In previous articles, we mentioned that balls hit at greater heights can result in greater speed; however, what exactly is the relationship between contact height and speed? Can increasing the contact height of a serve increase its speed? In this article, we will apply the equations of motion to find out. First, let’s look at a tennis serve.
How Fast is a Tennis Serve?
It has been reported that the fastest tennis serve ever measured exceeded 160 mph, but a pickleball serve is much slower. We can explain why by first looking at the mechanics of a tennis serve. A tennis court has the dimensions shown in Figure 1.
For a serve to count, it must be placed from outside the baseline and land inside the opposite service court while clearing the height of the net. Using these dimensions, let’s assume that the server wishes to serve down the center of the court. He contacts the ball with his racquet at a height of 9’, and the ball must travel a distance of 60’ (18’+21’+21’) to reach his opponents service line. Along the way, the ball must also clear the net, which is 3’ high at a distance of 39’ from the baseline (Figure 2).
Using this geometry, we can calculate the theoretical maximum speed of a tennis serve by knowing that it will travel along a straight line from the contact point to the service line. The angle (θ) with respect to the horizontal axis that the ball contacts the racquet is known as the contact angle, which is calculated by:
In this case, the contact angle is negative because the ball velocity is directed in the downward (-y) direction. At this contact angle, the center of the ball would clear the net by 1.8”. Since the diameter of a tennis ball is about 2.6”, the outer surface of the ball would clear the net by only 0.5”. Tennis ball trajectories that approach this straight line will also approach the theoretical maximum speed of a tennis serve. Because of the geometry of the serve, the speed of a tennis serve is limited only by the amount and efficiency of exchanging momentum between the tennis racquet and the tennis ball.
Tennis serves are faster than pickleball serves for several reasons, some of which are described below.
- The tennis racquet contacts the ball about six feet higher than the height of the net. While the downward acceleration due to gravity adds a small percentage to the overall ball velocity, the major contribution is derived by the server providing a significant downward force to the ball.
- The strings of a tennis racquet help to propel the ball using the so-called “trampoline effect”, which we described in our article, “Power vs Control Paddles”. In a future article, we will discuss why a pickleball paddle cannot exhibit a trampoline effect due to its construction.
- The center of gravity of the tennis racquet is farther from the pivot point, enabling a much larger moment of inertia resulting in a greater amount of momentum exchange with the tennis ball. This is discussed in our article, “Where is the Sweet Spot?” We will also examine the mechanics behind momentum exchange in a future article.
Effect of Height on Pickleball Serve Speed
In our article, “How Fast is a Pickleball Serve?”, we used the equations of motion to determine that the fastest average pickleball serve was only 40 mph. This is because the serving geometry dictates that the pickleball be served upward first to clear the top of the net, then gravity takes over to bring the ball back to the ground before its horizontal velocity takes the ball past the baseline. As we discussed in our article, “Can Topspin Enable a Faster Serve”, we showed that a modest amount of topspin (1200 RPM) can allow you to increase the speed of your serve by about 20%. In each of these cases, we set the contact point at a height of 1.5 feet. What happens if the contact point is higher or lower than 1.5 feet? Under what circumstances would you want the serve contact point to be higher or lower?
In a typical serve (Figure 3), pickleball players can change the following:
- How hard they hit the ball causing an increase or decrease in the initial velocity (v0)
- The orientation of their wrist to change the paddle contact angle (θ)
- The application of topspin, sidespin, or backspin to the ball (ω) to change its trajectory and to cause different interactions between the ball and ground and their opponent’s paddle
- The vertical contact point (y0) of the ball
Good players will understand the interdependency of v0, θ, ω, and y0 and can adjust these variables independently according to the type of serve they want to use and environmental conditions, such as the presence of wind.
Returning to the equations of motion, we can evaluate the effects of changing the vertical contact point (y0) on the velocity and time of flight (T) of the ball during a serve. Figure 4 shows the results of these analyses. In each case, the ball is served from one baseline to the other where the shortest time of flight (T) is obtained by serving the ball so that it just clears the net. Since a pickleball has a diameter of about 2.9”, the center of the ball in each case reaches a height of 3.125’, or 37.5”, clearing the top of the net by 0.1″.
These results show that every incremental increase in serve height of 6” results in an increase in serve speed (v) of 2-3 mph. While this may not seem significant, what may be more important is that the time of flight (T) decreases by about 0.04 – 0.05 seconds for every 6” increase in height.
The speed of a serve increases, and the time of flight decreases because a ball served from a higher contact point does not need to rise as much to clear the top of the net than a serve from a lower contact height. In the absence of spin, once the ball clears the top of the net at 37.5”, it is only the force of gravity that brings the ball back down to the ground. Since the acceleration of gravity and the distance to the ground are constants, the time it takes the ball to strike the ground once the apex is reached over the top of the net is the same, regardless of the contact height.
What Does This Mean on the Court?
Many of us are familiar with the person at the pickleball court who serves sidearm (either forehand or backhand) with the ball at almost waist level (about 3’). While this serve may be barely legal, it offers the server significant advantages over a traditional underhand server. Assuming that the contact point of a traditional underhand serve is 1.5’, the sidearm server can hit the same serve landing just inside the far baseline at a velocity that is 7.5 mph faster with a time of flight that is 0.13 seconds less than the traditional underhand server. This represents an almost 20% increase in speed and a 17% decrease in time of flight. The increased speed and decreased time of flight may provide an advantage, as the receiver may have less time to prepare for his or her return.
Although small variances in contact height may not significantly change a pickleball player’s serve under normal conditions, it may have a more pronounced effect on ball trajectory and speed in the presence of headwinds or tailwinds and if topspin or backspin is used. For example, a pickleball player may desire a lower contact point if the serve is with the wind and a higher contact point if the serve is against the wind. The scientific explanation for why this is so will be addressed in a future article when we look at the effects of wind on pickleball trajectory and speed. A pickleball player may want to develop a sidearm, backhand, or drop serve to change the contact height for different situations, as well as to offer a variety of different looks to their opponents.
