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

Using Munk’s (3) Equivalence Theorem, Prandtl's Theory can be extended to a staggered wing arrangement. Munk’s Equivalence Theorem states that ‘given a constant lift distribution, the total induced drag of any multiplane system is unaltered if any of the lifting elements is moved in the direction of motion. However, by staggering the wings, the induced flow between the wings changes. The forward wing experiences an upwash while the aft wing is subjected to a downwash. This results in the decrease of the lift-curve slope of the aft wing relative to the fore wing when the airfoil sections and angles of attack (assuming no fuselage is present) are equal (5). Consequently, one of the major challenges of developing the Box-Wing aircraft is the difficulty in optimizing the design to obtain equal lifts on the wings. Combining the Prandtl Best Wing System and the Munk Equivalence Theorem, Frediani (5) posits that Prandtl’s (4) ‘Best Wing System’, if applied to conventional aircraft configuration, could reduce induced drag by up to 20-30% based on a h/b ratio of 10-15%. Frediani (5) further established that for a Box- Wing or ‘Prandtl Plane’, the aerodynamic efficiency obtained is strongly linked to the ease of creating a stable aircraft with equal lift distribution on the wings. Additionally, Frediani (5) determined that induced drag accounts for approximately 43% of the total aircraft drag during cruise flight in still air. Thus, a decrease in induced drag provides design benefits such as reduced aircraft weight and thrust requirements. This would ultimately minimize the negative impact on the environment. These findings led to widespread interest in the Box Wing Aircraft. III. A irfoil I ssues According to Wolkovitch (1), airfoils used in the vicinity of Box-Wing aircraft inter-wing joints must consider the induced flow curvature. Consequently, the use of natural laminar flow airfoils was recommended (1). Subsequently, Addoms (4) corroborated this finding by proposing that biplane configurations must employ airfoils with remarkably different camber than those of a monoplane. This is because using monoplane airfoils on biplanes induces premature separation, leading to a low maximum lift coefficient. Wolkovitch (1) thus advocates reduce the unsupported column length of the aft wing, thereby decreasing drag and structural weight. Frediani (5) corroborated Wolkovitch views on the use of twin fins for Joined/Box-Wing aircraft when he disclosed that the aerodynamic channel created by the top of the rear fuselage, aft wing under-surface and the twin tail enhance the aerodynamic efficiency of the concept. These discoveries influenced Bernardini and Frediani (5) to design a Joined/Box-Wing configuration to harness the aerodynamic benefits of Frediani’s (5) aft-wing/twin fin design. IV. A erodynamic C oncepts and C onsiderations Bagwill and Selberg (7) advanced that positively staggered Joined-Wing aircraft are more aerodynamically efficient than negatively staggered joined wings. Positive stagger refers to an arrangement where the higher wing is placed in front of a lower aft wing, while negatively staggering refers to the reverse configuration. Mamla and Galinski (8) agree with Bagwill and Selberg (7) on the superior aerodynamic efficiency of positively staggered joined wing aircraft over negative stagger. However, Smith and Jemitola (8) highlighted the beneficial influence of a maximized vertical separation between the fore and aft-wings on a negatively staggered joined wing arrangement. For a medium-range airliner, Smith and Jemitola’s (8) study showed that the negatively staggered arrangement benefits from the use of the tail fin to maximize the wing’s vertical separation. In contrast, positively staggered arrangement provides comparable aerodynamic benefit but with significant mass penalties and directional stability issues. Global Journal of Researches in Engineering (A ) Volume XxXII Issue I Version I 31 Year 2022 © 2022 Global Journals An Analysis of Aerodynamic Design Issues of Box Wing Aircraft for the design of tailor-made airfoils by exploiting the advanced state of current airfoil design technology. In a similar vein, Wolkovitch (1) revealed that because the effective depth of a beam, d, of a Joined/Box-Wing is primarily determined by the chord of its airfoils, as sketched in Figure 5, their thickness is a significantly less important consideration. This finding justified the adoption of thin airfoils for Joined/Box- Wings aircraft design. Wolkovitch (1) thus concluded that twin fins of approximately 60 degrees dihedral