Thermodynarnic Limits of Body Dimension of Warm Blooded Animals

The metabolic rates tau(o) = a(omicron)M(0.73) [W], a(0) = 3.6, of animals of different body masses M [kg] determines their heat production Qʹ and their mechanical power output P. The metabolic heat production of small warm blooded animals living in a cold environment sets lower size limits for the body mass of birds and terrestrial mammals of M(t,b) > 0.01 kg and M(aq) > 10kg for fast aquatic mammals. Birds must travel at the speed U(fl) = 15M(1\6) [m/s] in order to stay aloft, but their muscles only generate the metabolic velocity U(tau) ~~ 50M ^-0.25 [m/s]. These conditions yield an upper body size limit for flying birds: M(b,max)< 15 kg- Walking speeds scale with body mass as U(walk = M^1\6, while propagation speeds for endurance running are nearly independent of body mass. This makes walking faster than endurance running for animals with body masses M > 600 kg.