Locomot ion of BI uef ish ARTHUR B. DuBOIS, GIOVANNI A. CAVAGNA AND RICHARD S. FOX Department of Physiology, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 191 74; Institute of H u m n Physiology, University of Milan, Milan, Italy, and Marine Biological Laboratory, Woods Hole, Massachusetts 02543
1. Pressures previously measured on the body surface of swimABSTRACT ming bluefish were resolved into their backward vectorial components to allow calculation of profile drag. It was 0.18 kg at a speed of 1.8 m/sec. Tangential drag was calculated as if for a thin plate of an area equal to that of the fish. It was 0.08 kg at 1.8 m/sec. Net drag, 0.26 kg, was the sum of profile and tangential drag. 2 . Thrust and drag also were calculated from the changes of acceleration measured during steady swimming, assuming that thrust took place only during the acceleration phase, whereas drag occurred during both acceleration and deceleration. This drag was 0.08 kg at a speed of 1.1 m/sec. It is compatible with the drag of 0.26 at 1.8 m/sec calculated from profile and tangential drag provided drag varies a s the square of velocity. 3. The force required to produce maximal acceleration was measured during a scare. It was calculated to be 6.9 kg at a peak acceleration of 3 g. 4. The compression strength of the vertebrae was found to be approximately 20 kg per cm2, or roughly three times the force encountered during maximal acceleration. This safety factor of 3 would be reduced when the back was curved, or if opposing groups of muscles were under tension. 5. The finding that a bluefish can accelerate at 3 g and that the vertebral column is strong enough to withstand this force indicates that the muscles and body structure of a bluefish would be able to withstand the force of gravity if the fish were otherwise equipped for terrestrial life. This fish may have evolved these strengths simultaneously with land animals. It is speculated that other fish may have evolved some degree of strength to overcome inertia and drag during aquatic locomotion, and this evolution may have been a prelude to terrestrial locomotion.
A fish, while swimming, is subject to hydrodynamic drag which is the sum of profile drag and tangential drag (skin friction). During a recent study (DuBois et al., '74) significant pressures were found on the body surface of swimming bluefish (Pomotamus saltatrix). From these pressures, the profile drag was calculated by summing the vectorial components of surface pressures in the caudal direction, and the approximate force overcoming skin friction was calculated using an equation for tangential force on a thin plate moving edgewise through the water. If the superficial and deep tissues of the body were soft, the forces described above would produce tissue deformation during locomotion. The vertebral bodies J. ExP. ZOOL., 195:
223-236
wouId be subjected to compression because they sustain the thrust of the tail against the inertia and drag of the body. The compressional strength of two vertebrae was measured and compared to the forces to which they would be subjected during maximal acceleration. They also would sustain this maximal thrust during steady swimming at peak velocity. During steady swimming the velocity varies rhythmically because acceleration occurrs during tail thrusts and deceleration takes place between thrusts The records of acceleration and velocity revealed that the patterns of swimming were different when the fish swam at different speeds. These patterns and the accompanying kinetic energy changes will be described. 223
224
A. B. DuBOIS. G. A. CAVAGNA AND R. S. FOX MATERIAL AND METHODS
Experimental material Ten bluefish (Pomotamus saltatrix) averaging 0.63 m in length, 1.9 kg in mass, and 0.30 m in maximal girth were used in this study. The fish were anesthetized in a 52 mg/l solution of tricaine methanesulfonate (Finquel, Ayerst Laboratories). The fish were then placed on a V board and supplied with half the concentration of anesthetic solution flowing through a tube into the mouth and over the gills. Accelerometer A two-axis accelerometer (Model MAC 2AD 5 MG, made by DSC, lnc., Bellevue, Washington) in a cylindrical case 4.1 cm in length and 0.8 cm in diameter was sealed into an acrylic block which had been carved to fit inside the bluefish’s stomach and to remain upright in conformity with the pressure of the abdominal wall. This was inserted through the mouth into the stomach, and connected by a 1.4 mm diameter cable to a Grass 4-channel direct writing oscillograph. The accelerometer and Grass recorder gave a 90% response in 0.015 sec with less than 10% overshoot. The record from the accelerometer in the stomach was compared with a simultaneously obtained record from a second accelerometer mounted in a balsa wood block clamped between the teeth of a bluefish resting on a V-board and oscillated by hand in air along the headward-tailward axis. The amplitude ration of the stomach accelerometer to the mouth accelerometer was 1.03 at 2.3 hz, and 1.2 at 3.5 hz, with no appreciable phase lag. Therefore, the dynamic calibration of the record from the stomach accelerometer was satisfactory for measurements made in this study. The accelerometer was calibrated before its insertion into the fish by tilting it u p or down or from side to side, presenting 1 g in each direction. Once in the stomach, it was calibrated in situ by tilting the fish from side to side, or head up or down, to verify the orientation of the axes. The fish was placed in the observation chamber of a water tunnel. Water tunnel and pool The water tunnel has been described
previously (DuBois et al., ’74). Briefly, it was a 5.5 m long, 0.3 m diameter octagonally sectioned wooden tunnel, mounted on an incline headed downward at 33” from the horizontal. The upper end of this was connected to a 3 m X 4.5 m oval pool from which sea water was allowed to flow through the tunnel. The rate of water flow was controlled by a hinged outlet door, cable, and handwinch. The fish was introduced through a removable hand-port into a central section of this tunnel. There were windows above and to the side, to allow observation of the fish, and grids above and below the compartment to limit the travel of the fish. The accelerometer cable was led out through a rubber stopper in the handport. Experimental procedure The recorder registered lateral acceleration on the first channel, forward acceleration on the second channel, electrically integrated forward acceleration (forward velocity changes) on the third channel, and mean water velocity on the fourth channel. Water velocity in the wooden tunnel was measured by using a pressure gauge to record the rate of decrease of depth of water in the pool. The area of the pool and the cross-sectional area of the wooden tunnel were known. After the fish had recovered from the anesthetic, measurements of acceleration were made while the fish swam at different water speeds during different runs. Each run lasted 15 to 30 seconds. The pool was refilled with sea water after two or three runs. The fish rested 5 to 20 minutes between runs. Three fish were placed in the pool to permit measurement of their acceleration during free swimming, and after a “scare.” After the study had been completed, the fish was transferred to the anesthetic solution, and a second calibration of the accelerometer was carried out in situ. The accelerometer was extracted through the mouth. The fish was weighed and measured, and then returned to the pool or to the sea. Vertebral strength A vertebral body was cut from the peduncle of the tail of a dead bluefish 0.63 m long and 2.3 kg in weight. The diameter was 1.0 cm, length 1.3 cm, density about
LOCOMOTION OF BLUEFISH
1.2 gm per cc. Another vertebra was taken from the mid-region of the back. It was 1.7 cm long, and 1.2 cm in diameter. Each of these was placed in an “Instron” slow crushing device which had a calibrated strain gauge in the load cell of the pedestal, and the force-length relationship was measured during two full cycles of compression and relaxation. Calculation of profile drag The net force responsible for drag was the sum of two forces both of which are directed backward on the body. One of these, profile drag, was calculated from the data in the preceding paper by DuBois et al. (‘74), for pressure measured at different points along the body surface of bluefish swimming at 4 mph (1.8 mlsec). The pressure on each point was multiplied by the area over which it acted, and this product in turn was multiplied by the sine of the angle formed between a line tangent to the skin at the point in question and
Fig. 1
225
another line drawn through the longitudinal axis of the fish. As part of the present study, we made measurements required for this calculation by using a fiberglass cast of a 0.69 m long dead bluefish. Strips of masking tape 2.54 cm in width were placed around the fish circumferentially at each 2.54 cm of length but not on the fins. Each tape was labelled with appropriate values for pressure on the corresponding parts of the body, using the measured pressure data, and interpolating where necessary (fig. 5). Tangents to the body surface were measured visually using a protractor. The sum of the products of pressure, area, and sine of the angle was determined in order to estimate the net profile drag at 1.8 m/sec. Calculation of tangential drag In the calculation of skin fraction, one can use the assumption that the drag acting on the surface of a fish and directed tangentially to that surface is equal to the
Single acceleration which resulted from scaring bluefish 5 of table 2 .
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A. B. DuBOIS, G. A. CAVAGNA AND R. S. FOX
drag that would act on a thin plate whose length and area would be equal to those of the fish, a plate moving edgewise through the water at a speed equal to that of the fish. This drag would be: D f = Cdf p SeV2
1
z
where Df = drag, in newtons, kg.m.sec-2; C d f = coefficient of drag, dimensionless; p = density, in kg/m3; Se = surface area exposed, in m2; V =velocity, in mfsec.
The coefficient of drag depends on Reynold’s number, which is calculated as follows:2.
where N = Reynold’s number, dimensionless; V = velocity, in mfsec; 1 =distance from the front of the fish, in m; u =kinematic viscosity, m2.
cycles, three forward accelerations decreasing in amplitude, and corresponding velocity changes. In some other sequences, not shown, the fish turned at the beginning of or soon after the start of his acceleration. We tabulated and measured the straight accelerations. Table 1 shows that one fish had 12 accelerations ranging from 1.0 to 2.5 g, resulting in velocity changes of 1.4 to 3.8 m/ sec in time intervals ranging from 0.10 to 0.36 sec. A second fish had ten accelerations ranging from 1.2 to 3.2 g with velocity changes 1.1 to 3.8 mlsec in time intervals of 0.1 to 0.2 sec. A third fish had five accelerations ranging from 1.1 to 2.3 g in 0.13 to 0.30 seconds.
Patterns of swimming The different patterns of swimming enThe kinematic viscosity is defined as: countered during the course of this study 3. u = yfp are listed in table 2. In the middle range where p =viscosity of water; p=density of of speed (0.5 to 1 m/sec), symmetric thrusts water. were found. Slightly asymmetric thrusts RESULTS occurred at middle and lower speed, and Maximal acceleration very asymmetric thrusts occurred at midRapid acceleration followed by coasting dle and higher speed. Measurements made occurred when the fish had been startled with the fish swimming in the pool showed by a sudden event such as a broomstick that these patterns occurred in the pool as inserted into the water or after he accel- well as in the water tunnel. Illustrations of the different patterns of erated spontaneously. Simple patterns of single accelerations are illustrated in fig- swimming are shown in figures 3 and 4. ures 1 and 2A. In figure 2B, a double for- The different patterns are described below: Single large accelerations occurred beward acceleration occurs accompanied by a two step increase of velocity. Figure 2C tween groups of small accelerations and is a variant of this; it is a double accelera- decelerations. An example of acceleration tion, but this time with a movement to one and velocity during this type of swimming side, then a pause, and a movement toward is shown in figure 3. There was an inthe other side. Notched forward accelera- crease of velocity, followed by lessening tion waves, and two step forward velocity of speed as normal tail beats occurred. changes, resulted from this motion. Fig- The illustration shows the sharp lateral ure 2D is a record of a spontaneous accel- accelerations which were accompanied by eration with three main lateral acceleration the increase of forward acceleration and sec -1.
TABLE 1
Accelerations of frightened bluefish, mean and range Fish (no)
Observations (no)
1
12 10 5
2 3
Acceleration (g)
2.0(1.0-2.5) 2.4(1.2-3.2) 1.9(1.1-2.3)
Duration of acceleration (sec)
0.21(0.10-0.36) 0.16(0.104.20) 0.19(0.13-0.30)
Velocity change (mlsec)
2.8(1.4-3.8) 2.2 (1.1-3.8)
-
Maximal acceleration attained with corresponding velocity change, and time to reach maximal velocity, after scaring bluefish.
Fig. 2 Accelerations produced by scaring bluefish 1 of table 2. A, B, C, and D represent different types of patterns described in the text.
LATERAL ACCELERATION
228
A. B. D u B O I S , G. A. CAVAGNA A N D R. S. FOX
LATERAL ACCELERATI
Fig. 3 One pattern of swimming: rapid accelerations separated by groups of lesser accelerations and decelerations. Fish 5 of table 2.
velocity. Therefore, there were a few lesser movements, and then a repetition of the sharp lateral movement, and so forth. Equal or symmetrical accelerations occurred rhythmically at double the lateral body frequency. Figure 4 A shows oscillations in the forward accelerometer record at twice the frequency of the lateral accelerometer record. Fluctuations of forward velocity also occurred at twice the frequency of the lateral body acceleration. This pattern indicates that the body is accelerated forward as the tail sweeps toward each side. Unequal accelerations were found during swimming. Figure 4B shows a record in which the frequency of forward acceleration is double that of the lateral acceleration, but where every other forward acceleration is large, whereas the ones in between are small. This pattern was sometimes seen at low speed. Often, one principal acceleration was found during each complete cycle, with a second acceleration of less amplitude (as in figs. 4C,D). The lesser acceleration in these records was shortly after or shortly before the greater acceleration. Sometimes the two peaks merged, forming a series of single large forward acceleration waves such as those seen in figure 3. A fish which has been anesthetized, instrumented, attached to a recorder by a
wire, and confined in a water tunnel may not be equal to one without these encumbrances. To control for this factor, we placed a bluefish which had not been instrumented beside one which had been. They swam together at low and moderate speed, usually in formation, in the pool. The fish with the accelerometer kept pace, tail beat for tail beat and glide for glide, with the uninstrumented fish. Yet, the instrumented fish showed asymmetric accelerations in the pool even though he was swimming straight ahead, and with no a p parent extra effort. Rhythmic fluctuations of momentum and kinetic energy during swimming The tail frequency and pattern of swimming, mean velocity, momentum, kinetic energy, and their peak to peak changes are listed in table 2. The speeds varied from 0.18 to 1.6 m/sec. The changes of momentum were calculated from the equation: change of momentum = mass X change of velocity. Only the mass of the fish, and not that of the entrained water, was used in this calculation. The kinetic energy (K.E.) was calculated from the equation : K.E. =
mass X (ve1ocity)z
where kinetic energy is given in joules, mass in kg, and velocity in m/sec. Kinetic
GI
-
0.1 G
SPEED:
A
B
0.47 M I S E C
C
1.05 M I S E C
D
Fig. 4 Other patterns of swimming: A. Forward accelerations at twice the fundamental frequency of lateral body motion. Fish 1, table 2. Accelerometers oriented well. B. Inequality of alternate peaks of forward acceleration. Fish 6, table 2. C. Unequal amplitude and spacing of alternate peaks. Fish 1, table 2. D. Similar to C, except for timing of peaks. Fish 6, table 2. Lateral accelerometer is tilted, underestimating amplitude of lateral acceleration in this fish.
0 . 5 0 M/SEC
0.2 M I S E C
,------.-__ -,--J
I
/
CHANGES OF FORWARD VELOCITY
1
FORWARD’AC GELERATION
1 0.1
LATERAL ACCELERATION
0.81 M I S E C
230
A. B. DuBOIS, G . A. CAVAGNA AND R, S. FOX TABLE 2
Fish (no)
Changes Changes of fwd. of Average velocity momentum K.E. (m.sec-1) (m.sec-1) (kg.m.sec-1) (joule)
Changes of K.E. (joule)
Amplitude oflateral velocity (m.sec.-l)
0.27
0.23 0.83 1.00
0.015 0.041 0.094 0.089 0.025 0.050 0.083 0.102
0.30 0.22 0.24 0.29 0.29 0.27
0.036 0.023 0.049 0.081 0.034 0.125
1.02 1.14 1.14 1.14 0.94 0.94
0.038 0.029 0.062 0.105 0.070 0.266
0.26 0.29 0.36 0.38 0.37 0.28
0.080 0.065 0.065 0.080 0.080 0.075
0.145 0.117 0.117 0.145 0.145 0.135
1.51 1.65 1.30 2.20 0.23
0.190 0.162 0.143 0.180 0.230 0.072
0.57 0.81 0.42 0.75 0.81 0.93 0.47
0.050 0.040 0.045 0.042 0.084 0.076 0.046
0.068 0.055 0.061 0.057 0.114 0.103 0.063
0.23 0.45 0.12 0.38 0.45 0.59 0.15
0.040 0.045 0.026 0.043 0.095 0.099 0.030
1.17 0.66 0.66
0.089 0.098 0.071
0.161 0.177 0.128
1.23 0.39 0.39
0.191 0.121 0.087
Tail freq. (hz)
(mph)
S1. asym. S1. asym. Vy. asym. Vy. asym. Symmet. Vy. asym Vy. asym. Vy. asym.
1.17 1.84 2.95 3.44 2.11 2.54 3.04 2.71
0.42 1.15 2.40 2.77 1.12 1.12 2.16 2.37
0.19 0.51 1.07 1.24 0.50 0.50 0.96 1.05
0.040 0.044 0.048 0.040 0.028 0.054 0.047 0.052
0.072 0.080 0.087 0.072 0.051 0.098 0.055 0.094
0.03 0.24 1.04 1.39 0.23
Symmet. Symmet. Vy. asym. Vy. asym. Symmet. Vy. asym.
3.00 2.83 2.73 2.57 2.15 2.24
2.38 2.40 2.40 2.40 2.29 2.29
1.06 1.12 1.12 1.12 1.02 1.02
0.020 0.013 0.027 0.045 0.019 0.069
Vy. Vy. Vy. Vy. Vy.
asym. asym. asym. asym. asym. Vy. asym.
3.26 2.91 2.86 2.94 3.38 2.94
2.91 3.02 2.70 2.69 3.49 1.13
1.29 1.35 1.20 1.20 1.56 0.50
1 2 3 4 5 6 7
Symmet. Symmet. S1. asym. S1. asym. Vy. asym. Vy. asym. S1. asym.
1.91 2.24 1.76 2.29 2.48 2.89 2.18
1.27 1.82 0.95 1.69 1.82 2.09 1.06
1 2 3
Vy. asym. S1. asym. S1. asym.
2.90 1.84 2.02
2.62 1.49 1.49
Run (no)
1 2 3 4 5
6 7 1 2
3 1 2 3
4 5 6
Swimming pattern
Forward velocity
1.30
0.37 0.30 0.30
Gait, tail frequency, mean forward velocity, changes of forward velocity with corresponding changes of momentum, average kinetic energy calculated from average forward velocity, changes of kinetic energy due to forward velocity changes, and peak to peak (negative to positive) amplitude of lateral velocity oscillations, at different speeds. The swimming pattern is classified a s slightly asymmetric, symmetric, or very asymmetric.
energy change was calculated from the K.E. at maximum minus K.E. at minimum speed. Although the speeds varied from 0.18 to 1.6 m/sec, the peak to peak changes of velocity, and therefore changes of momentum, seemed fairly constant throughout the speed range observed for each pattern o f swimming for any one fish. The velocity change was found to be greater with asymmetric patterns of swimming. And, different fish had different peak to peak excursions of velocity, possibly associated with the condition of the tail. The cyclical fluctuation of kinetic energy (AK.E. = K.E. max - K.E. min) increased as a function of speed at approximately the following rate: AK.E. (joules) = 0.1 X (m/sec)*, though with
considerable scatter. The frequency of the body cycle increased as the mean speed through the water increased (table 2). The last column of table 2 shows a p proximate figures for peak to peak excursions of lateral velocity (lateral velocity is the integral of lateral acceleration). Their mean was 0.30 mlsec, SD 0.048, SE 0.012. Since the lateral velocity oscillates around zero, the maximal velocity toward either side would be half the value of the peak to peak amplitude reported in table 2; it would be 0.15 mlsec for the velocity to each side. When the body moves laterally toward either side, the lateral velocity starts from zero, attains a maximum of 0.15 m/sec, then falls to zero again before the movement in the other direction begins. This lateral movement is translated
231
LOCOMOTION OF BLUEFISH TABLE 3
Calculation of profile drag
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24
15 3 0 -3 -7 - 7.7 -8 -6 -5 -4 -4 - 3.5 -3.5 -3 -2 -2 -2 -2 -1.5 -2 - 1.5 - 1.5
32 48 65 71 77 81 84 84 84 87 87 84 81 81 77 77 71 71 55 45 39 32 26 19
30 23 15 10 6.8 4.0 3.4 5.7 4.0 3.4 1.1 - 1.1 - 1.7 - 1.7 -5.7 -5.7 -6.3 -6.3 -6.3 -8.5 - 8.0 -5.7
0.0 0.0 0.0 0.0 0.0 -2.9 -2.9
-4.6 - 4.6 -4.6
0.50 0.39 0.26 0.17 0.12 0.07 0.06 0.05 0.04 0.03 0.01 - 0.01 -0.04 -0.04 -0.10 -0.10 -0.11 -0.11 -0.11 -0.12 -0.11 - 0.09
240 56 0 - 36 - 65 - 44 - 40 - 25 - 17 - 10 -3 11 11 10 15 15 16 16 9 11 6 4
A force acting on each inch of the bluefish is calculated as described in the text. Length intervals correspond with those shown in figure 5. 1 L is longitudinal segment, in inches. 2 P is pressure, in cm H20. 3 A is area in cm2. 4 8 is angle tangent to body surface; if there are two readings, the left one is tangential to dorsal surface, and the right one i s tangential to the lateral surface. 5 Sin 8 i s mean sine of the angles. 6 F is force in grams.
into a forward component which results in the changes of the forward speed of the fish seen in figure 4. One can compare the lateral speed changes with the resultant peak to peak oscillations of the forward speed. Thus in the same three fish, the mean oscillation of the forward velocity was 0.048 mlsec peak to peak, or 32% of the lateral velocity (half peak to peak amplitude) at an average forward velocity of 0.90 m/sec, range from 0.19 to 1.24 m/sec. Calculation of projik drag Using a fiberglass cast of a bluefish, measurements were made (table 3) in 2.54 cm bands showing mean estimated pressure on the surface (P) at 4 mph (1.8 mlsec), area (A), angle (0) of the surface (when the dorsal and lateral were unequal, they were listed separately as the left one dorsal, the right one lateral), mean sine of the angle (sin 0), and backward force calculated for each segment by the equation F =
P . A . sin 0. ZF (fig. 5) represents the sum of positive and negative profile forces at 4 mph (1.8 mlsec). The net profile drag was 0.180 kg force. This was the sum of a backward force of 0.296 kg due predominantly to the Pitot effect on the front part of the head, as far back as the eyes, then a forward directed force of 0.240 kg from the eyes to the widest part of the body near the center of the fish essentially due to the Bernoulli effect, and then a backward force of 0.124 kg from midbody to the peduncle of the tail. Thus, net profile force was 0.296 - 0.240 + 0.124 = 0.180 kg. Since the net profile drag represents the sum of large positive and negative numbers, each susceptible to errors of measurement, the final figure may be of questionable accuracy. The pressures on the body surface of the fish fluctuate as the fish swims (fig. 2 of DuBois et al., '74), but the time average was used in these calculations.
232
A. B. DuBOIS, G. A. CAVAGNA A N D R. S . FOX
LENGTH (INCHES) 0 I
I 2 3 4 5 6 7
8 9 10 It 12 13 14 15 16 17 18 19 20 21 22 23 24
I
I
I
I
d \ o
I
(gm)
I
I
I
I
-7
I
I
I
I
I
- 7 ) -3
I
I
I
-240
I
I
I
I
I
I
-3
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
-2
I
-I-
I
I
I
I
I
+ I24
-1
I
I
I
= 180gm
Fig. 5 Drawing of a fiberglass cast of a bluefish. Measurements were made in one inch bands showing mean estimated pressure on the surface in cm H,O at 4 mph. Interpolated pressures, area, angle of the surface, mean sine of the angle, and backward force calculated for each segment by the equation F = P . A . are listed in table 3. ZF represents the sum of positive and negative profile forces at 4 mph (1.8 mlsec).
Calculation of tangential drag of the dorsal, ventral, and caudal fins is Given that p = 1.02 X 10-3 kg . m-1 . taken into account, the surface would be sec-1 and p is 1,022 kg . m-3, and sub- about 20% greater, yielding a 20% greater stituting into eq. 3, we find that u = 1.00 tangential drag. Net drag at 1.8 mlsec would be 0.26 kg, X 10-6 m2 . sec-I. Given that the length of the fish is 0.61 m, and substituting this which is the sum of the profde drag, 0.180 and the above values into eq. 2, we find kg, and skin friction, 0.078 kg. that N = 1.79 X 0.61/1.00 X 10-6 = Compressional strength of the vertebrae 1.09 x 106, a value which is greater than 500,000, and this indicates that flow on the Force-length curves of the vertebrae were second half of the fish is transitional or measured (fig. 6). Hysteresis was observed, turbulent at this speed of 1.8 m/sec. and the compressed vertebrae did not fully The surface area of the body, measured recover their initial length. An inflection by application of strips of masking tape to point on the length-compression curve was the 0.69 m long fiberglass cast of a blue- seen at about 22 kg of force (28 kglcm2 fish, omitting the fins and tail, was 0.157 area) on the vertebra taken from the pemz. Using the relationship that area is duncle, and at about 19 kg (17 kglcm2) proportional to length squared, one can on the vertebra excised from the mid-length scale this surface down to that of a 0.61 m region. Definite slippage was seen at 45 kg. bluefish: 0.157 X 0.612/0.692equals 0.124 The maximal forces withstood were 65 and m*. This surface is like that of a plate 75 kg for these two vertebrates, respec0.61 m Iong and 0.10 m wide, with two tively. sides. The drag, Df, of such a plate is calcuThe relationship between thrust lated using eq. 1, as follows: Cd f is found and drag to be 3.72 X 10-3 for a Reynolds number of 1,090,000 according to a graph (J. K. Suppose a bluefish has a certain average Salisbury, ed., ’67). Substituting this into speed. To maintain this, he has to overeq. 1, Df = 0.00372 X 1,022 x 0.124 x come drag. When the force exerted by the 1.82 +- 2 = 0.76 newtons, or 0.76/9.8 = tail is greater than drag, there is a for0.078 kg force, or 78 gm force due to skin ward acceleration. Under steady state confriction at a speed of 1.8 m/sec. If the area ditions, the increase of velocity during
233
LOCOMOTION OF BLUEFISH
A
BONE LENGTH (mm)
B
LENGTH(mm)
Fig. 6 Compression and recovery stress-strain curves for two vertebrae removed from a fresh dead bluefish. Note inflection and yield points. A. Vertebra taken from peduncle of the tail, showing compression, relaxation, recompression, and relaxation. B. Vertebra taken from mid-back, also subjected to two full cycles of compression and relaxation.
acceleration must equal the decrease of velocity during deceleration. Or, the time integral of acceleration equals the time integr a1 of deceleration. The drag can be calculated during steady swimming on the following assumptions: 1. The thrust is limited to one half of each cycle. 2. The average drag during the acceleration period equals the average drag during the deceleration period. The decrease of speed during the deceleration would then be due only to drag. Conversely, the increase of speed during acceleration would be due to thrust minus drag. Since at steady speed the momentum gained is equal to the momentum lost, and since the thrust occurs during half the cycle, the force of thrust would equal twice the force of drag. The average deceleration occurring during each cycle was used to calculate the drag during swimming. The average of the two highest speeds of each of the five fish in table 2 was 2.45 mph or 1.1 m/sec, and the corresponding velocity changes averaged 0.065 mlsec., with a mean body frequency of 2.79 hz. Assuming a sinusoidal change of velocity (bottom tracings of fig. 4), the peak to peak acceleration would be 2 ?r f times the amplitude of the velocity change or 2 P X 2.79 X 0.065 = 1.13 m . sec-2, and this divided by 9.8 m . sec-2, which is the acceleration at 1 g, yields 0.12 g. The maximal deceleration drag would be half this, or 0.06 g, and the mean then would be this divided bv the sauare root of 2, or 0.06 X 0.7 = 0.04 g. F& the mean mass of 1.9 kg, this corresponds to a mean force to overcome drag of 1.9 X 0.04 = 0.08 kg at an
average speed of 1.1m/sec. The mean thrust would then be 0.16 kg, and the peak thrust 0.16 x *or 0.23 kg. DISCUSSION
In the present investigation, an accelerometer was placed in the fish, and used to record instantaneous acceleration in relation to the tail beat. Maximal thrust The maximal accelerations found following a scare of a fish ranged up to peak values of about 3 g. The time required to reach peak velocity amounted to about 0.2 seconds. The force necessary to produce such accelerations may be calculated from the equation: force = mass X acceleration.
Since the fish weighed 2.3 kg, at 3 g the force would be 3 X 2.3 = 6.9 kg. Drag during steady swimming The net drag calculated as the sum of profile and tangential drag at a velocity of 1.8 m/sec was 0.26 kg. The mean drag calculated from records of acceleration and deceleration during steady swimming at a mean velocity of 1.1 misec was 0.08 kg. These two calculations yield drag figures that are compatible with each other provided drag varies with the square of the velocity, as is commonly believed. The dif.erent patteTns of swimming of the bluefish The accelerometer records clearly show that the bluefish often uses an asymmetric forward thrust to propel himself through
234
A. B. DuBOIS, G. A. CAVAGNA AND R. S. FOX
the water, further substantiating a similar but tentative conclusion reached by DuBois et al. ('74), on the basis of the pattern of pressure fluctuation on the jaw during swimming, and movies of fish taken by others (Gray, '33). At speeds between 0.5 and 1 mlsec the bluefish tended to use both sides symmetrically, whereas at higher speeds he a p parently used a more asymmetric thrust. This asymmetry took the form of inequality of amplitude of the two accelerations which accompanied acceleration of the body to the right and left respectively or differences in time intervals such that the forward acceleration that accompanied lateral acceleration to the left followed quickly after that associated with the lateral acceleration to the right, or vice versa. The manner in which forward acceleration is coupled to lateral acceleration could not be deduced directly from the records obtained cluring this study. However, it was apparent that the amplitude of forward acceleration was related to the rate of increase and amplitude of lateral acceleration, whether to the right or left. The peak of forward acceleration was found at or before the peak of lateral acceleration. A concave upward lateral acceleration was accompanied or followed by a peak of forward acceleration. Because misalignment of the accelerometer theoretically could introduce false asymmetry into the accelerometer records, a careful review was made of each record to look for this artefact. In many of the experiments the swimming pattern would change from symmetric to asymmetric and back again, suggesting that the fish really changed his pattern of swimming. In some cases, individual rapid accelerations occurred when the lateral acceleration was either to the right or to the left, ruling out asymmetry of the accelerometer tracing. Furthermore, tilting the fish underwater confirmed excellent alignment in some fish which had asymmetric forward acceleration patterns. Oscillation of the body by hand from side to side then produced a negligible component of acceleration. All of these observations pointed to the conclusion that the asymmetric patterns were real and not artefactual. They were in keeping with the expectations derived from the previous paper.
Changes in m o m e n t u m and kinetic energy As the tail delivers a thrust to the water, the water is accelerated backward and the fish is propelled forward. This is the equivalent of saying that the tail beat imparts a forward momentum to the fish in exchange for a backward momentum given to the water, and this results in the observed changes of velocity. During the acceleration forward the thrust is greater than the drag, and during the deceleration the thrust is less than the drag, i.e. thrust = drag m . a. Assuming no thrust during the deceleration period, the kinetic energy imparted to the fish carries him forward throughout the interval between thrusts. However, during that time, the water drag slows his progress, dissipating part of the kinetic energy. This lost energy is replaced by the next thrust, and so forth. As mentioned above, the tail imparts velocity changes to the fish fairly independently of speed. Since the tail beat frequency increases with speed, the duration of the thrust is presumably less at high speed than at low speed. Therefore, in order to keep the momentum (force X time) constant, the force must increase as the duration of thrust decreases. In addition, it takes more energy to produce a constant velocity change at high speed than at low speed, because kinetic energy varies as the square of velocity. In conclusion, at higher speed each tail beat costs more energy, and also tail beats are more frequent.
+
Body surface pressures, locomotion, and body structures In a previous communication, we showed that the hydrodynamic pressure gradient along the body surface of the swimming bluefish was of the same order of magnitude as the hydrostatic transmural pressure gradient which would exist in the vertical direction in land animals if the body contained only liquid. We suggested that body structures capable of withstanding the hydrodynamic pressure gradient in fish would be useful to land animals in withstanding hydrostatic and gravitational forces. The present paper relates body surface pressures to the forces required for aquatic locomotion: Briefly stated, the forward thrust produces a forward body velocity which is
LOCOMOTION OF BLUEFISH
opposed by backward drag due to forces normal to and tangential to the body surface. The force normal to the surface is the source of the pressures that generate the transmural pressure gradients described above. The body structures withstand this transmural pressure and prevent soft tissue deformation. Strength required for aquatic and terrestrial locomotion A terrestrial vertebrate requires enough muscular strength to raise its weight off the ground against gravitational force. Since a bluefish can generate 3 g, it theoretically would be able to lift three times its own weight against gravity. This suggests that the strength required to accelerate and swim in water could be used in terrestrial locomotion if the fish had other attributes required for terrestrial life. In fact, bluefish can be seen to jump out of the water, thus momentarily raising their weight against a downward acceleration of 1 g. Common experience tells us that we can jump off the ground with either leg, implying a strength in each leg sufficient to overcome at least 1 g. Indeed, running and jumping yield measured upward accelerations of 2 or 3 g (Cavagna et al., ’64). Both the fish and the human have achieved a certain degree of strength. But, the fish overcomes inertia and hydrodynamic drag whereas the human overcomes inertia and gravitational force. Vertebral strength required for aquatic locomotion One question asked in this investigation was whether the vertebral bodies are just strong enough, but not stronger than necessary, to sustain the compression force exerted by the tail fin as it thrusts the fish through and against the water. The force which would be required to accelerate the fish at a rate of 3 g was calculated to be 6.9 kg. Measurements of the compression strength suggest that the tail vertebrae could comfortably withstand not more than 20 kg if the back were straight. If the back were curved, so that only a third of the vertebral body touched its neighbor, then the initial yield point would
235
be equal to the maximal thrust. The finding that the vertebrae are strong enough but not too strong supports the view that the vertebral column serves to prevent the collapse which otherwise would occur. A vertebra which can withstand a force of 3 g could support the vertical weight of three fish on the Earths surface, given the circumstances. When the weight acts perpendicularly to the vertebral column, as in quadrupeds, the upper part of the vertebrae would be compressed, and the lower part of the vertebrae, ligaments, and muscles would be placed under tension. Fish and land animals may have followed separate parallel pathways in evolving the muscles and body structures required for aquatic and terrestrial locomotion. However, an alternative possibility is that aquatic locomotion may have played an evolutionary role in selection of bodies of vertebrates capable of terrestrial locomotion. ACKNOWLEDGMENTS
The authors wish to thank Dr. James Mavor of the Woods Hole Oceanographic Institute and Dr. Nicholas Newman of the Massachusetts Institute of Technology for their kind assistance in the calculation of skin friction. Mr. Eugene Tassinari, of the MBL Supply Department caught most of the bluefish used in this study. Dr. DuBois was the recipient of a Research Career Award of the National Institutes of Health. This research was supported in part by contract NO00 14-67-A-0216-0017 between the Physiology Branch of the Officie of Naval Research and the University of Pennsylvania, and in part by a research grant 5 R01 HL 04797 from the National Institutes of Health. LITERATURE CITED Cavagna, G. A., F. P. Saibene and R. Margaria 1964 Mechanical work in running. J. Appl. Physiol., 19: 249-256. DuBois, A. B., G . A. Cavagna and R. S . FOX 1974 Pressure distribution on the body surface of swimming fish. J. Exp. Biol., 60: 581-591. Gray, J. 1933 See figure 5 (mackerel) and figure 6 (whiting) in: Studies in animal locomotion. I. The movement of fish with special reference to the eel. J. Exp. Biol., 10: 88-104. Salisbury, J. K., ed. 1967 Chap. 15 in Kent’s Mechanical Engineer’s Handbook. Twelfth ed. Power Volume. Wiley, New York, London and Sydney.
1. Pressures previously measured on the body surface of swimABSTRACT ming bluefish were resolved into their backward vectorial components to allow calculation of profile drag. It was 0.18 kg at a speed of 1.8 m/sec. Tangential drag was calculated as if for a thin plate of an area equal to that of the fish. It was 0.08 kg at 1.8 m/sec. Net drag, 0.26 kg, was the sum of profile and tangential drag. 2 . Thrust and drag also were calculated from the changes of acceleration measured during steady swimming, assuming that thrust took place only during the acceleration phase, whereas drag occurred during both acceleration and deceleration. This drag was 0.08 kg at a speed of 1.1 m/sec. It is compatible with the drag of 0.26 at 1.8 m/sec calculated from profile and tangential drag provided drag varies a s the square of velocity. 3. The force required to produce maximal acceleration was measured during a scare. It was calculated to be 6.9 kg at a peak acceleration of 3 g. 4. The compression strength of the vertebrae was found to be approximately 20 kg per cm2, or roughly three times the force encountered during maximal acceleration. This safety factor of 3 would be reduced when the back was curved, or if opposing groups of muscles were under tension. 5. The finding that a bluefish can accelerate at 3 g and that the vertebral column is strong enough to withstand this force indicates that the muscles and body structure of a bluefish would be able to withstand the force of gravity if the fish were otherwise equipped for terrestrial life. This fish may have evolved these strengths simultaneously with land animals. It is speculated that other fish may have evolved some degree of strength to overcome inertia and drag during aquatic locomotion, and this evolution may have been a prelude to terrestrial locomotion.
A fish, while swimming, is subject to hydrodynamic drag which is the sum of profile drag and tangential drag (skin friction). During a recent study (DuBois et al., '74) significant pressures were found on the body surface of swimming bluefish (Pomotamus saltatrix). From these pressures, the profile drag was calculated by summing the vectorial components of surface pressures in the caudal direction, and the approximate force overcoming skin friction was calculated using an equation for tangential force on a thin plate moving edgewise through the water. If the superficial and deep tissues of the body were soft, the forces described above would produce tissue deformation during locomotion. The vertebral bodies J. ExP. ZOOL., 195:
223-236
wouId be subjected to compression because they sustain the thrust of the tail against the inertia and drag of the body. The compressional strength of two vertebrae was measured and compared to the forces to which they would be subjected during maximal acceleration. They also would sustain this maximal thrust during steady swimming at peak velocity. During steady swimming the velocity varies rhythmically because acceleration occurrs during tail thrusts and deceleration takes place between thrusts The records of acceleration and velocity revealed that the patterns of swimming were different when the fish swam at different speeds. These patterns and the accompanying kinetic energy changes will be described. 223
224
A. B. DuBOIS. G. A. CAVAGNA AND R. S. FOX MATERIAL AND METHODS
Experimental material Ten bluefish (Pomotamus saltatrix) averaging 0.63 m in length, 1.9 kg in mass, and 0.30 m in maximal girth were used in this study. The fish were anesthetized in a 52 mg/l solution of tricaine methanesulfonate (Finquel, Ayerst Laboratories). The fish were then placed on a V board and supplied with half the concentration of anesthetic solution flowing through a tube into the mouth and over the gills. Accelerometer A two-axis accelerometer (Model MAC 2AD 5 MG, made by DSC, lnc., Bellevue, Washington) in a cylindrical case 4.1 cm in length and 0.8 cm in diameter was sealed into an acrylic block which had been carved to fit inside the bluefish’s stomach and to remain upright in conformity with the pressure of the abdominal wall. This was inserted through the mouth into the stomach, and connected by a 1.4 mm diameter cable to a Grass 4-channel direct writing oscillograph. The accelerometer and Grass recorder gave a 90% response in 0.015 sec with less than 10% overshoot. The record from the accelerometer in the stomach was compared with a simultaneously obtained record from a second accelerometer mounted in a balsa wood block clamped between the teeth of a bluefish resting on a V-board and oscillated by hand in air along the headward-tailward axis. The amplitude ration of the stomach accelerometer to the mouth accelerometer was 1.03 at 2.3 hz, and 1.2 at 3.5 hz, with no appreciable phase lag. Therefore, the dynamic calibration of the record from the stomach accelerometer was satisfactory for measurements made in this study. The accelerometer was calibrated before its insertion into the fish by tilting it u p or down or from side to side, presenting 1 g in each direction. Once in the stomach, it was calibrated in situ by tilting the fish from side to side, or head up or down, to verify the orientation of the axes. The fish was placed in the observation chamber of a water tunnel. Water tunnel and pool The water tunnel has been described
previously (DuBois et al., ’74). Briefly, it was a 5.5 m long, 0.3 m diameter octagonally sectioned wooden tunnel, mounted on an incline headed downward at 33” from the horizontal. The upper end of this was connected to a 3 m X 4.5 m oval pool from which sea water was allowed to flow through the tunnel. The rate of water flow was controlled by a hinged outlet door, cable, and handwinch. The fish was introduced through a removable hand-port into a central section of this tunnel. There were windows above and to the side, to allow observation of the fish, and grids above and below the compartment to limit the travel of the fish. The accelerometer cable was led out through a rubber stopper in the handport. Experimental procedure The recorder registered lateral acceleration on the first channel, forward acceleration on the second channel, electrically integrated forward acceleration (forward velocity changes) on the third channel, and mean water velocity on the fourth channel. Water velocity in the wooden tunnel was measured by using a pressure gauge to record the rate of decrease of depth of water in the pool. The area of the pool and the cross-sectional area of the wooden tunnel were known. After the fish had recovered from the anesthetic, measurements of acceleration were made while the fish swam at different water speeds during different runs. Each run lasted 15 to 30 seconds. The pool was refilled with sea water after two or three runs. The fish rested 5 to 20 minutes between runs. Three fish were placed in the pool to permit measurement of their acceleration during free swimming, and after a “scare.” After the study had been completed, the fish was transferred to the anesthetic solution, and a second calibration of the accelerometer was carried out in situ. The accelerometer was extracted through the mouth. The fish was weighed and measured, and then returned to the pool or to the sea. Vertebral strength A vertebral body was cut from the peduncle of the tail of a dead bluefish 0.63 m long and 2.3 kg in weight. The diameter was 1.0 cm, length 1.3 cm, density about
LOCOMOTION OF BLUEFISH
1.2 gm per cc. Another vertebra was taken from the mid-region of the back. It was 1.7 cm long, and 1.2 cm in diameter. Each of these was placed in an “Instron” slow crushing device which had a calibrated strain gauge in the load cell of the pedestal, and the force-length relationship was measured during two full cycles of compression and relaxation. Calculation of profile drag The net force responsible for drag was the sum of two forces both of which are directed backward on the body. One of these, profile drag, was calculated from the data in the preceding paper by DuBois et al. (‘74), for pressure measured at different points along the body surface of bluefish swimming at 4 mph (1.8 mlsec). The pressure on each point was multiplied by the area over which it acted, and this product in turn was multiplied by the sine of the angle formed between a line tangent to the skin at the point in question and
Fig. 1
225
another line drawn through the longitudinal axis of the fish. As part of the present study, we made measurements required for this calculation by using a fiberglass cast of a 0.69 m long dead bluefish. Strips of masking tape 2.54 cm in width were placed around the fish circumferentially at each 2.54 cm of length but not on the fins. Each tape was labelled with appropriate values for pressure on the corresponding parts of the body, using the measured pressure data, and interpolating where necessary (fig. 5). Tangents to the body surface were measured visually using a protractor. The sum of the products of pressure, area, and sine of the angle was determined in order to estimate the net profile drag at 1.8 m/sec. Calculation of tangential drag In the calculation of skin fraction, one can use the assumption that the drag acting on the surface of a fish and directed tangentially to that surface is equal to the
Single acceleration which resulted from scaring bluefish 5 of table 2 .
226
A. B. DuBOIS, G. A. CAVAGNA AND R. S. FOX
drag that would act on a thin plate whose length and area would be equal to those of the fish, a plate moving edgewise through the water at a speed equal to that of the fish. This drag would be: D f = Cdf p SeV2
1
z
where Df = drag, in newtons, kg.m.sec-2; C d f = coefficient of drag, dimensionless; p = density, in kg/m3; Se = surface area exposed, in m2; V =velocity, in mfsec.
The coefficient of drag depends on Reynold’s number, which is calculated as follows:2.
where N = Reynold’s number, dimensionless; V = velocity, in mfsec; 1 =distance from the front of the fish, in m; u =kinematic viscosity, m2.
cycles, three forward accelerations decreasing in amplitude, and corresponding velocity changes. In some other sequences, not shown, the fish turned at the beginning of or soon after the start of his acceleration. We tabulated and measured the straight accelerations. Table 1 shows that one fish had 12 accelerations ranging from 1.0 to 2.5 g, resulting in velocity changes of 1.4 to 3.8 m/ sec in time intervals ranging from 0.10 to 0.36 sec. A second fish had ten accelerations ranging from 1.2 to 3.2 g with velocity changes 1.1 to 3.8 mlsec in time intervals of 0.1 to 0.2 sec. A third fish had five accelerations ranging from 1.1 to 2.3 g in 0.13 to 0.30 seconds.
Patterns of swimming The different patterns of swimming enThe kinematic viscosity is defined as: countered during the course of this study 3. u = yfp are listed in table 2. In the middle range where p =viscosity of water; p=density of of speed (0.5 to 1 m/sec), symmetric thrusts water. were found. Slightly asymmetric thrusts RESULTS occurred at middle and lower speed, and Maximal acceleration very asymmetric thrusts occurred at midRapid acceleration followed by coasting dle and higher speed. Measurements made occurred when the fish had been startled with the fish swimming in the pool showed by a sudden event such as a broomstick that these patterns occurred in the pool as inserted into the water or after he accel- well as in the water tunnel. Illustrations of the different patterns of erated spontaneously. Simple patterns of single accelerations are illustrated in fig- swimming are shown in figures 3 and 4. ures 1 and 2A. In figure 2B, a double for- The different patterns are described below: Single large accelerations occurred beward acceleration occurs accompanied by a two step increase of velocity. Figure 2C tween groups of small accelerations and is a variant of this; it is a double accelera- decelerations. An example of acceleration tion, but this time with a movement to one and velocity during this type of swimming side, then a pause, and a movement toward is shown in figure 3. There was an inthe other side. Notched forward accelera- crease of velocity, followed by lessening tion waves, and two step forward velocity of speed as normal tail beats occurred. changes, resulted from this motion. Fig- The illustration shows the sharp lateral ure 2D is a record of a spontaneous accel- accelerations which were accompanied by eration with three main lateral acceleration the increase of forward acceleration and sec -1.
TABLE 1
Accelerations of frightened bluefish, mean and range Fish (no)
Observations (no)
1
12 10 5
2 3
Acceleration (g)
2.0(1.0-2.5) 2.4(1.2-3.2) 1.9(1.1-2.3)
Duration of acceleration (sec)
0.21(0.10-0.36) 0.16(0.104.20) 0.19(0.13-0.30)
Velocity change (mlsec)
2.8(1.4-3.8) 2.2 (1.1-3.8)
-
Maximal acceleration attained with corresponding velocity change, and time to reach maximal velocity, after scaring bluefish.
Fig. 2 Accelerations produced by scaring bluefish 1 of table 2. A, B, C, and D represent different types of patterns described in the text.
LATERAL ACCELERATION
228
A. B. D u B O I S , G. A. CAVAGNA A N D R. S. FOX
LATERAL ACCELERATI
Fig. 3 One pattern of swimming: rapid accelerations separated by groups of lesser accelerations and decelerations. Fish 5 of table 2.
velocity. Therefore, there were a few lesser movements, and then a repetition of the sharp lateral movement, and so forth. Equal or symmetrical accelerations occurred rhythmically at double the lateral body frequency. Figure 4 A shows oscillations in the forward accelerometer record at twice the frequency of the lateral accelerometer record. Fluctuations of forward velocity also occurred at twice the frequency of the lateral body acceleration. This pattern indicates that the body is accelerated forward as the tail sweeps toward each side. Unequal accelerations were found during swimming. Figure 4B shows a record in which the frequency of forward acceleration is double that of the lateral acceleration, but where every other forward acceleration is large, whereas the ones in between are small. This pattern was sometimes seen at low speed. Often, one principal acceleration was found during each complete cycle, with a second acceleration of less amplitude (as in figs. 4C,D). The lesser acceleration in these records was shortly after or shortly before the greater acceleration. Sometimes the two peaks merged, forming a series of single large forward acceleration waves such as those seen in figure 3. A fish which has been anesthetized, instrumented, attached to a recorder by a
wire, and confined in a water tunnel may not be equal to one without these encumbrances. To control for this factor, we placed a bluefish which had not been instrumented beside one which had been. They swam together at low and moderate speed, usually in formation, in the pool. The fish with the accelerometer kept pace, tail beat for tail beat and glide for glide, with the uninstrumented fish. Yet, the instrumented fish showed asymmetric accelerations in the pool even though he was swimming straight ahead, and with no a p parent extra effort. Rhythmic fluctuations of momentum and kinetic energy during swimming The tail frequency and pattern of swimming, mean velocity, momentum, kinetic energy, and their peak to peak changes are listed in table 2. The speeds varied from 0.18 to 1.6 m/sec. The changes of momentum were calculated from the equation: change of momentum = mass X change of velocity. Only the mass of the fish, and not that of the entrained water, was used in this calculation. The kinetic energy (K.E.) was calculated from the equation : K.E. =
mass X (ve1ocity)z
where kinetic energy is given in joules, mass in kg, and velocity in m/sec. Kinetic
GI
-
0.1 G
SPEED:
A
B
0.47 M I S E C
C
1.05 M I S E C
D
Fig. 4 Other patterns of swimming: A. Forward accelerations at twice the fundamental frequency of lateral body motion. Fish 1, table 2. Accelerometers oriented well. B. Inequality of alternate peaks of forward acceleration. Fish 6, table 2. C. Unequal amplitude and spacing of alternate peaks. Fish 1, table 2. D. Similar to C, except for timing of peaks. Fish 6, table 2. Lateral accelerometer is tilted, underestimating amplitude of lateral acceleration in this fish.
0 . 5 0 M/SEC
0.2 M I S E C
,------.-__ -,--J
I
/
CHANGES OF FORWARD VELOCITY
1
FORWARD’AC GELERATION
1 0.1
LATERAL ACCELERATION
0.81 M I S E C
230
A. B. DuBOIS, G . A. CAVAGNA AND R, S. FOX TABLE 2
Fish (no)
Changes Changes of fwd. of Average velocity momentum K.E. (m.sec-1) (m.sec-1) (kg.m.sec-1) (joule)
Changes of K.E. (joule)
Amplitude oflateral velocity (m.sec.-l)
0.27
0.23 0.83 1.00
0.015 0.041 0.094 0.089 0.025 0.050 0.083 0.102
0.30 0.22 0.24 0.29 0.29 0.27
0.036 0.023 0.049 0.081 0.034 0.125
1.02 1.14 1.14 1.14 0.94 0.94
0.038 0.029 0.062 0.105 0.070 0.266
0.26 0.29 0.36 0.38 0.37 0.28
0.080 0.065 0.065 0.080 0.080 0.075
0.145 0.117 0.117 0.145 0.145 0.135
1.51 1.65 1.30 2.20 0.23
0.190 0.162 0.143 0.180 0.230 0.072
0.57 0.81 0.42 0.75 0.81 0.93 0.47
0.050 0.040 0.045 0.042 0.084 0.076 0.046
0.068 0.055 0.061 0.057 0.114 0.103 0.063
0.23 0.45 0.12 0.38 0.45 0.59 0.15
0.040 0.045 0.026 0.043 0.095 0.099 0.030
1.17 0.66 0.66
0.089 0.098 0.071
0.161 0.177 0.128
1.23 0.39 0.39
0.191 0.121 0.087
Tail freq. (hz)
(mph)
S1. asym. S1. asym. Vy. asym. Vy. asym. Symmet. Vy. asym Vy. asym. Vy. asym.
1.17 1.84 2.95 3.44 2.11 2.54 3.04 2.71
0.42 1.15 2.40 2.77 1.12 1.12 2.16 2.37
0.19 0.51 1.07 1.24 0.50 0.50 0.96 1.05
0.040 0.044 0.048 0.040 0.028 0.054 0.047 0.052
0.072 0.080 0.087 0.072 0.051 0.098 0.055 0.094
0.03 0.24 1.04 1.39 0.23
Symmet. Symmet. Vy. asym. Vy. asym. Symmet. Vy. asym.
3.00 2.83 2.73 2.57 2.15 2.24
2.38 2.40 2.40 2.40 2.29 2.29
1.06 1.12 1.12 1.12 1.02 1.02
0.020 0.013 0.027 0.045 0.019 0.069
Vy. Vy. Vy. Vy. Vy.
asym. asym. asym. asym. asym. Vy. asym.
3.26 2.91 2.86 2.94 3.38 2.94
2.91 3.02 2.70 2.69 3.49 1.13
1.29 1.35 1.20 1.20 1.56 0.50
1 2 3 4 5 6 7
Symmet. Symmet. S1. asym. S1. asym. Vy. asym. Vy. asym. S1. asym.
1.91 2.24 1.76 2.29 2.48 2.89 2.18
1.27 1.82 0.95 1.69 1.82 2.09 1.06
1 2 3
Vy. asym. S1. asym. S1. asym.
2.90 1.84 2.02
2.62 1.49 1.49
Run (no)
1 2 3 4 5
6 7 1 2
3 1 2 3
4 5 6
Swimming pattern
Forward velocity
1.30
0.37 0.30 0.30
Gait, tail frequency, mean forward velocity, changes of forward velocity with corresponding changes of momentum, average kinetic energy calculated from average forward velocity, changes of kinetic energy due to forward velocity changes, and peak to peak (negative to positive) amplitude of lateral velocity oscillations, at different speeds. The swimming pattern is classified a s slightly asymmetric, symmetric, or very asymmetric.
energy change was calculated from the K.E. at maximum minus K.E. at minimum speed. Although the speeds varied from 0.18 to 1.6 m/sec, the peak to peak changes of velocity, and therefore changes of momentum, seemed fairly constant throughout the speed range observed for each pattern o f swimming for any one fish. The velocity change was found to be greater with asymmetric patterns of swimming. And, different fish had different peak to peak excursions of velocity, possibly associated with the condition of the tail. The cyclical fluctuation of kinetic energy (AK.E. = K.E. max - K.E. min) increased as a function of speed at approximately the following rate: AK.E. (joules) = 0.1 X (m/sec)*, though with
considerable scatter. The frequency of the body cycle increased as the mean speed through the water increased (table 2). The last column of table 2 shows a p proximate figures for peak to peak excursions of lateral velocity (lateral velocity is the integral of lateral acceleration). Their mean was 0.30 mlsec, SD 0.048, SE 0.012. Since the lateral velocity oscillates around zero, the maximal velocity toward either side would be half the value of the peak to peak amplitude reported in table 2; it would be 0.15 mlsec for the velocity to each side. When the body moves laterally toward either side, the lateral velocity starts from zero, attains a maximum of 0.15 m/sec, then falls to zero again before the movement in the other direction begins. This lateral movement is translated
231
LOCOMOTION OF BLUEFISH TABLE 3
Calculation of profile drag
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24
15 3 0 -3 -7 - 7.7 -8 -6 -5 -4 -4 - 3.5 -3.5 -3 -2 -2 -2 -2 -1.5 -2 - 1.5 - 1.5
32 48 65 71 77 81 84 84 84 87 87 84 81 81 77 77 71 71 55 45 39 32 26 19
30 23 15 10 6.8 4.0 3.4 5.7 4.0 3.4 1.1 - 1.1 - 1.7 - 1.7 -5.7 -5.7 -6.3 -6.3 -6.3 -8.5 - 8.0 -5.7
0.0 0.0 0.0 0.0 0.0 -2.9 -2.9
-4.6 - 4.6 -4.6
0.50 0.39 0.26 0.17 0.12 0.07 0.06 0.05 0.04 0.03 0.01 - 0.01 -0.04 -0.04 -0.10 -0.10 -0.11 -0.11 -0.11 -0.12 -0.11 - 0.09
240 56 0 - 36 - 65 - 44 - 40 - 25 - 17 - 10 -3 11 11 10 15 15 16 16 9 11 6 4
A force acting on each inch of the bluefish is calculated as described in the text. Length intervals correspond with those shown in figure 5. 1 L is longitudinal segment, in inches. 2 P is pressure, in cm H20. 3 A is area in cm2. 4 8 is angle tangent to body surface; if there are two readings, the left one is tangential to dorsal surface, and the right one i s tangential to the lateral surface. 5 Sin 8 i s mean sine of the angles. 6 F is force in grams.
into a forward component which results in the changes of the forward speed of the fish seen in figure 4. One can compare the lateral speed changes with the resultant peak to peak oscillations of the forward speed. Thus in the same three fish, the mean oscillation of the forward velocity was 0.048 mlsec peak to peak, or 32% of the lateral velocity (half peak to peak amplitude) at an average forward velocity of 0.90 m/sec, range from 0.19 to 1.24 m/sec. Calculation of projik drag Using a fiberglass cast of a bluefish, measurements were made (table 3) in 2.54 cm bands showing mean estimated pressure on the surface (P) at 4 mph (1.8 mlsec), area (A), angle (0) of the surface (when the dorsal and lateral were unequal, they were listed separately as the left one dorsal, the right one lateral), mean sine of the angle (sin 0), and backward force calculated for each segment by the equation F =
P . A . sin 0. ZF (fig. 5) represents the sum of positive and negative profile forces at 4 mph (1.8 mlsec). The net profile drag was 0.180 kg force. This was the sum of a backward force of 0.296 kg due predominantly to the Pitot effect on the front part of the head, as far back as the eyes, then a forward directed force of 0.240 kg from the eyes to the widest part of the body near the center of the fish essentially due to the Bernoulli effect, and then a backward force of 0.124 kg from midbody to the peduncle of the tail. Thus, net profile force was 0.296 - 0.240 + 0.124 = 0.180 kg. Since the net profile drag represents the sum of large positive and negative numbers, each susceptible to errors of measurement, the final figure may be of questionable accuracy. The pressures on the body surface of the fish fluctuate as the fish swims (fig. 2 of DuBois et al., '74), but the time average was used in these calculations.
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A. B. DuBOIS, G. A. CAVAGNA A N D R. S . FOX
LENGTH (INCHES) 0 I
I 2 3 4 5 6 7
8 9 10 It 12 13 14 15 16 17 18 19 20 21 22 23 24
I
I
I
I
d \ o
I
(gm)
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-7
I
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- 7 ) -3
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-240
I
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I
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-3
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I
I
I
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-2
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-I-
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+ I24
-1
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= 180gm
Fig. 5 Drawing of a fiberglass cast of a bluefish. Measurements were made in one inch bands showing mean estimated pressure on the surface in cm H,O at 4 mph. Interpolated pressures, area, angle of the surface, mean sine of the angle, and backward force calculated for each segment by the equation F = P . A . are listed in table 3. ZF represents the sum of positive and negative profile forces at 4 mph (1.8 mlsec).
Calculation of tangential drag of the dorsal, ventral, and caudal fins is Given that p = 1.02 X 10-3 kg . m-1 . taken into account, the surface would be sec-1 and p is 1,022 kg . m-3, and sub- about 20% greater, yielding a 20% greater stituting into eq. 3, we find that u = 1.00 tangential drag. Net drag at 1.8 mlsec would be 0.26 kg, X 10-6 m2 . sec-I. Given that the length of the fish is 0.61 m, and substituting this which is the sum of the profde drag, 0.180 and the above values into eq. 2, we find kg, and skin friction, 0.078 kg. that N = 1.79 X 0.61/1.00 X 10-6 = Compressional strength of the vertebrae 1.09 x 106, a value which is greater than 500,000, and this indicates that flow on the Force-length curves of the vertebrae were second half of the fish is transitional or measured (fig. 6). Hysteresis was observed, turbulent at this speed of 1.8 m/sec. and the compressed vertebrae did not fully The surface area of the body, measured recover their initial length. An inflection by application of strips of masking tape to point on the length-compression curve was the 0.69 m long fiberglass cast of a blue- seen at about 22 kg of force (28 kglcm2 fish, omitting the fins and tail, was 0.157 area) on the vertebra taken from the pemz. Using the relationship that area is duncle, and at about 19 kg (17 kglcm2) proportional to length squared, one can on the vertebra excised from the mid-length scale this surface down to that of a 0.61 m region. Definite slippage was seen at 45 kg. bluefish: 0.157 X 0.612/0.692equals 0.124 The maximal forces withstood were 65 and m*. This surface is like that of a plate 75 kg for these two vertebrates, respec0.61 m Iong and 0.10 m wide, with two tively. sides. The drag, Df, of such a plate is calcuThe relationship between thrust lated using eq. 1, as follows: Cd f is found and drag to be 3.72 X 10-3 for a Reynolds number of 1,090,000 according to a graph (J. K. Suppose a bluefish has a certain average Salisbury, ed., ’67). Substituting this into speed. To maintain this, he has to overeq. 1, Df = 0.00372 X 1,022 x 0.124 x come drag. When the force exerted by the 1.82 +- 2 = 0.76 newtons, or 0.76/9.8 = tail is greater than drag, there is a for0.078 kg force, or 78 gm force due to skin ward acceleration. Under steady state confriction at a speed of 1.8 m/sec. If the area ditions, the increase of velocity during
233
LOCOMOTION OF BLUEFISH
A
BONE LENGTH (mm)
B
LENGTH(mm)
Fig. 6 Compression and recovery stress-strain curves for two vertebrae removed from a fresh dead bluefish. Note inflection and yield points. A. Vertebra taken from peduncle of the tail, showing compression, relaxation, recompression, and relaxation. B. Vertebra taken from mid-back, also subjected to two full cycles of compression and relaxation.
acceleration must equal the decrease of velocity during deceleration. Or, the time integral of acceleration equals the time integr a1 of deceleration. The drag can be calculated during steady swimming on the following assumptions: 1. The thrust is limited to one half of each cycle. 2. The average drag during the acceleration period equals the average drag during the deceleration period. The decrease of speed during the deceleration would then be due only to drag. Conversely, the increase of speed during acceleration would be due to thrust minus drag. Since at steady speed the momentum gained is equal to the momentum lost, and since the thrust occurs during half the cycle, the force of thrust would equal twice the force of drag. The average deceleration occurring during each cycle was used to calculate the drag during swimming. The average of the two highest speeds of each of the five fish in table 2 was 2.45 mph or 1.1 m/sec, and the corresponding velocity changes averaged 0.065 mlsec., with a mean body frequency of 2.79 hz. Assuming a sinusoidal change of velocity (bottom tracings of fig. 4), the peak to peak acceleration would be 2 ?r f times the amplitude of the velocity change or 2 P X 2.79 X 0.065 = 1.13 m . sec-2, and this divided by 9.8 m . sec-2, which is the acceleration at 1 g, yields 0.12 g. The maximal deceleration drag would be half this, or 0.06 g, and the mean then would be this divided bv the sauare root of 2, or 0.06 X 0.7 = 0.04 g. F& the mean mass of 1.9 kg, this corresponds to a mean force to overcome drag of 1.9 X 0.04 = 0.08 kg at an
average speed of 1.1m/sec. The mean thrust would then be 0.16 kg, and the peak thrust 0.16 x *or 0.23 kg. DISCUSSION
In the present investigation, an accelerometer was placed in the fish, and used to record instantaneous acceleration in relation to the tail beat. Maximal thrust The maximal accelerations found following a scare of a fish ranged up to peak values of about 3 g. The time required to reach peak velocity amounted to about 0.2 seconds. The force necessary to produce such accelerations may be calculated from the equation: force = mass X acceleration.
Since the fish weighed 2.3 kg, at 3 g the force would be 3 X 2.3 = 6.9 kg. Drag during steady swimming The net drag calculated as the sum of profile and tangential drag at a velocity of 1.8 m/sec was 0.26 kg. The mean drag calculated from records of acceleration and deceleration during steady swimming at a mean velocity of 1.1 misec was 0.08 kg. These two calculations yield drag figures that are compatible with each other provided drag varies with the square of the velocity, as is commonly believed. The dif.erent patteTns of swimming of the bluefish The accelerometer records clearly show that the bluefish often uses an asymmetric forward thrust to propel himself through
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A. B. DuBOIS, G. A. CAVAGNA AND R. S. FOX
the water, further substantiating a similar but tentative conclusion reached by DuBois et al. ('74), on the basis of the pattern of pressure fluctuation on the jaw during swimming, and movies of fish taken by others (Gray, '33). At speeds between 0.5 and 1 mlsec the bluefish tended to use both sides symmetrically, whereas at higher speeds he a p parently used a more asymmetric thrust. This asymmetry took the form of inequality of amplitude of the two accelerations which accompanied acceleration of the body to the right and left respectively or differences in time intervals such that the forward acceleration that accompanied lateral acceleration to the left followed quickly after that associated with the lateral acceleration to the right, or vice versa. The manner in which forward acceleration is coupled to lateral acceleration could not be deduced directly from the records obtained cluring this study. However, it was apparent that the amplitude of forward acceleration was related to the rate of increase and amplitude of lateral acceleration, whether to the right or left. The peak of forward acceleration was found at or before the peak of lateral acceleration. A concave upward lateral acceleration was accompanied or followed by a peak of forward acceleration. Because misalignment of the accelerometer theoretically could introduce false asymmetry into the accelerometer records, a careful review was made of each record to look for this artefact. In many of the experiments the swimming pattern would change from symmetric to asymmetric and back again, suggesting that the fish really changed his pattern of swimming. In some cases, individual rapid accelerations occurred when the lateral acceleration was either to the right or to the left, ruling out asymmetry of the accelerometer tracing. Furthermore, tilting the fish underwater confirmed excellent alignment in some fish which had asymmetric forward acceleration patterns. Oscillation of the body by hand from side to side then produced a negligible component of acceleration. All of these observations pointed to the conclusion that the asymmetric patterns were real and not artefactual. They were in keeping with the expectations derived from the previous paper.
Changes in m o m e n t u m and kinetic energy As the tail delivers a thrust to the water, the water is accelerated backward and the fish is propelled forward. This is the equivalent of saying that the tail beat imparts a forward momentum to the fish in exchange for a backward momentum given to the water, and this results in the observed changes of velocity. During the acceleration forward the thrust is greater than the drag, and during the deceleration the thrust is less than the drag, i.e. thrust = drag m . a. Assuming no thrust during the deceleration period, the kinetic energy imparted to the fish carries him forward throughout the interval between thrusts. However, during that time, the water drag slows his progress, dissipating part of the kinetic energy. This lost energy is replaced by the next thrust, and so forth. As mentioned above, the tail imparts velocity changes to the fish fairly independently of speed. Since the tail beat frequency increases with speed, the duration of the thrust is presumably less at high speed than at low speed. Therefore, in order to keep the momentum (force X time) constant, the force must increase as the duration of thrust decreases. In addition, it takes more energy to produce a constant velocity change at high speed than at low speed, because kinetic energy varies as the square of velocity. In conclusion, at higher speed each tail beat costs more energy, and also tail beats are more frequent.
+
Body surface pressures, locomotion, and body structures In a previous communication, we showed that the hydrodynamic pressure gradient along the body surface of the swimming bluefish was of the same order of magnitude as the hydrostatic transmural pressure gradient which would exist in the vertical direction in land animals if the body contained only liquid. We suggested that body structures capable of withstanding the hydrodynamic pressure gradient in fish would be useful to land animals in withstanding hydrostatic and gravitational forces. The present paper relates body surface pressures to the forces required for aquatic locomotion: Briefly stated, the forward thrust produces a forward body velocity which is
LOCOMOTION OF BLUEFISH
opposed by backward drag due to forces normal to and tangential to the body surface. The force normal to the surface is the source of the pressures that generate the transmural pressure gradients described above. The body structures withstand this transmural pressure and prevent soft tissue deformation. Strength required for aquatic and terrestrial locomotion A terrestrial vertebrate requires enough muscular strength to raise its weight off the ground against gravitational force. Since a bluefish can generate 3 g, it theoretically would be able to lift three times its own weight against gravity. This suggests that the strength required to accelerate and swim in water could be used in terrestrial locomotion if the fish had other attributes required for terrestrial life. In fact, bluefish can be seen to jump out of the water, thus momentarily raising their weight against a downward acceleration of 1 g. Common experience tells us that we can jump off the ground with either leg, implying a strength in each leg sufficient to overcome at least 1 g. Indeed, running and jumping yield measured upward accelerations of 2 or 3 g (Cavagna et al., ’64). Both the fish and the human have achieved a certain degree of strength. But, the fish overcomes inertia and hydrodynamic drag whereas the human overcomes inertia and gravitational force. Vertebral strength required for aquatic locomotion One question asked in this investigation was whether the vertebral bodies are just strong enough, but not stronger than necessary, to sustain the compression force exerted by the tail fin as it thrusts the fish through and against the water. The force which would be required to accelerate the fish at a rate of 3 g was calculated to be 6.9 kg. Measurements of the compression strength suggest that the tail vertebrae could comfortably withstand not more than 20 kg if the back were straight. If the back were curved, so that only a third of the vertebral body touched its neighbor, then the initial yield point would
235
be equal to the maximal thrust. The finding that the vertebrae are strong enough but not too strong supports the view that the vertebral column serves to prevent the collapse which otherwise would occur. A vertebra which can withstand a force of 3 g could support the vertical weight of three fish on the Earths surface, given the circumstances. When the weight acts perpendicularly to the vertebral column, as in quadrupeds, the upper part of the vertebrae would be compressed, and the lower part of the vertebrae, ligaments, and muscles would be placed under tension. Fish and land animals may have followed separate parallel pathways in evolving the muscles and body structures required for aquatic and terrestrial locomotion. However, an alternative possibility is that aquatic locomotion may have played an evolutionary role in selection of bodies of vertebrates capable of terrestrial locomotion. ACKNOWLEDGMENTS
The authors wish to thank Dr. James Mavor of the Woods Hole Oceanographic Institute and Dr. Nicholas Newman of the Massachusetts Institute of Technology for their kind assistance in the calculation of skin friction. Mr. Eugene Tassinari, of the MBL Supply Department caught most of the bluefish used in this study. Dr. DuBois was the recipient of a Research Career Award of the National Institutes of Health. This research was supported in part by contract NO00 14-67-A-0216-0017 between the Physiology Branch of the Officie of Naval Research and the University of Pennsylvania, and in part by a research grant 5 R01 HL 04797 from the National Institutes of Health. LITERATURE CITED Cavagna, G. A., F. P. Saibene and R. Margaria 1964 Mechanical work in running. J. Appl. Physiol., 19: 249-256. DuBois, A. B., G . A. Cavagna and R. S . FOX 1974 Pressure distribution on the body surface of swimming fish. J. Exp. Biol., 60: 581-591. Gray, J. 1933 See figure 5 (mackerel) and figure 6 (whiting) in: Studies in animal locomotion. I. The movement of fish with special reference to the eel. J. Exp. Biol., 10: 88-104. Salisbury, J. K., ed. 1967 Chap. 15 in Kent’s Mechanical Engineer’s Handbook. Twelfth ed. Power Volume. Wiley, New York, London and Sydney.
