# Clever Humpback Whale

The leading edge of the flippers of a humpback whale is serrated with series of bumps called tubercles. We learn from The Influence of Passive, Leading Edge Turbercles on Wing Performance, by P. Watts and F. E. Fish that the tubercles can serve to decrease drag and even increase lift compared with a smooth leading edge without bumps:

*Tubercles on the leading edges of humpback whale flippers enhance maneuverability during prey capture. Tubercles may therefore be functional adaptations. By extension, leading edge modifications of streamlined bodies apparently offer cost-effective performance enhancements, including a passive means of increasing vehicle maneuverability.**We compare lift and drag forces for a wing with leading edge tubercles versus the same wing without tubercles at a 10 ̊ angle of attack. We find a 4.8% increase in lift, a 10.9% reduction in induced drag, and a 17.6% increase in lift to drag ratio.**Tubercles may also extend the operational envelope of a control surface by delaying the onset and severity of stall.*

# 3d Rotational Separation

Let us seek an explanation of the drag reduction effect of the tubercles in our New Theory of Flight.

We recall the separation pattern at a rounded trailing edge displayed in the following picture showing the flow around a circular cylinder:

We see an unsymmetric flow from left to right with attachment at high pressure and separation at alternating high/low pressure with tubes of of streamwise vorticity attaching to the cylinder at low pressure zones centered around points of stagnation. The separation pattern develops from the basic instability of potential flow with separation simply the reverse of attachment, which results from meeting opposing flows. We describe the separation pattern as **3d rotational separation **to be compared with **2d irrotational attachment. **

## 3d Rotational Attachment

3d Rotational Separation represents a quasi-stable quasi-stationary flow, which formally can be reflected into **3d Rotational Attachment** by formally reversing the direction of the flow. However, this flow no longer represents a quasi-stable quasi-stationary flow since it does not arise from opposing flows as 3d Rotational Separation does, but rather connects to diverging flow in approach to the leading edge.

3d Rotational Attachment thus represents a flow pattern which cannot be generated at a conventional leading edge without tubercles. However, with tubercles it is conceivable that attachment may occur under an alternating high/low pressure in some form of 3d Rotational Attachment, instead of 2d Irrotational Attachment under uniform high pressure. It is thus conceivable that the tubercles can have a drag reducing effect. Computational simulations to test this hypothesis are under way and will be reported. Experiments indicate that the effect is real.

## Summary

We have the combinations of different forms of attachment and separation:

- 2d Irrotational Attach + 2d Irrotational Sep = Potential Flow = zero lift/drag
- 2d Irrotattional Attach + 3d Rotational Sep without Bumps = non-zero lift/drag
- 3d Rotational Attach + 3d Rotational Sep with Bumps = reduced drag
- 3d Rotational Attach + 2d Irrotational = unstable unphysical.

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I was wondering if there is some ratio of tubercle to chord ratio?