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