Ant mound as an optimal shape in constructal design: Solar irradiation and circadian brood/fungi-warming sorties

R. G. Kasimova*, D. Tishin, Yu V. Obnosov, G. M. Dlussky, F. B. Baksht, A. R. Kacimov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Sizes, shapes, ambient and in-dome temperature, incoming solar radiation and illumination are measured on a Formica rufa anthill in a mixed forest of the Volga-Kama National Reserve in Russia. These data are used in a conceptual model of insolation of a right conical surface by direct-beam, descending atmospheric and ascending ground-reflected radiation. Unlike a standard calculation of the energy flux intercepted by a solar panel, the anthill is a 3-D structure and double-integration of the cosine of the angle between the solar beams and normal to the surface is carried out for a "cozy trapezium", where the insects expose themselves and the brood to "morning" sunbathing pulses ( Jones and Oldroyd, 2007). Several constructal design problems are formulated with the criteria involving either a pure solar energy gained by the dome or this energy, as a mathematical criterion, penalized by additive terms of mechanical energy (potential and friction) lost by the ants in their diurnal forays from a "heartland" of the nest to the sun-basking zone on the surface. The unique and global optima are analytically found, with the optimal tilt angle of the cone explicitly expressed through the zenith angle of the Sun and meteorological constants for the isotropic sky model.

Original languageEnglish
Pages (from-to)21-32
Number of pages12
JournalJournal of Theoretical Biology
Publication statusPublished - Aug 21 2014


  • Adaptive ant-mound
  • Direct-diffuse-reflected radiation on non-flat surfaces
  • Insolation
  • Optimal slope
  • Social insects

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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