Delivered Lie Angle: Why Toe-Up and Toe-Down Tilt the Face Normal
A 3D spatial geometry investigation into Delivered Lie Angle: how toe-up or toe-down orientation dynamically rotates the face normal vector and why higher lofts magnify directional error.
equipment · 6 min · EXACT_GEOMETRY
Delivered lie and face orientation
Delivered lie is the club's lie orientation at impact. In this model a lie rotation changes the three-dimensional face normal. Its effect depends on dynamic loft, face angle, handedness, and the rotation convention; it cannot be summarized by one universal miss direction or linear coefficient.
For a right-handed club at zero face angle, the implementation rotates the lofted normal around the forward axis before normalizing it. With toe-up lie deviation $\Delta_{\text{lie}}>0$ and loft $\delta$, the effective horizontal face azimuth in the lab frame is:
$\Delta\phi_{\text{face}} = -\arctan(\sin(\Delta_{\text{lie}})\tan\delta)$
For small lie deviations this is approximately $-\Delta_{\text{lie}}\tan\delta$ in radians. The sign reverses for toe-down and changes with handedness. This formula describes the app's orientation transform at zero base face angle; it is not a universal rule for the ball's final start or curve.
Use the sandbox carefully
The uneven-lie controls combine terrain, setup, and delivery assumptions. A real player's adaptation varies. The simulation can illustrate how a changed face normal affects the modeled launch, but it cannot claim an unavoidable pull, push, draw, or fade from slope alone. No empirical slope-to-face coefficient is asserted here.