# Spinning cricket balls and weight distribution

An article on ESPN Cricinfo discusses the possibility of the internal weight distribution of cricket balls having an impact on the ability of a bowler to achieve 'spin'.

In cricket, a spin bowler imparts rotations on the ball at the point of release and thereby seeks to deceive their opponent (the batter) through either (i) the trajectory of the ball through the air; or (ii) the ball's behaviour once it comes into contact with the playing surface. [The ball will, as a general rule, be delivered at an initial velocity of 80-90kph and will travel c. 15 metres after it is delivered prior to bouncing, and a further 3 metres before reaching the position in which the batter is initially situated]

In the article, a cricket ball manufacturer states:

You can change the construction of the core so that it is more conducive to spin bowling, by weighting the core more heavily in the middle. It has an effect like an ice skater on the rink: when she spins with her arms wide, she spins slowly, and as she brings her arms in, she accelerates. All she has done is bring her weight in, which has enabled her to spin faster.

Is this claim accurate?

• Is what claim accurate? It is not clear what you are asking. Have you done any research to find out for yourself? – sammy gerbil Aug 27 '16 at 1:21
• The claim in the quote, i.e. that different weight distributions in cricket balls affect how conducive they are to spin bowling. In terms of my own research, I have looked over my school mechanics notes and have spoken to a couple of friends with first class honours degrees (in Physics and Chemistry) from Oxford, neither of whom knew the answer but one of whom suggested this site... – Paul Aug 27 '16 at 9:25

Yes, different weight distributions in cricket balls affect how conducive they are to being spun.

The quote seems self-explanatory. You must have encountered this phenomenon in school physics. A solid cylinder rolls down an incline more quickly than a hollow cylinder of the same mass and radius. After rolling the same distance they lose the same PE and gain this same amount as KE. However, the solid cylinder has greater translational KE while the hollow cylinder has greater rotational KE.

How this distribution of mass is achieved can be seen in the following photo from your link. This core is made up of cork and rubber particles which have been heated and compressed. Surrounding it are alternate layers of cork bound by woollen yarn. The outer coating of the ball is made of smooth leather, but a heavy thread is used around the seam (just visible at the rim) to give the bowler enough grip to spin the ball.

How difficult a ball is to spin - its rotational inertia - is measured by its moment of inertia (MI). For a ball of mass $M$ and radius $R$ the MI about an axis through the centre can be written as $\frac25 kMR^2$ where $k$ is a fraction depending on the distribution of mass. If the mass of the ball is distributed uniformly then $k=1$ whereas if all the mass were concentrated in a shell at the rim then $k=\frac53$. If the mass were concentrated at the centre then $k=0$.

The Laws of Cricket require the mass of the ball to be within the range 156-163g and to have a circumference of 224-229mm, but there are no restrictions on internal construction or distribution of mass. National standards (eg British Standards Institute, BSI) cover seam height, hardness and wear.

Although all balls are traditionally made of cork and rubber inside a leather cover, there is considerable variety in construction even at international level. There is usually a core surrounded by 5-6 layers of cladding which alternate cork with wool or cotton yarn. Cores vary from solid cork to solid rubber, or a mixture of the two - or none at all - which may or may not be compressed. Cladding varies between winding the woollen yarn under tension when wet (which increases the tension when it has dried) or relatively loosely (as in the image above). With these options. the mass of the ball could be concentrated in the core (easy to spin) or in the cladding (more difficult to spin). Another variation is an irregularly-shaped core - which gives the ball a preferred axis of spin.

Assuming that core and cladding densities are in the ratio $d+1$, and the radii of the core and the ball are in the ratio of $r$, and ignoring any difference between cladding and leather cover, the MI of the ball is characterised by
$k=(dr^5+1)/(dr^3+1)$.

Cork and rubber have densities of about 14-16 and 69-74 lb/cu.ft respectively. Assuming these are the extreme densities possible for the core and cladding - giving $d \approx 4$ or $d \approx -\frac45$ - and assuming $r \approx \frac12$, then by switching cork and rubber between core and cladding we can achieve the extreme values $k \approx \frac34$ and $k \approx \frac{13}{12}$.

So the moment of inertia of a cricket ball could be varied in the ratio of about $13:9$ by shifting mass from the cladding to the core.

• Thanks - very useful answer. Would the way in which rotation is imparted on a cricket ball by a bowler (that is, by the rotation of the hand in which the ball is held whilst the bowling arm comes over, with the result that the forces imparted right up until the moment of release are in more than one direction) be relevant? (it will only be at the final moment of release that the force imparted is in one direction only)_ – Paul Aug 31 '16 at 6:14
• Yes, how much spin is imparted depends on torque and how long it acts. Overarm rotation itself imparts top-spin though the ball is not spinning in the bowler's hand. Further top-spin can be generated as the ball 'rolls' out of the hand, as on an inclined plane. Side-spin is (I think) mostly generated by the final flick of the wrist which you refer to. A lot depends on technique and strategy, which I am not very familiar with : deception might be more important than maximising spin. Physics explanations usually ignore how spin is imparted and focus on the aero-dynamics of spin. – sammy gerbil Aug 31 '16 at 12:24