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> fat reserves to increas Quoting David & Alison Webster <dwebster@glinx.com>: > 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. * angels being visual hallucinations, the wings (and halo) are a rationalization of their surrounding aura - http://www.julianjaynes.org/ fred. ============================================================= > 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 = 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 = 980.665 cm/sec^2, > One gram.cm = 2.3427 x 10^-8 kg.cal, > Tallow heat of combustion = 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 = 1/2 at^2 > So instantaneous ds/dt, to overcome gravity, is > ds/dt= at cm/sec = 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 = 2.297 x 10^-5 kg.cal . > And the grams tallow required to keep one gram weight airborne for one > second, > call this k, is > 2.297 x 10^-5 kg.cal/ 9.5 kg.cal/gram= 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= kw and conversely > dt/dw= 1/kw and dt= 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= 1/k x int(dw/w) > = 1/k x (ln w + c) and for initial and final values of 3 and 1 grams is > =1/k x [(ln 3 + c) - (ln 1 + c)] COMMENT =>+ > = 1.0986/k > = 4.5428 X 10^5 seconds > = ~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 > 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 > of rich gravy. > > Yours truly, Dave Webster, Kentville > END OF PASTE\\\\\\\\\\\\\\\ > > ----- Original Message ----- > From: Stephen Shaw > To: naturens@chebucto.ns.ca > Sent: Saturday, January 24, 2015 6:46 PM > Subject: Re: [NatureNS] Semipalmated Sandpiper migratory route > > > Hi Dave et al, > 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) -- so you need > proportionally more wing lift area as the body mass increases until > it finally becomes infeasible to fly at all -- from memory the Great > Bustard was reckoned to be the most massive bird that could still > manage to fly. > 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't 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. > Understanding flight is complicated. > Steve (Hfx) > > > 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 increase its body weight to 21 grams. Given an > in-flight fat > > consumption rate of 0.6% of its body weight per hour, the bird then has > > enough added fuel for approximately 90 hours of flight for a > journey which, > > under fair conditions, requires about 80 to 90 hours. > > This Warbler beats my upper limit, perhaps by being a good weather > forecaster and using rising air currents. > My k equates to a loss of 0.87% of body weight per hour > compared to 0.6% > loss in the Warbler. And when I plug 21 and 11 grams into my > model, I get 74 > hours of flight compared to 90 hours for the Warbler. > > Yours truly, Dave Webster, Kentville > END OT PASTE\\\\\\\\\\\\\\\ > > And the link below, for the Semipalmated Warbler, has 6 days > of non-stop flight over water (~144 hours). > > The Albatross beats all of the above of course by staying > aloft for years without beating a wing. Holding wings out and > tilting them and tail as required takes energy but still it manages > amazingly efficient flight. > > Yt, Dave Webster, Kentville > > > > > ----- Original Message ----- > From: Angus MacLean > To: naturens > Sent: Saturday, January 24, 2015 9:34 AM > Subject: RE: [NatureNS] Semipalmated Sandpiper migratory route > > > Can't imagine how thin that little guy was when it arrived at > the Orinoco Delta!! > Thanks, Eric. > Angus > > > > -------------------------------------------------------------------------- > From: E.Mills@Dal.Ca > To: naturens@chebucto.ns.ca > CC: davidmary3@eastlink.ca > Subject: [NatureNS] Semipalmated Sandpiper migratory route > Date: Sat, 24 Jan 2015 01:31:03 +0000 > > > Courtesy of BCVIBirds, here is a fascinating link about the > migratory paths of Semipalmated Sandpipers that stage in James Bay: > http://goo.gl/at0GMZ > > > I suspect that geolocators have been used with east coast > migrants as well, but I don't have that information. > > > Eric > > > Eric L. Mills > Lower Rose Bay > Lunenburg Co., NS > > > No virus found in this message. > Checked by AVG - www.avg.com > Version: 2015.0.5645 / Virus Database: 4273/8984 - Release > Date: 01/23/15 > > > No virus found in this message. > Checked by AVG - www.avg.com > Version: 2015.0.5645 / Virus Database: 4273/8993 - Release Date: 01/24/15 > ------------------------------------------------------------ Frederick W. Schueler & Aleta Karstad Mudpuppy Night - http://pinicola.ca/mudpup1.htm Vulnerable Watersheds - http://vulnerablewaters.blogspot.ca/ study our books - http://pinicola.ca/books/index.htm RR#2 Bishops Mills, Ontario, Canada K0G 1T0 on the Smiths Falls Limestone Plain 44* 52'N 75* 42'W (613)258-3107 <bckcdb at istar.ca> http://pinicola.ca/ "[The] two fundamental steps of scientific thought - the conjecture and refutation of Popper - have little place in the usual conception of intelligence. If something is to be dismissed as inadequate, it is surely not Darwin [, whose] works manifest the activity of a mind seeking for wisdom, a value which conventional philosophy has largely abandoned." Ghiselen, 1969. Triumph of the Darwinian Method, p 237. ------------------------------------------------------------
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