Gray's paradox

[2] Timothy Wei, professor and acting dean of Rensselaer's School of Engineering, videotaped two bottlenose dolphins, Primo and Puka, as they swam through a section of water populated with hundreds of thousands of tiny air bubbles.

Computer software and force measurement tools developed for aerospace were then used to study the particle-image velocimetry which was captured at 1,000 frames per second (fps).

In 2009, researchers from the National Chung Hsing University in Taiwan introduced new concepts of “kidnapped airfoils” and “circulating horsepower” to explain the swimming capabilities of the swordfish.

[4] They showed mathematically that drag on undulatory swimmers (such as dolphins) can indeed be greater than the muscle power it generates to propel itself forward, without being paradoxical.

Their findings can be summarized in a simple power balance equation: in which, It is important to acknowledge the fact that a swimmer does not have to spend energy to overcome drag all through its muscle work; it is also assisted by the thrust force in this task.