1. Introduction
Under cultivation, farmed chinook salmon have generally higher feed conver- sion ratios FCRs, higher mortality rates and lower growth rates than Atlantic
salmon. The FCR is the ratio of feed fed kg to weight gained kg. Note that throughout this paper, weight a force with the SI unit of Newton will have the
SI unit of kilogram, normally attributed to mass, following the convention used in fishery science. According to the Cooperative Assessment of Salmonid Health
program, which is being conducted through the British Columbia Salmon Farm- ers’ Association, typical FCR values in British Columbia in 1993 were 1.5 for
Atlantic salmon and 2.0 for chinook salmon over the entire production period. Atlantic salmon also had a much higher average harvest weight, at 4.3 as com-
pared with 2.5 kg for chinook salmon over the same growout period BCMAFF, 1993.
Chinook salmon are considered to be more environmentally sensitive than Atlantic salmon. Chinook salmon show symptoms of oxygen stress when dis-
solved oxygen is below saturation, whereas Atlantic salmon tolerate oxygen levels as low as 44 saturation Caine et al., 1987. Chinook salmon are
more sensitive to temperature fluctuations than Atlantic salmon, but Atlantic salmon become increasingly susceptible to Vibrio infections as salinity levels
drop below 15 parts per thousand Caine et al., 1987. Atlantic salmon show somewhat faster growth than chinook salmon at temperatures lower than 14°C,
which is the optimum temperature for growth for both species Pennell, 1992. Atlantic salmon can, therefore, be raised where chinook salmon cannot, for
example at a site with lower dissolved oxygen levels or greater temperature fluctuations.
Drag increases with swimming speed, bodily area exposed to flow and drag coefficient. Drag has been measured on some fishes dead drag, but only over a
small range of size and shape e.g. Blake, 1983. Chinook salmon tend to be deeper bodied with more area exposed to flow than Atlantic salmon. We hy-
pothesized that the higher FCRs and lower growth rates of chinook salmon are due, at least partly, to their higher energy expenditure while swimming. The
objectives of this research were to: 1 compare the swimming speeds and body dimensions of the two species over a wide range of size; 2 calculate drag and
power; and 3 determine whether differences in FCR and growth rate could be accounted for by differences in body morphology, drag and power.
2. Materials and methods
Utilizing data collected over a five year period and appropriate equations, drag coefficient and planform area were calculated for each species, and used to
calculate both drag and the power requirements of swimming. Details follow.
2
.
1
. Swimming speed data Average speed, length taken at the tail fork if present, height distance between
the dorsal and ventral sides at the widest point along a fish and weight of fish were measured while testing Fish Image Capturing and Sizing System FICASS on
salmon farms Shieh, 1996; Jones, 1997. FICASS includes underwater stereo cameras and an image capturing and analysis system Petrell et al., 1997. To obtain
the data, cameras were first lowered into a cage to videotape fish. Images were later used to calculate average swimming speed, length and weight. The number of
images sampled for swimming speed per sampling position, n, within a cage varied from ten to 60 depending on variability and was calculated for each sampling
position using
n = [t
2
s
2
]d
2
where t is the tabulated t statistic for a 95 confidence interval, d is the half-width of the confidence interval for our purposes, it was set to be 0.1 of the average value
of the swimming speed and s is the sample standard deviation Steel and Torrie, 1960. The low sample numbers were not considered a statistical concern, as
Boisclair 1992 found that sample size did not have a significant influence on mean speed estimates of fish. The same method was used to determine the number of
images needed to calculate the average fish weight per sampling position, except that d was set to be 0.05 of the average value of the weight. The sample size varied
between 56 and 120 fish. Individual swimming speed and length measurements were accurate to 9 3, while measurements on average fish weight were accurate to
9
7. Five different farming sites of Atlantic salmon totaling 26 different cages and three farming sites of chinook salmon totaling 14 different cages were
sampled to cover the growth cycle for each species 1 kg to harvest weight. In total, 24 and 81 measurements of average swimming speed, length and weight were
recorded for chinook and Atlantic salmonids, respectively.
Data were taken directly from production cages. Fish were held in cages 15 × 15 × 15 m
3
deep and were fed by farm workers to apparent satiation by broadcasting feed over the surface of the cage. Sites were low current sites
averaging 0.1 m s
− 1
. In addition to fish measurements, water temperature near the cameras was also measured.
2
.
2
. Body measurements Direct physical measurements were obtained over the course of developing the
FICASS system. These included length, height and weight measurements on 1539 Atlantic salmon from 18 cages, ranging in size from 0.42 to 8.50 kg and 840
chinook salmon from 17 cages, ranging in size from 0.009 to 4.91 kg. Girth measurements were done on fewer fish 445 in total to minimize handling stress.
Body measurements were accurate to 0.5 cm with the exception of the 9-g chinook salmon, which were accurate to 0.125 cm. Mass was accurate to 3 – 5 of the total
mass, depending on fish size. The data set included but was not limited to data from the sites where swimming speed was measured.
2
.
3
. Drag and power calculations Drag arises from two sources, pressure form and shear stress friction drag.
The total or profile drag, D, was calculated using the equation: D = 0.5rC
d
AV
2
1 where V equals swimming speed, r equals fluid density, C
d
equals drag coefficient and A is a reference area. Working estimates of drag coefficient can be determined
from listed data provided shapes are geometrically similar Gerhart and Gross, 1985. In some previous hydrodynamic models, fish have been assumed to have a
streamlined and rotationally symmetrical shape Blake, 1983; Tang and Wardle, 1992. The drag coefficient we used was calculated as in Eq. 2, assuming a
streamlined but not rotationally symmetrical body, similar to an airfoil Hoerner, 1958.
C
d
= 2C
f
[1 + 2HL + 100HL
4
] 2
For an airfoil, H is the height of the airfoil, L is the cord length and C
f
equals the friction drag coefficient. For our application to be analogous to an airfoil, we have
set H equal to the height of the fish and L equal to the length of the fish. The friction drag coefficient was calculated using Schoenherr’s formula for turbulent
skin friction drag on a plane surface Hoerner, 1958:
C
f −
0.5
= 3.46 log R
l
− 5.6
3 where R
l
is the Reynolds number based on fish length Reynolds number is defined as velocity times length over kinematic viscosity. In Eq. 2 HL is multiplied by
two to account for both sides of the fish. Eq. 2 implies that streamlining elongating the rear portion of the body as reflected in a lowering of the HL ratio
reduces profile drag. Streamlining for drag reduction is only effective up to a point, as with elongation comes an increase in ‘wetted surface area’ Eqs. 1 and 3,
which increases friction drag and therefore increases profile drag. Eqs. 2 and 3 were used to calculate the drag coefficient for both chinook salmon and Atlantic
salmon because both have the same general shape of an airfoil see Section 3, roundness. As well, calculated R
l
values indicated that the flow conditions were turbulent, and theoretical values for the skin friction drag coefficient for a flat plate
in turbulent flow have been shown to reasonably approximate the drag coefficient for salmonids Blake, 1983. Equation 1 calculates the effect of drag quite conserva-
tively as actual values would be higher due to turning, fins and added mass Blake, 1983.
The reference surface area was taken to be the planform area i.e. the area you would see if you looked at a swimming fish from above Gerhart and Gross, 1985.
Consistent with convention, the platform area of a fish was calculated as its length times its thickness. To obtain a value for thickness, data for girth and height, and
the equation representing the perimeter of an ellipse were used as follows. First, the shape of the cross section of a fish at its widest point was assumed to be an ellipse
with minor axis, T, equal to the thickness and major axis, H, equal to the height.
The perimeter of the ellipse which is defined mathematically to be approximately equal to [2p0.5T
2
+ H
2 0.5
] is therefore equal to the girth of the fish. The equation for perimeter was then rearranged to solve for T thickness given both H
height, and perimeter girth. To summarize, the drag formula that was used Eq. 1 is rewritten below
showing the substitutions for A and C
d
to illustrate the reliance that drag has on differences in body morphology and swimming speed.
D = rTLC
f
[1 + 2HL + 100HL
4
]V
2
As mentioned previously, drag would increase as the HL heightlength ratio increases or the fish becomes more blunt form drag increases, andor if the body
becomes longer friction drag increases. As girth was not measured on all fish, drag was calculated using the average
swimming speed found for each species on a subset of the fish 146 individual chinook salmon and 298 Atlantic salmon ranging in size from 1.0 to 6 kg which
had a complete data set of physical measurements of weight, girth, height and length. Power was calculated as drag Eq. 1 times swimming speed Blake, 1983.
Both power and drag were graphed against fish weight for both species. To further our understanding of how a fish might use available energy, the power data was
also used to calculate the distance a fish could move and the weight a fish could carry given 1 W s of available energy.
2
.
4
. Data transformation and statistical analysis Regression equations and coefficient of determination r
2
were calculated to compare relationships between direct measurements of weight and the various
dimensions of girth, length and height. For these variables, a power law model i.e. lnweight vs. lnheight was tested because the ln transformations were able to
produce linear plots. We did not imply by the use of these models a dependence of weight on girth, length or height; rather we used them to compare regression
coefficients between species. The average swimming speed of fish at every sampling location in a cage was compiled, and the strength of a relationship between speed,
water temperature and fish weight was determined by calculating r
2
. The F
max
test was used to test homogeneity of variance of swimming speed. Roundness, defined
as ‘a measure of the sharpness of the corners of a solid’, was also examined Mohsenin, 1986. Roundness of a fish was calculated as girth or circumference
Pheight or diameter. The strength of the straight-line relationship between roundness and fish weight was determined by calculating r
2
. For comparison of regression parameters between species, a modified t-test was
used. The t-test was used for comparison of means between species i.e. for roundness, speed. Normality was verified using Kolmogorov-Smirnov goodness of
fit tests, and homogeneity of variance was tested with the Hartley test. All of the above statistical tests were performed at the 95 confidence level.
2
.
5
. Effect of swimming on growth To examine the effect of swimming on growth, the total daily energy require-
ments for fish were compared to the energy requirements for swimming and growth only. Values for the total energy required were obtained from literature while the
energy required for swimming was calculated using our calculated values of power, as follows.
The total daily energy requirement was found by analyzing feed components, and assuming satiation and a balanced diet. Commercial salmon feeds are high-energy
diets comprised of 44 protein and 23 oil Jackson, 1988. The average caloric value of these two major energy sources, corrected for digestibility and the portion
present as nitrogen and therefore unavailable as energy is 3.9 kcal g
− 1
of protein and 8.0 kcal g
− 1
of fat Phillips, 1972. Based on these values and the percent breakdown of the diet, 1 kg of food has a total of 3556 kcal of energy from protein
and oil. This translates into a total of 16.0 kcal kg fish
− 1
day
− 1
calculated with a ration level of 4.5 × 10
− 3
kg of feed kg fish
− 1
day
− 1
, which is the recom- mended level for salmonids weighing over 2 kg in 8°C water Moore Clark Feed
Tables, 1993. The total energy requirements of swimming W s as a fraction of the energy
available in the diet can be calculated by integration i.e. determining the area under the curve generated by plotting power required for swimming against time.
However, our data produced plots of power against fish weight. To perform the integration, the unit of mass horizontal axis was converted to time by calculating
the time needed to grow from one size class to another. Hence, a 1 kg-sized fish might represent 100 days and a 2 kg-sized fish, 200 days. The transformation from
weight to time was achieved by employing the standard exponential growth equation and published growth rates, m day
− 1
as below: Time days = ln W
t
2
− ln W
t
1
m
− 1
where W
t
2
and W
t
1
represent fish weights at the end and beginning of a growth period, respectively. For this analysis the class size change during a growth period
was set at 0.5 kg. The average growth rates of Atlantic salmon at 8 – 12°C and ranging in size from 150 to 3000 g were obtained from Austreng et al. 1987. They
range from 1.9 to 0.67 day
− 1
. The growth rates of chinook salmon were set in a lower range to reflect the fact that they grow to a size of 2.5 kg during the same
time period it takes to produce a 4.3 kg Atlantic salmon. Next, the percentages of the energy budget used for swimming and growth were
determined. Published mass-balance equations provided the means of modeling the partitioning of food energy between the various metabolic processes within a fish,
such as tissue function and repair, synthesis of new tissue, and swimming. An energy budget for an individual fish takes the basic form: I = M + G + E where I is
the energy content of the food consumed over the time period, M is the energy lost in the form of heat produced during metabolism, G is the energy in both somatic
and reproductive growth, and E is the energy lost in faecal and excretory products Wootton, 1990. The energy budget for salmonids was taken to be similar to the
balanced energy budget of a carnivorous fish based on published data for 15 species of fish; 100I = 44 9 7M + 29 9 6G + 27 9 3E Brett and Groves, 1979.
The total metabolism can be further broken down into standard metabolism M
S
, feeding metabolism M
F
, active metabolism M
A
including swimming, and the heat increment, or energy of specific dynamic action SDA Fig. 1. The above
numeric model was used to reflect the change in growth due to a change in energy expenditure due to swimming. For example, if a species used 10 instead of 6.75
of its available energy for swimming, then according to Fig. 1 the energy available for growth would decrease from 29 of total energy to 25.75.
3. Results
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