Question 18.87

57. The accompanying table lists the weights and wingspans of some birds and of some fully loaded airplanes. (Idea and most of the data contributed by Florence Gordon, New York Institute of Technology.)

  1. Use a calculator or spreadsheet to take the logarithms of all the numbers and then graph logarithm of weight versus logarithm of wingspan on ordinary graph paper.
  2. For the birds, is the relationship that you graphed in part (a) proportional? Is it allometric? How about for the planes?

    774

    Birds Weight (lb) Wingspan (ft)
    Crow 1 2.9
    Harris hawk 2.6 3.2
    Blue-footed booby 4 3
    Red-tailed hawk 4 4
    Horned owl 5 5
    Turkey vulture 6.5 6
    Eagle 12 7.5
    Golden eagle 13 7.3
    Whooping crane 16.1 7.5
    Vulture 18.7 9.3
    Condor 22 9.9
    Quetzalcoatlus northropi 100 36
    Planes
    Boeing 737 117,000 93
    DC9 121,000 93.5
    Boeing 727 209,500 108
    Boeing 757 300,000 156.1
    Boeing 707 330,000 145.7
    DC8 350,000 148.5
    Howard Hughes’s “Spruce Goose” 400,000 320.9
    DC10 572,000 165.4
    Boeing 747 805,000 195.7
    Boeing 747-400 895,000 212.6
    Anton An-225 1,323,000 290.2
  3. Does the same relationship of wingspan to weight seem to hold for birds and planes?
  4. A 25-million-year-old fossil recently discovered in South Carolina is of a seabird with a wingspan of 24 ft, Pelagornis sandersi. (That wingspan is larger than that of the largest living bird that can fly, the wandering albatross, 11 ft.) From your graph in part (a), what would you estimate the weight of a P. sandersi to have been?

57.

(a) The accompanying graph shows birds along the lower line (in green) and planes along the upper line (in red).

(b) Both relationships are allometric, since the results are good fits to straight lines whose slopes are not 1.

A-40

(c) The slope for birds is less steep than for planes.

(d) 64 lb

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