Figure 1.
Apteronotus albifrons, the black ghost knifefish of South America.
(A) Photograph courtesy of Per Erik Sviland. (B) Posture of fish while swimming forward in search of prey, with body pitch angle typically
[16]. The angle
is the fin base insertion angle, typically approximately
in this species.
Figure 2.
Computed wakes of a model of the black ghost at different pitch angles, at a velocity of 15 cm/s.
The body is shown colored by the surface pressure deviation with respect to the hydrostatic pressure. Vorticity contours are shown in gray scale in the mid-sagittal plane of the fish. Wakes of the body at pitch angles of (A) ; (B)
; (C)
; (D)
.
Figure 3.
Measured and computed drag on the fish body at different body pitch angles.
––,
–
–;
; –
–;
. Dashed lines indicate experimentally measured drag, while solid lines show the drag estimated with computational fluid dynamics. Insets show orientation of fish cast while being towed at these angles.
Figure 4.
How search volume changes with body pitch.
(A) Electrosensory case. A black ghost knifefish is shown with the sensorium for detecting 3 mm long water fleas (Daphnia magna). Prey anywhere on or within the surface are detectable by the fish. From [12]. The volume of water which is scanned for prey will be the fish's velocity times its duration of movement, times the projected area of the sensorium in the direction of travel. In this case, the projected area is the height h times the width (dimension out of the plane of the figure) of the sensorium. As the body pitch increases, h increases and so does the projected area. (B) Visual case, assuming no swiveling of the eyes to compensate for body pitch. A stone moroko is shown with the sensorium for detecting
2 mm long water fleas (Daphnia pulex). From [22], as visualized in [12].
Figure 5.
How the projected sensorium area and the energy needed to encounter one prey vary with body pitch angle and elongation factor.
In each case, the number on the curve indicates the ratio of the length of the sensorium to its height. The natural case is that the sensorium is 2.2 times longer than its height. (A) Projected sensorium area in the direction of travel. (B) Energy needed to move to a single prey.
Table 1.
Figure 6.
Net propulsive force from fin calculated from Eq. 5 across a set of ribbon fin undulation frequencies versus body pitch angle, compared to drag force.
In order to be free swimming at constant velocity, the generated thrust must equal drag. Dash-dotted line shows the estimated drag on the body using the equation where
is the total power needed to overcome measured drag at 15 cm/s and zero pitch angle for the fish cast (0.3 mW), and the velocity of the fish is allowed to vary (see Materials and Methods).
Figure 7.
Two hypothetical scenarios: an electric fish hunting with a visual sensorium and with a movable sensorium.
(A) An electric fish with vision-like sensorium. A sector of the normal omnidirectional sensorium has been cut to simulate the situation of a sensorium with a similar initial projected area as the normal omnidirectional case, but mediated by vision. In this scenario, we are keeping the sensorium body-fixed. (B) An electric fish with a movable sensorium. In this scenario, the fish is able to swivel the sensorium in pitch, around an axis between the eyes, without pitching the body, similar to the effect of moving eyes in a visual animal. (C) Energetic consequences of the hypothetical sensorium geometries. The solid line is the original case, from Figure 5B. The ‘+’ curve shows the simulation of the effect of a visual sensorium. The ‘x’ curve shows the result of allowing the sensorium to swivel up from the tail while not changing the pitch of the body.
Figure 8.
A black ghost with its sensorium for prey, showing computed flow patterns resulting from two different pitch angles.
As shown by the high degree of flow separation behind the fish pitched at (the orientation it hunts prey in), compared to the laminar flow behind the fish at
, there's significant energy costs associated with angling the body downward due to drag. However, the area scanned for prey by its sensorium while swimming forward increases, as shown by the plot at right. The net effect is that the fish needs less energy to get to its next prey when its body is pitched at
. While pitch angles of around
are best in terms of reducing the energy to get to the next prey, this does not incorporate the diminishing propulsive effectiveness of the ribbon fin as the body pitches more. Propulsion drops by about 25% at
(Figure 6). Because of this effect, the best angle for the fish to swim at will be less than
.
Figure 9.
Schematic showing simplified model with cuboidal sensorium.
is the pitch angle of the body.