Mantle's Griffith Stadium Home Run Revisited
On April 17, 1953, a young Mickey Mantle stepped up to the plate in Griffith Stadium. It was the 5th inning with two outs and Yogi Berra on first. Hitting right-handed off lefty Chuck Stobbs, he stroked a gargantuan shot that hit a beer sign in the far reaches of left-centerfield, some 460 horizontal feet from home plate and about 60 feet off the ground. The ball glanced off the sign, exited the stadium, crossed 5th St NW, and ended up in a residential neighborhood. There seems to be no controversy about that much of the story.
What happened next is both unknown and quite likely unknowable with any certainty, given the long passage of time and the lack of eye-witnesses. The generally accepted story is that of Yankee publicist Red Patterson, who was sitting in the press box that day. Recognizing the publicity value of this very long home run, he left the stadium to try to retrieve the ball. According to him, he encountered 10-year-old Donald Dunaway with the ball; young Donald showed him where he found it in the backyard of 434 Oakdale Place. Patterson then paced off 105 ft from that location to the edge of the stadium, added to it the 460 ft to home plate, and concluded that the ball traveled 565 ft. Thus the Mantle legend was born and the phrase "tape measure home run" was coined, despite the fact the Patterson never actually used a tape measure. The ball and Mantle's bat are in the Hall of Fame Museum. This account of the event has been described in detail by Dan Valenti in his book Clout.1
The veracity of the Patterson account has been investigated extensively by baseball historian Bill Jenkinson in researching his book Baseball"s Ultimate Power, an historical account of tape measure home runs. In his research of the contemporary newspaper accounts of the home run, he found no mention of Patterson claiming that Dunaway showed him where the ball actually landed, as opposed to where it was found. In Jenkinson's interview with Patterson in 1984, Red admitted that he never asked Dunaway if he saw where the ball landed. Nevertheless he stuck with his story that the ball actually traveled 565 ft on the fly. Unfortunately Patterson died some years ago so it is no longer possible to question him about what actually occurred. In his book, Jenkinson says, "...several physicists with whom I have consulted agree that [the ball] could not have [traveled] more than 510 feet."2 Jenkinson's result is similar to that given by Prof. Robert K. Adair in his classic book The Physics of Baseball: "[A] more precise calculation gives an answer of 506 ft, with an uncertaintly I put at no more than 5 ft."3 Adair also remarks that the distance was aided considerably by a stiff wind, without which the ball would have traveled around 430 ft, still a very long home run.
So, we have two competing claims about how far the ball would have traveled unimpeded: the largely unverifiable claim of 565 ft by Red Patterson and the 506-510 ft claims of various physicists. This was the state of affairs as of several years ago when I was contacted by author Jane Leavy. At the time, she was doing research for her new biography of Mickey Mantle, which has since been published in October 2010 under the title The Last Boy.4 Jane was seeking my help to determine the fate of Mantle's long home run, using new information that she uncovered in the course of researching her book. The fascinating story of her research is told in Chapter Six "One Big Day" in her book, including her extensive interview with Donald Dunaway, whom Jane tracked down 55 years after the event. Dunaway confirmed that he did not actually see where the ball initially landed, but he provided important new information about where he actually retrieved the baseball. That information will play a critical role in my analysis, which I present in the remainder of this paper.
Let us start by enumerating those things that we know with some degree of assuredness, aided by the scale drawing in Fig. 1. First, we know that the ball glanced off the beer sign 460 horizontal feet from home plate and approximately 60 ft above home plate level. We further know from weather reports that there was a steady 20 mph wind blowing out, with gusts up to 40 mph. Finally, we have the claims of both Donald Dunaway and Red Patterson that the ball was retrieved by Dunaway behind the row houses across from the Griffith Stadium wall on 5th St. NW. It is also useful to enumerate the things that we don't know that would aid considerably in determining the ultimate fate of the ball. We don't know anything about the batted ball parameters, such as the batted-ball speed, the vertical launch angle, or the spin on the ball. We don't know how long it took for the ball to reach the beer sign. We don't know the precise speed and direction of the wind, nor do we know the precise height of the location where the ball hit the sign. Given what we know and what we don't know, let us then pose the following questions:
Figure 1. Sanborn map of Griffith Stadium and the surrounding neighborhood. Home plate is denoted by the small dot on the lower left; the first-base and third-base lines are denoted by the heavy lines. The dotted line points to straightaway centerfield. The dashed line is the likely path of the ball and connects home plate with the edge of the beer sign (460 ft). 5th St. runs parallel to the stadium wall and Oakdale Pl. is perpendicular to 5th St., nearly on a line with the trajectory of the ball. On the right-hand side of the map, the black square is the location where Patterson claims the ball was found, behind 434 Oakdale Pl. The black dot is the location where Dunaway told Leavy he found the ball, in the back yard of 2029 5th St. The front of that house is 512 ft from home plate and the front of the roof is 22 ft off the ground.
(1) Is there a scenario for the trajectory of the home run that is consistent with all the available information and with the laws of physics?
(2) How far would the ball have traveled unimpeded?
As we shall see, the answer to the first question is a definite "yes". As for the second, read on!
Let's first start with the information that the ball hit the sign 460 ft from home plate. For the sake of definiteness, I will assume that the ball hit 60 ft above ground level. I will further assume the steady wind of 20 mph, blowing horizontally straight out in the direction of the fly ball. Given these assumptions, what can we say about the trajectory of the fly ball? The answer is, not very much, as one can appreciate from an inspection of Figs. 2 and 3. These figures are calculations of four possible trajectories, each labeled by the vertical launch angle and each constrained to hit the sign at the indicated location. Between some minimum and maximum launch angle it is always possible to find a batted ball speed such that the resultant trajectory hits the sign. The figures show that the landing point of the ball depends on that vertical launch angle, traveling farther for a line drive and less far for a pop fly. For the trajectories shown in the figure, the landing point is 578, 538, 517, and 504 ft for launch angles of 20o, 30o, 40o, and 50o deg, respectively. With no knowledge of the actual launch angle, the ball could have even traveled outside of those ranges. The location of where the ball hit the sign is simply not enough information to determine the landing point of the ball. By the way, this conclusion has nothing to do with aerodynamic effects such as air drag. It would exist even for a "Physics 101" trajectory acting only under the influence of gravity.
Figure 2. Possible trajectories of the Mantle home run, all of which are constrained to pass through a point located 460 ft from home plate and 60 ft off the ground. The numbers label the vertical launch angle.
Figure 3.Expanded view of the trajectories in Fig. 2
So, we need to find a way to resolve the ambiguity, which will require either additional assumptions or additional information. Fortunately there is one additional piece of information that seems not to have been used in the previous physics analyses. Namely, regardless of whether Patterson's or Dunaway's version is correct, the ball was retrieved behind the row houses on 5th St. NW (see Fig. 1). The houses are no longer there. However, as part of her research, Leavy determined that the distance of the nearest house to home plate was 512 ft and the height of the roof was 22 ft. How did the ball get behind the houses? A possible scenario, shown schematically in Fig. 4, is that the ball hit the roof of the house at 2029 5th St., then bounced into the back yard where it was retrieved by Dunaway.5 Such a scenario allows us to set a very precise lower limit on how far the ball would have traveled unimpeded. The lower limit occurs when the ball hits the roof at the front of the house. The two fixed points on the trajectory--the beer sign and the front of the roof--leave little freedom on the extrapolation to ground level. We find the minimum distance to be 538 ft. with an uncertainty no greater than 2 ft, a result which is significantly larger than that found by the Adair or Jenkinson analyses. The result is very insensitive to details of the aerodynamic effects, the precise wind speed and direction, the spin on the batted ball, etc. The inferred parameters of the batted ball are reasonable: 114 mph batted ball speed and 30o launch angle. The ball was considerably aided by the 20 mph wind; it would have traveled only 464 ft in the absence of wind and only 359 ft had the wind been blowing in at 20 mph. Of course, this scenario only gives a lower limit, since the ball had to at least hit the roof to get into the back yard.6
Figure 4. A possible scenario (dashed line) for the home run trajectory, showing the beer sign, the house on 2029 5th St. NW, and the house on 434 Oakdale. The ball was retrieved by Dunaway between the two houses. This plot indicates that the minimum distance the ball would have traveled unimpeded is 538 ft.
It is interesting to examine the consequences of assuming that the ball was hit optimally, meaning that for the given wind condition, the ball was hit at an angle that results in the longest distance when extrapolated to ground level. The rationale for the assumption is that hitting a ball out of Griffith Stadium is an extremely rare event, so it is reasonable to expect that it only occurs under optimal conditions. This argument is that used by Adair in his analysis, although we differ in the effect of spin on the flight of the baseball,7 leading to numerically very different results. The result of my analysis is shown in Figure 5, from which we find a vertical launch angle of 31.8o, a batted ball speed of 113 mph, and a corresponding range of 535 ft. The "just hits the roof" scenario is therefore very close to the optimum.
Figure 5. Optimization curves for the fly ball trajectory, all plotted versus the vertical launch angle (VLA). The upper solid curve shows the contour of batted ball speed (BBS) such that the ball hits the beer sign at the proscribed location. The dotted curve is the corresponding plot of the fly ball distance extrapolated to ground level. The dashed curve is the contour showing how the optimum VLA depends on BBS. The intersection of the solid and dashed curves gives the optimum VLA for a ball hitting the sign, 31.8o, with a corresponding batted ball speed of 113 mph and distance of 535 ft.
In the discussion thus far, I have ignored any change to the velocity of the ball as a result of hitting the sign. We know it was a glancing collision, changing the direction of the ball by approximately 20o, as estimated from Fig. 1. In such a collision, the ball would lose at most about 20% of its velocity, so that to "just hit the roof", the ball would need a slightly larger initial speed and slightly smaller launch angle. Under such conditions, the unimpeded distance would increase, but only by about four feet.
In conclusion, I have presented a new analysis of the trajectory of the famous Mantle home run. The principal new piece of information used in the analysis is that the ball was retrieved behind the row houses facing 5th St. For the ball to get to the back yard of those houses, it had to travel far enough to at least hit the roof, which allows a precise determination of a minimum distance that the ball would have traveled unimpeded. As it happens, that minimum distance is very close to the distance one would expect for a ball hit optimally. Thus, a physically plausible scenario has been found for the trajectory that is consistent with all the available information and the laws of physics. The minimum distance is found to be 538 ft.
It is pleasure to acknowledge my very pleasant collaboration with Jane Leavy. I also acknowledge informative discussions with Bob Adair and Bill Jenkinson.
ReferencesDan Valenti, Clout (Viking Penguin, New York, 1989), pp 98-107.
Bill Jenkinson, Baseball's Ultimate Power (Lyons Press, Guilford CT, 2010), pp 214-215. Click here for an on-line account by Jenkinson.
Robert K. Adair, The Physics of Baseball, 3rd ed.(Harper-Collins, New York, 2002), pp 102-103.
Jane Leavy, The Last Boy (HarperCollins, New York, 2010), pp 83-102.
A skeptic could argue that the ball could have hit the street between the stadium wall and the nearest house, then bounced over the roof. I have investigate that possibility and find that for that scenario to be viable, the launch angle of the batted ball would have to be unreasonably large, greater than 50o and very far from optimal.
A spreadsheet with the calculations corresponding to the lower limit scenario can be downloaded by clicking here. For those so inclined, the parameters of the calculations can be modified and the consequences explored.
Alan M. Nathan, "The effect of spin on the flight of a baseball," American Journal of Physics 76, 119-124 (2008).