130 



Fishery Bulletin 104(1) 



C/ =o.o72i^-"^ 



where R is Reynold's number, estimated here as 

 R = LV/v, 



where v = kinematic viscosity ( = 0.01 Stokes). 



The calculations above generated estimates of the 

 power required for a whole dolphin of a given size to 

 swim at a given velocity (P,, in watts). Power required 

 per kilogram of wet weight muscle (P„, ), for a given 

 velocity was estimated as 



where M„, = total muscle mass (wet weight in kg), esti- 

 mated from total body mass (M,, wet weight in kg) as 



M„ 



-2.97M' 



based on In-ln regression of measurements from a sample 

 of 26 Stenella attenuata from the ETP ranging in size 

 from 0.71 to 2.06 m. Total muscle was used rather than 

 some portion of measured musculature because the com- 

 plex and interconnected muscle and connective tissue of 

 dolphins makes it difficult to isolate any particular por- 

 tion as uniquely responsible for locomotion (Pabst, 1990). 

 M-i was estimated from total length (L, in cm) as 



M, =0.0000119L-^' 



based on In-ln regression of measurements from a sample 

 of 23 Stenella attenuata from the ETP ranging in size 

 from 0.71 to 2.01 m. 



Results 



Model corroboration 



Model estimates of the cost of swimming compared 

 reasonably well with the cost of swimming in published 



reports for other species of dolphins swimming 1-6 m/s, 

 in cases where the published reports can be appropri- 

 ately compared with the present model. Although a 

 number of studies present a variety of estimates of drag, 

 thrust power, and metabolic power at various swimming 

 speeds for a variety of dolphins (reviewed by Fish and 

 Rohr, 1999), comparisons of present results with many 

 of these earlier studies would be inappropriate because 

 either the estimates were derived from completely dif- 

 ferent models from the one used in the present study 

 or from generally similar models but where different 

 assumptions were made about model parameters, such 

 as propulsive efficiency, metabolic efficiency, drag for- 

 mulation, and body structure (Edwards'). Only appro- 

 priately comparable published results are discussed in 

 the present study. 



All weight-specific measurements in the following 

 paragraph refer to total body mass. At estimated opti- 

 mum velocities ranging from about 1.2 m/s in neonate 

 spotted dolphins to about 1.7 m/s in adults (Edwards^), 

 model estimates are approximately 3 W/kg for all sizes 

 of spotted dolphin, compared to measurements (de- 

 rived under various methods) of about 2.5-5.5 W/kg 

 for adults of various species of dolphins, either resting 

 or swimming about 2 m/s (Hui, 1987; Worthy et al., 

 1987; Williams et al., 1992; Fish, 1993; Yadzi et al., 

 1999). Observed average total metabolic rates calculat- 

 ed from oxygen consumption by two Tursiops (average 

 weight 162 kg), swimming 2 and 3 m/s, were approxi- 

 mately 2.5 and 3.7 W/kg (Yadzi et al., 1999), compared 

 to model estimates of approximately 2.9 and 5.9 W/kg 

 for an adult spotted dolphin (about 70 kg) swimming 

 at the same speeds. Model estimates of thrust power 

 output for an adult spotted dolphin (about 70 kg) also 

 compared well with thrust power estimated as a func- 

 tion of velocity from videos of five Tursiops swimming 

 between 1 and 6 m/s (Fish, 1993). Given an average 

 adult Tursiops weight of 230 kg, average estimated 

 thrust power for Tursiops swimming 1, 3, 5, and 6 m/s 

 was 1, 3, 14, and 23 W/kg, compared to spotted dolphin 

 model estimates of 1, 3, 13, and 21 W/kg, respectively. 

 These comparisons refer to mechanical power output 



