New Softball Simulation Captures Spin and Friction of Oblique Impacts

When a softball slams into the ground or a rigid surface at an angle, what happens in the next millisecond and a half determines how the ball will spin, skid, and rebound — and ultimately how a play unfolds on the field. That fleeting moment has long resisted accurate computer simulation. Now, engineers at Washington State University have built the first finite element model of a softball subjected to oblique impacts, and their work reveals that two factors long ignored by simpler models — the ball’s uneven mass distribution and the way friction changes over the course of contact — are essential to getting the physics right. The study, published in the journal Sports Engineering, offers the most complete picture yet of how a solid sports ball converts straight-line motion into spin when it strikes a surface off-center.

The research, led by Charlotte Mabbs with Lloyd Smith, both of Washington State University, addresses a gap that has persisted in sports ball mechanics for years. While the behavior of balls in head-on, or normal, impacts is routinely measured and modeled, oblique impacts are considerably more complicated. During such an impact, a ball can either slide across the surface — if it comes in at a shallow angle or the friction between ball and surface is low — or it can grip the surface, momentarily bringing its contact patch to a halt. When the ball grips, frictional forces stretch and shear the compliant cover and core, storing elastic energy that is later released as rotation. Capturing this transition between sliding and gripping has proven a stubborn challenge for previous simulations of tennis balls, soccer balls, and golf balls.

Earlier models typically relied on a constant coefficient of friction, treating the resistance between ball and surface as a single fixed value throughout the collision. Those models could reproduce sliding behavior or gripping behavior, but not both. A tennis ball study that achieved good agreement compared its simulation to only one impact condition, leaving its general validity uncertain. Other investigations varied the friction coefficient numerically under fixed conditions without experimental validation at all. The Washington State team took a different route: they implemented what they call a temporal friction model, in which the friction coefficient evolves during contact, transitioning between independently measured static and dynamic values depending on the relative sliding velocity between ball and surface.

To build the model, the researchers first needed to characterize the softball itself. They studied adult fastpitch softballs with a circumference of 306 millimeters and a mass of 0.2 kilograms, constructed with a rigid polyurethane foam core surrounded by a thin leather cover stitched with raised seams. Upon impact, a softball dissipates roughly 75 percent of its energy, so the material model had to capture severe energy loss. Using the explicit finite element solver LS-DYNA, the team employed a non-linear viscoelastic foam material model governed by a high-speed stress-strain loading curve, with parameters controlling hysteresis and energy dissipation tuned until simulated normal impacts at 21.4 and 30.6 meters per second matched measured stiffness and coefficient of restitution within 4 percent of laboratory results.

One of the study’s most striking findings concerns the ball’s moment of inertia — a measure of how its mass is distributed around its center. A homogeneous sphere, the standard simplification in sports ball modeling, underestimated the measured moment of inertia by 9.1 percent because the dense leather cover and seams push mass toward the outside of the ball. That seemingly small discrepancy had outsized consequences: the homogeneous model overpredicted the final angular velocity of a sliding impact by about 13 percent. By adding a thin shell of massless-stiffness elements to the ball’s radius and adjusting densities to match the measured inertia, the researchers brought the angular velocity error down to just 3 percent. For balls with seams — softballs, baseballs, cricket balls — the lesson is clear: assuming a uniform sphere is not good enough when rotation is at stake.

The experimental half of the study was equally ambitious. The team fired softballs from a pneumatic cannon at a steel plate across a wide envelope of conditions: speeds from 20.1 to 63.5 meters per second, spin rates up to 117 radians per second, and impact angles from 14 to 80 degrees. A triaxial load sensor recorded normal and shear forces during contact at 150 kilohertz, while high-speed cameras filming at up to 14,100 frames per second tracked the ball’s position and rotation through the roughly 1.5-millisecond collision. Ball rotation was computed by detecting and matching distinctive features on a randomly patterned leather cover frame by frame. Between every shot, the steel plate was cleaned with 1000-grit sandpaper to keep friction conditions consistent.

Friction measurements fed directly into the model. Sliding impacts — those in which the ball skids through contact — yielded a dynamic friction coefficient of 0.360, while an inclined plane test using a panel of leather removed from an actual softball gave a static coefficient of 0.625. The dynamic value carried a relatively large uncertainty of about 22 percent, consistent with the scatter reported in prior dynamic friction measurements on other balls. The static value aligned well with published engineering data for leather against metal, which typically cites values around 0.6. The temporal friction model blended these two values with an exponential decay governed by a transition parameter, tuned to match representative sliding and gripping impacts and then validated against the full range of angles and speeds.

The validation results were emphatic. Compared with a constant friction model using the dynamic coefficient, the temporal friction model reduced the mean normalized root-mean-square error in predicted angular velocity during contact by 29 percent, and by 81 percent compared with a constant friction model based on the static coefficient. Crucially, it was the first friction formulation for any sports ball to describe both sliding and gripping behavior simultaneously. In gripping impacts, the simulated friction coefficient lingered near the dynamic value for only about 10 percent of the contact duration before climbing rapidly to the static value as the ball’s contact patch came to rest; in sliding impacts, the coefficient stayed near the dynamic value for nearly half the impact. Predicted peak normal forces came within 2.5 percent of experiment, and tangential forces within 6.1 percent.

The model also reproduced the distinctive energy landscape of oblique impacts. As impact angle decreases from vertical, more of the ball’s incoming kinetic energy is converted into transverse motion and rotation, with rotational energy peaking at the shallowest angles at which the ball still grips the surface. The simulation correctly captured the inflection point — between 25 and 30 degrees — below which the ball slides through contact rather than gripping. Interestingly, the frictional force did not substantially reverse during contact, unlike the dramatic reversals seen in highly elastic superballs, a difference the researchers attribute to the softball’s prodigious energy dissipation. One residual discrepancy remained: the simulated frictional force peaked slightly earlier than measured, by roughly 0.1 to 0.16 milliseconds. Tests on a coverless ball, with the leather stripped away, largely eliminated the timing gap, suggesting the thin cover — only 10 percent of the ball’s volume — measurably influences shear response, perhaps through slip at the core-cover interface or the cover’s own compliance.

The implications extend beyond softball. Because softballs are simple in construction compared with the layered pills, yarn windings, and seams of baseballs and cricket balls, the inhomogeneity effects documented here are likely even more pronounced in those sports. The work also marks the first dynamic measurement of friction coefficients for a solid sports ball at speeds representative of actual play, and the first controlled laboratory experiments on softball oblique impacts of any kind — previous on-field studies of softball-bat collisions had reported lower tangential restitution values, consistent with the greater energy dissipation expected when a compliant, curved bat is involved. For governing bodies, equipment designers, and modelers of ball flight, the message is that both the velocity-dependent nature of friction and the true mass distribution of the ball must be respected. As the authors conclude, ball inhomogeneity and temporal friction are not refinements but necessities for accurately modeling how solid sports balls shear, grip, and spin when they meet the ground.

Subject of Research: Finite element modeling and experimental validation of oblique, frictional impacts of softballs

Article Title: Finite element modeling of oblique impacts of softballs

Article References: Mabbs, C., & Smith, L. (2026). Finite element modeling of oblique impacts of softballs. Sports Engineering, 29(2), Article 31. https://doi.org/10.1007/s12283-026-00564-5

Image Credits: AI Generated

DOI: 10.1007/s12283-026-00564-5

Keywords: softball, finite element model, oblique impact, friction, spin, sports engineering, coefficient of restitution, moment of inertia, LS-DYNA, sliding and gripping, shear deformation, sports biomechanics