The science of sport
by Chris Woodford. Last updated: August 2, 2021.
Think "sport" and the words that spring to mind are
likely to be fitness, exercise, competition, endurance... and fun;
"science" is probably not among them. It's obvious to anyone who loves sport that
it's a powerful demonstration of pushing the human body its limits.
What's less obvious is that sport is an equally powerful demonstration of science. From the cutting-edge
composite materials packed into
racing bikes and tennis rackets to the
17th-century maths that bends baseballs through the air, science
is the foundation of almost every sport you care to mention. How can
Usain Bolt sprint so much faster than you? Is a wooden baseball bat going to make
you play better than one made from aluminum? Exactly what's happening to a soccer ball as it
curves off your boot, swerves through the sky, and punches into the net?
As you'll see in a moment, questions like these
have fascinating, scientific answers!
Photo: Golf: You learn to play a game like this by hitting a ball hundreds or thousands of times.
Your brain learns to correlate the way you move your muscles with the places where the ball ends up; eventually, after enough practice, you can place the ball wherever you want. In theory, a robot could play just as effectively if you programmed it with the laws of physics, or if you let it practice and learn from its mistakes using
a neural network (a type of computer model that learns from experience like a brain). Photo by Eric Tretter courtesy of US Navy.
Why do we say sport is scientific?
Science is all about understanding how the world works using theories tested through experiments.
At first sight, sport appears to be something different: training
hard to beat an opponent (another person or team, a clock or
measuring tape, or maybe just that pesky little voice inside
your head that keeps pushing you to do better). Look into sport a bit more closely and it soon becomes
obvious that science plays a big part in it. The human body
itself is obviously a scientific miracle that
can turn a hearty breakfast into a soccer championship, a record-breaking sprint, or
a heavyweight boxing title. But leaving the basic biology to one side, there are
many more ways in which sport relies on science. Physics, for example, tells us how far
you can hit or throw a ball, but it also explains how fast a swimmer can cut through the water, how a
diver can somersault, and even why long jumpers have to move their arms
in such a drastic way as they fly through the air. Let's look more closely at the science
behind a few different kinds of sports: ball sports (including tennis,
soccer, and baseball), track and field (athletics), speed sports (such as cycling
and swimming), and sports that defy gravity and balance (gymnastics, BMX and
Hit and run: ball sports
If you've studied physics at school, you'll know that we can use a few relatively
simple math equations to predict the parabolic (upside-down U-shape) path of an object flying through the air. The science is called
ballistics—and it governs everything from
how bullets fire out of rifles to how cricket balls soar through the sky. The basic idea is
simple. When you throw or hit a ball upward, you apply a force that
makes it accelerate (gaining both a vertical and a horizontal
velocity). The vertical (upward) velocity and the horizontal (sideways)
velocity are independent of one another, though both are important if
you're trying to make a ball go as far as possible. As the ball shoots up, the force of gravity pulls it back down, slowing its vertical velocity to zero (when it reaches the peak of its trajectory)
and then accelerating it back toward the ground. It's easy to
calculate how long the ball will stay airborne and, using this, you
can figure out how far it will travel (its range, in
other words) by multiplying the time in the air by the ball's horizontal velocity.
In theory, the way to make a ball travel
furthest is to strike it at an angle of 45°; simple math
tells us that angle should give the maximum range. In practice, you
need to take into account various other factors such as air resistance (which
depends on the size and surface texture of the ball and how fast it's going),
ball spin, and so on; factor those things in and you'll find the
perfect angle can be more or less than 45°, depending on what kind of ball you're hitting and how. If you're
hitting a golfball with the wind behind you, for example, you might
hit it at a steeper angle. That means it'll stay in the air longer.
Although it would normally travel a shorter distance in that case,
the wind will carry it further in the same time than if you'd hit it
at a shallower angle. Not only that, but the wind speed will be
higher further from the ground so you may tap into a higher airflow
and gain more distance that way as well. If you're driving into an oncoming wind,
you might be better going for a shallower angle than 45°. Although the ball will fly lower,
it will have a higher horizontal velocity, giving it more power to overcome the
wind and potentially going further. (In practice, for reasons I'm not going to go into,
hitting a golfball is more skillful and complex than this and involves factors such as how
fast you make the ball spin, the way the angled club face strikes the ball, and so on. I'm talking
about theoretical science here, not trying to offer practical golfing lessons.)
Photo: Scoring a goal: sheer skill or cunning physics? Your brain calculates the trajectory of the ball and figures out how to kick it to reach a particular spot. If there are people in the way, you might spin the ball so it curves through the air and bends around them. Skillful players learn how to do this by trial and error, but a scientist could also figure out how to achieve the same effect using the laws of aerodynamics. Photo by Gary Nichols courtesy of US Navy.
When you try to hit or kick a ball as hard as you can, what you're
attempting to do, in scientific terms, is transfer as much kinetic energy from your body to
the ball as possible. In a sport where you use a bat, the bat serves as
a go-between in the process, helping you to transfer energy more
efficiently. One of the really interesting things about ball sports is the wide range of different bats
and balls that are used; although the basic dimensions of the bat and ball may be specified in the rules
of a particular sport, you can still find huge variety. Bats come in all shapes and sizes, in woods of various kinds, metals
such as aluminum, and high-tech composites and carbon fibers;
the design of a bat has a huge effect on how a ball with respond, and different bats will give very different results even if you apply exactly the same force. Balls are hugely varied too: everything from perfectly smooth, very hard billiard balls and slightly softer golf balls (with their aerodynamic dimpled surface), through cricket balls and baseballs (with their complex outer stitching patterns called "seams"), and squishy rubber tennis balls, right up to soccer and basketballs and those weird-shaped rugby footballs.
Photo: When two billiard balls collide, we can get almost total energy transfer—known as an elastic collision.
Photo by Brittany Y. Bateman courtesy of US Air Force.
Hit a hard ball with a hard bat and you're attempting to pull off
what physicists call an
Confusingly, "elastic collision" doesn't mean there's any elastic
involved or anything remotely rubbery or bouncy; it's just a formal,
scientific way of saying that all the kinetic
energy your bat has before the collision is transferred to the
ball (and bat) after the collision. When a billiard ball crashes
into a second, identical ball and comes to a sudden stop, knocking the
second ball away with almost all the momentum the first ball had originally, that's about as close
as we ever get to an elastic collision. The forces involved in collisions like this
can be considerable. One of the most basic laws of physics, Isaac Newton's second law of motion, tells us it takes twice the force to
accelerate a ball to a certain speed if you do it in half the time. So fast, elastic
collisions between hard balls (or hard balls and hard bats) involve more force than slower, gentler collisions
between softer balls (or softer balls and softer bats), where the energy is passed from bat to ball over a longer period of time and with less force. (That's why cars are designed to crumple up when they crash: slowing down a
collision reduces the forces experienced by the people inside, increasing their chances of survival.)
Photo: Soccer uses a medium-sized, fairly soft, inflatable ball. Heading involves an inelastic collision in which momentum and energy are transferred imperfectly from your head to the ball. Imagine what kind of soccer boots you'd need to wear if soccer balls were made out of solid wood. According to my quick calculations, a wooden soccer ball would be about nine times heavier, so you'd need to give it nine times more energy to kick it to the same height. If all that energy came from your leg, your leg would need to be moving about three times faster during the kick to have nine times more energy to pass on. You'd need to use nine times more force to kick a stationary wooden ball to the same speed or kick with the same force for nine times longer, neither of which sounds possible. Using so much force to kick the ball would tire the players very quickly and make the game much less interesting. Photo by Kristopher Radder courtesy of
Hitting a hard leather cricket ball with a hard wooden bat is somewhat less elastic than a collision between two billiard balls because the ball and the bat do bend and deform slightly during the collision (which
wastes a certain amount of energy), and, for various other reasons, energy isn't perfectly transferred. In sports that involve hard balls, you generally have to hit the ball pretty hard to get it to move quickly, because it's fairly dense and heavy. (Again, Newton's second law of motion tells us that you need a bigger
force to accelerate a heavy ball than a lighter one.)
Animation: A soft ball deforms as it hits a hard surface. The materials the ball is made from squash and compress, and the air inside is also compressed, exerting a pressure that makes the ball quickly return to shape. Although this process looks completely reversible, some energy is always lost, which is why a bouncing ball can never return to exactly the same height from which it originally fell.
Not all sports use hard bats and balls. In some sports, we use part of the human body (our arms or legs) or a softer instrument (maybe a tennis racket) to accelerate a lighter and softer ball
that's typically filled with air or some elastic material. Kick a soccer ball and what happens is
very different to what goes on when you whack a golfball with an iron club. What we get
is a much more inelastic collision where the ball initially deforms
and squashes inward as you kick or hit it, then springs back to shape
and pushes away from your foot. In collisions like this, kinetic
energy isn't conserved: the ball and your body have less energy after the collision
than your body had beforehand. Balls like this are generally much lighter and (fortunately) we don't need
to hit or kick them quite so hard to accelerate them to high speed.
Chart: Which sports balls have most energy? We can figure out the kinetic energy of a ball with the formula ½mv2. Plugging in the masses and (higher-end) speeds, we get these sorts of estimates. I would have guessed that golf balls had most energy because they seem to be going so fast, but they're also very light. Soccer balls, kicked hard, have surprisingly high energy because they go faster than you think and weigh almost 10 times more than golf balls. Which balls hurt most when they hit you? Generally, harder and smaller balls (golf balls) because they dissipate their energy very quickly over a small area, which means they exert more force and pressure on your body. That's also the idea behind bullets, except they're pointed to move faster and help penetrate your body. Interestingly, if you check out the similar chart I drew in my bullets article, you'll find modest handgun bullets have comparable energy to fast-moving sports balls (hundreds of joules).
Playing area and surface
Different balls sports are played on different surfaces—and over different sized areas—and that also
plays a big part in the balls we use and how they're designed.
One reason is because balls made from different materials bounce to
different heights, even on the same surface; the same ball also
bounces very differently on different materials.
You might have noticed how tennis players often specialize in playing on
a particular surface such as clay, asphalt, or grass; each of these
affects the speed and bounce of the ball in a radically different
way, with softer clay absorbing more of the ball's energy and
effectively slowing down the strokes, and grass speeding them up.
There's no reason why we couldn't play golf on a table top with clubs the size of pencils and balls
made of cotton—but it wouldn't be a very interesting or challenging
game. Golf is a game people like to play outdoors over long ranges
and that decrees the type of ball needed to play it. The ball has to
travel a relatively long way (at least in the initial "drive"),
so it has to be small to reduce air resistance. (The dimples on a
golf ball help it to travel further by reducing the drag even more.) To stop it from being
deflected too much by the wind, it has to be relatively dense and
heavy—and that means the thing you hit it with (the club) has to be
dense and heavy too (made from wood, metal, or carbon fiber, golf
clubs have a thin shaft and a heavy weight at the end where they
contact the ball).
Different people can achieve very different effects with the same bat and ball.
Tennis is a subtle game that can be played in many different ways, but one of its
key features is the serve: the fast, powerful opening shot. Taller
players with longer arms naturally have an advantage here: the taller
you are and the higher you reach, the faster the tip of your racket
is traveling when it hits the ball (because the velocity of any
point on a rotating wheel is greater as its distance from the point of rotation increases)
and (in theory) the faster the ball will go when it blasts toward
Photo: When you bowl, your brain instantly works out how to control your muscles to throw the ball to reach a precise position in space. On paper, that's simple physics, but it's amazing that our brains and bodies can do things like this instinctively, with no calculations at all. Photo by Jon Dasbach courtesy of
What do world-class footballers, cricket and tennis players, baseball champs, and even billiard
players have in common? An instinctive ability to put a ball
precisely where they want it to go, and often where their opponent
least expects it. That doesn't just mean being able to hit or kick a
ball as far as possible, but using things like spin to make it curve
to one side. Spinning balls bend because of science—usually
through something called the Magnus effect: as a ball spins, it
changes the way air moves around it, speeding it up on one side and
stopping it on the other, producing a force that pushes the ball
in an unexpected direction. Balls with seams and cricket balls that have
been polished on one side curve through as they fly because they make
the air more turbulent on one side than the other.
It's much easier to see these things demonstrated in videos and animations than to read about them.
Derek Muller of Veritasium and Australian physics professor and sports-physics expert Rod Cross
have made two great YouTube videos showing how these
effects occur: the first is a simple demonstration of how the Magnus effect
makes a ball curve; the second explains the physics of balls with seams.
Might as well jump: track and field sports
Track and field sports are contests in which each individual athlete pits their body against
other people's bodies; attempting to run faster, jump higher, or throw further is
the name of the game. Although much of athletics is about harnessing
the biology of the body—using the strength of individual muscle
groups, for example—there's a lot of science going on outside the
body too. Who'd guess that a long jumper or a pole vaulter is
secretly harnessing the power of physics?
Photo: Long jump is all about conservation of energy and momentum. Once you're airborne, there's no way to get any more energy, so the run-up is crucial: the more kinetic energy you give you body the further you'll go. In midair, you can move your legs further forward by bringing your arms around and down, as this jumper is just about to do. Photo by Matthew A. Ebarb courtesy of
You might think the long jump it's simply a matter of running fast, hurling yourself
into the air, and hoping for the best. Not if you want to win a gold
medal! As a jumper, what you want to achieve is to land your legs as
far forward as possible (in front of your body), but you can't
possibly take off with them in that position: they have to be pushing
backward (behind your body) to launch you into the air. So what you
have to do is radically alter the position of your legs while you're
in midair. Now once you're airborne, if you move either your arms or your
legs away from your torso, your body will rotate about your center of gravity
(the point on your body where all your mass seems to be concentrated).
Moving either your arms or your legs nearer to or further from your body
will change your moment of inertia (the distribution of your mass
about your center of gravity). It's a basic law of physics that your
angular momentum (the momentum your body has because it's rotating)
cannot increase or decrease (angular momentum is "conserved," as physicists say). If you want
to throw your legs forward and outward, the way to do it is to throw
your arms upward, then bring them down quickly. As your arms shoot
back, your legs shoot forward to compensate. It's a bit like when
you're swimming and you want to stand up: if you bring your arms down
quickly in front of you, your legs shoot down beneath you to ensure
the conservation of angular momentum. Almost the same move
happens mid-air in the long jump.
Pole vaulting is another example of a sport where physics can give you a hidden hand. Pole vaulting is a
bit like a super-high high jump where you use a long, bendy, carbon-fiber pole to
throw yourself over a bar. Just like long jump, it looks simpler and
less scientific than it really is. And just as long jump is all about
the conservation of angular momentum, so pole vaulting is about the
conservation of energy. Consider what happens during a pole
vault: you start off running toward the bar with the pole in your
hands. After you've picked up speed, you have a fair bit of kinetic
energy (energy of movement because you have both mass and speed).
To lift your body a certain distance in the air, you need to give it
a certain amount of potential energy.
The pole helps you convert horizontal into vertical motion, and
it does so by converting your kinetic energy into potential energy.
After you've reached the end of your run-up, you
stick the pole into the ground. Your momentum and energy is now
transferred into the pole, which bends into a curve and converts
your kinetic energy into elastic potential energy, slowing you down
in the process. Being elastic, the pole quickly springs back to its original shape, straightening out and lifting you
upward, and converting its elastic potential energy into kinetic energy and gravitational potential energy (the energy your body has when it's up in the air). Ideally, all of the kinetic energy
you had in the run-up is converted into potential energy when your
body reaches its highest point and stops climbing. That explains why
the run-up is so crucial to a pole-vaulter: if you don't run at top
speed, and plant your pole correctly or hold it firmly, your kinetic
energy won't be completely converted to potential energy and you
won't gain as much height.
Artwork: Pole vault is a good example of the conservation of energy. 1) During the run-up, your body tries to gain as much kinetic energy as possible. This is vital because, once you're airborne, there's no way to gain extra energy. 2) When you stick the pole into the ground, it bends and converts your kinetic energy into elastic potential energy. 3) As the pole straightens, it gives the kinetic energy back to your body. The pole's job is to help you convert kinetic energy (your running energy) into potential energy (the energy you have when you climb into the air) and horizontal motion into vertical motion. 4) When you let go of the pole, you're climbing upward, working against the force of gravity. Your body's kinetic energy is gradually converted to potential energy as you climb, which is why you start to slow down. 5) At your highest point, as you cross the bar, your body has maximum potential energy. All the energy you have at this point came from the kinetic energy of your original run-up.
Physics is even at work in the simplest sport of all—running—and it can help us understand why a
super-star like Usain Bolt can run so much faster than the rest of
us. According to Newton's second law of motion,
you can make a mass accelerate (gain speed) by applying a force to it.
We can describe the same law in a slightly different way: you can give something more momentum by
applying a force to it for a certain amount of time (with what's
called an impulse). If you're a world-class sprinter, what
makes you run faster is your ability to deliver impulses with your
legs that accelerate you faster. But the more massive you are, the
more force you need to accelerate. If you have huge muscular legs,
you'll need more force to pick them up and put them down and keep
your body moving quickly. In the case of Usain Bolt, a very
large and tall man, his ability to generate powerful impulses with his legs
(to gain acceleration) outweighs his considerable mass (which needs
more force to accelerate it). And that's why he's so fast.
Feeding your speed: sports that beat the clock
Photo: Aerodynamics is as important to cyclists as it is to designers of race cars and jet planes, which is why they wear tight clothes and lean forward like this. Although you can't see it in this photo, racing cyclists also use special handlebars that position their elbows much closer to their torsos, significantly reducing drag.
Cycling, swimming, skiing, and bobsleigh are all about beating the clock—but they're also about
beating another type of science called fluid dynamics, which
is the physics of how liquids and gases (fluids) move around objects
(or how moving objects slice through fluids, which is exactly the
same thing). Have you noticed how Olympic swimmers wear those
super-streamlined body suits and cyclists put on teardrop-shamed
helmets and crouch over their bikes? The reason is the same in both
cases: the swimmers are trying to minimize the resistance their body
offers to relatively dense, liquid water, while cyclists (who move
quite a bit faster) are attempting to reduce air resistance
(drag) by making their bodies more aerodynamic. Most of us don't
notice air resistance because we never really go fast enough; when
you're walking, gravity is the force that causes you most bother.
You certainly notice the force of air resistance on a cycle—and it's very obvious if you
speed along in a car with the windows or the roof down.
Drag is even more of a problem for swimmers because water is so much more dense than air. It's much
easier to swim (horizontally) through water than to walk through it (vertically)
because your body assumes a tube-like shape that can move forward by
pushing less water out of the way (it has what we call less form
drag because it presents less of an obstacle to the water trying
to move past it). Those streamlined suits you see swimmers wearing
work in two very interesting scientific ways—one involving biology, the other physics.
The biological effect is achieved with tight-stitching throughout the suit that compresses the swimmer's muscles so they work more efficiently, producing less fatigue. The physical effect comes from the texture of the suit.
There are tiny V-shaped ridges on the surface designed like the dermal denticles (placoid scales) on a shark's skin. These help to
reduce friction drag (the resistance between your body and the layers of water sliding past it) by creating tiny vortices, reducing the water's tendency to become turbulent as it flows past your skin. If you're doing a speed sport, understanding how to minimize form drag and friction drag is the way
to go faster, but it's also the way to go further. Pushing against the air or the water wastes energy, and there's
only so much of that available to your body. The more efficiently you use your limited energy supply (the further you go with each stroke or your arms or push of your legs), the longer you can go without getting tired.
Beating your balance: sports that defy gravity
If you're a tennis or golf player, your brain has an intuitive understanding of ballistics: you know
exactly where a ball will go when you hit it. If you're a cyclist or
a swimmer, you learn about fluid dynamics very quickly. On the track
or field, you soon master force, energy, and acceleration even if you
don't actually think about them scientifically. What about sports like skateboarding and BMX? What
science do they involve?
Skating is a supreme demonstration of physics. Even the most basic move of all—kicking against the curb to get
yourself moving in the first place—is an example of Newton's third law of motion: you kick back against the curb to make your body and the board go forward. Pull off a cool stunt in mid-air and you're nothing
less than a mini Albert Einstein: you're instinctively harnessing the power of physics to maintain your balance, which we can define as the way your body keeps itself upright despite gravity's pesky determination to pull it to the ground.
The general approach to skating is to bend your knees and stand in a kind of flexed position.
Why? The lower you stand, the lower your center of gravity and the easier it is to keep your balance (bending your knees also helps to absorb impacts when you land and reduces the shock to your legs and spine).
Photo: Skateboarders master physics instinctively: skating is all about center-of-gravity, Newton's laws, conservation of energy, and conservation of angular momentum. In this trick, widely spread arms give better balance by increasing the skater's moment of inertia. Photo by J.D.Yoder courtesy of US Navy.
If you pull a trick where you shoot off a ramp and lift your legs off the board,
so your body and your board briefly separate, travel independently for a time, then
come together again when you put your feet back down, you're making use of
inertia: as Newton's first law of motion tells us,
objects either stay
still or keep moving at a steady speed unless a force acts on them.
Even though your body and your board part company for a few seconds,
both keep moving in a predictable way because of their inertia, and
that allows you to reconnect with your board again further down the
Skaters put their arms out to balance their bodies.
Why? For the same reason that a tightrope walker often holds a long,
heavy pole. If you're trying to keep your balance on a skateboard,
you're trying to stop your body from rotating. If you're on the ground,
and your center-of-gravity is too far to one side (not directly over the board),
the top of your body will tend to rotate about your feet: in physics terms,
your body will experience a moment that will make it turn—
in other words, you'll fall over! A lower center-of-gravity is one way to make balancing easier; a
higher moment of inertia is another way. What that means is arranging
your body so some of its mass is further from the point of
rotation (in other words, you put your arms out). You'll have noticed
how ice skaters can slow down their spinning moves by putting their
arms out, and speed themselves up by bringing their arms in; since
their angular momentum has to stay constant, bringing their arms in
(reducing their moment of inertia) means their angular velocity has
to increase, so they spin faster. When you're skateboarding, if your arms are outstretched
and you start to lose balance, your body will rotate more slowly, so you'll have more
time to compensate. Instinctively, you'll shift the position of your arms to cancel
the rotation of your body, balancing yourself once more. A
top skater has an instinctive ability to control his or her angular
momentum—like a kind of human gyroscope!
Diving for gold
Photo: Diving is all about mastering momentum: converting linear momentum to angular momentum
and conserving angular momentum as you spin. Photo by R. Jason Brunson
courtesy of US Navy.
Sports that involve precise rotations of your body, such as diving, are all about mastering the
conservation of angular momentum. You'll have noticed how divers tuck
their arms and legs in after they spring off from the board, rotate a
couple of times in a somersault, then extend their limbs to enter the
water cleanly and safely. Why spring off the board? It's much the
same as the pole vault: the energy you put into the board by jumping
down on it is temporarily stored inside the bent wood as elastic potential
energy. The elasticity of the board makes it spring upward and gives
your body first kinetic energy, then potential energy. As you tuck
your limbs in and start the dive, your body starts to rotate so your
linear momentum (your movement straight upward) is converted into
angular momentum (spinning motion). Once you're diving, the
conservation of angular momentum comes into play. With your arms and
legs tucked tight to your body, your moment of inertia is as small as
it can possibly be so you spin at your fastest speed. By extending
your arms and legs, you increase your moment of inertia, slowing down
and then cancelling your rotation so your body enters the water
vertically, ideally without rotating.
Sport + science = win
Some people are born sports players and some aren't—and no amount of science will turn a
clumsy person like me into a world-class athlete. Many sporting stars
understand instinctively how to be the best in their
field—and that built-in understanding, gained through years of
practice by trial and error, can achieve the same or better results as a
theoretical, scientific approach and by totally different means. When Usain
Bolt sprints for the line, the last thing he's doing is calculating
how much force his legs can turn into acceleration through Newton's
laws of motion. But understanding a little bit of the science behind
your favorite sport can help you harness your natural
abilities and achieve more; it can help you run faster,
swim further, or pull off neater skating tricks.
I'm not suggesting for one moment that success in sport is purely about science:
many other factors, including physical ability, natural talent, endurance, courage, and
determination are at least as important (and sometimes much more so). Does science take
the fun out of sport? Not a bit of it: it adds an extra level to our
understanding and helps us appreciate our amazing sports stars even