Best Launch Angle for a 3-Pointer? This Professor Knows

August 18, 2023 By Andrew Ramspacher, Andrew Ramspacher,

For a couple of hours on a recent Friday afternoon in Nau Hall, a University of Virginia classroom could have been mistaken for a sporting goods store.

A multitude of items were on display, from a tennis racquet to a baseball bat to a badminton shuttlecock. One desk featured a basketball, a football and a bowling ball. One shelf had a pingpong paddle.

To emphasize his teaching points, professor Richard Lindgren doesn’t limit himself to only a few pieces of equipment when he leads his “Physics of Sports” course.

“This is a tough course,” Lindgren said. “There’s a lot of problem-solving. There’s a lot of physics. And I just try really hard to teach it in a way that they can understand.”

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The course, which has been offered each of the past three summers, is intended to help students better understand motion in sports and, perhaps, gain an advantage the next time they compete.

It’s well attended. This summer’s course roster included UVA men’s basketball players Blake Buchanan, Elijah Gertude, Isaac McKneely and Anthony Robinson, plus baseball player Matt Augustin.

Among the specific course objectives was for students to understand the best launch angle to make a 3-point shot in basketball.

McKneely is a rising sophomore for coach Tony Bennett’s team. As a freshman, he finished second on the Wahoos with 51 3-pointers out of 130 attempts.

Professor holds baseball bat
“Physics of Sports,” led by professor Richard Lindgren, taps into the science behind a number of sports actions, including the baseball swing. (Photo by Sanjay Suchak, University Communications)

Any Cavalier fan who watched McKneely last season can attest that the 6-foot-4 guard has a pure shooting stroke, punctuated by the shape of his ball flight.

McKneely has long known that a high shooting arc leads to better results than a live-drive attempt, but now he says he has a feel for the limits of the strategy.

“You have to have at least a 32-degree launch angle to make it. If you don’t, and you have less than (32 degrees), the ball will just hit the front rim,” he said, crediting Lindgren for the added insight. “Obviously I was familiar with arc and all that, but (Lindgren) went a little deeper and it was really cool to learn about it.”

In addition to “Physics of Sports,” Lindgren, a member of UVA’s faculty since 1985, teaches “How Things Work,” a course made popular by Lou Bloomfield that explores the science behind everyday activities.

Lindgren said in the summer of 2018, he taught “How Things Work” to a class roster that had five members of the men’s basketball team.  That following April, Bennett’s Hoos won the national championship.

“Intentionally, I focused the course in the sports area of interest of students attending the class,” Lindgren said. “This time around I focused discussion a little more on basketball and baseball. I would like to think that I helped them a little bit.”

Students and athletes participate in experiment
Matt Augustin, an incoming Wahoo baseball player, takes part in a demonstration that explains the center of mass. (Photo by Sanjay Suchak, University Communications)

Lindgren said he’s had conversations with Bennett about proper shooting techniques.

“If you have more arc, you have more leeway to make a mistake and still make nothing but net,” Lindgren said. “And he told me they have a camera on the top of the backboard that they use to look at a player’s arc, to be sure they’re shooting it at the right launch angle.”

Augustin is an incoming freshman pitcher for coach Brian O’Connor’s baseball team. During UVA Today’s visit to “Physics of Sports” earlier this month, Augustin volunteered to demonstrate with Lindgren to show the best area of the bat to use for success in hitting.

A multifaceted apparatus featured a hanging bat and weighted ball. A black piece of tape was placed just above the handle of the bat. A white piece of tape was placed more toward the middle of the barrel. A red piece of tape was also on the barrel, but more toward the end of the bat. A piece of putty sat on the bat’s knob.  

When Augustin swung the weighted ball, held by a pendulum, to the red tape, the putty stayed – “That’s good,” Lindgren said. The putty fell off, however, when the weighted ball connected with the black and white pieces of tape.

More athletes participate in experiments
Four members of the UVA men’s basketball team took part in Lindren’s course, including incoming freshmen Anthony Robinson, in navy hoodie, and Blake Buchanan, in gray hoodie. (Photo by Sanjay Suchak, University Communications)

This was Lindgren’s way to explain the center of percussion. In baseball terms, this is the “sweet spot” of the bat, or the location which produces the least vibrational sensation (sting) in the batter’s hands. When the putty is knocked loose, the hands sting. When the putty remains stationary, that represents a good feeling of contact for the batter.

There’s little sting, Lindgren said, because the translation and rotational motion of the end of the bat handle cancel each other out.

“Therefore,” Lindgren said, “the putty feels no force.”

Such an example is just one of many lessons Augustin said he’s taking with him as begins his baseball career with the Cavaliers. The right-hander from New Jersey said he throws five types of pitches and, through Lindgren, he’s learning more about the impact of spin on each one.

“With a curveball, if I get the highest spin on it, it will tumble a lot more,” Augustin said. “But a slider will move left to right more. (Lindgren) has us solve problems that really show how all that works. It’s really cool.”

Beyond the sports they play in, both Augustin and McKneely said they’ve found value in knowing more about the games they see on television.

Lindgren’s course also teaches why golf balls have dimples, why a soccer ball curves, why going low is the best option in blocking and tackling in football and the effects of motion on the cue ball in billiards, among other lessons.

“Usually you watch sports just to watch it because it’s entertaining and you enjoy it,” McKneely said, “but I feel like now I might watch it and be like, ‘Oh, the low man’s winning [in a football pile] because of torque.’

“I just feel like I can apply that a little bit more to when I'm watching sports and be like ‘Yeah, I learned about this. That’s pretty cool.’”

Media Contact

Andrew Ramspacher

University News Associate University Communications