Patterns Of Support Force Available In A Bending Leg

    This new study by Bob Mackenzie shows the importance of straighter leg action in many events, especially jumping events and particularly for well-trained athletes. Allowing greater bend in performing an event reduces available force.

By Robert J. Mackenzie, Physics Teacher and Jumps Coach Webb School of California, Claremont, California
 

ABSTRACT

    The leg strength of athletes is seen to vary with the straightness of the leg. Athletes, as well as non-athletes, gain strength with straighter legs and lose strength with more leg bend. For relatively untrained athletes, the leg gains around a third of a percent in strength with each degree of increased straightness. For athletes, especially those trained in plyometrics, the leg strength gain is two to three times more-up to one percent for each degree of reduced bend. Increased leg strength with leg straightness gives a partial explanation for the advantages of the flop technique in the high jump and one of the several reasons for some of the typical coaching cues, such as "Keep the toes up" or "Run tall" in sprinting and "Take off vertically" in the high jump. Attaining strong takeoff force through leg strength is a goal in all jumps.
 

INTRODUCTION

    The thigh, the calf, and the knee joint make up key components of the leg support system used throughout track and field. A complex system of muscles, tendons and bones keeps the knee joint stable under stress and allows the leg to perform its functions in support, running, and jumping. Any system that can rotate is stable when the torques, or rotational forces, acting on the members of the system are in balance.
    A simplified stick figure representing the knee joint, thigh, and calf in static equilibrium is shown in Figure 1.

    The force of the athlete's weight pushes down and a ground reaction force acting in an opposite direction, but with an often greater magnitude than the weight, pushes up and both forces act at a lateral distance from the knee joint, which is the center of rotation. Since the compressive forces under discussion do not point through the knee joint, but at an offset distance, they cause torques, which act to cause the knee to rotate closed. These torques are balanced by opposing supportive torques from the muscular system of the knee, which is usually attributed to the quadriceps muscle group. That is, torque derived from muscular forces keeps the leg straight while gravity and ground reaction forces act to bend the leg. The sum of the torques of half of the simplified system is: F d = F 1 cos θ/2 = Fq dq where 'F' is the force that is supported by the musculature of the knee, '1' is the length of the thigh or calf member, 'd' is the distance by which the force 'F' misses the knee joint, θ/2 is half of the angle between the thigh and calf members of the system, and 'Fq dq' is the torque of the knee musculature, typically attributed to the quads (Fig 2).

    If the quads were simple and only pulled in one location with a fixed force, the force that the leg could support would be: F = leg muscular torque / (1 cos θ/2) This means that a nearly straight leg could support a very large force and a bent leg could only support a lesser force. It is assumed that the knee is not locked at exactly 180º at any time and that the leg system is not subject to longitudinally uniform columnar buckling loads. It is assumed that the knee musculature is weaker than the bone strength of the legs. This simplified model is not by any means a complete representation of the true situation, however. It simply shows that it is expected that the knee joint system should be stronger with straighter legs and weaker with legs that are more bent. The simplified model predicts that the supportable force would radically decrease with the first bending of the knee and then the loss would taper off (Fig. 3). It is hoped that this study will show more accurately the true nature of the supportable force of the leg as the leg bends.

METHODS

    Twenty-two volunteers, sixteen male and six female of athletic ability ranging from completely novice non-athletes to somewhat well-trained high school and collegiate sprinters and jumpers, were asked to perform a seated leg press release with steadily increasing weight supported by one leg. After lifting the weight with two legs, the volunteers were asked to drop one foot off the press platform and then to slowly lower the weight with the one remaining leg until the leg could no longer support the weight and the leg buckled (Fig 4).

    The angle that the calf made with the thigh at the moment of buckling was visually estimated against a large protractor in the background. The percent of maximum force was then plotted against the leg angle. A sample measurement is shown in Figure 5. The volunteers were given rest as desired between each measurement. Weights were added and removed by random amounts. The number of data points for each volunteer varied with the ability of the volunteer and with his or her patience. Most volunteers had five or six data points. Some had more, as they could press over a greater range of weights and tolerated repeated measurements. Some beginners only had three data points, which was the least number.

RESULTS

    The resulting graphs of the percent maximum force versus leg bend angle for all volunteers were roughly linear, instead of a concave upward curve. In fact, if there was any curvature shown, it was slightly concave downward, but any such curvature was slight. Six of the subjects showed slightly concave down relationships and two could be viewed as ever-so-slightly concave upward. The remainder were extremely linear. The least slope of the strength/ angle graph was 0.3 for a completely untrained, un-athletic volunteer. He lost about a third of a percent of leg strength as his leg bent each degree more. The greatest was a slope of 0.9 for a well-trained athlete, who trained quite a bit in the weight room. He gained nearly one percent in strength for each degree straighter that he kept his leg.
    The trend of greater slope was observed with athletic volunteers and lesser slope was observed for un-athletic volunteers. A rough estimate of athletic training from 1 to 10 was fairly subjectively assigned to each volunteer. Training level 1 was assigned to the absolutely nonathletic volunteers and a high of 8 was assigned to four well-trained high school and collegiate sprinters and jumpers. An elite athlete would be a 10. When the slope of the strength/ angle graph was plotted against the assigned training level number, it was observed that there was an increase in slope from non-athletes to athletes (Fig 6). The trend was similar for both females and males. It is surmised that the increase in slope for trained athletes can be substantially attributable to improved neuromuscular coordination gained with plyometric training that caused more muscular engagement and recruitment among the trained athletes and emphasized action with little leg bend. It is also possible that the trained athletes did not try as hard during the bent-leg failure lifts with lesser weights.

    Among the level 8 athletes, the lowest slope (0.4) was for a girl who emphasized deep squats in her program and who focused very hard during the lesser weight portion of the testing; the highest (0.9) was for a boy who sprinted, jumped, and did lots of plyometric work. It is guessed that the squats of the girl enabled her to support greater weights with her bent leg and that the dominantly straight leg training of the boy overemphasized that aspect of his performance. The girl who emphasized squats was the only athlete sampled who made extensive use of weight training in her regimen. This might possibly explain why her data point lies far off the trend of those measured here. Nevertheless, even she experienced a straight-line relationship of increased strength as her leg became straighter.

APPLICATIONS

    Beginning jumpers are often observed to bend their legs excessively in the takeoff. Typical beginning long or high jumpers, for example, might bend the leg to somewhere in the ballpark of 110 degrees. They are also seen to change their direction of motion comparatively little in the jump because they exert little force in the takeoff. An experienced jumper of comparable size and strength might bend the leg to 150-plus degrees from thigh to shin, or about 40-plus degrees less leg bend from straight than a beginner.
    This study shows that beginners push with little relative strength --- possibly less than 70 percent of their maximum --- and that experienced jumpers can command a greater percent of their maximum strength in the jump-maybe more than 85 percent. Furthermore, experienced jumpers can command a greater maximum force. So, the maximum force that an experienced jumper could recruit might be more than double that of a less well-trained athlete who allows excessive bending. It appears that all athletes can command greater forces by keeping their legs straighter at critical times.
    The volunteers measured in this study all (with the exception of the girl trained in squats) supported similar weights relative compared to their body weight, with a 90° leg bend. Since these athletes started with roughly similar strengths at a 90° leg bend and the experienced athletes gained a much better percentage from that point with increased straightness, experienced athletes have more to gain with straighter legs and more to lose if they allow their legs to bend at those critical times.
    In the high jump, it has often been expressed that the success of the Flop technique can be attributed to a clearance form that allows an a thlete to clear a bar sometimes higher than the center of mass trajectory. But it is seen that most jumpers do not effectively use clearance techniques that can give them much, if any advantage over the old straddle style. The center of mass of many flop high jumpers is seen to pass several inches over the bar in jumps where the athlete barely clears. Yet, floppers still almost always jump better than the old straddlers.
    In any high jump, a jumper needs to lower the center of mass in the penultimate step in order to set himself up to push effectively against the ground and gain height in the takeoff. In the straddle, jumpers trying to get low would scrape their feet against the ground in the takeoff. This limited their ability to get very low in preparation for the jump. Straddlers lowered the body while remaining in an upright plane, so the point of a straddler's maximum leg bend occurred when the center of mass was close to being over the takeoff foot.
    Floppers, on the other hand, lean away from the bar in the plant, so they take off in a twisting motion, beginning in an oblique, non-vertical plane and ending with the body vertical. A flopper's point of maximum leg bend occurs when the center of mass can be farther from the takeoff foot for the same amount of pre-jump lowering.
    Consequently, floppers can keep the takeoff leg straighter during the takeoff than straddlers can. This allows floppers to exert a greater impulse in the takeoff than straddlers by means of stronger forces. A greater force available to floppers allows them to use more speed in the approach than straddlers, have more change in the velocity direction angle, or both. This study suggests that straighter legs causing greater takeoff forces partially contribute to the greater heights achievable by floppers over straddlers.
    High jumpers are taught to take off exactly straight up and down. This is partially explained by the fact that taking off straight up and down maximizes the center of mass height upon leaving the ground. Taking off straight up and down also maximizes the amount of rotational velocity (flip) that the flopper can generate in the jump because of a more complete time-application of torques through the vertical and because of an avoidance of applying any reverse torques past vertical. Additionally, taking off exactly vertically has force ramifications.
When a high jumper takes off vertically, the leg can remain straighter than if the takeoff is inclined because if the takeoff is vertical, the center of mass can stay farther from the takeoff foot than if the jumper leaves the ground inclined to the vertical. The curved path on which the jumper travels in the takeoff dictates the distance from the takeoff foot and the straightness of the leg.
    Figure 7 illustrates how a jumper who takes off inclined to the bar gets "closer" to the takeoff foot. Thus, with the body getting closer, the leg bends more. As has been shown, when the leg bends more, the leg weakens. The weaker leg contributes to the leg buckling, if the athlete goes fast. The athlete who allows his center of mass to pass over his takeoff foot in an inclined takeoff might also simply approach more slowly, subconsciously avoiding the buckling that might otherwise occur. So, taking off vertically gives the high jumper more takeoff force and he can use more speed.

    As the jumper passes over the takeoff foot, the time of the jump takeoff is extended slightly. The time during which an athlete pushes against the ground has been observed to be an "energy drain." That is, as a jumper is in contact with the ground, the total kinetic and potential energy package that the athlete develops in the approach is drained away the longer the athlete is in ground contact.
    This is possibly attributable to a loss of elasticity in the muscle group with time, which in turn is possibly due to the muscular contractile elements giving way with time. Contact with the ground is a necessary factor in any jump, but excess contact with the ground takes away from the athlete's speed/ height combination.
    As athletes are in contact with the ground more, the leg bends more at maximum flexion. It is possible that a portion of this decrease in energy, as the athlete is in excess contact with the ground, comes from a reduced ability to push as the leg bends to a greater extent.
    The cues sprinters get, as well as jumpers, can also be seen to have straight leg and force ramifications. Sprinters are encouraged to "Run tall" and to "Keep the toes up" and athletes often ask why. It is often explained to sprinters that the calf and Achilles tendon are pre-tensioned with the toes up and that the foot strike is thereby made with a "stronger spring" than if the toes point down. It is often explained that both "'staying tall" and "keeping the toes up" help to avoid overstriding, which produces negative forces, slowing the athlete.
    In addition to this, if the sprinter settles down in the sprint, or points the toes down, the support leg, either at foot strike or in passing over the hips, will be bent more than if running tall or keeping the toes up. In this situation, the athlete cannot push as effectively or as quickly off the ground because there is less force available from the bent supporting knee musculature. The results of this study suggest that a straighter leg can provide much greater forces that can be exerted through the ground with a tall running stance and with the toes up.
    Long and triple jumpers need to exert huge forces up and back in the takeoff in order to change the direction of motion as much as possible. There is evidence to suggest that the takeoff leg force available to the jumper acts as a bottleneck to the jump in addition to the limits imposed by the jumper's speed. At the nearly maximum speeds of the approach, the takeoff angle is largely determined by the available force of the takeoff leg. Pushing slowly and allowing the leg to bend excessively in the takeoff greatly reduces the available force to the jumper. Conversely, a fast push keeps the leg straighter and keeps the leg from buckling as easily, yielding greater forces, greater takeoff angles, and less time on the board.
    In many cases in track and field, it can be seen that a straighter leg gives better results than a more bent one because of more available force. The forces sought by athletes can be turning forces, supporting forces, or accelerating forces. In many, many cases, a straighter leg giving more force is beneficial to the athlete.

FROM TRACK COACH 182