Parametric Analysis of Trapezoidal Segmentation for Wing Planform Efficiency

This paper introduces a refined criterion for evaluating and optimizing the aerodynamic efficiency of compound planform wings, specifically those whose half span is formed by multiple trapezoidal segments. While elliptical lift distribution is known to minimize induced drag, practical manufacturing constraints have led to widespread adoption of tapered wings. However, conventional single-trapezoid planforms deviate significantly from the ideal elliptical distribution, resulting in increased induced drag and reduced fuel efficiency. This study proposes an adjustment to the ellipticity factor, enabling quantitative assessment of how well a multi-trapezoid wing approximates elliptical chord distribution. The methodology is validated through analysis of existing transport aircraft, identifying configurations with ellipticity factors below 5% (e.g., Lockheed C-5A, Antonov An-124) that achieve near-optimal induced drag performance. A comparative case study of a virtual 40-ton aircraft with a 100 m2 wing area quantifies trade-offs between three planform configurations. Computational fluid dynamics simulations confirm that increasing trapezoidal segmentation improves spanwise loading and delays flow separation. Results demonstrate that two-trapezoid configurations with total inverse taper ratios of 3.3–4.2 and break coordinates at 35–45% half span achieve ellipticity factors under 7%, offering an optimal balance between aerodynamic efficiency, structural feasibility, and tail surface requirements. The proposed criterion provides aircraft designers with a rapid, computationally efficient tool for planform optimization at the conceptual design stage. The proposed criterion is valid for subsonic cruise conditions (M ≤ 0.85) and does not account for wave drag or aeroelastic effects.