## 2 Methods  
Balls were projected horizontally at 36 \(\pm\) 1 m/s (\(Re\) = 1.8 \(\times\) 10\({}^{5}\)) using a pneumatically actuated piston, as shown in Figure 2. Ball speed was measured from a speed sensor from the time for the ball to pass between light screens (iBeam, ADC) spaced 0.4 m apart. Ball acceleration, \(a\), was found from subsequent speed measurements (\(V_{1}\) and \(V_{2}\)), taken \(D\) = 3 m apart along the ball's trajectory, or  
\[a=\frac{{V_{2}}^{2}-{V_{1}}^{2}}{2D} \tag{1}\]  
The drag force was found from the ball's mass (145 g) and acceleration. The measured diameter of each ball was used to find \(C_{d}\). The drag coefficient from three balls was taken from the average of four measurements per ball.  
Balls are commonly projected with spin from a wheeled pitching machine. Rubber wheels, rotating at different speeds, accelerate the ball and impart spin. Baseballs used in play have a leather cover, which is abraded by the rapid acceleration from spinning pitching machine wheels. The aerodynamic properties of baseballs roughened by the pitching machine can be significantly different from those used in play. In this work, the spin was imparted to balls using a cradle attached to the end of the pneumatic piston [19]. The cradle, shown in Figure 3, had an opposing high and low friction surface, which imparted spin as the piston reached the end of its travel and the ball rolled out of the cradle.  
The spin rate increased with the cradle length. By adjusting the ball's position in the cradle prior to firing, the spin rate was controlled. The orientation of the spin axis was controlled by the orientation of the cradle prior to firing. In this work, a horizontal spin axis was used to create a backspin and lift. Visual inspection and repeated drag measurements demonstrated an ability to impart spin without damaging the ball or altering its drag.  
The accuracy of the drag measurement is a function of the air density, light screens, ball geometry and ball mass. The distance between the screens was controlled to within 0.2 mm, and the seam on the baseball was 0.9 mm high. If the ball rotates while passing through the screens, the seam can add an error to the drag measurement. The screen spacing error, the 36 m/s ball speed and 0.4 m screen spacing used here resulted in \(\Delta C_{d}\) = 0.004. The distance between screen pairs, \(D\), was within 3 mm, where \(\Delta C_{d}\) = 0.0003. The average ball mass was 145 g and was within 15 mg, where \(\Delta C_{d}\) = 0.002. The average ball diameter was 75 mm and measured with a pi tape to within 0.2 mm, where \(\Delta C_{d}\) = 0.003. Temperature affects air density, which was within 1 \({}^{\circ}\)C along the ball path, where \(\Delta C_{d}\) = 0.002. The time between successive light screens was measured at 80 MHz (VG03, ADC), making the error in time negligible in comparison to the other factors considered here. By assuming the  
Particle Image Velocimetry (PIV) measurements were conducted in the Aerodynamics Laboratory of TU Delft to visualize the baseballs' wake in free flight for the non-spinning case. The air was seeded with micron-size water-glycol particles produced by a Safex seeding generator. The particles were illuminated via a Quantronix Darwin Duo Nd:YLF laser (25 mJ pulse energy at 1 kHz, 527 nm wavelength). Images were recorded by a LaVision HighSpeedStar6 camera (CMOS, 1024 \(\times\) 1024 pixels, 20 mm pixel pitch, 12 bit) in frame-straddling mode (\(\Delta\)t = 40 ms), at a repetition rate of 500 Hz. The camera used a Nikkor lens with a focal length of 60 mm and an aperture f stop of 2.8. The image magnification was M = 0.12, resulting in a digital image resolution of 0.166 mm/pix. The images were processed using the cross-correlation-based algorithm (LaVision, DaVis 8.4) with image deformation and interrogation windows of 32 \(\times\) 32 pixels with a 75% overlap factor.