Sports Science of Baseball - Project

Since my CCA is softball and I have been actively participating in my CCA, i felt that doing something that was both scientific and fun at the same time would be fun.
So how fast can you throw a baseball? 



 In 2006, Joel Zumaya while playing in the American League Championship, threw a fastball at the speed at 104mph. So why is it so hard to threw a ball at the speed at 104mph? Is there a sound barrier? So lets be technical now.
Lets say a 104mph fastball as thrown from the pitcher which translates to about 132 feet per second and since the batter is at the middle of the plate and not at the back of it, we're talking about 55 feet from the pitcher. That means the batter has .4167 seconds to react.    Boosting that speed to 104 is bordering on unthinkable to hit 
So if we know exceptional humans can pitch 95 MPH and up, we at least have some ranges to work with, just like we know a human will likely never run a 30 second mile - there are physical limits to the possible.    Basically, it takes energy to throw a ball.

We discussed drag forces on a ball before and we know that at the moment of release a ball has about 1/6th horsepower of energy.    A horsepower-second is  the energy of a 1 HP motor running for 1 second, which would lift 550 lbs. one foot.

If a throw takes .11 seconds that means an average force on the ball of 12 lbs. - a mean acceleration equivalent to 40 G's.   Yep, 40  times gravity.  So a pitcher is transmitting power of 1.5 horsepower to the ball but his body is also in motion, the total power is more like 3 HP.   It takes 20 lbs. of muscle to generate 1 HP so 3 HP is obviously impossible using just a human upper body.   This is why pitchers talk about the importance of leg strength - 60 lbs. of muscle has to come from somewhere. 

 What about the physics of a moving baseball? 




In 1876 the baseballs in use had a size of 9-9.25 inches in circumference and weighed 5-5.25 ounces.    They will do so again this June .    Not many cultural traditions can claim that kind of heritage.

When people think of baseball, they often think of home runs, which is a blessing to marketing people and a curse to purists.    Prior to 1920, home runs were something of a rarity.   A stadium might have a center field over 500 feet, for example, and balls were used until they began to unravel.  

But people liked them so the talk among conspiratorialists has always been that baseball teams were selling out the game for offense.   In 1920 it was the ball, in the 1950s it was bats, in 1968 it was the mound (though they have something there, as physics will show us later) and the ball and bats came up a few more times before people decided it was steroids in the last decade.

Balls are not just required to have size and weight controls, they also have performance controls.   That control is called the Coefficient of Restitution.    The coefficient of restitution says that if they fire any random ball at 85 feet per second into a piece of wood at a distance of 8 feet, the rebound must be 54.6% of the initial velocity.   Because manufacturing is not that precise, there is an allowed deviation of +/- 3.2 percent.

If the ball's size and weight are controlled, and bats are controlled, what else can be 'juiced', besides maybe the players?  The seams, it is said.    While balls have not changed much since 1876 (they changed from horsehide to cowhide in 1975) the seams might, and seams are responsible for drag.

Baseballs have been manufactured by Rawlings in places as diverse as the USA, Taiwan and Haiti - what they all have in common are 216 red cotton stitches.    There was a power boom in  1987, 37 percent more than 1984.    One of the reasons  were 'happy Haitians.'   Jean-Claude "Baby Doc" Duvalier was one of countless petty tyrants who perpetually seem to run the vast majority of the world's countries and in 1986, the Haitian people had finally had enough.   These rejuvenated people were winding the ball tighter inside, it was said, or making the seams tighter (or both) and it made the ball more lively.

Tough to say.  Home runs went down in the next two years and it so happened the people of Haiti were again pretty miserable during that time.   That's the problem with correlation/causation reasoning.

In the late 1990s home runs surged again and this time the implication is that it was steroids but much of that reasoning was correlation/causation too.   Most interesting is that we have some common metrics.   In 1987, for example, during a huge surge in homeruns, a team (Oakland Athletics) that we know had two steroid users - Mark McGwire and Jose Canseco - had a team home run performance about the same as the 1927 Yankees and much less the 1961 Yankees - but nowhere near the individual totals of Ruth and Gehrig or Maris and Mantle.   Supposedly people who played in a more pure era.

In other words, lots of things can account for home runs; more pitchers meaning lower quality, higher altitudes of some stadiums, steroids or even happy Haitians.   The great thing about baseball is that it's quantifiable enough we can have those debates.