Scientific Sources, Vector Formulations, and Methodology
A transparent technical exposition of the scientific literature, 3D Cartesian vector formulations, and Runge-Kutta aerodynamic trajectory integration behind D-Plane Lab.
science · 8 min · EXACT_GEOMETRY
Source records and claim scope
The bibliography contains academic, vendor, engineering, coaching, and framework references. A citation record gives provenance; it does not by itself show that a particular claim was checked in the original source. The source page lists the four public TrackMan definitions reviewed on 2026-10-18 with a precise scope and boundary for each.
Those checks support vendor definitions for spin loft, smash factor, carry/curve/side/total, and the reference locations used in club-data parameters. They do not validate the app's empirical launch weights, gear-effect coefficients, aerodynamic coefficients, or carry predictions. No calibration against a launch-monitor dataset is claimed.
Coordinate frame used by the model
The lab uses a right-handed frame with $+X$ to the right of target, $+Y$ down the target line, and $+Z$ upward. Horizontal angles are measured from $+Y$ toward $+X$. At attack angle $\gamma$ and club-path angle $\theta_{\text{path}}$, the unit club velocity is:
$\hat v_{\text{club}} = [\cos\gamma\sin\theta_{\text{path}}, \cos\gamma\cos\theta_{\text{path}}, \sin\gamma]$
With face angle $\phi$ and dynamic loft $\delta$, the no-lie-tilt face normal is:
$\hat n_{\text{face}} = [\cos\delta\sin\phi, \cos\delta\cos\phi, \sin\delta]$
The implementation normalizes the face vector and applies delivered-lie rotation about the forward axis with a handedness-dependent sign. This is a model convention; it is not the claim that a real clubface is fully described by a single center-face orientation at every impact location.
For a centered strike, the D-Plane normal is computed from the cross product of the club velocity and impact-point face normal. Off-center gear-effect response is an explicitly approximate extension.
Flight model and limits
Flight integrates gravity, drag, and a Magnus term using the ball's fixed world-space spin vector and air-relative velocity. The direction follows the normalized cross product of spin and relative-air velocity; a spin component parallel to the airflow contributes no Magnus force. Coefficient functions remain educational assumptions and have not been empirically calibrated here.
Golden Fixtures test deterministic identities, geometry, and regression cases. They are not independent experimental measurements and do not establish strict parity with radar data. FX-02's research JSON and expected values are disputed and are not an acceptance target; see the current clarification in docs/DOMAIN_MODEL.md.