In connections with the comments about FORMATION FLIGHT
FORMATION FLIGHT by PETER LISSAMAN The formation flight of birds has long been of interest to natural scientists. Leonardo da Vinci discussed this in 1504, as did Lord Rayleigh in 1889. The Vee formation produces significant energy saving. There is no debate about this. It has been established unequivocally theoretically, measured in flight tests with aircraft, and also, indirectly, in the remotely monitored pulse rate of formations of our feathered friends, actually Brown Pelicans. The mathematics is complicated. It relates to the flows induced by the vortex wake behind a lifting wing. Outboard of the wing a large upwash is induced, proportional to the circulation on the wing, and the wing man (bird?), if he tucks up tight on the tip, is flying in a strong upwash, with big drag savings. Thats all there is to it! But, Ah, the Details! As Leonardo said "God is in the Details"! It would be boring to go into those mathematics, except to say that the procedure is considered well-understood and correct, but a helluva mess! The birdies jus' do it, and could care less! The first paper I know of that treated the topic mathematically (and brilliantly) was Wieselsberger in ZFM, 1914; and there has been a fairly lively activity since then, as computers have removed the formidable and intelligent math required, and made it possible for anyone to get results without understanding them. In 1969 Carl Shollenberger, my valued friend and colleague, and I worked on this, and published the results in Science. The paper (Lissaman & Shollenberger, Formation Flight of Birds, Science, Vol. 168, 1970) shows the very large size of these savings. We used the impressive new IBM 360 computer at Caltech. It occupied a three storey building about the size of a four unit apartment block, and had mens and womens toilets inside, as well as 12 real people who punched cards, fed data and generally dealt with the I/O. One picked up outputs at about 3:00 am each night. My wife never really believed that was what kept me up, although I did my thesis on mathematics of wing theory some years before using that old 360! And used the same story! Computation is clumsy, but more than Doktor Wieselsberger ever had! Carl was killed a few years later, flying in night mountain turbulence over the Sierra Madres. It was a great loss to aviation he was a fine pilot and aerodynamicist. I acknowledge his contribution fondly. He would be glad that his work was still used. Recently I revisited this subject in a paper Simplified Analytical methods for Formation Flight (Lissaman, AIAA. Jan. 2005) and next week will give a paper Neutral Energy Cycles for a Vehicle in Sinusoidal and Turbulent Vertical Gusts (Lissaman & Patel, AIAA. Jan 2007) The Science paper shows that in theVee, for tight formations, one can almost double the range for a given energy input. Also that there is a stability mechanism, by which a member finds that moving ahead of the line of the Vee requires power increases. So theres a comfortable groove to fall into, which animals love! One should always be skeptical of attributing effects derived from theoretical calculations to animal behavior, but the general consensus of ornithologists and aerodynamicists is that this Vee formation saving is so significant, and its application so ubiquitous, that migrating birds DO use it to extend their range. The paper addressed the savings for different positions in the Vee. In line abreast, the center birds experience twice the saving of the tip members, but if the tip members find this hard work and fall back to take advantage of the increased favorable downstream upwash of the vortex wakes of the inner members, then a balancing of savings occurs. We calculated the angle of the Vee for equipartition. It is about the same as is observed with migrating birds. We also showed that it was not necessary have equal legs of the Vee. Provided there are at least about 6 birds on one side of the Vee, the other leg can be almost as long as the birds choose to make it. Interestingly, for a linear Vee, the wing at the apex of the Vee has the maximum saving. In 1971 I was in communication with ornithologists in Florida, who noted that their observations validated our Vee estimates and indicated that the apex position was usually taken by the older and more powerful birds. They wondered why the more powerful members of the flight should take the easiest jobs! My answer was that most intelligent species are pretty anthropomorphic! It may be noted that the savings are not related to drafting, that is following behind a draggy object to take advantage of its lower dynamic pressure wake. I am very familiar with this, and, as an automobile aerodynamicist, have utilized this theory in race car design, and as is obvious, the slingshot maneuver is very significant. But not in flight! It is, in fact, horrible to fly directly astern of another flight vehicle, as every pilot knows. Folks can, and do, get killed tangling with wake vortices, as I know to my sadness, when an old friend and experienced Navy pilot died as a consequence of following too close on final. Peter Lissaman, Da Vinci Ventures Expertise is not knowing everything, but knowing what to look for. 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 TEL: (505) 983-7728 FAX: (505) 983-1694
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