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Rotational lift: something different or more of the same?

Jeffrey A. Walker

Department of Biology, University of Southern Maine, 96 Falmouth St, Portland, ME 04103, USA

View larger version (18K): [in a new window]   Fig. 1. Cross section of an airfoil illustrating geometry of the principal model parameters. (A) The arrows indicate that the wing is translating to the left due to root-flapping and rotating about the point r due to active supination or pronation. Point i is the location of the incident flow, which is illustrated in (B). The subscript (r) has been removed from r, i and c for clarity. (B) The relevant flow velocity components due to root-flapping and wing rotation and their resultant, (r,t). Also illustrated are the wing pitch, , the geometric attack angle, g, and the angle of incidence, ', acting at the point i in (A).

View larger version (17K): [in a new window]   Fig. 2. Comparison of (A) drag and (B) lift across one stroke cycle for physical wing model 1 (PM1). The red line indicates the unsteady blade-element (USBE) model, the green line indicates the quasisteady model with the Magnus force included, and the blue line indicates the measured forces on the physical wing model.

View larger version (19K): [in a new window]   Fig. 3. Comparisons of lift across one stroke cycle for the (A) rotation-advance case (PM2) and (B) rotation-delayed case (PM3). The red line indicates the unsteady blade-element (USBE) model, the green line indicates the USBE model with the Magnus force included, and the blue line indicates the measured forces on the physical wing model.

View larger version (16K): [in a new window]   Fig. 4. Comparisons of (A) drag coefficient (CD) and (B) lift coefficient (CL) across one stroke cycle for virtual wing models VM1 and VM2. The unsteady blade-element (USBE) model results are shown with solid lines, while the computational fluid dynamic (CFD) model results are shown with broken lines. The low-magnitude, translational-acceleration case (VM1) is shown in blue. The high-magnitude, translational-acceleration case (VM2) is shown in red.

View larger version (21K): [in a new window]   Fig. 5. Decomposition of the unsteady blade-element (USBE) model (red line) of VM2 into circulatory (green) and added mass (blue) components. CL, lift coefficient.

View larger version (19K): [in a new window]   Fig. 6. Comparisons of (A) drag coefficient (CD) and (B) lift coefficient (CL) across one stroke cycle for VM1, VM3 and VM4. The unsteady blade-element (USBE) model results are shown with solid lines, while the computational fluid dynamic (CFD) model results are shown with broken lines. The rotation-advanced case (VM1) is shown in red, the symmetric case (VM3) is shown in blue, and the rotation-delayed case (VM4) is shown in green.

View larger version (18K): [in a new window]   Fig. 7. Comparisons of lift for cases (A) PM2 and (B) PM3 estimated by the unsteady blade-element (USBE) model (red line) and a quasi-steady model that separately estimates a translational circulatory force and a rotational circulatory force using rotational coefficients (green line). The measured forces (blue line) are shown for comparison.