Parameters
Pitch preset
km/h
rpm
Β°
m
Results
β
Elapsed time (s)
β
Current pitch speed (km/h)
β
Magnus force (N)
β
Vertical break (Magnus) (cm)
β
Horizontal break (cm)
β
Time to plate (s)
Trajectory
Actual trajectory (Magnus effect)
No-spin ghost (gravity only)
Magnus force vector
Spin axis
Theory & Key Formulas
The animation plays the flight at near-real-time speed. The graph below numerically shows displacement from release to home plate; blue is the actual trajectory, gray is the no-spin ghost trajectory (without Magnus force), and their difference is the break.
Theory & Key Formulas
$$\vec{F}_{Magnus} = \tfrac{1}{2}\,\rho\,C_L\,A\,|\vec{v}|^2\,\hat{n},\qquad A=\pi r^2$$ \(\rho\): air density (1.225 kg/mΒ³), \(C_L\): lift coefficient, \(A\): cross-sectional area, \(\hat{n}\): direction of deflection
The lift coefficient \(C_L\) depends on the spin factor \(S = r\omega / v\) (surface speed/pitch speed). This tool models it as \(C_L = 0.1 + 0.4\,\min(S,0.5)\) (for a baseball, \(C_L \approx 0.1\sim0.3\)).
$$F_{magY}=F_{Magnus}\sin\theta,\quad F_{magX}=F_{Magnus}\cos\theta$$ Spin-axis angle \(\theta\): at 90Β°, vertical break is maximized (lift from backspin / drop from topspin); at 0Β°, horizontal break is maximized.
$$F_{drag} = \tfrac{1}{2}\,\rho\,C_D\,A\,v^2\quad(C_D\approx 0.35)$$ The seams produce a higher drag coefficient than that of a smooth sphere. Air resistance reduces the ball's speed during flight.