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Physics professor shares the secret to playing your best game of catch

A gentle throw is all you need during a game of catch, but what’s the best angle to get that perfect pitch? Jeff Marx, chair of the Department of Physics, published an answer to this question in the January 2023 issue of The Physics Teacher.

Photo of a green McDaniel hat with an M on the front on top of a towel and bright yellow softballs.

Jeff Marx, Physics professor and chair of the Department of Physics, recently published the article “The Optimal Throwing Angle for a ‘Soft’ Toss” in the January 2023 issue of The Physics Teacher. The simplicity of the premise — what is the best angle to throw a ball to make it a soft throw — makes it all the more surprising that Marx’s research is the first peer-reviewed study to answer that particular question. Here, Marx shares his thoughts on sports physics, inspiration in the everyday, and physics research at McDaniel.

Jeff Marx

Professor Jeff Marx.

So, what is the best way to throw a ball in a game of catch?
When you’re playing a game of catch with a little kid, you want to maximize the likelihood that they’ll catch it. So, you have to optimize a certain parameter, like having the ball come in as slow as possible to the receiver. In simple terms, the optimal angle for a soft throw — for any distance, on any planet — is 45 degrees.
What inspired you to investigate that particular question?
I was playing a game of catch with my son and started to wonder at what angle I should throw the ball to minimize its incoming speed for the receiver. I also polled my colleagues in Physics and Chemistry, people who might know the answer. Everyone thought they knew it, but they didn’t actually. People have been studying trajectories and throwing things for hundreds of years, but there are so many questions to ask that sometimes the simplest ones get overlooked.
Could a physicist determine the ideal way to perform other activities?
People are always applying physics to optimize different things, particularly in sports, like the best way to throw a football or make the safest helmets. But you need to closely and narrowly define what you mean by “optimized” or “the best” or “the safest.” Determining the ideal way of doing something can be challenging, because you’ve got a lot of parameters to consider. When you’re talking about sports, safety, and making complicated moves and plays, then it becomes almost as much of an art as it does a science.
Do sports-related research problems resonate with your students?
We have Physics majors who are into football, swimming, you name it. They often look into sports problems for their capstones or our Investigations in Physics course, but those topics are often more complicated or subtler than the students expect.
A number of years ago, one of our Physics majors, Jim Petrillo ’07, was captain of the lacrosse team, and he wanted to figure out how to hold a lacrosse stick to optimize an overhand throw. After he set up a model, he found that your bottom hand remains fixed while you do the movement with your top hand. At first, we couldn’t believe it, so we carefully observed how he and other experienced lacrosse players completed an overhand throw. It turned out that his model was right on! Going through the mechanics in a clinical light gave us a new understanding.

People have been studying trajectories and throwing things for hundreds of years, but there are so many questions to ask that sometimes the simplest ones get overlooked.

Jeff Marx
Is physics research often inspired by daily life?
Absolutely, you can be surprised by things. For instance, one day I happened to notice a fly on the surface of the water in a pool. It couldn’t fly away, because it was stuck, so it just zipped across the pool. In doing so, it left a wake, just like a duck or a boat, but I knew immediately that wake was dominated by surface tension.
The triangular wakes from larger objects, like ducks and boats, are always the same shape, no matter how big or how fast the object is moving. It’s called a Kelvin wake or Kelvin wedge, and the dominate force is gravity. A wake governed by surface tension is called a capillary wake, and I wanted to know if those followed a similar rule as Kelvin wakes.
David Ruth ’15, who is now a post-doctoral researcher in particle physics at the University of New Hampshire, worked on this problem as his senior capstone project. It turns out that capillary wakes are not all exactly the same, and whether the wake’s triangular shape is narrow or wide actually does depend on the speed of the object creating it.
Does “everyday physics” relate to more complex or abstract topics in physics?
It is kinda the opposite. Many students are attracted to physics because it goes beyond the everyday. They want to know about strange stuff like entanglement, the origins of the universe, and black holes. But then they become interested in the everyday stuff.
In fact, I was that student. I chose physics because I thought quantum mechanics and cosmology were really cool. Then I took a course called Light and Color in the Open Air when I was an undergraduate at Rensselaer. We talked about optical phenomena that happens every day in our atmosphere that people rarely notice. It expanded my understanding of what it meant to do physics and how much fun it could be. Professors Apollo Mian, Bill Pagonis, and I developed the course A World of Light and Color here at McDaniel to similarly inspire not just our Physics majors but students from all disciplines.
What research opportunities can Physics students find at McDaniel?
Professor Apollo Mian wearing shaded glasses while looking at laser instruments in McDaniel's optics lab.

Professor Apollo Mian in the optics lab.

Physics students can do research in our optics lab, where my colleague Apollo Mian investigates how light interacts with matter, and professor Farzad Ahmadi is a great resource for engineering topics. We recently acquired a new industrial shaker to study granular materials, and I have expanded my research into astrometry, which involves the precise measurement of, in my case, binary star systems. So, there are lots of exciting opportunities for our Physics students to make discoveries.