Volleyball science: Physicist/beach player Heureux examines the float serve


The float serve, when hit well, confounds opponents.

Pete Heureux, who graduated with a degree in physics from California Polytechnic State University, San Luis Obispo (Cal Poly), is not only an avid beach player for more than 20 years, he’s our go-to guy to break down the float serve.

We asked him to examine the physics of the float serve: What makes a serve float and how a server can maximize float. What follows might be more than you ever considered about serving a volleyball and perhaps information that might just make you a better player.

Pete Heureux is not only an avid volleyball player but a physicist ad student of the game/Ed Chan, VBshots.com
Pete Heureux is not only an avid volleyball player but a physicist and student of the game/Ed Chan, VBshots.com

Watching the video of Dalhausser serving four aces in a row at Long Beach inspires me to improve my serve, but I have to be realistic. If I put all my energy into a hard-hit jump serve I’d have nothing left over for the rest of my game. At 53 I also need to be kind to my shoulder if I want to play for another 30 years.

But I still want those aces!

I love it when I contact the ball just right and it sails smoothly to the net then starts moving all over the place. The changes in my opponent’s facial expressions give me great satisfaction as his emotions pass from confidence, to focus, to concern then rapidly through alarm, panic and despair. Watching this unfold is so distracting that I often forget to run back into the court to defend against the one-over that is the best offense the other team can hope for.

If only I could do that every time. Problem is that I have no idea how I did that serve in the first place, other than to hit it flat so it doesn’t spin.

The high-speed top-spin serve is daunting, but at least it is predictable. Anyone who has had to face a typical jump serve knows how the ball behaves. It dives. The faster it is coming or spinning the quicker it plummets toward your feet or drops behind your shoulder. The physics of the jump serve is straight forward. As the ball rotates with top spin it drags more air under the ball, which must move faster than the air on top to get by in the same amount of time.

Bernoulli’s Principle states that faster air has lower pressure so more air pressure on top and less on the bottom forces the ball down. A player has less time to react to a jump serve but one can still develop intuitive responses to the predictable flight path.

By contrast, the physics of float serve guarantees that you cannot know where it is going to go. A non-rotating ball is subject to the unpredictable interactions between drag, lift, and a narrow window of opportunity called the “drag crisis.” With a better understanding of the details of these forces we can begin to improve our intuition of how to manipulate the two things we can control on a float serve; the contact speed and angle. Once it leaves our hand we trust physics to take over to generate the ace for us.

Air moving past a sphere travels in a ‘laminar flow’ as the speed of the moving air increases from zero. Friction between the ball and the moving air causes a boundary layer of air to form close to the surface.


At very low speeds the air that touches the ball does not move at all (with respect to the ball), from the leading edge to trailing point. As it rubs against the next layer the air is slowed down. The thickness of a boundary layer is measured by how far away from the surface the air speed is the same as the air before it contacts the ball (the straight lines in figure 1). The “drag coefficient” is a measure of how tenaciously the air sticks to the surface of the ball. When the ball is moving faster through the air is more difficult for the air to hold on the trailing edge. As these molecules lose their hold the ball becomes less sticky and the drag coefficient decreases.

Eventually there comes a speed where the boundary layers are no longer able to hold together at all and they break away, somewhere along the trailing edge of the ball. This state is called “turbulent flow.” (see figure 2)


After the ball is fully into the turbulent state, the drag is significantly reduced. The transition from laminar to turbulent flow is known as the “drag crisis.” There are many factors that contribute to determining at what speed a particular ball will suffer this dramatic change. The size and shape of the ball, the smoothness of its surface, the air it travels in as well as the weather all interact in a complicated way that cannot be predicted, only measured, in a wind tunnel. Physicists have combined many of the factors that contribute to this change of state into a single figure they call the “Reynolds Number.” The Reynolds Number (Re) accounts for the mass density and viscosity of air (which depend mostly on temperature), the diameter of the ball, and the speed of air passing over its surface in the following relationship.


While all of these factors can change from day to day or from ball to ball it is the speed that makes the biggest difference from one serve to the next. The velocity at which a sphere reaches true turbulent flow is called the “critical speed.” For a typical volleyball the Reynolds number at the critical speed can vary from 170,000 to 300,000. Numbers like those are hard for me to feel intuitively so for practical purposes I will instead refer to the ball speeds they represent, which gives us a range between 10 meters per second and 25 m/s, respectively. Since the slowest you can serve a ball from the baseline and expect to get it over the net is about 12 m/s and the best pros can launch a jump serve around 30 m/s this is the range in which a float serves must exist.

When the scientist in me looks at the graph below I see a world of information about the physics of a sphere in flight. As a volleyball player I am struck by one thought: My opponents are in big trouble next time I step up to serve.


Figure 3 describes the results of wind tunnel tests done in Japan back in 2010 on the aerodynamics of a new volleyball designed by Molten. The graph shows the relationship between the drag on a sphere and the speed of air moving across it, specifically in the range we are interested in. Takeshi Asai and his colleagues from various universities around Japan found that a perfectly smooth sphere (thick dashed line, above) went through an abrupt drag crisis in the neighborhood of 25 m/s going from a very high drag coefficient to a very low one. The conventional volleyball they tested, a Molten MTV5SLIT (thin dashed line above), finished with a similarly low drag but with a critical speed significantly lower than the reference sphere. Their newest ball, a Molten V5M5000 with the honeycomb patterned surface, began with similar characteristics to the standard ball but had lower critical speed and higher final drag. Though they did not publish the details, the Japanese engineers also tested the new Mikasa MVA200 dimpled ball and found it had a critical speed slightly lower than the conventional ball.

In order to explain my new-found serving confidence let’s take a look at how drag coefficient tells us what forces will be acting on the ball after it leaves our hands. The force exerted on the ball due to drag is dependent on a number of things.


The most important thing to notice is that the drag force goes up as the speed squared. That means that twice as much speed turns into four times as much drag! Now if we rearrange Newton’s second law (F = ma; force equals mass times acceleration) we see that the acceleration (well, really the deceleration) of the ball is


Taking a look at figure 3 again imagine that we strike the ball hard so that it starts with a higher medium speed, say 22 m/s. Drag will cause the ball to slow down (moving your finger along the solid line from right to left) until it reaches the critical speed. At that moment (hopefully just as it crosses the net) the drag suddenly increases dramatically, the ball seems to fall out of the sky, and your opponent curses while diving to the sand.

The variability of air friction during flight alone would be enough to make for an effective serve but there is more. Drag is not the only force in play during the drag crisis and turbulent flow. The same wind tunnel tests done by Asai and his team also showed forces perpendicular to the direction of travel, which scientists call ‘lift’. Unlike an airplane wing, a volleyball is radially symmetric so lift can be in any direction around the ball at a right angle to the path of its flight.


While in laminar flow the boundary layer is uniform and so there are no lift forces measured on the smooth sphere or either type ball. Figure 5 below is a comparison of lift forces to Reynolds number for the Molten balls. During the wind tunnel tests the balls experienced a sharp, unpredictable sideways force at the drag crisis and then a small but steady lift under turbulent flow.


The collapse of the boundary layer at the beginning of the drag crisis causes a chaotic swirling of air in the wake of the ball as each small vortex breaks free from the surface. At Peking University in China, Wei Qing-ding and his team believe that the random nature of the creation of these vortices causes the separation line (a ring around trailing side represented by the dashed line in figure 2) to form off-axis to the flow, which probably accounts for the lift we see at higher speeds. Asai speculates that the orientation of the ball panels controls the direction and force of deflection.

One guy I play with is convinced that striking near the valve affects the direction a float serve will drift. Regardless of the cause, it is clear that even if you hit the ball fast enough that is stays in turbulent flow, the effect of lift will cause the ball to veer left or right, float long, or add to the downward effect of gravity.

And my favorite zig-zag serve? Wei also found that early in the drag crisis there is a narrow range of velocities where the boundary layer can shed vortices from alternating sides (see Figure 6) causing the lift force to switch back and forth from one side to the other.


When you put all these factors together the result is an unpredictable serve? But just how unpredictable is it?

Asai and company used an impact-type ball ejection device to launch non-rotating volleyballs with precise contact speed and angle to answer this very question. They ran tests on the two styles of Molten balls and the Mikasa dimple ball. Each was served twenty times and with three different panel orientations. The very tightest landing zone they achieved was one meter wide by two meters long (area A in figure 7 below) for the honeycomb ball struck on the main panel. Most other balls and orientations resulted in a possible area about 1.5 m by 4m (B). The Mikasa ball, struck perpendicular to the panels, could be expected to land anywhere inside an oval five meters long! And that is with no wind.


Now that we know what happens to the ball in a float serve, and have some idea of why it moves around during its flight, how do we make it happen? Let’s quickly review the physics.

1. Volleyballs experience a drag crisis (a jump from low to high drag) as they slow down. The speed at which this happens is dependent on ball type and air conditions. Smoother balls have a higher speed drag crisis. Higher air temperature equals a lower critical speed.

2. During higher speed turbulent flow a volleyball will experience both drag and perpendicular lift which increases as the square of the velocity.

3. The unpredictability of a float serve is from 1 to 5 meters of landing area.

4. All of the effects listed above ONLY occur with a non-rotating ball.

What should we do when we step up to the line to serve?

1. Eliminate rotation! Even the smallest tumble reduces lift and restricts it to the direction of rotation. Spinning also forces the state of turbulent flow, keeping drag coefficient in the region above the drag crisis.

2. Assess your equipment for the best way to get your ball to pass through the drag crisis.
a. Smooth balls can be served faster than rough balls
b. Bigger, lighter balls can be served faster than smaller heavier balls
c. Off-panel contact may result in more movement.

3. Assess how the conditions will affect movement
a. A headwind can be served into faster to get more lift and drag but a tail wind can be served slower and closer to the drag crisis.
b. Standing back from the service line gives more time for lift and drag to move the ball around but slower serves from the baseline are easier to control when targeting the critical speed.
c. Serve slower when it is hot and faster when it is cold if targeting the critical speed.

4. Choose your ball trajectory to account for the range of movement.
a. Higher arc serves start and finish faster because of gravity. Perpendicular movement may be a bit greater as the ball is falling down from a height but drag only slows the ball down without changing its trajectory. Flat serves are easier to manipulate because they rely almost entirely on contact speed.
b. Aim inside the lines. Float serves are supposed to move. Target your landing spot at least 1 meter from the sidelines and 2 meters from the net or baseline.

5. Eliminate rotation!! It bears saying again. In my experience the harder I strike the ball the more difficult it is to hit it just right. The closer I stand to the baseline the softer I can make contact and the more precisely I am able to target the center of the ball.

Since researching this article my float serve is generating many more aces. I am better able to see the changes in ball movement. Slowly my intuition for how the wind and feel of the ball and my position will combine to create the most unpredictable results. Now I just have to stop watching my beautiful float serve and hustle into my defensive ready position.

1. Asai T., Ito S., Seo K., Hitotsubashi A. (2010)Aerodynamics of a New Volleyball. In 8th Conference of the International Sports Engineering Association, Procedia Engineering 2, Elsevier.
2. Wei Q.D., Lin R.S., Liu Z.J. (1988) Vortex-induced dynamic loads on a non-spinning volleyball. Fluid Dynamics Research 3, North-Holand.



  1. In serving my float serve, I have always copied Ron Von Hagen who hit the ball on the valve. My theory is the valve is a slightly heavier spot on the ball. To fly straight, an arrow has the heaviest spot in front. Reverse that putting the heavy spot in back and the ball goes wacky. This is empirical knowledge only by observation. Hey, it worked for Von Hagen!

    • Having a weight int the back is actually stabilizing. that is why kites have tails. An arrow has mass in the front to punch momentum into the target. It is the high drag on the tail feathers that keeps it stable.

  2. Your description of why the drag drops at higher Reynold’s numbers is wildly wrong. It is not because the separation reduces the drag. The separation actually causes almost all the drag. The reason for the drag reduction is because a turbulent boundary layer will delay the separation compared to a laminar boundary layer. Higher Re means turbulent boundary layer which means smaller separation which means less drag.

    • Thank you for thinking critically about the science. I don’t understand what you mean by the term ‘separation’. As mentioned, higher speed (Reynolds number) means that a larger surface area of the ball is in turbulent flow and thus cannot contribute to drag. Figure three is very clear (not theory, but actual measurement); highest drag is during full laminar flow where no kind of ‘separation’ could be thought of to exist.

  3. 1. Can the ball vibrate significantly after the serve contact? Doesn’t that make its trajectory less predictable?

    2. Aren’t serves passing within a few inches over the top of the net harder to pass?

    3. For the passer, can the ball’s trajectory be tracked better if it is off to one side, rather than right on center?

  4. 1. If you are referring to oscillations caused by the ball returning to its normal shape after the contact deformation then probably not. The ball is stiff enough to be ‘critically damped’ and should return to normal in a few milliseconds.
    2. I used to think that before doing this research. After paying closer attention to float serves lately I can actually see the drag crisis happening. In general it happens at around the time in the ball’s travel when it is about half way there, even 10 feet above the net.
    3. That is very true with respect to drag. That is why it is important for your partner to give you information if the serve is coming at you short or deep.