Baseball. A game founded upon simple principles. Here’s a ball, there’s a bat, see if you can make contact. The baseball is a round object, made up of layers of rubber, yarn windings, horsehide, and 108 red-stitches.
Intermixed with these simplistic principles, is a complicated, analytical world, comprised of science and mathematics.
Many fans attend games for the ambiance.
Others, such as myself, have gravitated towards the physics of baseball and mathematical (sabermetrics) analysis.
This post is the first of a multi-part series, geared towards explaining the physics of baseball pitches. This post will focus mainly on the general principles of baseball movement and the physics of the various types of fastballs.
Check back later for the completion of the other articles, that discuss off-speed pitches and the knuckleball. Links will be provided at the end of the article, once completed.
Physics of Baseball Flight
Let’s first start with the principles of flight and basic concepts of aerodynamics.
Imagine an airplane wing. Air flows over the top of the wing and passes under the bottom of the wing. The shape of the wing causes the air flowing over the top, to reach the end of the wing, before the air below the wing. This delay causes a pressure differential between the two surfaces.
Huh? Explaining this concept further, let’s consult Bernoulli’s Principle, which states that pressure decreases when air moves faster. Therefore, the faster moving air on the top of the wing creates a low-pressure field, and the slower moving air below the wing creates a high-pressure field. This pressure differential (low on top, high below) between the two surfaces causes lift.
See the video below for a nice explanation from Cambridge University.
So how does this relate to the spherical baseball?
When a baseball pitcher or baseball player throws the ball, there is spin (back-spin or top-spin). The spin of the baseball creates a similar effect as the shape of the airplane wing and creates similar air pressure differences on the surface of the baseball.
Let’s focus specifically on the four-seam fastball that has back-spin (orange in image below).
Imagine a baseball being thrown to the right of the page. Air will counteract the baseball, to the left of the page, and gravity will pull the baseball down to the bottom of the page. Air will flow over the surface of the baseball, similar to the airplane’s wing.
The back-spin of the four-seam fastball allows for air above the baseball to reach the end of the ball’s surface, before the air below the ball. The air above the baseball is aided by the spinning baseball, whereas the air below the baseball is impeded by opposite rotation of the baseball.
A high-pressure region forms below the ball, and a low-pressure region above the ball. This pressure differential creates a lifting force (green) that acts on the baseball. As you may have inferred by now, low pressure regions are created by increased air velocities, and high pressure regions are created by decreased air velocities.
This concept is why the four-seam fastball can stay aloft longer than many other types of pitches and also why positional players utilize the four-seam fastball grip for throwing the baseball. (The other reason is this type of grip minimizes horizontal movement, which will be discussed further below).
Who said physics cannot be fun? Now some of your heads may be spinning (pun-intended), so we will provide some contextual examples to further explain each of the forces on the ball.
Magnus Force – Baseball Physics
What is the magnus force?
The image above denotes a lift force (green arrow) pointing to the top of the page. This lift force is not due to external loads acting on the ball, such as a person pushing the ball up, rather it is created by pressure differentials.
This lifting force, which is also known as the magnus force, after the German physicist Heinrich Magnus, is the dominant spin-dependent force acting on baseball.
More simply stated the ball’s flight path is often determined by the rotation of the baseball.
There are also other forces in play here besides the magnus force, backspin, and the pitcher’s throwing force.
Gravity acts downwards on the ball, and as we all know, forces the ball towards the ground as it travels forward. Gravity, in the case of the four-seam fastball, acts opposite to the magnus force.
Some people have stated that the four-seam fastball rises, however, what is actually happening is that the backspin keeps the ball aloft longer then an equally thrown ball without spin. Therefore, the drop rate of a baseball with backspin is less than that of a ball without spin.
The other force is drag (air-resistance) that acts opposite the pitcher’s force. Air has a density, albeit a relatively negligible one in stagnant conditions. If you do not think that air-resistance exists we recommend you complete the following exercise.
Hold a piece of paper on the edge and swing it forward. The paper will bend backwards, opposite the direction of motion. This is air exerting a force on the piece of paper. Something else to keep in mind; drag (air resistance) increases as the velocity increases.
Let’s reexamine the model with the magnus force, the drag force, and gravity included.
Physics of Four-Seam Fastball, Key Takeaways
The key with the four-seam fastball and magnus force is the uniform pressure on the fingers with the grip. The low pressure occurs uniformly across the upper half of the baseball and higher pressure occurs uniformly across the lower half of the baseball. This causes the perception of “rise” that we previously discussed, with little or no horizontal movement.
That is, of course, unless the pitcher changes pressure on the fingers to purposely generate horizontal movement, such as with the cut-fastball or two-seam fastball.
Magnus Force and the Cut-Fastball
The cut-fastball or cutter is a pitch that has late horizontal movement towards the pitcher’s glove side as the ball reaches home plate.
This offset grip changes the baseball’s center of rotation and adds a slight clockwise rotation in the baseball. This in turn changes the air pressure fields from the four-seam fastball.
Let’s examine a graphical depiction of the baseball. The previous graphics of the four-seam baseball showed the baseball oriented along the path of travel to the plate (i.e. a view standing from third base). The graphic below shows the baseball from reference of standing at home plate (i.e. what the hitter sees from a right handed pitcher).
The cutter is thrown at a slight angle, the axis of rotation is offset from the vertical. The baseball has backspin towards the top of the page (red arrows) and is traveling towards you out of the page, while also rotating about the offset axis. Now we have a physics background, but understand not all do, so let’s break that down further.
More simply stated, this offset of rotation causes a high-pressure field to occur on the left side of the ball (thrown by a right-handed pitcher) and low pressure field to occur on the right portion of the baseball.
As we learned earlier, the ball tends to move towards the low-pressure field (higher velocity moving air) or the magnus force. The horizontal movement on the cut-fastball is late, as the ball is attempting to first overcome the back-spin (like the four-seam fastball) before succumbing to the rotational spin. We should also remember that the rotational “offset” spin is caused by different finger placement on the edge of the baseball seams.
Let’s dive into the movement of the two-seam fastball next.
Magnus Force and the Two-Seam Fastball
Spatially, the two baseball has late movement towards a right-handed hitter (as released by a right-handed pitcher). Depending on the grip, the ball also has vertical drop, creating two plane movement.
The two-seam fastball is different than many fastballs, in the sense that it has top-spin instead of back-spin, that we have discussed throughout the article. Effectively, the top-spin means that to start out, the top of the baseball is in a high-pressure region and the lower half of the ball is in the low-pressure region.
The pitcher achieves the top-spin (for the two-seam fastball) by a slight inward twist of the wrist, towards the body, right before releasing the ball. The top-spin allows for the ball to drop vertically and also means that the resulting magnus force will be in a downward direction.
A baseball pitcher will also increase the pressure on the inside finger (pointer finger) to create the sideways rotation on the ball. As before, the different grip changes the rotation of the ball, that in return changes the air pressure on the surface of the baseball.
We will touch on this concept further in the upcoming article, The Magnus Force and Breaking-Balls.
In the interim, let’s examine a graphical depiction of the baseball. The graphic below shows the baseball from reference of standing at home plate (i.e. what the hitter sees).
The two-seam fastball is thrown at a slight angle, the axis of rotation is offset from the vertical. The baseball has topspin (red arrows) towards the bottom of the page and is also traveling towards you out of the page, while rotating about the offset axis.
More simply stated, the top-spin causes a low-pressure field at the lower half of the ball. The offset rotation shifts the rotational axis which helps to create the lateral movement of the baseball.
Mastering the vertical and horizontal movement is very difficult and is why many pitchers often only have two-seam movement in one plane. Movement in the horizontal plane is simpler to master in comparison to the vertical drop of the baseball, which requires flexibility in the wrist and perfect timing at release.
Physics of Baseball: Magnus Force Conclusion
The pressure differential creates movement in the baseball as it heads towards home plate. This pressure differential creates a force known as the magnus force. The baseball pitcher can play with grips, rotation, and release points to change these pressure fields to increase the effect of the magnus force on the baseball. So even if you did not know it, baseball pitchers are masters at physics, just without the credentials.
Hopefully we here at Innings Pitched, helped you easily understand the physics of the four-seam fastball, cut-fastball, and two-seam fastball. 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.
Let us know if you have any questions or even suggestions for an upcoming article in the comment section below.
Next Articles in the Series
To be completed at a later date, links to be provide here
- The Magnus Force and Breaking Balls
- The Magnus Force and the Knuckleball
- How Does Spin Rate Affect the Fastball?
- How Does Spin Rate Affect the Breaking Ball?
- How Does Spin Rate Affect Off-Speed Pitches?