VLYMEN: SWIMMING ENERGETICS OF THE LARVAL ANCHOVY 



The difference between this and 77/2 is about 

 4'7(: . Thus, we expect the projected length and 

 real body length to differ only slightly. With 

 this confidence we make the following addi- 

 tional assumptions: 



F(Xxp, t) = XL. 



This assumption based on the error calculation 

 above postulates a linear relation between pro- 

 jected length and real length. Now xp/L =xp(t) 

 and is obtained from excursion analyses. We 

 can rewrite this as 



= L 



Xp(t) 



XXp 



Xp(t) 



X 



Xp ( t) 



XL 



= s 



A^l 



X^Xr 



Thus we chose to identify 



F(x, t) = xlxp(t) = s(x, t). 



The determination of the contour his) was 

 made using biologically accurate drawings of a 

 1.84-cm anchovy larva. The term h(s) was es- 

 tablished for the body distal to a vertical line 

 tangent to the gill plate as shown in Figure 4. 



Figure 4. — Lateral cross section of 1.84-cm anchovy larvae dis- 

 playing relationship of idealized contour function h{s) (see text) 

 to appropriate nondimensionalized morphometric parameters. 



From that point to the beginning of the tail h{s) 

 was taken as a constant and the relation his) = 

 0.038 L was found to hold. The dorsal and anal 

 fin contributions were neglected because the 

 plate approximation already constitutes an 

 upper bound estimate for Wj.. Thus, the neglect 



of these fins quantitatively yields a more realis- 

 tic estimate ofWj^. Using the notation of Figure 

 4 we have, 



his) 



fors^/ 



H 



X^l his) = 0.038 L for l^ <s^iljf + Ij.) 



(Th - 0.038 L) 

 his) = 0.038 L + ^-^ [s - ilfj + I J, )] 



for (//y + It) <s^L 



or using values in Figure 4 the last relation 

 may be written 



his) = 0.038L + 0.766 is - 0.906L;. 



The cross-sectional area A^ which appears in 

 the work integral for the head was determined 

 by randomly selecting Formalin-preserved an- 

 chovy larvae from 0.5 to 1.5 cm in length and 

 affixing them, via the Formalin surface tension 

 on their bodies, upright on the side of a small 

 inverted beaker. The largest cross section of the 

 head was then viewed directly with a Nikon op- 

 tical comparator and an outline traced from the 

 lighted viewing screen. Lengths of the bodies 

 were also measured with dial calipers at the 

 time the tracings were made. Subsequently the 

 tracing areas were measured with a planimeter 

 and corrected to the true value. A least squares 

 analysis of the results yielded the relation 

 Ah = 0.00423L where L is in centimeters and 

 Af^ is in square centimeters. The graph is plot- 

 ted along with the data in Figure 5. 



The representation for pis), the linear density 

 of the body, was regarded as constant for any 

 given length and calculated from data in 

 Lasker, et al., (1970). Assuming 90% water, the 

 wet weight of 0.5- to 1.6-cm larvae is then 

 given by 0.00319L^^^^' = pis) where L is in 

 centimeters and pis) is in grams per centime- 

 ter. 



The density of the seawater was taken for 

 T = 17°C and was 1.02454. This value was ob- 

 tained from tables published by the U.S. Navy 

 Hydrographic Office (1956). 



In my formulation I assume that the head is 

 propelled through the water as an inert object 

 attached to an undulating body. We want to 

 know the virtual mass and drag coefficient of 

 the inert head for use in the W^^ integral. Since 

 the shape of the anchovy larva's head is 



891 



