Studies of Batted Ball TrajectoriesI.Analyzing the FFX trajectoriesII.Determining landing point/hang time from HFXCombining HFX and HittrackerDo drag coefficients vary with ball?

Alan M. NathanUniversity of Illinois

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I. Analyzing FFX Trajectories

WWAD = What Would Alan Do?Actually, what DID Alan do?Scottsdale, March 2009 experiment10 Cameras uses2 PFX/HFX cameras8 IP cameras*All* data used to analyze trajectoriesPFX+HFX+FFX

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Analyzing FFX Trajectories

Track pitch9P PFX Track initial batted ball6P HFXGet intersection of batted ball and pitched ball trajectories to establish contact timeTrack batted ball using FFX camerasDo constant acceleration fit to first 0.5 sec of FFX dataKey step: Velocity vector fixed at HFX valueLook for intersection with HFX trajectory to synchronize IP and HFX clocksNow fit the synchronized FFX and HFX data to using your favorite model

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Analyzing FFX Trajectories

Modeling the batted ball trajectoriesPiecewise (~0.5 sec) constant accelerationConstant jerk (12P) might workNonlinear model with drag, Magnus, wind, will work bestPossible compromises9P*or 10P* models: Initial position and velocity vectors (6) plus constant Cd (1) and spin vector (2 or 3)

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Examples Using 9P* and 12P12P = constant jerkInitial positions, velocities, accelerationsRate of change of acceleration (jerk)

9P* = aerodynamic modelInitial positions, velocitiesConstant drag coefficientBackspin and sidespinBoth models utilize nonlinear L-M fitting applied to pixels directly

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Line DriveLine DriveFly BallV0=96 mph 0=16 deg

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Fly BallLine DriveTopspin Line DriveV0=106 mph 0=6 deg

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Fly BallLine DriveIncomplete LongFly BallV0=104 mph 0=23 deg

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Fly BallLine DriveLine DriveLine DriveV0=99 mph 0=7 deg

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Fly BallBad FitV0=101 mph 0=6 deg

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Some Remarks12P and 9P* work equally welISometimes bad fitsProbably bad fits due to bad data, not bad model12P provides handy way to parametrize the trajectoryThe Arizona data came from an initial experiment. Quite possibly the current setup in SF provides higher quality dataI recommend further studies of this typeSide note: the FFX data can be used to correct the HFX data, which systematically underestimates v0 and 0

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II. Determining landing point/hang time from HFX

Utilize ball tracking data from 2009, 20102900 batted balls2367 batted balls with VLA>0Initial velocity (BBS, VLA, Spray angle)Location when z=0 and hang time (extrapolated)Not a theoretical analysis; based entirely on data

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Total Distance

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Fit vs Data

DistanceRMS=25 ft

Hang TimeRMS=0.4 sec

BearingRMS=8 deg

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SummaryDistance: RMS=25 ftHang Time:RMS=0.4 secBearing: RMS=8 deg

(Data precision almost surely more accurate

It is hard to do any better than this without additional information (spin? wind? )Is it good enough?What about reverse (Hittracker)?

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III. Combining HFX with HittrackerHITf/x (v0,,)Hittracker (xf,yf,zf,T)Together full trajectoryHFX+HTT determine unique Cd, b, s Full trajectory numerically computed (9P*)T bhorizontal distance and T Cdsideways deflection sAnalysis for >8k HR in 2009-10

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How well does this work?Test experimentally using radar tracking device

For this example it works amazingly well! A more systematic study is in progress

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Ex. 1 The carry of a fly ball Motivation: does the ball carry especially well in the new Yankee Stadium? carry (actual distance)/(vacuum distance)for same initial conditions

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HITf/x + Hittracker Analysis:4354 HR from 2009DenverClevelandYankee Stadium

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Ex. 2: Effect of Air Density on Home Run Distance2009+2010 HR

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The Coors Effect~26 ft

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Phoenix vs. SF Phoenix +5.5 ftSF -5.5 ft

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Ex. 3:Whats the deal with the humidor?Coors Field in Denver:Pre-humidor (1995-2001): 3.20 HR/gamePost-humidor (2002-1020):2.39 HR/game25% reductionCan we account for reduction?How does elevated humidity affect ball COR and batted ball speed?How does reduced batted ball speed affect HR production?See Am J Phys, June 2011

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HR & Humidors: The MethodMeasure ball COR(RH)From 30% to 50%, COR decrease by 3.7%Measurements @ WSU (Lloyd Smith)Physics + ball-bat collision modelBatted ball speed (BBS) reduced by 2.8 mphHittracker+HITf/xWe know landing point, distance/height of nearest fenceCalculated new trajectory with reduced BBSMean HR distance reduced by 13 ftDoes ball make it over the fence?

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HR & Humidors: ResultsThe result:27.0 4.3 % calculated25% actual (!)

Side issue:If humidor employed in Phoenix, predicted reduction is 37.0 6.5 %

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Ex. 4 And what about those BBCOR bats? Starting in 2011, NCAA regulates non-wood bats using bbcor standardBBCOR=ball-bat coefficient of restitutionFor wood, 0.498For nonwood, >0.500 due to trampoline effectNew regulations: bbcor0.500

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BBCOR bats: The MethodPhysics+ball-bat collision model~5% reduction in BBSHittracker + HFXReduction in fly ball distanceReduction in HR

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60% reductionNormalized HR vs. % Reduction in BBS

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NCAA Trends in Home RunsActual Reduction ~50%:science works!

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Chart1

0.66

0.74

0.69

0.76

0.78

0.92

0.89

0.89

0.84

0.67

0.66

0.73

0.68

0.72

0.69

0.7

0.77

0.96

1.06

0.95

0.8

0.81

0.83

0.74

0.77

0.7

0.68

0.68

0.84

0.96

0.94

0.52

Runs Per Game

Division I Home Runs Per Game/Per Team

Sheet1

Runs Per Game

800.66

810.74

820.69

830.76

840.78

850.92

860.89

870.89

880.84

890.67

900.66

910.73

920.68

930.72

940.69

950.70

960.77

970.96

981.06

990.95

000.80

010.81

020.83

030.74

040.77

050.70

060.68

070.68

080.84

090.96

100.94

110.52

Additional CommentsThis technique can be used to investigate many different things such asEffect of changing the COR of the baseballEffect of moving or changing height of fencesImplications of a higher swing speed

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IV. Does Cd Vary with Ball?PFXTMPFX-TMPFX:TM0.0320.0330.023

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Data suggest some measurement-independent variation in Cd

RMS from measurement ~ 0.016RMS in common ~ 0.028

Is the common due to variations in the ball?

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Analysis:Find grand average of Cd over all pitches Identify consecutive pitches with same ballGet mean Cd for each ball i: Shift Cd for each pitch so that ball average=grand averageCompare with original distribution of CdPerform same procedure on random pitchesAnalysis uses 22k pitches3.7k involve at least three pitches with same ball1.1k different balls0.96k in 90-92 mph range

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RANDOMRawAdjusted

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Conclusions About CdThere is compelling evidence that Cd varies significantly with ballPerhaps as much as 8% RMSMeasurement variation is lessA controlled experiment is plannedIs this information useful to anyone?(e.g., Rawlings)

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In ConclusionThanks to all those who provided me with dataThanks to Rand Pendelton for lots of interesting discussionsThanks to all of you for patiently listeningAnd now that you think you understand everything, have a look at thisGarcia video removed to save space

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Outline of this section:StL 2009-2010 TM data

Outline of this section:StL 2009-2010 TM data

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