Subtitles section Play video Print subtitles Babe Ruth, a legend of Major League Baseball 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 The magnitude of Magnus force is probably proportional to the air flow speed V and the angular frequency ω of the ball So the empirical formula for Magnus force is given by 1/2 times "Magnus coefficient CM" "air density ρ" "baseball cross-sectional area A" "radius R" "angular frequency ω" and the "flow speed V" The Magnus coefficient is a dimensionless quantity and is the only one parameter to be determined from experiments Rotation is the motion characterize with direction and can be well described by a "Vector" For example, a spin vector S