Effect of Slenderness Ratio on Free-to-Roll Wing Aerodynamics

Abstract

M ANNED fighter aircraft and unmanned combat air vehicles may require high angle-of-attack maneuvers where the roll dynamics become crucial. Small unmanned air vehicles (UAVs) and fixed-wingmicro air vehicles often have separated flows [1,2]. These small vehicles fly at relatively high angles of attack and close to the stall conditions due to the poor lift. Vertical gusts might induce roll instabilities at high angles of attack. This possibility is suggested based on the recent experiments in which rectangular, elliptical, and Zimmerman planforms exhibited self-induced roll oscillations, even before the stall angle [3,4]. Most of the knowledge on the aerodynamics of free-to-roll wings is on slender delta wings [5–7], which exhibit well understood freeto-roll oscillations about a zero mean roll angle. Free-to-roll aerodynamics of delta wings with lower sweep angles (or higher aspect ratios) have been investigated in recent experiments [8–14]. The existence of equilibrium at nonzero roll angles was reported for sweep angles 65 . The roll asymmetries are demonstrated in Fig. 1a for a simple delta wing with sweep angle of 55 (taken from [14]). The variation of themean roll angle as a function of angle of attack shows that nonzero roll angles are observed until the wing stalls. Here, we use the term “stall” to describe the onset of the flow regime for which there is no flow reattachment, and hence the roll angle becomes zero. Previouswork [12] confirms that the “stall angle of the free-to-roll wing” is near the stall angle of the fixed wing (at zero roll angle) at which the lift force is maximum. The stall of the free-to-roll wing is very sudden as the angle of attack is increased. In contrast, for a slender delta wing with sweep angle 70 , roll asymmetries mostly disappear, as shown in Fig. 1b. Contour plots in Fig. 2 are adapted from the data in [14], which show the mean roll angle and the standard deviation of roll angle in the free-to-roll experiments. The variation of the angle of attack at which the vortex breakdown appears at the trailing edge of the wing, as well as the stall angle of attack at which the lift is maximum (for zero roll angle), is added from another source [15] (shown as dashed lines). It is seen in Fig. 2a that, for wings with low sweep angles, roll asymmetries appear when the vortex breakdown is over thewing and becomes maximum near the stall angle. The magnitude of the mean roll angle decreases with increasing sweep angle and almost disappears for the most slender wing. The stall of the free-to-roll wing also becomes more gradual with increasing sweep angle. Figure 2b shows that, in a certain range of sweep angles and near the stall, self-induced roll oscillations are possible. In this Note, we extend our experiments to cropped delta wings with an initial leading-edge sweep angle of 55 , as shown in Fig. 3. We anticipate that the slenderness ratio, defined as the chord length divided by the span, may be important. It was shown [7] that if the distance from the vortex origin divided by the span is larger than two, the wing rock of aircraft configurations is likely. Similarly, this ratio may be important for the onset of the roll asymmetries for the nonslender free-to-roll wings. Table 1 lists the aspect ratio and slenderness ratio for the wings shown in Fig. 3. For comparison, we also added the simple delta wing with 70 into our study.