Inputs
SI units
Key results
| Flight time | 2.205 s |
|---|---|
| Horizontal distance when grounded (x) | 39.18 m |
| Apex height | 4.61 m |
| Impact speed at final point | 0.00 m/s |
| Lateral curl at goal plane (y @ x = 25.0 m) | 4.84 m (right) |
| Height at goal plane (z) | 4.56 m |
| Within goal frame at plane | No |
Side view — height vs distance (x–z)
Top view — curl vs distance (x–y)
How this model works
- Drag: Force = ½ ρ A Cd v² opposing motion. A = πR².
- Lift (Magnus): CL ≈ k · R|ω|/v. Direction follows ω × v. Backspin (negative rpm here) produces upward lift.
- Integration: Semi‑implicit Euler with small time step for stability.
- Goal test: Checks ball position at x = goal distance against 7.32 m width and 2.44 m height.
Real balls show speed dependent Cd and complex seam effects; tune parameters to match match footage or ball lab data.
FAQs
Sidespin is rotation about the vertical axis and curves the ball left or right. Backspin or topspin is rotation about a lateral axis and mainly changes the vertical lift or dip.
Magnus lift scales with the dimensionless spin parameter R|ω|/v. At the same rpm a faster ball has smaller spin parameter and relatively less lift, and vice versa.
For a modern match ball, Cd is often 0.20–0.35 in the relevant speed range. A reasonable k is 0.6–1.2. Use video measurements to tune for your ball.
It assumes still air and smooth coefficients. Knuckleballs arise from unsteady separation and panel seams, which are beyond this simplified steady‑state model.
Either the elevation angle is too low or drag and downward topspin are too high. Increase angle or speed, reduce Cd, or use more backspin for lift.
Positive lateral deflection is to the right when facing the goal. With a right‑footed out‑swinger, a positive sidespin rpm curves to the right in this convention.