## Drag and Streamlining

Commonly, drag is determined by [20]:

where

Ac = characteristic area of the drag-producing body [m2]

Cd = drag coefficient ur = fluid's velocity relative to an object [m s-1] (cf. Figure 3.3)

With flexible organisms, it is commonly observed that the drag coefficient is not constant but changes with increasing velocity as the body reconfigures itself [10,21,22]. Consequently, comparisons between different individuals or different species often are restricted to a certain velocity [6,11]. Additionally, a constant drag coefficient typically does not yield the expected increase of drag with the velocity squared [23]. The process of reconfiguration, which leads to a lower increase of drag than would be expected, is described by Vogel [24,25]. The deviation from a second-power relation between drag and velocity is maintained by the introduction of a "figure of merit" as an addend in the power function. Since the shape is not constant, a more general shape factor can be introduced, leading to the following extended equation for drag [6]:

Fbuoyancy Fnet

Fbuoyancy Fnet

where Sd is the shape coefficient and B is the figure of merit. For clarity and simplicity, Gaylord et al. [10] have introduced the term "Vogel number" for this figure of merit, which is used henceforth in this study.

The more negative the Vogel number, the lower is the increase in drag with increasing velocity. It is therefore a means of quantifying the effect of reconfiguration.

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