Hyper-angulation isn’t something widely discussed within the context of the tennis serve however it is observed in rec tennis, competitive tennis and professional tennis. The term hyper-angulation is related to the arm angle and shoulder joint at around the trophy position of the serve. It is more of a concern for baseball pitchers that lag too much with their arm and over rotate their upper body in the initial delivery. In general it when the elbow gets behind the plane of the scapula, this is considered hyper-angulation. Some believe that hyper-angulation increases the range of motion of the serve in turn providing additional acceleration up to contact and ultimately increasing racquet head speed(serve speed). Others claim this is a common source of shoulder problems and can lead to shoulder surgery long term. One of the more common examples of hyper-angulation is the serve motion of Novak Djokovic. While one of the more flexible humans on the planet, he does push the envelop a bit in his shoulder position. During the fluid motion of the serve, it can be difficult to identify when or if hyper-angulation occurs, however stepping through a serve motion frame-by-frame can provide the tale-tell signs. Observing the elbow moving laterally, almost like you are poking a friend standing next to you or the appearance of “sticking your chest” out can be the clues to identify when hyper-angulation occurs. In the snapshot below, you can also observe Dimitrov sticking his elbow behind his back. However as you step through his motion frame-by-frame, he repositions his elbow prior to his upper body getting involved.
It is not uncommon for tennis coaches to advise players to stretch out their pectoral muscles when serving and this does seem reasonable to an extent. I’ve seen many college players reach the point of hyperangulation in the serve and it doesn’t seem uncomfortable or even look dangerous. So long as the elbow starts traveling forward and up, before the chest starts dragging the arm, I think this position is not of concern and certainly does increase the range of motion. Again, the key here is to be sure everything is working in a coordinated fashion and not let the upper body get too far ahead and lag the elbow into an uncomfortable position.
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