Dynamic Soaring Upwind and Downwind

1. Can an albatross use dynamic soaring to travel against the wind?

 Classic albatross dynamic soaring does not allow upwind dynamic soaring because the bird is flying cross-wind at low G and there is always a large downwind drift angle. However, there is anecdotal and data-logged evidence of upwind soaring but with a suggestion of higher metabolic rates on upwind legs compared with downwind or crosswind-soaring. This suggests that a different technique is being used to achieve upwind soaring and that if the bird is not actually flapping then one reason for this greater effort may be higher-G manoeuvring. In classic dynamic soaring, the load-factor in a 10 degree angle of bank windward turn is 1.015G. The leeward wing-over can be flown at a similar load-factor. In the upwind dynamic soaring manoeuvre described below, a 30 degree turn requires a load-factor of 1.15G. A difference of 0.135G may not seem like much but it represents an increase of 13% in the effort needed to keep the wings extended which must have an effect on the  energy budget of an albatross during a foraging trip lasting many days.

 On reflection, (this website is a work-in-progress) the significance of the wind-gradient in cross-wind dynamic soaring is minimal but it may be that regular wind-gradients or wind-shears, not necessarily depending on breaking waves, are used by albatrosses to achieve upwind and downwind dynamic soaring because the average heading is closer to the wind direction. Also, the high-G manoeuvring associated with upwind dynamic soaring may work in normal winds but will depend on how much effort the bird puts into it.  It now seems likely that the crosswind, upwind and downwind dynamic soaring techniques all blend seamlessly together according to the birds  desire to fly in a particular direction. These manoeuvres use essentially the same dynamics decribed in the RC gliders Lee-Soaring section; the difference being the specific parameters such as angle of bank and load-factor which lead to the shape of the manoeuvre. Therefore the reader will have to read that section as well to fully understand the process.

                   Figure 1

2. GPS tracking and albatross foraging

 Albatross are thought to home-in on their prey using their sense of smell and their primary mode of travel is dynamic soaring how do these two facts meld into a foraging strategy? If scent plumes drift downwind then the birds must fly upwind to find their meal. Their foraging technique clearly involves long-distance, high speed, low-energy dynamic soaring, mainly flying crosswind but drifting downwind. Presumably when their flight path intersects a scent plume they change to a higher-energy upwind soaring technique in the expectation of an imminent feast.

 There is now GPS data logged evidence of upwind dynamic soaring; an example of which is shown in figure 1. This comprises 46 hours of data and shows the track of a Laysan Albatross setting off from Oahu in the Hawaiian Islands and tracking North regardless of the relatively light Northerly wind. Of course, we don’t know whether the bird is dynamic soaring or flapping, although the flight path has the characteristic sinuous shape of dynamic soaring - sometimes very ordered, sometimes more chaotic. Unfortunately this particular research project did not record height information, which would have given a clue. This is analysed in more detail on the Laysan albatross tracking data page.

 The data I am using here is GPS tracking of an albatross, which was published on the website datadryad.org and comes from a research paper entitled: Flight paths of seabirds soaring over the ocean surface enable measurement of fine-scale wind speed and direction by Yonehara et al, University of Tokyo 2017.  The paper was concerned with the calculation of the wind-velocity by analysing seabird tracking data. They demonstrated that this method could help to verify and fill-in the gaps in wind-velocity data derived from other sources such as ships, buoys and satellites. The data comprised approximately 46 hours of latitude and longitude coordinates recorded at one second intervals.

 So, if classic dynamic soaring results in downwind drift, how is upwind dynamic soaring possible? There are two possible mechanisms involved.

 The first method happens when the bird is in a steeply banked turn passing through a  crosswind heading. It gets a pulse of thrust, the kick, as it penetrates a shallow shear boundary; perhaps in the lee of  a breaking wave. How does a gust accelerate a gliders airspeed?

 3. The Kick

 In normal straight 1G flight at the best lift/drag ratio angle of attack (3-4 degrees), the total aerodynamic force resolves into lift and drag respectively normal to and opposite to the direction of flight. If a vertical gust causes the angle of attack to increase close to the stalling angle of attack (about 15 degrees), the aerodynamic force is increased and tilted forward of the aircraft vertical and then resolves into lift and thrust. The aircraft accelerates forward and upward (the surge experienced by glider pilots flying into rising air). This accelerated motion reduces the angle of attack and the aircraft returns to a state of equilibrium, so that the effect can only be brief.

Figure 2

 Consider the albatross making a regular leeward turn as a steeply banked wing-over but close to the lee side of a steep swell or a breaking wave (figure 2). In the lee of the wave the wind may break away leaving a wind-shadow of relatively still air in the trough and a marked horizontal shear boundary between the strong wind above and the still air below.  As the bird penetrates the horizontal shear boundary at a steep angle of bank, it encounters a sudden increase in horizontal wind-speed and a sudden increase in airspeed and angle of attack. The lift and drag forces increase and tilt forward (Figure 3). This will cause a component of aerodynamic force T to act momentarily as a pulse of thrust and cause the airspeed to increase. The other component C acts as the centripetal force, maintaining the turn. Because of the increased angle of attack, this will be inherently high-G and therefore will require more effort on the part of the bird. Having gained an increment of airspeed, the bird then reverts to normal angles of attack. The bird can use the excess airspeed in any of three ways:

1 - It can gain height, or

2 - It can continue the turn and drop below the shear boundary in the downwind trough and gain distance downwind or crosswind, or

3 - It can reverse the direction of turn and drop below the shear boundary into the upwind trough and gain distance upwind, gliding as far as the next wave crest. If the swell is deep enough to create an air-flow separation in the troughs between wave crests, it may be possible to find still air, although the swells may be moving downwind.

 The pulse of propulsive force is similar to the process of auto-rotation which drives windmills and spins helicopter rotors in power-off glides. The increased load-factor due to the gust and the reversal of turn for upwind progress, will take more effort than rolling out of the turn into the downwind trough, hence the greater effort and metabolic rate during upwind dynamic soaring. The Kick model depends upon there being a gust or a wind shear which will most likely occur in the lee of a breaking wave but cannot be guaranteed especially in light winds or in the absence of steep waves. Therefore paradoxically it appeared that this particular dynamic soaring manoeuvre is only possible in strong winds.

 This gain of airspeed when penetrating a shear boundary is not the same as the Rayleigh cycle of wind-gradient dynamic soaring. However, it is similar to the lee-soaring model of dynamic soaring practised by RC model glider pilots.

Figure 3

4. A variation of the Windward Turn Theory

Figure 4

 The second effect happens when the bird deliberately uses high-G manoeuvring in the leeward turn while climbing and descending in a wind-gradient. (Fig 4). This would require greater energy expenditure on the part of the bird to maintain its flight posture under high-G. The mechanism here is the same as the Windward Turn Theory as explained in the Analysis section, but with a different shape to the manoeuvre and a different combination of bank-angle and load-factor. For more on this see the RC gliders Lee-soaring section. The upwind dynamic soaring manoeuvre is a hybrid of the classic albatross method and the RC glider method. Once again, the manoeuvre is modeled in an Excel spreadsheet, using the same set of equations as in the other sections and the output is in the form of graphs of each parameter.

 Here is the output from the spread sheet. Figure 5 is a plan view of the path through the air with the wind from the top (North). Figure 6 shows bird height against wind-angle, starting at 1m and ending with a slight increase in height.

Figure 5

This time, the manoeuvre starts at a wind-angle of 60 degrees off the wind, at low level. The bird has just made a turn reversal from right to left. It turns upwind and across the wind at a minimum of about 30 degrees angle of bank to the left. It pitches up, gaining height through the wind-gradient until, at a wind-angle of 300 degrees, 60 degrees off the wind to the left and at the top of the climb, the bird reverses the angle of bank again to 30 degrees angle of bank to the right. It begins to descend, turning right through North, ending up at a wind angle of 060 degrees again and back at sea-level but with a couple of metres per second excess speed (see figure 9) and a slight excess of height (see figure 5).

Figure 6

 

This gain of airspeed will not be achieved simply by climbing and descending upwind without turning or by turning without climbing and descending. It requires a minimum angle of bank at least 30 degrees which increases the load-factor and therefore the effort on the part of the albatross.

 

Figure 7

 It also requires the wind-gradient to help generate the rate of change of airspeed and ground-speed. In the spreadsheet the wind used depends on the glider height above an arbitrary datum as in figure 7. The wind is proportional to logbase 10 of the glider height. The total wind (as opposed to the headwind component) encountered by the bird at each wind-angle is shown in figure 8.

 

Figure 8

 

 

Figure 9

 The ground plot (fig 9) is a plan view,showing the path over the ground, compressed by the Northerly wind. The drift is greatest in the middle of the manoeuvre, at the greatest height and wind speed.

 The resulting airspeed and ground speed are shown in figure 10. Reading from left to right, the first quarter is a windward turn, both speeds decrease. The second quarter is a leeward turn with the wind and the drift increasing; both speeds increase. The roll reversal occurs at the mid-point, into another partial windward turn with the speeds decreasing. Finally this turn becomes a leeward turn and the speeds increase as the wind reduces with height. The net result is a slight overall gain of airspeed.  Remember this is the result of applying the aerodynamic forces and the rate of change of headwind component to calculate rate of change of airspeed and ground-speed during turning flight.

 Figure 10

 

Figure 11

 This result is similar to the result in the RC gliders lee-soaring section except with the right-hand half of the diagram inverted because of the roll reversal.

 For comparison, figure 11 is the airspeed and ground-speed in the RC gliders circular lee-soaring model. Here, there are no turn reversals in the circular flight path, although the drift flips between left and right drift at wind-angles 360 and 180. Both diagrams show a slight gain of airspeed at the end.

 Note that in this diagram the circle starts at 270degrees turning right (upwind). The curves are the same if the starting heading is 090degrees turning left.

 

 

 

Figure 12

5. Soaring downwind

 If the albatrosses can soar crosswind and upwind, can they soar downwind? You might think obviously yes; if crosswind dynamic soaring inevitably leads to down-wind drift, due to the drift angle, then surely they can dynamic soar directly downwind, albeit in the usual undulating fashion. Well maybe not.

 Figure 12 shows the circular RC gliders manoeuvre which produces the variation of speeds shown in figure 10. The manoeuvre starts at the lowest point on a crosswind heading and turns upwind, climbing through the wind-gradient. The highest point is at the upwind apex and the turn continues downwind descending back through the wind-gradient to the starting point. The quadrants are numbered and labelled as windward turns or leeward turns corresponding to figure 10.

 Next, in figure 13, are diagrams of the upwind and downwind dynamic soaring manoeuvres.

Figure 13

 We can see that the upwind manoeuvre, on the left, comprises only the sector 1 and sector 2 quadrants, with a turn reversal in the middle at the highest point. Whereas, the downwind manoeuvre on the right, comprises only sector 3 and 4 quadrants, again with a turn reversal in the middle but this time at the lowest point. Bear in mind that this involves climbing and descending through a wind gradient, as indicated by the high and low labels and also a greater angle of bank and load factor with consequently greater effort on the part of the bird, compared with crosswind dynamic soaring.

 Referring back to Figure 11 we can see that sectors 1 and 2 yield a net gain of airspeed; whereas sectors 3 and 4 give a net loss of airspeed. So it looks like dynamic soaring upwind using sectors 1 and 2 is feasable. However,  dynamic soaring directly downwind using sectors 3 and 4 in this fashion is not possible.

 On the Laysan albatross tracking data page there are many examples of crosswind and upwind dynamic soaring but nowhere is there any direct downwind dynamic soaring.

 

 

 

6. More downwind soaring

 But wait, it is possible to get a result for downwind dynamic soaring by reducing the amplitude of the turns and reversing the high and low spots, so that the manoeuvre becomes a variation of the classic crosswind dynamic soaring. This can be achieved at lesser G loading and results in an average ground track at about 140 degrees to the wind, as in figure 14 which is a plan view with the bird flying towards the South-West with a North wind. Although the bird begins and ends the manoeuvre close to the downwind heading, the overall track-made-good is about 40 degrees off the directly-downwind track; in other words at about 140 degrees of wind-angle.

  This is seen in figure 15 which is a close-up of a section of the actual albatross tracking data from the Tacking and gybing paragraph on the Laysan albatross tracking data page, also shown above; the section at about 897km North of departure. The bird travels a mean track made good of North-West, compared to the wind speed of 4m/s from the South-East. The straight line distance is 3000m in 5 minutes which is 10m/s ie faster than the wind. The birds track is seen to zig-zag downwind as it links 4 or 5 dynamic soaring manoeuvres on one side of the wind and then turning across the wind and doing another 4 or 5 DS manoeuvres on the other side and then switching back again.  This is a bit like gybing downwind in a sailboat and achieving a downwind speed greater than the wind. Other sections of the tracking data show the albatross moving downwind but apparently meandering at random and drifting downwind at the speed of the wind; so zig-zagging is apparently a more efficient way of travelling downwind; achieving greater speed with less effort.

Figure 14

Figure 15

 

 

 

 

 

 

 

 

 

 

 

 

7. Optical illusions

 I came up with this idea before I realised that upwind dynamic soaring really is possible. I was trying to debunk the idea that some people on ships under-way were reporting upwind dynamic soaring and this seemed impossible according to my theory. I can now show that upwind dynamic soaring is possible according to the Windward Turn theory so this paragraph is somewhat redundant.

 However, it is still a valid exercise in navigation and just goes to show how difficult it is to determine what a seabird is doing without any fixed references against which to compare its motion.

 When it appears that albatrosses are dynamic soaring upwind in light winds, there is an optical effect which can mislead the observer. There is an explanation for this optical illusion and it is down to those pesky triangles of velocity again!

 See Figure 16. Here is a diagram showing how the bird appears to fly upwind. The ship velocity is CB, the wind velocity is AB and the wind velocity relative to the ship is AC . A glance at the flag at position C suggests the ship is steaming approximately into the wind. The bird is seen dynamic soaring along path DH relative to the ship (average direction DG) and is actually keeping up with the ship. The observer only sees the bird following path DH relative to the ship. He cannot see the motion described by triangle DEF. The observer on the ship concludes that the bird is making distance upwind.

 In reality the bird is flying the dynamic soaring pattern along a mean air-velocity DE (that is the path relative to the air). Applying the wind velocity EF (same as AB) to that air-velocity DE, the birds track-made-good (path relative to the ‘ground’ ) is DF. The track-made-good resolves into components DG, lateral to, and GF parallel to the motion of the ship. Velocity component GF means the bird keeps up with the ship, (same as velocity CB). Angle d is the birds actual drift angle while angle tmg is the track-made-good relative to the wind. Angle tmg is greater than 90 degrees and therefore the bird is actually losing distance downwind.

Figure 16