Global Journal of Researches in Engineering, A: Mechanical & Mechanics, Volume 22 Issue 1

linking the tips of the fore and aft wings together in what is appropriately called a Box-Wing aircraft. II. B ox W ing T heory Prandtl’s (3) ‘Best Wing System’ states that a closed rectangular lifting system produces the least possible induced drag for a given span and height. In making this assertion, Prandtl (3) established that all biplanes have less induced drag than their equivalent monoplane with equal spans. The study further highlighted that biplane drag decreases as the wing gap increases (4). Accordingly, Prandtl (4) posits that the ideal arrangement for minimum induced drag is a closed biplane with equal lift distribution and total lift on each wing. In this arrangement, the top of the end-plates is exposed to outward pressure while the bottom parts experience inward pressure. Figure 3 shows a front view schematic of 2 lifting surfaces with equal spans joined at the tips thus positioning the ideal pressure distribution on the endplates. As the gap between the wings increases, trailing edge vortices are reduced, thus lowering induced drag (5). The lower induced drag makes the Box Wing configuration an attractive proposition for reducing the environmental impact of aviation. This is because induced drag accounts for a significant portion of the total drag count of a commercial flight. Hence, reduced induced drag lowers fuel burn and minimizes pollutants emission leading to reduced environmental impact. Figure 4 depicts the effect of wing gaps on induced drag of a biplane as provided by Prandtl (3). In the plot, the horizontal axis represents the wing gaps while the vertical axis represents the induced drag. The Plot illustrates the inverse proportional relationship between the induced drag and wing-gap. This implies that the lower the wing gap, the higher the reduction in induced drag. For example, for a wing-gap/span (h/b) of 0.25, the induced drag is about 71% of an equivalent monoplane with the same aspect ratio while a wing gap/span (h/b) of 0.15 gives an induced drag reduction of almost 80% (78%). Consequently, a closed biplane arrangement produces the greatest reduction in induced drag. However, this aerodynamic benefit is relative as there is an attendant increase in wing mass increase and practicability of the design. Figure 4: Effect of Wing Gap on Induced Drag Reduction An Analysis of Aerodynamic Design Issues of Box Wing Aircraft © 2022 Global Journals Global Journal of Researches in Engineering (A ) Volume XxXII Issue I Version I 30 Year 2022 Lift Distribution on a Biplane Figure 3: