Anatoly Antipin 1. The General Description of the Tennis Strokes The tennis is the game about movement. There is a lot of body activity, a racquet and ball motions etc. It is the common practice to use Vectors to describe any object motion. Definition: The vector is a straight line segment whose length is magnitude and whose orientation in space is direction. Mostly, I will examine a velocity of the different objects. Definition: The velocity is the vector. Its magnitude defined as the speed and orientation in space is the direction of the moving object. All these vectors stuff maybe is not really very important, but can be helpful for understanding different tennis techniques. I’ll try to keep the matter as simple as possible. The main distinction among the different tennis strokes Definition: Flat stroke – the ball is not rotating after the stroke. Definition: Spin stroke (topspin, sidespin, backspin, etc) - the ball is rotating after the stroke. Question: How can tennis player produce the strokes according to their definitions? Answer: If and only if the velocity of the racquet VR (Figure. 1.1) is the perpendicular to the strings plane around impact spot, the stroke is flat. Or, in other words, if the racquet is moved in the direction of the perpendicular to the strings plane around impact spot, the shot will be flat. Figure 1.1. Racquet velocity (VR) in the case of the flat shot. Coordinate axis OZ and vector VR are perpendicular to the strings plane In all other cases, there would be spin strokes. Since, it is practically impossible to maintain the velocity of the racquet perpendicular to the strings plane, in reality, there are no pure flat strokes. What happens if the velocity of the racquet VR (Figure. 1.2) has an arbitrary direction? Accordingly to the linear algebra, every vector of the racquet velocity VR can be decomposed as a sum of two orthogonal (perpendicular to each other) components (vectors). The flat (or normal) component VF is the perpendicular to the strings plane and the spin (or tangential) component VS is the parallel to it. Figure 1.2.The arbitrary vector of the racquet velocity (VR) along with its components (VF, VS). The strings plane exists in the XOY plane The flat component is mostly responsible for the boll velocity after impact VB (its direction and speed). The spin component provides the ball rotation, but with some strings interference can also change the velocity of the ball VB. It can happen due to the racquet strings could “bite” the ball or provide enough friction between the ball and strings and move the ball in direction of the spin component. In case of the flat stroke, the spin component usually is equal to zero. Something else about spin component Since, the spin component VS is the vector, it can be also decomposed on two orthogonal components in the strings plane. I assume that racquet stings bed is perpendicular to a ground. Then, the vertical spin component VSpinVer resides in plane perpendicular to the court’s ground. The horizontal spin component VSpinHor belongs to the plane parallel to the court’s ground (Figure 1.3). Figure 1.3. Vector of the spin component along with its components Relationship between defined vectors and common tennis slang The upward vertical spin component VSpinVer brushes the ball up, makes topspin, and also can drag the ball upward. The downward vertical spin component brushes the ball down, produces backspin, and pushes the ball down. The horizontal spin component VSpinHoz makes right/ left sidespin and moves the ball to the right/left. In general, the boll spins in the direction of the spin component VS (brushing ball direction) and moves in direction of the flat component VF (perpendicular to the strings plane). Digging effect Sometimes the spin component cannot produce any significant ball rotation but can change considerably the ball direction and speed. For instance, if the point of contact is the sweet spot and the flat component VF has very high speed. The ball just digs into strings bed; the strings hug the ball very hard and do not allow creating any ball’s rotation during “digging” phase of the impact. Then strings catapult the ball very fast and the spin component does not have enough time to rotate the ball. However, while the ball is in digging and catapult phases the spin component still moves the racquet in its direction and as a result it varies the ball’s direction and speed.