Wind Tunnel Test

The Reynold's number of a standard Wilson U.S. Open ball (2.586 inch diameter) was calculated based on the serve velocity that a top elite player can generate - 120 MPH. An 11" diameter Wilson novelty tennis ball and one other ball (8.83" diameter ball) will be used. The second ball is "bald" (no fuzz).

The circumference of the balls and diameters are in Table A:

Table A	Standard Tennis Ball	11" Tennis Ball Model	8.83" Bald Model (Gumball - Child's Beach Ball)
Circumference (inches)	8.125	34.6875	--
Diameter (inches)	2.586	11.04	8.83
Diameter (meters)	0.06569	0.2804	.224

In calculating Re =rUD/m, a value of r=1.2255 kg/m3 and a value of m = 1.8 E-5 kg/m s (1 atm 20 degrees C) was used. For Res (Re of the small ball) to equal Rel (Re of the large ball) based on the difference in the diameters of the balls, the velocity of the large ball needs to be scaled. Setting the Reynold's number of the large ball equal to that of the small ball, the following chart was derived.

The tunnels lowest speed is 20 ft/sec (6.096 m/s or 13.636 mi/hr) and the high speed is 170 ft/sec (51.82 m/s or 115.907 mi/hr). Since speed statistics in tennis are recorded in miles per hour the team would like to vary wind tunnel speed settings in 10 MPH increments.

Since the highest ball speed observed in tennis is approximately 140 MPH, the equivalent speed for the 11" Wilson ball will be 48.11 feet/second.

Additionally, the rotational speed (spin) was scaled using a Reynolds number based on the angular velocities.