Non-Monotonic Effective Drag in Finned Spherical Projectiles: Evidence from Range-Based Inversion

Abstract

We validate an inverse-drag estimation pipeline for finned spherical projectiles and, within this experimental regime, detect a robust non-monotonic effective-drag anomaly near L≈1.00. The pipeline pairs a custom fourth-order Runge–Kutta trajectory simulator with a monotonicity-based bisection inverse solver, bootstrap uncertainty quantification (n=5,000) that jointly propagates launch-speed uncertainty, and a leave-one-out isotonic-regression null model. A synthetic Monte Carlo study (n=1,000 trials) established reliability: the method recovers known k_eff values with a median absolute error of 9.1%, and the anomalous ordering is preserved in every trial, confirming the inversion reflects signal rather than a noise artefact. Applied to a spring-launched 250 g steel sphere with triangular fins across nine length-to-diameter ratios (L ∈ {0.00, …, 2.00}), the pipeline revealed a pronounced dip near L=1.00, where k_eff fell from 0.02888 to 0.01274 kg m⁻¹ - a 55.9% reduction (p<0.0002) that persisted under launch-speed and drag-law perturbations. The anomaly was detectable only through inversion, not through a simpler velocity-decay summary metric, a dissociation explained by range integrating a brief mid-flight drag reduction that the global average smooths out. The effect is consistent with wake-modification or splitter-plate-like behaviour, but the present evidence is indirect; direct flow diagnostics or CFD validation is identified as the primary next step.

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