The ingredients to the perfect tennis serve with Simcenter Amesim.

Aug 4, 2021 | Simcenter Amesim, Simcenter FLOEFD, Simulation Software

Here in BSIM almost 50% of our team is made up of tennis players or fans: we could pretty easily set up an in-house BSIM tournament!

Our application engineer Giancarlo De Giuseppe has been playing around with Simcenter Amesim to simulate the perfect serve – and beat us all.

Yes, Simcenter Amesim was born as a 0D/1D simulation tool, and we’ll be talking about the specificities of this type of simulation very soon in one of our next post, but it does contain 2D and 3D mechanical modelling libraries.

These libraries allow the user to simulate the movement of a body in a 2D plane or in a 3D space, and assess the effect of contact forces and of the body’s elasticity.

Our tennis serve application example, is perfect to showcase this feature: a racket hitting a ball, a ball traveling in a 2D plane and then hitting the court!

Let’s here all about it in from Giancarlo, in today’s fun Friday post.


“First off, I set the icons in proper positions. To simulate our tennis serve, at least 3 bodies are necessary and 2 contacts: 1 body for the field, 1 for the ball and 1 for the racquet, the 2 contacts are for ball-field and ball-racquet.

For each body and contact a dimensional characterization is necessary, while for the moving bodies, just like the ball and the racquet, mass and stiffness properties are also needed.

Then I worked on the initial conditions in order to achieve the proper cinematics: I aligned the ball’s initial position to a few centimeters before the end-line, same as the raquet’s initial position and rotation.

Another important element for the serve (and for the simulation) is the height at which the ball is hit. The higher the toss and the higher the ball is hit, the better the serve. This is why the player’s height has such an important role in his game.

I have just joined the sport, so I asked a veteran tennis player and colleague, Marco Longhitano, for some help.

From this highly-scientific test, we took some measures for the initial positions and the typical arm lengths.

Then I had to set the racket speed at the moment of impact.

Marco could only help me to a certain extent here, so I looked-up the serve speed of one of the best players ever (sorry Marco): John Isner’s serve is 249.4kph/155.0mph. We’re quite aware of our athletic limits here in BSIM, so I set our serve speed at about the half of Isner’s speed (~120 km/h).

But, just for fun, let’s take a minute to admire Isner’s serve and recognize we will never in our wildest dreams be anywhere close to it.

Ok, moving on.

As you can see, the ball starts its trajectory with 0 speed, when it’s at its highest position. Then we have a slow speed increase, due to the gravity effect, till we have the impact (~0.08 s) where the racquet hits the ball and the velocity rises up to 125 km/h.

The whole trajectory until the first soil impact (~ 0.6s) is about 0.5 s. As you can see, after the racquet impact, the velocity slightly continues to raise, this is due to the physics considered: no air resistance was set, and so the gravity effect won pushing the ball to accelerate a little bit more.

So, to obtain the ‘definitive’ solution with a more realistic velocity profile, the air resistance has to be estimated.

Since we are managing a simple shape (sphere) we can use tabled coefficient easily findable in literature:

Using this coefficient associated with the drag force formula:

Out sketch now looks more complete:

Lets look at the comparison before/after Air Resistance introduction:

Now the ball decelerates, as it should, in a physically coherent way.

And here we can see the ball’s trajectory along a X-Y plane. Its initial position is to the right of the graph.:

Obviously with the air resistance the ball hit the ground at a shorter distance.

Just a quick look at the impact moment:

Didascalia: the ball and the racquets chords seems to compenetrate, but this is just an optical effect since in the contact a certain stiffness was been considered, while the CADs are simply linked to the centre of gravity of the objects. This prolonged contact is at the basis of the ball spinning and cinematics.

“Is the ball spinning?” I can here you asking. The answer is:  Yes!

Let’s take a look at this graph:

Before the racquet impact the ball’s absolute angular velocity was null. After the racquet impact it reaches the value of about 280 rpm.

After the impact with the court, the ball continues to spin at about 35 rpm but in the other direction. 

This means that the ground-impact just reversed the ball spinning direction, making it even more difficult for the other player to respond to our serve.

Looking at the future, a more complex model can be obtained only in cosimulation with a CFD 3D software:

In the tail behind the ball, due to ball rotation, there are some perturbations in the flow caused by the ball streaks placed on the surface. This is an additional level of detail that with some work we could be able to address. 

But this, is another story…

The standard features mentioned in this analysis, are part of Simcenter Amesim software. However, based on real Simcenter Amesim capabilities, several simplifications were applied to this light-hearted application example.

But we do hope they inspire you to use and explore Simcenter Amesim capabilities for new and interesting applications!

What are your strategies for the perfect ace tennis serve?

Let us know in the comments!

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Mechatronic, model-based simulation software for the design of multi-domain systems and components

Simcenter Amesim is a powerful simulation and engineering design tool, developed by Siemens Software Industry and distributed by BSim Engineering.Use Simcenter Amesim to study the design of a component and its control, identify the ideal layout of a subsystem or check the integrated performance of several machine systems.