1. Nathan, Summit20101 Studies of Batted Ball Trajectories I.Analyzing the FFX trajectories II.Determining landing point/hang time from HFX III.Combining HFX and Hittracker IV.Do drag coefficients vary with ball? Alan M. Nathan University of Illinois

2. Nathan, Summit20102 I. Analyzing FFX Trajectories WWAD = What Would Alan Do? Actually, what DID Alan do? –Scottsdale, March 2009 experiment –10 Cameras uses 2 PFX/HFX cameras 8 IP cameras –*All* data used to analyze trajectories PFX+HFX+FFX

3. Nathan, Summit20103 Analyzing FFX Trajectories Track pitch—9P PFX Track initial batted ball—6P HFX –Get intersection of batted ball and pitched ball trajectories to establish contact time Track batted ball using FFX cameras –Do constant acceleration fit to first 0.5 sec of FFX data –Key step: Velocity vector fixed at HFX value –Look for intersection with HFX trajectory to synchronize IP and HFX clocks Now fit the synchronized FFX and HFX data to using your favorite model

4. Nathan, Summit20104 Analyzing FFX Trajectories Modeling the batted ball trajectories –Piecewise (~0.5 sec) constant acceleration –Constant jerk (12P) might work –Nonlinear model with drag, Magnus, wind, … will work best –Possible compromises 9P*or 10P* models: Initial position and velocity vectors (6) plus constant C d (1) and spin vector (2 or 3)

5. Nathan, Summit20105 Examples Using 9P* and 12P 12P = constant jerk –Initial positions, velocities, accelerations –Rate of change of acceleration (jerk) 9P* = aerodynamic model –Initial positions, velocities –Constant drag coefficient –Backspin and sidespin Both models utilize nonlinear L-M fitting applied to pixels directly

6. Nathan, Summit20106 Line Drive Fly Ball V 0 =96 mph  0 =16 deg

7. Nathan, Summit20107 Fly Ball Line Drive Topspin Line Drive V 0 =106 mph  0 =6 deg

8. Nathan, Summit20108 Fly Ball Line Drive Incomplete Long Fly Ball V 0 =104 mph  0 =23 deg

9. Nathan, Summit20109 Fly Ball Line Drive V 0 =99 mph  0 =7 deg

10. Nathan, Summit201010 Fly Ball Bad Fit V 0 =101 mph  0 =6 deg

11. Nathan, Summit201011 Some Remarks 12P and 9P* work equally welI –Sometimes bad fits –Probably bad fits due to bad data, not bad model –12P provides handy way to parametrize the trajectory The Arizona data came from an initial experiment. Quite possibly the current setup in SF provides higher quality data I recommend further studies of this type Side note: the FFX data can be used to “correct” the HFX data, which systematically underestimates v 0 and  0

12. Nathan, Summit201012 II. Determining landing point/hang time from HFX Utilize ball tracking data from 2009, 2010 –2900 batted balls 2367 batted balls with VLA>0 –Initial velocity (BBS, VLA, Spray angle) –Location when z=0 and hang time (extrapolated) –Not a “theoretical” analysis; based entirely on data

13. Nathan, Summit201013 Total Distance 65 75 85 95 105

14. Nathan, Summit201014 Fit vs Data Distance RMS=25 ft Hang Time RMS=0.4 sec “Bearing” RMS=8 deg

15. Nathan, Summit201015 Summary Distance: RMS=25 ft Hang Time:RMS=0.4 sec Bearing: 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)?

16. Nathan, Summit201016 III. Combining HFX with Hittracker HITf/x  (v 0, ,  ) Hittracker  (x f,y f,z f,T) Together  full trajectory –HFX+HTT determine unique C d,  b,  s –Full trajectory numerically computed (9P*) T   b horizontal distance and T  C d sideways deflection   s Analysis for >8k HR in 2009-10

17. Nathan, Summit201017 How well does this work? Test experimentally using radar tracking device Tracking Data from Dedicated Experiment For this example it works amazingly well! A more systematic study is in progress

18. Nathan, Summit201018 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 (379,20,5.2)

19. Nathan, Summit201019 HITf/x + Hittracker Analysis: 4354 HR from 2009 Denver ClevelandYankee Stadium

20. Nathan, Summit201020 Ex. 2: Effect of Air Density on Home Run Distance Denver Phoenix SF 2009+2010 HR

21. Nathan, Summit201021 The Coors Effect ~26 ft

22. Nathan, Summit201022 Phoenix vs. SF Phoenix +5.5 ft SF -5.5 ft

23. Nathan, Summit201023 Ex. 3:What’s the deal with the humidor? Coors Field in Denver: –Pre-humidor (1995-2001): 3.20 HR/game –Post-humidor (2002-1020):2.39 HR/game –25% reduction Can 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

24. Nathan, Summit201024 HR & Humidors: The Method Measure ball COR(RH) –From 30% to 50%, COR decrease by 3.7% –Measurements @ WSU (Lloyd Smith) Physics + ball-bat collision model –Batted ball speed (BBS) reduced by 2.8 mph Hittracker+HITf/x –We know landing point, distance/height of nearest fence –Calculated new trajectory with reduced BBS Mean HR distance reduced by 13 ft –Does ball make it over the fence?

25. Nathan, Summit201025 HR & Humidors: Results The result: 27.0  4.3 % calculated 25% actual (!) Side issue: –If humidor employed in Phoenix, predicted reduction is 37.0  6.5 %

26. Nathan, Summit201026 Ex. 4 And what about those BBCOR bats? Starting in 2011, NCAA regulates non- wood bats using “bbcor” standard –BBCOR=ball-bat coefficient of restitution –For wood,  0.498 –For nonwood, >0.500 due to trampoline effect –New regulations: bbcor  0.500

27. Nathan, Summit201027 BBCOR bats: The Method Physics+ball-bat collision model –~5% reduction in BBS Hittracker + HFX –Reduction in fly ball distance –Reduction in HR

28. Nathan, Summit201028 60% reduction Normalized HR vs. % Reduction in BBS

29. Nathan, Summit201029 NCAA Trends in Home Runs Actual Reduction ~50%: science works!

30. Nathan, Summit201030 This technique can be used to investigate many different things such as… –Effect of changing the COR of the baseball –Effect of moving or changing height of fences –Implications of a higher swing speed Additional Comments

31. Nathan, Summit201031 IV. Does C d Vary with Ball? PFXTM PFX-TM PFX:TM 0.032 0.033 0.023

32. Nathan, Summit201032 Data suggest some measurement- independent variation in C d –RMS from measurement ~ 0.016 –RMS in common ~ 0.028 Is the “common” due to variations in the ball?

33. Nathan, Summit201033 Analysis: –Find grand average of C d over all pitches –Identify consecutive pitches with same ball Get mean C d for each ball i: Shift C d for each pitch so that “ball average”=“grand average” Compare with original distribution of C d –Perform same procedure on random pitches –Analysis uses 22k pitches 3.7k involve at least three pitches with same ball 1.1k different balls 0.96k in 90-92 mph range

34. Nathan, Summit201034 RANDOM Raw Adjusted

35. Nathan, Summit201035 Conclusions About C d There is compelling evidence that C d varies significantly with ball –Perhaps as much as 8% RMS Measurement variation is less A controlled experiment is planned Is this information useful to anyone? (e.g., Rawlings)

36. Nathan, Summit201036 Thanks to all those who provided me with data Thanks to Rand Pendelton for lots of interesting discussions Thanks to all of you for patiently listening And now that you think you understand everything, have a look at this –Garcia video removed to save space In Conclusion…