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Tactics and Vectors 98/99 |
Flight stability of gliding monarch butterflies. (adapted from dplex-l)
In a post to dplex-l on October 7, 1997 (reprinted in part below), Michael Lastufka asked how gliding monarch butterflies achieve lateral stability. From Michael Lastufka, dplex-l, October 7, 1997: A question for Dr. Gibo that others may be interested in: But first a note on a phrase Dr. Gibo used - I believe the "center of lift" you mentioned in your previous message - "center of lift during gliding flight for Monarchs is located about where the abdomen joins the thorax" is really the horizontal center of pressure for the whole butterfly - is it not? I mention this to qualify my question: For a glider (made of balsa or paper, for example) using the flat-plate lift effect, the main wing lift (technically the component of main wing pressure drag perpendicular to the air stream at the main wing's center of pressure) causes a nose-down pitch since the center of mass is typically in front of it. This must be offset by a tail-down pitch which can be achieved by: (1) a stabilizer set at a negative incidence angle to the angle of glide (perhaps the aft wings of the Monarch do this by the way they articulate on the distal side of the fore wings), or (2) by the mere pressure drag of the aft portion of the glider, providing the center of pressure of that part is back far enough (it is already above the center of mass since the aft wings are above the body - though in updrafts the center of pressure is probably raised by increasing the dihedral angle of all the wings). Do you know which means, or one not mentioned, the monarch uses to stabilize its glide or perhaps it is resourceful and uses both depending on the dynamics of the wind? (You mentioned it can change its center of mass by ballasting with water - not a transient means of stability, but one for the long haul!). Do you have other rule-of-thumb or statistical aero-measurements you can share with us similar to "center of lift during gliding flight for Monarchs is located about where the abdomen joins the thorax"? Michael Lastufka has asked a very interesting question - How does a gliding monarch butterfly achieve stability along its horizontal axis, the axis running through the center of mass and parallel to the wings. In other words, how do gliding butterflies prevent themselves from pitching down into a dive? I have always assumed that his first suggestion, a negative angle of incidence of the hind wings, was the primary mechanism. After all, this is the method of choice for aircraft designers. I also thought that Michael Lastufka's second suggestion was likely. The drag on the trailing edge of the hind wings and the abdomen could offset the tendency of the butterfly to pitch down. Because the wings are set higher on the body than the center of mass and this difference is increased during gliding by holding the wings at about 15 degrees of dihedral. With this in mind, I confidently got my two main references on insect flight, Insect Flight, edited by G. Goldsworthy and C. Wheller (1989, CRC Press), and The Evolution of Insect Flight by A. K. Brodsky (1994, Oxford Press). The only section on gliding in butterflies in Insect Fight was in the introductory chapter by W. Nachigall. Near the end of a good discussion about gliding flight in general, I came across the following sentences about airflow across the wings of gliding butterflies: "However, the airflow around gliding Lepidoptera is complex." [snipped a sentence about measurements of the airflow in a gliding swallowtail and a gliding cabbage butterfly] "However, the functional significance of this complicated flow system is not known." That was the end of the section on gliding flight. Not a word on pitch stability. The Evolution of Insect Flight was much more informative. I learned that, unlike the machines I'm use to, gliding butterflies are not satisfied with just a single pair of counter-rotating wingtip vortices. In addition to the normal pair or vortices at the wingtips, gliding butterflies have a second, inboard (my term) pair located along the trailing edge of the hindwings at about 30% of the distance from the body to the wingtip. Furthermore, the inboard vortex of each wing rotates in the opposite direction of corresponding wingtip vortex. How does this relate to stability? In gliding swallowtails, the tails on the hindwings are directly in the path of the inboard vortices and the little twist in each tail matches the direction of rotation of the corresponding vortex. Brodsky suggested that the tails serve as 'catchers' that increase the butterfly's stability (presumably stability in pitch) during gliding. Another difference among the two sets of vortices is the direction that they trail off from the wing. The wingtip vortices are not deflected downward. They flow backwards nearly in line with the oncoming air. In contrast, the inboard vortices flow backwards and downwards, in line with the air deflected downward by the wings. Brodsky assumes from the vortex pattern that the drag from that wingtip vortices is a considerable component of the total drag. He states that by lifting the wings in a small dihedral angle, the drag from wingtip vortices is reduced and roll stability is increased. Furthermore, because the problematic pitching down force caused by the center of pressure being located behind the center of mass, it seems reasonable that with a modest angle of dihedral, the backward drag of the wingtip vortices, combined with the backward and downward drag of the inboard vortices, would result in a sufficient offsetting pitching up force. Although tails on the hindwings help, they are not necessary for this system to work. There's more. Brodsky goes on to explain that butterflies without tails often have a rough surface on their lower wing surface. This roughness has been shown to slow down air flow and increase the overall lift for the same angle of attack, allowing faster glides at shallower angles of attack. However, this surface roughness also generates a lift component opposite to that of the upper wing. If the roughness is distributed such that the hind margin of the wing has a net downward force when gliding, this would be equivalent to having the hind wings set at a negative angle of incidence (which could be true anyway). At one point during an entomology lab on Wednesday, I had a moment to briefly examine the lower wing surface of preserved specimens of a mourning cloak, a red admiral and a monarch. No obvious negative angle of incidence was seen, but none would be expected on pinned specimens that had been mounted and dried on pinning boards. Both the mourning cloak and red admiral clearly had rougher surfaces on the undersides of their wings than on the top. the difference was due to coarser scales and more hairs. This condition extended to the rear margin of the hind wings. There was much less difference between the under surface and the top surface of the monarch. The wing veins were more prominent on the underside and there appeared to be more hairs but there was no obvious difference in the scales. Was this modest difference enough to generate a significant downward lift vector in area of the rear wing margin? I wish I knew. So my answer to Michael Lastufka's question is - I don't know. But there sure are a lot of interesting possibilities. Someone will probably have to do some more measurements with wind tunnels. Does anyone else have more information? |