[Show abstract][Hide abstract] ABSTRACT: A new modeling approach is presented for mathematically describing the drag due to wing flapping. It is shown that there is an aerodynamic cost of flapping in terms of an increase in the drag when compared with non-flapping. The drag increase concerns the induced drag which results from lift generation. There are two effects that yield the induced drag increase caused by flapping. The first effect is due to changes in the direction of the lift vectors at the left and right wings during the flapping cycle by tilting them according to the flapping angle of the wings. Because of tilting the lift vectors, more lift has to be generated than is required for the vertical force balance in flapping flight. This lift enlargement causes an increase of the induced drag. The second effect that increases the induced drag is due to changes in the magnitude of the lift vector in the course of the flapping cycle. Changes in the magnitude of the lift vector are necessary for generating thrust which is required for the longitudinal force balance. As a result, both effects of lift vector changes cause a drag increase when compared with non-flapping. Solutions on an analytical basis and as well as results using a computational fluid dynamics method are presented.
No preview · Article · Jan 2015 · Journal of Bionic Engineering
[Show abstract][Hide abstract] ABSTRACT: Dynamic soaring is a small-scale flight manoeuvre which is the basis for the extreme flight performance of albatrosses and other large seabirds to travel huge distances in sustained non-flapping flight. As experimental data with sufficient resolution of th ese small-scale movements are not available, knowledge is lacking about dynamic soaring and the physical mechanism of the energy gain of the bird from the wind. With new in-house developments of GPS logging units for recording raw phase observations and of a dedicated mathematical method for postprocessing these measurements, it was possible to determine the small-scale flight manoeuvre with the required high precision. Experimental results from tracking 16 wandering albatrosses (Diomedea exulans) in the southern Indian Ocean show the characteristic pattern of dynamic soaring. This pattern consists of four flight phases comprising a windward climb, an upper curve, a leeward descent and a lower curve, which are continually repeated. It is shown that the primary energy gain from the shear wind is attained in the upper curve where the bird changes the flight direction from windward to leeward. As a result, the upper curve is the characteristic flight phase of dynamic soaring for achieving the energy gain necessary for sustained non-flapping flight.
Full-text · Article · Nov 2013 · Journal of Experimental Biology
[Show abstract][Hide abstract] ABSTRACT: Results from in-flight measurements of dynamic soaring of albatrosses over land are pre-sented. Using a new computational method based on L1 phase measurement as well as min-iaturized and low cost GPS logging devices featuring a sufficiently high data sampling rate, it was possible to determine precisely the flight path and the motion quantities of the birds. The recorded data of the flight over land show the characteristic pattern of dynamic soaring that consists of continually repeated cycles comprising a windward climb, an upper curve, a leeward descent and a lower curve. A further point is the mechanism of the energy transfer from the wind to the bird. It is shown that the upper curve of a dynamic soaring cycle is the decisive flight phase of the energy gain.
[Show abstract][Hide abstract] ABSTRACT: THE MALE ALBATROSS IS FINALLY BACK FROM his foraging, and now there is no time to lose. His mate has been patiently sitting on their nest awaiting his return, without food, for nearly a month, and we have to get to her before she flies off to forage for herself. · Our colleague, biologist Anna Nesterova, crawls slowly toward the bird. All of a sudden, she lunges: With her left hand she expertly grabs the 10-kilogram albatross by the beak, and with her right arm she hugs its body and lifts it off the nest and its precious cargo, a single egg. Together we then fix a GPS logger onto the feathers of the bird's back with adhesive tape and glue. · Soon after we release her, the mother albatross takes two or three steps into the furious wind, opens her 3-meter-wide wings, and takes flight. Four weeks from now, she'll return to this island in the southern Indian Ocean bearing a data log of where and how she flew-data that at last will put to the test our theories of how she stays aloft so long, almost never touching down, barely even flapping her long, elegant wings. If we could get our aerial robots to emulate that feat, they might someday orbit Earth for months, surfers of the winds of the uttermost sky.
[Show abstract][Hide abstract] ABSTRACT: The maximum-range flight of a powered sailplane with a retractable
electric motor is treated as a periodic optimal control problem. The
periodic nature of the maximum-range flight, known as saw-tooth mode, is
due to the high drag when the motor is extended and the low drag when
the motor is retracted. An optimization treatment based on energy
considerations is performed to develop analytical solutions and to
deepen the insight into the physical mechanism underlying the
superiority of the saw-tooth mode. This is complemented by a treatment
using a modeling based on point mass dynamics and an efficient
optimization method to construct solutions for maximum-range saw-tooth
flight. As a main result concerning the range performance, it is shown
that the maximum range achievable with optimal saw-tooth flight is
considerably larger than the greatest range possible with the best
[Show abstract][Hide abstract] ABSTRACT: The effects of the wind on the energy expenditure of bounding flight and on the travelling speed are dealt with. For this purpose, a mathematical model of bounding flight in moving air is developed. Introducing an appropriate non-dimensionalization, results and findings of generally valid nature are derived. It is shown that bounding flight yields a flight mechanical advantage in headwinds when compared with continuous flapping flight. This is because the minimum energy expenditure is lower and the associated travelling speed is higher. The body lift in the bound phase has an advantageous influence. The effects of tailwinds yield less differences between bounding flight and continuous flapping flight.
No preview · Article · Sep 2012 · Journal of Theoretical Biology
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] ABSTRACT: A new modeling approach is presented which accounts for the unsteady motion features and dynamics characteristics of bounding flight. For this purpose, a realistic mathematical model is developed to describe the flight dynamics of a bird with regard to a motion which comprises flapping and bound phases involving acceleration and deceleration as well as, simultaneously, pull-up and push-down maneuvers. Furthermore, a mathematical optimization method is used for determining that bounding flight mode which yields the minimum energy expenditure per range. Thus, it can be shown to what extent bounding flight is aerodynamically superior to continuous flapping flight, yielding a reduction in the energy expenditure in the speed range practically above the maximum range speed. Moreover, the role of the body lift for the efficiency of bounding flight is identified and quantified. Introducing an appropriate non-dimensionalization of the relations describing the bird's flight dynamics, results of generally valid nature are derived for the addressed items.
No preview · Article · Aug 2011 · Mathematical biosciences
[Show abstract][Hide abstract] ABSTRACT: Flap-bounding flight which is a flight mode consisting of continually repeated cycles with flapping and non-flapping phases is treated as a periodic optimal control problem. Two modelings of flap-bounding flight are developed. One modeling is based on energy consider-ations. The goal is to derive analytical solutions using an appropriate non-dimensionaliza-tion. The other model accounts for the unsteady behavior of the state and control variables. Furthermore, an efficient optimization procedure is used to construct solutions. It is shown where flap-bounding flight is superior in the required energy per range when compared to the best continuous flapping flight.
[Show abstract][Hide abstract] ABSTRACT: The effects of a constant head-, tail- or crosswind on the maximum range which powered sailplanes with a retractable engine can achieve are treated. The maximum-range flight of this type of vehicle has periodic properties because there are alternating flight phases where the engine is extended or retracted. Optimization of this flight mode which is known as sawtooth flight is a periodic optimal control problem where the best operating conditions of the powered and gliding phase have to be determined. Saw-tooth flight enables a significant increase in the maximum range when compared with the best steady-state cruise. It is shown that wind conditions (head-, tail- or crosswind) have a considerable influence on the achievable maximum range. Solutions of the periodic optimal flight problem were obtained using an efficient optimization method and applying a realistic mathematical model for describing the motion of the vehicle as well as the procedure for extending and retracting the engine.
[Show abstract][Hide abstract] ABSTRACT: Results from in-flight measurements of dynamic soaring in wandering albatrosses are presented. The experimental results were obtained using a new computational method based on L1 phase measurement as well as miniaturized and low cost GPS logging devices featur-ing a sufficiently high data sampling rate. Thus, it was possible to determine precisely the flight path and the motion quantities of the birds. Wind information was obtained using SeaWinds on QuikSCAT Level 3 Daily, Gridded Ocean Wind Vectors (JPL SeaWinds Pro-ject). The presented results show how albatrosses manage to make progress against the wind in non-flapping flight by means of dynamic soaring.
[Show abstract][Hide abstract] ABSTRACT: Heat input reduction by appropriate, optimal trajectory control is considered for the range cruise and the return-to-base cruise of a hypersonic vehicle propelled by a turbo/ram jet engines combination. A mathematical model is developed for describing the unsteady heat transfer through the thermal protection system. This model is coupled to the model of the dynamics of the vehicle. An efficient optimization technique is applied for constructing a solution for the two cruise problems. The results show that significant heat input reductions can be achieved with only a small penalty in fuel consumption.
No preview · Article · Aug 2010 · Mathematical and Computer Modelling of Dynamical Systems
[Show abstract][Hide abstract] ABSTRACT: Results from in-flight measurement of dynamics soaring in wandering albatrosses are presented. With data from these measurements, it was possible to compute the flight paths and the motion quantities of the birds with high precision. This has been achieved using a new computational method for determining the position by applying L1 phase measure-ments and a miniaturized and low cost GPS logging device featuring a sufficiently high data sampling rate. The results from in-flight measurements show the characteristic altitude profile and the related motion quantities of the dynamic soaring maneuver which is repeated in a cyclic manner.
[Show abstract][Hide abstract] ABSTRACT: The focus of this paper lies on the treatment of a new class of bilevel optimal control problems, where the optimal solution of the upper-level parameter optimization problem depends on optimal solutions of two lower-level optimal control problems. An efficient way for the solution of such bilevel programming problems is introduced. In every iteration step of the upper-level optimization problem, the two lower-level optimal control problems are solved by applying a multiple shooting method. Furthermore, in each iteration, a sensitivity analysis with respect to selected parameters of the lower-level optimal control problems is carried out. The sensitivity analysis allows for a direct computation of the gradient of the objective of the upper-level parameter optimization problem with respect to the just-mentioned parameters of the lower-level optimal control problems. Thus, a time-consuming evaluation of the gradient of the upper-level optimization problem can be avoided, allowing for an efficient solution of the entire bilevel optimal control problem. As an illustrative example, the layout of an air racetrack such that two different aircraft have, in fact, exactly the same chance of winning is presented.