Introduction
When playing tennis, I have found that the serve is the most crucial part of the game. The serve is the first shot for any point, so the ability to utilize the serve as needed will give an advantage to the serving player. A great server could win a game with just four winners (shots that the opponent fail to return). Although the serve is a great weapon, it can backfire if the player serves a fault (a shot that hits the net or passes the lines). Just as a player could win a game with four winners, he can also lose with four double faults (a player is given two serves for each point). Personally, I have experienced back fire side of the serves than the edge giving one. My coach recommended that I tried switching my serve type. Currently, I'm serving a flat serve which is basically a serve without spin. My coach showed me the topspin serve which put a backward spin to the ball. At his recommendation, a question struck me: what is the extent of the advantage of a topspin serve over a flat serve?
For this investigation, I will explore how can a topspin serve be consider a "safe shot" than a flat serve. Data such as the speed of the serve, the height of the contact between the racket and the ball, and the layout of the court will be collected from my own tennis career and the local court. I plan on finding the angle of availability (the angle range for a serve to be in) for both the topspin serve and the flat serve through the use of formulas found in research. By manipulating these formulas, I also intend to explore the other factors of the serve which could benefit from the spin such as the height of contact and the speed.
Background on the Serve
To some tennis may seem like a complicated sport, but behind the jargon ...
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...high. Thus θ=-0.0137 is accepted as the maximum angle.
Converting to degrees: -0.0137•180/π=-0.7849≈-0.785˚
The range for θ is {θ|-0.0622≤θ≤-0.0137}
Thus, the angle of availability is [-3.57˚,-0.785˚]
The trajectory of the maximum angle and minimum angle serves can be graphed as:
The minimum θ function(A): X=27cos(-0.0622)t
Y=2.61+27sin(-0.0622)t-1/2•9.81t²
The maximum θ function(B): X=27cos(-0.0137)t
Y=2.61+27sin(-0.0137)t-1/2•9.81t²
Function A above passes Y=0 when t=0.578. This value of t represents the time the ball first hits the ground. Function B passes Y=0 when t=0.693 . As both functions passes Y=0, they show the time the ball bounced up from the moment it first hit the ground. Function B takes has longer flight time compared to function A; this is reasonable since function B has more distance to travel and it has the same velocity.
Years of playing the game and not improving, Gawande incidentally finds himself play tennis with a young man who is a tennis couch. The young man gives Gawande a tip about keeping his feet under his body when hitting the ball. At first he is uncertain, stating, “My serve had always been the best part of my game….. With a few minutes of tinkering, he’d added at least ten miles an hour to my serve. I was serving harder than I ever had in my life” (Gawande, 2011, p.3).
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