Your ideal serve will consistently land in-bounds and will arrive in your opponent’s court at the desired location and velocity. Discovering your ideal serve may require several hours of experimentation, practice, and training to determine what works and what does not. Once we are satisfied with our serve, we will normally “lock it in” so that we can hit the ball consistently and accurately. However, small variations in swing speed, timing, and spin may cause you to occasionally hit the ball into the net or over the baseline. The key to improving serve accuracy is to understand the sources of variability and reduce their margins of error. In a previous article, “Can Topspin Enable a Faster Serve?” we showed how topspin can be used to increase the velocity of your serves, but did you know that topspin can also improve your serve accuracy? We will first look at the mechanics of a serve without topspin and demonstrate how topspin can reduce potential errors.
Serve Mechanics
During a serve, a player normally has control of three things:
- Swing Speed – According to the impulse-momentum equation, the force that you can apply to the ball is directly proportional to the velocity that you can swing your paddle. A higher paddle swing speed will create more momentum and greater force that is applied to the ball. This will enable you to hit the ball faster, with more power, and deeper into your opponent’s court.
- Timing – The ball must be struck at a precise height to create the ideal inclination angle at impact for the ball to clear the net and fall within the opposite baseline. Variability is introduced if you hit the ball too late or too early. If you contact the ball too late, the inclination angle will be low, and you may hit the ball short or into the net. If you contact the ball too early, the inclination angle will be high, and the ball may sail over the opposite baseline.
- Spin – The angle that you hold your paddle and the mechanics and trajectory of your swing determines the direction and speed of spin. For our discussion, we will consider topspin only. Topspin applies a downward pressure to the ball, allowing you to hit it faster or harder while keeping it in bounds. Of course, too much topspin without enough forward velocity can cause the ball to fall short or into the net.
In the following sections, we will examine how variances in swing speed, timing, and spin may affect the accuracy of our serves.
Swing Speed
In our article, “Paddle Spin Capability, Friction & Stiffness”, we measured the diameters of the residue left on the paddle by striking balls during a game. Knowing the stiffness of the ball, it was possible to determine that the force applied to the ball was about 40 lbs. It was not clear whether these marks were left on the paddle face from overhead smashes, groundstrokes, or volleys, which may register a higher force than serves. For our analysis, we assume that most recreational players do not hit the ball as hard as they could during serves. We will therefore “de-rate” the force by 20% or 8 lbs, and assume that the force applied to the ball during a serve is about 32 lbs.
Knowing that the mass of the ball is 0.9 oz and the contact time is about 4 milliseconds (0.004 sec), we can develop a relationship between ball speed (in MPH) and the force applied by the paddle (in pounds) by using the principals of impulse-momentum, as follows:
Δv = 1.56 F
Therefore, a force (F) of 32 lbs can generate a ball velocity (Δv) of about 50 MPH at impact. We will use this ball velocity as the “baseline” for our studies.
Figure 1 shows the results of hitting a “flat” serve (i.e., no topspin) at a speed of 50 MPH. Because all other variables are fixed, we can only change the inclination angle to control the height of the ball above the net and the depth that the serve lands in your opponent’s court. Note that the range for the inclination angle is very tight (1.2 degrees) and must fall between 9.1 degrees on the low side to 10.3 degrees on the high side. Impacting the ball outside of this range will cause the ball to land into the net or sail over the opposite baseline. Furthermore, we can also see that the range of the ball clearance over the net is 0-6” and can be placed within a narrow range of 0-30” from the baseline. What do these differences in inclination angle mean in regards to timing?
Timing (or Inclination Angle)
For an underhand serve, we assume that the arm swings like a pendulum, with the point of rotation at the shoulder joint. The distance from the shoulder joint to the center of the palm is about 24”, and the distance from the palm to the center of the paddle is about 10”. This makes the effective length of the pendulum 34” (Figure 2). We further assume that we bend our knees during a serve, putting the shoulder joint at a height of about 52”. The contact point between the paddle and the ball is therefore about 18” above ground (i.e., 52-34=18).
Based on simple geometric considerations, at an inclination angle of 10.3 degrees, we must strike the ball at a height of 34.55”. At an inclination angle of 9.1 degrees, we must strike the ball at a height of 34.43”, a difference of only less than ⅛”! Knowing that the acceleration of gravity is 32.2 ft/s2 (386.4 in/s2, we can calculate that the difference in timing is less than 25 milliseconds (0.025 sec)! A blink of an eye takes between 100-150 milliseconds (0.100 – 0.150 sec), so the difference in timing between hitting the ball into the net verses hitting the ball over the opposite baseline is four to six times faster than the blink of an eye! A 25-millisecond margin of error, together with a 6” clearance over the net and a 30” allowance inside of your opponent’s baseline is much too narrow of a window for you to serve consistently and accurately.
One relatively easy way to increase the margin of error is to slow down your swing speed. Figure 3 shows the effects of reducing the velocity of your serve at impact from 50 MPH to 40 MPH. This shows that the range of inclination has been increased from 1.2 degrees to 6.0 degrees, which almost triples the allowable timing margin of error from less than 25 milliseconds to about 70 milliseconds. We can also see that the clearance over the net has increased by a factor of five, from 6” to 30”, and the allowable distance in front of the baseline has increased from 30” to over 96”. The downside of reducing your serve speed is that it will arrive at the opposite baseline in 1.08 seconds for the 40 MPH serve verses 0.82 seconds for the 50 MPH serve, a difference of 0.26 seconds! The problem with reducing the velocity of your serve is that the ball will bounce higher and your opponent has more time to react and set-up a better return.
Topspin
As we discussed in a previous article, we know that the addition of topspin enables us to increase the velocity of our serves. Topspin has the added advantage of increasing the margins of error for timing, clearance over the net, and landing location in your opponent’s court. Figures 4, 5, and 6 show serves at 50 MPH with topspin of 500, 1000, and 2000 RPM.
Results, which are summarized in Table 1, show that by increasing the amount of topspin, it is possible to increase the margins of error for inclination angle, clearance over the net, and landing location. Of particular interest is the fact that the ball trajectory for the 40 MPH serve with no topspin looks identical to the ball trajectory for the 50 MPH serve with 2000 RPM topspin. However, that is where the similarity ends. The serve at 50 MPH with topspin arrives at the baseline more than 200 milliseconds faster than 40 MPH serve without topspin. Furthermore, the ball served at 50 MPH with topspin will “kick” when the ball lands, bouncing higher and faster, making it more difficult to return.
Table 1. Margins of Error With and Without Topspin
Conclusions
In this article, we examined how variability in swing speed, inclination angle, timing, and spin can affect the ball clearance over the net and the ball landing area. Although we commonly know that topspin can be used to increase serve velocity, we also showed that even a modest amount of topspin can improve serve accuracy. All players should therefore learn or improve their abilities to apply topspin during their serves and groundstrokes. We discussed the mechanics of topspin in our article, “How is Topspin Generated?“. The proper technique to generate topspin can be obtained by working with a professional trainer.
