Scaling of swim speed and stroke frequency in geometrically similar penguins: They swim optimally to minimize cost of transport

Katsufumi Sato, Kozue Shiomi, Yuuki Watanabe, Yutaka Watanuki, Akinori Takahashi, Paul J. Ponganis

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


It has been predicted that geometrically similar animals would swim at the same speed with stroke frequency scaling with mass-1/3. In the present study, morphological and behavioural data obtained from free-ranging penguins (seven species) were compared. Morphological measurements support the geometrical similarity. However, cruising speeds of 1.8-2.3m s-1 were significantly related to mass0.08 and stroke frequencies were proportional to mass-0.29. These scaling relationships do not agree with the previous predictions for geometrically similar animals. We propose a theoretical model, considering metabolic cost, work against mechanical forces (drag and buoyancy), pitch angle and dive depth. This new model predicts that: (i) the optimal swim speed, which minimizes the energy cost of transport, is proportional to (basal metabolic rate/drag)1/3 independent of buoyancy, pitch angle and dive depth; (ii) the optimal speed is related to mass0.05; and (iii) stroke frequency is proportional to mass -0.28. The observed scaling relationships of penguins support these predictions, which suggest that breath-hold divers swam optimally to minimize the cost of transport, including mechanical and metabolic energy during dive.

Original languageEnglish
Pages (from-to)707-714
Number of pages8
JournalProceedings of the Royal Society B: Biological Sciences
Issue number1682
Publication statusPublished - 2010 Mar 7
Externally publishedYes


  • Accelerometer
  • Buoyancy
  • Energy
  • Free ranging
  • Isometric model
  • Morphology

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)


Dive into the research topics of 'Scaling of swim speed and stroke frequency in geometrically similar penguins: They swim optimally to minimize cost of transport'. Together they form a unique fingerprint.

Cite this