Physics on the Flight to Spring Training

David is leaving on a jet plane. (via Atomic Winter)

David is leaving on a jet plane. (via Atomic Winter)

This year as I slide from middle age to senior status and Vin Scully’s voice will no longer waft through my summer, it is more comforting than ever to be on my way to Phoenix to experience the sense of renewal that only spring training can provide.

As my flight, cruises along at 35,000 feet I imagine the “Boys of Summer” stretching as if they have awaken from winter’s hibernation to greet the warmth of early spring. Just then my daydream is violently interrupted by the first sharp bump of turbulence.

As I tighten my seatbelt it occurs to me that the forces that transport me to the Valley of the Sun are the same as the forces on a baseball – save one. Below is a sketch of the forces on my plane. They are shown as red arrows. The velocity is a blue arrow.


Since my plane is cruising at constant speed, the thrust from the engines must be equal in size to the drag force from the air. Furthermore, our constant altitude requires the lift force from the air must be the same size as the weight or force of gravity.

The forces on a baseball in flight are shown below. Again they are red arrows are the forces and the velocity is a blue arrow. Note that the baseball in flight is missing the thrust force because the plane has engines while the ball does not.


Let’s hope the plane continues to feel the additional force of the thrust created by its engines or else it will head for the sands of the southwest desert like a 2-0 curveball dives toward the dirt on the outside corner.

The flight of a ball is the beneficiary of a thrusting force only while it is still in contact with the pitcher’s hand or during its ever-so-brief encounter with the bat. During the remainder of its travels (shown in the sketch) only gravity and the air affect its motion.

As a result, the ball can never just cruise along at a constant speed and altitude. It always has a bending trajectory as evidenced by a high fly ball or a 12/6 curveball. Even a line drive must have at least some curvature to its motion.

For a typical passenger plane, the thrust (and also the drag while cruising) is about 25 percent of the weight while the lift must equal the weight. In contrast to a Clayton Kershaw four-seam fastball, where the drag is nearly equal to the weight and the lift is only about half of the weight.

The ratio of the lift to the drag of an airplane is part of the design of the size, shape, and inclination of the wings. During the flight, the pilot can adjust this ratio by raising or lowering the flaps. You know, those things movable parts along the trailing edge of the wing.

As the flaps are lowered the lift increases, but the drag increases. So, you’ll notice the flaps are down during takeoff to give more lift when you need to go upward and during landing when you need more drag to come downward. That sounds ridiculous.

The part I left out was that both the drag and the lift also depend upon the speed of the plane through the air. At take off when the speed is low, the flaps can create more lift but the engine must be at full throttle to create enough thrust to overcome the drag. During landing the lowered flaps increase the drag substantially, but that is fine because the plane needs to slow down. Anyway, the point is flying requires great skill because of the complex interconnection between drag and lift.

A baseball has no flaps to adjust. So you ask, how can a hurler adjust the lift and drag to create the variety of pitches in their arsenal? Gee, you’re starting to ask questions that sound like you have some training in physics! As a baseball fan you already know the answer. The pitcher can adjust the spin and the speed of the ball as it leaves their hand.

When the flaps are down, the plane deflects air downward. Newton’s Third Law assures us that if the plane exerts a downward force on the air, the air will exert an equal upward force upon the plane. This is the origin of the lift force.

A Hardball Times Update
Goodbye for now.

A baseball with backspin also deflects air downward. Since the ball exerts a downward force on the air, the air will exert an equal upward force on the ball. The Magnus Effect that I have written about before explains this lift force, to some degree. I’ll spare you explaining it again here.

An airplane is designed so the upward force the air exerts on it can be bigger than its weight so the plane can actually rise. Isn’t that a gobsmacker! The wings of a plane are actually held up by air. The very same stuff you effortlessly breathe in and out every second…and remember, at 35,000 feet the air is ever so much thinner.

In contrast to an airplane, no pitcher has ever thrown a baseball with enough spin to cause the lift to be greater than the weight. If one could, then there would actually be a true rising “rising fastball.” The pitch called a “rising fastball” just doesn’t fall as fast as it would without the lift force.

Even though the best pitchers can’t make a fastball rise, even a kid can throw a rising fastball. They just need to use a Wiffle ball or a Styrofoam ball. If you throw it with enough backspin, it will actually move upward.

Some would argue that pitchers have greater skill than pilots. After all, as the ball hums toward the target, pitchers don’t have the luxury of making fine adjustments mid-flight. On the other hand, all pilots do is make mid-flight corrections.

Anyway, my flight is starting its bumpy descent into Phoenix Sky Harbor (The best name for an airport ever!) If you read this, you’ll know that my pilot – though less talented than Clayton Kershaw – is a highly skilled aviator.

David Kagan is a physics professor at CSU Chico, and the self-proclaimed "Einstein of the National Pastime." Visit his website, Major League Physics, and follow him on Twitter @DrBaseballPhD.
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Jim S.
5 years ago

Hey, Dave, any chance you’ll be at the Dodgers game today? I’d like to meet you and shake your hand for all the great work you’ve done.

5 years ago
Reply to  Jim S.

Alas, no…it will have to be some other time.

Jason C
5 years ago

Hi Dave, thanks for giving me a short reprieve from my duties advocating on behalf of the good professors at Chico State.

The whiffle ball comment was especially nostalgic for me since I remember being able to through a side arm pitch (with the holes up) that certainly seemed to rise. It occurred to me that this is a bit different backspin though since I was really creating side spin. It was the shape of the ball I’m sure that made it rise (or appear to rise).

If I understand the stuff I’ve read of yours so far, I think the the rising effect of throwing a side-arm whiffle ball with holes up is the result of air pressure pushing the side without holes with more pressure than the side without holes.

Enjoy spring training and spring break.

Marc Schneider
5 years ago

You have just made me terrified to fly! 🙂

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5 years ago

The kicks will reportedly look a lot like the original “Beluga” Yeezy Boost 350 V2 which released last Fall and officially kicked off the next generation of low-top Yeezys.