Flying at no mechanical energy cost: disclosing the secret of wandering albatrosses

Abstract

Albatrosses do something that no other birds are able to do: fly thousands of kilometres at no mechanical cost. This is possible because they use dynamic soaring, a flight mode that enables them to gain the energy required for flying from wind. Until now, the physical mechanisms of the energy gain in terms of the energy transfer from the wind to the bird were mostly unknown. Here we show that the energy gain is achieved by a dynamic flight manoeuvre consisting of a continually repeated up-down curve with optimal adjustment to the wind. We determined the energy obtained from the wind by analysing the measured trajectories of free flying birds using a new GPS-signal tracking method yielding a high precision. Our results reveal an evolutionary adaptation to an extreme environment, and may support recent biologically inspired research on robotic aircraft that might utilize albatrosses' flight technique for engineless propulsion.

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.

Figure 2. 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.

Figure 3. Total energy mapped to flight trajectory (for the cycle from Fig. 1c ).

The total energy, , is indicated by colour coding. Quantification is possible with reference to the bar (at the top) which establishes a relation between colour and total energy. The energy gain is achieved in the part of the curve where the colour changes from blue to red. The total energy reaches a maximum at the end of the upper curve, after the bird has changed its flight direction from wind- to leeward (dark-red colouring). Thereafter, the total energy begins to decrease and reaches a minimum past the lower curve where the bird has changed its flight direction from lee- to windward. Both the minimum and the maximum total energy states correspond with the ones in Figs. 2a and 2b (as indicated by red cycles in each Fig.). The coloured part of the trajectory coincides with the time span of the diagrams in Fig. 2. The depicted trajectory part shows an error drift of 1.5 cm/s yielding an estimated bias of 23 cm at the end of the cycle. The direction and the speed of the wind are also indicated. The wind speed holds for 10 m altitude.

Figure 4. Mechanical power balance during dynamic soaring cycle (for the same cycle as in Fig. 1c ).

The mechanical power in terms of the surplus of the power obtained from the wind over the dissipative drag effect is presented. The mechanical power related to the mass, (solid line), can be divided mainly into two parts: A part showing a high positive power level which is correlated with the upper altitude region where the energy gain from the wind is achieved. This part is opposed by a negative power level which is correlated with the flight phase close to the water surface where the energy loss occurs. The level of negative power is smaller than the one of positive power. The resulting integral power surplus is just sufficient to compensate for the dissipative drag effect. The data of are virtually unbiased. The mechanical power available in flapping flight, (dashed line), is shown for comparison purposes. It is based on the albatross power data described in the Introduction section (maximum lift-to-drag ratio of 20, 8.5 kg mass, and 70 km/h speed). is much smaller in magnitude than . This holds for both the positive and the negative parts of .

Figure 5. Relationship between energy gain, altitude and wind gradient.

The left and right diagrams show the relationship between the shear wind layer above the sea surface and the altitude region where the energy gain from the wind is achieved (during the dynamic soaring cycle shown in Fig. 2a and 2b). On the left diagram, the energy gain phase is indicated by grey shading. This corresponds with the phase between the minimum and maximum of the total energy shown in Fig. 2a and 2b by red circles. The right diagram in Fig. 4 shows the wind speed (dashed line) and the wind gradient (solid line) as functions of altitude. The wind speed at 10 m altitude was determined to yield . The shear wind profile, , is based on a logarithmic wind model . The altitude region where the energy gain is achieved is indicated by red dashed lines which establish a link between the left and right diagrams. At small altitudes, large changes in the wind speed occur, resulting in a high wind gradient. As the altitude increases, the changes in the wind speed continually decrease to become very small in the altitude region where the energy gain is achieved. As a result, the wind gradient is very weak at this stage.