How To Use Physics To Improve Your Game

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Feature Image for the Physics of Badminton Article

I graduated from one of the UK’s top three Universities with a First Class Degree when I was 21 years old. That University was Hull and the course was Applied Physics. I’ve played racket sports from about 8 years old. I’ve been living on Planet Earth since birth. I’ve only recently understood the significance of all three combined as I’ve strived to improve my Racket Rankings in the racket sports that I play (Badminton, Squash, Padel, TT, Pickleball, Tennis). By watching great players and by thinking deeply about what’s going on, and why they are so good, I’ve come to realize that these top players are amazing at performing complex Physics calculations in split seconds whilst under pressure from a ruthless opponent. In fact, all Racket Players do this all the time, but it’s so second nature we don’t seem to consciously realize it.

This article highlights this subconscious activity for those interested in the interaction of Physics with Racket Sports, but it also contains insights into the fundamentals of racket sports sharing an understanding which will help you get to the next level of awesome play, whatever your racket sport.

The Gravity Effect

That’s no Moon. It’s a Space Station

A Star Wars Gif "That’s no Moon. It’s a Space Station"

One of the Universe’s fundamental forces is Gravity, an often misunderstood concept with a massive impact on racket sport. From toddlers learning to stand, by positioning their center of mass in a vertical line with their feet, and chasing falling balloons and balls, we’ve grown to appreciate gravity and its constancy in all situations at all times.

A Star Wars Gif "That’s no Moon. It’s a Space Station"

 It is surprising then that so many points end with the shot hitting the net rather than going over it! Why is this? At first thought MARGINS spring to mind, but on deeper reflection, I doubt it. In mathematics and engineering, Margins are used when precision isn’t known well. But the Gravitational Constant on Earth is quite fixed and accurate and if not, any margin needed to account for its variability is clearly not the answer to why we hit the net so often. For example, Gravity does vary around the globe, and from time to time – gravity on Earth will be strongest when the moon is furthest from your court on the far side. There will also be an additive gravity effect when all the planets are aligned (try coaching that fact when your next tournament coincides with planetary alignments!)  Gravity will change if your court is next to a big mountain or on a harbourside when a supertanker docks. These are all real measurable effects, but the point is they are tiny and can’t be blamed for the reason you hit into the net!

Perceiving the speed, direction, and time of your racket’s target as it drops from the sky for a smash is generally quite straightforward for most Club Standard racket players. They rarely get this split-second speed/position calculation wrong when lining up to smash. If the acceleration due to gravity was more variable we would see a lot more air shots with players miscalculating and mistiming the swing of their shot. This doesn’t happen. Taking the target out of the air when it’s dropping seems to be a simple calculation we can mostly do by the age of 10 or so.

But what does happen, even for adults that supposedly understand Gravity is the target hitting the net with a horizontal stroke like a drive. It seems that 1-dimensional gravity calculations are generally fine, but mix in a horizontal speed component (i.e. how much the shuttle will drop) and too many players seem to think that Gravity doesn’t then apply. Not true. Things still drop no matter how hard they are whacked sideways. And they drop as fast as they fall for a smash. If you can learn to perform the smash falling calculation (which most clearly can) then players need to learn to perform the drive falling calculation and your game will rise to the next level.  The most advanced Racket Players clearly understand the battle against their opponent and simultaneously against Gravity and can calculate the trajectory fall to avoid the projectile hitting the net, whether it is a shuttle or a ball.

Time Perception

Traveling through hyperspace ain't like dusting crops, boy!

A Star Wars Gif "Traveling through hyperspace ain't like dusting crops, boy!"

Next, I’d like to explain about speed/distance/time perception.

When first learning a racket sport, a friendly adult feeds the ball or shuttle exactly in the swing path of a beginner so the swing catches the ball and the youngster hits it.  Hooray, Play has started!

A Star Wars Gif "Traveling through hyperspace ain't like dusting crops, boy!"

The beginner has to time the swing and usually with a good feed, needs to do nothing more. The beginner learns the drop of the target due to gravity and a swipe with an open-faced racket is usually good enough to start a rally.

Next, the coach stands on her side of the net and feeds from a distance. The beginner has to learn to make complex speed distance time calculations to now hit the ball.  These calculations will need to occur in our every day 4 Dimensions of X, Y, Z, and Time. The beginner has to learn to make a split-second complex calculation of pinpointing the start position, the direction, and the speed of the target and then predict when and where the target will arrive in their swing envelope. This is not straightforward and so the beginner tends to simplify by using a very short swing with the feeder aiming the ball along the path of the swing. This means a “hit” will still occur if the swing is slightly late or early, building the confidence of the beginner. More important than building confidence is the learning of these calculations. Watch a beginner and they are usually very alert and attentive perhaps with a furrowed brow as their brains churn at these unknown equations of initial speed, acceleration due to gravity in only 1 axis, deceleration due to air resistance in X Y and Z, and attempting to calculate where the target will be. Like I say, it’s not easy. But it is something you can learn as you can see from watching any Club Level Player.

I’d just like to add that this article, like most Physics articles, is a simplification of the real world.  The real world is just too complex and chaotic to claim we can compute everything accurately.  So instead computer programs use approximations and ignore subtleties to convey general principles.

Computing the Millimetres

In sports though, we are actually in the real world in its entirety and we cannot exclude factors for convenience’s sake. Two added complications that cannot be ignored and must be computed and learned by the aspiring athlete are both related to speed and time. The first is what I call action at a distance and it refers to the distance between the player and the central area of the racket head. You can see the calculations I have previously talked about relate to the position of the target as it moves through time and space. But the player is interested in a critically important offset from their internal point of reference – where the racket head needs to be at a precise instant. It’s probably around 1 year old that a toddler begins to learn, clumsily at first, that a feeding spoon is a few inches away from the hand. The toddler will bob his head forward towards his hand and messily encounter the spoon in between his mouth and hand. And the same learning process of a greater “I” happens when holding your first racket. Stretching out your arm and seeing the racket head frame more than a meter from you makes you realize this offset is significant and important. It’s why the beginner often swipes at the shuttle and misses it as it drops by the shaft of the racket to the floor, inches short of the head.  The beginner hasn’t learned to incorporate this offset into the target calculations. The advanced player though understands this to millimetre accuracy as can be witnessed by squash players taking the ball off the side wall, and playing tight returns off tight drives. It’s why scrambling, defending players can shuffle their grip a centimeter downwards to get extra reach to return that penetrating smash. They have quickly calculated that the offset from the shuttle to them is too far and the racket must be held right at the very base to get the strings of the racket under the shuttle.

And the second factor which cannot be ignored and makes all these complex calculations fry your brain is what I call “intersection”. And it’s the opposite of the coach feeding a beginner in the first example. Remember at the very beginning a good coach feeds the target right to the swing of the player. In a Tournament Final, your opponent actively hits it away from you. You have to move at pace to the calculated offset position and firmly plant your feet whilst preparing your stroke to make that INTERSECTION. Obviously, if you don’t make it in time you lose the point, but make it too fast or not accurately enough and you can’t swing properly at the target. Even after playing sports for more than 40 years, I find this INTERSECTION position the hardest to calculate and often find myself too close to the target so cramping my swing.

The world’s top players sometimes seem to glide or step effortlessly around the court and it’s because they are amazing at calculating this INTERSECTION. They do utilize a full swing with stretched-out limbs and this means they do not need to take as many steps. They take fewer steps or shorter steps as they move around the court. They make it look simple because they have simplified the movements involved, whereas a club player will not use a stretched full swing so they have to move further to that intersecting point, and they often have to stutter their steps to be in this (incorrect) position. It all comes across as scrambling and disjointed when compared to a pro athlete’s movement.

Body Shots are Strong with this One

A Star Wars Gif "The Force is Strong WIth this one"

Finally, in this section on calculating positions and speeds and intersection points it has made me understand the physics of why body shots create winning situations. A body shot is when you hit the target at the body of your opponent – the exact opposite of playing into space. 

A Star Wars Gif "The Force is Strong WIth this one"

And I’m not talking about targeting the right hip of a right-handed badminton player or the elbow of a table tennis player, common tactics in these sports. I’m talking about speed-position PERCEPTION. Realize how we judge the movement of the target – I’ll call it RELATIVITY (ok borrowed from some other well-known Physicist). When calculating the coordinates of a ball played into space you use the movement of the target against its background to calculate its future position in space. You see it move meter by meter across the background of the court. Play at the body and there is no relative motion between the target and its background. How can you perceive its forward movement if it’s coming straight at you? The growth in diameter as it approaches is not perceptible. You might see a bit of up-and-down movement but no direct data points on direct velocity. So my enlightenment today is if you’re going to play a smash or a slow smash or fake a smash to a drop, do it along the sight line of your opponent. If you don’t win the rally outright, anticipate a weak return.

Feel The Force Luke

A Star Wars Gif "Use the Force Luke"

One cue that helps in the Relativity problem can be described as FORCES. It’s watching the swing of the opponent to see how much Force they are hitting the target with. If you can’t see the movement of the target against its background then just see how hard a swing they use to hit with. 

A Star Wars Gif "Use the Force Luke"

Perhaps this is an easier mental calculation to make than the positional speed calculations discussed earlier. Perhaps not. Applying the force of a stroke is a simple concept when its physics is simplified. We’re just exerting a force on an object to change its momentum. Just use Sir Isaac’s formulas in your head in the match and you will be fine. Sounds easy and actually the beginner player can perform the basic force calculations in the first session of play as they learn the “feel” of the ball on the bat. But Newton’s equations are a simplification and life on the court is actually in the real world (and this is why Virtual Reality Games are still a long way off). In the actual Universe, your calculations must encompass the coefficient of restitution (COR) of your racket and the target, the absolute force, the resolved force components between the racket head and the target direction, the positional difference between the sweet spot and the actual hit, and from there air resistance and wind drift. And for racket sports where the ball bounces (so not Badminton), there is the COR of the floor surface and friction of the floor surface.

Let’s look at the Physics of each of these components to help you understand what’s going on when you hit your target with your racket. First let’s consider the action of testing a shuttle before a game begins, which is a similar case to a full-on tennis first serve. In both instances, the player uses a full, open racket swing, with little or no spin imparted to the target. The speeding racket head transfers force through the strings so the target, which was close to being stationary when hit, zooms off with energy and momentum transferred to the speeding target. This is a simple case where the player uses almost or close to maximum force, rather than calculating precisely how much force to use. It’s also a simple case because the target starts stationary.

Perhaps the most demanding example is a net shot return made from a smash, although all kinds of returns from all areas on a court demand massive amounts of brain computing power to get the shot just right. On hitting a return, the player needs to calculate the momentum of the projectile (basically the speed) and calculate how much force to apply to the target through the racket to return the target back over the net. A trickling net shot just over the tape demands a precise quick calculation that encompasses racket speed and resolved forces and the coefficient of restitution of the shuttle and strings. Switch the shuttle mid-game for a squash ball or a table tennis ball (it’s against the rules but good thought fun), and the mass change and the coefficient of restitution change screws up the calculation and the shot can’t be completed. Or alternatively try making the shot with a racket with a broken string.  You can no longer make this precise shot because the COR of the shuttle/racket pair has changed and is now an unknown quantity.

This is why high-level players change a used squash ball for a new squash ball – to bring the COR range back into the known computing range. It’s why tennis players and badminton players change rackets even when the strings haven’t broken. It’s why TT players clean and change rubbers. The COR or the bounce factor from the strings is such an important part of the hitting calculation. It’s why “New Balls Please” is a thing. Restoring COR values back to the normal range. A weird alternative would be starting a match and then making Gravity slowly weaker and watching players trying to adjust their game calculations for the trajectory change due to a weaker gravity. It would be fun to try this one day!

However, once players learn the COR calculation, it’s another amazing feat to get their limbs and hands to impart just this right amount of force to the target – but it happens. You can’t say it’s luck when a top player can land the target exactly where they want it to go again and again. You can’t say they are not calculating this hitting force, of course they are. They perform the calculations so well, so accurately, so quickly, and all while under pressure from their opponents – it’s amazingly sublime.

Help me Spin. It’s my only Hope.

A Star Wars Gif "Help me, Obi Wan Kenobi. You're my only hope"

The top players in all sports make it look easy. But I personally have to give greater credit to the mental calculations of TT and tennis players because they incorporate into their already difficult calculations SPIN. Not only are they calculating the linear momentum transfer of the ball, but they also need to take into account the rotational spin energy of the ball. 

A Star Wars Gif "Help me, Obi Wan Kenobi. You're my only hope"

Adding this spin rotation differentiates top players from even some good-level club players. It’s probably the short answer as to why tennis is so difficult to play. Send a slow loopy non-spinning ball over the net and many a good player can’t make a good return stay in. Their calculation formulae are based on a large amount of momentum transfer as a fast ball is decelerated and turned in the opposite direction  A slow ball doesn’t have this high momentum and so doesn’t need a high returning force. It will go OUT if the force isn’t toned down. Unless of course spin is involved. A better player can still use a ferocious swing against a slow ball so long as a calculation is made of how much spin to impart and how much linear momentum to impart. Such a calculation is beyond many club players because it is very difficult (especially when you stop and remember all the other physics calculations that are part of a racket game).

Tiredness is the Path to the Darkside.

A Star Wars Gif "Fear is the path to the Dark Side"

The computing power used in a racket match for all these physics calculations is beyond my computing capacity. It’s a lot and I guess it’s evidence that the human brain is the most complex object in the known Universe. But in a long match, the brain gets tired just as the body gets tired.

A Star Wars Gif "Fear is the path to the Dark Side"

As the match lengthens, physics calculations aren’t worked out as accurately and sometimes they are just downright wrong. Tiredness causes bad calculations causing bad shots causing errors and losing points. Some of the World’s best players can still make these calculations even when the body is fatigued. Other top players understand their calculations are going awry and can modify their game strategies to continue to pressure their opponents to make errors. What will you do differently now you understand how hard your brain works throughout an intense match?  Now I’ve reintroduced you to Gravity will you hit the net less?  Now you understand COR will you keep your rackets strung to a common tension? Now you understand it’s a game of Physics, will you admire your opponent’s sliced smash but also congratulate your own calculated return as you see it tumble over the tape?

I love you Physics. I know.

A Star Wars Gif "I Love you. I Know."

Thank you for reading this, I hope we meet on the court and can demonstrate these calculations for real. In conclusion, in the interest of making everything more interesting, I’d like to share my summary tip to elevate your game and get you to the next level. You will have heard it before, but probably not presented like this. 

A Star Wars Gif "I Love you. I Know."

We call it VISUALISING and it’s great. It’s when you quietly and calmly visualize your future actions. Sometimes you play them out in slow motion or ghost, but the more important factor is that you are playing it out in your head. If you do this with the new knowledge of these Physics calculations I want you to know that actually, Visualisation is a basic term for “Performing complex Physics calculations”. It’s not quite as catchy as Visualisation but I think it describes better what is happening in your head as you visualize your return shot as the target is traveling to you at however many miles per hour. Other coaches’ “Visualisation” might be performed on the sofa when quietly reflecting on your last match. My “Visualisation” is a more conscious sub-conscious preliminary physics calculation of the future made fractions of a second before your subconscious makes the actual physics calculations to move your body to create the future that you want.

If you can do this pre-hit Visualisation, you will instantly discover an improvement in your game by increasing your shot accuracy. It’s a better way to improve your game compared to miming a shot (or ghosting or rehearsing a shot). With rehearsing a shot you are consciously thinking about controlling your body with certain movements. This conscious thought control of movement has two problems – it’s too slow, it’s not accurate or correct (enough) and it’s not all-encompassing of all the body parts (it’s not fully smooth). The opposite of this is when you experience FLOW. All, and I mean ALL, of your body, is automatically and instinctively controlled by the part of the brain that makes these high-speed Physics calculations without you realizing it. It’s an amazing experience and it’s the subject of another of my Racket Sport Articles to improve your game to the next level.


More Articles By Simon

Picture of Simon Lau

Simon Lau

Simon Lau is Mens Over-55s Racketlon UK Champion, Mens Over-55s Racketlon Doubles World Champion, Team Over-45s World Champion, Welsh Over-50s Badminton Mixed Double Champion and has achieved a Squash Wales Cap for representing his country in the Annual Home Internationals.

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