How Bumps on Whale Flippers Delay Stall: An Aerodynamic Model

Wind tunnel experiments have shown that bumps on the leading edge of model humpback whale flippers cause them to “stall” (i.e., lose lift dramatically) more gradually and at a higher angle of attack. Here we develop an aerodynamic model which explains the observed increase in stall angle. The model predicts that as the amplitude of the bumps is increased, the lift curve flattens out, leading to potentially desirable control properties. We find that stall delay is insensitive to the wavelength of the bumps, in accordance with experimental observations.

Figure 1

(a) Humpback whale lunging for food; note the bumps on the leading edge of the pectoral fins. Photograph by Brett Atkins, obtained from www.dreamstime.com. Sketch of the flipper geometry: (b) the planform from above; (c) cross section of a bump and trough of amplitude $\eta$.

Figure 2

(a) Calculated pressure profiles on top of a typical bump and trough and (b) calculated pressure distribution on the top of a bumpy wing. Note the pressure minimum in the troughs near the leading edge. Here, $\alpha =6°$, $\eta =0.1$.

Figure 3

(a) Local stall angle on a wing section calculated as a function of thickness to chord ratio, showing a monotonic decrease. (b) Percentage of wing area in stall for: (dashed line) uniform downwash terms, i.e., including ${\alpha }_{0,0}^e$ and ${\alpha }_{0,1}^e$ in (6) only and neglecting the influence of the bumps in the downwash; (solid line) full downwash including all ${\alpha }_{i,j}^e$ and thus the influence of the bumps ($\eta =0.1$, $s=3.6\mathrm{m}$, $k=36$).

Figure 4

Lift curves from (a) our model and (b) Johari et al. [4]. The black solid lines correspond to the unperturbed wing; the other solid lines correspond to 8 bumps per wing, while open symbols denote 4 bumps. Amplitudes are color coded: red $\eta =0.025$; green $\eta =0.05$; blue $\eta =0.12$. In both (a) and (b), planform sketches are included for $\eta =0$, 0.025, 0.05 and 0.12.