Aircraft Energy Gain From an Atmosphere in Motion

J. Philip Barnes www.HowFliesTheAlbatross.com May 2015
Aircraft Energy Gain From an Atmosphere in Motion 01-02 May, Santa Rosa, CA J. Philip Barnes It is a pleasure and honor to present today and tomorrow to this focused, international audience. Both of my presentations study aircraft energy gain from an atmosphere in motion. With tomorrow’s presentation, I hope to convince you that the most efficient electric aircraft is one that is configured for regeneration, whether or not we intend to use that feature. Today’s presentation describes the ultimate air vehicle in terms of efficiency, range, and endurance. Part 1 of 2 J. Philip Barnes May 2015

Part I of 2: How Flies the Albatross The Flight Mechanics of Dynamic Soaring 24 May J. Philip Barnes 6X / year It is my pleasure to share the recent discoveries of most of what we need to know to understand how the wandering albatross uses its dynamic soaring technique to remain aloft indefinitely on shoulder-locked wings, progressing in any overall direction of its choice. Of course, the albatross occasionally dips down behind a wave and then punches up into the wind, and this in itself is a subset of dynamic soaring. But the albatross leaves the waves far behind as it circumnavigates Antarctica several times per year. J. Philip Barnes May 2015

Presentation Contents ~ How Flies the Albatross
Observations The visionaries Simulation Analysis Simplification Wind data The presentation will first introduce observations of well-known naturalists. We’ll then quote two visionaries whose work forms the basis of our analysis. We’ll show an automobile moon roof and model aircraft analogy which explains the essence of dynamic soaring, and which also shows that flight kinetic energy must be based on airspeed, not groundspeed or inertial speed. We’ll then investigate applicable properties of the wind. Next we review/renew the equations of motion, but just before you fall asleep, we’ll run a real-time simulation showing the albatross conducting a selection of maneuvers from its dynamic soaring repertoire. J. Philip Barnes May 2015

Presentation Contents
J. Philip Barnes May 2015

Observations of Well-known Naturalists
“The albatross ….. manages to remain master of its own course, either carried ... around the globe or ... against the strong winds without a beat of its wings.” -- Jacques Cousteau “The albatross can maintain this swooping soaring flight for hours on end without a single wing beat.” -- David Attenborough On shoulder-locked wings, the albatross can make net overall progress in any direction, including upwind. That the albatross can do these things is a matter of fact, documented by well-known naturalists, including David Attenborough and Jacques Cousteau. What may be controversial is the explanation of how this is done, and the controversy is largely based on two camps, one using airspeed to characterize flight kinetic energy, and the other camp using bird-backpack GPS/INS inertial speed which nearly equals groundspeed at the shallow climb and dive angles flown by the albatross. Depending on which camp we choose, we will draw entirely different conclusions as to where the bird gains kinetic energy in its cyclic trajectory. After I published my original SAE paper on dynamic soaring, I discovered Lord Rayleigh’s paper and was delighted to learn that I was firmly in the “airspeed camp” that he founded over a century ago. So, we are in good hands. Royal Albatross

Quoting the Visionaries
Isaac Newton, Principia, 1725 Wellcomeimages.org Lord Rayleigh, Nature, 1883 “Quantity of motion [momentum] is a measure...that arises from the velocity and the quantity of matter” “A change in motion [acceleration] is proportional to the motive force.” “Centripetal force is the force by which bodies are drawn from all sides...toward...a center.” “ ... suppose that above and below a certain plane ... there is a uniform horizontal wind, but that ascending through this plane the [wind] velocity increases...” “... energy at the disposal of the bird depends on his velocity relatively to the air” “....it is only necessary ... to descend ... to leeward, and ... ascend ... to windward.” We will take strong advantage of the work of these two visionaries in our dynamic soaring study. Although for my original SAE paper I certainly knew of Isaac Newton’s 1725 Principia, I was not aware of Lord Rayleigh’s 1883 paper in Nature. When it was shared with me, I was delighted to find complete agreement with my own approach and conclusions.

Moonroof & Model Airplane Flight kinetic energy depends on airspeed, not groundspeed Wow! Now I understand dynamic soaring well, say 50%..... 90 km/hr airspeed 90 km/hr 90 km/hr groundspeed This chart shows the essence of dynamic soaring, while also showing the importance of airspeed versus groundspeed. Let’s say we are driving our car at 90 km/hr with the moonroof open. Just beneath the moonroof we hold a model airplane. Although the model at this point has 90 km/hr groundspeed, releasing it would cause it to fall to the floor. So groundspeed is of no use for the purpose of remaining airborne. If instead the model were raised above the moon roof, it would suddenly gain 90 km/hr airspeed, climbing high into the sky. Thus, kinetic energy for flight must be based on airspeed, not groundspeed. Also important, we have in effect applied Lord Rayleigh’s two-step wind profile to reveal the better half of dynamic soaring, and that is to “ascend to windward” if windspeed increases with elevation. The other half: “descend to leeward.” J. Philip Barnes May 2015

Albatross GPS/INS-backpack velocity ~ equals ground speed “Backpack” INS/GPS velocity is very close to groundspeed, but the bird is rarely aligned with its ground track Vcosg Airspeed shadow Local wind w The bird is aligned with relative wind, representing its airspeed. y Lift & drag ~ airspeed squared. This sketch: INS/GPS velocity for K.E. yields error factor of 4 INS/GPS V Vg The albatross, a skillful flyer indeed, always remains pointed into the relative wind, thus with "coordinated turning." In the above sketch looking down at the top of the maneuver, the flight velocity vector projects onto the water an "airspeed shadow vector" (sun directly above) which, when vectorially combined with the local "true wind" vector (w), yields the groundspeed vector (Vg). Although the groundtrack of the albatross follows the groundspeed vector, the bird flies in accordance with the magnitude and direction of airspeed which, in the sketch above, is about twice the groundspeed. Some researchers recently fitted INS or GPS transmitters to the back of one or more birds. At the shallow flight path angles flown by the albatross, the INS or GPS velocity will closely represent groundspeed and reveal the ground track. This data proves quite useful for recording the vast distances covered by the albatross, and for observing elevation excursions and maneuver cycle times, but it proves utterly useless for drawing conclusions as to where in the dynamic soaring trajectory energy is gained, unless it is converted to airspeed by vectorial combination with the wind at each elevation. Unfortunately, these researchers neglected to measure the wind profile, and thus they neglected to vectorially synthesize the airspeed. Dynamic soaring, to quote from Lord Rayleigh, depends on the “speed relatively to the air.” This principle is illustrated in our automobile moon roof cartoon. Using raw INS or GPS velocity to characterize flight kinetic energy leads to an error factor of four at the conditions of the sketch above. Ground speed “…relatively to the air…” - Lord Rayleigh Nature, 05 April 1883 J. Philip Barnes May 2015

Wind speed data ~ Southern latitudes Real-time snapshot W, 10 m elev. Courtesy of the Department of Meteorology, University of Reading, UK, this is an interesting snapshot of a real-time update of the distribution of wind speed at 10m elevation in the southern hemisphere. Antarctica sits in the middle of the graphic, and the color contours reveal that the albatross flies in m/s winds as it circumnavigates Antarctica. W, m/s Data courtesy of Department of Meteorology, University of Reading, UK – J. Philip Barnes May 2015

Wind profile ~ First Vs. updated estimates The logarithmic profile is more representative and is founded on theory The wind profile which I had estimated a decade ago for my SAE paper, and which has been retained for today’s simulation, is found at the lower left, assuming a maximum wind of 7 m/s in a 20-m boundary layer. A far more accurate profile is shown at the right, based on off-shore wind-turbine data which became available after my paper was published. This shows that the boundary layer height exceeds 250-m. The profile has been shaped to include the well-known “power law,” while also passing through the 10-m : 15 m/s data of the previous slide. Although the wind speed largely determines how fast the albatross is blown downwind during its dynamic soaring cycles, the wind gradient is the key to dynamic soaring, and for the albatross, such gradient is of interest in the range of about 1-to-6 meters above the waves which no doubt will reshape the effective wind profile in some way which is exploited by the albatross. Anyway, we next compare the wind gradients for the elevations of interest. J. Philip Barnes May 2015

Wind gradients compared ~ First Vs. updated estimates Similar gradients, 1-to-6 m elevation Even though the wind speed profiles of the previous chart showed large differences, we see here that the wind gradients in the dynamic soaring region are roughly the same. Only subtle differences would be seen if our simulation were updated to use the updated gradients. J. Philip Barnes May 2015

f L V D g mw mg w Dynamic Soaring ~ Force Diagram y
Dynamic Soaring Force Vector (F) F = m(dw/dt), directed upwind Wellcomeimages.org Lord Rayleigh mg f y g D L mw V w Dynamic Soaring Thrust , T = F∙V Isolate dynamic soaring thrust (ignore weight & drag for now) T = m (dV/dt) = m (dw/dt) (dV/dw) = m (dw/dt) cosg cosy = m (dw/dz) (dz/dt) cosg cosy = m w’ V sing cosg cosy Here we show all the forces, including lift, weight, drag, and in particular, the dynamic soaring force which had been postulated in our 2004 SAE paper. As the albatross maneuvers, the dynamic soaring force of magnitude (m dw/dt) remains steadfastly level and pointed directly upwind. Since the wind profile is assumed fixed, only by moving vertically within the wind profile does the albatross experience the rate (dw/dt) and the corresponding dynamic soaring force. During descent, (dw/dt) is negative. Therefore, if the albatross descends downwind the dynamic soaring force vector will in effect point downwind, thus providing thrust. The component of dynamic soaring force aligned with the airspeed vector represents the dynamic soaring thrust. We now prove what had previously been postulated. To isolate the dynamic soaring thrust we momentarily ignore both weight and drag. Then applying Newton’s Law along the flight path, we find that the dynamic soaring thrust is proportional to the mass (m), wind gradient (w’), airspeed (V), flight path angle (g), and a “cosine product.” The latter becomes negative when the albatross turns downwind, whereby the dynamic soaring thrust becomes “negative upwind” and thus “positive downwind.” Note that the wind gradient (w’) does not itself change sign as the rate (dw/dt) changes sign. Thus, in accordance with Lord Rayleigh’s original assertion, the albatross gains energy with both upwind ascent and downwind descent. This represents the first direct quantitative characterization of Lord Rayleigh’s qualitative description of the essence of dynamic soaring. Direct quantitative equivalent of Lord Rayleigh’s qualitative dynamic soaring description J. Philip Barnes May 2015

Black-browed Albatross
The black-browed albatross, significantly smaller than the wandering albatross, also travels great distances with dynamic soaring. This one, which accompanied our ship for some time in the Drake Passage, was photographed in the howling wind from the stairs just above an aft deck which was awash with a foot or so of heaving, freezing water. Black-browed Albatross

Three orthogonal accelerations ~ Newton’s Law Applied g Loop Radius Vg V Vcosg g Isaac Newton V [Vcosg]y y Turn Radius A three-dimensional trajectory can be computed by breaking down the motion into two components, one in a horizontal plane, and the other in a vertical plane. At any point the airspeed vector is tangent to the flight path, with a horizontal velocity component given by V cos gamma. We can then look down on the trajectory to fit a local horizontal radius of curvature, with attendant turn rate “psi dot.” As shown to us by Isaac Newton, the acceleration toward the center of the horizontal circle is the product of horizontal velocity and turn rate. Similarly, we can stand off to the side and fit a roller-coaster-loop radius to the motion in a vertical plane. The corresponding acceleration toward the center of that loop is then given by the product of airspeed and pitch rate, “gamma dot.” The third acceleration is along the flight path itself, and this is determined by thrust in relation to drag and the weight component tangent to the flight path. J. Philip Barnes May 2015

Equations of motion ~ three orthogonal accelerations 1 1: Normal load factor 2 Thrust group Drag group 2: Dimensionless drag 3: Tangent. load factor 3 4: Heading rate 5: Lift coefficient 4 6: Drag-to-lift ratio 7: Trajectory 5 CL = nn W / (½  V2 S) It is convenient to non-dimensionalize the equations of motion and we begin by relating the drag-to-weight ratio to the product of normal load factor and drag-to-lift ratio. Along the flight path, the vehicle responds not only to gravity, but also to the difference between the thrust and drag groups. With this formulation, we see that the drag is in effect made worse when the bird maneuvers with a load factor greater than unity. It is interesting to see that the motion is entirely determined if we know the flight path angle and its rate, together with the bank angle and airspeed. The trimmed angle of attack then becomes a by-product of the lift coefficient corresponding to the given maneuvering conditions. For a flight simulator with smooth and realistic motion, we have the option of calling for, and numerically integrating, accelerations in gamma and phi. Alternatively, to simulate dynamic soaring, we can schedule gamma and phi with psi to not only follow the dynamic soaring rule (upwind ascent and downwind descent in a positive wind gradient), but also to yield the desired overall direction of motion. Later we will show that the albatross can dynamically soar in any overall direction, including upwind. Given the motion of the bird relative to the “current layer” of air, we can then superimpose any applicable atmospheric motion to obtain the trajectory seen by a stationary observer. D/L  (CDo /CL ) + CL /(3A) 6 Schedule any two angles, say g(t) & y(t) ; get dg/dt, dy/dt Eqns. yield all other parameters x = w – V cosg cosy downwind y = V cosg siny crosswind z = V sing vertical 7 J. Philip Barnes May 2015

Sensor platform is maintained level
The albatross, as well as apparently all other soaring birds, keeps its “sensor platform” perfectly level when turning. Indeed, soaring birds can be seen with wings banked at greater than 90-deg while holding the head perfectly level. Our interactive wireframe simulation includes this feature. J. Philip Barnes May 2015

Maneuver Angle Schedules ~ Math-modeled Examples Sine Wave Heading or time/period t 1 0.0 0.5 1.0 2 Dt Midpoint Shift Auxiliary Time, t1 t 2 0.0 0.5 1.0 3 Endpoint “dwell” Auxiliary Time, t2 Sin2 “adder” Flight Path Angle Schedule Heading or time/period Bank Angle Schedule The best way to simulate the graceful flight of the albatross is to schedule selected maneuver angles with equations. Naturally, the sinusoidal functions are well suited for this. Climbing and diving in accordance with the dynamic soaring rule is readily modeled with a sine wave, together with a “sine-squared” adder which allows us to adjust the relative amplitudes of the climb and dive angle excursions. Also, we can adjust the mid-point of the maneuver with an auxiliary time, and we can model the short period where the albatross skims its wingtip on the water with second auxiliary time which operates on the first. The result represents the flight path angle versus either heading or non-dimensional time. Usually, the bank angle will be computed in terms of scheduled inputs. In other cases, specifically for the “snaking-upwind” maneuver, we schedule the bank angle versus non-dimensional time. With these simple and powerful mathematical formulations, we need only adjust a handful of parameters by trial and error until the trajectory meets the various constraints, such as skimming the water, maintaining the energy balance, and traveling overall in the intended direction such as downwind, crosswind, or upwind. J. Philip Barnes May 2015

As noted earlier, a pair of maneuver angles such as (g, y) or (g, f) can be scheduled to satisfy the Dynamic Soaring Rule, with all other parameters determined by the equations of motion. Such scheduling can be taken versus a dimensionless time (t ≡ t/tc) where (tc) represents the cycle duration. In the figure above, we model the most challenging maneuver of the albatross’ repertoire, that of “snaking” upwind on shoulder-locked wings. At upper left are found the math-modeled schedules g(t) and y(t). The required bank angle (f) is determined by the equations of motion. At mid-left, we see that the total specific energy (E/g) is conserved. At the top-center we show three orthographic views of the trajectory, including “wind off” for the plan view. The objective of penetrating upwind, while observing the dynamic soaring rule and preserving total energy overall, requires maximizing the time spent headed upwind, minimizing the time spent headed crosswind or downwind, optimizing the airspeed to enhance dynamic soaring thrust, preserving aerodynamic efficiency (L/D), and avoiding a large altitude excursion which would promote greater downwind drift. Furthermore, the trajectory must yield reasonable bank angles and a peak normal load factor consistent with wing structural limits. At bottom left we see that the maneuver includes 2g and 3g turns. The chosen trajectory then consists of a 21o left “tack” upwind, rapid diving right turn across the wind, and rapid climbing left-hand turn, returning to the original tack. Although the maneuver rates and angles (g, y) are scheduled with symmetry, the right-hand turn at the top of the maneuver is taken at lower airspeed (V) than the left-hand turn taken at the bottom. Thus the lower turn radius [r ≈ V/(dy/dt)] is larger, leading to overall crosswind drift. This is best illustrated by the “wind off” trajectory (dashed curve) seen at the top-center of the figure. Nevertheless, by tracking the limits of the “wind on” trajectory (solid curves, top-center and bottom-right), we see the albatross making overall progress of 2.9 m/s upwind against a 13 m/s headwind, while drifting laterally at 3.4 m/s. Presumably, the albatross will periodically “mirror image” the maneuver to cancel the lateral drift overall, should it so desire. J. Philip Barnes May 2015

Real-time simulation Our interactive, real-time simulation of the albatross' repertoire of dynamic soaring maneuvers was originally hosted on Windows XP. With XP, the simulation runs as-is with the icon embedded in the graphic above at lower left. To run the simulation on newer platforms, first copy the legacy graphics module MSVBVM50.DLL which must be both “found and approved.” Such combination may require that it reside in the windows/system32 directory. This will not conflict with newer graphics modules. In perhaps most cases both files can reside conveniently together in whatever directory is preferred by the user. After copying the files, to run the simulation click moving ~ ... ~ ok ~ fly. The simulation shows the albatross conducting its dynamic soaring maneuvers with overall net progress direction chosen by the user. An additional maneuver illustrates flight along a tilted circle with both the wind and drag turned off (this maneuver was independently conceived by both Lord Rayleigh and the present author). This “tilted circle” in still air closely represents the flight path perceived by the bird as it conducts its circumpolar downwind spiral. Due to a minor bug in the software, this maneuver should be studied last to avoid numerical instability which, if encountered, is resolved by closing and re-opening the simulation. J. Philip Barnes May 2015

J. Philip Barnes www.HowFliesTheAlbatross.com
Dynamic soaring in the jet stream We are naturally led to ask if terrestrial dynamic soaring is feasible. Here we restrict ourselves to dynamic soaring over flat terrain, as the albatross maintains its total energy over the sea. Unfortunately, we learn that wind gradients near the ground are usually inadequate to support UAV dynamic soaring. Even in the Jetstream, the highly-repeatable wind gradients based on the data shown above are at best an order of magnitude below those exploited by the albatross. Thus a jetstream dynamic soaring aircraft will fly much faster than the albatross. Of course, the aircraft must avoid outright the commercial transport cruising altitude band, and it must at all altitudes have reliable collision-avoidance autonomy. Fortunately, a 1-km band for dynamic soaring is available at an altitude near 8.5 km. J. Philip Barnes

Dynamic soaring in the jet stream
Dynamic soaring thrust offsets drag overall in zoom cycle Basic feasibility test: w' (V/g) (L/D) sin g > 1 Notional conditions Altitude ~ 8.5 km Mach ~ 0.85 L/D ~ 25 The formula above, derived in our “Future Flight: Learning From the Birds” presentation at gives a first assessment of dynamic soaring feasibility, where the product of wind gradient, airspeed, lift-drag ratio, and climb angle must exceed unity by a sufficient margin to accommodate crosswind turns and other losses. Pending forthcoming simulations, we predict that a dynamic soaring UAV must exhibit a lift-drag ratio (L/D) of at least 25 and must attain a maximum speed approaching 0.85 Mach number. This entails high wing loading. One of the many extraordinary aspects of dynamic soaring is its favoritism for high weight (actually wing loading), a result of its demand for high velocity. Indeed, a given successful dynamic soaring aircraft can be rendered unsuccessful by reducing its weight below a certain threshold. The weight of the wandering albatross, in relation to its wingspan and wing area, has been optimized over 50 million years to best enable wind-profile penetration without preventing running-and-flapping takeoff from the water. Energy From an Atmosphere in Motion - Dynamic Soaring and Regen-electric Flight Compared J. Philip Barnes

Conclusion ~ How Flies The Albatross
Flight without flapping Wind gradient, not windspeed Airspeed, not groundspeed Net progress, any direction 50M-yr evolutionary opt. It was the author's privilege to witness a lengthy dynamic soaring performance by this Wandering albatross in between our ship and an iceberg which was over a kilometer in length. With or without the iceberg, the thrill of seeing a wandering albatross for the first time cannot be expressed in words. As noted earlier, the wandering albatross circumnavigates Antarctica several times per year. Every two years, it navigates with pinpoint accuracy to the island of its maiden flight where, with good fortune, it rejoins its life-long mate. A mature wandering albatross, reaching with luck 80 years, will have "greyed" by replacing most of its black feathers with white. The albatross in the photo above is relatively young. The albatross has graced our blue planet for over 50 million years, evolving a perfect match of its weight, size, shape, and variable geometry to the wind profile which constitutes its home over water as far as the eye can see. Now, with the sudden appearance of “modern” humans and their activity within just the last million years, the albatross faces the grave threat of extinction. Let not the albatross go extinct on our short watch. - J. Philip Barnes, May 2015 Let not the albatross go extinct on our short watch

About the Author Phil Barnes has a Master’s Degree in Aerospace Engineering from Cal Poly Pomona. He is a Principal Engineer and 34-year veteran of air vehicle and subsystems performance analysis at Northrop Grumman, where he presently supports both mature and advanced tactical aircraft programs. Author of several SAE and AIAA technical papers, and often invited to lecture at various universities, Phil is presently leading several Northrop Grumman-sponsored university research projects including an autonomous thermal soaring demonstration, passive bleed-and-blow airfoil wind-tunnel test, and application of Blender 3D software for aircraft parametric geometry modeling and flight simulation. Outside of work, Phil is a leading expert on dynamic soaring, and he is pioneering the science of regen-electric flight. J. Philip Barnes May 2015

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