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Thanks to Anatoly Antipin (fellow Tennisopolis member)! Posted on TW forum:

Anatoly Antipin

Twist Serve 

To create twist serve we have to brush a ball approximately from 8:00 to 2:00 o’clock, but above the ball’s equator. This kind of brushing motion creates topspin, sidespin, and spiralspin (gyrospin). 

The spiral/gyro spin would be in clockwise direction causing the ball bounce deviation toward the right. The gyrospin motion rotates the ball about an axis pointing towards the target. That sort of spin is used to throw a gridiron football, but it has no effect on curvature of the ball through the air. 

We can hit the ball above its equator if and only if the racquet face is tilted forward - slightly closed. 

There is example of the racket motion around impact in case of twist serve.

Figure 1. The racquet’s movement around contact

The frame #2 is point of contact. The arm itself moves relatively slowly forward, to the right, and downward and practically doesn’t affect racquet brushing motions. 

On the other hand, the wrist ulnar deviation rotates, very fast, the racquet upward and to the right almost perpendicular to the ball outgoing direction.

It seems, the wrist ulnar deviation produces the main contribution to the topspin, sidespin, and gyrospin. All others motions of the body (arm pronation, wrist flexion, and so on) create mostly translational motion of the ball. 

Figure 2. The tilted forward racquet

The theta (ϴ) angle defines magnitude of the gyro and side spins.

Figure 3. Vector of the spin component along with its components

About fig.3 see also

Assume that the racquet face tilted forward with theta angle (ϴ). Then gyrospin, sidespin, and topspin vector velocity components would be:

VGyrospin = VSpinHor*sin(ϴ) (1) 

VSidespin = VSpinHor*cos(ϴ) (2) 

VTopspin = VSpinVer (3) 

The more we tilt the racquet face forward (increase ϴ), the more efficient would be gyrospin and less effective sidespin. 

If ϴ =45° then VGyrospin = VSidespin , but I doubt that one can hit successful twist serve with so large theta angle. 

Btw, topspin component isn’t affected by ϴ

The theta angle also determines coordinates of the point of contact, see picture below.

Figure 4. The tilted forward racquet

IMO ϴ should be less than 30° and thus point of contact would be next to ball’s equator, otherwise the ball goes into net.

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