MECHANICS OF FORMATION FLIGHT -- PETER LISSAMAN
Here are some actual facts, which folks may wish to use for discussion on
tother 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 Newtons Laws!.
1. A lifting wing develops one half its induced wash AHEAD of it. Yeah, folks,
before the air has even met the wing. Its 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 Cs 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 its 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 its 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. Its my idea of reality --
not talking, and not (God forbid!) computer simulation its 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
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