D. H. Feener, Jr., J. R. B. Lighton, G. A. Bartholomew, Curvilinear Allometry, Energetics and Foraging Ecology: A Comparison of Leaf-Cutting Ants and Army Ants, Functional Ecology, Vol. 2, No. 4 (1988), pp. 509-520
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Feener et al. (1988) studied this question.