Introduction forces on a spinning baseball in flight
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F M. F d. mg. Introduction: Forces on a Spinning Baseball in Flight. gravity: “physics 101” drag: “wind resistance” lift: Magnus force on spinning baseball. F M. F d. mg. Introduction: Forces on a Spinning Baseball in Flight. drag is opposite to direction of motion

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Introduction: Forces on a Spinning Baseball in Flight

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FM

Fd

mg

Introduction:Forces on a Spinning Baseball in Flight

  • gravity: “physics 101”

  • drag: “wind resistance”

  • lift: Magnus force on spinning baseball


FM

Fd

mg

Introduction:Forces on a Spinning Baseball in Flight

  • drag is opposite to direction of motion

  • “lift” is in direction that leading edge is turning


Effect of Drag and Lift on Trajectories

  • drag effect is huge

  • lift effect is smaller but significant


Some Effects of Drag

  • Reduced distance on fly ball

  • Reduction of pitched ball speed by ~10%

  • Asymmetric trajectory:

    • Total Distance  1.7 x distance at apex

  • Optimum home run angle ~350


Some Effects of Lift

  • Backspin makes ball rise

    • “hop” of fastball

    • undercut balls: increased distance, reduced optimum angle of home run

  • Topspin makes ball drop

    • “12-6” curveball

    • topped balls nose-dive

  • Breaking pitches due to spin

    • Cutters, sliders, etc.


Some Effects of Lift

Balls hit to left/right curve toward foul pole


Some Effects of Lift

Tricky popups with lots of backspin


Let’s Get Quantitative:Measurements of Drag and Lift

  • What do we know?

  • How do we know it?

  • How well do we know it?

  • Two types of experiments:

    • Wind tunnel

      • Measure forces directly

    • Video tracking of trajectory

      • “You can observe a lot by watching”

      • Infer forces from measured acceleration


Motion Capture System

ATEC 2-wheel pitching machine

Baseball with reflecting dot

Experiment #1: Tracking Trajectory(UC/Davis; Illinois)


~15 ft

Joe Hopkins

Motion Capture Geometry


  • Motion Capture System:

  • 10 cameras

  • 700 frames/sec

  • 1/2000 shutter

  • very fancy software

  • www.motionanalysis.com

  • Pitching Machine:

  • project horizontally

  • 50-110 mph

  • 1500-4500 rpm


Typical Data


Results for Lift Coefficient CL

Conclusion: data qualitatively consistent (~20%)

FL= 1/2ACLv2

S=r/v

100 mph, 2000 rpm

S=0.17


Results for Drag Coefficient CD

FD= 1/2ACDv2

Conclusion:

Major disagreements for v= 70-100 mph


Experiment #2: Sportvision—A Potential New Tool

  • Track pitched baseballs with 2 cameras

    • High-speed not necessary

    • Tracking of MLB game pitches

    • Used by ESPN for K-Zone

  • From trajectory, determine

    • lift,drag,spin axis

  • Spin rate not measured

Thanks to Marv White, CTO, for providing a wealth of data


Sportvision Data

batter’s view

225o

Backspin:

up and in to RHH


Sportvision Data

batter’s view

135o

Backspin:

up and away to RHH


Sportvision Data

game pitches

warmup


Synthesis of Results


Synthesis of Results

Uncertainty in drag  50 ft!


Summary

  • We have much empirical knowledge of lift and drag

    • …and some promising new tools for future research

  • Things we would like to know better:

    • Better data on drag

      • “drag crisis”

      • Spin-dependent drag?

      • Drag for v>100 mph

    • Dependence of drag/lift on seam orientation?

    • Is the spin constant?


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