The Path of a Home Run

As of Sunday, 28 April 2013, the longest home run hit in the Major Leagues so far was hit by Anthony Rizzo of the Chicago Cubs.  The left-hander hit a shot off righty Alexi Ogando of the Texas Rangers on a rainy day in Wrigley Field on the 18th of April in the bottom of the third inning with nobody out and a man on first.  Video of the home run may be found here.  Though the ball hit the back of the bleachers, an estimate of where the ball would have landed on the ground (really North Sheffield Avenue) has been made.  A great website that tracks all Major League home runs is Hit Tracker, which may be found here.  If one sorts all home runs by true distance, one finds that Rizzo's shot would have traveled 475 ft (145 m) horizontally.  Also provided are the launch speed off the bat, which was 115.0 mph (51.4 m/s = 185 km/hr), and the launch angle measured from the horizontal, which was 24.5 degrees.  The maximum height of 86 ft (26 m) is also given.

With all the great data provided, anyone can play with real home-run trajectories.  I describe how one may do this in an aerodynamics review article I wrote that just appeared online (click here to access the paper).  By choosing the appropriate drag and lift coefficients, I can fit a model trajectory to one that matches the data on the website.  I use constant aerodynamic coefficients as a first approximation, and I ignore the tiny difference between initial and final heights (about a meter, which is only about 0.7% the size of the horizontal range).  My model doesn't include wind or effects of rain, but it does give quite reasonable estimates of the sizes of the forces on the ball while in flight.

The buoyant force on the baseball was just under 0.2% of the ball's weight (my online article has a typo; the buoyant force I consider there should have been 0.15% of the ball's weight instead of 1.5%).  Clearly that force isn't a big player here!  The drag force is about 1.5 times the ball's weight just after the ball left Rizzo's bat.  If you solve a projectile motion problem with "ignore air resistance" in the problem statement, know you are not solving a realistic problem!  The initial lift force, which is due to the roughly 2000 rpm backspin the ball had when it left the bat (only around 500 rpm when the ball landed), was about 80% of the ball's weight.  Ignoring the effect of the ball's spin is also highly unrealistic!

The graph below shows three trajectories (click on the image for a larger size).

The dotted curve is what the trajectory would have looked like in vacuum.  That trajectory is nearly 41% too far.  If one includes drag, but not lift, one gets the dashed trajectory.  But that one is just over 17% too short.  The Goldilocks trajectory is the solid trajectory, which is my model of Rizzo's home run.  I missed the actual range by just 0.005% and the actual maximum height by 0.05%.  I could, of course, tweak my drag and lift coefficients to do even better, and I could include the slight difference in launch and landing heights, but pursuing this much further is silly because I don't know the true atmospheric conditions on that rainy day in Chicago.  The fun part is getting a trajectory that matches the real-world trajectory quite well and then studying the forces involved.

Sports and Terrorism

"I don't have a single American friend, I don't understand them."

-- Boston terror suspect, killed on 19 April 2013

For anyone having trouble understanding Americans, allow me to help you.  Nobody can help the person who authored the words quoted above, and it's doubtful anyone can help his younger brother, who is in custody right now.  I couldn't possibly speculate on the motives of those involved in what happened in Boston this past week.  People in various agencies will do their best to sort all that out.  What immediately stood out for me was the contrast between the scene at the conclusion of a marathon and the desire to end life.

I have never run a marathon, never come close to running anywhere near 26-plus miles (42-plus km) in a single day.  One of my cousins did it, and I was extremely proud of and amazed by what he did.  Imagine what it takes to run a marathon.  Weeks and weeks of training, disciplined diet, targeted exercises, and putting one's mind into the proper place to endure such a grueling task are all part of the preparation.  People who run marathons do so for a variety of reasons.  They may want to improve fitness, achieve a goal they thought unreachable, or maybe they hope to inspire someone else.  From what marathon runners have told me, crossing that finish line is a special moment.  Runners feel great about themselves and loved ones are inspired by what they've just witnessed.  The finish line of a marathon is a celebration.

On 15 April 2013, the finish line of the Boston Marathon turned from celebration to tragedy.  One of the great days in sports became a day during which people were killed and other people were maimed.  For anyone who doesn't understand Americans, or, more generally, people capable of courage and empathy, traits in the majority of human beings, regardless of nationality, look at what happened this past week.  Immediately after the bombs went off, people ran into the smoke to help people they had never met.  Nobody was asked what religion they belong to, what political party they support, or what sports team they support.  None of that mattered.  People simply helped their fellow creatures because those creatures were suffering.

Think about the medical professionals who tended to the wounded at the bombing scene, during ambulance transport, and at hospitals.  Many more health professionals have a lot of work ahead of them as they care for those physically and mentally scarred.  All will be helped and it won't matter what color the victims are, how the victims feel about various social issues, or what the victims' countries of origin happen to be.

Consider the images of the large number of law enforcement officers charged with keeping people safe and hunting down the suspects.  Those officers were made up of people of both sexes, all colors, numerous religious and nonreligious beliefs, political alliances, and so on.  A police officer is charged with protecting people, even people who may be as different from that officer as one can imagine.

Have those who don't understand us seen images from sporting events?  It was common to see baseball and basketball games with slogans like "We are all Boston" from shirts to big stadium screens.  As a passionate alumnus of both Vanderbilt University and Indiana University, I root for my Commodores and my Hoosiers.  I especially root for my teams when we play against bitter rivals like Tennessee and Purdue.  But if terrorism ever hits my rivals' campuses in Knoxville or West Lafayette, I'll feel solidarity with those who suffer and I'll want to help.  When people were murdered at Virginia Tech in 2007, I was warmed by the fact that not only did my own school help, but so did Virginia Tech's rival, the University of Virginia.  When tornadoes tore through Tuscaloosa in 2011, people from Auburn came to help, and there is no more bitter rivalry in sports than the one between Alabama and Auburn.

Nothing I write here is meant to suggest that all sports fans or all Americans are perfect people.  Many of my fellow creatures are quite capable of behaving badly toward one another.  There are roughly 45 murders per day in my country, a number embarrassingly too high by 45.  But most of us are able to put aside tribalism for solidarity when circumstances demand such a replacement.  We may feel more comfortable around those who look like ourselves or share common beliefs or root for the same sporting teams or vote for the same political parties.  It is natural to feel comfort in similarity and caution when facing differences.  A long, long time ago, it helped that our ancestors felt solidarity around each other and wary of lions and tigers, to give a cartoonish example.  In civilized 21st-century societies around the globe, people are enlightened enough to know that some differences among humans are trite and some differences help make societies stronger.  For those not lucky enough to have born into enlightened societies, know that there are many of us who feel solidarity with those seeking freedom.

Sport often brings out the best in people.  Athletes try to better themselves and inspire and entertain others.  The events in Boston gave us a vivid contrast between the best and worst of what human beings can do.  For those who don't understand America, I urge you to find a television and watch the Boston Marathon in 2014.  Bombs and the random taking of human life did not create the solidarity most Americans feel for people in need, they merely revealed what was already there.

Two Great Birthdays Today

On my drive to the gym this morning, I passed right by Poplar Forest, which was Thomas Jefferson's retreat home.  Just over a mile from my own home, Poplar Forest greets me during my drives to my place of work, Lynchburg College, as well as my trips to the gym.  Today's pass by Jefferson's second home got me thinking more about him because he was born on the 13th of April in 1743 (because Jefferson was born before the 1752 calendar adjustment, his birthday is sometimes given as 2 April 1743).  Can you even imagine what the world was like 270 years ago when Jefferson was born?  I consider myself fortunate to have been born in the 20th century in a country that Jefferson played such a pivotal role in founding.  Born out of the Philadelphia enlightenment of the latter half of the 18th century, my country has codified laws that protect our freedoms.  We are free to think what we want and pursue happiness.  Our founders, particularly Jefferson, saw the need to separate church and state, an idea integral to what makes my country great.

Another person I think about today is Christopher Hitchens, who was also born on the the 13th of April (in 1949).  One of my favorite modern writers, Hitchens moved me to think about politics and philosophy in so many new and different ways.  Though he died at the end of 2011, I continue to read his writings and listen to his speeches and debates (YouTube is a great resource!).  I am in awe reading and listening to Hitchens because I  know that it would take me the rest of my life to even be half as well read as he was.  I recently read Thomas Jefferson:  Author of America by Christopher Hitchens (get it here at Amazon).  I can't recommend it highly enough.

The two aforementioned polymaths certainly had their flaws, but one indelible character trait they shared was a lifelong commitment to learning.  I have found that I do better science when I exercise my mind in nonscientific arenas.  Studying history, philosophy, politics, and so forth have helped me think in better ways about how I approach problems in science.  Both Jefferson and Hitchens were well traveled.  I did not take my first real steps away from my own country until I was 30 years old.  Living in another country and visiting a half dozen other countries have opened my mind considerably.  I've also learned how people in other countries approach scientific problems, which has benefited me greatly in the past decade.  If you've never done so, I urge you to see how other people in countries foreign to your own live and do things -- it's well worth it!

Earning high school, college, and universities degrees are significant achievements.  But I've always thought that degrees are merely the keys that open doors to opportunities to learn even more.  Don't ever walk across a graduation stage and think that learning is finally over and you can relax.  Too much enjoyment of life awaits you if you choose to keep learning.

Great national title game!

Congratulations to the Louisville Cardinals for beating Michigan and winning the men's national title in college basketball.  A great game was played tonight, and it was tough seeing either team lose.  I've got friends and family from Michigan and they are certainly disappointed.  Don't hang your heads, Wolverines fans!  Your team had a fantastic year and is bound to be great for the next few seasons given how young its players are.  As an Indiana alumnus, I fear how good Michigan will continue to be.

For those itching for a little basketball science, check out The Physics of Basketball by John J Fontanella (click here for the Amazon page).  My publisher, The Johns Hopkins University Press, publishes Fontanella's book.  It's a fun read!

The Louisville women will try to match the men's team when they take on UConn tomorrow night.  UConn will be very tough to beat.  Can Louisville do it two nights in a row?