[Feature: Sports and Science] Yuji Ohgi: The Science Hidden in Sports—Cats, Hurdlers, and Astronauts

2024/07/05

My specialization is sports biomechanics, which uses Newtonian mechanics to decipher human movement in sports. When I was asked to write for this feature titled "Sports and Science," I felt a slight sense of incongruity because it gave the impression that "sports" and "science" are separate entities. For me, "the science of sports" feels more appropriate, as I believe sports is one of the representations of science.

Sports are a form of physical movement, but compared to daily movements like sitting, standing, or reaching for an object, sports movements are generally dynamic—with the exception of extremely static competitions like archery. In other words, they are often "fast" movements, involve a wide range of travel, or involve swinging equipment at speeds much higher than the body parts themselves. This factor of fast movement decisively dictates our actions, and it can be deciphered thanks to Newtonian mechanics.

However, "deciphering" is a perspective from the observer's side. For the athlete receiving coaching, "acquiring and mastering" is more important than "deciphering." It is only when one can "apply what has been deciphered to the process of mastering" that scientific knowledge can be said to have been utilized in coaching. Sports coaching that utilizes such scientific knowledge is undoubtedly what any researcher claiming to study sports science in academia would aim for. However, "understanding" and "doing" are different. Therefore, the academic field of coaching exists in sports science as the middle ground of "how to teach what is understood," but it remains a fact that coaching is still often conducted based on empirical rules.

Writing this far, it still sounds like I am based on the idea that sports and science are separate and that scientific knowledge is applied to sports. However, when you listen to the voices of athletes, you find very interesting and seemingly strange physical phenomena hidden in their performance and form. I believe the role of a sports biomechanics researcher is to properly observe and listen to these voices and decipher the essence of the physical phenomena—the science—lurking behind those words.

Ken Toyoda, the captain of the Keio University Athletic Association Track and Field Team in my laboratory, is a 110m and 400m hurdler aiming for the 2024 Paris Olympics at the time of writing (Editor's note: Mr. Toyoda won the 400m hurdles at the Japan Championships on June 29 and was unofficially selected as the representative for the Paris Olympics in that event). Even globally, there have been very few athletes who compete in both events from the past to the present. He is only the sixth person in history to achieve times within "13.49s and 48.49s" and is a rising star. There are various forms for clearing hurdles even among top athletes, and the differences are significant even at the world champion level. In other words, neither athletes nor coaches can judge which form is best. The answer to the simple question, "Whose movement should I imitate to get faster?" probably cannot be found through observation alone. The differences in form are particularly striking during the aerial phase of clearing the hurdle. Since winning simply means reaching the goal first, one could dismiss it by saying any movement is fine as long as it is the individual's unique form. However, for an athlete constantly trying to improve their form, I want to provide some kind of suggestion.

The difference between hurdling and running is that an asymmetrical movement must be incorporated to clear the hurdle. The movements of the arms and legs are asymmetrical, and the torso bends significantly to the side in the air; this happens even if the athlete does not intend to bend it. The athlete's question of "Why?" is intriguing. In the aerial phase where the body clears the hurdle, no forces other than gravity act upon it. The original momentum—more accurately, linear momentum—is maintained, the athlete's center of gravity falls in a parabolic arc, and the angular momentum of the rotation maintains the state it had at takeoff. However, while the angular momentum representing the rotational force is maintained, the "angular velocity of the body" can change. By changing the posture of the limbs and torso, the rotational speed of the body parts and the whole changes. Athletes seem to call this a "compensatory movement." To answer his own question of "What kind of compensatory movement is best?", Mr. Toyoda himself is tackling this difficult problem for his graduation thesis while aiming for the Olympics.

When he intentionally changes his arm swing or folds his legs to improve his form through trial and error, "unintended movements" actually occur in the air. This is the interesting point from a mechanical perspective. It is widely known that this phenomenon also appears in the magnificent rotational techniques of gymnastics, trampolining, and diving. When a human jumps into the air with rotational momentum and tries to initiate a twist around a certain axis, a rotation around a third axis—different from the original axis of rotation and the axis they just tried to create—ends up occurring.

In physics, this is sometimes called the gyroscopic effect based on the law of conservation of angular momentum, and this gyroscopic effect is recognized in various situations in sports where the limbs move in high-speed rotation. If a trampolinist jumping with a front flip wants to twist around the longitudinal axis of the body (the axis connecting the head to the toes), they must not try to twist on that axis directly; instead, they must swing their arms as if rotating on the plane of their face. The mainstream coaching for mastering this involves accumulating experience from a young age.

Back in the 1990s when I was a graduate student, NASA issued a request to biomechanics laboratories around the world to research specific proposals on how astronauts should change their posture in a zero-gravity environment during extravehicular activities.

In a zero-gravity space with no lifeline, no external forces act, so even trying to look behind oneself cannot be easily achieved. However, cats are born with the divine skill of the "cat righting reflex." Even if dropped upside down from a high place with their limbs held, starting from a state of zero angular momentum with no rotation at all, they can land perfectly. Cats are smarter than astronauts.

Therefore, astronauts must master the technique of the cat twist. This remains a cutting-edge topic that JAXA researchers continue to study today, serving as an example of complex physics. However, the goal is not just to know the principles of complex physics; the expectation here is for astronauts to be able to move their bodies into any desired posture by their own will. While respecting cats, hurdlers and astronauts share the commonality of needing to master ideal movements. However, the difference between a hurdler and an astronaut is that while the former has considerable forward angular momentum (momentum around the mediolateral axis) created by the takeoff leg at the moment of jumping, the latter is in a stationary state with almost no rotation. Furthermore, since a hurdler must control their own posture within the brief time they are in the air, the level of difficulty is considerably higher than that of an astronaut's more leisurely movements.

As for advice for Mr. Toyoda, the best I can think of for now is: "The rotation occurring in the air as a visible phenomenon is a result following mechanical principles; the observed tilt of the body (which could be rephrased as the torso they perceive as the body axis) is not caused by an attempt to tilt it, but is triggered as a result of the movement of the limbs." Unfortunately, I do not have the confidence to solve the optimal control problem for the body movements of a multi-link structured athlete sprinting at high speed, and looking across the research field, I don't think there are researchers in the world who can solve this. Knowing that the astronaut problem is still a subject of continuous research today makes me realize once again how difficult the problem is.

It is interesting that in high-speed human movement, as in this case, even if one exerts muscle strength to move a joint with the intent to move it, a movement contrary to that intention can occur. Training for sports that embody this can be seen as a process of iteratively seeking an optimal solution. In some cases, one might fall into a local optimum and be unable to escape, even if there is a global optimum that would further improve performance. In other words, there are likely many athletes in slumps who are unable to change their form. In many musculoskeletal optimization simulations, objective functions such as minimizing energy from muscle activity or minimizing the load on muscles around joints are prepared, but in any case, the focus is placed on muscle activity.

However, observing the muscle activity of a 100m sprinter running at full speed, it has long been known that in the phase where the leg that kicked the ground is swung forward and the thigh is raised high, the activity of the quadriceps—the muscle group that raises the thigh—disappears. In other words, it is a fact that "the phenomenon of the thigh rising is not the act of raising the thigh; it is not muscle activity." It has also been clarified that the mechanical principle here is governed by the intersegmental force acting on the hip joint at the base of the thigh. It is generated by the acceleration of the pelvis acting on the hip joint.

In the past, farmers used a tool called a flail for threshing. This is a structure where two sticks are connected by a joint; when one stick is moved back and forth, the other connected at the tip spins around. Even without rubber or a power source equivalent to muscles around the joint, it was possible to make the tip side spin just by the force acting on the axis of the joint. The human body is exactly like a flail mechanism; if force acts on the base joint, the tip side will spin at high speed. The appearance of a sprinter's thigh rising high is a case of "it is rising, not being raised."

Dr. Archibald Hill, who won the Nobel Prize in Physiology or Medicine, clarified that "when moving muscles at high speed, reduce the force exerted to zero; if you want to exert maximum force, do not move the muscle." Therefore, "relaxing" without exerting muscle strength when you want to move at high speed makes sense from a physiological perspective. And sprinters are already practicing and embodying the results of science.

Many coaches who see the fact that the thigh is rising high try to make athletes do "thigh-raising training." As a result, many athletes are forced into training that contradicts both mechanics and physiology, despite it being a phase where they should originally stop muscle activity and relax. This is an error committed by coaching that does not understand science, believing that the athlete is causing the observed phenomenon through muscle activity.

I understand the need for coaching that utilizes science based on various findings and research, but I believe that a coaching stance of always thinking deeply about the essence of the physical phenomena lurking behind the athlete's words is what constitutes sports coaching that utilizes science. However, to repeat, "understanding" and "doing" are different, and there is still room for improvement in the "how to teach" part. One could say there is a profound depth in the act of a human teaching another human rooted in science. I believe this part will likely not be replaced by AI for some time.