Neeraj Chopra about to launch his winning javelin throw at the Tokyo Olympics. Photo: Olympics/YouTube
- In 1984, World Athletics decided to change the rules of javelins’ construction based on the laws of physics that govern their flight.
- Since then, javelins have had to have a parabolic flight path – and Uwe Hohn’s record throw of 104.8 metres became unbeatable.
- Sporting bodies, coaching staff and sportspersons all use physics to make the best of the rules that limit them and the technologies that enable them.
By the time the Tokyo Olympic Games concluded over last weekend, Indian sportspersons had returned home with seven medals – four bronze, two silver and one gold. The last one – India’s first gold in an athletic sport at the games – was the result of Neeraj Chopra’s stunning javelin throw of 87 metres.
The motto of the Olympics is ‘citius, altius, fortius’ – Greek for ‘faster, higher, stronger’. As such, at the heart of all the events in which athletes compete is motion, either of the sportsperson themselves or of something thrown (shot put, discus, javelin) or propelled (rowing, sailing) – and often a mix of both (football, hockey). And the games prize those who go faster and higher, and are stronger while they’re at it. However, while the events test the physical and mental strength, stamina and skills that produce this motion, the humans wouldn’t have been able to accomplish a lot of what they have without advances in physics, mathematics and computing.
For example, champion gymnast Simone Biles has been able to perfect complicated jumps, flips and mid-air pirouettes that wouldn’t have been possible without sensors and computer simulations to define what moves are possible, and in which order. Even the surfaces around and over which athletes like her move and the fabrics they wear required years of painstaking research and modelling to improve for speed, density, flow, heat regulation and texture.
Advances in sensors and modelling feeding into physical training routines have also contributed to the bars of success moving higher. Anna Kiesenhofer, the Austrian mathematician who won gold in the women’s individual cycling race at the Tokyo games, tweeted (and then deleted) about how she used a sensor to monitor her core body temperature during training.
Since we’re still celebrating Neeraj Chopra’s golden achievement, let’s consider javelin-throwing itself in a bit more detail.
In 2011, SportsRec published an article describing the sequence of muscle movements involved in throwing a javelin – from ‘carrying’ it to launch:
Your biceps contract to flex your elbow during the carrying phase. Your deltoid, or shoulders, flex to lift your arm up so the javelin can be held higher and raised to your forehead. During the withdrawal phase, your back muscles contract as you bring the javelin back. The non-throwing arm is extended forward as your throwing arm is brought back. This movement stretches your pectoral, or chest, muscles. From there, a stretch reflex, an involuntary contraction of your chest, helps bring your throwing arm forward with increased force. During the delivery phase, your shoulder initiates the movement, transferring movement through your triceps, wrists and fingers to extend your throwing arm forward to release the javelin.
By elucidating these biomechanical characteristics of athletic activity, and the underlying training and dieting regimens required to hone them, an athlete’s coaching staff can isolate and improve even smaller parts of her performance. Since even the tiniest difference in the various aspects go into an athlete’s ability to throw can all add up to making a winning performance, there is intense effort to come up with innovations in equipment, training, nutrition and post-exercise recovery.
All this innovation is fundamentally focused on reconciling the athletes’ instruments with their skills. And not just any skills – the skills that are now codified in excruciating detail by the world’s sporting bodies.
For example, the sport of throwing javelins has its roots in ancient human hunters throwing their spears to kill animals – either for food or self-defence. As long as their spear pierced a charging bull, they were okay. It didn’t matter how quickly the spear flew or what its trajectory was. Not many of us throw spears to kill animals these days – but those who throw javelins at the Olympics need to follow some rules defined by a body called World Athletics (formerly International Amateur Athletic Federation).
Neeraj Chopra, who won gold for India, was coached by German track and field athlete Uwe Hohn. In 1984, Hohn created a world record by throwing a javelin 104.8 metres. It hasn’t been broken to this day. Any prehistoric hunting party would have been elated to have Uwe Hohn in its ranks. But shortly after Hohn’s feat, World Athletics changed the rules of javelin-throwing such that records like his became impossible to repeat.
The javelins of his day had been modified to get aerodynamic lift – like a wing – which made them fly longer. However, they also flew almost flat, making it difficult to pinpoint the location when they eventually hit the ground.
So World Athletics decided to change the rules of their construction based on the laws of physics that govern their flight.
Specifically, the body moved the javelin’s centre of mass forward by 4 cm for reasons that were not technically sport-related. One of them was that Hohn’s throw, of nearly 105 metres, was in danger of going past the size of normal stadiums! By moving the centre of mass forward, and away from the javelin’s centre of pressure, World Athletics could ensure there would be no flat throws.
Now, did the decision limit the amount of speed, altitude and strength of the athletes themselves? Probably not. Even if athletes can’t throw javelins much beyond 100 metres under the new conditions, they still have to figure out how best to combine their physical (and mental) abilities to throw javelins farther. Put another way, the sport tests the athletes’ abilities; and as long as the sport tested them well, it needn’t matter how far or high they could throw.
(And by confining the sport to normal-sized stadiums, they ensured sporting events could remain economically feasible, including through TV coverage. This could only be good for javelin-throwing itself.)
As a branch of science, physics is concerned predominantly with objects in motion. And because the Olympics are all about being in motion with the most efficiency that humans can muster, concepts in physics can teach us a lot about what kind of thinking and practice goes into throwing a javelin so far that people celebrate you for it.
For starters, you may remember from high-school physics that to throw a ball as far as possible, the angle of launch – or release – should be 45º relative to the ground. But your teacher probably didn’t tell you that it’s 45º only if the point from which the ball is thrown and the point at which the ball will land are on the same plane. What happens when you’re holding a javelin 1-2 m above the ground but the javelin needs to land in the ground, which is on a lower plane? It means the ideal angle of release is around 36º, not 45º.
But this isn’t the only angle that matters. The angle of attack is related to how far the javelin will travel. It’s equal to the difference between the angle of attitude and the angle of velocity vector. The angle of attitude is the angle the javelin (from tip to tip) makes with the ground. The angle of velocity vector is the angle the javelin makes with the ground near its centre of mass.
Normally, the force of gravity acts on the entire javelin. But what if it were to act only on one point on the javelin, and the javelin still behaved as it would have if gravity had acted throughout its body? This is possible: this point in the javelin’s body is called its centre of mass.
The ideal angle of attack is 0º. Throwers don’t have the luxury of solving math problems with their bodies on the field. (Imagine Neeraj Chopra stopping to use a protractor at the moment of throw or P.V. Sindhu pondering the number of seconds she has to flick the shuttle down before her opponent can get under it.) Instead, they use more intuitive solutions. Javelin-throwers, for example, attempt to throw “through the point”.
Let’s get even more technical. When World Athletics moved the centre of mass forward by 4 cm in 1986, it moved the point 4 cm ahead of the javelin’s centre of pressure.
Those on or near Earth’s surface will always feel gravity acting downward. The same is true for the javelin: gravity will dictate the javelin’s rate of downward motion. The javelin’s horizontal motion is, on the other hand, influenced by its centre of pressure – the point through which all the aerodynamic forces on the javelin act. These forces include the lift (which pushes the javelin upward) and drag (air friction, which limits how well the javelin can pierce forward).
The trajectory of every javelin throw is determined by how well these three components of motion – upward, downward and forward – come together.
When the centre of mass and centre of pressure are at the same point, flat throws like that of Uwe Hohn in 1984 become possible. Here, if the aerodynamic lift is high enough and the drag low enough, they can together almost counteract the effect of gravity and keep the javelin moving straight and low through the air. The momentum it accumulates will also allow it to slide on the ground once it lands. But when the centres of mass and pressure are separate, the amount of aerodynamic lift available to the javelin will be lower than its downward tendency. So once it starts dipping, it will continue dipping, and land by piercing the ground.
This was the other reason World Athletics modified the javelin rules in the late 1980s. Even before Hohn’s throw, judges had been having a tough time determining where flat throws should be measured. And after the rules were modified, for men in 1986 and for women in 1999, the effects on distances of throw were clear.
Given the three broad kinds of forces acting on a javelin – upward, downward and forward – we can also guess how other changes to the rules of javelin-throwing could affect the sport. For example, a hollow javelin would be lighter and travel higher, but it also resulted in flatter landings that World Athletics prohibited from 1986.
For another, and also as part of the 1986 rules, World Athletics required javelins to have less surface area in front of the centre of mass and more behind it. As a result, once the javelin starts to travel towards the ground, it ‘feels’ compelled to point even more towards the ground. And once it lands, it pierces the ground more firmly.
Third, the 1986 rule-change doesn’t directly lead to the sport of javelin-throwing as we know it today. Instead, between April 1986 and August 1991, many sportspersons used the so-called ‘new javelin’ – a javelin that met World Athletics’ requirements but also had a rough surface that was intended to reduce drag. In this time, Seppo Räty of Finland set the men’s world record of 96.96 m. But from late 1991, World Athletics demanded smooth surfaces, annulling previous records and commencing the (ongoing) era of the ‘current javelin’.
Today, both men’s and women’s javelins must be made of steel. The men’s javelin needs to weigh at least 800 g and span 2.6-2.7 m. The women’s javelin must weigh at least 600 g and span 2.2-2.3 m. In both cases, the thrower must hold the javelin by the grip – 150 mm wide, made of cord wrapped around the javelin’s centre of mass. The grip must be 0.9-1.06 m from the tip for men and 0.8-0.92 m from the tip for women.
The laws of physics have a way of imposing limits on what we can do no matter how much we practice doing them. For example, however light an object is, it can’t escape completely from Earth’s gravity short of a velocity of 11.2 km/s. Similarly, the laws impose real, hard limitations on how far humans can throw spears according to the World Athletics rules.
The current world-record holders for javelin-throwing are Jan Železný (men, 98.48 m) and Barbora Špotáková (women, 72.28 m). The next-longest throws have been short by 72 cm and 58 cm, respectively. The progression of the records paints a similar picture. Between 1993 and 1996, the men’s record advanced thrice, by 4.08 m, 12 cm and 2.8 m (all by Železný). Similarly, between 2001 and 2008, the women’s record advanced thrice, by 2.06 m, 16 cm and 58 cm (twice by Osleidys Menéndez and the latest by Špotáková).
These numbers go to show that the more we practice and the more we innovate, the margins of victory are also becoming smaller. In the match that Neeraj Chopra won with a throw of 87.58 m, the silver and bronze medallists were only 91 cm and 2.14 m behind.
From 708 BC (when javelin-throwing became part of the Olympic Games) to the 20th century, athletes may have been able to intuit their way to success. But in the 21st century, physics doesn’t just offer interesting trivia about the mathematics of a victory, and intuition alone doesn’t triumph. Sportspersons and their coaching aides (must) use both to improve their team’s performance to the extent possible, or they may miss the gold by a few millimetres or milliseconds.
This article was composed based on Arnab Bhattacharya’s Twitter thread on August 8, 2021.
Arnab Bhattacharya is the director of the Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai.
Vasudevan Mukunth edits The Wire Science.