Design & SimulationAugust 1, 2024

# Game, Set, Match! Simulation of the Magnus Effect in TennisđźŽľ

The Magnus effect is a well-known effect that impacts the motion of a spinning object through a fluid. One of the most common ways to experience the impact of this principle is through the motion of balls in sports. Indeed, this physics principal is used by amateurs and professional athletes in sports such as tennis, soccer, cricket, baseball etc. In the below example, we ask Nicolas Fougere, SIMULIA Fluids, Industry Process Consultant Manger, to walk us through a tennis ball simulation workflow.
Katie Corey

Why does this workflow need to be analyzed?

In tennis, to minimize unforced errors, players try to get some margin above the net and use top spin to help the ball to fall back inside the lines of the court. Due to the rotation of the ball, the air below the ball is accelerated while the air above the ball is slowed down, resulting in a pressure gradient (Bernoulliâ€™s equation) and an upward shift of the wake from earlier flow separation at the top of the ball, which creates a downward force that will work along gravity to keep the ball inside the court.

When keeping the ball low, the net becomes more of an obstacle and it can become challenging to keep the ball deep to neutralize the opponent. Players then use the opposite effect (high pressure below the ball and low pressure above the ball) with backspin, which will create an upward force that will keep the ball flight longer and give the â€śfloatingâ€ť behavior to the ball to get some depth to the shot despite playing close to the net.

Describe the workflow.

Tennis players use the advantages of different spins they can provide to the ball. When the ball spins, aerodynamic forces created by the airflow (so-called Magnus effect) help players control the ball in specific plays during rallies. Note that there has been attempts to use such an effect in planes in the early 20th century and, there are ships that use Flettner rotors or stabilizers based on the Magnus principle.Â Â

SIMULIA Fluids solutions allow us to simulate such a phenomenon to better visualize the effect of the rotation of the ball on the fluids and, subsequently, how the aerodynamics forces will impact the trajectory of the ball.

A rotating sphere modeling a tennis ball is being analyzed. Here, we use headwind (i.e. no angle of the incoming flow vs the ball motion), but that is something that could be studied through a Design Of Experiment.

Applicable industries are CPG through sporting goods, but as mentioned in the previous answer, there are other industries (such as ships) that use the same physics principal so MDO could also benefit from it.

What are the key simulation goals?Â  What are you trying to learn from the simulation?

The simulation is trying to get us information regarding how the rotation of the ball affects the airflow around the ball and how the aerodynamic forces will impact the trajectory of the ball.

Which SIMULIA solutions (products, roles, etc.) did you use?

This simulation was done with SIMULIA PowerFLOW on the SIMULIA Cloud. Customers can access PowerFLOW on the SIMULIA Cloud with SUT-1K-OC/SUT-100K-OC. PowerFLOW is also available on premise and on the 3DEXPERIENCE Cloud.

What were the advantages (benefits) of using simulation?

Simulation allows us to see the flow and directly get an understanding of the impact of the ball rotation on the flow. We can see the separation/wake shifting and the pressure changing around the ball. Simulation gives us an accurate way to compute the aerodynamics forces on the ball and how these change with rotation (top spin, back spin etc.) that tennis players would use. Such changes will affect the trajectory of the ball and one could imagine a manufacturer to use such an approach to change the mechanical characteristics of their product.

Interested in the latest in simulation? Looking for advice and best practices? Want to discuss simulation with fellow users and Dassault SystĂ¨mes experts?Â TheÂ SIMULIA CommunityÂ is the place to find the latest resources for SIMULIA software and to collaborate with other users. The key that unlocks the door of innovative thinking and knowledge building, the SIMULIA Community provides you with the tools you need to expand your knowledge, whenever and wherever.

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