When Zachary Lindsey, a physicist at Berry College in Georgia, decided to run an experiment on how to get the best speed and torque while playing disc golf (aka Frisbee golf), he had no trouble recruiting 24 eager participants keen on finding science-based tips on how to improve their game. Lindsey and his team determined the optimal thumb distance from the center of the disc to increase launch speed and distance, according to a new paper published in the journal AIP Advances.
Disc golf first emerged in the 1960s, but “Steady” Ed Hendrick, inventor of the modern Frisbee, is widely considered the “father” of the sport since it was he who coined and trademarked the name “disc golf” in 1975. He and his son founded their own company to manufacture the equipment used in the game. As of 2023, the Professional Disc Golf Association (PDGA) had over 107,000 registered members worldwide, with players hailing from 40 countries.
A disc golf course typically has either nine or 18 holes or targets, called “baskets.” There is a tee position for starting play, and players take turns throwing discs until they catch them in the basket, similar to how golfers work toward sinking a golf ball into a hole. The expected number of throws required of an experienced player to make the basket is considered “par.”
There are essentially three different disc types: drivers, mid-rangers, and putters. Driver discs are thin and sharp-edged, designed to reduce drag for long throws; they’re typically used for teeing off or other long-distance throws since a strong throw can cover as much as 500 feet. Putter discs, as the name implies, are better for playing close to the basket since they are thicker and thus have higher drag when in flight. Mid-range discs have elements of both drivers and putters, designed for distances of 200–300 feet—i.e., approaching the basket—where players want to optimize range and accuracy.
Enlarge/ Washington State University scientists conducted batting cage tests of wood and metal bats with young players.
There’s long been a debate in baseball circles about the respective benefits and drawbacks of using wood bats versus metal bats. However, there are relatively few scientific studies on the topic that focus specifically on young athletes, who are most likely to use metal bats. Scientists at Washington State University (WSU) conducted their own tests of wood and metal bats with young players. They found that while there are indeed performance differences between wooden and metal bats, a batter’s skill is still the biggest factor affecting how fast the ball comes off the bat, according to a new paper published in the Journal of Sports Engineering and Technology.
According to physicist and acoustician Daniel Russell of Penn State University—who was not involved in the study but has a long-standing interest in the physics of baseball ever since his faculty days at Kettering University in Michigan—metal bats were first introduced in 1974 and soon dominated NCAA college baseball, youth baseball, and adult amateur softball. Those programs liked the metal bats because they were less likely to break than traditional wooden bats, reducing costs.
Players liked them because it can be easier to control metal bats and swing faster, as the center of mass is closer to the balance point in the bat’s handle, resulting in a lower moment of inertia (or “swing weight”). A faster swing doesn’t mean that a hit ball will travel faster, however, since the lower moment of inertia is countered by a decreased collision efficiency. Metal bats are also more forgiving if players happen to hit the ball away from the proverbial “sweet spot” of the bat. (The definition of the sweet spot is a bit fuzzy because it is sometimes defined in different ways, but it’s commonly understood to be the area on the bat’s barrel that results in the highest batted ball speeds.)
“There’s more of a penalty when you’re not on the sweet spot with wood bats than with the other metal bats,” said Lloyd Smith, director of WSU’s Sport Science Laboratory and a co-author of the latest study. “[And] wood is still heavy. Part of baseball is hitting the ball far, but the other part is just hitting the ball. If you have a heavy bat, you’re going to have a harder time making contact because it’s harder to control.”
Metal bats may also improve performance via a kind of “trampoline effect.” Metal bats are hollow, while wood bats are solid. When a ball hits a wood bat, the bat barrel compresses by as much as 75 percent, such that internal friction forces decrease the initial energy by as much as 75 percent. A metal bat barrel behaves more like a spring when it compresses in response to a ball’s impact, so there is much less energy loss. Based on his own research back in 2004, Russell has found that improved performance of metal bats is linked to the frequency of the barrel’s mode of vibration, aka the “hoop mode.” (Bats with the lowest hoop frequency will have the highest performance.)
Enlarge/ Some cricket bowlers favor keeping the arm horizontal during delivery, the better to trick the batsmen.
Although the sport of cricket has been around for centuries in some form, the game strategy continues to evolve in the 21st century. Among the newer strategies employed by “bowlers”—the equivalent of the pitcher in baseball—is delivering the ball with the arm horizontally positioned close to the shoulder line, which has proven remarkably effective in “tricking” batsmen in their perception of the ball’s trajectory.
Scientists at Amity University Dubai in the United Arab Emirates were curious about the effectiveness of the approach, so they tested the aerodynamics of cricket balls in wind tunnel experiments. The team concluded that this style of bowling creates a high-speed spinning effect that shifts the ball’s trajectory mid-flight—an effect also seen in certain baseball pitches, according to a new paper published in the journal Physics of Fluids.
“The unique and unorthodox bowling styles demonstrated by cricketers have drawn significant attention, particularly emphasizing their proficiency with a new ball in early stages of a match,” said co-author Kizhakkelan Sudhakaran Siddharth, a mechanical engineer at Amity University Dubai. “Their bowling techniques frequently deceive batsmen, rendering these bowlers effective throughout all phases of a match in almost all formats of the game.”
As previously reported, any moving ball leaves a trail of air as it travels; the inevitable drag slows the ball down. The ball’s trajectory is affected by diameter and speed and by tiny irregularities on the surface. Baseballs, for example, are not completely smooth; they have stitching in a figure-eight pattern. Those stitches are bumpy enough to affect the airflow around the baseball as it’s thrown toward home plate. As a baseball moves, it creates a whirlpool of air around it, commonly known as the Magnus effect. The raised seams churn the air around the ball, creating high-pressure zones in various locations (depending on the pitch type) that can cause deviations in its trajectory.
Physicists have been enthusiastically studying baseballs since the 1940s, when Lyman Briggs became intrigued by whether a curveball actually curves. Initially, he enlisted the aid of the Washington Senators pitching staff at Griffith Stadium to measure the spin of a pitched ball; the idea was to determine how much the curve of a baseball depends on its spin and speed.
Briggs followed up with wind tunnel experiments at the National Bureau of Standards (now the National Institute of Standards and Technology) to make even more precise measurements since he could control most variables. He found that spin rather than speed was the key factor in causing a pitched ball to curve and that a curveball could dip up to 17.5 inches as it travels from the pitcher’s mound to home plate.
Enlarge/ The first recorded photo of a cricket match taken on July 25, 1857, by Roger Fenton.
Public domain
In 2018, we reported on a Utah State University study to explain the fastball’s unexpected twist in experiments using Little League baseballs. The USU scientists fired the balls one by one through a smoke-filled chamber. Two red sensors detected the balls as they zoomed past, triggering lasers that acted as flashbulbs. They then used particle image velocimetry to calculate airflow at any given spot around the ball. Conclusion: It all comes down to spin speed, spin axis, and the orientation of the ball, and there is no meaningful aerodynamical difference between a two-seam fastball and a four-seam fastball.
In 2022, two physicists developed a laser-guided speed measurement system to measure the change in speed of a baseball mid-flight and then used that measurement to calculate the acceleration, the various forces acting on the ball, and the lift and drag. They suggested their approach could also be used for other ball sports like cricket and soccer.
Enlarge/ The Armfield C15-15 Wake Survey Rake measured pressure downstream of the ball.
A.B. Faazil et al., 2024
Similarly, golf ball dimples reduce the drag flow by creating a turbulent boundary layer of air, while the ball’s spin generates lift by creating a higher air pressure area on the bottom of the ball than on the top. The surface patterns on volleyballs can also affect their trajectories. Conventional volleyballs have six panels, but more recent designs have eight panels, a hexagonal honeycomb pattern, or dimples. A 2019 study found that the surface panels on conventional volleyballs can give rise to unpredictable trajectories on float serves (which have no spin), and modifying the surface patterns could make for a more consistent flight.
From a physics standpoint, the float serve is similar to throwing a knuckleball in baseball, which is largely unaffected by the Magnus force because it has no spin. Its trajectory is determined entirely by how the seams affect the turbulent airflow around the baseball. The seams of a baseball can change the speed (velocity) of the air near the ball’s surface, speeding the ball up or slowing it down, depending on whether said seams are on the top or the bottom. The panels on conventional volleyballs have a similar effect.
There’s rarely time to write about every cool science-y story that comes our way. So this year, we’re once again running a special Twelve Days of Christmas series of posts, highlighting one science story that fell through the cracks in 2020, each day from December 25 through January 5. Today: Using markerless motion capture technology to determine what makes the best free throw shooters in basketball.
Markerless motion-capture technology shows the biomechanics of free-throw shooters. Credit: Jayhawk Athletic Peformance Laboratory.
Basketball season is in full swing, and in a close game, the team that makes the highest percentage of free throws can often eke out the win. A better understanding of the precise biomechanics of the best free-throw shooters could translate into critical player-performance improvement. Researchers at the University of Kansas in Lawrence used markerless motion-capture technology to do just that, reporting their findings in an August paper published in the journal Frontiers in Sports and Active Living.
“We’re very interested in analyzing basketball shooting mechanics and what performance parameters differentiate proficient from nonproficient shooters,” said co-author Dimitrije Cabarkapa, director of the Jayhawk Athletic Performance Laboratory at the University of Kansas. “High-speed video analysis is one way that we can do that, but innovative technological tools such as markerless motion capture systems can allow us to dig even deeper into that. In my opinion, the future of sports science is founded on using noninvasive and time-efficient testing methodologies.”
Scientists are sports fans like everyone else, so it’s not surprising that a fair amount of prior research has gone into various aspects of basketball. For instance, there has been considerable debate on whether the “hot hand” phenomenon in basketball is a fallacy or not—that is, when players make more shots in a row than statistics suggest they should. A 1985 study proclaimed it a fallacy, but more recent mathematical analysis (including a 2015 study examining the finer points of the law of small numbers) from other researchers has provided some vindication that such streaks might indeed be a real thing, although it might only apply to certain players.
Some 20 years ago, Larry Silverberg and Chia Tran of North Carolina State University developed a method to computationally simulate the trajectories of millions of basketballs on the computer and used it to examine the mathematics of the free throw. Per their work, in a perfect free throw, the basketball has a 3 hertz backspin as it leaves the player’s fingertips, the launch is about 52 degrees, and the launch speed is fairly slow, ensuring the greatest probability of making the basket. Of those variables launch speed is the most difficult for players to control. The aim point also matters: Players should aim at the back of the rim, which is more forgiving than the front.
There was also a 2021 study by Malaysian scientists that analyzed the optimal angle of a basketball free throw, based on data gleaned from 30 NBA players. They concluded that a player’s height is inversely proportional to the initial velocity and optimal throwing angle, and that the latter is directly proportional to the time taken for a ball to reach its maximum height.
Enlarge/ Graphic showing the contrast in release angles between proficient and nonproficient shooters.
Jayhawk Athletic Performance Laboratory.
Cabarkapa’s lab has been studying basketball players’ performance for several years now, including how eating breakfast (or not) impacts shooting performance, and what happens to muscles when players overtrain. They published a series of studies in 2022 assessing the effectiveness of the most common coaching cues, like “bend your knees,” “tuck your elbow in,” or “release the ball as high as possible.” For one study, Cabarkapa et al. analyzed high-definition video of free-throw shooters for kinematic differences between players who excel at free throws and those who don’t. The results pointed to greater flexion in hip, knee, and angle joints resulting in lower elbow placement when shooting.
Yet they found no kinematic differences in shots that proficient players made and those they missed, so the team conducted a follow-up study employing a 3D motion-capture system. This confirmed that greater knee and elbow flexion and lower elbow placement were critical factors. There was only one significant difference between made and missed free-throw shots: positioning the forearm almost parallel with an imaginary lateral axis.
