[This post is dedicate to my physics teacher at college, who always encouraged us to find joy in the physics of the everyday. He sadly passed away in 2012.]
The Bodyline series of 1932-33 where England skipper Douglas Jardine employed questionable tactics (at least for that time) of having his quick bowlers, specifically Harold Larwood, bowl bouncers at the body of the Australian batsmen in an attempt to contain them in general and Don Bradman in particular to win the Ashes back, is one of those divisive chapters in cricket that changed definitions of cricketing laws in both letter and spirit.
However, this post is not about examining the social or cultural impact of Bodyline on the game. (Incidentally, I did that for the website cricking.com here.) This post is about examining the physics of the Bodyline tactics. Because cricket is as much about the laws laid down by the MCC as it is about Newton’s Laws of motion. Bodyline created such an upheaval that not only did purists think bouncers hurled at the batsman’s body at serious velocity would tear apart the fabric of the spirit of cricket, but maybe the more relativistic physics oriented among them feared that a cricket ball delivered close enough to the speed of light would tear a hole into the space-time continuum. As of now, the fastest recorded cricket delivery remains at around 100 miles per hour, thus keeping the current universe intact. But the physics is still interesting.
Technical note: For the sake of the casual reader who does not need the horror of high school physics triggered in them, I will be skipping formulas and calculations for the most part here, focusing on just the fundamentals; however, more technical treatment for similar ideas can be found here and here.
The whole Bodyline tactic, or Fast Leg Theory as Jardine called it rested on the idea of a bowler being able to hurl the cricket ball at a batsman’s body at pace and at an uncomfortable height (somewhere around the chest ideally) with a packed ring of fielders close on the leg side ready to pounce on catches if the batsman fended the delivery poorly with his bat. I checked Jardine’s educational background and he was no physics genius but coincidentally or by design, two key ingredients needed for the physics of this to work came together for him in Australia that summer. To understand why, we first need a quick primer on cricket balls, their speed and their bounce and something called the coefficient of restitution (COR). Don’t worry, it might sound science-y, but it really means ‘bouncebackability’ of the ball.
A cricket ball is delivered with force (generated by the bowler’s run up, his arm movement and wrist action) on to the pitch (i.e. the playing surface) and then it bounces on its way to the batsman. How high it bounces and how fast it goes depends on its COR which is basically the ratio of the velocity at which the ball is hurled on to the ground (let’s call it vg) and the velocity at which bounces off the pitch (let’s call that vp)
[For you formula nuts, that translates to COR = vp /vg]
The surface plays an important part in what the COR is like. Higher the COR (i.e. closer that ratio is to ‘1’) the more the ball will bounce up; the lower the COR, the less it will bounce. In 2011 at the International conference of mechanical engineering research, Adil Haron and K A Ismail presented a paper titled “Coefficient of Restitution of Sports Balls: A normal drop test” where they detailed results of a vertical drop test they conducted on two different surfaces – wood and steel – with four types of sports balls – golf, table tennis, hockey and cricket. The golf ball showed consistently high COR (bounced a lot and with almost the same velocity that it was dropped at; the drop height varied from 1.2m to 1.8m) regardless of surface, though as expected it bounced back up less and slower on wood than it did on steel. Its COR was about 0.8. In similar experiments, the COR of a tennis ball was found to be 0.75. Cricket ball’s COR? On the steel surface around 0.6 and on wood around 0.35. On a cricket pitch, a reasonable assumption is that the COR would be around 0.5. So, the only thing you need to remember right now is that the ball will leave the pitch at about half the speed it was delivered at.
The second piece of this puzzle is the delivery speed. At the page on the University of Sydney website called ‘The Physics Of Cricket’ they mention that if we drop a cricket ball out of a “helicopter hovering 300m above the ground it will accelerate up to 123km/hr in about 5 seconds falling through about 100m” (the acceleration is due to gravity – the force, not the Sandra Bullock movie). It will fall through the rest of the 200m without accelerating any further because the drag force of the air that pushes the ball up balances gravity which is pulling it down, thus hitting the ground at 123km/hr or the approximate speed of a Bhuvaneshwar Kumar delivery or a Wahab Riaz delivery circa 2008. Now unless you are Mohammed Irfan delivering the ball while stacked on top of Ishant Sharma standing on a step ladder that is on an elevated platform on the Qutub Minar, it is impossible to ‘vertically’ drop the ball on to a cricket pitch.
Thus it is delivered at an angle in between being perpendicular to the pitch (90 degrees) and parallel (horizontal) to the pitch, so rather than have a vertical or drop velocity it will have an angular velocity (which is a mix of the ball’s horizontal velocity component and vertical velocity component). The angle of delivery also affects the COR, and on a typical surface the COR would drop somewhat but for simplicity’s sake we will continue with the nice, semi-round number that is 0.5.
There are just a couple of final things to consider before we dive into the final calculations of how a cricket ball turns into a weapon of intimidation. First the mass of the cricket ball. A cricket ball, if you recall an infamous sledge from Greg Thomas of Glamorgan to Viv Richards after he had played and missed at a couple of his deliveries, “is red, round and weighs about five and a half ounces, in case you are wondering”1 That’s about 160 grams (an ounce is 29 grams approx). Lastly, there is air resistance that creates drag force on the ball when delivered horizontally or at an angle. At usual bowling angles, the ball slows down by about 10-12% on delivery, i.e. the speed with which it hits the pitch is that much slower as compared to the speed at which it leaves the bowler’s hand.
And now for our finale, let’s welcome into the studio, the great Seventeenth Century cricket pundit and all round scientist, Sir Isaac Vivian Richards Newton. Newton’s second law of motion was about how much force a body would have when in motion based on its mass and its acceleration.
[Hi formula nuts, you surely remember the formula Force = mass X acceleration]
That force plays an important part in the intimidation of batsman, but more on that in just a bit. Here’s the thing – the bowler delivers the ball with a certain acceleration (depending on his action and strength – think Micthell Johnson vs Stuart Binny – and the higher the acceleration the more would be the force (the mass being constant). So to strike fear in the hearts of the batsmen, the bowler needs to be able to apply a fairly large acceleration in a short amount of time; maybe impart enough speed to beat Stuart and his dad’s delivery speeds combined.
In 1932-33, Jardine consciously or unconsciously solved this part of the problem by scouting Harold Larwood to be his main man to implement the Leg Theory. Larwood bowled at speeds (i.e. the speed at which the ball left his hand) of almost 100 mph, much faster than almost all bowlers, so could whip in that extra bit of acceleration needed as per Newton’s second law’s equation.
But once released, remember the ball hits the pitch and loses velocity, partly due to the air resistance and partly due to the COR. Nevile Cardus, one of the greatest cricket writers to have ever lived, observed that Jardine may have succeeded because he got an assist from the COR of the pitches in Australia that summer. He wrote:
“For years and years, the Australian turf in good weather has been all against the rising fast ball…Even MacDonald could not bump the ball breast high is Australia…(but) Australian wickets today (i.e. at the time of that series) are not what they were: different soil is used in preparing them. This enables the…fast bowler to “lift” more than formerly.”
That ‘lift’ was because of a higher COR on the new surfaces – think of it as shifting from wood to steel in that vertical drop test. Incidentally in that paper the authors mention in the introduction that ball-surface interaction can have a great “effect on the style of play adopted by players” and even affect “the outcome of a match”. Or, as was in the case in 1933, the outcome of the Ashes.
So, finally this brings us to the Force. (The Newtonian variety, not the George Lucas variety.) Once the cricket ball has been delivered at a speed close to 160 kmph (100 mph) it will lose about 40% of its speed thanks to our friends, the COR and air resistance, but still reach the batsman in less than half a second. So, when a Shane Warne raves on air about Mitchell Johnson getting a ball past a batsman at 90 miles an hour, he is plain wrong, it is more like 60 miles an hour; still fast enough and deadly though, as we will soon find out.
A tall bowler will deliver at an angle close to about 60 degrees and the delivery will pitch and thanks to the jiggery-pokery of angular velocity and momentum, leave the pitch at a slightly lower angle (what they call ‘skiddish bounce’ in the comm. Box or studio analysis) but have enough distance to travel so that the arc takes it into the rib cage or the head of the batsman. That’s why the bowler has to bowl ‘short’, that is closer to his end of the pitch than the batsman’s. The vertical speed a cricket ball gets when dropped from about a 2m height is about 6.3 meters/second and after bouncing it becomes about 3.6 meters/second accounting for the slowdown because of COR. A bowler will bowl it also at similar speeds. Even with a COR of 0.5 and air resistance, our cricket ball will gather a lot of momentum (mass X velocity) as it leaves the pitch and heads towards the batsman. At the other end the ball will either come into contact with the bat, zip through to the keeper or hit the batsman if he is in the way or too late in getting out of the way.
The moment it hits something, there will be a ‘transfer of momentum’ (momentum of the colliding body i.e. the ball will transfer onto the body it collides with, say, the batsman) and the force with which it hits will depend on the change in velocity i.e. the acceleration of the ball. Usually when it hits a dead bat or the body of the batsman, for all purposes practical, the ball comes to a complete halt. That is pretty rapid reverse acceleration; think of it as what happens a car going from 60 to 0 in 3 seconds but only in case of the ball it is 8,000 to 10,000 times faster because all of it happens in the fraction of a second, about 0.001 to be precise.
That exerts a force of 8000 Newtons (N) [basic calculation of force = mass X acceleration], enough to lift a small car off the ground. Even at the reduced speed, that’s a lot of concentrated force. Which is why it is so dangerous to get hit by the ball2 – Bert Oldfield’s skull suffered a fracture when he was hit by a Larwood delivery, Chris Rogers suffered a bad blow to the back of his head during the recent Ashes Test match at Lord’s from a Jimmy Anderson delivery, and we all know the tragedy that befell Philip Hughes.
While the laws of physics are universally constant, as a tennis player, Devashish Joshi, who is on the Caltech team that competes in the College tennis circuit in the US and has members who are incredibly smart with rattling off physics equations and quick calculations, put it “I never think about science when playing.” That’s because out there in the middle, there is too little time to do all the calculations. Indeed, during the Bodyline series, Jardine’s tactics hit upon a fortuitous mix of the right physics in the right conditions and became important in winning the Ashes back, but it’s preposterous to think that he methodically put the pieces together with a copy of Principia Mathematica in his hand.
- Viv, as usual, had the last laugh by hammering Thomas’s next delivery out of the ground and replying “Greg, you know what it looks like, now go and find it.”
- In fact, the force is dangerous even at way more reduced speeds. I was casually bowling in the nets once to a friend of mine and got one delivery to rear up from a good length and it hit him on the ribs. I am barely 100 pounds and hardly generate any express pace but the next day I found out, my friend had suffered a fractured rib!