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ous mu This is a multi-part message in MIME format. ------=_NextPart_000_13E3_01D03819.89501890 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Hi Steve & All, Jan 24, = 2015 Haldane was just putting the gullible reader on because angels, = being spirits, would be weightless (or massless if you wish) so the = wings would be used variously for ornament, supporting harps, modesty or = maneuvering but not for lift.=20 But as you say understanding flight can be complicated, as = illustrated in a poem (Amer. Sci. 53(1): p. 78, 1965. Philosophers gravely expound Metaphysical concepts profound. While they argue all night On the meaning of "Flight," The Wrights get a plane off the ground. I leave it to evolution to iterate a useful balance between wing = dimensions and body weight and approached the question of flight = duration by calculating rate of fuel consumption (g tallow to keep one = gram airborne for one second =3D k) and assumed no additional energy for = forward motion; i.e. fighting gravity with a suitable angle of attack = would provide both at little additional cost. Then used differential = equations to allow for decrease in weight kept aloft as a function of = time and integration to calculate the time required to burn a specified = amount of tallow. I used 3 g initial and 1 g final (2 g tallow used) but = any initial and final weights could be substituted by replacing 3 and 1 = (2 equations up) with the other numbers. The full text, with the two typos corrected as noted and with spurious = carriage returns thrown in is as follows-- START OF PASTE\\\\\\\\\\\\\\\\\\\\\\\\\ Hi Chris & All, Jan 7, 2002 Your post about 70 hours of non-stop flight got me wondering about = energy equivalents of fat reserves so I cobbled together an estimate of the = upper limit. This is unfamiliar territory so don't bet your life savings that this = upper imit is correct. Assumptions are 100% efficiency and zero energy consumed by = life processes; obviously both wrong but I don't know probable values of = efficiency and metabolic consumption. No energy is reserved for air resistance or = forward motion, the idea being that forward motion is a practical way to climb = against gravity and maintain height. GIVEN, ASSUMED: Acceleration due to gravity (a); a =3D 980.665 cm/sec^2, One gram.cm =3D 2.3427 x 10^-8 kg.cal, Tallow heat of combustion =3D 9.5 kg.cal/g Model bird weighs 3 grams, 2 grams being tallow. GRAMS TALLOW TO KEEP ONE GRAM WEIGHT AIRBORNE FOR ONE SECOND: A body at uniform acceleration a, will move in time t, a distance = equal to s, i.e. s =3D 1/2 at^2 So instantaneous ds/dt, to overcome gravity, is ds/dt=3D at cm/sec =3D 980.665 cm/sec So the work (energy) required to keep one gram weight airborne for one = second is 980.665 gram.cm which is equal to 980.665 x 2.3427 x 10^-8 kg.cal =3D 2.297 x 10^-5 kg.cal . And the grams tallow required to keep one gram weight airborne for one=20 second, call this k, is 2.297 x 10^-5 kg.cal/ 9.5 kg.cal/gram=3D 2.4183 x 10^-6 grams = tallow/grams weight.seconds TIME THAT MODEL BIRD CAN REMAIN AIRBORNE; 3 GRAMS WEIGHT INITIAL, 1 GRAM = WEIGHT FINAL, 2 GRAMS TALLOW USED: So if w is instantaneous bird weight, the loss in weight per second will = be dw/dt=3D kw and conversely dt/dw=3D 1/kw and dt=3D 1/k x dw/w and T, the seconds to burn 2 g tallow, is the integral (int) of 1/k x = dw/w, i.e. T=3D 1/k x int(dw/w) =3D 1/k x (ln w + c) and for initial and final values of 3 and 1 grams = is =3D1/k x [(ln 3 + c) - (ln 1 + c)] COMMENT =3D>+ =3D 1.0986/k =3D 4.5428 X 10^5 seconds =3D ~126 hours Note that (ln 30 - ln 10) is also equal to 1.0986, so as long as = proportions of initial and final weight remain the same, the same upper limit for = airborne=20 time will apply. COMMENT ln 20 THREE LINES UP CHANGED TO ln 10 This also explains why it is so difficult to work off that extra = serving=20 of rich gravy. Yours truly, Dave Webster, Kentville END OF PASTE\\\\\\\\\\\\\\\ ----- Original Message -----=20 From: Stephen Shaw=20 To: naturens@chebucto.ns.ca=20 Sent: Saturday, January 24, 2015 6:46 PM Subject: Re: [NatureNS] Semipalmated Sandpiper migratory route Hi Dave et al,=20 This is perhaps splitting hairs because the Sandpiper (28g) and = Blackpoll Warbler (European, probably ~10-11g) are both quite small = birds and therefore may be nearly equivalent, but any calculation needs = to be framed in terms of what mass has to be kept aloft. It would take = far more fuel consumption per hour to keep a heavy crow (450g) in the = air compared to that for a small light warbler, if they have similarly = efficient lift-generating wings (doubtful). It is usually framed in = terms of body mass being proportional to the cube of the average linear = dimension (LD^3), while lift generation is proportional to the square of = the LD (LD^2) =97 so you need proportionally more wing lift area as the = body mass increases until it finally becomes infeasible to fly at all = =97 from memory the Great Bustard was reckoned to be the most massive = bird that could still manage to fly. =20 I may have used this example before: biologist J.B.S. Haldane (an = atheist) once penned a mischievous essay on the impossibility of the = existence of angels, at least in their depiction in medieval = manuscripts, because to power wings that size (a big LD^2) would require = a breastbone extending down to the ground to carry the enormous muscles = required to flap them (humungous LD^3), not so illustrated in the = manuscripts. Albatrosses don=92t count much in this because an engineer C. = Pennycuick (sp?) in the 1960s calculated that one species he looked at = mostly used the updraft from wave crests to glide along on a sinuous = path using lift energy derived from that, somewhat analogous to the = larger scale thermals used by some migrating raptors and storks.=20 Understanding flight is complicated. Steve (Hfx)=20 =20 On Jan 24, 2015, at 3:33 PM, David & Alison Webster = <dwebster@glinx.com> wrote: Hi Angus & All, Jan 24, 2015 In an e-mail of Jan 7, 2002 I estimated maximum flight duration = based on energy content of tallow and with initial conditions of 3 g = total weight of which 2 g is tallow to be 126 hours (what I call weight = would usually now be called mass). In scanning this quickly I noticed = two typos but whether these introduced error I don't know. At that time Richard dug out an example which showed this simple = model to considerably underestimate actual endurance-- START OF PASTE\\\\\\\\\\\\\\\ Hi Richard, Elizabeth & All, Jan 9, 2002 <SNIP> > -- "A typical Blackpoll Warbler at the end of its > breeding season weighs about 11 grams, equivalent to the weight of = 4 > pennies. In preparing for its transatlantic trek, it may = accumulate enough > fat reserves to increas