He led the league in home runs during a season 12 times

and made a record of 60 home runs in 1927 season

as well as 714 home runs of his life time record

In the dead-ball era

Ruth's home run and slugging percentage dominated the league

He creates an unchallengeable position in the heart of baseball fans

and was respectfully named "Baseball Demigod"

Roger Maris, an outfielder of New York Yankee

who challenged Ruth's record after 34 years-

- 60 home runs in a season

With his home run number getting close to 60

however, there was no joy for fans

because there can be only one hero in their heart

Roger, up here

Hey it's the voice from above

Hey Maris up here

it's the Babe

Hey you wnat my record? you want my record?

Catch this you ape piece of shit

Stop

In the game 154 in 1961

Maris hit number 59 in the 3rd inning

Two outs, in the top of 9th

and it's the last chance for Maris

Orioles was behind but made an unusual substitution

The closer Hoyt Wilhelm was called on to stop him tying Ruth's record

I hate that knuckleball

In this weather it's gonna be dancin' all over the place

Even if he gets wood on it it's not goin' anywhere

Bushlinger

Wilhelm takes the sign

but we all know what's coming

Does Roger Maris have one last home rum in him

he fouled it back

Roger had a good cut on that ball, but it's dancin' all over the place

Wilhelm's got it

Out

The knuckleball dominated the hitter and Maris failed to tie the record on that day

Knuckleball is a very special pitch in baseball games

It may suddenly change in direction during its flight

and dance all over the place with erratic movement

so that it can fool the batter

In the following we will investigate knuckleball

base on aerodynamics

Furthermore, we will then introduce various pitches of baseball

When it comes to aerodynamics, most people are familiar with Bernoulli's principle

But, to establish enough background knowledge

we need to learn more about the fluid theories

besides the Bernoulli's principle

First let's talk about boundary layer theory

When a fluid flows over a obstacle, they would interact with each other

Let's look into a simplest case

When a fluid passing through a flat plate with velocity V

it causes friction on the surface

In general, fluids are viscous

so the flow speeds decrease gradually when it get close to the surface

and end up at zero

The region where flow speeds gradually decrease

is called the "Boundary layer"

Viscosity dominate physical phenomenon in this thin layer

and the Bernoulli's principle does not apply in this region

However, viscosity has no effect on the region outside the boundary layer

where the fluid behaves like a inviscid ideal fluid

such that the Bernoulli's principle applies

We will back to Bernoulli's principle soon

Now pay attention to the phenomenon inside the boundary layer

If the flow velocity V is not large

The airflow inside the boundary layer is stable

and the streamlines look like a Mille Crepe

This is named a "Laminar boundary layer"

The geometric shape of obstacles have effects on boundary layer

For example, when substitute the plate by a sphere

a new physical phenomenon may occur

Streamlines are drew around the sphere

and the green part represents a boundary layer

which is a important region

Let's study the region outside boundary layer first

where the Bernoulli's principle applies

Observe the motion of a small volume element

Since the speed of a baseball is much lower than sound speed

the compression effect can be ignore

and the volume of this small element keeps unchanged

Imagine it moves in a tube that continuously changes in diameter

When it moves toward A

its speed decreases

A is called the "stagnation point"

around which the fluid separates to both sides

The speed increases from A to B

and reach the highest value at B

After passing through B the speed decreases

and reach the minimum speed when it arrive at C

Bernoulli's principle states that

high speed corresponds to low pressure

and low speed corresponds to high pressure

Therefore, the pressure maximums occurs at A and C

and B has the minimum pressure

Interesting thing occurs in the downstream region

The pressure gradually increases from B to C

Outside the boundary layer, when the external pressure variation is large enough

it can force the downstream boundary layer to move in opposite direction

Once the inverse flow occurs

upstream boundary layer can be pushed away from the surface

This phenomenon is called "Boundary layer separation"

The location of "Separation point" is near B

and the flow is very unstable behind the separation point

Round and round

When various scales of vortices emerge, it is called "Turbulence"

The tail-like turbulent region behind a obstacle is also named a "Wake"

Since the separation points occur close to B and D

the wake width is comparable to the diameter of the sphere

As a whole, wake is a low pressure region

and this is the main reason for air resistance

However, the location of separation points

are sensitive to the geometric shape of obstacles

For a streamlined body

the separation occur near its tail

The smaller the wake width

the smaller the drag

This is the reason why airfoils and solar cars

are designed to be streamlined form

Besides the geometric shape of obstacles

the surface roughness also determines the location of separation points

Take a look at this interesting experiment

The left photo represents a smooth sphere in wind tunnel

and the separation points are close to the largest cross section of the sphere

The right photo shows that with a thin trip wire in the upstream

the separation points move backward and the wake shrinks

What's going on here?

Why a small raised surface leads to this result?

The reason is that the state of boundary layer has been changed

It is originally a laminar flow in the upstream boundary layer

however, since the raised surface creats small scale vortices

the boundary layer becomes turbulent

This is called a "Turbulent boundary layer"

Fluid flows faster outside the boundary layer because no viscous effect there

A turbulent boundary layer is stirred by vortices

which makes it mixed with the outer and faster fluid

Therefore, the average velocities of boundary layer increases

and get more momentum toward downstream

So that the separation points retreat and the wake shrinks

The purpose of dimple design on a golf ball

is to create a turbulent boundary layer and reduce the drag

Baseballs are not smooth spheres, too

The seam lines on the surface of a balseball can disturb boundary layer

In general, baseball seams can cause the retreat of separation points

Baseball seams are not uniformly distributed on the surface

and this could result in the wake deflection

Moreover, the rotations of a baseball are classified into two types

One is four-seamer: There are 4 seams passing by in one full rotation

The other one is two-seamer: There are 2 seams passing by in one full rotation

The changes in attack angle results in non-symmetric force

which can be measured by wind tunnel experiments

This figure shows the force versus attack angle

for a four-seamer at zero rotation speed

As you can see, the force has four periods of variation in one full rotation

The detail explanations for that figure are given in the following computer graphics

The air flows in steadily from the left

In the beginning the attack angle is zero

and the seams are symmetrically distributed

therefore, the wake is right behind the ball without being deflected

But the wake deflects dramatically when the attack angle changes

The largest upward deflection occurs when the attack angle is about 22 degree

What is the reason for wake deflection ?

The air in upstream boundary layer becomes turbulent after passing by the seams

Notice the seam in the lower half part is more close to the stagnation point

and the lower half turbulent boundary leads the upper one

With longer path and more chance for mixing

the boundary layer gets more velocity and momentum moving downward

so the lower half part separation point retreats more

On the contrary

the upper half part separation point is in advance and the average velocity is lower

After mixing of these two sides of boundary layer flow in the wake

the average velocity deviates upward

and this is the explanation for wake deflection

To realize how the force acting on the ball

one can regard the complex interaction processes as a black box

The horizontal air flow deflects upward after passing through the black box

implies that a upward force acting on the air flow

Simultaneously, there must be a reaction force in the black box exert on the ball

which is equal in magnitude and opposite in direction

as specified by Newton's third law

This is the result of non-symmetric seam distribution

Keep on varying the attack angle

the force vanishes at about 45 degree

beyond which the wake deflects to another side

and the force reachs its maximum at about 68 degree

Then the force vanishs again at 90 degree

that it has goes through a period

As a result, there are 4 periods in a full rotation of 360 degree

In the case of two-seam rotation for a knuckleball

there are two main periods of force variation

The maximum force is equivalent to 2/3 of baseball weight

and the period is two times larger than the case of four-seam rotation

Define the coordinate system first before follow-up discussions

Use the rectangular coordinate system

and let X axis pointing toward home plate

Y axis pointing toward first base

Let XY plane be parallel to the ground

so Z axis stands vertically

For this coordinate system

The lift force is in the positive Z direction

the gravity is in the negative Z direction

the lateral force is in the positive/negative Y direction

and the drag force is in the negative X direction

Now consider the rotation axis of a knuckleball is perpendicular to the ground

Observe the trajectory from top view

and assume the ball spins half a rotation during the flight

The wind tunnel experiment implies that

there are two periods of left and right motion for a four-seam knuckleball

In the case of two-seam rotation

the knuckleball trajectory has one period of variation

In practice

a pitcher would try to throw the ball as no spin as possible

The way is to push the ball with fingertip

but it makes the ball hard to be controlled

Since the spin axis may not be fixed in some specific direction

and since the force is sensitive to attack angle

the knuckleball trajectory becomes hard to be predicted

This is a demonstration of knuckleball's movement

by Tim Wakefield in a Japan TV show

From the research of knuckleball we learn that at extremely low spin rate

the seam locations or say attack angle

determines the force on the baseball

In baseball games, however

other kinds of pitches have spin rate over 10 times higher than knuckleball

and a new physical effect of force enters in-

- the "Magnus force"

To get rid of the disturbance by seams

let's begin with a smooth sphere

When it start to spin

The B-side surface and the ambient air move in the same direction

while C-side moves reversely

Since the fluid inside boundary layer is governed by viscosity

the B-side boundary layer flows faster than that of C-side toward downstream

and carries more momentum

Therefore, the B-side separation point becomes relative backward

so the wake deflects downward after mixing of these two sides of air

and the transverse force arises

This is called the "Magnus effect"

that resulted from the rotation of moving object in the fluid