Fig 1.
Model of the factors affecting the launch and spin directions of the batted ball.
(A) Oblique impact on the horizontal plane. (B) Oblique impact along the short axis cross-section of the bat. (C) Oblique impact when the distal side of the bat is tilted downward. (D) Side spin generation because of the bat velocity toward the proximal side. (E) Backspin or topspin generation because of the upward or downward path of the bat velocity.
Fig 2.
(A) Schematic of the position of 15 optical cameras. (B) Locations of reflective markers (stickers).
Fig 3.
Definition of each variable.
Table 1.
Definition and description of parameters in ball−bat interaction.
Fig 4.
Calculation procedure of spin axis and spin rate of the batted ball.
Fig 5.
Distribution chart of launch direction for each hitting condition.
Fig 6.
Mean and standard deviation of each variable for each group of the launch direction.
V*H indicates the p-value and partial η2 of the vertical and horizontal interactions of the batted ball; V indicates the p-value, with partial η2 indicating the main effect of the vertical direction group and H indicating that of the horizontal direction group. Alphabets indicate significant differences between corresponding groups observed by the simple main effect analysis. Vertical bars indicate that interaction was absent, but a main effect existed between the vertical direction groups.
Fig 7.
Direction of the spin axis of batted ball for each group sorted according to the horizontal launch direction.
Each plot on the spherical surface represents the direction of the spin axis, and they are shown in two directions, with views seen from the near side (upper side) and from above (lower side) relative to the travel direction of the ball (y’-axis). The plot on the spherical surface does not display the front and back side of the sphere separately, and both are also shown on the front side. The spin rate of the batted ball is only represented in some plots that deviate from the overall trend.
Fig 8.
Changes in the mean value of all participants in the horizontal launch group used in the stepwise multiple regression analysis.
Fig 9.
Association with the undercut and line of impact angles on the vertical launch angle, angular velocity of batted ball, and ball exit velocity.
The horizontal axis in A, C, and E (top) indicates the line of the impact angle, whereas that in B, D, and F (bottom) indicates the undercut angle.
Fig 10.
Practical application for improving the performance of the opposite-field hitting.
Fig 11.
Association with the impact location from barrel end on the ball exit velocity and horizontal launch angle.
Impact location indicates the ball coordinates along the bat’s long axis (x′-axis) relative to the coordinate system fixed in the bat. The positive and negative directions of x′-axis were reversed with an emphasis on clarity.