Mathematica Files for AJP Paper

Know_CL_Range_AJP This Mathematica file determines CD using an experimentally-determined range. The user also supplies CL, which we take to be zero for no-spin launches. We used this file to determine that CD = 0.2 for the 2D trajectory shown in Figure 12 in the AJP paper. This file contains numerous comments.

Sample_Excel_Trajectory_Analysis This Excel file determines CD and CL using Camera 1 data. The idea with this file is to use a computational tool simpler than Mathematica. We fit our data using quadratics, which assumes a constant net force. The ball does not, of course, have a constant net force on it. During the time Camera 1 records, however, the net force on the soccer ball does not change too much. By smoothing the data, we can use equations (14) and (15) in our AJP paper to obtain estimates of CD and CL, respectively. The Mathematica file below shows that the CD obtained in the Excel file is reasonable due to the fact that the CL obtained in Mathematica is not terribly sentistive to our choice of CD.

Trajectory_Coefficients_Camera_1_KnowCD_AJP This Mathematica file determines CL using Camera 1 data and a user-supplied CD. The assumption is that both CD and CL are constant during the short time Camera 1 records the launch of the soccer ball. We set this up so that the data are equally-spaced in time, and the data set is of the form {t, x(t), y(t), z(t)}. All y values are 0; the reason we include y values is for future extensions to our work. This file contains numerous comments. Click here for a the data file we used to make the graph in the Mathematica file. We shift the origin to match the measured launched position (shifting the orgin does not, of course, change the physics!). It corresponds to the Camera 1 data in the lower-left corner of Figure 14 in the AJP paper. Note that this file may be modified to include CD as a free parameter as well. Of course, the more free parameters, the more challenging it is to optimize them all. Our strategy is to find CD from the first Mathematica file and then determine CL once we know CD .

Know_CD_CL_Range_AJP This Mathematica file determines CS using an experimentally-determined range. The user supplies CD and CL; the latter we take to be zero for pure side-spin launches. This code solves the 3D trajectory problem; it contains numerous comments. Our goal in the future is to obtain experimental data for the full three-dimensional trajectory, and then use that data to determine CS in the same way we found CL from the Camera 1 data. Assuming a constant CS, however, gives us a Mathematica-produced value of CS that is consistent with Figure 7 in the AJP paper.