HUNTER and ZWEIFEL: SWIMMING SPEED AND TAIL BEAT FREQUENCY 



Table 5. — Slopes for the velocity-frequency relationship 

 for individual Carassius studied by Bainbridge (1958) 

 when the general relationship is slope ^= 0.68L; esti- 

 mated minimum speed when Vq = O.SIL-/^; observed 

 minimum swimming speed (I'obs) > the tail beat fre- 

 quency Fq estimated by substitution of Vg into the cor- 

 rected slope equation ; and the lowest observed tail beat 

 frequency (F„f,J. 



1 Data from Bainbridge (1958). 



Table 6. — Minimum speed (Vq), minimum tail beat fre- 

 quency (Fq), the coefficient K in equation V — F„ = 

 L(KF — Fq) arranged in order of K. 



1 y theoretical estimote based on equation of Magnuson (1970). 

 3 One deviant fisli omitted; if fish included. A' = 74, K = 0.66. 

 » Original dota from Bainbridge (1958). 



4 beats/sec on the abscissa were from this single 

 deviant fish. If the deviant fisli is included K = 

 0.66, but if not, K = 0.82. We are inclined to 

 use K = 0.82 because the values for the four 

 fish were very similar and the protocol indicated 

 that the deviant fish may have been overly fa- 

 tigued when tested. Triakis appears to have 

 a relatively high coefficient but not too much 

 significance can be attached to the exact value 

 for Triakis or for Sardi^iops because these were 

 based on so few measurements. 



In sum, the speed-tail beat equation (Case II) 

 — Table 6 — was biologically as well as statisti- 

 cally relevant, was sensitive to specific differ- 

 ences in swimming behavior, provided an un- 

 biased correction for length, and made possible 

 a more accurate estimation of swimming speed 

 from tail beat frequency than heretofore has 

 been possible. 



TAIL BEAT AMPLITUDE 



We pointed out previously that tail beat ampli- 

 tude was a constant and was directly propoi-- 

 tional to length and consequently the size coeffi- 

 cients for amplitude are probably the same as 

 those for length. Thus amplitude (A) in centi- 

 meters can be substituted for length in the ori- 

 ginal Case II equation V = a^vl^/s -j_ ^ L * F. 

 When this was done for Trachurus using all 

 individual amplitude values (iV = 176) , we ob- 

 tained the equation; V = —6.5767/12/3 + 

 3.5637/1 * F. The amplitude coefficient may 

 be also estimated by substitution of the ampli- 

 tude-length relationship for Trachurus (A = 

 0.23177L) , into the Case II equation. 



The tail beat amplitude data collected by 

 Bainbridge (1958) were insufficient for specific 

 estimates of an amplitude coefficient. The mean 

 amplitudes for each of the fish we studied and 

 for each of those studied by Bainbridge were 

 nearly the same, when adjusted for body length. 

 Variation within a species was as great as that 

 between species (Figure 6). The relationship 



UJ 

 Q 



3 



Q. 



s 

 < 



Z 

 < 

 UJ 



S 



3- 



 CorosBius (FROM BfllNeRlOGE, 19581 

  Enq roulis 



• Leuciscus (FROM BfilNBRIOGE, 19581 

 D Solmo (FROM BaiNBRlDGE, 1958) 



Sofdino ps 



* Scomber 



o Trachurus 

 ^ Tnokis 



DO 



o i 



10 15 20 25 



TOTAL LENGTH (cm) 



30 



35 



Figure 6. — Relationship between mean tail beat ampli- 

 tude and length for every fish we studied and all those 

 studied by Bainbridge (1958), A = 0.21L. 



between mean tail beat amplitude and length 

 for all species combined was A = 0.21L. 



263 



