Swimming, Lake Insects

Insects of many types, such as beetles (Coleoptera), true bugs (Heteroptera), and fly larvae (Diptera), can be observed swimming in ponds and lakes. Of these, the water beetles in the family Dytiscidae are reputed to be the best swimmers. The trunks of their bodies are well adapted to flow, and they generate thrust by executing synchronous power strokes with their flattened rear legs, which bear two rows of “swimming” hairs.

FLOW ADAPTATION

Measurements on flow adaptation have been carried out on trunks of several Dytiscidae, especially with the large European water beetle Dytiscus marginalis.
The technical term coefficient of drag, or cd, is used as an indicator of flow adaptation. A small coefficient indicates that a beetle with a given frontal area and at a given swimming speed generates little drag; that is, it is well adapted to flow. However, one cannot readily compare the drag created by objects moving at different speeds because the coefficient of drag is a function of the Reynolds number (i.e., of its swimming speed in water and its body length). For certain ranges of Reynolds numbers, there are sufficient data available, ranging from the most streamlined bodies (e.g., drop-shaped trunks; lowest cd values) to the objects that produce the greatest drag (e.g., parachute forms; highest cd values). Figure 1A shows the trunks of four Dytiscus species viewed from above, from the side, and from the front (the front projection shows the frontal area A). Figure 1B shows the measured cd within the spectrum of coefficients that are possible for the range of Reynolds number (Re) obtained from swimming water beetles (103 < Re < 104). The coefficients of the beetle fluctuate between 0.38 for D. latissimus and 0.43 for D. pisanus, with
 (A) Trunks from four large species of Dytiscus viewed from above, from the side, and from the front. (B) Classifying the four cd values of these beetles at zero angle of attack (cf. Fig. 2) within the spectrum of possible coefficients of drag in the range 103 <Re < 104.
FIGURE 1 (A) Trunks from four large species of Dytiscus viewed from above, from the side, and from the front. (B) Classifying the four cd values of these beetles at zero angle of attack (cf. Fig. 2) within the spectrum of possible coefficients of drag in the range 103 <Re < 104.
the smallest possible value being 0.2 or slightly less, and the highest possible value approximately 1.4. Compared with the possible spectrum, the beetles ‘ trunks seem to be well adapted to flow, although they do not reach the extreme values technically possible. Low-drag technical constructions are unstable; in the presence of oblique flow they turn immediately broadside, and stabilizing surfaces preventing this behavior would increase drag. Enlarged prothoracic and elytra edges in large Dytiscus beetles (extreme in D. latissimus) serve as stabilizing surfaces for swimming by damping oscillations around the longitudinal and lateral axes and by creating stabilizing moments. If one reduces these stabilizing surfaces along the edges, drag at almost all angles of attack between trunk and flow is perceptibly reduced. But the trunk then is distinctly unstable. These two contradictory demands have led to the evolution of an optimal shape with good swimming stability and good flow adaption.
Geometrically similar, 10-times-enlarged models of large Dytiscus beetles have been used to measure the pressure distribution along the dorsal midline of these trunks, with numerous pressure holes. A positive pressure dent appears on the head-prothoracic region (and also on the abdomen), whereas the remaining upper abdominal side is under negative pressure (Fig. 2). Thus, a Dytiscus trunk is very similar to a small-span wing profile and should therefore create a certain dynamic lift during fast swimming.
Because the drag coefficient of bodies increases with smaller Reynolds numbers, one may expect that the smallest, most slowly moving Dytiscidae (e.g., Hyphydrus, Bidessus) are characterized by relatively high drag coefficient values. Thus, they seem to be less well adapted to flow simply by their smallness (i.e., by their low Reynolds numbers). From flow mechanics, we know that streamlining is less effective at lower Reynolds numbers. Indeed, these small beetles are characterized by blunt body forms that may have biological advantages (more effective space for the organs). Because these beetles are energetically better equipped, this inherent physically disadvantage may not be of primary importance.
 Pressure distribution in the median plane of a model of D. marginalis (male) enlarged 10 times, measured in a wind tunnel: dashed lines, pressure above atmospheric ("pressure"); solid lines, subatmospheric pressure (" suction " ).
FIGURE 2 Pressure distribution in the median plane of a model of D. marginalis (male) enlarged 10 times, measured in a wind tunnel: dashed lines, pressure above atmospheric (“pressure”); solid lines, subatmospheric pressure (” suction ” ).


FUNCTIONAL MORPHOLOGY

Leg Flattening and Position of Swimming Appendages

The functional formation of a swimming leg is easy to understand because of the simple mechanical demands made upon it. A swimming leg should produce strong thrust (i.e., a force component in the swimming direction) during a rowing stroke (i.e., a power stroke), and little counterthrust while being drawn forward (i.e., a recovery stroke). This action is aided by morphological and kinematic adaptations.
At a given speed the hydrodynamic drag force Fd is proportional to the leg surface A. Therefore, A must be as large as possible during rowing stroke, and as small as possible when drawn forward. This is achieved by flattening the leg segments and by means of thrust-inducing processes such as swimming hairs (e.g., Dytiscus, Corixa) or swimming platelets (Gyrinus). During the rowing stroke, the flat broadside of the leg is brought perpendicular to flow, and the hairs and platelets spread out automatically under the pressure of flow, thus increasing the rowing surface. When the leg is drawn forward, it is turned so that the flattened surface lies parallel to flow, and the rowing appendages are folded together and pressed against the leg by the flow; their additional surface disappears completely (Fig. 3).
Stroke phases of the hind legs of A. sulcatus during power stroke and recovery stroke.
FIGURE 3 Stroke phases of the hind legs of A. sulcatus during power stroke and recovery stroke.
Leg oscillation is an angular movement. Therefore, the drag, which is created by an element of surface, is proportional to the square of its rotating radius r, or its distance from the coxa-trochanter joint. A component of the counterforce of this drag, parallel to the median, is the thrust force. The thrust-creating area during a rowing stroke should lie as far out as possible (r large) during the power stroke, and as far in as possible (r small) during the recovery stroke. Thus, the broad area and its hairs can be called a thrust-creating area. This is achieved principally because the distal leg segments, the tibia and the tarsus, are greatly enlarged and carry thrust-creating swimming hairs or swimming platelets, and because the legs are outstretched during stroke and then bent and drawn forward as close as possible to the median.

Stroke Areas and Radii of Rotation

The leg segments in Gyrinus have been flattened so extensively that their surface area is approximately five times that of a round leg; because of the simultaneously increasing coefficient of drag, a hydrodynamic force roughly eight times larger is created. During the power stroke, the leg segments spread out like playing cards, thus increasing their size by roughly 1.6 times over their projection area when not spread. The supplementary surface areas of the swimming platelets increase the stroke surface in Gyrinus even more: by roughly 230% in the tibia and roughly 130% in the tarsus.
In Acilius, the flattened tarsus positioned very distally occupies 80% of the total stroke area. Its mean rotational radius is also roughly 80% of the leg length. In Gyrinus, the corresponding values are approximately 40 and 80% for the tarsus and approximately 50 and 60% for the tibia.
During the recovery stroke, Acilius tilts the broad side of its leg parallel to the flow and presents the narrow edge of its leg to the flow. At the same time, the swimming hairs and swimming platelets are flattened and lie close to the leg. Because the exterior leg sections lie more or less parallel to the median during the first phase of drawing forward, its area of projection in the direction of flow is smaller yet. In Gyrinus, this projection area in proportion to the area of the power stroke is reduced to 1/13 for the middle legs and 1/16 for the hind legs. The tarsus from Gyrinus collapses completely and disappears partly into a groove in the tibia, which in turn slips partly into a hollow in the femur, so that the leg surface area is dramatically reduced by roughly 70% of the leg surface during the recovery stroke.
By folding the legs when they are drawn forward nestled against the body, Gyrinus reduces the mean rotational distance relative to that of the power stroke from 60% to approximately 35% of total leg length. The values for the tarsus alone are 80 and 50%.
Two additional phenomena should augment swimming efficiency, although their precise contribution remains to be measured. First, pressure drag is created mainly during the power stroke, and fric-tional drag is probably more important when the legs are drawn forward. Second, the leg segments, insofar as they nestle against the ventral surface with their broad side when drawn forward, move within the boundary layer of the trunk, thus creating less drag than when moving through free water.
During steady swimming, the relations are more complicated because the leg interferes with flowing water so that the speed of the leg’s rowing surface relative to the surrounding water changes.
Newer investigations (Nachtigall, 2008) have revealed that the drag coefficient of water beetle trunks is markedly reduced at higher flow speeds (higher Reynolds numbers) that exceed the biological range. So an equalized trunk of Dytiscus pisanus (body length 3.0 cm) revealed a drag coefficient of only 0.14 at Re = 6.8 X 104. Compared to the unchanged trunk at physiological flow speeds (drag coefficient 0.43 at Re = 4.5 X 103), this means a reduction of 67%.
It seems therefore likely that bigger models at even higher Reynolds numbers reach extraordinarily good flow adaptation exceeding that of existing submarines. To test this a 10-to-1-model of an equalized Dytiscus-trunk was built (Fig. 4) that is now analyzed in wind- and water tunnels.
 Equalized 30-cm-model of the trunk of Dytiscus pisanus.
FIGURE 4 Equalized 30-cm-model of the trunk of Dytiscus pisanus.

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