Sport isn't just a display of physical strength or natural talent. It's also a complex series of movements, reactions, and decisions, all influenced by the laws of physics. By harnessing the technology at our fingertips, we can not only enhance our performance but also deepen our understanding of the scientific principles underlying each movement, every jump, every strike. So, ready to combine your passion for sports with a dash of science? Grab your smartphone and let's begin the exploration!

*Before we start however, a word of caution: smartphones are delicate devices, so care must be taken to secure them when used as measuring instruments.*

**Table of contents**

__Measuring Instruments__ - __Running__ - __Trampolining__ - __Pole Vaulting__ - __Basketball__ - __Discus Throw__ - __Cycling__ - __Boxing and Martial Arts__ - __Diving__ - __Pétanque__ - __Badminton__ - __Soccer__ - __Parasports/Adaptive Sports__ - __Conclusion__.

**Measuring Instruments **

To carry out the experiments described in this article, you will use __the sensors of a smartphone or tablet__. The ones we will use are present in most digital devices. The data from these sensors can be collected using scientific applications available on the iOS or Android stores. The __free FizziQ app__, available for iOS and Android, is perfectly suited to analyzing data for the experiments we offer.

**The GPS:**Through the analysis of signals from satellites, a smartphone's GPS chip allows for measuring speed, altitude, and distances. This data is useful for assessing the performance of runners or cyclists and identifying the factors influencing their results.**The pedometer:**The pedometer measures the cadence of a walk or run. In sports, it evaluates the rhythm of a race and its consistency.**The accelerometer:**This instrument measures linear and absolute acceleration. It provides valuable information for analyzing jumps in trampoline activities or the energy of impacts in boxing.**The video camera:**Used with video analysis software, it can determine an object or person's position over time, from which one can deduce speed, acceleration, or energy. The collected data provides insights into trajectories in basketball, energy transformation in pole vaulting, the path of a shuttlecock in badminton, the collision of pétanque balls, the Magnus effect in soccer, or the position of the center of gravity during a dive.**The gyroscope:**This sensor determines the rotation speed of the smartphone. It can be used in analyzing rotational movements such as discus or hammer throws.**The microphone:**Used in conjunction with another instrument like the accelerometer, it measures athletes' reaction speeds, for example, at the start of a race.

Now, let's explore how we can use these measurement tools to better understand various sports.

**Running**

Running is probably the sport that can be most easily studied. Seemingly simple, it is in reality a complex dance of biomechanics, physiology, and psychology. Its study addresses the themes of performance, reaction speed, and human body physiology.

**Firstly, the analysis of performance.** By measuring the speed recorded by the GPS or the number of steps over time measured by the pedometer, one can study the speed of the race relative to the distance, its regularity, the cadence of the steps, and their length. By comparing these parameters for different runners, one can begin to understand what determines each one's performance.

Another topic of interest concerns **the start sequence for running**. This crucial moment can be studied by simultaneously recording the sound volume and the acceleration measurement (Duo Screen function in FizziQ). By comparing these two pieces of information, one measures the runner's reaction speed, which is the delay between the sound signal and the athlete's movement. This time can be compared with that of other athletes.

A final topic concerns **the medical risks associated with running**. By using the accelerometer, one measures the impact force of each step on the legs, which is typically 5 to 10 times the runner's weight, or 5 to 10 g. This observation opens discussions on many questions, such as whether it's healthier to run barefoot or with shoes, or if practicing this sport from a certain age is recommended for the joints.

**Trampolining**

The trampoline, much more than just a child's play, is in fact **an extremely interesting experimentation field for gravitation**. Using the accelerometer, one can study numerous aspects of the jump, especially bounces and flight.

It's always a bit challenging to conceptualize that during the flight phase, the athlete is not only in free fall, but from their reference frame,** he is also in weightlessness,** __as Einstein demonstrated in a famous thought experiment__. During the flight phase, the accelerometer will thus display zero acceleration, confirming that the athlete is in a state of weightlessness. The phenomenon, which may seem fleeting on a trampoline, can be accurately evaluated: how much time does an athlete actually spend in a state of free fall? Do we verify that the absolute acceleration is zero?

Upon landing, other questions can be addressed: what is the acceleration when the athlete makes contact with the mat again, and how does it influence the next jump? What is the damping if the athlete takes no action?

**Pole Vaulting**

The pole vault, an aerial ballet where humans seek to defy gravity, is a tribute to human biomechanics and the laws of physics. Behind every launch lies a choreography of angles, forces, and pivotal moments, each playing a crucial role in the quest for height.

During the run, **the athlete-pole system acquires a certain kinetic energy**. This energy is transformed into the pole's elastic energy after planting, and the athlete takes off. Through a swinging motion, the vaulter further increases the elastic energy. During the ascent, the pole releases, converting the elastic energy into the athlete's potential energy. During the inversion phase, the athlete continues to rise upside down and clears the bar after a final push. The pole vault is, therefore, a highly complex and technical movement.

The best tool for studying the mechanics of pole vaulting **is the kinematic analysis of a video or chronophotography**. One can film a vaulter or __use a video from the FizziQ kinematic library__. With this tool, one can study how, during each phase, the transformation and input of energy allows the athlete to reach the highest possible point. For example: what is the contribution of the run to the height gain? What is the elastic energy stored in the pole? Does the final push help the athlete go higher? How does the tipping movement create more elastic energy?

To delve deeper, we have written an__ article that provides details of the various sequences and the energy balance that kinematic analysis allows__.

**Basketball**

The flight of a basketball towards the hoop is more than just a sporting gesture; it's a living parabola, a perfect illustration of the laws of physics that can be easily studied using a smartphone's camera and the __FizziQ kinematic analysis module__.

Studying the trajectory of a free throw in basketball is a very interesting exercise for students, __who can also make their own video for analysis.__ For this, the smartphone is positioned at a sufficient distance to avoid distortions due to the wide-angle. The shot must remain fixed during the video's duration. A frame rate of 30 or 60 frames per second will be used. The hoop's height can serve as a scale (see this link for more details on creating videos for kinematics).

From this video (or one downloaded from the internet), the motion curve is then analyzed. Its equation, which is a parabola, will be determined. This calculation will allow high school students to estimate the acceleration due to gravity, g.

**Discus Throw**

The discus throw is an energy transformation exercise that requires precise technique to achieve the best results. During the rotation phase, the athlete accumulates kinetic energy using muscle force and exploiting the friction between their feet and the ground. This energy, acquired by body rotation, is then transmitted to the disc during the throw phase.

One of the critical elements of this technique is the athlete's rotation speed. A rapid rotation allows more energy transfer to the disc, resulting in a longer throw.

To analyze the throw, one can use a smartphone's gyroscope attached to the athlete's arm. __The measurements will determine the athlete's rotation speed __and provide an estimate of the disc's kinetic energy during the throw.

A spinning disc's trajectory is not a parabola. If the disc is launched with a negative angle relative to the initial trajectory angle, the disc can travel much further than an equivalent weight thrown at the same speed. One can try to estimate the trajectory difference based on field data.

**Cycling**

A mechanical sport, cycling addresses other sporting issues, especially the means of multiplying effort and resistance forces.

The first analysis concerns the bicycle's functioning and a crucial part: gear shifting. Thanks to this invention, cyclists can maintain optimal pedaling cadence regardless of bike speed. It also allows for applying significant torques for climbs or starting. To better understand the usefulness of gear shifting, why not undertake the following analysis? Choose a certain distance (50 meters, for example) and measure the time it takes for a cyclist from a standing start to reach this mark as quickly as possible. Also, measure the speed reached using GPS. Which gear is best?

A second analysis relates to friction. Indeed, the equation for cycling on a flat road is simple: the energy input is dissipated as friction energy, of which the main one beyond a certain speed is air resistance, proportional to the frontal surface area. To study the impact of air resistance, one can measure the slowdown caused by different cyclist positions using GPS: in a racing position or standing on the pedals.

**Boxing and Martial Arts**

__Bruce Lee's 1-inch punch is an iconic testament__ to the amalgamation of technique, speed, and power. While it may seem mystical to the untrained eye, the physics underlying this move can be explored using our smartphone. This exploration will help answer one of the most common question asked in boxing and martial arts : "What is the real power of a punch?".

To dissect this legendary punch, you can use the smartphone's accelerometer. Attach the smartphone securely to a punching bag or a target that can absorb the impact. When the 1-inch punch is executed on the target, the smartphone will register the force's intensity through changes in acceleration. This acceleration, combined with the bag's mass, allows one to calculate the punch's force using Newton's second law (Force = mass x acceleration). Moreover, by knowing the duration over which this force is applied, we can estimate the punch's energy. Although this method doesn't directly measure the boxer's punch force, it provides a valuable indication of the impact felt by an opponent (or, in this case, the bag).

It is also possible to analyse the movement and speed of the arm or leg during a kick by attaching a smartphone directly onto the wrist and analyse the acceleration. Or, to get a more global view, to record a slow-motion video recording from the smartphone's camera, that can be analyzed with the kinematics module.

Boxing and martial arts are largely unused ways to introduce students to the concepts of energy through a practical and popular example. However they should be careful not to harm anyone through experimentation.

**Diving**

It is commonly accepted that a ball thrown into the air, in the absence of friction, will follow a parabolic trajectory. But when it comes to a diver performing a somersault, does the trajectory of the center of gravity remain parabolic? To answer this question, a practical study can be undertaken during a visit to a swimming pool where an athlete's dive is filmed. For those without nearby pool access, one can refer to a diver's video available in the FizziQ video library.

__Using the video of a somersault dive that you can find in FizziQ's kinematic video library__, you can perform the complete analysis of a somersault diving movement. In a first analysis, we can study the movement of different body parts like the diver's head, and in a second one, their feet. It is observed that the curves generated from these points differ considerably.

However, mechanics assures us that the center of gravity of a free-falling body, unaffected by friction, describes a parabola. To conduct this analysis, one can try to estimate the athlete's center of gravity position in each image, thus obtaining a parabolic trajectory for this point.

One can also model the diver's center of gravity more precisely by pinpointing each body part, then exporting their coordinates into Excel and __applying the weights from Leva's tables that provide the human body's mass distribution__. Using this frequent biomechanics analysis method, we then verify that the center of gravity's trajectory is indeed a parabola.

**Pétanque**

Pétanque provides a very interesting playing field for studying a phenomenon we hadn't previously explored: collisions. Using a smartphone, we can deepen our understanding of the physical interactions that occur when one ball strikes another.

The first analysis involves studying the result of a collision when a player shoots "au fer", meaning the ball is thrown in the air and strikes the opponent's ball before hitting the ground. This sequence will be filmed at a rate of 60 or 120 frames per second. By analyzing the video using kinematic analysis tools, such as the FizziQ application, we can determine the coefficient of restitution during a shot. What can we deduce about the strategy during the "au fer" shot?

Another analysis involves measuring the sound frequency when two balls strike each other. Does this frequency vary depending on the balls? Do higher-quality balls produce a different sound?

**Badminton**

Badminton stands out from other racquet sports due to its specific projectile: the shuttlecock. Its unique shape results in a distinct trajectory without a bounce, requiring players to anticipate its movements. The shuttlecock allows for a range of shots, from fast smashes to subtle drops, promoting tactical exchanges. This specificity requires players to be in excellent physical condition to move quickly and a refined strategy to outplay the opponent.

The specific trajectory of the badminton shuttlecock can be easily studied through video analysis. If one does not have a venue to capture it, one can use a video __from a badminton throw from the FizziQ library__. It's impossible to formally determine the trajectory equation, but one can still identify three distinct phases. An initial rapid trajectory: Just after being hit, the shuttlecock travels at a relatively high speed, appearing almost linear over a short distance. A strong deceleration: Due to its shape and construction, the shuttlecock decelerates quite rapidly, giving its overall trajectory a generally parabolic shape. An almost vertical drop: The end of the trajectory when the shuttlecock is launched very high has the characteristics of a vertical fall.

**Soccer**

Studying the lift or Magnus effect with a football is particularly interesting, as it highlights the principles of fluid mechanics in action in the sport. This phenomenon is often observed when a footballer imparts spin on the ball, making it follow a curved trajectory rather than a straight one. The Magnus effect occurs when the ball's rotation creates a pressure difference from one side to the other, causing a force perpendicular to its trajectory.

To study this effect accurately, video analysis is a powerful tool. By filming a footballer's shot from different angles, one can trace the ball's trajectory in real-time. Using kinematic analysis software like FizziQ, one can then mark the ball's position frame by frame, visualizing its curved trajectory and measuring the extent of curvature based on the initial rotation given to the ball. Furthermore, by comparing shots with and without spin, one can better understand the influence of rotation on the ball's trajectory. Thus, using video analysis to study lift in football provides a tangible means of exploring and understanding this fascinating phenomenon that's central to many memorable sporting moments.

**Paralympic Long Jump**

The Paralympic long jump, with the use of carbon blades, offers a fascinating blend of human determination and technological prowess. Like all other Paralympic sports, it embodies adaptability in the face of adversity and provides a unique platform for studying the biomechanics of movements. Furthermore, this discipline raises crucial questions about fairness in sports while serving as a powerful symbol of inclusion and inspiration. The interaction between the athlete and modern technology in this specific context evokes both admiration and curiosity.

All the analyses we conducted before are possible for Paralympic sports, but other analyses can also be undertaken, shedding light on the understanding of these sports.

For example,__ in the case of the Paralympic long jump with "blades", one can explore the following questions__: What asymmetry is created by using prosthetics during the run, and is it a disadvantage? How does the stiffness of a "blade" or "lamina" compare to that of a valid leg? Is the take-off angle similar between a Paralympic and non-Paralympic athlete? Some of these questions can be studied using a smartphone, either through direct measurement or video analysis.

**Conclusion**

Over the years, the symbiosis between science and sport has strengthened, paving the way for remarkable advancements in understanding human performance. Sciences, whether physical, biological, or social, provide valuable insights into the mechanisms, techniques, and strategies that enhance athletic performance. They dissect, analyze, and propose innovative solutions to push the boundaries of what the body and mind can achieve.

However, sports are not just an application field for sciences; they also become a fascinating subject of study in their own right. In schools and universities, sports analysis, facilitated by the availability of digital measurement devices like smartphones, offers a unique opportunity to address scientific concepts concretely and vividly while stimulating students' curiosity and enthusiasm.

The upcoming Olympic Games in Paris further highlights this interdependence. This global event showcases athletic excellence, where every fraction of a second matters, and where scientific innovations can make a difference. But it's also an open-air laboratory for researchers, drawing attention to the importance of continuing interdisciplinary studies between sports and sciences.

**Références **

Prothèses tibiales de saut en longueur handisport - Jean BOUTEILLER, Pierre-Adrien BREARD, Paul FRAPART, Cyril VOISARD, Maxime VRAIN

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