1. 1. Can a curveball be hit farther than a fastball? Some Aerodynamicsmg Fd
FL (Magnus) 
Drag: Fd = ½ CDAv2
“Lift”: FL = CMARv
(in direction leading edge is turning)
CD, CM ~
NSBP Meeting, February 18, 2005

2. Measurements of Lift and Drag Joe Hopkins, Lance Chong, Hank Kaczmarski, AMN
Motion Capture System
Two-wheel pitching machine
Baseball with reflecting dot
NSBP Meeting, February 18, 2005

3. Experiment: MoCap Datay z
y = ½ ayt2
topspinay>g
NSBP Meeting, February 18, 2005

4. Effect of Spin on Baseball Trajectory
77’
Hubbard: CL based on wind tunnel and other experimental data
Adair: Lift is “differential drag”lift is small whenever drag is not changing much with v (such as near 100 mph)
All calculations done assuming no spin-dependent drag and constant angular velocity of ball (no “spin-down”).
Lift …
scales approx. linearly with 
has major effect on trajectory
NSBP Meeting, February 18, 2005

5. Oblique Collisions: Putting Spin on the Ball
Sliding friction …
reduces transverse velocity
increases 
sliding-to-rolling transition
Results
Balls hit to left/right break toward foul line
Topspin gives tricky bounces in infield
Pop fouls behind the plate curve back toward field
Backspin keeps fly ball in air longer f
NSBP Meeting, February 18, 2005

6. Undercutting the ball  backspin
Ball100 downward
Bat 100 upward
D = center-to-center offset
trajectories
Undercut too much: popup with lots of backwpin
Undercut too little: low trajectory with little backspin
More friction does not help
NSBP Meeting, February 18, 2005

7. Fastball: spin reverses
Curveball: spin doesn’t reverse
  larger for curveball
Undercut too much: popup with lots of backwpin
Undercut too little: low trajectory with little backspin
More friction does not help
NSBP Meeting, February 18, 2005

8. In summary…. Can a curveball be hit farther than a fastball?
Higher pitch speed  higher hit ball speed on fastball
But…more backspin on curve ball
Net result: curveball goes farther
by a little bit
Mont Hubbard, AJP 71, (2003)
See also February 2005 issue of AJP for a debate: Hubbard vs. Adair
NSBP Meeting, February 18, 2005

9. Physics Description of Ball-Bat Collision
forces large (>8000 lbs!)
time is short (<1/1000 sec!)
ball compresses, stops, expands
bat compresses ball
ball bends/compresses bat
lots of energy dissipated
distortion of ball
vibrations in bat
ball-bat COR related to energy dissipation
why is aluminum better?
Courtesy of CE Composites
NSBP Meeting, February 18, 2005

10. NSBP Meeting, February 18, 2005

11. Wood versus Aluminum Aluminum has thin shell Less mass in barrel
easier to swing and control 
but less effective at transferring energy 
Hoop modes
trampoline effect
larger COR 
This summarizes the important properties of bats
NSBP Meeting, February 18, 2005

12. The “Trampoline” Effect: A Simple Physical Picture
Two springs mutually compress each other
KE  PE  KE
PE shared between “ball spring” and “bat spring”
PE in ball mostly dissipated (~80%!)
PE in bat mostly restored
Net effect: less overall energy dissipated
...and therefore higher ball-bat COR
…more “bounce”
Ask question:
Which give more “power”: tighter strings or looser strings on tennis racket?
Then ask (if they get it wrong): can a person bounce higher from a hardwood floor or from a trampoline?
NSBP Meeting, February 18, 2005

13. “Trampoline” Effect tennis ball/racket strings Softball/bat
DEMO:
DEAD BALL ON FLOOR, bongo paddle
SUPERBALL ON FLOOR,bongo paddle
The issue: springiness of surface. Bat compresses ball, ball compresses bat--same size force--which one gives depends on how easily compressed.
NCAA: e<.228
Wood bat, for given force, compresses 2% of ball. Or…only 2% of energy in collision is stored in bat, rest is in ball. Makes no difference how much of energy stored in bat is returned
Al bat: 10% in COR==>7 mph==>35’ or more
Just like tennis racket....looser strings gives a higher ball speed!
All sorts of tricks.....thinner wall..etc. More later.
new rule changes in NCAA: e<.228
Better bat: a tennis racket
Better ball: spherical metallic shell
NSBP Meeting, February 18, 2005

14. Experimental Modal Analysis
Impact hammer (force transducer)
35 points along length
Accelerometer
fixed location
on barrel
FFT Analyzer
Frequency
Response
Function
(accel / force)
Dan Russell, Kettering U.
NSBP Meeting, February 18, 2005

15. Hoop Modes of Hollow Bats
Lowest hoop mode…
--that annoying “ping”
--“trampoline effect”
NSBP Meeting, February 18, 2005

16. COR correlated with fhoop
Energy left in hoop vibrations...
Wood bat
~30’ on long fly ball
Each .01 of COR1.6/1.25 in vf, or 1.3 mph6’ on fly ball
Courtesy of Dan Russell
NSBP Meeting, February 18, 2005

17. Summary: Why Does Aluminum Outperform Wood?
Trampoline effect reduces energy dissipation
More pop
Longer fly ball
NSBP Meeting, February 18, 2005

18. Final Summary
Physics of baseball is a fun application of basic (and not-so-basic) physics
Check out my web site if you want to know more
Go Red Sox!
NSBP Meeting, February 18, 2005