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Thanks. Thinking about it overnight, I now mostly agree with you.You’re right that the sponge and topsheet are coupled and that their behavior is nonlinear with impact speed, so no single efficiency applies across all conditions. But there's a big difference here. Normal compression of the sponge stores and returns energy far more efficiently than tangential shear or stretch of the topsheet. The reason is structural. The sponge is a cellular foam whose cells act like miniature springs—large, reversible deformations with relatively low internal friction—so most of the compression energy is returned as rebound speed. The topsheet is a solid viscoelastic rubber; tangential stretch and shear involve molecular sliding and frictional losses, so much of the energy turns into heat rather than restored motion. Tangential compliance is crucial not for storing and returning rotational energy, but for allowing frictional torque to act long enough to change the ball’s spin.
The topsheet and sponge are coupled, so when we deform the topsheet, we’re also compressing the sponge. This is what I had in mind, and you’ve convinced me we would generally want to maximize sponge deformation and minimize topsheet deformation in terms of storage efficiency.
But even if we suppose the energy storage of the topsheet itself is neglible, I still think the geometry of the sponge can be relevant. The sponge is thinnest normally to the racket surface, so hitting obliquely could allow for greater sponge deformation than impacting the ball normally. This would only really be relevant at sufficiently high impact speeds that the sponge is compressed close enough to the physical constraints determined by 1) its thickness and 2) its attachment to the topsheet and blade. But I do think those impact speeds are realistic for in-game situations. As indirect evidence, we know that changing sponge thickness perceptibly changes a rubber’s performance in play, so real-world sponges are often deformed close enough to this limit. In any case, none of this argument deals with how the physical constraints on the sponge affect how efficiently it (and the rest of the racket) can store and return energy, let alone whether it can overcome the energy lost to topsheet deformation.