The Wind Tunnel (Page 9)

You read in all the popular tennis columns about the speed of the game - "it's too fast" or "it's a game of serves". How would you slow it down - change the pressure in the ball? Make the ball a little bigger? It's been considered!

Let's go with this last suggestion. It makes sense - the ball is a little bigger and will have a little more surface area and thus a little more drag. But what happens to Re when the ball is made larger (i.e. a longer diameter)? Remember - Re is a combination of viscosity, density, velocity, and length. The viscosity and density of the air remain the same and let's assume you can still hit the ball at the same velocity too. So with that in mind when the diameter of the tennis ball goes up, Re goes up. Now look at the C_d Versus Re chart. This isn't the curve for a tennis ball - but let's use it. (As we mentioned above the surface roughness of the tennis ball has shifted this curve to the left.) In the range of 10⁴ - 10⁵ you can see that as Re increases, C_d is increasing a tiny bit. So the argument above would be true. A slightly bigger ball (with the same velocity, air density and viscosity) would have a little higher C_d - more drag will mean a slower ball. (Again we must keep in mind that this is not the data and curve for a tennis ball.)

There's just one problem - what if you're in the range where the flow transitions into a turbulent boundary layer. Look at that C_d drop - WOW! The drag will be reduced drastically. Instead of slowing the game down it could speed it up!

So tennis researchers want to determine and understand this C_d Versus Re curve for a tennis ball and understand where Re_crit is. Other tennis researchers are conducting wind tunnel tests and no one has determined that number yet. Dr. Rabi Mehta feels the ball is so rough that in tennis you are always playing in the "post critical regime", i.e. the ball is so rough that transition occurs at a very low velocity.