Grusha and Patterson: Quantification of the drag and lift of pop-up satellite archival tags 



67 



not been measured; however, with visual 

 observation. Smith (1980) reported witness- 

 ing several undisturbed schools of cownose 

 rays swimming near the surface at -4-5 

 knots (2.06-2.57 m/s). Using data reported 

 in first sightings during spring migration 

 of cownose rays along the South Atlantic 

 Bight, Smith estimated migration speeds as 

 high as 12.5 nautical miles per day. Assum- 

 ing the rays migrated continuously, that 

 rate would require a swimming speed of 

 0.27 m/s; if they were actively migrating 

 50% of the time, they would have to swim 

 at 0.54 m/s. 



Published metabolic rates can be used to 

 estimate the energy required for an animal 

 to swim at various speeds. When informa- 

 tion is not available on a study species, 

 a suitable proxy species can be used. In 

 the example of the cownose ray, no data 

 are currently available regarding meta- 

 bolic rates; however, DuPreez et al. (1988) 

 published metabolic rates for the bull ray 

 (Myliobatis [=Myliobatus] aquila) over a 

 range of temperatures. Myliobatis aquila is 

 a good proxy species for R. bonasus because 

 the two species are morphologically similar, 

 similar in size, and both inhabit temperate 

 to subtropical coastal waters. Because the 

 flume measurements were obtained at 20°C 

 and this is also a typical mid-range tem- 

 perature for either species, the equations 

 for metabolic rates at this temperature will 

 be used (Eq. 6, a-c). Metabolic rates are 

 expressed as a set of three equations that yield the 

 standard metabolic rate (SMR), the routine metabolic 

 rate (RMR), and the active metabolic rate (AMR). 



Wildlife Computers PAT 



Microwave Telemetry PTT 



Velocity (m/s) 



Figure 3 



Comparison of force-velocity curves of two brands of PSAT. Total 

 force (in newtons, N) and its component forces, lift and drag, are 

 plotted against flume velocity (m/s). The angle of deflection of the 

 PSAT as measured upward from horizontal is indicated above each 

 set of points 



SMR log 10 R = 2.86 - 0.32 x 

 log 10 (M x 1000), 



where SP, MR = swimming power (W) for RMR or AMR. 



Making the appropriate substitutions into Equation 7 

 yields SP RMR = 0.76 W and SP AMR = 1.99 W. Drag can 

 then be expressed as %TAX: 



(6a) 



%TAX = (P I SP /MP ) x 100. 



(8) 



RMR log 10 r? = 2.79 -0.27 x log 10 (M x 1000), (6b) 



AMR log 10 r? = 2.74- 0.22 x log 10 (Mx 1000), (6c) 



where M = mass (kg) of the ray (DuPreez et al.'s 1988 

 equations have been modified so as to 

 express M in MKS units); and 

 R = metabolic rate (mg 9 /(kg x h)). 



Using the size of an average female cownose ray of 15.5 

 kg (Smith, 1980) and solving for R, the SMR, RMR and 

 AMR are estimated as 33.0, 45.6, and 65.8 mg 2 /(kg x 

 h) respectively. These rates can then be used to estimate 

 swimming power at routine and active swimming speeds: 



SP-, MR =(?MR-SMR)x 

 (lW/kg)/(256mg0. 2 /(kgxh))xM, 



(7) 



For swimming speeds of 0.15 m/s and 0.30 m/s, SP RMR is 

 used, and for swimming speeds of 0.45 m/s and 0.60 m/s, 

 SP AMR is used (Table 2). 



Although lift has not been considered in the above 

 analysis, it is an important component of the total force 

 affecting a study animal. As a chronically applied force 

 acting against the anchor site where the PSAT attaches, 

 this total force may contribute to premature release of 

 the PSAT from the study animal. Moreover, for ani- 

 mals where diving behavior is important for survival 

 (e.g., diving for prey or diving to escape predators) lift 

 becomes an additional tax on the animal's energy re- 

 souces. Using total force as an approximation of the 

 force to be overcome by the animal when diving, we can 

 estimate the total power required to dive as Total force 

 as %TAX (Table 2). 



We propose that an increase in energy requirement, 

 %TAX, of <5% will not negatively impact a study ani- 



