.
Forward and backward running differ in their utilization of major thigh muscles during running propulsive and swing phases with respect to the hip and knee joints. During the BR propulsive phase, the rectus femoris is involved in hip flexion and the entire quadriceps group (rectus femoris, vastus lateralis, medialis, and intermedius) extends the knee. During the FR propulsive phase, the quadriceps group is responsible for knee extension only. Additionally, hip extension is aided by the hamstring group (biceps femoris, semitendinosus, and semimembranosus). FR's greater muscle utilization over BR during the propulsive phase gives FR the potential for more force production. During swing phase, BR utilizes the same muscles as FR does during its propulsion phase. Conversely, FR swing phase muscular utilization is similar to the BR propulsion phase. This means that more muscles are at work in BR than in FR during the non-propulsion or resting phase. Thus, FR employs a greater muscular potential during propulsion and is muscularly more efficient during swing phase than is BR.
BIOMECHANICS OF BACKWARD LOCOMOTION
Backward locomotion studies have only been conducted for the past 15 or so years. Most of the backward walking studies have been from a motor control perspective, attempting to determine what gait parameters and motor programs were used. BR studies have been conducted primarily from an aid to injury rehabilitation viewpoint.
The first published BR study came from Bates, Morrison, and Hamill (1986) who compared joint angles during BR and FR in 9 female runners at one backward and two forward running speeds. They compared equivalent speeds for BR and FR (2.7 m¥s-1 FR vs. BR) and equivalent efforts (3.0 m¥s-1 FR vs. 2.7 m¥s-1 BR). The study results indicated BR, when compared to FR, had lesser ranges of motion at both the knee and hip with respect to stance phase. This study did not measure stride rate. However, one can surmise that BR stride rate is greater than FR stride rate given decreased range of motion (which should equate to decreased stance phase time) of the 2.7 m¥s-1 BR compared to the 2¥7m¥s-1 FR.
Vilensky, Gankiewicz, and Gehlsen (1987) conducted a study that employed incremental increases in backward walking velocity. Their results showed a decrease in the subject's maximum knee angle as velocity increased. This is different than the trend seen in forward running where knee angles increased as velocity increased (Mero & Komi, 1986).
Another backward walking study was conducted by Winter, Pluck, and Yang in 1989. They found that backward walking was a 95% reversal of forward walking when both were done at moderate walking speeds. This was true for joint movement patterns and joint power.
Conversely, Devita and Stribling (1991), in their investigation of lower extremity joint moment and joint muscle power with respect to BR, found that BR was not simply a reversal of FR. Their study used five volunteer male participants, one with experience using BR. Measurements were taken from digitized video and combined with force platform analysis including ground reaction forces. Their results indicated the muscular structure supporting the ankle and knee reversed roles in FR and BR -- During BR, the knee provided the primary power while the ankle plantarflexors absorbed shock.
Threlkeld, Horn, Wojtowicz, Rooney, and Shapiro (1989) investigated BR ground impact forces. They had an experimental group practice BR for 8 weeks as part of a daily running routine, while a control group only practiced FR. Their study investigated BR at 3.5 m¥s-1, attempting to emulate the FR training speed of good to elite distance runners. They concluded there were significant increases in muscular strength of the knee extensors within the BR group as a result of BR training. They also noted that the BR stance time was 10% shorter than FR stance time. There was a 6% lesser maximum vertical force and a 30% lesser impulse force in BR compared to FR (at 3.5 m¥s). The investigators hypothesized that the decrease in the BR group impact forces was seen because the toe landed first in BR and allowed more shock absorption than the heel that struck first in FR.
Flynn and Soutas-Little (1993) investigated muscle power and action during FR and BR, analyzing the sagittal plane of the right knee. The study compared EMG and kinetic parameters during the stance phases of FR and BR using 6 active male subjects. Their results indicated that during the initial stance phase of running, more work was required for FR than BR. This was found true especially for eccentric muscle contractions where four times more work was required for FR than BR.
Flynn, Connery, Smutok, Zeballos, and Weisman (1994), when studying oxygen consumption during forward and backward walking and running, found 40% of their participants were not able to complete the BR test at a relatively slow (compared to FR) speed over a 6 minute time. The researcher's qualitatively observed the subjects and concluded that high fatigue and or loss of coordination was the cause. The study also noted that the participants who dropped out of BR were not the slowest at FR.
All the above studies can be combined for some general conclusions. Firstly, BR and FR are not just reversals of the same movement. Secondly, an individual who possesses skill and speed in FR may not possess them in BR. Thirdly, high speed BR has not been investigated. With respect to forward running, sprinting has been extensively researched, and answers on how to improve performance have been determined and implemented. The same cannot be said for BR with respect to sprinting. Any BR sprinting judgments would be guesses from FR or interpolations from BR rehabilitation research. This project aimed to answer many BR sprinting questions, as well as lay the ground work for future BR studies.
The purpose of the study was to quantify the kinematic and kinetic parameters associated with backward running (BR) and to compare them to: (a) BR parameters at submaximal velocities, (b) forward running (FR) parameters at maximum velocity, and (c) FR parameters at a velocity equal to BRmax (FRequal). In addition, two groups were compared. One group was comprised of individuals who used BR during athletic competition. The other consisted of individuals who habitually ran for exercise.
SUMMARY OF PROCEDURES
Thirty male volunteers served as subjects for the study and were placed into either an Elite or Athletic group. The Elite group was comprised of 15 subjects who were members of a National Collegiate Athletic Association (NCAA) Division I university athletic team for which they performed high velocity BR as a part of competition. The Athletic group consisted of 15 university students who ran regularly. At the beginning of the testing session, each subject completed an Informed Consent Form approved by the Office of Human Subjects Compliance at the University of Oregon, and a BR questionnaire.
Kinematic and kinetic data were obtained for each subject during five different running conditions. Kinematic data were collected (200 Hz) using a two-camera Motion Analysis Corporation video system. Kinetic data were obtained (1000 Hz) using an AMTI force platform. Each subject completed three BR trials at maximum velocity (BRmax), then three BR trials each at 80% and 60% of their BRmax velocity (BR80, BR60). Following these trials, each subject performed three FR trials at maximum velocity (FRmax) followed by three FR trials at their BRmax velocity (FRequal).
Three repeated measures analyses of variance (ANOVAs) were used to evaluate group and dependent variable differences. The first compared the three BR conditions, (BRmax, BR80, and BR60) to determine kinematic and kinetic parameter changes as BR velocity increased. The second compared the differences between the two maximum velocity conditions (BRmax and FRmax). The third compared the differences between the two equal velocity conditions (BRmax and FRequal). Level of significance was set at 0.05. In addition, effect size (ES) was used to determine whether condition or group values were statistically similar. Values being compared were considered similar if the effect size was 0.1 or less.
SUMMARY OF RESULTS AND DISCUSSION
Most of the parameters that increased or decreased with BR velocity also had significant linear trends in the same direction. Four parameters displayed no significant changes as BR velocity increased (knee angular velocity at toe-off, time to resultant impact peak (as a percentage of stance time), hip to toe support length at ground contact and hip to toe support length at toe-off). Three parameters decreased as BR velocity increased (stance time, vertical oscillation and time to resultant active peak). Ankle range of motion was the only parameter that remained statistically similar over the increases in BR velocity.
The FRmax condition had greater parameter values than the BRmax condition for most of the comparisons. BRmax did, however, result in greater stride frequencies, stance times, hip angular velocities at toe-off and times to resultant active peak. The maximum velocity conditions were statistically similar in trunk angles at ground contact and resultant active peak forces. There were no significant differences between trunk angles at toe-off, trunk angle changes or times to resultant impact peak (as a percentage of stance time).
There were no significant differences between equal velocities of BR and FR (BRmax and FRequal) in hip to toe support at toe-off or vertical oscillations. Furthermore, there were statistical similarities between trunk angles at toe-off, trunk angle change and resultant active peaks. The other parameters were fairly evenly divided between greater values for BR or FR.
Group comparisons across the conditions showed that the Elite group performed BR faster than the Athletic group and exhibited significantly different values corresponding with increased BR velocity for most parameters. Parameters that were not significantly different during BR group comparisons included: trunk angle at toe-off, knee range of motion, angular velocities of the hip, knee and ankle joints at toe-off and final A-P braking force. In addition, trunk angle change and hip range of motion were statistically similar. Several of the parameter differences between the groups could have been related to the Elite group's greater velocity rather than contributors to that greater velocity. Factoring out velocity, the following parameters remained to separate the two groups: stride length, hip to toe distance at toe-off, time to resultant impact peak, loading rate, resultant active peak, time to resultant active peak and initial A-P peak.
A purpose of the study was to quantify the kinematic and kinetic parameters associated with high velocity BR as demonstrated by individuals who used it as part of a competitive sport. Specific objectives were: (a) to describe BR parameters at maximum velocity, (b) to compare BR to FR, and (c) from a clinical or coaching perspective, to determine which BR parameters appear to be the most important in order to give information to coaches regarding effective training.
As BR velocity increased from 60 to 100 percent of maximum, the velocity of the foot during the swing phase increased, stride length increased, intrinsic support length did not change, stride frequency increased, stance time decreased, trunk lean was greater during stance and trunk angle change was greater between ground contact and toe-off, there were greater hip and knee but not ankle ranges of motion (ROM), there were greater hip and ankle but not knee angular velocities at toe-off, the body's vertical oscillations decreased, resultant impact peak increased while time to resultant impact peak (as a percentage of stance time) did not change, loading rate increased, resultant active peak increased while time to resultant active peak (as a percentage of stance time) decreased, initial A-P positive peak increased, and final braking force demonstrated a tendency to increase.
Two BR to FR comparisons were conducted, an equal effort comparison (BRmax vs. FRmax) and an equal velocity comparison (BRmax vs. FRequal). In the maximum velocity comparison, FRmax exhibited significantly greater values for 12 of the 21 parameters. BRmax demonstrated greater stride frequencies, stance times and hip angular velocities, as well as later resultant active peaks during stance phase. Resultant active peaks, times to resultant impact peak, and trunk angles were either not statistically different or were similar. In the equal velocity comparison, results were slightly different, with two additional parameters, hip to toe distance at toe-off and vertical oscillations demonstrating no significant differences.
The Elite group performed BR faster than the Athletic group, with most parameters exhibiting significantly different values corresponding with increased BR velocity. Several of the parameter differences between the groups could have been related to the Elite group's greater velocity and not contributors to that greater velocity. With velocity factored out, the following parameters differed between the two groups: stride length, hip to toe distances at ground contact and toe-off, time to resultant impact peak, loading rate, resultant active peak, time to resultant active peak and initial A-P peak.
Some of these parameters could be related to each other. The first grouping includes: resultant active peak, time to resultant active peak, and hip to toe distance at toe-off. Elite hip to toe distances at toe-off were significantly longer. The longer hip to toe distances could facilitate the greater resultant active peaks and longer times to resultant active peak. Hip to toe distance is the horizontal distance during which the runner's foot is in position to create a propulsive force. If this distance is greater, then there is potential for, (a) greater peak force production (as seen by the Elite group), and (b) later peak force occurrence in the stance (as seen by the Elite group). Elite group resultant active peaks were greater (indicating greater force production), and came later in the stance phase.
Hip to toe distance at ground contact, time to resultant impact peak, initial A-P peak and loading rate could also be related. Kinematically, the group differences in hip to toe distance at ground contact would have resulted in the time to resultant impact peak, initial A-P peak and loading rate differences. A greater hip to toe distance at ground contact (in front of the body's center of gravity) generally means a greater A-P braking force (though not initially in BR). The shorter hip to toe distance for the Elite group, especially in the BRmax condition, could have been a result of the foot moving opposite to the direction of movement (initiating a positive A-P force) prior to ground contact This foot motion (opposite of body movement) prior to ground contact is hypothesized to be the cause of the initial positive A-P peak and could have resulted from the anatomical constraint of maximum hip extension. This foot movement may result from the rebounding of the thigh segment from maximum hip extension with its concomitant knee extension. This peak was dramatically greater for the Elite group compared to the Athletic Group. Also, the shorter Elite hip to toe distance at ground contact compared to the Athletic group could have resulted in less time during the initial impact phase, and a shorter time to resultant impact peak. When time to resultant impact peak is shortened and resultant impact peak remains the same, loading rate increases, which was observed in the Elite group.
Stride length is the remaining parameter that separated the two groups once velocity was factored out. The Elite group's stride length did not change between BR80 and BRmax. This leveling off is similar to reported results for FR of sprinters (Mero, Komi & Gregor, 1992). To achieve a true maximum velocity, a runner has an optimum stride length to stride frequency ratio. Only one combination of the two can produce maximum velocity at any one given instant in time. As velocity decreases, however, a runner can manipulate his stride length and/or frequency to achieve the desired speed. During BR80, the Elite group might have chosen to maximize stride length, but if this was their choice, it was a group choice. It could also have been an effect of their sports training.
The Elite group subjects were expected to be faster at BR because they used it in their sport. It was hypothesized that the Elite group would show a BR training effect, superior natural BR ability, or both. While the Elite group was clearly faster at BR than the Athletic group, they were clearly faster at FR as well, and the percentage difference of maximum BR to FR velocity was only one percent between the groups. This could suggest that to get faster at BR, one should get faster at FR or, simply, that faster forward runners are faster backward runners. Looking at the population data, this conclusion appears sound. However, the more homogeneous the group, such as the Elite group, the less likely a correlation will exist. The correlation of the 30 subject's maximum BR to FR velocities did not explain a significant portion of the variance. Thus, it is more than FR speed that makes one fast at BR.
The Elite group in this study used BR during athletic competition, but it was unclear how much BR they actually practiced. The majority of the Elite subjects were football players who practiced multi-directional movement drills, but not a lot of pure BR drills, or BR drills especially for speed. The fastest Elite subject recorded a velocity about 2 m¥s-1 slower than the average pace of the World Record 100 yard backward run. This difference in velocities could have been due to the short length of the runway as mentioned in the Limitations section of Chapter I. However, several subjects did experiment with shortening their runway length during the BRmax conditions. These changes of between three and five meters did not seem to influence their overall velocity, which could indicate subjects were at maximum BR velocity prior to the data collection area.
If an athlete could run backwards at greater than 7.5 m¥s-1, they would be able to "cover" their opponent while running backwards for up to 20 meters (about 3 seconds), which is a long time in some sports. Perhaps these findings, along with others to follow will give coaches and athletes greater knowledge of BR so that greater velocities can be achieved.
In conclusion, coaches and athletes should understand three findings from this study. First, though specific kinematic and kinetic parameters were identified which separated the Elite from the Athletic group, more study is needed to determine how an athlete could improve these parameters. Second, if an athlete is already fast at FR, then they are not likely to improve their BR speed with FR training alone. BR training may increase BR speed through specific muscular development beneficial to BR velocity and enhance BR balance and timing. Finally, increasing stride length could be the one understandable concept for a coach to pass on to athletes. An athlete's attempt to increase BR stride length by increasing leg drive or propulsion could promote greater levels of the other kinematic and kinetic parameters such as initial A-P peak, resultant active force, and intrinsic support length, that separated the two groups in this study.
Bates, B. T., Morrison, E., & Hamill, J. (1986). A comparison between forward and backward running. M. Adrian & H. Deutsch (Eds.). The 1984 Olympic Scientific Congress Proceedings: Biomechanics (pp. 127-135). Eugene, OR: Microform publications.
Devita, P., & Stribling, J. (1991). Lower extremity joint kinetics and energetics during backward running. Medicine and Science in Sport and Exercise, 23, 602-610.
Dick, F. W. (1989) Developing and maintaining maximum speed in sprints over one year, Athletic Coach, 23, 3-8.
Flynn, T. W., Connery, S. M., Smutok, M. A., Zeballos, R. J., & Weisman, I. M. (1994). Comparison of cardiopulmonary responses to forward and backward walking and running.
Medicine and Science in Sport and Exercise, 26, 90-94. Flynn, T. W., & Soutas-Little, S. M. (1993). Mechanical power and muscle action during forward and backward running. The Journal of Orthopedic and Sports Physical Therapy, 17, 108-112.
Flynn, T. W., & Soutas-Little, S. M. (1995). Patellofemoral joint compressive forces in forward and backward running. The Journal of Orthopedic and Sports Physical Therapy, 21, 277-282.
Hamill, J., Bates, B. T., Knutzen, K. M., & Sawhill, J. A. (1983). Variations in ground reaction force parameters at different running speeds. Human Movement Science, 2, 47-56.
Hamill, J., & Knutzen, K. M. (1995). Biomechanical basis of human movement. Baltimore: Williams & Wilkins.
Hreljac, A. (1992). The determinants of gait transition during human locomotion. Doctoral dissertation, Arizona State University, Tempe.
Jackson, K. M. (1979). Fitting mathematical functions to biomechanical data. IEEE Transactions on Biomedical Engineering, 26, 122-124.
Mann R. A., & Herman J. (1985) Kinematic analysis of Olympic sprint performance: Men's 200 meters. International Journal of Sport Biomechanics, 1, 151-162.
Munro, C. F., Miller, D. I., & Fuglevand, A. J. (1987). Ground reaction forces in running, a reexamination. Journal of Biomechanics, 20, 147-155.
Nilsson, J., Thorstensson, A., & Halbertsma, J. (1985). Changes in leg movements and muscle activity with speed of locomotion and mode of progression in humans. Acta Physiological Scandia, 123, 457-475.
Nordin, Margareta, & Frankel, Victor H. (Eds.). (1989). Basic Biomechanics of the Musculoskeletal System. Philadelphia: Lea & Febiger.
Thomas, J. R., Salazar, W., & Landers, D. M. (1991). What is missing in p < 0.05? Effect size. Research Quarterly for Exercise and Sport, 62, 344-348.
Threlkeld, A. J., Horn, T. S., Wojtowicz, G. M., Rooney, J. G., & Shapiro, R. S. (1989). Kinematics, ground reaction force and muscle balance produced by backward running. The Journal of Orthopedic and Sports Physical Therapy, 11, (2) 56-63. Vilensky, J. A., Gankiewicz, E., & Gehlsen, G. (1987). A kinematic comparison of backward and forward walking in humans. Journal of Human Movement Studies, 13, 29-50.
Winter, D. A., Plauck, N., & Yang, J. F. (1989). Backward walking a simple reversal of forward walking? Journal of Motor Behavior, 21, 291-305.
Winter, D. A. (1990). Biomechanics and motor control of human movement. New York: Wiley.