Experimental results on dynamic soaring

In the longest track the GPS recorded 4,850 km during the first six days of a total 30-day foraging trip (Fig. 1a). While showing a large distance covered on a global scale, this trajectory does not provide any information about the small-scale flight manoeuvres involved in the whole flight. It is only at small scale resolution (Fig. 1b) that the typical pattern of dynamic soaring becomes visible. The whole flight consists of curved trajectory segments that are continuously repeated close to the water surface. A visual inspection of all our records (based on the coarse 1 Hz online solution) revealed that birds never fly in straight lines and are always confined to a low altitude region.

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larger image TIFF original image Download: Figure 1. Large- and small-scale movements and dynamic soaring cycle. (a) Large -scale movement. The 4850 km path (projected to the sea surface) of a long-distance flight of a wandering albatross is shown. Logging stopped after the first 6.0 days of this 30-day-long foraging trip. (b) Small-scale movements. A 14 min portion of the long-distance flight from Fig. 1a shows a sequence of three connected parts. The flight path consists entirely of winding and curving segments, not exhibiting any straight horizontal sections. (c) Dynamic soaring cycle. The small-scale movements consisted of dynamics soaring cycles featuring distinct motions in the longitudinal, lateral, and vertical directions. Each dynamic soaring cycle consists of (1) a windward climb, (2) a curve from wind- to leeward at the upper altitude, (3) a leeward descent and (4) a curve from lee- to windward at low altitude, close to the sea surface. https://doi.org/10.1371/journal.pone.0041449.g001

Analysing further details of the individual flight cycles required an even smaller scale (Fig. 1c). Whereas no special GPS raw data analysis was necessary for previous plots (Fig. 1a.b), bird's position here was calculated using fine-scale 10 Hz position fixes derived from a GPS post-processing software. According to the built-in error estimator of our program, we could identify the total position error with respect to the starting point of the cycle to stay below 4 dm. One recognizes immediately that the manoeuvre was made up of horizontal curve phases superimposed by climbing and descending phases. With regard to the local wind direction, the manoeuvre could be partitioned into four flight phases which are representative for each cycle: (1) a windward climb, (2) the upper curve from wind- to leeward flight direction, (3) a leeward descent, and finally (4) a lower curve from lee- to windward flight. We considered such flight cycle as the essential key to understanding how the birds extract energy from the wind – this cycle is the fundamental element of dynamic soaring.

A closer examination of the cycle's quantities related to dynamic soaring was intended to expose the physics of the manoeuvre (Fig. 2a). The time of the cycle was in the order of 15 s. The altitude region extends from approximately 0 to 15 m. In this region, the wind speed increases from zero to values approaching the free airflow [18], and the bird's speed varies between about 10 and nearly 30 m/s.

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larger image TIFF original image Download: Figure 2. Dynamic soaring cycle (same cycle as Dynamic soaring cycle (same cycle as Fig. 1c ). (a) Altitude and inertial speed . The altitude shows a cyclic behaviour (between lowest point near to the sea surface and top of trajectory). The speed, which is also cyclic, follows the altitude with a time lag. Speed starts to increase during the climbing phase, despite an increase in altitude. This indicates that there is a simultaneous increase of potential and kinetic energy to yield an increase of the total energy. The altitude is affected with an estimated error drift of 2 cm/s yielding a maximum bias of 31 cm after 15 s. is biased by 2.5 cm/s (0.1–0.2% relative error). (b) Total energy and potential energy . The total energy, , presented in form of a solid line has cyclic characteristics, too. It begins to increase during the windward climb and continues to do so until the peak of the trajectory has been passed. The maximum value of the total energy is reached during the leeward descent. This is indicated by a red circle and a dashed line linking Figs. 2a and 2b. There is a large energy gain (∼360% relative to the beginning of the dynamic soaring cycle). The total energy curve is smooth and continuous. As a consequence, the extraction of energy from the shear wind is also smooth and continuous, without any discontinuities or energy pulses. Furthermore, the energy gain is achieved not at the low level, but in the upper part of the altitude region, around the top of the trajectory. The bias of is estimated to 0.2–0.5%. The potential energy, , presented in form of a dashed line is considerably smaller than the total energy. Thus, the kinetic energy given by the difference between the solid and dashed lines exceeds significantly the potential energy. This holds particularly for the phase of the energy gain from the wind. In the second part of that phase, the potential energy is even decreasing to reach again its lowest level. https://doi.org/10.1371/journal.pone.0041449.g002

An interactive visualization of the discussed 3-dimensional dynamic soaring trajectory is provided in Text S2.

The results of an analysis of the bird's total energy state during the manoeuvre are presented in Fig. 2b (solid line), which shows the time history of where is the total energy in terms of the sum of potential and kinetic energy, is the mass of the bird, is the acceleration due to gravity, is the altitude, and is the speed with respect to the Earth (which is used as an inertial reference system). Dividing by mg yields the specific total energy which does not require any assumptions regarding the bird's mass.

The energy transfer has the following characteristics. The total energy begins to increase during the windward climb. At the top of the trajectory, the energy gain does not come to a stop, but continues to increase. The total energy finally reaches its maximum value during the leeward descent, after the bird has already started to loose altitude. This is indicated by the red circles in Fig. 2b and the dashed lines linking Figs. 2b and 2a. These dashed lines establish a direct relation between the total energy and the motion quantities (altitude, speed). As a result, energy gain as high as 360% is achieved in relation to the starting point of the cycle. After having reached its maximum, the total energy decreases in the last part of the descent.

Furthermore, Fig. 2b also presents the time history of the potential energy related to the weight (dashed line). The difference between the solid and dashed lines yields the kinetic energy. Since there is a large difference, the total energy is primarily made up of the kinetic energy whereas the potential energy remains on a significantly lower level throughout the entire dynamic soaring cycle. In particular, the gain in the total energy gain is predominantly due to an increase of the kinetic energy.