PBCOR Only Measure Swingweight

PBCOR Only Measure Swingweight

Written by: Brian Laposa

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Time to read 1 min

Expanded Analysis of the PPL Spin Rate Methodology with Physical Proofs

1. Environmental Conditioning

Error: Limited environmental range (72°F ±2°F, 50% RH ±10%) fails to account for real-world variations.

Physical Basis:

  • Ideal Gas Law: Ball pressure varies with temperature:
    Pinternal = (nRT) / V
    Temperature changes alter ball stiffness, affecting contact time (tc) and spin generation.
  • Coefficient of Restitution (COR):
    e = vrebound / vimpact
    COR decreases with lower temperatures due to reduced polymer elasticity in paddles/balls.
  • Friction Dependence: Relative humidity (RH) modulates surface adhesion via:
    μ = μ0 + khumid ⋅ RH
    where μ0 is dry friction and khumid is material-specific.

2. Ball Preparation & Marking

Error: Sharpie-based markers introduce tracking inaccuracies.

Physical Basis:

  • Angular Velocity Calculation:
    ω = Δθ / Δt = (θframen+1 - θframen) / (tframen+1 - tframen)
    Marker edge detection errors (Δθ) propagate as:
    δω = Δθ / Δt
    A 1-pixel error in marker position at 10,000 fps introduces δω ≈ 50 rad/s error.

3. Paddle Clamping & Angle

Error: Fixed clamping vs. dynamic hand-held use.

Physical Basis:

  • Impulse-Momentum Theorem:
    ∫ Fhand dt = Δppaddle
    Clamping eliminates hand-force variability, altering dwell time (tc) and spin torque:
    τ = r × Ffriction = Iball ⋅ α
    Fixed angles constrain the moment arm (r), favoring paddles with anisotropic surface textures.

4. Cannon Velocity Control

Error: ±1 mph (0.45 m/s) velocity tolerance.

Physical Basis:

  • Kinetic Energy Transfer:
    ΔKE = ½mball(vimpact2 - vrebound2)
    A 1 mph velocity change alters KE by 5.1% (for 40 mph baseline), directly affecting spin energy:
    Espin = ½Iballω2

5. Ball Rotation & Quadrant Impacts

Error: Non-uniform ball wear across quadrants.

Physical Basis:

  • Moment of Inertia Variations:
    Ieff = Inominal + ΔIwear

6. Laser Alignment

Error: Parallax and beam divergence (θdiv).

Physical Basis:

  • Geometric Error Propagation:
    Δx = 2 ⋅ tan(0.1°) ≈ 3.5 mm

7. High-Speed Camera System

Error: Four-point method calibration inaccuracies.

Physical Basis:

  • Perspective Projection Error:
    θmeasured = θtrue + k1θtrue3 + k2θtrue5

8. Limited Sample Size

Error: n=6 tests per paddle.

Statistical Basis:

  • Confidence Interval Width:
    CI = μ ± tα/2 ⋅ (σ / √n)

Key Achievements

  • Standardizes impact energy via vimpact = 40 mph
  • Controls paddle orientation (θincident = 20° ± 1°)
  • Provides repeatable ωspin measurements under lab conditions

Critical Limitations

  • Non-Holonomic Constraints
  • Inadequate Error Budgeting
  • Neglected Tribology

Conclusion

While the methodology provides a first-order comparison framework...

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