Edwards: Duration of unassisted swimming by Stenella attenualo 



127 



three fetuses, six immature, and four mature individu- 

 als. Female specimens included three fetuses, six im- 

 mature, one mature resting, one mature lactating, and 

 11 mature pregnant individuals. All specimens were 

 killed during tuna fishing operations in the eastern 

 tropical Pacific Ocean. Two of the specimens were col- 

 lected in February 1980, one in July 1983, nine in July 

 1985, two in August 1985, seventeen in December 1985, 

 and four were collected without a date noted (Edwards, 

 1993). All specimens were processed according to the 

 same procedures prior to dissection. Immediately after 

 the sets, the dolphin specimens were brought on board 

 the vessel and frozen whole in the brine wells of the 

 vessel. The specimens were transported frozen to port 

 and then transported frozen to the Southwest Fisheries 

 Science Center. Specimens were kept frozen until thawed 

 in fresh water (about 27°C) just prior to dissection. Not 

 all measurements were made on all specimens; therefore 

 sample sizes differ between the regression equations 

 presented below. 



Energetics model The energetics model used to esti- 

 mate total body cost of swimming was taken from 

 Edwards (1992, based on Magnuson, 1978), except that 

 1) new data were used to estimate dolphin body param- 

 eters and 2) the estimate of fin plus induced drag was 

 replaced by the multiplier 3 (see below). The model 

 used standard hydrodynamic equations and methods 

 (Hoerner, 1965; Hertel, 1969; Webb, 1975) to estimate 

 hydrodynamic drag on a fully submerged streamlined 

 body of revolution moving steadily in turbulent flow. 

 Body surface area was increased to specifically include 

 the surface area of fins and flukes (Fish''), and drag 

 estimates were increased to account for body and fin 

 movements. Because energy to move forward (thrust 

 energy) must exactly balance the drag experienced by a 

 steadily swimming animal, estimating total drag energy 

 is equivalent to estimating thrust energy, i.e., the energy 

 cost to swim (Fish and Rohr, 1999). 



studies by Fish (1998), Webb (1975), and Yates (1983). 

 P was estimated as a function of total hydrodynamic 

 drag (Di, in dynes) and velocity (V, in m/s) as 



P,„=D,V/lOl 



where the factor 10" converts (D,V) to watts. 



Total drag was estimated as a function of drag due to 

 body, fins, and movements of body parts as 



D,=0.5pV'S,.C,, = 1.5pV%,C„ 



where p = density of seawater (1.025 g/cm'^); 

 iS,,, = wetted surface area; 

 Cj = coefficient of total drag; and 

 3 = drag augmentation factor. 



S,^ includes surface area of body plus fins and flukes, 

 where estimated planar area of fins was increased by 

 69c to account for the curvature of the fins, based on 

 measurements of individual slices from fins and flukes 

 from one small and one large dolphin, 1.32 m and 1.93 m 

 in length, respectively (Edwards, unpubl. data). Drag 

 augmentation factor generally varies between 3 and 5 

 (e.g., Lighthill, 1971; Fish, 1993) and was assumed equal 

 to the value of 3 in the present study, based on studies of 

 gliding vs. actively swimming dolphins (Skrovan et al., 

 1999). The factor 3 accounts for the increase over gliding 

 drag caused by body movements during active swim- 

 ming. Use of a squared relationship between V and JD, 

 is supported by the observed relationship between total 

 drag and velocity in free swimming Tursiops truncatus 

 (Skrovan et al. 1999, Eq. 6). Use of a cubic relation- 

 ship between V and P, is supported by observations of 

 swimming kinematics of Tursiops truncatus swimming 

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

 Sj,, (in cm^) was estimated as 



S, =0.299L2°5, 



Model formulation Total power (P,, in watts) required 

 to overcome drag during steady, submerged swimming 

 (Hertel, 1969) by a modeled dolphin of a given total 

 length (L, rostrum to fluke notch) was estimated as 



where P^ = mechanical power (in watts) required to 

 overcome hydrodynamic drag; 

 £„, = muscle efficiency; and 



E = "propeller efficiency" (efficiency of propul- 

 sion by flukes). 



based on measurements from 19 Stenella attenuata 

 ranging in size from 0.71 to 2.01 m, where L is total 

 length (in cm). 



Cj was estimated from the formula for drag of sub- 

 merged streamlined bodies of revolution moving at 

 constant velocity (Hoerner, 1965; Hertel, 1969; Webb, 

 1975) as 



Cj=Cf\\ + [l.b(d I Lf'^) + l[(d I L\^]^, 



Cf = the coefficient of friction drag; and 

 d = 0.12 



£„, was assumed to be 0.2 from studies of muscle efficien- 

 cies in terrestrial animals (e.g., Goldspink 1988), man 

 (Alexander, 1983; quoting Dickinson, 1929) and dolphins 

 (Fish, 1993, 1996). E^ was assumed to be 0.85 based on 



5 Fish, F. 2002. Personal comniun. Liquid Life Laboratory, 

 West Chester Univ. Pennsvlvania, West Chester, PA. 



where d = maximum body diameter (in cm) based on 

 measurements from 24 Stenella attenuata 

 ranging in size from 0.71 to 2.01 m. 



C, was estimated from the formula for submerged stream- 

 lined bodies of revolution moving at constant velocity in 

 turbulent flow (e.g., Webb, 1975) as 



