Why Bumblebees Can Fly

The secret of insect flight

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Abstract


We present a new explanation of the generation of lift during a wing stroke of flapping flight based on computing turbulent solutions of the Navier-Stokes equations at moderate to large Reynolds numbers. The new theory suggest a resolution of the enigma of why bumblebees can fly.


First prompted by the fact of aviation, I have applied the laws of the resistance of air to insects, and I arrived at the conclusion that their flight is impossible. (Antoine Magnan in Le Vol des Insectes)

Based on the Knols

we present an explanation of the mechanism for the generation lift in the flapping flight of insects. The Reynolds number for flapping insect flight varies from 100 for small to 10.000 for large insects. We here focus on larger insects with Reynolds number above say 1000 with skin friction small compared to lift and drag.

                                  Bumblebee, the Movie.  Listen to The Flight of the Bumblebee.

The movie shows the wing stroke of a bumblebee in hovering flight consisting of forward motion with an angle of attack of about 20 degrees followed by a twist of about 140 degrees before completing the stroke by backward motion thus keeping the same leading edge. 

Existing Theory Insufficient

Insect flight is not well understood according to state-of-the-art literature:

  • What force does an insect wing generate” has been the driving force behind much of the research described here. An innocent question, but a difficult one to answer. The difficulty is, in part, due to our lack of simple theories of unsteady fluids stirred by a moving geometry. In search for the answer, we are forced to explore solutions beyond the classical theories and develop appropriate tools. One hopes that the insight gained in studying insect flight might lead to our finding efficient ways to interact with fluids. Besides insects, birds, fish, leaves, flags, kites, sails, oars, and heart valves, all live in fluids and encounter a similar set of problems [1].
  • Understanding force generation on a flapping wing, though a difficult feat, is only a beginning of our understanding of insects or flapping flight in nature as a whole. “Why do insects or birds flap their wings the way they do? ” and “how does flapping flight come about in the course of evolution? ” For us who are bound to Earth, to fly like birds may always be a temptation. Fundamental to such an  endeavor are efficiency and stability. “Can flapping flight be more efficient and stable than a fixed-wing flight?” [1].
  • A detailed aerodynamic analysis was used to show that quasi steady aerodynamic mechanisms are inadequate to explain even fast forward flight.[2]
  • Engineers say they can prove that a bumblebee can’t fly. And if you apply the theory of fixed wing aircraft to insects, you do calculate they can’t fly. You have to use something differen. If you treat a bird wing like an airplane wing and at any given time calculate the speed and lift, then sum it up over the entire stroke, it works fairly well to explain how the bird can stay aloft. With insect flight it fails miserably Dickinson.
  • Insects use three distinct but interacting techniques to gain lift: delayed stall, rotational circulation and wake capture Dickinson.
  • We discovered that the flapping motion causes the leading edge vortex to spiral out to the wingtip, siphoning off the vortex and delaying stall. The augmented lift, coupled with the delayed stall, is the principle mechanism that insects use for generating lift…An inappropriate use of the quasi-steady assumption is certainly one way to ‘prove’ that bumblebees cannot fly.

The consensus seems to be that the clever bumblebee is able to fly by somehow exploiting some very intricate combination of vortex dynamics, which however is beyond quantitative mathematical analysis:
  • Rapid oscillations pose one of the most difficult questions for fluid dynamics. Things become very messy Z. Jane Wang.

Yes, the bumblebee can fly, but existing fluid dynamics does not seem to offer a clear explanation of why
this is possible, except hand-waving insufficient for take off.
 


New Theory

The new theory of flight presented in Why It Is Possible to Fly is captured in the following plots of the lift and circulation (left) , drag (middle) and lift/drag quotient (right) as functions of the angle of attack aoa (see larger plots ) of a Naca0012 3d wing:


We see that the lift coefficient has a peak value at 2.5 for aoa = 20 with a lift/drag = 3.

The basic mechanisms generating lift and drag of a wing for aoa < 15 can be described as follows:



We see potential flow (upper left) with zero lift/drag modified by low-pressure counter-rotating rolls of streamwise vorticity from instability mechanism at separation (upper right), switching the pressure on rear wing (lower left) to give both lift and drag (H high, L low pressure).  Computational simulation with sideway of velocity and pressure and topview of streamwise vorticitity at 14 degrees angle of attack is show lower right.

A crucial aspect of this mechanism is that it acts very quickly: The streamwise rolls and redistribution of pressure are established almost instantly when started from rest, because the rolls have small diameter and the flow is incompressible,  thus much quicker than the time of a flap which is about the time required for a fluid particle to pass from leading to trailing edge. In other words, quasi-steady flow is established during each flap and thus lift can possibly be explained by the above mechanism.
The final boost of lift for 15 < aoa < 20 also engages the the rear upper part as shown in movies of pressure and velocity of the Naca0012 wing.
With a computed maximal lift coefficient of 2.5 of a Naca0012, it seems entirely plausible that the measured lift coefficient of 0.8 for a flat a bumblebee wing [2] can be explained by the new theory. Computations are under way and will be reported shortly.

Comparing New and Old Explanation

In the new theory the same mechanism is used to explain lift and drag of airplanes, birds and larger insects in both gliding and flapping flight. 
In the existing theory based on variants of Kutta-Zhukowsky circulation theory, the time required to generate lift from rest is the same as the flap time, which means that there is not enough time for substantial lift to develop during the flap. Therefore existing theory of quasi-steady flow has shown to be incapable of explaining the generation of sufficient lift, and speculative ideas about effects of unsteady flow have been 
suggested as indicated above.
The existing theory is either insufficient, or suggests complex dynamics which has not been verified and would require very intelligent design if actually true. The new quasi-steady theory requires less intelligence and thus may be favored by bumblebees.
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