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Leading-Edge Vortex Improves Lift in Slow-Flying Bats

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Science  29 Feb 2008:
Vol. 319, Issue 5867, pp. 1250-1253
DOI: 10.1126/science.1153019

Abstract

Staying aloft when hovering and flying slowly is demanding. According to quasi–steady-state aerodynamic theory, slow-flying vertebrates should not be able to generate enough lift to remain aloft. Therefore, unsteady aerodynamic mechanisms to enhance lift production have been proposed. Using digital particle image velocimetry, we showed that a small nectar-feeding bat is able to increase lift by as much as 40% using attached leading-edge vortices (LEVs) during slow forward flight, resulting in a maximum lift coefficient of 4.8. The airflow passing over the LEV reattaches behind the LEV smoothly to the wing, despite the exceptionally large local angles of attack and wing camber. Our results show that the use of unsteady aerodynamic mechanisms in flapping flight is not limited to insects but is also used by larger and heavier animals.

Generating enough lift during hovering and slow forward flight is problematic according to traditional quasi–steady-state wing theory (1, 2). Yet several species of small flying vertebrates are adapted to foraging using this flight mode. Insects are able to hover by using a range of possible unsteady high-lift mechanisms, including rotational circulation (3), clap-and-fling (4, 5), wake capture (3, 6), and added mass (7, 8). However, arguably the most important mechanism is a leading-edge vortex (LEV) (5, 912), which may generate up to two-thirds of the total lift in insect flight (13, 14). Although unsteady lift mechanisms have been studied extensively in insects or scaled models of their flapping wings (5, 6, 1117), vertebrates have only been studied indirectly. Such measurements derived from kinematics or wakes suggest that some birds (18) and bats (19) require additional lift for weight support, other than quasi–steady-state lift alone (2). A recent study of hovering hummingbirds found traces of previously shed LEVs in their wakes (20), and sharp-edged model wings of gliding swifts with high sweep (60°) developed stable LEVs (21).

We quantitatively measured the airflow, using digital particle image velocimetry (DPIV), around the wings of three individuals of Pallas' long-tongued bat, Glossophaga soricina (table S1), flying freely in front of a feeder in a low-turbulence wind tunnel at a forward flight speed U = 1 m/s (22). At this flight speed, the average local Reynolds number of the bat wing is Re ≈ 5 × 103 (23) and the Strouhal number St ≈ 1.36 (24).

The DPIV image plane was orientated vertically in the freestream flow direction, and measurements were made at different span-wise locations along the wing, when the wing was positioned horizontally. At this wing position, the wing does not block the DPIV image, the wingspan is at its maximum, and the wing is two-thirds into the downstroke (22). Cross-stream DPIV measurements were also performed closely behind the bats (a distance of ∼3 mean wing chord lengths at U = 1.35 m/s). From the DPIV data, we determined the two in-plane velocity components of the airflow, resulting in a planar velocity field. Spatial gradients of this planar velocity field also yield the divergence, which is a measure of the variation in out-of-plane velocity (25), and the vorticity, which is a measure of the local angular velocity.

From the streamwise DPIV data, the wing profile and its motion (Fig. 1, A to D) were also determined by tracking the part of the wing profile illuminated by the laser sheet (22). The velocity of the wing profile was used as a no-slip boundary condition in the DPIV calculations (22). The average wing camber is 18 ± 3% (mean ± SD, n = 68 observations) of the wing chord (fig. S5D), and the average effective angle of attack is 51° ± 19° (n = 68 observations) (fig. S5F) (22). Both are high values for steady-state wing theory: A fixed wing at similar Re with such high camber and angle of attack would stall and lose lift (26).

Fig. 1.

Velocity and vorticity fields around a bat wing in slow forward flight (1 m/s), when the wing is positioned horizontally in the downstroke. The vectors show the disturbance caused by the wing with the uniform mean flow (of 1 m/s) removed. (A to C) show streamwise measurements at different positions along the span. The span locations are 33, 50, and 65% of the semi-wingspan for (A), (B), and (C), respectively, as indicated on the bat silhouettes to the left. The flight direction is from right to left. Instantaneous two-dimensional streamlines of part of (C) are shown in (D). In (A) to (D), The bat wing and its shadow in the DPIV laser sheet are visible; the local wing profile and its relative motion are shown with a red curve and arrows. (E) Data derived from cross-stream measurements, with the position of the bat indicated by the bat silhouette. The vorticity field is scaled according to the color bar; it ranges from –1750 to +1750 s–1, for (A) to (D) and from –700 to +700 s–1 for (E). The velocity vectors are scaled to the reference vector at the left of the color bar for (A) to (D) and at left of (E). Space scale bars are located at left of (A) for (A) to (C), at left of (D), and at left of (E).

The vorticity field and velocity vectors around the bat wing (Fig. 1) show that the flow separates at the leading edge, generating a patch of high negative vorticity (clockwise spin). But, remarkably, behind this patch of vorticity the airflow reattaches, resulting in attached and laminar flow at the trailing edge. The vorticity patch at the leading edge of the wing was present at all measured span-wise locations but was stronger near the wingtip (Fig. 1C) than toward the wing root (Fig. 1A). Instantaneous streamlines computed from the measured streamwise flow (Fig. 1D) form a recirculating region at the vorticity patch, which also spirals inward at the core. All these facts are consistent with the presence of an attached LEV (10). In the neighborhood of the LEV, the divergence of the flow in the image plane is on average positive (source flow) (25) and small compared to the vorticity magnitude (fig. S4). Both sign and magnitude differ from theoretical expectations for LEV stabilization (10), which could imply that no LEV stabilizing mechanism is needed (27).

In some of the images (mainly distally on the wing), an area of high negative vorticity is also found near the trailing edge but without recirculation (Fig. 1D). The presence of negative vorticity near the trailing edge is associated with the outer wing making a strong rotational (pitch-up) movement before the end of the downstroke (Fig. 1D). Therefore this patch of high vorticity could be a result of rotational circulation (3), which is an alternative aerodynamic mechanism for enhanced lift generation.

To investigate the contribution of the LEV to the total lift, the circulation of the LEV was determined at different span locations (Fig. 2). The average chord length and average effective wing velocity ( = 0.042 m and Ūeff = 4.0 m/s) were used to nondimensionalize the circulation (Γ/Ūeff) (22). The results show that the LEV circulation increases toward the wingtip (Fig. 2), which is consistent with LEV structures found for some insects (1). When assuming that a LEV enhances lift by adding its own circulation to the bound circulation of a wing (1), the nondimensional circulation of the LEV is related to its associated lift coefficient by CLEV ≈ 2 · ΓLEV/Ūeff (22, 28). The average nondimensional LEV circulation is about 1 (Fig. 3), which corresponds to a CLEV ≈ 2.

Fig. 2.

Circulation ΓLEV (top) and ΓTEV (bottom) at different wing positions for three bats. The circulation was nondimensionalized using and Ūeff of the measured points (fig. S5). Diamonds represent bat 1, squares represent bat 2, and triangles represent bat 3.

Fig. 3.

Mean ± SD for circulations in different parts of the wake structure during the downstroke when the wing is horizontal, at a forward speed of 1 m/s. The circulation was nondimensionalized using and Ūeff (fig. S5). For the LEV and TEV, n = 119 observations; for the tip and root vortex, n = 98 observations (22).

During the downstroke of a flapping wing, positive vorticity is generated at the trailing edge and is shed into the wake. This vorticity can be generated throughout the downstroke, and we will label it trailing-edge vorticity (TEV). According to Kelvin's theorem (29), the circulation of the TEV (ΓTEV) is related to the bound circulation on the wing and thus to the total lift coefficient by CL ≈ 2 · ΓTEV/Ūeff (22). The shed TEV is clearly visible in Fig. 1, A to C, as a distinct patch of positive vorticity (counterclockwise spin) to the right of the wing, called the start vortex, and a trail of positive vorticity between this start vortex and the trailing edge. Because the tip of the wing travels a larger distance during the downstroke than does the wing root, the start vortex is located further behind the wing near the wingtip (Fig. 1C) than near the wing root (Fig. 1A). This pattern of vorticity shedding is strikingly similar to that of a hawkmoth (30). ΓTEV was determined at different span locations (Fig. 2), but no systematic variation was found. The average nondimensional ΓTEV is 2.4 (Fig. 3), for an effective lift coefficient of 4.8 (22), which is beyond that considered to be the maximum possible for quasi–steady-state wings (2) at the same Re and aspect ratio (26), but is similar to results from previous studies of bats (19) and within the possible range of pitching and heaving plates (31).

As mentioned above, the nondimensional ΓLEV ≈ 1, which means that the LEV contributes to more than 40% of the total lift (ΓLEV/ΓTEV = 0.42) (22). This value is similar to LEV contributions reported for insects [hawkmoth, up to 65% (13, 14), and fruit fly ≈ 45% (3)] but is considerably higher than the 15% estimated from the wake of hovering hummingbirds (20). The TEV minus the LEV nondimensional circulation is 1.4, resulting in a non-LEV lift coefficient of 2.8 (22). This value is also higher than conventional quasi–steady-state wing models at similar conditions (26), suggesting that other unsteady lift mechanisms may also be involved, such as rotational circulation (3) and delayed stall (15), resulting in high lift due to a high angle of attack.

To obtain an image of the three-dimensional wake structure, near-wake cross-stream DPIV measurements were performed for two bats (Fig. 1E). The vorticity field and velocity vectors show the presence of a tip vortex with negative vorticity (clockwise spin) and a weaker vortex near the wing root (root vortex) with positive vorticity (counterclockwise spin). The average tip- and root-vortex circulation were nondimensionalized using the mean wing chord length (c) and the average effective wing velocity (Ūeff) determined from kinematic measurements (22). The average tip-vortex circulation has a similar strength as ΓTEV, and the average ΓLEV is 65% of the root-vortex circulation (Fig. 3).

Based on the qualitative and quantitative data, we suggest a cartoon model of the vortex system around the bat wing during the downstroke (Fig. 4). At the beginning of the downstroke, a start vortex is formed at the trailing edge of the wing. During the downstroke, this vortex travels downward and backward because of self-convection, creating a trail of vorticity between the start vortex and the trailing edge of the wing. In inviscid vortex dynamics, a line vortex must terminate either as a closed loop or at a solid surface, and so the start vortex connects to two tip and two root vortices, which grow in length during the downstroke. The tip and root vortices are connected to the wing and to the LEV. The start vortices of each wing are probably connected to each other behind the body (19). Because the LEV circulation strength is similar to the root-vortex circulation, these are probably connected, hence the absence of a LEV across the body. The near wake of slow-flying bats did not show a separately shed LEV (19), suggesting that the LEV stays attached throughout the downstroke and merges with the stop vortex.

Fig. 4.

Cartoon of the primary vortex structure for a bat during the downstroke when the wing is horizontal, at a forward speed of 1 m/s. The structure consists of two closed loops, one for each wing, consisting of a LEV on top of the wing, connected to a start vortex shed in the wake via a tip vortex (Tip) and a root vortex (Root). The color coding indicates the absolute value of local circulation; yellow is low circulation and red is high circulation.

For hovering and slow-flying insects, three different types of LEV systems have been proposed (14): a helical-shaped LEV starting at the inner wing, increasing in size along the wingspan, and finally connecting to the tip vortex (9, 27); a cylindrical-shaped LEV that expands across the thorax and is connected to the two tip vortices (6, 14); and a LEV that is connected to a small root vortex and a large tip vortex (5). The vortex system proposed here (Fig. 4) is most similar to the latter case.

The sharp leading edge of the bat wing probably facilitates the generation of the LEV (21), whereas the ability to actively change the wing shape and camber (32) could contribute to the control and stability of the LEV.

LEVs have now been observed in active unrestricted bat flight, with a strength that is important to the overall aerodynamics. Unsteady aerodynamic mechanisms for enhanced lift are therefore not unique to insect flight, and larger animals adapted for slow and hovering flight, such as these nectar-feeding bats, can (and perhaps must) use LEVs to enhance flight performance.

Supporting Online Material

www.sciencemag.org/cgi/content/full/319/5867/1250/DC1

Materials and Methods

Figs. S1 to S5

Table S1

References and Notes

References and Notes

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