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Equations & Assumptions Reference

Drag Coefficient (Physics-Based)

Cd=2mg(dvacuum−dactual)ρAdactualv02C_d = \frac{2 m g (d_{vacuum} - d_{actual})}{\rho A d_{actual} v_0^2}

This formula estimates the drag coefficient using physical constants and compares the actual distance a ball traveled to the distance it would have traveled in a vacuum (no air resistance).

Variables:
  • C_d: Drag coefficient (dimensionless)
  • m: Mass of baseball (kg)
  • g: Acceleration due to gravity (9.8 m/s²)
  • d_{vacuum}: Calculated distance in a vacuum (meters)
  • d_{actual}: Actual hit distance (meters)
  • ho: Air density (kg/m³)
  • A: Cross-sectional area of baseball (m²)
  • v_0: Initial velocity (m/s)
Assumptions & Limitations:
  • No wind or environmental effects
  • Ball is a perfect sphere
  • Only air resistance is considered
  • Data quality filters applied (e.g., plausible values for all variables)
Used In: ETL drag coefficient calculation, Drag vs HR chart, Physics lesson: 'Air Resistance'
Related Lessons:

Vacuum Distance Formula

dvacuum=v02sin⁡(2θ)gd_{vacuum} = \frac{v_0^2 \sin(2\theta)}{g}

This formula calculates the distance a ball would travel in a vacuum (no air resistance), based on its initial velocity and launch angle.

Variables:
  • d_{vacuum}: Distance in a vacuum (meters)
  • v_0: Initial velocity (m/s)
  • heta: Launch angle (radians)
  • g: Acceleration due to gravity (9.8 m/s²)
Assumptions & Limitations:
  • No air resistance
  • No wind or environmental effects
  • Ball is a point mass
  • Flat ground, no spin effects
Used In: Drag coefficient calculation, Physics lesson: 'Projectile Motion'
Related Lessons: