National Football League - Part 1
We’re in the midst of the NFL playoffs, leading up to Super Bowl LVI, and I thought it would be fun to show how CFD can be used to simulate and compare the trajectory of a pass thrown by a quarterback with that of a field goal attempt made by a placekicker. Some assumptions were made to simplify these models, but all of the “physics of flight” have been included. In both cases, the ball has the same initial position, the same initial velocity and direction, and the same rotation rate. The only difference between the two cases is the axis of revolution. For the pass, the ball rotates around the major axis of the ball and for the kick, the ball rotates around the minor axis of the ball (see Figure 1). The only force acting on the ball, besides the force imparted on it by the prescribed initial velocity, is its own weight. The trajectory of the ball is determined by the flow solver.
Figure 1: Description of the football rotation and subsequent motion
Ansys Fluent is the preferred code for this simulation due to its overset mesh feature. In an overset mesh analysis, there are two independent grids, a relatively coarse background mesh and a relatively fine mesh around the object of interest. An enclosure is defined around the object of interest in order to provide a transition region between the fine mesh around the object of interest and the coarse background mesh. The background for this simulation is a simple rectangular volume and the enclosure is a sphere around the ball (see Figure 2).
Figure 2: CFD Model with a detailed view of the overset region
The background object (in grey) consists of a coarse hexahedral mesh while the enclosure (in red) consists of a tetrahedral mesh which is very fine near the ball and gradually coarsens toward the outer surface of the sphere (see Figure 3). The two meshes are independent of each other. The sphere moves as a rigid body through the domain and at each time point in the transient simulation, the solution is interpolated between the external boundary of the sphere (overset region) and whatever portion of the stationary background mesh it happens to be intersecting with at that point in time.
Figure 3: Mesh on a Plane through the midplane of the model with a detailed view of the overset region
The ball was oriented at 17 deg from horizontal at the start of each simulation, with an initial velocity of 30 mph and a rotation rate of 300 RPM. These values were found to be “typical” after a brief internet search. A kick likely has a larger initial velocity and rotation rate (compared to a pass) but the author wanted to make a comparison of the aerodynamics between two types of rotation, spiral and an end-over-end.
This project proved to be more involved than originally expected. Therefore, a thorough analysis of the results is not included here. More work on this project will be done in the future (hence the Part 1 description in the title). This was an initial “proof of concept” analysis. The results are encouraging and have motivated the author to pursue this study in more detail at a future date. However, a couple of interesting conclusions can still be made from these preliminary results. Namely, the end-over-end rotation (kick) causes greater air velocities in the vicinity of the ball (due to inertia) and it also creates more drag. It is evident from the images in Figure 4 that after just 0.264 seconds of flight, the spiraling pass has already moved ahead of the end-over-end kick. The spiral further outdistances the kick at 0.55 sec as can be seen in Figure 5.
Figure 4: Velocity Contours Near Football at 0.264 seconds (kick – Top, Pass - Bottom)
Figure 5: Velocity Contours Near Football at 0.55 seconds (kick – Top, Pass - Bottom)
The spiraling football simulation showed some nonphysical behavior on its descent which likely indicates that the rotation rate is too low. Future work will focus on varying the angle of release, the initial velocity, and the initial rotation rate. Additionally, more effort will be put toward quantifying the results. This proved to be a very interesting and informative simulation. Stay tuned for additional discoveries and results to be presented in future blogs!
