Semi-Analytical Closed-Wing Weight Estimation during Conceptual Design

Abstract

One of the novel configurations that could revolutionize the aviation industry is the PrandtlPlane. The closed-wing design features a low front wing and a high rear wing, connected by a lateral surface. In this research, the rear wings of the configuration are attached to a set of fins. Previous conceptual closed-wing design studies have failed to accurately predict the wing weight of the configuration, by using empirical relations or semi-analytical methods designed for conventional wings. These methods fail to capture the three major structural characteristics of a closed-wing design: an over-constrained structure, significant secondary bending moments and shear forces, and a different lay-out of the constraints definition. Therefore, a semi-analytical closed-wing weight estimator was developed. The primary weight is estimated analytically, while the secondary weights are defined by empirical relations. The primary structure is sized using an equivalent beam method, which is designed to withstand the aerodynamic, inertial and fuel loads applied to the structure. The aerodynamic loads are estimated with a vortex lattice method, at a 2.5g pull-up manoeuvre. For the PrandtlPlane configuration, the fin is modelled as a support to the rear wing. Due to the over-constrained nature of the structure, a stiffness iteration loop is implemented in which the internal loads are determined using the displacement method and all cross-sections are sized. The cross-sectional design features four booms, which are cross-coupled and four skins, which are sized independently. A total weight estimation of a closed-wing design takes 20-30 seconds. Sensitivity analyses are performed to establish the main drivers of the total wing weight and its distribution. Wingspan, wing sweep angle, fin sweep angle and longitudinal center of gravity position were determined to have the most influence on the total wing weight and its distribution. The new tool was implemented in the conceptual design workflow of the Initiator. A comparison between a design study in the Initiator with the closed-wing weight estimator and the previous methodology showed large discrepancies. Three design studies were performed with missions varying in payload weight, number of passengers and range. The total offset in the wing weight between the two methods ranged from 4.5\% to 30.4\%, leading to discrepancies in the required fuel mass of 1.6% and 5.7% respectively. Apart from the large offsets in total wing weight, the previous methodology also failed to accurately predict the distribution of the weight between the front, rear and lateral wing. Furthermore, the offsets between the methodologies are case-dependent and no clear relationship between them can be distinguished. Future conceptual design studies should thus include a closed-wing weight estimator. Finally, a parametric study was performed to identify the effect of altering the wing area ratio between the front and rear wing on the required fuel mass. For a single aisle, medium range mission, a design with and area ratio of 1.25 is 2\% more fuel efficient compared to a design with an even area distribution between the front and rear wing.