Gottfried Sachs

Technische Universität München, München, Bavaria, Germany

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Publications (74)25.12 Total impact

  • Gottfried Sachs
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    ABSTRACT: A new modeling approach is presented for describing flap-gliding flight in birds and the associated mechanical energy cost of travelling. The new approach is based on the difference in the drag characteristics between flapping and non-flapping due to the drag increase caused by flapping. Thus, the possibility of a gliding flight phase, as it exists in flap-gliding flight, yields a performance advantage resulting from the decrease in the drag when compared with continuous flapping flight. Introducing an appropriate non-dimensionalization for the mathematical relations describing flap-gliding flight, results and findings of generally valid nature are derived. It is shown that there is an energy saving of flap-gliding flight in the entire speed range compared to continuous flapping flight. The energy saving reaches the highest level in the lower speed region. The travelling speed of flap-gliding flight is composed of the weighted average of the differing speeds in the flapping and gliding phases. Furthermore, the maximum range performance achievable with flap-gliding flight and the associated optimal travelling speed are determined. Copyright © 2015. Published by Elsevier Ltd.
    Journal of Theoretical Biology 04/2015; DOI:10.1016/j.jtbi.2015.03.022 · 2.30 Impact Factor
  • Gottfried Sachs
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    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.
    Journal of Bionic Engineering 01/2015; 12(1). DOI:10.1016/S1672-6529(14)60100-1 · 1.33 Impact Factor
  • Gottfried P. Sachs
    AIAA Atmospheric Flight Mechanics (AFM) Conference; 08/2013
  • Gottfried P. Sachs, Jakob Lenz, Florian Holzapfel
    AIAA Atmospheric Flight Mechanics (AFM) Conference; 08/2013
  • Johannes Traugott, Anna Nesterova, Gottfried Sachs
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    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.
    IEEE Spectrum 07/2013; 50(7):46-54. DOI:10.1109/MSPEC.2013.6545122 · 0.94 Impact Factor
  • Gottfried Sachs
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    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.
    Journal of Theoretical Biology 09/2012; 316C:35-41. DOI:10.1016/j.jtbi.2012.08.039 · 2.30 Impact Factor
  • Source
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    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.
    PLoS ONE 09/2012; 7(9):e41449. DOI:10.1371/journal.pone.0041449 · 3.53 Impact Factor
  • Gottfried Sachs, Jakob Lenz
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    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.
    Mathematical biosciences 08/2011; 234(2):75-83. DOI:10.1016/j.mbs.2011.08.005 · 1.49 Impact Factor
  • Gottfried Sachs, Jakob Lenz, Florian Holzapfel
    AIAA Guidance, Navigation, and Control Conference; 08/2011
  • Gottfried Sachs, Jakob Lenz, Florian Holzapfel
    AIAA Atmospheric Flight Mechanics Conference; 08/2011
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    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.
    AIAA Guidance, Navigation, and Control Conference and Exhibit; 01/2011
  • Gottfried Sachs, Jalkob Lenz, Florian Holzapfel
    AIAA Guidance, Navigation, and Control Conference; 08/2010
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    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.
    AIAA Atmospheric Flight Mechanics Conference; 08/2010
  • AIAA Guidance, Navigation, and Control Conference; 08/2010
  • Gottfried Sachs, Mochammad Agoes Moelyadi
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    ABSTRACT: Using a sophisticated aerodynamic method, the effects of extremely large dihedral on the aerodynamic characteristics of birds are determined. With this method, it is possible to generate solutions for the addressed aerodynamic problem, which shows a high complexity due to interference effects caused by dihedral and pronounced 3-dimensional flow properties as well as due to complex wing geometries. From the obtained results it follows that extremely large dihedral has substantial effects on the aerodynamic force characteristics. There are significant changes in the lift, the drag and the side force, thus affecting the flight performance. Furthermore, the obtained results show that the aerodynamic rolling and yawing moment characteristics are influenced by extremely large dihedral to a high degree. This is a significant outcome for lateral-directional stability because the aerodynamic rolling and yawing moment characteristics have a determinative influence here.
    Journal of Bionic Engineering 03/2010; 7(1):95-101. DOI:10.1016/S1672-6529(09)60191-8 · 1.33 Impact Factor
  • Gottfried Sachs, Jakob Lenz, Florian Holzapfel
    AIAA Guidance, Navigation, and Control Conference; 08/2009
  • AIAA Atmospheric Flight Mechanics Conference; 08/2009
  • Gottfried Sachs, Jakob Lenz, Florian Holzapfel
    AIAA Guidance, Navigation, and Control Conference; 08/2009
  • Gottfried Sachs
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    ABSTRACT: Solutions for the speed stability problem in bird flight at low speed are developed. Speed stability is usually considered not to exist in flapping flight at speeds below the speed of the minimum power required, and in gliding flight below the speed for maximum range. Approaches thus far for solving the speed stability problem are relating to a 1-degree-of-freedom model of the bird where the speed is regarded as the only motion variable involved. However, a speed deviation is inherently associated with a deviation in the height. In this paper, an expanded treatment with an appropriate mathematical model is presented. The expanded treatment is based on a 2-degree-of-freedom model of the bird. Thus, it is possible to account for the speed and the height changes. With this expanded treatment, it can be shown that there is speed stability in the gliding flight of birds, whether the speed is below the speed for maximum range or above. This also holds for flapping flight with regard to speeds below the speed of the minimum power required. Further, it is shown that there can be speed instability if the bird acts as a controller to suppress height deviations. For this purpose, a model of the bird acting as a controller is presented.
    Mathematical biosciences 05/2009; 219(1):1-6. DOI:10.1016/j.mbs.2008.10.009 · 1.49 Impact Factor
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    ABSTRACT: Cycle slips are a common error source in Global Navigation Satellite System (GNSS) carrier phase measurements. In this paper, the cycle slip problem is approached using Receiver Autonomous Integrity Monitoring (RAIM) methodology. Carrier phase measurements are used here in a single-receiver time-differential positioning method where integer ambiguities are canceled, but any cycle slips remain. The performance of the method was assessed by comparing the detection results to a Real-Time Kinematic (RTK) solution and by manual data examination. Postprocessing results obtained using authentic Global Positioning System (GPS) measurements logged by low-cost single-frequency receivers show that the method is able to reliably detect and identify single errors but fails in an exemplary multiple outlier scenario. As no reference receiver is needed, the method is a potential means to produce cycle-slip-corrected data usable in any postprocessing application.
    Proceedings of the IEEE Workshop on Signal Processing Systems, SiPS 2009, October 7-9, 2009, Tampere, Finland; 01/2009