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Optimal fineness ratio for minimum drag in large whales

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The optimum fineness ratio (X = L/d, where L and d are body length and profile height, respectively) for minimum drag is about 4.5 and many fast swimming fish are characterized by values of this order. However, values for large whales that undergo extensive migrations (e.g., Balaenopteridae, Balaenidae, and Physeteridae) are as high as 8. A plot of fineness ratio versus mass (M) for different species of large whales shows that the optimal fineness ratio for minimum drag and therefore the minimum cost of transport increases slowly with increasing mass (X = 4M0.06). Optimal fineness ratio was determined from a simple hydromechanical model based on the sum of friction and pressure drag on an equivalent cylindrical body, which indicate a small positive dependence (0.11) of optimal fineness ratio for minimum drag with increasing body mass, suggesting an adaptation for reducing the energy cost of swimming.

Le rapport optimal de finesse (X = L/dL et d sont respectivement la longueur du corps et la hauteur de profil) pour une traînée minimale est d’environ 4,5 et plusieurs poissons à nage rapide ont des valeurs de cet ordre. Cependant, les valeurs chez les grandes baleines qui font d’importantes migrations (par ex., Balaenopteridae, Balaenidae et Physesteridae) peuvent atteindre 8. Un graphique du rapport de finesse sur la masse (M) chez diverses espèces de grandes baleines montre que le rapport optimal de finesse pour une traînée minimale, et par conséquent le coût minimal du déplacement, augmente lentement en fonction directe de la masse (X = 4M0,06). Nous avons déterminé le rapport optimal de finesse à partir d’un modèle hydromécanique simple basé sur la somme de la friction et de la traînée de pression sur un corps cylindrique équivalent qui indique une faible dépendance positive (0,11) du rapport optimal de finesse pour une traînée minimale en fonction directe de la masse corporelle, ce qui semble être une adaptation pour réduire le coût énergétique de la nage.

Document Type: Research Article

Publication date: February 1, 2009

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