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

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

Sports are a form of physical movement. 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. These fast movements decisively define our actions, and they 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 mastery" that scientific knowledge can be said to have been utilized in coaching. Any researcher in academia who advocates for sports science would undoubtedly aim for this kind of science-based sports coaching. However, "understanding" and "being able to do" are different. Therefore, within sports science, there exists the academic field of coaching—the middle ground of "how to teach what is understood"—but it is also a fact that coaching is still often performed based on empirical rules.

Writing this far, it may still sound like I believe sports and science are separate and that my thinking is based on applying scientific knowledge 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 it is also the role of a sports biomechanics researcher to carefully 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 Athletic Association Track and Field Club and a member of my laboratory, is a 110m and 400m hurdler aiming for the 2024 Paris Olympics as of 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, past or present. He is the sixth person in history to achieve times of "under 13.49s and under 48.49s" in the world rankings, making him a rising star. Even among top-tier athletes, various forms exist for clearing hurdles, and the differences are striking even at the world champion level. In other words, neither athletes nor coaches can easily 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 the goal is obviously to reach the finish line 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 who is constantly trying to improve their form, one feels compelled to provide some kind of insight.

The difference between hurdling and running is that asymmetrical movements must be incorporated to clear the hurdles. The movements of the arms and legs are asymmetrical, and the torso bends significantly to the side while in the air; this happens even if the athlete does not intend to bend it. The athlete's question of "Why?" is fascinating. During the aerial phase when the body clears the hurdle, no forces other than gravity act upon it. The original momentum—more accurately, the 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 posture, including the limbs and torso, the rotational speed of the body parts and the whole can change. Athletes seem to call this "compensatory movement." To answer his own question of "What kind of compensatory movement is best?", Mr. Toyoda is tackling this difficult problem in his graduation research while simultaneously 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 as a result.

In physics, this is sometimes called the gyroscopic effect based on the law of conservation of angular momentum, and this gyroscopic effect is observed in various situations in sports where the limbs move in high-speed rotation. If a trampolinist jumps out while doing a front flip and wants to twist around the body's long axis (the axis connecting the head to the toes), they must not try to twist on that axis; 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 environment with no tether, no external force acts on the body, 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 by their four legs with zero angular momentum and no initial rotation, 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 is for astronauts to be able to move their bodies into any desired posture of 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 significant forward angular momentum (momentum around the lateral axis) created by the takeoff foot at the moment of jumping, the latter is in a stationary state with almost no rotation. Furthermore, because 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 relatively slow movements.

My advice to Mr. Toyoda is that "the rotation occurring in the air as a visible phenomenon is a result following mechanical principles, and the observed tilt of the body (which could be rephrased as the torso, which they perceive as the body axis) is not occurring because he is trying to tilt it, but is being triggered as a result of the movement of the limbs." This is currently all I can think of. 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 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 power 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 are prepared such as minimizing the energy from muscle activity or minimizing the load on muscles around joints, but in any case, the focus is placed on muscle activity.

However, when observing the muscle activity of a 100m sprinter running at full speed, it has long been known that in the phase where the foot 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, the fact is 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 that the intersegmental force acting on the hip joint (the base of the thigh) governs this movement. It is generated by the acceleration of the pelvis acting on the hip joint.

In the past, farmers used an agricultural 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 rapidly 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 means it is "not being raised, but is rising."

Dr. Archibald Hill, who won the Nobel Prize in Physiology or Medicine, clarified that "when moving muscles at high speed, set the exerted force to zero; if you want to exert maximum force, do not move the muscle." Therefore, "relaxing" without exerting muscle power 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 "training to raise the thigh." As a result, many athletes are forced into training that goes against both mechanics and physiology, despite it being a phase where they should originally stop muscle activity and be relaxed. This is a mistake made by coaching that does not understand science, believing that the athlete is triggering the observed phenomenon through muscle activity.

I understand the need for coaching that utilizes science based on various insights 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 reiterate, "understanding" and "being able to do" 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.