A unified framework for the prediction of cricket ball trajectories in spin and swing bowling

Abstract

This paper builds on earlier work of the author that calculated the trajectories of cricket balls under fast swing bowling conditions, and develops a unified analytical framework for the consideration of both slow spin bowling and fast swing bowling. A classification of different types of bowling delivery, in so far as they relate to the flight of the ball through the air, is set out, and from this classification four generic cases of seam and spin plane angle are identified for further consideration. The force coefficient characteristics on spinning balls due to auto-rotational effects (due to the spin of the ball) are then derived, and these are used to develop the full equations of motion that can predict both swing and spin bowling trajectories. The four generic cases are then investigated using approximate solutions of these equations, the trajectories of spin bowling in lateral and vertical directions are explored and the relative magnitudes of flight displacements due to the boundary layer asymmetry (the cause of swing bowling displacements) and auto-rotational forces are discussed. Finally, the effects of cross winds on spin bowling trajectories are considered. In summary the paper presents an overall methodology that enables the various flow phenomenon associated with cricket ball flight to be considered in a unified manner.

Keywords

Cricket spin bowling drag Magnus effect auto-rotation

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References

Baker

. The calculation of cricket ball trajectories. Proc IMechE, Part C: J Mechanical Engineering Science 2010; 224(2): 61–74.

Mehta

. A review of cricket ball swing. Sports Engng 2005; 8: 181–192.

Sayers

. On the reverse swing of a cricket ball – modelling and measurements. Proc IMechE, Part C: J Mechanical Engineering Science 2001; 215(1): 45–55.

Brouy

Alam

Watmuff

. New methods of initiating reverse swing on a cricket ball. In: The engineering of sport III, Honolulu, HA, 2009.

Wikipedia. Bowling (Cricket), http://en.wikipedia.org/wiki/Bowling_(cricket) (accessed 23 August 2011).

Coverdale Cricket Masterclass videos. Swing bowling: http://www.youtube.com/watch?v=wBa1OxNYI-Y; spin bowling: http://www.youtube.com/watch?v=vlWYcuaTosc; http://www.youtube.com/watch?v=Si48Ch1EbRQ (2007, accessed 23 August 2011).

Sayers

Hill

. Aerodynamics of a cricket ball. J Wind Engng Ind Aerodynamics 1999; 79(1–2): 169–182.

Nathan

. The effect of spin on the flight of a baseball. Am J Physics 2007; 76(2): 119–124.

Carre

Asai

Akatsuka

. The curve kick of a football II: flight through the air. Sports Engng 2002; 5: 193–200.

10.

Baker

. The debris flight equations. J Wind Engng Ind Aerodynamics 2007; 95(5): 329–353.

11.

Quinn

Hayward

Baker

. A full-scale experimental and modelling study of ballast flight under high speed trains. Proc IMechE, Part F: J Rail and Rapid Transit 2010; 224(2): 61–74.