Similarity is a concept applicable to technical model testing. A model is supposed to have the resemblance to the actual application, if both share geometric resemblance, cinematic resemblance, and dynamic resemblance. Resemblance and resemblance are in this context interchangeable. Note that although the model is smaller, the water speed must be increased to be tested. This remarkable result shows how often nature is counterintuitive. This problem is illustrated by the influential book « Scaling » by Schmidt-Nielsen (1984), which shows dozens of relationships between physiological variables in species and body mass, kleiber`s so-called law, between basic turnover (energy consumption per unit of time) and body mass. None of the non-trivial relations respect the principle of similarity, including Kleiber`s famous law, with one notable exception: the allometric relationship between the speed of fish swimming and the frequency of tail beats (Bainbridge 1958). If the speed of swimming fish is properly normalized by ddividing them by their body length, so that frequency units are present as tail beats, the data between different fish in a single curve are in the same way that, for example, Kármán (1957) combined different experiments of turbulent currents in tubes and dimensional analysis only. The term dynamic resemblance is often used as a generic term, as it implies that the geometric and kinematic resemblance is already filled. Around the world, inhabited model schools have chosen to apply the William Froude (1810-1879) Resemblance Act for his inhabited models. This means that gravity compared to the other forces acting on the shell (viscosity, capillary, cavitation, compressibility, etc.) is preponderant. In the case of mammals, the heart rate evolves as Wu20120.25 (Brody 1945, steel in 1967), which implies for a , a fracture dimension of D=2.25, in accordance with the fracture dimension determined by Kleiber`s law. A similar result is obtained if we use the respiratory rate of peaceful mammals as a characteristic frequency (Calder, 1968).

For example, in subgroups, marsupials have metabolic rates ∝ M0.74 and heart rates ∝ Mu20120.27, which gives a dimension of D~2.2 in both cases. In invertebrates like spiders, metabolic rates range in M0.59 (Anderson 1970, 1974) and heart rates as Mu20120.41 (Carrel & Heathcote 1976), very different from those of mammals, but metabolic rates and heart rates involve the same fractional dimension of D~1.8. For birds, the scale is similar to that of mammals, in proportion to M0.72 (Lasiewski & Dawson (1967) and Mu20120.23 (Calder 1968), resulting in slightly different dimensions of D = 2.2 and 2.3 respectively. The Vaschy Buckingham-Π theorem defines the rules that must be respected by any useful relation that aims to be the natural law, and it is a formalization of rayleigh`s principle of resemblance. . . .