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Originally Posted by Dilbert1234567
Come on will... the density of a bird foot is not comparable to that or a solid metal engine turbine.
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If you compare the size of the birds foot to a directly proportional mini-chimney interesting similarities can occur. For the sake of science, let's use a Pacific Parrotlet (Forpus coelestis coelestis); being of small bird size (comparably to the plane).
The average weight of a Pacific Parrotlet, also known as the Ridgway's Parrotlet, can be noted as an average of 31-34 grams. A recent journal published by Wilson Bulletin via
BioOne: EMS Provider Program found that
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Birds can gain an advantage in flight efficiency by reducing the size and mass of body parts that are not essential during flight.
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Taking this into consideration, we can then assume that the foot of a bird would weigh less during flight, and thus carry less kenetic energy upon impacting a chimney (unless the bird prepared itself for the blow, but lets stay on topic). In the classic work,
On Growth and Form, D'Arcy Thompson gives measurements of the relative weight of bones of various mammals and their body weights: bone is about 8% of the body weight of a mouse or a wren, 13% of a goose or a dog, and about 17 to 18% of a man's weight. As the animal becomes larger, the bone becomes a greater proportion of body weight because the bones are proportionally larger in diameter. Notice that for the smaller animals, D'Arcy Thompson pairs a mammal with a bird showing that the principle holds for two different groups of animals.
Now, for the specific mass of the bird's foot. This article from Harvard shows a correlation in the allometry of bat wings and legs in comparison with bird wings and legs.
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Originally Posted by Smithsonian/NASA ADS General Science Abstract Service
Title: Allometry of Bat Wings and Legs and Comparison with Bird Wings
Authors: Norberg, Ulla M.
Publication: Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, Volume 292, Issue 1061, pp. 359-398
Publication Date: 06/1981
Origin: JSTOR
Bibliographic Code: 1981RSPTB.292..359N
Abstract
Allometric equations on wing dimensions versus body mass are given for eight species of megabats and 76 species of microbats, on forearm length versus mass for 14 species of megabats and 90 species of microbats, and on lower leg length versus mass for 11 species of megabats and 45 species of microbats. Megabats have, on average, shorter wing span, small wing area, higher wing loading and lower aspect ratio than have frugivorous microbats and the insectivorous vespertilionids of similar mass. Vespertilionids have the longest span, largest wing area and lowest wing loading in relation to body mass of the bat groups for which regression lines were calculated (megabats, frugivorous microbats, vespertilionids, molossids), characteristics that are important for slow flight and manoeuvrability for insect capture. Molossids have the highest wing loading of the groups. There is a weak tendency towards higher aspect ratio for larger bats than for smaller ones (positive slope). The slopes for most characters fit geometric similarity or have confidence intervals including the value for geometric similarity. Only in three cases does the slope lie nearer that for elastic similarity: for the forearm in nycterids and emballonurids and the lower leg length in molossids. Also in these cases the confidence intervals are wide and include the value for elastic similarity and that for geometric similarity as well. In megabats the slope for the lower leg length is much steeper than for geometric similarity. The slope for the forearm length is rather similar to that for wing span in the various groups. Megabats and frugivorous microbats have rather similar slopes for all the characters measured, but differ from the other groups only in wing area, wing loading and aspect ratio. The two frugivorous bat groups also have about the same elevation of the regression lines for aspect ratio and forearm length. Megabats and frugivorous microbats thus show a close convergence in wing area, wing loading, aspect ratio and forearm length. The regression equations provide `norms' for the respective bat groups. Those species that deviate 10% or more from the mean trends for wing measurements are divided into different groups, based on the wing's aspect ratio and loading. Bats with low aspect ratio wings usually have large pinnae, which improve the ability to discover small objects such as insects on leaves. Families or species of bats with wings of low aspect ratio are, for instance, Megadermatidae, Nycteridae, Rhinolophus ferrumequinum (Rhinolophidae), Chrotopterus auritus (Phyllostomidae) and Plecotus (Vespertilionidae). The group with average aspect ratio wings contains bats with different kinds of flight style and foraging behaviour, for instance many pteropodids, phyllostomids and vespertilionids. Bats with high aspect ratio wings are, for instance, Molossidae, Rhynchonycteris naso (Emballonuridae) and Nyctalus leisleri (Vespertilionidae). The regression lines for wing span, area and loading in megabats lie almost in the region of the lines for Greenewalt's (1975) passeriform group, whereas the span and area for vespertilionid bats are larger and the wing loading much smaller than for most birds of similar mass. Molossid bats have a larger relative wing span and aspect ratio than have most birds, and a wing area and loading similar to those of small birds of the passeriform group. Vespertilionid bats have about the same aspect ratio as birds of the passeriform group, whereas megabats have somewhat lower ratios. Molossid bats show strong convergence with swifts and swallows in foraging behaviour and in wing form. Similar convergences can be found between various vespertilionid bats, flycatchers and swallows.
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In
The Journal of Experimental Biology 206, 1085-1097;
Leg morphology and locomotion in birds: requirements for force and speed during ankle flexion let's take a closer look at page 1087.
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To avoid problems associated with colinearity between body mass and tarsometatarsus length (which affects the confidence interval for the regression), a principal components analysis (PCA) was conducted (on the natural logarithms for body mass and tmt) by rotating these data sets using the correlation matrix. This procedure first standardizes the variables by subtracting the mean for all species and then dividing the variables by the standard deviation (S.D.) before the analysis is conducted. The scores for PC1 and PC2 were then used as independent variables in a multiple linear regression where loged was treated as the dependent variable, so that:
loged = a1+ b1PC1+ b2PC2+ ?1, (1)
where PC1 and PC2 are the first and second principal components of logeMand logetmt, a1is the intercept, and b1 and b2 are the regression coefficients of PC1 and PC2, respectively. The term ?1 represents the residual, which is independent of PC1 and PC2 and hence also independent of logeMand logetmt. In this way dcan be viewed as normalized describing the orthogonal vectors that maximally separate the groups. The means of the DF scores for the groups were calculated along with the 95% confidence intervals of the means. All analyses were conducted with SPSS 10.0, except for the PCA and the Wilcoxon signed-rank test, which were performed according to SAS procedures (version 8.0). During the last decade, the effect of phylogeny on comparative studies has been fully recognized (e.g. Felsenstein, 1985; Cheverud et al., 1985; Harvey and Pagel, 1991; Martins and Hansen, 1996). It is possible that the groups identified in this work coincide with phylogenetic groups, consequently the species should not be considered as statistically independent units (Felsenstein, 1985; Harvey and Pagel, 1991). Several methods have been developed to allow for the phylogenetic effect (for a review, see Martins and Hansen, 1996), but they all have some limitations. The main problem with these methods is that they depend on a good estimate of the phylogeny, including estimates of branch lengths as well as interpretations of excluded branches.
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After plugging in the proper weight, and measurements, we can assume (within 95% accuracy) that the average weight of a Pacific Parrotlet's foot is 4.03 - 4.42 g (avg.= 4.22 g). The average flight speed of a Parrotlet it 36.9 km/h^–1. Now, to find the foot's kinetic energy:
KE = 1/2 • m • v^2
where m = mass of object
v= speed of object
KE = 1/2 • 4.22 g • 36.9 km/h
KE = 77.859 g/km/h
A 757 weighs, at maximum, 255,000 lb (115,680 kg). Thus the ratio between a 757 and a Pacific Parrotlet is about 7,500 parrotlets : 1 757 (not taking into account the lightened foot mass during flight).
The typical masonry chimney has a traditionally wide-framed 36x28 doorset (with doors wide open) which will usually have a clear opening of about 30" by 25" high, and a height of 30'. That's 750 square inches of opening area. The WTC reached 1,450 feet high and had a width of 208 feet (63.4 m) x 208 feet (63.4 m). Thus the comparison between the typical masonry chimney and the WTC is around 5662.5265 chimneys : 1 WTC. The kinetic energy generated by the 757 (assuming it was traveling around 540 mph (868 km/h) 530 knots (982 km/h)):
KE = 1/2 • 115,680 g • 982 km/h
KE = 567,988 g/km/h
After combining the two ratios, and kinetic energies, the final ratio is 564,375 Pacific Parrotlet/chimney : 567,988 757/WTC. Thus we may conclude that the foot of a Pacific Parrotlet, 7,500% its normal size, would create a similar impact to the 757's. And we can also conclude that a 757, 7.5 • 10^-4% smaller than its usual size, would impact a chimney in the same way.
