Stadium Dugout Announcer's Booth Batting Cage Bullpen Behind the Plate

## Path and Range of a Baseball

It's a lot more fun running around the bases than going to first and stopping
- George Brett, Kansas City Royals third baseman, 1977

## III. The Role of Air Friction

If you were an astute reader from the "Range of the Ball" lesson, you might have noticed that the equation is not too realistic. For example, try using 100 miles per hour and 45 degrees ( both values are average values for a hit ball). The result from the equation would be far larger than possible. If the equation was correct, there would be multiple homeruns per game, guaranteed. So what is going on here? Have I given you a wrong equation? No, the equation is correct, except that we have not accounted for one thing: air friction.

Air friction is a fairly easy concept to grasp, but lets start with friction in general.

Friction is another force not unlike the force exerted on the ball by the bat. Friction is a force which opposes the force moving an object. For example, push a book across a table. When you push it, the book moves forward but after a few seconds, it stops (assuming your table is long enough). What has stopped the book? The answer is friction.

If you can look at a piece of wood with a microscope, you will see many cracks along the edge. Even something that feels smooth like a surface of the table is very rough on an atomic scale. This is the same case with almost all surfaces. So when a projectile passes through even a "smooth" object, the little cracks will eventually slow the projectile down.

So what is happening to a baseball? Is the baseball going through anything? Yes, air. While it is easy to discount air as an effective force, it can and will slow down an object.

So the question now is how much will air slow down the baseball? Let's ask Dr. Dell.

The drag force Fd = CdpAv2
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 or in our case pi r2
• v is the velocity of the object
What does this equation tell us? It tells us many useful facts:
• The faster the ball is traveling the larger the drag force will be
• The drag force may change significantly between different stadiums due to change in p, density of the air. This equation might explain why more home runs are hit inside the Colorado Rockies' stadium.