How do we establish the complete explanation of how dynamic soaring works? The answer will be found in data logged from albatross in free flight. It will be necessary to use both GPS derived position, speed and height data combined with airspeed, heading and height above the surface and also actual wind velocity data. Unfortunately, so far only the GPS derived flight data has been obtained. Air-velocity and wind velocity can only be estimated.
However, given the GPS data at suitable high resolution intervals, say half a second, it is possible to make some informed guesses as to the wind velocity and thence to solve the triangle of velocity at each data point, and obtain heading and airspeed. That data can then give an insight into the relationships between the various parameters.
The data with which I am working is published in a paper entitled In-Flight Measurement of Dynamic Soaring in Albatross by G Sachs et al AIAA 2010. The purpose of the paper was to develop high-resolution GPS tracking and albatrosses were chosen as a suitable tracking vehicle. The data appears as three diagrams comprising 30 seconds of GPS derived position, speed and altitude covering three dynamic soaring cycles. As published it looks like Figure 24 and is highly compressed in its horizontal axes.
To extract some useable data the diagrams were expanded to give all three the same horizontal scale. The GPS ground track diagram is adjusted to give the same vertical and horizontal scales as in Figure 25.
The top line is GPS position, with North upward and East toward the right and the bird flies from left to right. The diagram has been expanded so that the X-axis scale is the same as the Y-axis scale in metres and true track can be measured directly with a protractor as the direction of the tangent to the line at suitable intervals. The middle line is GPS altitude with the horizontal scale in seconds but with an expanded vertical scale in metres. The lower line is GPS speed in m/s against time in secs. Again the middle and lower lines are expanded horizontally to correspond with the upper line.
What can we deduce from the raw GPS data, without airspeed or wind data. The main point to be seen is that there are places, highlighted in blue, where both altitude and speed are increasing, indicating a net energy gain. This is very obvious during height gain. In fact, when kinetic and potential energy are summed (not illustrated here) the energy gain is seen to occur throughout the hump manoeuvre (the leeward wing-over turn). (Sachs conclusion was that the birds gain energy during the ‘upper turn’ implying a connection with the wind-gradient).
What is not clear is how this energy gain relates to the wind-velocity and to the birds airspeed and heading. The total energy depends on whether ground-speed or airspeed is used in the calculation. Kinetic energy is a square law while potential energy is a direct law and therefore the plotted line of total energy will be similar to whichever speed data is used. In my view ground-speed gives the KE of the bird using the mass of the bird, whilst airspeed gives the KE of the relative airflow using the density of the air. (Bear in mind the important thing in dynamic soaring is not speed but acceleration)
Deducing the wind-velocity
Once the bird departs from the place where the tracking device is attached, it is not possible to know what wind-velocity the bird is experiencing. However, from the information given in the paper and generalised observation of albatross flight we can make the following deductions:
1 - the hump manoeuvres on the altitude line are leeward turns flown as wing-overs (belly to the breeze if you like)
2 - the humps correspond to the left turns on the position line therefore the left turns are leeward turns (headwind to tailwind) and the right turns are windward turns (tailwind to headwind).
3 - the bird is flying from West to East therefore the wind is from the birds right-side giving left-drift and the birds heading is track plus drift
4 - the wind is probably from between South-West through West to North-West because the data is from the vicinity of the Kerguelen Islands in the Roaring Forties in the Southern Indian Ocean.
5 - the birds average heading is probably crosswind at 90 degrees to the wind.
6 - the wind speed, at a first guess, is probably similar to the birds airspeed at about 20 m/s and therefore the maximum drift is about 45 degrees
7 - from the position line, the average track made good is about 095degrees therefore the average heading is 095 + 45 = 135 degrees and the wind direction is approximately 135 + 90 = 225 degrees (South-West)
8 - using an assumed uniform wind of 225 deg 20 m/s and the measured ground-speed and track data, we can solve the triangle of velocities at each data point (half second intervals) and calculate the birds airspeed and heading. (Using other values of wind velocity within +/-10m/s and +/-20deg gives similar curves but different values of airspeed. Radically different wind-velocities like due East or due West give chaotic results)
The results are as follows:
See Figure 26. The horizontal scale is time in seconds and the vertical scale is degrees, metres or metres per second as appropriate.
Heading and track
The top two lines are the birds calculated heading and raw-data track. This is not position information but purely numerical heading or track versus time. The ascending lines represent increasing headings and are therefore right turns and are windward turns (turning from tailwind component to headwind component). The descending lines have reducing headings and are therefore left turns and are leeward turns. The difference between the two lines is the drift angle which is approximately constant because we are assuming constant wind. The heading changes by about 40 to 50 degrees in each turn (crosswind plus and minus 20 to 25 deg) so that the drift angle does not vary by much. The point of roll reversal is much easier to see compared with the raw GPS position data.
The durations of the windward turns are much shorter than I have seen in film of albatross where the windward turns took 10 to 15 seconds. Also, as mentioned earlier, the average track is Easterly and the wind South-Westerly compared to the prevailing Westerly winds at these latitudes, which suggests the wind has backed (in the Southern hemisphere) and possibly increased due to a passing squall. I therefore conclude that this particular data set is not typical. The angle of bank is probably similar in both the windward and leeward turns because the lengths of the turns are similar and is probably about 45 degrees.
Ground-speed and airspeed
The red line is raw-data GPS speed (ground-speed). There is a clear correlation between ground-speed and heading. Ground-speed and therefore momentum, reduces in the windward turn due to the unbalanced aerodynamic force. Ground-speed and momentum increase in the leeward turn due to a horizontal component of the lift force acting as a propulsive force in the direction of the ground track due to the reversal of bank angle and the large drift angle.
The green line is calculated airspeed. I expected the airspeed to be nearly constant but actually it increases in the windward turn and decreases in the leeward turn. In the windward turn the airspeed tends to increase due to the increasing headwind component due to turning toward the wind. This despite nearly constant height. In the leeward turn the airspeed reduces due to a decreasing headwind component.
The yellow line is raw-data GPS altitude. The vertical axis is expanded for clarity. During the windward turns the altitude is nearly constant and in the leeward turns there is a gain and loss of height due to the turn being flown as a wing-over. If the bird is skimming the surface to take advantage of ground effect, altitude should vary somewhat due to passing waves and depending on the sea-state.
Results with an assumed wind-gradient
The airspeed and heading data in Figure 26 are calculated using a uniform wind. However, if there is a wind-gradient, its effect will be included in the GPS ground velocity data. To see a wind-gradient effect on the airspeed calculation, an allowance has to be made and we are back to theory again. What is the structure of the wind-gradient? Instead of assuming a uniform wind, the wind can be modified to be uniform at an altitude of 10m and reduced at lower altitudes proportional to the logarithm of the birds altitude. This gives a non-linear wind-gradient with the greatest change of wind-speed close to the surface. The effect on the calculated data is seen below in Figure 27:
The GPS data is the same as before. The top blue line is the calculated heading. The light blue second line is the raw GPS ground speed. The difference between the heading and track lines is the drift and this is variable due to the wind-gradient, reducing at low altitude due to the lesser wind.
The GPS speed is again the raw data. The green airspeed line is slightly flatter compared to the airspeed with a uniform wind in Figure 26. This suggests that the effect of the wind-gradient is to reduce airspeed variability and reduce drag losses in the leeward turn. Aerodynamic drag follows a square law and the greater the variation of airspeed about a mean value the greater the total drag losses. The loss and gain of airspeed with height in the leeward wing-over turn is easier to see.
Can we conclude anything from this? There is no proof of anything here because the wind-velocity is an informed guess and not actual data. Nevertheless it demonstrates that on the balance of probabilities, the wind gradient theory of dynamic soaring is unlikely to be the whole answer. Contrary to the Wind Gradient theory or Rayleigh Cycle, there is no significant gain of airspeed in the climb and descent and no significant loss of airspeed in the windward turn. In any event, the effect of the wind-gradient is quite small because the bird is flying approximately crosswind and never gets near to an into-wind or downwind heading and the effect of the wind gradient is diminished by the angle off the wind. Also the effect is negligible above a height of three meters.
On the other hand, the data is entirely consistent with the Windward Turn Theory which can explain why the windward turn is flat and the leeward turn is a wing-over; how the bird gains momentum in the leeward turn and loses momentum in the windward turn and how the bird can maintain or gain airspeed and height in the windward turn.
These data comprise relatively short windward turns compared to film of albatrosses in moderate winds. Therefore I conclude that the wind here is stronger than normal and that the albatross is probably flying faster than normal and with steeper bank angles in the windward turn to mitigate the extremely large drift angles.