1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The effect of spin on the flight of a baseball
Rent:
Rent this article for
USD
10.1119/1.2805242
/content/aapt/journal/ajp/76/2/10.1119/1.2805242
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/76/2/10.1119/1.2805242

Figures

Image of Fig. 1.
Fig. 1.

Forces on a spinning baseball in flight. The drag force acts in the direction, the Magnus force acts in the direction, and the force of gravity acts downward.

Image of Fig. 2.
Fig. 2.

Experimental results for . The closed circles are from the present experiment. Open circles are from Watts and Ferrer (Ref. 18), open triangles are from Briggs (Refs. 12 and 17), open diamonds and squares are from Alaways two- and four-seam (Ref. 23), respectively (Refs. 8 and 9), and closed triangles are from the pitching machine data of Jinji (Ref. 11). Also shown are the parametrizations of Ref. 5 (solid) and Eq. (3) (dashed), the latter calculated for a speed of .

Image of Fig. 3.
Fig. 3.

Calculated ratio of the Magnus force to weight for . The solid and dashed curves utilize the parametrizations of Refs. 5 and 7, respectively, the latter essentially reproducing Fig. 2.2 of Adair (Ref. 7).

Image of Fig. 4.
Fig. 4.

Trajectory data (top) for one of the pitches, where and are the coordinates of the dot on the ball in the coordinate system shown in the inset. The ball is projected at a slight upward angle to the direction and is spinning clockwise (topspin) about an axis perpendicular to the plane. Solid curves are least-square fits to the data using Eq. (4b), resulting in and . The long dashed curve is the center-of-mass trajectory for the coordinate, which is consistent with a downward acceleration of due to the combined effects of gravity and the Magnus force. The short dashed curves are the center-of-mass coordinates for both and with both and set to zero, indicating that the data are very sensitive to but not to . The fit residuals for the (points) and (curve) coordinates are shown in the bottom plot.

Image of Fig. 5.
Fig. 5.

Results for from the present motion capture experiment.

Image of Fig. 6.
Fig. 6.

Results for from the present experiment for in the range 0.15–0.25, demonstrating that does not depend strongly on (or Re) for fixed values of .

Image of Fig. 7.
Fig. 7.

Calculated trajectories of a hit baseball with an initial speed of , angle of 30°, height of , and backspin of (solid), (long-dashed), and (short-dashed). The points indicate the location of the ball in intervals. These calculations utilize the values of Adair (Ref. 7) and the values from the parametrization of Sawicki et al. (Ref. 5).

Image of Fig. 8.
Fig. 8.

Calculated range of a hit baseball with an initial speed of , height , and backspin of (solid), (short-dashed), and (long-dashed), as a function of the initial angle . These calculations utilize the values of Adair (Ref. 7) and the values from the parametrization of Sawicki et al. (Ref. 5).

Tables

Generic image for table
Table I.

Calculated deflection of a pitched baseball thrown with an initial horizontal velocity , spin , and spin factor after traversing . These calculations utilize the values of Adair (Ref. 7) and the values from the parametrization of Sawicki et al. (Ref. 5). These deflections are in accord with experimental observations (Refs. 11 and 28).

Loading

Article metrics loading...

/content/aapt/journal/ajp/76/2/10.1119/1.2805242
2008-02-01
2014-04-21
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The effect of spin on the flight of a baseball
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/76/2/10.1119/1.2805242
10.1119/1.2805242
SEARCH_EXPAND_ITEM