Aerodynamics in the classroom and at the ball park
(a) Conventional swing of a new cricket ball results from the asymmetric air flow around the ball. The stitching is inclined at about 20° to the ball path and is maintained in that orientation by rotation of the ball about an axis perpendicular to the stitching. Black dots denote the boundary layer separation points. (b) Reverse swing of a new ball occurs at high ball speeds due to asymmetrical separation of the turbulent boundary layers on each side of the ball.
The three types of ball used in this study: (a) smooth ball, (b) smooth ball modified by gluing a circular loop of string around the ball to simulate a raised seam, and (c) smooth ball modified by gluing a single length of string to the ball as an artificial baseball seam. Each ball was projected in the x-direction with backspin.
Lacrosse type launcher used to throw balls.
Experimental arrangement used to measure the vertical (z) and horizontal (y) deviation of a ball over the horizontal distance D from the launch point to the impact point with a vertical target. Camera A was used to record the ball trajectory in the vertical xz-plane, while camera B was used to measure the horizontal launch angle, the ball spin, and the impact point on the target.
The forces acting in the xz-plane on a ball with backspin include the gravitational force mg, the drag force , the lift force , and the buoyant force .
Results obtained with a 101-mm diameter polystyrene ball launched with backspin at 28 m/s showing (a) z vs. x and (b) drag force () vs. ball speed (v). Experimental data points are shown at intervals of 1/60 s. The curved line in (b) is a best fit power law of the form , which gives n = 1.73 (enhanced online) [URL: http://dx.doi.org/10.1119/1.3680609.1]. 10.1119/1.3680609.1
(a) Drag and lift coefficients calculated from the data shown in Fig. 6 (Reynolds number on top axis). (b) The lift coefficient as a function of the spin parameter , where R is the ball radius.
Results obtained with a 228-mm inflatable plastic ball launched with backspin at 10.8 m/s showing (a) x (left scale) and z (right scale) vs. time and (b) values of the drag coefficient () and the lift coefficient () calculated from the results in (a). The solid and dashed curves in (a) are best fit polynomials of order n = 2 and n = 3, respectively. Experimental data points are shown at intervals of 1/60 s.
Drag and lift coefficients for the 228-mm plastic ball as a function of speed v. Each data point corresponds to a different throw. Results for the two boxed data points are shown in Fig. 8. The solid and dashed lines are best-fit curves to the experimental data.
Sideways break of a 98-mm diameter polystyrene ball plotted as a function of average speed over the 5-m distance from the launch point to the target. The ball was fitted with an artificial seam and projected as shown in Fig. 2(b) with backspin. The curved line is a quadratic fit to the experimental data, each point representing a different throw.
Rotation of a polystyrene ball with a baseball seam, as viewed by the batter, shown at intervals of 10 ms. The time for one revolution was 126 ms, corresponding to backspin of 474 rpm. The ball was thrown at 11.8 m/s and curved to the left as viewed by the pitcher or to the right as viewed by the batter. The break in the y-direction was 90 cm over a distance of 5 m in the x-direction. The region enclosed by the dashed circle around the axis remained smooth since the seam did not rotate into that region (enhanced online) [URL: http://dx.doi.org/10.1119/1.3680609.2]; [URL: http://dx.doi.org/10.1119/1.3680609.3]; [URL: http://dx.doi.org/10.1119/1.3680609.4].10.1119/1.3680609.210.1119/1.3680609.310.1119/1.3680609.4
A negative Magnus force can arise as shown here if the air flow is laminar on the upper side of the ball and turbulent on the lower side. In this example, the peripheral speed of the ball due to spin is 4.4 m/s, the center of mass speed is 10 m/s, point A translates to the right at 5.6 m/s and point B translates at 14.4 m/s. The air flow near A is laminar, and the flow near B is turbulent.
Mass (M) and diameter (D) of the four balls used in the experiments. The ball type is shown in Fig. 2.
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