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Doesn't the player know when he/she hits the spot? Maybe you should focus on where that spot is hit, not whether it has been hit.

 

... a possible approach to this objective ... pending experimental trial, might utilize a conductive elastomer sheet fastened to one side of the racket web:
https://en.m.wikipedia.org/wiki/Conductive_elastomerThe idea is based on the degree of deflection that an impacting tennis ball would have on the racket surface. It is assumed that a hit to the center of the racket would produce more change in conductivity on the elastomer sheet than an off center strike. It would be necessary to confirm that changes in racket web deflection would produce a practical index of merit, such as the change in elastomer resistance measured from one edge of the sheet to the other.

 

3. Using the a gyroscope and accelerometer. I could maybe calculate the location by combining the readings of the gyroscope and accelerometer sensors. This seems like the better option by I don’t have a lot of experience with gyroscopes and accelerometers.

sounds most realistic (if the gyroscope survives)
before i forgot -- the differential 3D orientation change with accelerometer data sould allow you to uniquely find the point of impact
? but what if balls momentum is variable (e.g. if it's spinning) (the friction would add some of the balls momentum to the bat . . . )
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you option 1 requires a precise tension to be calibrated to bat and preserved (or the change to be predictable)
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? if you can measure the speed of the ball and also relate it as a relative speed of the bat . the Opt 2 could work . . . maybe
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you likely want to re-formulate your task
Parameters (against the bat as a still frame at ? during the impact time-front) :
1 ball vx, vy, vz , ωyz , ωxz , ωxy
but to compensate/transfer the bat to the still frame you also need
2 bat vx, vy, vz , ωyz , ωxz , ωxy
i don't want to start with it . . .
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So the modified option 2 would be to measure / triangulate the ball position (momentums = don't care) by impact survivable position sensors ←← since the bat frame is conditionally of the fixed shape →→ you need only 2 sensors
. . . but the ball will have a non stereo-homogenous deformation requires sensor No.3
. . . but you can hit the ball sliding & "at the angle" so the "IMPACT" would be a "PARABOLIC SECTTION" = you need multi-frame ← description/record of the last
. . . there are real time video processing chips . . . but i dont know their cost

 

How about an array of vertical and horizontal IR LED emitters and photoelectric sensors in the plane of the strings.
The ball would block part of the light when hitting the strings, which which would give an XY location for its position.