In the literature vertical swimming movements of the krill are described and investigated (FISCHER, 1976; NAST, 1977; MARR, 1962) . Whether the animals are also able to conduct horizontal wanderings over a long period of time, is not clarified, although many hypotheses of reproduction biology and distribution are connected to migration questions. In the following experiments it is to be estimated how much energy the krill must produce at different veiocities. The influence of the swimming angle, the body position, the filtering basket and the tpdrodynamic lift force are taken into consideration.
The force that an animal must produce to move forward at a given velocity is equal to the water resistance of the animal 's body at this velocity. In order to measure this water resistance, krill were moved at different velocities through the water and the forces acting on the body were measured. For these investigations a flume was built, in which velocities of 2 - 50 cm*s-1 could be set (in a cross-section of 13.5 cm * 8 cm). A special apparatus was used to hang up the delicate body of the krill, allowing measurements of the very small forces (fig.56):
A thin (0.8 mm diameter) wire (c), drawn through the krill’s body (fixed in formalin) at the caudal third of the carapace, fixes the animal in the flow. This holding bar has a hole, through which a very fine needle runs lengthwise through the animal's body, to prevent twisting or distortion of the krill. Through two slits in the left and right wals of the canal (passage for holding bar) the bar reach out of the stream and is carried by two poles (a). These pass on the horizontal force Fh ( = water resistance) to a pendulum (b) (on both sides, out of the flow submerged under water). The deviation of the pendulum is measured aver a mirror reflecting a collimated light beam onto a matt screen. With hanging up a knife edge bearings (fig.: Knife edge bearing) and a light path of 4.1 m, the precision of measuring was + 15 micro Newton. A maximal deviation of 6 degree = 15 mN was not exceeded, so that the precision is maintained over the entire measured range. The poles (a) also rest in bearings (on the pendulums) and make up together with the equalizing weights (e) a balance for quantifying the vertical force Fv acting on the krill, using sliding underwater weights (f) measuring precision +- 60 microN), allowing for a splitting of the total force into horizontal and vertical components (Fh* and Fv).
The connection between the holding bar (c) and these balances (a) is formed by two friction bearings (d), which allow the holding bar (c) to be turned with the help of a small lever (g), to vay the angle of the animal towards the flow (angle of attack). For this purpose the flow was turned off, so that the weight of the animal presses the wire into the funnel-shaped ends of the slits (h); at this position a careful manipulation, for the purpose of changing the angle, causes no disalignment of the highly sensitive bearings. The water resistance of the holding bar (as a function of v) was calibrated without an animal and compensated.
The calibration of the flow was performed with drift particles whose path and velocity were determined photometrically by stroboscope flashing. The influence of the wall friction upon the water velocity extended for only ca. 1.5 cm, so that the middle 5 cm of the canal had a close to laminar flow. The measuring precision was +- 5 % of the water velocity.
667 Measurements were attempted with 12 animals at a water temperature of 1 degree Celsius and a salinity of 35.6. The experimental animals were 46 - 59 mm long. On board ship, especially well preserved animals were chosen under the binocular and preserved in small glasses without air with 4 % formalin. For the experiments (performed on land), all pleopods were removed, since these produce the propulsion in the swimming animal and thus have no water resistance.
In order to determine the resistance coefficient
cw = F * A-1 * (0.5 * d)-1 * v-2
F = force (N)
A = cross section area (m2)
d = density of the fluidum (kg * m-3 )
v = velocity (m*s-1)
the projected surface A, which is set against the stream, had to be deermined. For this purpose the krill was photographed out of the flow direction at different angies, under water, with a macro-lens of long focal distance: Object distance = 30x picture size, - angle error negligible. The surface was determined on the projected outline figures with a planimeter (each two times, max. error +- 1 % of the surface).
The projected area at 90 degree line of sight grows exactly quadratically with the length:
A = 0.112 L2.00
r = 0.998
A = area (mm2) L = length (mm)
Euphausia superba and Meganyctiphanes norvegica again show a common regression (fig.57). At smaller angles the area decreases; this is shown in fig.58 and 59 as a percent of the 90' area. Flow aimed directly from the front (0'), a smallest possible area of 20.9 % (s = 2.62) of. the 90' area results; for example, for a 50 mm long krill it amounts to 59 mm2. The animals with folded abdomen in the "shooting" phase of tail swimming have a similarly small surface.
Fig.57 Cross section area (projected area) at 90' at different lengths
A = 0.112 L 2.00 r + 0.998 A = area (mm2) L = length (mm)
Fig.58 Cross section area (projected area) at angles smaller than 90' relative to the 90' area
Fig.59 Cross section area (projected area) at angles smaller than 90' relative to the 90' area; mean and standard deviation from fig.58
A% = -56.4*10-9 $5 + 16.22*10-6 $4 - 1.787*10-3 $3 + 82.68*10-3 $2 - 0.2094 $ + 21.08 ($ = ' angle alpha)
The horizontal force is the force which a krill must produce to swim at a certain velocity. It is represented in fig.60 as dependent on v.
Fig.60 Horizontal force (water resistance) at increasing flow at 0' and 90' angle of a 57 mm long krill
F0 = 2.91*10-3 v1.73 (mN, cm per second) r = 0.985 cw = 0.314
F90 = 8.24*10-2 v1.41 (mN, cm per second) r = 0.976 cw = 1.11
The curve 0' corresponds to a krill swimming in a horizontal position through the water. The force rises with a power of 1.73 to v; the relation is not exactly quadratic because of a slight dependence on the Reynolds figure which does not need to be discussed further here. With a propulsion force of, for example, 1 mN, the krill can move itself forward at ca. 30 cm*s . The resistance coefficient (cw) of the krill 's body is quite favorable; cw = 0.31 (s = 0.066, v = 0.21, Reynolds number 50 - 850).
For comparison:
plate standing vertical to flow 1.1
hollow sphere opening to flow 1.3 - 1.6
sphere 0.4
racing car 0.3
streamlined body down to 0.006
The curve 90' corresponds to a krill moving crosswise through the water. This krill would have a resistance coefficient of cw = 1.11 (s = 0.219, v = 0.197, Reynolds number 50 - 850), or approximately that of a plate moved crosswise through the water. Naturally, a krill does not swim thus through the water, but these conditions correspond to those of sinking krill. If one calculates with the determined cw = 1.11 the theoretical sinking speed of a 57 mm long krill, it would sink at 5.0 cm*s-1. This value agrees remarkably well with the actually measured 5.3 cm*s-1 (fig.50) and thus gives proof for the usefulness of the flow-tank experiments.
cruising: Fp = 0.00424 v 1.61 r = 0.970 cw = 0.39
escape: Ft = 0.00364 v 1.58 r = 0.970 cw = 0.33
(units: milliNewton, centimeter per second)
The macro-slow motion pictures showed that the Krill lays the filtering basket close to its body at high velocities; therefore, the thoracopods were normally glued to the body in such a close-lying position with cyan-acrylate.
But in some experiments the filtering basket was also left unaltered; here it opened up because of the water flow (from 3 - 4 cm*s ) and took on a position similar to that shown by the krill with open filtering basket on the macro-slow motion pictures. After further velocity increase this position remained almost unchanged up to ca. 25 cm * s-1. At still higher velocities the ischiopodites folded over approximately in the middle and the filtering basket lost its shape and solidity. These observations allow one to suspect that the filtering basket does not need to be opened actively by the krill; it is probably forced into a certain shape by the water flow during swimming; i.e., it is set up in a position that is maintained without muscular work. The muscles work antagonistically to this and draw the thoracopods, when necessary, toward the body, so that the filtering basket may be closed. Fig.63 shows the horizontal force both with a closed and with an open filtering basket. The difference, or the force for "fishing with the filtering basket" is significant: for example, at 15 cm * s-1 ca. 150 % more force (curve d% = 0.6 mN) must be produced, in order to pull the filtering basket with its fine meshes through the water (fig.62).
Fig. 62 Filtering basket of Euphausia superba. Photo taken on an exuvie
closed: Fc = 0.00291 v 1.73 r = 0.985 cw = 0.34
open: Fo = 0.01860 v 1.41 r = 0.972 cw = 0.81
(units: milliNewton, centimeter per second)
This difference decreases with increasing velocity; an explanation for this decrease would only be possible after further, detailed knowledge about the filtration mechanism of the krill. The following interpretation is a possibility: similar to a fishing net, the filtering basket has a relatively small opening and large side filter surfaces, which are arranged like a pointed V. If such a net is dragged too fast, the water cannot flow off quickly enough through the meshes and a barrage builds up in front of the net opening. This barrage causes more and more water to be pushed away to the sides and flow around the outside of the net. This also seems to be the case with the krill: the mentioned difference in force is velocity-dependent: At 5 cm*s-1 it is 300 %, at 35 cm*s-1only 100 % (curve d %), i.e. less end less water is filtered in proportion to the distance swum. On the other hand, the absolute quantity of water filtered per time increases only slightly up to a velocity of ca. 15 cm*s-1, so that in this range the meshes are streamed through at almost the same velocity, i.e. the filter characteristic does not change. This could be an indication that it is a net which can be engaged and is capable of working even at higher velocities.
The absolute force only for the open filtering basket is at v = 3 cm*s-1 0.l mN and at v = 15 cm*s-1 0.6 mN.
Besides the horizontal force, another force is produced on a krill, which moves at an angle position (angle of attack, see fig.23) through the water: this force is directed upwards - the hydrodynamic lift (fig.56: Fv). It is this force which holds birds and airplanes in the air. With birds and gliders the air resistance during forward movement is about 1/30 of the flying weighC, i.e. with a propulsion force which is only 1/30 of the flying weight (= vertical force), the bird can already fly without losing height. The krill certainly has no wings, but since it always swims at a certain angle of attack (fig.23), and its side body profiie is not dissimilar to a wing profile, the Polars of the krill were measured for different velocities (fig.64).
(units: milli Newton, cm per second)
Polars show the dynamic lift plotted against the vertical force at increasing angles of attack (for details see manuals of aerodynamics). In the figure the resulting curves for six different velocities are plotted. These relations are not to be discussed in detail, but it can be seen that there is a range (shaded) in which the produced lift (= vertical force) is larger than the driving force (= horizontal force), at angles of attack between 20' - 40'. The krill could use the hydrodynamic iift to carry its heavy underwater weight. That it can succeed herein without such iarge surface as the bird is because of the high density and viscosity of water. In order to find out at which angles and velocities the underwater weight is just supported by the hydrodynamic lift, the krill was dragged at a given angle and the velocity varied until a balance was produced between the mentioned forces. This velocity and the necessary horizontal force to produce it are shown in fig.65, 66, 67 and 68. The horizontal dashed line represents the underwater-weight-force of the animal. The shading shows the conditions in which the propulsion force to be produced is smaller than the weight force.
Fig.65-68 Combinations of horizontal force and velocity (small numbers) at different angles of attack, exactly resulting in a neutralization of the underwater weight (dashed line) by the hydrodynamic lift. For explanation see text
However, the krill certainly is no "technical test object"; because of biological factors it is not able to perform all the above measured angle/velocity combinations. For example, the ranges to the right of the vertical line in fig.65 - 68 are not attainable for anatomical reasons. With the actual angle/velocity combinations determined by means of the macro time-zoom imgages and the forces measured in the flumes, we can discuss a rough budget of the complex swimming dynamics of the krill.
A 49 am long krill hovering at the spot exactely compensates its weight force (Fg = earth's force of gravity; F = 0.28 mN) with an equal force directed upwards (fig.69a).
It produces this force by exercising a propulsion force (Fp) on the water in the direction Fg with its pleopods. These forces are only in balance at a swimming angle of 55 degrees (compare fig.10, 22, 23).
At a velocity of 3 cm per s (fig.69b) the animal swims at a 30' angle (fig.23); under these low conditions a small hydrodynamic lift is produced (Fl = 0.08 mN), which reduces the weight force. The remaining force (Fd = Fg - Fl) and the horizontal force (Fh) vectors add up to the propulsion force (Fp) directed downwards, diagonally backwards.
At a velocity of 5 cm per s (angle of attack = 20') the lift is equivalent to the horizontal force (= drag). Comparing this condition with that of the krill hovering on the spot, two things are remarcable from physical considerations (fig.69c): a) the total propulsion force is allready smaller in the cruising animal; and b) the water is thrown back towards the back line at a more acute angle; this corresponds well with actually quantified flow field (compare fig.10 with fig.11).
Krill can swim at a velocity of 10 cm per s (angle of attack = 10') with approximately the same amount of energy needed to fight sinking while hovering on the spot. From velocities of 13 cm per s upward, the force increases then very quickly: exponentially with the power of 1.7 (v1.7 - fig.70). For the total bio-energetics of krill, this means that it can criuse over a range of 0 - 13 cm per s without having to exceed its "standard metabolism". The "activity metabolism" sets in only for higher speeds.
Fig.70 Resulting total propulsion force. This force the krill has to transfer to the water via the pleopods in order to cruise at the specified speeds and simultaneously carry its relatively heavy body
For the interpretation of results of the flow-tank experiments, the following must be considered: the determined cw values are always higher (i.e. more unfavorable) than those of living animals (GRAY, 1936; HILL, 1950; LANG, 1966), since the latter are able to adapt themself to the flow field much better. For example, a blue whale, which has at maximum 68 PS available, can cruise over long times with 15 knots; if the same whale is dragged behind a boot at the same speed, 170 PS are needed. This means for the interpretation of the experiment that in the figures the shaded areas would grow larger, or that the krill would swim faster with the same force, and probably can cruise 15 - 20 cm per s while still within the lowest possible "standard metabolism".
From the measured forces, the underwater weight and the observed flow field of fig.10 and 11, one can, in turn, estimate the swim angles which a krill swimming horizontally through the water should show at different velocities. These agree well with the actually observed angles of attack represented in fig.23. This is a further evidence that swimming behavior and bio-energetics of krill are strongly influenced by earth's gravity.
all the images are not jet edited for web serving - just simple scans