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Pre-Reading: Why Swimmers Must Spread Their Fingers & Toes
The constructal-law physics of why swimmers must spread their fingers and toes.
Lorente, S., Cetkin, E., Bello-Ochende, T., Meyer, J.P., & A. Bejan. Journal of Theoretical Biology 308 (2012) 141-146.
In this paper, the authors attempt to show that an optimal finger spacing exists for maximal paddling force in human swimming. Previous studies have modeled the human hand and shown through simulation that slightly spaced fingers have higher drag coefficients than hands with either no spaces between fingers or with large spaces between fingers. However, since these simulations have been based on models of specific individual hands, they have not allowed appropriate scaling rules to be adopted; and, have not mathematically optimized the spacing between fingers.
The results of this study validate previous results that drag force is greatest when fingers, or in this case four cylinders, are spaced slightly apart. The authors offer a theoretical prediction that the fingers must be spaced twice the boundary layer thickness of one finger. Subsequently, the authors use computational fluid dynamics to predict that the optimal spacing between cylinders is 0.2-0.4 times the diameter of each cylinder (finger) at Reynolds numbers from 20 to 100. Fortunately, these findings can be interpreted with a basic understanding of fluid dynamics and biomechanics…
First, these simulations are performed on four cylinders that are not connected in any way. Human fingers are connected to hands, which are connected to forearms, and so on. The fingers occupy a small proportion of the propelling area of the arm, so any gains offered by optimizing finger spacing are negligible compared with gains offered by optimizing the orientation of the hand, forearm and upper arm during pulling actions.
Second, the authors use the thickness of a boundary layer as a reference for spacing, which is far too small to measure or control. When water flows around a solid object the molecules that directly contact the object’s surface stick to it, and slow down the adjacent molecules. This thin layer of water surrounding the object is called the boundary layer. Since the thickness of a boundary layer is measured in molecules, this spacing is not something that can be detected by the human eye or actively controlled by a human swimmer.
Third, the simulation results do not appear to be congruent with the initial theoretical predictions (0.2-0.4 times the diameter of a finger is a lot larger than twice the thickness of the boundary layer!). This is easily addressed by looking at the range of Reynolds numbers used in this simulation. The Reynolds number (Re) indicates whether the flow around a rigid body is laminar (smooth) or turbulent (chaotic). A very low Re indicates the flow is predominately laminar, whereas a very high Re indicates predominately turbulent flow. In competitive swimming this number is high, in the range of 10,000 1,000,000, indicating predominately turbulent flow. Thus, since these simulations were performed in low Re, these specific findings are irrelevant to human swimming.
Finally, humans come in very different shapes and sizes. Fingers are rarely of uniform thickness, and for most, the joints are thicker than the rest of the finger. This results in small spacing between each finger even when the joints are pressed together. Thus, it is nearly impossible to eliminate finger spacing!
Ryan Atkison (Canadian Sport Institute Ontario) is a Biomechanist based out of the High Performance Training Centre in Toronto. Ryan completed both his B.Sc. (2008) and M.Sc. (2010) in Kinesiology at the University of Western Ontario, specializing in sport biomechanics, and is also a Certified Strength and Conditioning Specialist with the National Strength and Conditioning Association.
Originally from London, ON, Ryan formerly worked with the Canadian Sport Centre Pacific team from Halifax, NS where he coached with the Halifax Trojan Aquatic Club. For the past two decades, Ryan has been heavily involved in competitive swimming as both a coach and national level athlete.