Simulation of a soccer ball impact on a goal post.
Figure 1.
This is an example for demonstration purposes: During the Champions League final, 1976, between
FC Bayern Munich and AS St. Etienne two shots of the French team rebounded off the
opponent’s goal post. The fact that England was the only European country that has
not replaced its goal posts with round poles has made French supporters believe that
St. Etienne could have won the final if the goal posts had been replaced. Based on a
simulation, an answer should be provided to these speculations. However, this
controversy will undoubtedly continue.
Options and Keywords Used
4-node shell (Q4) and 3-node shell (T3), Fabric Law for Elastic Orthotropic
Shells
One-chambered airbag with hybrid input of injected gas (/MONVOL/AIRBAG1)
During the European football (Soccer) Cup final in 1976 (Bayern of Munich versus
Saint Etienne), a shot from Bathenay and a header from Santini rebounded off the square
cross-section frame of the German team's goal. The purpose of this demonstration is to
determine the influence of a square or a round cross-section bar for both cases.
The main differences between both shots are the incidence, the velocity and the impact point of the ball on the bar (its vertical value).
The material used for the ball follows a linear elastic orthotropic law
(/MAT/LAW19) with the following characteristics:
Initial density
2.01x10-3[gmm3]
Young modulus (dir. 1 and 2)
20000 [MPa]
Shear modulus (12, 23 and 31)
10000 [MPa]
Poisson ratio
0.29
Units: mm, ms, g, N, MPa
Figure 4. Geometry of the Problem
Model Method
The ball is modeled using 60 3-node shells and 1420 4-node shells. The shell element
formulations are set by default. For display purposes, the goal post and the ground
are also modeled with 4-node shell elements, but their mesh will not be used for the
computation. Instead, rigid walls are defined for the goal post and the ground.
Figure 5. Ball Mesh
Radioss Options Used
A rigid body is created, containing all the nodes of the ball. It is deactivated
just before impact on the bar.
A rotational and translational initial velocities are applied to the rigid
body’s master node using /INIVEL/AXIS. The velocities are
defined in a local coordinate system using /FRAME/FIX.
The goal posts are modeled with a cylindrical rigid wall for the round post and
two rigid parallelograms for the square post.
Gravity is taken into account using a gravity load.
The ball is considered as an airbag, which is activated when the rigid body is
deactivated.
Multiple Engine files are used. The second Engine file deactivates the ball rigid
body using /RBODY/OFF. The time animation output is also
increased to every 1 ms, so more details about the ball impacting the goal can be
viewed. The third Engine file changes the animation output back to every 12.5
ms.
Results
Figure 6. Impact of the Soccer Ball on a Square and a Round Cross-section
Figure 7. Trajectory of the Ball for Bathenay's Shot. (impact on a square and a round bar, respectively)
Figure 8. Trajectory of the Ball for Santini's Head. (impact on a square and a round bar, respectively)
Conclusion
Even using a simple modeling of the impact (bars modeled with rigid walls instead of parts), the
simulation provides quite accurate results in the case of a square cross-section
when simulations are compared to reality. The results obtained for the bars with a
round cross-section show that the ball enters the goal for both shots. However,
several impact parameters, such as friction and rotational velocity are estimated as
calibrating the case of a square cross-section.
