The One Degree Error: Why The Game of Tennis Is So Difficult

The One Degree Error Why The Game of Tennis Is So Difficult If you hit the ball on the baseline and the racquet face points straight toward the net, the ball will go perpendicular to the net – meaning in a straight line. If you move the racquet by just one degree (1°) how much will the trajectory of the ball change? D=? 23.77 m (78 feet) Length of Tennis Court 1° Formula: In a right triangle, the length of the opposite side is the tangent of an angle multiplied by the length of the adjacent side. D = tan1° x 23.78 m = 0.41m (1.35 feet) Answer: if you move the racquet by only one degree while hitting the ball above your baseline, you will miss the desired target on the opposite baseline by 41 cm (1.35 feet). How much does the racquet head move if it changes the angle by just one degree? If you move the racquet by one degree just by turning your wrist, then the lever length is the length from the wrist to the contact point, which is at around 68.5cm. 68.5cm 1° Distance = tan 1° x 68.5 cm = 1.2 cm The racquet moves roughly 1.2 cm (0.5 inch) forward when the angle changes by one degree. How much time does the player have to time the ball perfectly within that one degree if the racquet keeps changing angle while we're swinging at the ball? The speed of the incoming ball just before contact in recreational play is approx. 10 m/s (36 km/h) and the speed of the racquet is roughly the same. Speed of Racquet 10m/s (36 kmh) Speed of Racquet Speed of Ball Speed of Ball 10m/s (36 km/h ). 20m/s How much time does the player have to hit the ball within that1 cm where the racquet would change the angle by just one degree? Time = distance / speed= 0.012 m / 20 m/s = 0.0006s That's 0.6 thousandths of a second! If you make a timing error of only 0.0006 seconds and you're NOT guiding the racquet straight through the contact point but rather use your wrist to slap the ball, you will miss the direction you're aiming at by 41 cm (1.35 feet). If you make for example a timing error of only 1/ 100 s (one hundredths of a second) and don't keep the racquet head straight through the contact zone, you will miss by: D = (0.01 / 0.0006) x 0.41 m (1.35 feet)= 8.2m (27 feet) which is exactly the width of a singles tennis court! Note: All these calculations are theoretical and do not take into account the deformation of the ball and the strings at contact, the time the ball is on the strings, friction and other factors. That would make calculations much more complex and hard to understand. The purpose of presenting these equations and calculations is to show you both how extremely difficult tennis is and how timing the ball correctly is many times more important than all the small technical details you're messing with - except, of course, the detail of keeping the racquet face straight through the contact point and not changing the angle of the racquet by slapping the ball with your wrist. FeelTennis.net