12HPCI magazine Vol.

A Supercomputer
Reveals the True Natureof the ‘Disappearing MagicBall’
One of the most exciting aspects of baseball is the interaction between thepitcher and the batter. The main players in this interaction are the various
breaking pitches that pitchers have developed, but the reasons why theirtrajectories change are not well understood. In particular, there is a theory as
to why the forkball falls so sharply, but it has never been properly
demonstrated. A joint research team of the Tokyo Institute of Technology,
Kyushu University, and Keio University, led by Dr. Aoki, took on the challengeof elucidating the “fall mechanism” by using a supercomputer and thus
discovered a previously unknown mechanism.

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HPCI magazine Vol.

Does Forkball Fall
Due to the Action of Gravity?
The first person to throw a forkball in Japan was Chunichi Dragons pitcher
Shigeru Sugishita, some 70 years ago and it took the world by storm. It
was called the “disappearing magic ball” because of its large drop and thefact that it seemed to disappear from the batter’s view. Since then, many
famous pitchers have used the forkball as a trump card when facing

Photo 1 :The research team that has been working to elucidate the breaking balls
Back row, from left: Dr. Seiya Watanabe (Assistant Professor, Research Institute forApplied Mechanics, Kyushu University), Dr. Hiromichi Kobayashi (Professor, Faculty ofLaw, Keio University), Yuwei Yin (2nd-year master’s student, Tokyo Institute ofTechnology). In the front row is Dr. Aoki. In the lower right circle is Ryoga Ohashi, whocompleted his master’s degree at Tokyo Institute of Technology in 2021.

batters. “For many years, it has been said that gravity is the reason thatthe forkball falls so rapidly. However, I have always believed that there
must be other factors besides gravity,” Dr. Aoki recalls. In April 2020, theresearch team led by Dr. Aoki (Photo 1) began studying forkballs usinghydrodynamic simulations.
Normally, a thrown ball follows gravity and falls in a parabolic curve,
but a fastball thrown by a pitcher flies in a straight line. This is due tothe “Magnus effect” working on the ball. When a pitcher throws afastball, he applies a strong backspin to the ball. Backspin means thatthe upper side of the ball rotates in the opposite direction of thedirection the ball is going.
The air around a flying ball has a layer that flows along the ball,so-called boundary layer, but when it separates from the surface of theball, in the process it creates turbulence behind the ball. As shown in
Fig. 1, in the case of a ball with backspin, the airflow above the ball isdragged by the rotation of the ball, and the point where the layer
flowing along the ball separates is shifted backward. Conversely, on
the underside of the ball, the rotation of the ball and the surrounding
flow oppose each other, causing the separation point to shift forward.
As a result, the airflow behind the ball is biased downward. This adds
an upward force to the ball, weakening the downward force generated
by gravity. This phenomenon of a force (lift force) perpendicular to thedirection of motion acting on a rotating object is called the “Magnus
effect.” This effect increases with the number of rotations of the object.
In other words, a ball with a strong backspin will be lifted by the
Magnus effect, resulting in a fastball.
On the other hand, in the case of a forkball, the pitcher throws the ballwith as little rotation as possible. This reduces the Magnus effect andmakes the ball more susceptible to gravity, so it has been thought thatthe ball falls rapidly before reaching the bat.

A Supercomputer Reveals
the True Nature of the ‘Disappearing Magic Ball’

Magnus effect

Top : Main flow velocity-- Rotation velocity
Pressure : Low

Moving direction of the ballPressure : High
Main flow velocity + Rotation velocity● Boundary layer separation point

Fig. 1 :Magnus effect working on a ball with backspin

A side view of a ball moving from right to left. The Magnus effect reduces thedownward force generated by gravity.

Flow Simulation around a Ball with Seams
Dr. Aoki, who has been questioning the commonly accepted forkballtheory, focused his attention on the seams of the ball. The surface of abaseball has a seam only 0.9 mm high. It has long been known thatthese seams affect the airflow. However, it was not well understood
how it affected the ball. As the ball rotates at high speed, the positionof the seam changes from moment to moment. It was impossible toevaluate the impact of the stitches on the ball without the help ofadvanced computational technology and high-performancesupercomputers.
In recent years, however, the performance of supercomputers has
improved dramatically. Furthermore, Dr. Aoki and his team havedeveloped methods to perform state-of-the-art fluid calculations
utilizing the capabilities of such supercomputers, which allowed themto achieve their results. At the same time, the development of accurate
sport measurement devices has made it possible to measure detailed
data about a pitcher’s ball, such as its velocity, rotation speed, andtrajectory drop. Recently, the Major League Baseball has begun
publishing these measurements, which has made it possible tocompare and verify the results of supercomputer simulations withactual data.
In fact, it was found that the direction of the ball’s seam differs between
a fastball and a forkball. When looking at a fastball from the batter’sside, the seam appears four times per rotation of the ball, while on a
forkball, the seam appears only twice (Fig. 2). For this reason, therotation of the fastball is called “four-seam rotation,” while the rotationof the forkball is called “two-seam rotation.”
Dr. Aoki and his team used the TSUBAME3.0 GPU supercomputer at
the Tokyo Institute of Technology to determine the difference in the way
the ball falls between four-seam and two-seam rotations. For thenumerical calculations, they used the cumulant lattice Boltzmann
method, which is optimal for performing turbulence calculations. They
set the same values for ball velocity and rotation number for four-seam

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HPCI magazine Vol.

reducing the time to about one week by improving the efficiency of parallel
distributed processing and reducing the number of unnecessary grids,"
said Dr. Watanabe, looking back on the development efforts.

Discovery of the “Negative Magnus Effect”
The main results obtained from the simulation are as follows.

Movingdirectionof the ballFour-seamMovingdirectionof the ballTwo-seam

Fig. 2 : Four-seam rotation and two-seam rotationand two-seam rotations. The space around the ball was then divided
into approximately 370 million grids to simulate how the airflow was
generated and how this flow affected the ball.
The simulation code was developed mainly by Dr. Seiya Watanabe, a
graduate of Dr. Aoki’s laboratory who is now an Assistant Professor at
Kyushu University. “In the beginning, the calculation time needed tocomplete the process of a pitcher throwing a ball to a catcher was
estimated at 200 days, even using TSUBAME3.0. We succeeded in

First, in the case of a four-seam rotation it was found that the point where
the boundary layer separates from the surface of the ball shiftedbackward each time the seam came up, and conversely, on the undersideof the ball, the point where the boundary layer separates was pulledforward by the appearance of the seam. Lift forces were also always
positive. In other words, it was confirmed that the seam enhances theMagnus effect described above.
Second, in the case of a two-seam rotation (Fig. 3), when the seam wasat the top, it was confirmed that on the upper side, as in the four-seam
case, the boundary layer was less likely to detach and a downward flow
behind the ball was generated. However, when the smooth part of the ballwith no seam was on the pitcher side of the ball, the airflow behind the ballchanged to an upward direction. Then, when the ball rotates and theseam was on top again, the flow changed downward again. When the
airflow behind the ball turns upward, the ball is considered to be subjected
to a force in the opposite direction of the lift force.
Mr. Ryoga Ohashi, then a second-year master’s student in Dr. Aoki’slaboratory, and Dr. Hiromichi Kobayashi, Professor at Keio University
specializing in turbulence analysis, worked with colleagues in Dr. Aoki’slaboratory to analyze in detail a large number of images obtained throughsimulations. As a result, they found that the lift force was always positivein the four-seam rotation, whereas in the two-seam rotation, the lift force

A Supercomputer Reveals
the True Nature of the ‘Disappearing Magic Ball’

Lift characteristics of two-seam
One rotation of the ballFlow velocity

151.2 km/h

Rotation number

1,110 rpm

-180°

1.5

-90°

0°

90°

180°

Lift force[N]1Moving directionof the ball

0.5
0
-0.5
-1

Lift force

-1.5
0

0.025

0.05

0.075

0.1

0.125

0.15

0.175

0.2

Time[sec]

Positive Magnus effect

Negative Magnus effectFig. 3 : Analysis of two-seam turbulence

Negative Magnus effect

Negative Magnus effect

When the smooth part of the ball is on the pitcher side, a “negative Magnus effect” occurs, in which the lift force is negative, working to make the ball fall.

Positive Magnus effect

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HPCI magazine Vol.

Pressure : High

Main flow velocity-- Rotation velocity

Moving direction of the ballPressure : Low
Main flow velocity+ Rotation velocity● Boundary layer

separation point

Negative Magnus effectFig. 4 : Negative Magnus effectwas negative at moments, as shown in Fig. 3. They found that when thestitch angle of a two-seam ball is in the range of -30 to 90 degrees, theforce is in the opposite direction of the lift force.
It is known that on a slippery (no seam) ball, turbulence in the layers
flowing along the surface causes a “negative Magnus effect” in the
opposite direction of the “positive Magnus effect” that acts as a lift

force (Fig. 4). Dr. Aoki recalled, “Mr. Ohashi pointed out that thenegative Magnus effect might also occur on the slippery surface intwo-seam rotation.” As a result of the calculations and analysis, it was
found that the forkball with two-seam rotation falls sharply not only due
to gravity but also due to the negative Magnus effect. Furthermore,when the velocity and rotation number of the ball were set to the samevalue, the two-seam forkball fell about 19 cm lower on the home basethan the four-seam forkball.
“This result shows how much the stitching affects the ball. This was thefirst time in the world that a negative Magnus effect was shown to occur
on a baseball, and it was the moment when my long-held question was
answered. This was also made possible by the fact that thesupercomputer was able to capture the air changes around a ball withseams from moment to moment,” Dr. Aoki explained.

The Mystery of Ohtani’s Forkball
Unraveled, Too
Next, Dr. Aoki and his team took on the mystery of the forkball thrown by
Shohei Ohtani of the Los Angeles Angels and Roki Sasaki of the Chiba
Lotte Marines, who achieved a perfect game in 2022. This was because
the forkball they threw was said to have a sharper drop, even though it
was spinning faster.
Dr. Aoki explained, “As the speed of the ball increases, the number ofrotations of the ball increases. As the number of rotations increases, thefrequency of the appearance of the seam increases, and the positive
Magnus effect increases, so the ball’s fall should decrease. However, it
falls more sharply. I speculated that this was due to gyro-rotation rather
than backspin.” Gyro-rotation is a rotation in which the moving direction
and the axis of rotation coincide (Fig. 5). Unlike backspin, when the ball

A Supercomputer Reveals
the True Nature of the ‘Disappearing Magic Ball’makes one rotation, the forces received from the top, bottom, left, andright are canceled, so the Magnus effect does not occur.
“However, in the case of gyro-rotation, the airflow around the ball is more
complex than in backspin, so the space around the ball must be divided
into smaller grids and analyzed in several different patterns, including ball
speed, number of rotations, and direction of the axis of rotation,” said Dr.
Aoki. Therefore, Mr. Yuwei Yin, a graduate student in the Aoki Lab,
conducted the simulation using Nagoya University’s “Flow” Type II
subsystem (CX2570), a GPU supercomputer. In addition, Dr. Watanabe
rewrote the code for CPUs and conducted detailed simulations on the
supercomputer Fugaku. In this research, Mr. Yin played a major role bycreating shape data from a 3D scan of an official MLB ball and analyzing
turbulence together with Dr. Kobayashi.
The simulation results confirm that when the ball makes one rotation, theforces due to the airflow are canceled out in the vertical and horizontal
directions, and only gravity remains. It is now clear that a forkball due tobackspin receives lift forces, albeit with a negative Magnus effect,
whereas a gyro-rotating forkball falls sharply because only gravity is at work.
Furthermore, Dr. Aoki and his team are gaining new knowledge by trying
to elucidate Ohtani’s sweeper, a pitch that makes a big curve across thehome base.
Thus, Dr. Aoki’s research team’s simulations have revealed that baseballbreaking pitches are produced by the ball’s velocity, number of rotations,angle of the axis of rotation, and the effect of the ball’s seams. “In the
future, I would be happy if we could combine the results of this researchwith virtual reality (VR) and augmented reality (AR) to create a device thatwould allow anyone to experience Ohtani’s magic ball. We may even see
the emergence of a second or third Ohtani among the children who havepracticed with such a device,” said Dr. Aoki with a smile.

Moving directionof the ballFig. 5 : Gyroball rotation

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HPCI magazine Vol.

A Supercomputer Reveals
the True Nature of the ‘Disappearing Magic Ball’

About theResearcher

Dr. Aoki specializes in fluid dynamics. As an undergraduate, he studied in the Department of Applied
Physics, where he began researching the dream energy, nuclear fusion, in his graduation project.
In graduate school, he went on to the Department of Energy Science, where he began conducting
research using theory and simulation. It was during this time that the Tokyo Institute of Technology
developed the world’s first GPU supercomputer, TSUBAME. Dr. Aoki started hydrodynamic
simulations using TSUBAME and received the Gordon Bell Prize Special Achievements for his
numerical simulation of dendritic solidification of metallic crystals using TSUBAME2.0 in 2011. He iscurrently working on a wide range of topics from dolphin swimming to torrential rain disasters andtsunamis containing large amounts of debris and driftwood. Why did Dr. Aoki choose the theme of“breaking ball” for this project? “I thought that if I could do numerical calculations for complex
torrential rain disasters, I would also be able to do so for breaking balls,” he said. Working on thistheme has changed the way he watches baseball games, which used to be a hobby of his. “I started
to think, ‘They should put in more slow motion so you can see the stitching on the ball’,” he said. He
hopes to continue to enjoy watching baseball games in between research projects.

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