Swing Direction vs. Club Path: The Inclined Plane Effect
Shows how attack angle and vertical swing-plane angle constrain the impact tangent for an ideal circular swing plane.
geometry · 7 min · EXACT_GEOMETRY
Two related directions
Swing direction describes the horizontal orientation of the swing arc at its reference point. Club path is the horizontal component of clubhead velocity at impact. They coincide at a level-attack reference point and can differ elsewhere on an inclined plane.
Use the lab frame: $+X$ right of target, $+Y$ downrange, $+Z$ up. Horizontal angles are measured from $+Y$ toward $+X$. With attack angle $\gamma$, path $\theta_{\text{path}}$, and swing direction $\theta_{\text{dir}}$, the idealized club direction is:
$\hat v = [\cos\gamma\sin\theta_{\text{path}}, \cos\gamma\cos\theta_{\text{path}}, \sin\gamma]$
For a planar circle with elevation $\beta$, the plane-normal constraint yields:
$\sin(\theta_{\text{path}}-\theta_{\text{dir}}) = -h\tan\gamma\cot\beta$
Near zero, the principal-branch small-angle approximation is $\Delta\theta_{\text{path}} \approx -h\gamma\cot\beta$ in radians. A tangent relation is also only an approximation and should not be labeled exact.
What the app computes
Couple AoA-to-Path uses the forward branch of the fixed-plane tangent constraint:
$\theta_{\text{path}} = \theta_{\text{dir}} - h\arcsin(\tan\gamma/\tan\beta)$
Here $h=+1$ for right-handed and $h=-1$ for left-handed delivery under this app's sign convention. The solution exists only when $|\tan\gamma/\tan\beta|\le1$. This is conditional ideal geometry: real delivery need not follow one fixed circular plane. When path and AoA are authored independently, the display keeps that tangent and reports its angular mismatch with the selected plane.
The app's low-point readout is the signed horizontal projection of the circle minimum along the swing-direction axis, relative to the ball. For an ideal circle of radius $R$ and plane elevation $\beta$, $d=-R\sin\gamma/\sin\beta$. This is not presented as a vendor-defined TrackMan low-point distance. Club radius, AoA and plane angle all matter. The stance hold control keeps the point's stance coordinate fixed; changing ball position then changes AoA to preserve it.
Swing direction and club path are measurements with their own vendor conventions. This article describes a conditional model relation, not a fitting prescription.