Tennis: Computational Fluid Dynamics (CFD)

Tennis: Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics of Tennis Balls

Computers are used extensively throughout aeronautics to aid in the design and analysis of aircraft, watercraft, and even sports equipment. Scientists have developed mathematical models which emulate the physics of fluids. These mathematical fluid models are programmed into software applications which can be used on the computer.

An engineer can take an object, like an airplane or ball, and use the fluid model to analyse how this object would perform in "flight". It's kind of like having a virtual wind tunnel. There is a special name for this type field of work. It's called "Computational Fluid Dynamics" or "CFD" for short. In this section we will show you the steps we take in doing a CFD simulation, by performing a simulation of the tennis ball.

Gathering the Correct Information

Before we can start we must first gather information about the tennis ball. Information like the tennis ball's size, the speed of the tennis ball, and the rate at which the tennis ball spins. We also need to note any distinguishing features of the tennis ball, such as the shape of its seam and its fuzz.

The tennis ball is roughly a 2.5 inch sphere. It has a continuous hourglass shaped seam, and a felt-like fuzz. The fuzz of the tennis-ball is a very porous and non-uniform surface. This makes the fuzz surface very difficult to simulate with a CFD model. For this reason we chose to leave out the fuzz, and model the tennis ball as if it had a smooth surface. The seam of the tennis ball, however, can be modeled easily. We left this feature of the tennis ball in our simulation.

The average professional tennis player serves the ball at 120mph, and the spin of the ball during a serve can reach around 1000rpm.

Determining What Cases to Run

Once we have taken down all the information about the tennis ball we need to decide what cases to set up so we learn what we want to from our CFD model.

One thing that is often done in aeronautics, and science in general, is comparing and contrasting. Scientists compare and contrast in their experiments in order to see how much little changes effect their results. Here we set up four different cases, so that we can compare and contrast between them. The first case is a smooth ball with no seam and no spin. The second case is a smooth ball with no seam spinning at 1000rpm. The third case is a ball with a seam but no spin. The fourth case is a ball with both a seam and spin. By comparing these four cases, we hope to see how much spin and the seam of the tennis ball effect its flight.

Creating a Computer Model of the Flying Body: Grid Generation:

In order to simulate fluid flow on the computer, the space around the object we are observing must be divided up into small pieces or sections; much like how street maps are divided up into squares. A divided portion of space is called a "grid" or "mesh", and individual sections are called "grid cells". The following pictures show the grids for a tennis ball with seams and a tennis ball without seams.


Tennis Ball with Seam	Tennis Ball without Seam

Getting the Results and Analysing Them

Once the grids are done and we know what cases we want to study, we can run our CFD simulation! CFD simulations can take a long time to run. Depending on the problem, running simulations can take an from and hour to a few weeks! The tennis ball simulations we ran took about a half a day. The links here will take you to the results.

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