Physics of Baseball

Physics of Baseball

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Introduction


Baseball is a fairly simple game, once you understand the simple mix of science involved in baseball.

Also, there is much more to the game of baseball than simply hitting and pitching the ball.

Here is a few bits of information about a baseball that is hit 400 feet.

1. For each 1000 feet of altitude you can add 7 Feet.
2. For each 10 degrees of air temp you can add 4 Feet.
3. For each 10 degrees of ball temp you can add 4 Feet.
4. For each 1 inch drop in Barometer you can add 6 Feet.
5. For each 1 mph following wind you can add 3 Feet.
6. With the Ball at 100 % Humidity you can subtract 30 Feet.
7. When the ball is Pitched, for every 5 mph you can add 3.5 Feet.
8. For a ball Hit along the foul line you can add 11 Feet.
9. When an Aluminum Bat is used you can add 30 Feet.

A couple more bits of general information.

1. A curve ball that seems to break over 14 inches never actually deviates from a straight line by more than 3 inches
2. There is no such thing in baseball as a rising fastball!
3. The collision of a ball on the bat lasts only about 1/1000th of a second.
4.
That a batted ball should be able to travel no farther than 545 Feet.

The Path of a Baseball

A baseball will always follow a parabolic motion when hit with the bat. This is mainly due to the force of gravity acting on the baseball after it is hit.

A baseball like most other things follows the three laws of motion that were created by Sir Isaac Newton.

The three laws of motion are:

1.
Law 1. An object continues in its initial state of rest or motion with uniform velocity unless it is acted on by an unbalanced, or net external, force.
2.
Law 2.

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The acceleration of an object is inversely proportional to its mass and directly proportional to the net external force acting on it.
3.
Law 3. Forces always occur in pairs.

When the ball is hit by the bat, the bat exchanges its momentum to the ball and the ball flies away. While the ball flies, both gravity and air will exert a force on the ball, with gravity pulling the ball downward.

In knowing what the parabolic equations for motion are you can in general determine how far a ball will travel, and how long it will take to get to that point. The equation you could use would be:


x = 2(Vxi)*(Vyi) / g

Where x is the final position, Vxi is the initial horizontal velocity, Vyi is the initial vertical velocity, and g is the force of gravity which is normally 9.8 m/s/s.

t = x / Vxi

Where t is the time when, x is the current position, and Vxi is the initial horizontal velocity.

The above equations work very well in ideal situations mainly without air. The air causes a friction on the ball called the drag force. Which is represented by

Fd = (Cd)(p)(Av)^2

Where Fd is the drag force, Cd is the drag coefficient, p is the density of the air, A is the surface area of the object, and v is the velocity of the object.

The Pitch


Have you ever wondered whether a curve ball really curves, or is it just an optical illusion?

Now with the current technology, like fast photography, we can show that a curve ball really does curve.

Physicists began to wonder what made the baseball actually curve, and in research the found that a force called the magnus force is actually what cause the baseball to curve.

It is just like when a plane is flying and the air on top of the wing is less than the air on the bottom of the more which pushes the plane up. Well when a baseball is spinning, the spinning baseball will cause there to be more pressure on one side then the other causing the baseball to curve.

The amount that a curve ball will curve can be determined by the equation:

FMagnus Force = KwVCv


Where FMagnus Force is the Magnus Force, K is the Magnus Coefficient, w is the spin frequency measured in rpm, V is the velocity of the ball in mph, Cv is the drag coefficient.

The Bat



The baseball bat is quite a unique piece of equipment

Have you ever wondered why so many baseball bats get broken during a baseball season?

Well, like all things in nature a baseball bat has a natural resonance frequency, and since bats are not totally stiff objects they will vibrate. Although this may not be felt every time, there is always some vibration.

That vibration is determined by the amount of oscillation, and the oscillation is determined by the frequency and the amplitude. The frequency and amplitude will be determined by where the ball hits the bat.

Two waves will be generated, one where the ball hits the hat and one where the ball leaves the bat.

The place where the two waves meet are called the nodes. The nodes are called points of destructive interference, and the places where the two waves are furthest apart are the anti nodes.

If the ball hits the anti node, the bat will break or string. Anti nodes are the points where the maximum amplitude will be generated. At nodes, the two waves will cancel out stopping the oscillation.

The node is the sweet spot of the bat, and the anti nodes are the end or middle of the bat.

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