The relation of weight to wing area in the flight of animals
E. Banks, Curator of the Sarawak Museum, published this quantitative study in 1930, drawing on specimens collected during four years of comparative isolation in Borneo to test and extend the earlier German work of Mullenhoff (1885) on the mathematical relationship between body weight and wing area in flying animals. The paper’s central thesis is that the ratio of wing area to body weight follows a predictable inverse relationship across birds, bats, and insects, and that the cube root of this ratio approximates a near-constant value of about 4, a property Banks and his advisor Prof. Huxley argued is primarily geometrical rather than biologically determined.
Summary
Banks set out to determine whether a general law governed the scaling of wing area relative to body weight across the major groups of flying animals. His method was straightforward but rigorous: specimens were laid breast-up, one wing stretched at right angles to the body, its outline traced in pencil, and the area measured with a surveyor’s planimeter. Weights were recorded in grammes and areas in square centimetres. A critical methodological departure from earlier workers (Mullenhoff, Harting, Mouillard) was Banks’s decision to measure wing area only, excluding the surface area of head, body, and tail, which he noted made direct numerical comparison with prior data impossible even where the general trend agreed (p. 335).
The data comprised approximately 123 species of birds, 40 of bats, and 186 of insects collected for the Sarawak Museum, supplemented by Mullenhoff’s published measurements of 192 bird specimens, 12 bats, and 75 insects. Banks plotted the ratio of total wing area to weight against body weight for each taxonomic order or sub-order, producing curves that revealed a consistent pattern: relative wing area decreases very sharply among the lightest fliers, declines more gradually through middle weights, and approaches a plateau at maximum weights. The curves for different orders are approximately parallel but not identical; orders with high relative wing area (such as owls and small passerines) show disproportionately large wing areas at low weights compared to orders with low relative wing area (such as game birds and ducks) (pp. 335–337).
Banks also addressed the so-called “constant” ³√(Wing Area/Weight) identified by Mullenhoff and others. His data confirmed that this value clusters around 4 across all groups but is subject to variation, particularly among insects where it ranges from 1.6 to 12.6. He noted that strong, swift, direct fliers among birds (ducks, partridges, waders, pigeons) occupy the lowest positions on the relative wing area scale, while orders containing many very light species (owls, small passerines) occupy the highest. The paper concludes with extensive tables of individual and group measurements and four graphs comparing his own Bornean data with Mullenhoff’s European series (pp. 339–360).
Key Findings
- The ratio Wing Area:Weight reaches approximately 300 in some insects but not more than 10 in birds, with bats and gliding mammals (flying squirrel, flying lemur, flying lizard) falling in between (p. 337).
- The “constant” ³√(Wing Area/Weight) ranges from 5.8 to 2.8 in birds and bats, and from 12.6 to 1.6 in insects, clustering mostly between 6 and 3, with a central value of approximately 4 (p. 336).
- Banks’s Bornean dataset comprised approximately 123 bird species, 40 bat species, and 186 insect species; Mullenhoff’s comparative dataset comprised 192 bird specimens of 88 species, 12 bats, and 75 insects of about 50 species (p. 335).
- The Argus Pheasant (Argusianus grayi) is identified as an exception with an inflated wing area due to enlarged secondary feathers as a secondary sexual character, while the Nightjar, Frogmouth, and Giant Swift are noted as unexplained outliers among Piciform birds (p. 337).
- The male Flying Fox is typically heavier than the female but has the same wing area, which Banks interpreted as an adaptation to the female’s increased weight when carrying young (p. 337).
- Mullenhoff’s flying fish data place them below any order of birds on the relative wing area scale, suggesting they are gliders rather than flappers (p. 337).
Conclusion
Banks concluded that the inverse relationship between relative wing area and body weight is a robust, cross-taxon pattern best expressed as a set of approximately parallel curves when data are grouped by taxonomic order. The near-constant value of ³√(Wing Area/Weight) ≈ 4 is, in his and Prof. Levy’s assessment, a geometrical property of three-dimensional scaling rather than a consequence of any essential biological factor, and the variation around this constant reflects genuine biological differences in flight strategy among orders (p. 336).
Context
- Banks was Curator of the Sarawak Museum, a colonial scientific institution in British Borneo, and the paper explicitly frames his four years of “comparative isolation” as a constraint on access to the existing literature, positioning the work as a contribution made from the periphery of the European scientific establishment (p. 334).
- The study’s historiographical contribution lies in providing the first large-scale dataset of wing-area measurements from a tropical fauna (Borneo) and in introducing the methodological refinement of measuring wing area exclusively, which Banks acknowledged prevented direct numerical integration with prior European data (p. 335).