And we are back.

In case you do not know, this is the second part of a multi-part series.

The first part of the series, comprehensively explained the principles of flight, via our friend Bernoulli.

The article also described the forces that cause fastballs to move vertically and horizontally, via our companion, German physicist, Heinrich Magnus.

If you missed the first part, we implore you to take a few minutes and read that article, before diving in feet first here. The second part of the series builds off the first.

Here’s the link for you: Physics Spotlight: Understanding Fastball Movement

Before we dive in, I want to touch base on some simple ideas, as a refresher.

A baseball moves due to the differential of air pressure across the surfaces of the ball. This is similar to how a soccer ball moves, you know, “Bend it Like Beckham”.

The introduction of the seams can create additional air turbulence, which in return can magnify the effect of the magnus force. Greater seam height equals greater magnus force. However, across Major League Baseball, the seam height remains constant. The seams do not dictate movement, but rather enhance movement.

Okay, the longwinded introduction is behind us, let’s move onto the main course.




 

Physics of Baseball, the Magnus Force and Top-Spin

Off-speed pitches are thrown with top-spin. The curve ball (overhand and three-quarters arm slot) and the slider come to mind.

Top-spin changes the pressure fields, but opposite in comparison to the fastball.

Physics of Baseball, Offspeed Pitches, Top-Spin Magnus Force

Physics of Baseball, Offspeed Pitches, Top-Spin Magnus Force

Top-spin allows for the air below the baseball to reach the end of the ball’s surface, before the air above the ball.

That is, the air below the baseball is aided by the spinning action, whereas the air above the baseball is impeded by opposite rotation of the baseball.

A high-pressure region forms above the ball, and a low-pressure region below the ball. This pressure differential creates a downward magnus force (green) that acts on the baseball.

As we learned in the last article, low pressure regions are created by increased air velocities, and high pressure regions are created by decreased air velocities.

Let’s jump into the specifics of the curveball.

Physics of Baseball, Magnus Force and the Overhand Curveball

The pitcher achieves the top-spin by turning their wrist (similar to how you would throw a football).

The pitcher then snaps their wrist, and thrusts their arm downwards.

This action lets the ball tumble out of their throwing hand and off their middle finger (depending on your grip).

This action is often correlated with turning a door-knob and equates to substantial wrist rotation.

We will not touch on every grip here, (we will save that for another article), but the conventional overhand, basic curve grip is shown below.

Overhand Curveball Grip

Overhand Curveball Grip

Different grips can change the rotation of the ball, that in return changes the air pressure on the surface of the baseball.

The upper half of the baseball is in the high-pressure region, and the lower half of the baseball is low pressure region.

As we learned in the previous post, the path of the ball follows the magnus force (low pressure region).

Rotation is downwards with top-spin, the magnus force is pointing down.

Refer to the figure below.

Physics of Baseball, Curveball and Magnus Force

Physics of Baseball, Curveball and Magnus Force

The curveball of elite pitchers exhibits late action.

This means, the baseball is a not traveling on a long sweeping curve.

The baseball travels straight, then once the magnus force becomes so strong, the baseball “drops off a table”.

Clayton Kershaw of the Los Angeles Dodgers has one of the more effective overhand curveballs in all of Major League Baseball.

Clayton Kershaw, Overhand Curveball

Clayton Kershaw, Overhand Curveball

Although you cannot see the physical rotation of the baseball in the clip above, top-spin is what has induced the vertical drop.

Let’s examine the vertical movement charts from Brooks Baseball.

Clayton Kershaw, Overhand Curveball Movement

Clayton Kershaw, Overhand Curveball Movement

You can see from the image above Kershaw’s curveball is one the best, achieving around 10 inches of vertical break.
Just remember this would not be possible without the magnus force.
Next let’s examine the slider and the subtle differences.

Physics of Baseball, Magnus Force and the Slider

The slider is noted as one of the most difficult pitches to hit.

I recall facing my first slider in my late teens, and let’s just say, I am glad not too many baseball pitchers knew how to throw a slider.

The magnus force, acting on the slider, is generally higher in magnitude than many of the other pitches.

(Side note: when we first wrote that sentence, it read “the magnus force is strong with the slider”, and I had to fight every urge to avoid a Star Wars reference).

The slider spins differently than the curveball.

The pitcher throws the baseball like a fastball, but at the last minute adds a small twisting action in the wrist.

The twisting action is often compared to adjusting a knob on a car radio.

Pitching Mechanics, Slider Arm Action

Slider Arm Action

The clip above from NESN shows, think fastball, until the last second. The wrist then twists.

The late twist of the wrist means the ball can be thrown at higher velocities, which means that spin rates are likely high.

As you may have inferred by now, higher spin rates create more turbulence in the pressure fields.

More turbulence can equate to higher differential of the pressure fields, which magnifies the magnus force, and creates more movement.

Who would have thought pitchers are masters of physics? At least unintentionally.

The twisting action of the wrist creates top-spin and side-spin. The resulting action of the ball is vertical drop and horizontal movement.

Let’s examine the free-body diagram from the slider.

Physics of Baseball, Slider and Magnus Force

Forces Acting on the Slider

Something you may notice is that the diagram looks somewhat similar to the two-seam fastball, but mirrored.

The two-seam fastball moves due to inner rotation of the wrist, often described as pronation. Whereas, the slider moves due to top-spin and side-spin created by wrist movement.

When a right-handed baseball pitcher throws, the baseball will rotate about an axis (shown in red). The ball will follow the magnus force and move down and away from a right-handed hitter.

Kenley Jansen of the Los Angeles Dodgers has one of the more effective right-handed sliders in all of Major League Baseball.

Andrew Miller of the Cleveland Indians, of-course has the best left-handed slider, but we wanted to remain consistent with our right-handed analogies.

Kenley Jansen Los Angeles Dodgers Slider

Kenley Jansen Los Angeles Dodgers Slider

Pretty nasty huh? That is the pitch that pretty much single handedly ended my playing career.

Let’s examine the horizontal and vertical movement to see the beauty of the magnus force at work.

Kenley Jansen Los Angeles Dodgers Slider, Horizontal Movement

Kenley Jansen Los Angeles Dodgers Slider, Horizontal Movement

On average, Kenley Jansen has approximately 3.75 inches of late horizontal movement.

Kenley Jansen Los Angeles Dodgers Slider, Vertical Movement

Kenley Jansen Los Angeles Dodgers Slider, Vertical Movement

Kenley Jansen’s slider on average has approximately 2.25 inches of late vertical drop.

If we dig into our grade school geometry and break out the Pythagorean Theorem.

2.25^2 + 3.75^ = C^2

Square root (5.0625 + 14.0625) = 4.37 inches

Let’s put that in perspective.

Kenley Jansen’s slider has 4.37 inches of late break. That is tough to hit.

Lastly let’s discuss the most “controversial” and most looked over pitch.

Physics of Baseball, the Magnus Force and the Changeup

The changeup is the most misunderstood pitch in all of baseball and the main reason why we left it for last.

Some think it is merely a slow four-seam fastball.

However, four-seam fastballs have backspin and “rise” due to floating effect.

Changeups do have back spin, just not the back spin of the four-seam fastball.

Instead, the changeup rolls off the fingers at an angle from the hands.

Similar to the curveball, the four-seam fastball pressure fields are parallel to the ground. This means that only vertical movement will occur.

Changing up the pace here, pun intended.

Let’s first look at the movement charts for Pedro Martinez’s changeup.

Pedro Martinez Changeup, Vertical Movement

Pedro Martinez Changeup, Vertical Movement

The image above Pedro Martinez’s change up from 2008 to 2009.
As we expect, the back-spin keeps the ball aloft (net zero vertical movement), but it does not cause the same rise like a four-seam fastball (in the image below).

Pedro Martinez Four-Seam Fastball, Vertical Movement

Pedro Martinez Four-Seam Fastball, Vertical Movement

This is where some people get confused and argue that a changeup is useless.

The fastball has massive rise, due to the back spin, as evident by a positive value on the y-axis in the image above.

The change up is near stagnant.

Now we also have to remember that here on earth we have gravity. If we are to add gravity back into the equation, the changeup will have vertical drop. More accurately, let’s call it fade.

Pedro Martinez Changeup, Vertical Movement Including Gravity

Pedro Martinez Changeup, Vertical Movement Including Gravity

Now this graphic above might be a bit misleading.

The vertical movement on the Y-axis depicts the change in height of the baseball, from the hand at release to where the catcher receives the ball. On average, the change up drops approximately 42 inches.

Let’s compare this to Pedro Martinez’s four-seam fastball graphic with gravity.

Pedro Martinez Four-Seam Fastball, Vertical Movement Including Gravity

Pedro Martinez Four-Seam Fastball, Vertical Movement Including Gravity

Pedro Martinez’s four-seam fastball has on average 20.5 inches of vertical drop.

Why the drastic change between the four-seam fastball and the changeup when we add gravity back into the equation?

The answer is simple.

Velocity.

The changeup will take longer to reach the catcher’s mitt and will fade more along its flight path.

The four-seam fastball will get their faster. The velocity of the baseball will be great enough to minimize the parabolic arc that objects in motion follow.

A good analogy of this phenomenon is a bow and arrow. Pull the line on the bow back far with the arrow and the arrow will travel in a relatively straight line over a short distance. Barely pull the line back on the bow, while aiming the arrow higher, a nice parabolic trajectory will be created.

Okay, now that we got the vertical movement down, let’s examine the horizontal movement.

Pedro Martinez, Change Up Horizontal Movement

Pedro Martinez, Change Up Horizontal Movement

Pedro Martinez’s changeup has a devastating 10” of horizontal movement.

Now image thinking that a fastball was coming.

Instead, a low 80’s change up with 10” horizontal movement and fade (due to gravity) shows up.

Yeah, guess I am glad the slider ended my playing career, so the changeup would not make me look even more like a fool.

Let’s looks at the grip of the changeup and corresponding free body diagram.

Circle Change Up Grip

Circle Change Up Grip

The circle changeup is one of my favorite pitches.

The pitcher literally makes a circle with the thumb and pointer finger. The remaining three fingers sit across the seams with slight pressure. The arm slot is similar to the fastball, but the pitcher lets the baseball roll off his fingers.

Physics of Baseball, Magnus Force and the Changeup

Changeup, Magnus Force

The changeup has back-spin, but the axis of rotation (angle of ball at release) allows for fade to occur.

This is reiterated in the magnus force (green arrow) being down and away from the right-handed hitter.

Still not convinced? Pedro Martinez’s changeup almost speaks for itself.

Pedro Martinez Changeup, Strikeout

Pedro Martinez Changeup, Strikeout

We would also like to note that some pitchers add a slight pronation of before release, but not enough to great top-spin.

Physics of Baseball, Magnus Force Conclusion

Top-spin creates downward movement in baseball pitches.

Slightly changing the axis of rotation manipulates the pressure fields and helps aid in lateral movement.

Changeups have both lateral and downward vertical movement.

Hopefully we here at Innings Pitched, helped you easily understand the physics of the curveball, slider, and controversial changeup. The topics can be overwhelming at first, but understanding some basics can help any pitcher better hone their arsenal or any statistician better understand the numbers.

Have questions?

Articles in the Series
The Magnus Force and the Fastball.
The Magnus Force, the Breaking Ball, and Off-Speed Pitch
To be completed at a later date, links to be provide here
The Magnus Force and the Knuckleball
How Does Spin-Rate Affect the Fastball?
How Does Spin-Rate Affect the Breaking Ball and Off-Speed Pitches?
How Does Spin-Rate Affect the Off-Speed Pitches?