Revisiting Mantle`s Griffith Stadium

Revisiting Mantle’s Griffith Stadium
Home Run, April 17, 1953
A Case Study in Forensic Physics
Alan M. Nathan
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Lots has been written….
Good introduction to the
cast of characters and
the story:
Mickey Mantle
Donald Dunaway
434 Oakdale Pl.
Red Patterson
2
Griffith Stadium, ca. 1960
Mickey Mantle
Donald Dunaway
434 Oakdale Pl.
Red Patterson
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4
Baseball historian Bill Jenkinson
no more than
515 ft. and
probably 10 ft
less
5
Baseball Physicist Bob Adair
Page 103:
“…a more precise calculation gives… 506 ft,
with an uncertainy … no more than 5 ft”
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Chapter 6: One Big Day
(includes my analysis)
Due out October 2010
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Sanborn Map of Area
460 ft
434 Oakdale
565 ft
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What We Know
(at least approximately)
• Ball hit glancing blow on sign and exited
the stadium
– 460 ft horizontal ft from home plate
– 50-60 ft above ground level
• Donald Dunaway retrieved ball behind row
houses that face 5th St. NW
– at a distance of ~565 ft from home plate
• Wind was blowing out steadily at ~20 mph
– with gusts up to 40 mph
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What We Don’t Know
• Batted ball parameters
– speed, launch angle, and spin
• How long it took batted ball to reach sign
• Precise wind speed and direction at time
of hit
• Precise height where ball hit sign
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The Big Questions:
• Is there a plausible set of conditions
consistent with the known facts?
– Answer: yes, as we shall see
• Given all the uncertainties, what
constraints can we place on the distance
the ball would have carried unobstructed?
– I’ll tell you later
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How to Constrain the Trajectory?
• Ball hit beer sign
– 460 horizontal and 60 vertical ft. from home plate
• Not enough to determine landing point
– Different combinations of batted ball speed (BBS)
and vertical launch angle (VLA) will hit the sign
– Ambiguity nearly removed by knowing flight time (T)
• Technique used by hittrackeronline.com
– But we don’t know any of those things
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An Example
250
7
200
6
150
5
100
4
50
0
0
100
200
300
400
h o riz o n ta l d is ta n c e (ft)
500
600
100
80
60
40
20
0
400
450
500
550
horizontal distance (ft)
600
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120
118
6
0 0
Ball hits sign@460/60
2000 rpm spin
20 mph wind
5
8 0
116
5
6 0
114
5
4 0
112
110
25
560
5
2 0
30
35
40
45
50
5
0 0
1
2 4
550
1
2 2
540
1
2 0
530
1 8
520
1 6
510
500
25
1 4
30
35
40
VLA (degree s)
45
50
1 2
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• We have a dilemma… Need more info to
remove ambiguity
– e.g, BBS, VLA, T, …
– An aside: I don’t know how previous analyses
avoided this dilemma
• But we have one additional piece of
information…
– Ball was retrieved behind row houses
• …a fact seemingly ignored in previous analyses
• …and one leading to considerably longer distance
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..but not ignored in compempory accounts
From Louis Effrat, NYT
April 19, 1953
Louis Effrat. "Mantle Homer Hit Into Hall of Fame; Cooperstown
Shrine Will Get Ball and Bat Used by Yanks in Wallop at Capital.”
New York Times. 19 April 1953, p. S1.
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• Dunaway says he retrieved the ball behind the
houses facing 5th St.
– Nearest house 512 ft from home plate with roof
22 ft high (thanks to Jane Leavy for that info)
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5th St NW
beer sign
434 Oakdale
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Sanborn Map of Area
512 ft
434 Oakdale
460 ft
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250
7
200
6
150
5
100
4
50
0
0
100
200
300
400
h o riz o n ta l d is ta n c e (ft)
500
600
100
80
60
nearest house
40
20
0
400
450
500
550
horizontal distance (ft)
600
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Some Preliminary Conclusions
• Analysis shows hitting 5th St. and bouncing
onto or over roof not a credible option
• Ball hitting roof constrains the trajectory:
– VLA < 310
– BBS > 113 mph
– Distance > 535 ft (!)
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Further Observations
• Lower limit = 535 ft
• If ball “just hits root”, then we can place an
upper limit of 542 ft
• Therefore, distance is in range 535-542 ft
– BBS ~ 113 mph
60
VLA ~ 310
22
460
512
542
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Summary
• Distance = 535-542 ft
– BBS ~ 113 mph
VLA ~ 310
– Result insensitive to poorly know details
• precise wind speed
• spin on ball
• …
• Is this result credible?
– Yes: it is nearly identical to a home run hit in
2009
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Wladimir Balentien Home Run
October 2, 2009
• Greg Rybarczyk
(hittracker) provides
landing point and flight
time
• Sportvision (hitf/x)
provides BBS and VLA
• Together, these
constrain the full
trajectory
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Balentien vs. Mantle
Balentien
BBS
112.5 mph
VLA
290
D
442 ft
H
62 ft
Wind
15 mph*
Distance 517 ft*
Mantle
113.3 mph
310
460 ft
60 ft
20 mph
537 ft
very similar trajectories!
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*
My analysis using hittrracker and hitf/x
Balentien vs. Mantle
height above ground (ft)
120
100
Mantle
Balentien
80
60
40
20
0
0
50
100
150
200
250
300
350
400
450
500
550
horizontal distance (ft)
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Final Remarks
• A plausible scenario for the HR exists
• Distance is significantly longer than previously
thought
– 535-542 ft
– But certainly not 565 ft
• And it was aided considerably by the wind
– 460 ft w/o the wind
– which is still a very long drive
• Thanks to Jane Leavy for a very enjoyable
collaboration!
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• Thanks for your attention!
• Questions & Comments:
–[email protected]
–go.illinois.edu/physicsofbaseball
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