My thanks as well for the clear and educational presentation. If I understand correctly (which I very well may not be), then essentially all the birds, including the one at the front reach an equipartition of power output, although it sounds like possibly there is maximal drag reductions in the front three positions at the apex (depending how closely abreast the two following the leader are), and the least for the birds at the back of the vee. Getting to one of the front three positions would require a short term high power output burst by a trailing bird, which might explain why the weakest ones end up in the worst positions, since the strongest ones are able to make the short term bursts required to get into the best positions.
In any event, your notes certainly require me to rethink some things, but I should clarify that my own discussions have been about the underlying principle of energy savings among coupled agents which allows for the emergence of complex dynamics among the system as a whole. Being a "forest for the trees" exercise, the details of the aerodynamics affect my analysis only to a small extent, although it certainly helps that I understand them. I also realize now I need to be careful about using the term "drafting" when types of energy savings dynamics other than drafting may be happening. Perhaps it is more accurate to refer to the principle as "energy savings by coupling". Regardless, there are still universal complex dynamics that occur - for example, if there is a rotation dynamic within a vee formation, then that is a dynamic shared among rotating penguin huddles and rotating bicycle pelotons. In any event, thanks again for the very useful and helpful outline. Hugh Trenchard ----- Original Message ----- From: Peter Lissaman To: [email protected] Sent: Sunday, January 07, 2007 4:59 PM Subject: [FRIAM] Mechanics of Formation Flight MECHANICS OF FORMATION FLIGHT -- PETER LISSAMAN Here are some actual facts, which folks may wish to use for discussion - on t'other hand maybe they just prefer their own opinions! Doesn't matter to anyone who just wants to ramble on a fascinating subject. I am designing flight systems to use turbulent energy, in test flight right now, so, unfortunately, gotta stick to Newton's Laws!. 1. A lifting wing develops one half its induced wash AHEAD of it. Yeah, folks, before the air has even met the wing. It's a continuous fluid, remember! The balance of the induced wash due to the trailing system develops downstream of the wing and is reaches its asymptotic value about 3 spans downstream. Within the span of the wing this induced flow is downwash, more or less spanwise uniform; outboard it is upwards, very intense just beyond the tip and attenuating rapidly as one moves away from the wing. 2. If another wing system is positioned outboard of the wing, it experiences a strong upwash, that will greatly reduce its power requirements. This effect is mutual, and its integrated intensity depends only on the tip separation as a fraction of span. 3. Consider three identical wings, line abreast, call them Left (L) Center (C) and Right (R). In this configuration the wing R experience a favorable upwash due to C and L, but the L contribution is fairly small. So it has a certain saving in its induced drag. But the wing C experiences the full upwash effect from both L, R and consequentially C has approximately double the saving. Good news for C! 4. If the wings L, R get pissed off at all that hard work, and drift downstream, they will experience stronger upwash due to the trailing system of C, but their influence on C will be attenuated, so they will experience larger savings at the expense of C. If they drift very far downstream, then they will have no influence on C, but L, R will still experience the induced flows of C so that ALL the saving will now be transferred to R , L. In the vernacular, C doesn't even know the wingmen are there, far astern, but they can see C's fully developed wake lying right between them! There is a configuration providing equipartition which defines the Vee angle of this little "Vic". 4. This mechanism continues for flights with larger numbers of wings. The calculations indicate, as so often in aerodynamics, that infinity is not far away, and reached very soon, so that large flights are advantageous but with diminishing returns. 5. The stability mechanism (we have the math, but it's too much for here) is that if a formation were in echelon (a single skewed line) then the front bird would have a hard time, and he'd drift downstream. His wingman would then be leading and think, "Jesus, I'm in front now! No way". And he'd drift downstream. This would proceed until you had about three or four birds in one file of the Vee. By that time the current lead bird would be experiencing maximum favorable induction from both sides, and would be quite comfortable and equipartition would have been achieved. 6. Steady winds have no effect on formation flight, of course. Chap called Galileo Galilei (1564-1642) had some wise words on that topic, almost a century after Leonardo had made some nearly right hypotheses re flight. But wind variation due to shear layers or turbulence due to these shear layers can always be exploited. Albatrosses use the marine shear layers to fly thousands of Km across the southern oceans with flapping a wing. This dynamic soaring has recently been validated in manned flight with a two place L-23 Super Blanik in a recent (May, 2006) USAF project out of Dryden. Energy extraction from random turbulence is also attractive, but requires wings with rapid sensing and response systems. The Santa Fe ravens are pretty good at riding the gusts of the Sangres, but it's hard for machines to operate at this time scale. A Ph.D. student of mine is investigating this with a 2 m R/C IMU instrumented computer controlled flight model at Stanford. He and I are giving a paper on this at the Annual AIAA meeting in Reno this week. It's my idea of reality -- not talking, and not (God forbid!) computer simulation - it's a real airplane flying in a real atmosphere. 7. Flight speeds, size and other physical aspects of the wing system have no effect on the benefits of formation flight, but the savings are reflected only in the induced drag term. 8. There is no favorable drafting effect in any flight system. Drafting is always bad news for the draftee and has no effect on the lead vehicle. Anyone who has flown under tow, or seen movies of glider towing, will know that you have to stay high above your tow plane to get away from that bloody wake. Brown Pelicans are often observed flying line astern on fishing forays, but one sees each bird stays well above the preceding one. 9. All the above mechanisms apply to gliding, powered or ornithopter flight, and to the first order, the savings are independent of the propulsion system. 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 ------------------------------------------------------------------------------ ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
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