J Phys Fitness Sports Med, 2(1): 63-68 (2013)

JPFSM: Review Article How spin influences the performance of a

Tomoyuki Nagami1, Takatoshi Higuchi2 and Kazuyuki Kanosue1*

1 Faculty of Sport Sciences, Waseda University, 2-579-15 Mikajima, Tokorozawa, Saitama 359-1192, Japan 2 Graduate School of Sport Sciences, Waseda University, 2-579-15 Mikajima, Tokorozawa, Saitama 359-1192, Japan

Received: January 17, 2013 / Accepted: January 23, 2013

Abstract In the present review, we include a series of recent experiments in order to update and summarize the characteristics of ball spin in baseball pitching. The motion of a ball thrown by a pitcher is influenced by three forces: gravity, the drag force due to air resistance, and the lift force which deflects a ball vertically or laterally due to the Magnus effect (Magnus force). The forces acting on a baseball are influenced by the ball’s translational speed and spin rate as well as the orientation of the spin axis. The lift force acting on the ball becomes greater with in- creases in the “spin parameter” (proportion of the spin rate and the movement speed) when the spin axis of the ball is orthogonal to the direction of movement. On the other hand, when the spin axis is located in line with the direction of the movement (so-called “gyro ball”), the drag force becomes smaller and the lift force decreases to nearly zero regardless of the spin param- eter. The orientation of the spin axis also affects the direction of the lift force on the ball; that is, the lift force acts perpendicular to the cross product of the spin axis and the direction of mo- tion. There are great variations in the spin of ; both spin rate and orientation of the spin axis vary widely across individual . When the spin rate is extremely low, such as with a knuckle ball, the amount and direction of lift force changes irregularly during flight. This is caused by seams on the ball surface, which cause an unpredictable “fluttering” trajectory. The reason for the success of pitchers that can produce abnormal or unique ball spins is discussed. Keywords : lift force, drag force, wind tunnel experiment, video analysis

the gravitational force is constant, differences in a ball’s Introduction flight trajectory are due to alterations in the drag force In the faceoff between a pitcher and a batter, two skilled and lift force. In the case of an airplane, the shape and athletes have diametrically opposed goals. The goal of the orientation of the airfoils have a significant influence on batter is to make a clean hit, while that of the pitcher is the drag force and lift force. Although a baseball has no to get the batter out. Although the pitcher must throw the such structures, the drag force and lift force nevertheless ball in an area where the batter has the potential to make affect a baseball’s flight trajectory. In this review, we first contact, pitchers have many ways of thwarting the bat- describe previous research on the determinants of the drag ter’s ultimate goal. Good pitchers can throw many kinds and lift forces acting on a pitched ball, and subsequently of pitches, including fastballs and various kinds of break- summarize recent studies that elucidate how these forces ing balls, such as and forkballs. Each type of are affected by ball spin. has a unique flight trajectory. For example, a curve- ball has a larger amount of vertical drop as compared Drag force with a fastball1). Even the trajectories of pitches of similar speed and expressed with the same word can be different The drag force acts on a ball in the direction opposite to between pitchers, and these subtle differences can have translational movement, and thereby decreases ball veloc- a major influence on the pitcher’s overall performance. ity. In general, drag force is expressed by the following Thus, a particular individual’s fastballs are typically dis- equation: tinguishable from those of other pitchers due to slight dif- 2 ferences in lateral trajectory and/or the appearance of an FD = 1/2 ρ v A CD, upward “hop”. *** (N) is given below, but it is not in the equation*** Flight trajectory of an object is affected by the par- ticular forces acting on it. For a pitched ball, the three where FD is the drag force on a ball (N), ρ is air density main forces are gravity, drag force and lift force2). Since (kg/m3), v is the translational velocity of the ball (m/s), A

is the ball’s cross-sectional area, and CD is the drag coef- 2) *Correspondence: [email protected] ficient . CD is an independent variable whose value de- 64 JPFSM: Nagami T, et al. pends upon the shape, orientation, spin and other aspects that location. This produces an upward force. If Fig. 1 is of a flying object. Clarifying these factors would lead to a viewed from an alternative perspective, such that the axis greater understanding of the drag force acting on a ball. of spin points directly at the viewer, then the view is from To analyze the drag force acting on a baseball, the most the top, and the upward (lift force) force acts on the ball commonly conducted experiments involve wind tunnels so that it moves toward the right. in which the tension on a wire suspending a spinning ball In general, the magnitude of the lift force (FL) on the is measured. This experimental setting allows the control flying object is expressed by the following equation: of the ball spin rate and ball speed (speed of the air cur- 2 rent). However, the direction of the spin axis is limited to FL = 1/2 ρ v A CL, horizontal, and is perpendicular to the airflow. Wind tun- nel experiments have been utilized to analyze the aerody- wherein ρ is the air density, v is the velocity of object (m/ namics of not only , but also balls used in many s), A is the cross-sectional area of the ball, and CL is the 3-7) 2) sports . lift coefficient . As with CD, CL depends on several fac- For a baseball, when the spin axis of the ball is or- tors such as shape, orientation, and spin of the flying ob- thogonal to the direction of motion, CD increases with an ject; so it is obtained only experimentally, by monitoring increase in the “spin parameter”8). Spin parameter (Sp) is the object’s flight under various conditions. expressed by the following equation: A series of wind tunnel experiments8,13-15) and high- 2,16,17) speed motion analyses indicate that the effect of CL

CD ∝ Sp = r ω / v on a baseball with back spin, axis of which is perpendicu- lar to the movement direction, has a linear relationship wherein r is the radius of the ball (0.036 [m]), ω is the with a spin parameter greater than 0.1. Under conditions angular velocity [radian/s] of ball spin, and v is the free- when other factors are equal, the faster the spin rate, the stream velocity (= ball speed) [m/s]. The faster the ball greater the CL and lift force. spin, the bigger the CD; that is, the bigger the drag force. The above results are true only when the ball is spin- When the spin axis is located in line with the direction of ning with its axis perpendicular to the movement direc- 9) 18) movement (the so-called “gyro ball” ), the CD receives tion. Jinji and Sakurai made a detailed video analysis almost no influence from the spin parameter and tends to and calculated the spin rate and spin axis of fastballs and be smaller than the CD at the spin axis orthogonal to the curveballs thrown by ordinary collegiate pitchers. They 8) direction of motion . In this manner a “gyro ball” has a demonstrated that the CL for the balls thrown by actual smaller drag force than a with an identical ball pitchers was not correlated with the Spin parameter, but speed and spin rate; and it thus reaches home plate with a was closely correlated with the product of the spin rate faster ball speed. and the sine of the angle between the spin axis and the movement direction. Mizota et al.8) also demonstrated, utilizing a wind tunnel, that no lift force acts on a ball Lift force having a spin axis in line with the direction of forward Lift force acts on a ball in a direction perpendicular to movement. A pitch with these characteristics is sometimes the line of ball motion and deflects the ball vertically and termed a “gyro ball”. Thus, the lift force on a spinning laterally. (Some researches have defined the lift force as baseball is influenced not only by its spin rate, but also by the force acting on the ball in a vertical direction, and the the angle between the spin axis and movement direction. “side or lateral force” as a force acting on the ball in a Additionally, the orientation of the seams on a baseball lateral direction. In this review, however, any force acting may influence the lift force acting on the ball. An official on the ball perpendicular to the line of ball motion, either baseball is covered with 2 pieces of hide that are stitched vertical, lateral or a combination of both, is termed a “lift together with strings. The seam is approximately 1 mm force”.) Magnus10,11) noted that the spin of a flying object in fluid (including air) creates a force that pushes the ob- ject sideways. This phenomenon is commonly called the “Magnus effect”, and two different mechanisms have been invoked to explain this effect. One mechanism is based on conservation of momentum and the other based on Bernoulli’s principle12). As pictured in Fig. 1, when the ball moves leftward while spinning clockwise, the air under the ball decelerates as it is dragged by the spinning ball’s surface. On the other hand, the air above the ball accelerates. As a result, a pressure gradient is created with lower pressure above the ball due to the faster air speed at Fig. 1 Airflow around a spinning baseball in flight. JPFSM: Baseball pitching and spin 65 high and approximately 8 mm wide, so it is likely that in the movement direction, then the middle finger will differences in seam orientation relative to flight direc- point in the direction of the spin-induced deflection (the tion would have an effect on movement of the air stream. coordinate right-hand rule) (Fig. 3)20). For example, in the This effect is reflected in popular baseball terminology, case where the azimuth angle is 0° and the elevation angle which differentiates between “four-seam” and “two-seam” is -45° (45° downward, Fig. 4), the lift force will act on fastballs. Technically, this terminology refers to the num- the ball in an upward and rightward direction as viewed ber of seams per rotation that pass a point in the plane from the pitcher. In the case where the elevation angle is perpendicular to the axis of rotation (Fig. 2). In general, -90°, no upward lift force acts on the ball, but it increases since they are much more commonly thrown, the term the rightward deflection. Thus, in order to have optimal “fastball” generally refers to a four-seam fastball. All the control over the ball flight trajectory, the ability to control studies cited above examined four-seam fastballs. Data not only the ball’s spin rate but also the direction of its from a study by Sikorsky and Lightfoot13) show that a dif- spin axis is required. ference in seam orientation has a large effect on the lift coefficient, and hence the lift force and lateral deviation Spin on fastballs thrown by actual pitchers for spin parameters less than 0.2. Alaways and Hubbard16) examined the difference in CL between four-seam and Until recently, little was known about the spin of balls two-seam fastballs. The lift force on fastballs launched actually thrown by baseball pitchers. Jinji and Sakurai18) by a pitching machine was bigger for four-seam spin than showed that the spin axes of fastballs thrown by colle- two-seam spin, although their spin parameters showed the giate pitchers were tilted vertically and horizontally. In same values. On the other hand, Mizota et al.8), using a their terminology, the orientation of the spin axis was de- wind tunnel, found that the CL of two-seam backspin was fined by azimuth θ and elevation φ (Fig. 4). In their study unchanged when the spin parameter was between 0.2 and the mean initial ball speed was 34.5 ± 0.2 m/s and the 0.3. These results do not coincide with those of Alaways mean ball spin rate was 31.2 ± 1.5 rps. The mean angles and Hubbard16). High-speed motion analysis by Takami of θ and φ were 31 ± 13°, and -26 ± 11°, respectively, for et al.19) showed that differences in the orientation of the right-handed pitchers. Given these values, the lift acts on seams did not directly affect the aerodynamic character- the fastball upward and rightward; the ball would move istics of the ball. There is still controversy regarding the effect of seam orientation on a ball’s flight trajectory, and it is likely that other factors, as yet unappreciated, are in- volved.

Direction of the lift force As already described, the lift force deflects a ball verti- cally or laterally, and orientation of the spin axis is the main factor determining the direction of the lift force. Ba- hill and Baldwin20) have demonstrated that the direction of deflection of the ball is perpendicular to the cross product Fig. 3 A) Angular velocity - right hand rule. B) Coordinate of the spin axis and the direction of motion. Thus, when system right hand rules. (cf. Bahill and Baldwin20)) the spin axis of the ball is orthogonal to the direction of motion, the direction of the spin-induced deflection of the ball can be determined using the right-hand rule (Fig. 3). As shown in Fig. 3A, if the fingers point in the direction of rotation, the thumb points in the direction of the spin axis (the angular right-hand rule). If the thumb points in the direction of the spin axis and the index finger points

Fig. 2 Difference in the direction of seams between 4-seam Fig. 4 Definition of the direction of ball spin axis with azimuth spin and 2-seam spin. θ and elevation φ. (Cited in Nagami et al.21)) 66 JPFSM: Nagami T, et al.

0.37 ± 0.12m upward and 0.20 ± 0.12m rightward as However, this expectation would cause a misestimate of compared to a trajectory with free fall. The authors also the trajectory of this experiment’s 36 m/s fastballs that noted a significant, important correlation: the higher the had backspin rates other than 30 rps. This result and per- ball speed, the greater the spin rate. formance of the collegiate pitcher described above (Sub. We recently examined the direction of the spin axes of C in Fig. 5) suggest that throwing pitches with abnormal fastballs thrown by 11 elite professional and 11 elite col- ball spin rates and/or unique spin axes make pitches more legiate pitchers21). There was no significant difference in difficult to hit. the spin rate or direction of the spin axis between the pro- fessional and collegiate pitchers. Also, there was a posi- Spin on a tive correlation between the initial ball speed and the spin rate (Fig. 5A), which agrees with the results of Jinji et There have also been relatively few studies on the spin al.23). It should be noted that spin rate was more variable of breaking balls. Selin24) filmed flight trajectories of vari- across subjects as compared with ball speed (Fig. 5B). ous kinds of pitches and reported that each pitch showed The spin parameter (the ratio of the spin rate to the ball vertical and horizontal deviations. Jinji et al.18) also ana- speed) of the fastball thrown by one of the collegiate lyzed the spin and flight trajectories of curveballs thrown pitchers (Sub. C in Fig. 5) was greater than those of any by collegiate pitchers. Curveballs rotated in a top-spin other subjects. In addition, the direction of the spin axis direction, and the balls moved 0.29 ± 0.09 m downward was closer to true back spin (a spin axis that is completely and 0.20 ± 0.10 m leftward compared to a trajectory with horizontal and perpendicular to the direction of motion) free fall. These ball movements were the opposite of the than that of any of the other subjects (Figs. 6, 7). So his movements of fastballs. Therefore, this feature of the fastballs would have a larger upward lift force than fast- would make it an effective option for retiring a balls of similar speed thrown by the other pitchers. This batter. particular pitcher led his collegiate league in strikeouts Recently, we had the chance to analyze the spin on eight per 9 innings, and batters facing him described his fastball different types of pitches thrown by an elite professional as having good hop. pitcher25). Each type of pitch had a unique combination We also examined baseball batters’ accuracy in hitting of speed, spin rate, and orientation of the spin axis. His fastballs with different backspin rates (30, 40, 50 rps) at “” had an orientation of the spin axis that was al- a constant ball velocity (36 m/s) and with a constant ori- most identical to the direction of movement. These same entation of the spin axis (straight back spin)22). We found characteristics describe the so-called “gyro ball”. This that ball spin rate was positively correlated with increases pitch would have a minimal lift force, and the ball would in the distance from the optimal contact point of the just drop with the gravitational force. His “” swung bat (sweet spot) to the actual point of contact (r = showed a spin rate and orientation of the spin axis just be- 0.38, p < 0.001. Fig. 8). One explanation for this result is tween those of the four-seam fastball and the slider. Thus based on the positive correlation between launched veloc- the flight trajectory of the cut fastball was intermediate ity and ball spin rate that exists for real pitchers (Fig. 5A). between those of the four-seam fastball and the slider. This correlation may allow batters to estimate spin rate These examples indicate that practicing pitchers really from their judgment of a launched ball’s velocity. Since do throw pitches with a wide variety of flight trajectories the typical spin rate is around 30 rps for the 36 m/s fast- by manipulating ball spin rate and orientation of the spin ball that was used in our study, this is likely the spin rate axis. that the batters assumed was occurring for the pitches. Recently, advances in the techniques employed in the

Fig. 5 A) Relationship between initial ball speed and ball spin rate. B) Variability of initial ball speed and ball spin rate. (Cited in Nagami et al.21)) JPFSM: Baseball pitching and spin 67

Fig. 6 Direction of spin axes: A) view from pitcher, B) view from top. (Cited in Nagami et al.21))

Fig. 7 Differences in orientation of the spin axis of fastballs thrown by two subjects. (From Nagami et al.21))

is subject to forces from causes other than the Magnus effect. Future investigations will hopefully clarify the de- tails and mechanisms of these phenomena.

Pitches with a lower spin rate The pitches termed “forkball”, “change-up”, and “knuck- le ball”, generally have spin rates that are lower than the pitches previously described. They would thus have a low- Fig. 8 Average impact location (±SD) for batters hitting er lift force, and the pitched balls would follow the trajec- pitches with different back spin rates. tory close to that of a ball in free-fall. However, a knuckle ball, which is thrown with almost no spin, seems not to be flying solely in a state of free-fall, but in addition is wind tunnel domain have enabled investigators to cal- characterized by a “fluttering movement”28). Watts et al.29) culate the force on a ball with a spin axis which is not and Mizota and Kawamura30) elucidated the irregular perpendicular to the direction of movement26). The cal- movement of these pitches by determining the variable culations indicate that even if the elevation angle of the lift forces created by changes in airflow that result from spin axis is 0°, the lateral component of the lift force cre- different seam orientations relative to the direction of ball ated depends on the degree of the azimuth angle. Indeed, movement. In addition, the investigators also noted that Nathan27) reported a similar phenomenon through visual slight changes of seam orientation throughout the flight observation of the video image captured by a baseball of a ball with lower spin rates resulted in changes in the game broadcast. The above results suggest that a baseball magnitude and direction of the lift force. This could also 68 JPFSM: Nagami T, et al. lead to a fluttering movement of the ball. These charac- 12) Watts RG and Bahill AT. 1990. The origin of forces on a base- teristics of pitches with lower spin rates cannot be found ball, chapter 3. 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