## Baseball Aerodynamics

**Baseball Trajectory Calculator**
Click on the link to go to a page with a description and download of a tool that can be used to do baseball trajectory calculations, including the effects of air drag, spin and the Magnus force, and wind.

The article is an analysis of an amazing throw by Oakland A's leftfielder Yoenis Cespedes the previous day, thowing out a runner at home plate with a perfect strike carrying about 300 ft on the fly. Note the comment I posted on the article where I used updated information to re-analyze the trajectory. Using a total distance of 300 ft and a hang time of 2.80 sec, I find that the ball was released with a speed of 101.5 mph and a vertical launch angle of 10.0 degrees. The correct trajectory is shown in the plot just above. In a followup, my student Eric Lang has analyzed some other historic throws in an article, **A Physics Comparison of Great Throws From Years Past**, published in The Hardball Times, June 24, 2014. A composite plot of the Cespedes throw plus seven others is shown below.

**The motion of an arbitrarily rotating spherical projectile and its application to ball games**, link to an article by Garry Robinson and Ian Robinson published in Physica Scripta (vol. 88, No. 1). The authors set up a formalism for numerically calculating trajectories of spherical sports balls, including the effect of wind. They then use their formalism to study some interesting effects for both golf and cricket balls. The formalism is identical to that used in my own
trajectory calculator (see link above). Nevertheless, the applications are quite interesting.

**Determining Aerodynamic Properties of Sports Balls In Situ,** a pdf file of the MS thesis of Jeff Kensrud of Washington State University (Professor Lloyd Smith, Advisor). This research is the most comprehensive set of measurements of drag and lift coefficients of sports balls without the use of wind tunnels. One particular notable resuls: The drag coefficient on the flat-seam MLB baseball is about 25% smaller than that of a raised-seam NCAA baseball, leading to considerably more "carry" for the MLB ball. Jeff summarized his results in a **paper** presented at the 2010 ISEA conference.

**How Far Did That Fly Ball Travel?**

Baseball Prospectus, January 8, 2013

Suppose we have data telling us the velocity of a fly ball just after leaving the bat, so that we know the batted ball speed, vertical launch angle, and horizontal spray angle. How well does that information determine the landing point? Such a question might arise, for example, in a batting cage situation. You measure the batted ball velocity—perhaps with a portable HITf/x or TrackMan system—and immediately tell the batter that he just hit a 385-ft home run, without the ball ever leaving the batting cage. But is this really possible? In a simpler, gravity-only world—I like to refer to it as the “Physics 101” world—it most definitely is possible. Under such conditions, once the initial velocity is known, the ball follows a trajectory that is completely predictable, landing in a location that can be calculated precisely with no more knowledge than one learns in the second week of Physics 101. End of discussion, right? Wrong! To learn how we know and speculation as to why that might be, read the article, which appeared in Baseball Prospectus on January 8, 2013. The comments are interesting, so be sure to read those also.

**The Gyroball** What's all this gyromania about? To find out, click on the link.

**How Much Does a Fly Ball "Carry"?** Read a brief account
on an analysis I did to quantify the term "carry". Included is an analysis of the home runs in the new Yankee Stadium to see if there is any measurable effect of wind.

**Baseball At High Altitude**. A brief description of the forces on a ball in flight, how thoses forces differ at Coors, and their effect on the flight of both pitched and batted baseballs. Also discussed here is the effect of the famous humidor in which the baseballs are stored at Coors.

**Home Runs and Humidors: Is There a Connection?**,
an article I wrote for Baseball Prospectus. Be sure to read the comments, since near the bottom I give my "best and final" numbers for both Coors and Chase. The article is based on a paper I co-wrote with Lloyd Smith entitled **Corked Bats, Juiced Balls, and Humidors: The Physics of Cheating in Baseball**, published in June 2011 issue of American Journal of Physics.

**Revisiting Mantle's Griffith Stadium Home Run**. A writeup of my reanalysis of The Mick's famous tape measure shot from 1953. An account of this work also appears in Chapter 6 of the new
biography of Mantle, **The Last Boy**, by **Jane Leavy**, published in October 2010. I gave a
**
public presentation** of this topic in Urbana on November 12, 2010 as part of the program of the
**
Baseball Music Project**.

**ESPN Home Run Tracker**: A web site due to Greg Rybarczyk that reports on home run distances,
meaning how far the ball would have traveled had it made it back to ground level without hitting something first. Greg's algorithm is based on his measurement of the precise location where the ball hit and the total flight time, both of which serve as input to his aerodynamic model to extrapolate the trajectory to ground level. The model takes into account drag, lift, and atmospheric conditions. In the absence of additional information about the batted ball, it is the best algorithm currently in use for determining home run distances. **Listen** to an interview Greg gave on hittracker on October 26, 2011 for 1080TheFan ESPN radio.

**Bonds
756 ^{th} home run. ** My analysis of the trajectory of Barry Bonds'
record-breaking 756

^{th}home run.

**Dissecting a Mystery Pitch**, an article published January 31, 2012 at **The Hardball Times**

The article is about a pitch from April 29, 2011 during the top of the 1st inning of a Toronto at New York game. Yankee pitcher Freddie Garcia threw a split-fingered fastball to the Jay's Juan Rivera. Using the high-speed video shown to the right, it is possible to measure the rotation on the ball, including the rotation axis. The ball breaks in a direction not consistent with the rotation axis, assuming the usual Magnus effect. The article unravels this mystery, with the aid of some experiments by
by frequent collaborator Rod Cross. There was lots of **discussion** about this topic at Tom Tango's **Inside the Book** blog. Note that the first 32 comments appeared prior to the article appearing in The Hardball Times. Finally, the New York Times got into the act with a story that appeared in the August 5, 2012 edition entitled
**
Challenging Batters and Physics Experts Alike**, by Zach Schonbrun. Zach conducted a telephone interview with me a few days earlier. I was sitting in the stands at Doubleday Field in Cooperstown when we had the interview! See also **The Yankee Analysts** for a discussion by Michael Eder of a nearly identical pitch Garcia threw to Pedro Ciriaco of the Red Sox on July 7, 2012.

**The effect of spin decay on the flight of a baseball.**: A brief unpublished essay in which an estimate is made of the rate of spin decay of a baseball in flight and the effect of the spin decay on the flight of a baseball.