Hostname: page-component-5d59c44645-7l5rh Total loading time: 0 Render date: 2024-02-25T00:53:10.268Z Has data issue: false hasContentIssue false

How to extract energy from turbulence in flight by fast tracking

Published online by Cambridge University Press:  30 June 2021

Scott A. Bollt
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY14850, USA Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA91125, USA
Gregory P. Bewley*
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY14850, USA
Email address for correspondence:


We analyse a way to make flight vehicles harvest energy from homogeneous turbulence by fast tracking in the way that falling inertial particles do. Mean air speed increases relative to flight through quiescent fluid when turbulent eddies sweep particles and vehicles along in a productive way. Once swept, inertia tends to carry a vehicle into tailwinds more often than headwinds. We introduce a forcing that rescales the effective inertia of rotorcraft in computer simulations. Given a certain thrust and effective inertia, we find that flight energy consumption can be calculated from measurements of mean particle settling velocities and acceleration variances alone, without the need for other information. In calculations using a turbulence model, we optimize the balance between the work performed to generate the forcing and the advantages induced by fast tracking. The results show net energy reductions of up to approximately 10 % relative to flight through quiescent fluid and mean velocities up to 40 % higher. The forcing expands the range of conditions under which fast tracking operates by a factor of approximately ten. We discuss how the mechanism can operate for any vehicle, how it may be even more effective in real turbulence and for fixed-wing aircraft and how modifications might yield yet greater performance.

JFM Papers
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



Ákos, Z., Nagy, M., Leven, S. & Vicsek, T. 2010 Thermal soaring flight of birds and unmanned aerial vehicles. Bioinspir. Biomim. 5 (4), 045003.CrossRefGoogle ScholarPubMed
Al-Ghussain, L. & Bailey, S.C.C. 2020 An approach to minimize aircraft motion bias in multi-hole probe wind measurements made by small unmanned aerial systems. Atmos. Meas. Tech. 14, 173184.CrossRefGoogle Scholar
Ayyalasomayajula, S., Warhaft, Z. & Collins, L.R. 2008 Modeling inertial particle acceleration statistics in isotropic turbulence. Phys. Fluids 20 (9), 95104.CrossRefGoogle Scholar
Bewley, G.P., Saw, E.W. & Bodenschatz, E. 2013 Observation of the sling effect. New J. Phys. 15, 083051.CrossRefGoogle Scholar
Bostan, A., Marynych, A. & Raschel, K. 2019 On the least common multiple of several random integers. J. Number Theory 204, 113133.CrossRefGoogle Scholar
Bowlin, M.S. & Wikelski, M. 2008 Pointed wings, low wingloading and calm air reduce migratory flight costs in songbirds. PLoS ONE 3 (5), e2154.CrossRefGoogle ScholarPubMed
Chabot, D. 2018 Trends in drone research and applications as the journal of unmanned vehicle systems turns five. J. Unmanned Veh. Syst. 6 (1), vixv.CrossRefGoogle Scholar
Chudej, K., Klingler, A.-L. & Britzelmeier, A. 2015 Flight path optimization of a hang-glider in a thermal updraft. Intl Fed. Automat. Control 48 (1), 808812.Google Scholar
Dávila, J. & Hunt, J.C.R. 2001 Settling of small particles near vortices and in turbulence. J. Fluid Mech. 440, 117145.CrossRefGoogle Scholar
de Divitiis, N. 2002 Effect of microlift force on the performance of ultralight aircraft. J. Aircraft 39, 318325.CrossRefGoogle Scholar
Falkovich, G., Fouxon, A. & Stepanov, M.G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419, 151154.CrossRefGoogle ScholarPubMed
Fernández-Perdomo, E., Cabrera, J., Hernández-Sosa, D., Isern, J., Domínguez-Brito, A., Redondo, A., Coca, J., Ramos, A.-G., Alvarez Fanjul, E. & Garcia, M. 2010 Path planning for gliders using regional ocean models: application of Pinzón path planner with the ESEOAT model and the RU27 trans-atlantic flight data. In 2010 OCEANS IEEE, Sydney, pp. 1–10. IEEE.CrossRefGoogle Scholar
Fisher, A., Marino, M., Clothier, R., Watkins, S., Peters, L. & Palmer, J.L. 2015 Emulating avian orographic soaring with a small autonomous glider. Bioinspir. Biomim. 11 (1), 016002.CrossRefGoogle ScholarPubMed
Gabrielli, G. & von Kármán, T. 1950 What price speed? J. Am. Soc. Nav. Engrs 72, 775781.Google Scholar
Garau, B., Alvarez, A. & Oliver, G. 2006 AUV navigation through turbulent ocean environments supported by onboard H-ADCP. In Proceedings of the 2006 IEEE International Conference on Robotics and Automation (ed. S. Hutchinson), pp. 3556–3561. IEEE.Google Scholar
González-Rocha, J., De Wekker, S.F.J., Ross, S.D. & Woolsey, C.A. 2020 Wind profiling in the lower atmosphere from wind-induced perturbations to multirotor UAS. Sensors 20 (5), 1341.CrossRefGoogle ScholarPubMed
Good, G.H., Ireland, P.J., Bewley, G.P., Bodenschatz, E., Collins, L. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.CrossRefGoogle Scholar
Gorisch, W. 2011 Glider's climb in turbulent air. Tech. Soaring 35 (4), 116124.Google Scholar
Hover, F.S., Techet, A.H. & Triantafyllou, M.S. 1998 Forces on oscillating uniform and tapered cylinders in cross flow. J. Fluid Mech. 363, 97114.CrossRefGoogle Scholar
Johnson, W. 1980 Helicopter Theory. Courier Dover Publications.Google Scholar
Katzmayr, R. 1922 Effect of periodic changes of angle of attack on behavior of airfoils. NACA Tech. Rep. NACA-TM 147.Google Scholar
Kraichnan, R.H. 1970 Diffusion by a random velocity field. Phys. Fluids 13 (1), 2231.CrossRefGoogle Scholar
Koay, T.-B. & Chitre, M. 2013 Energy-efficient path planning for fully propelled AUVs in congested coastal waters. In 2013 MTS/IEEE OCEANS, Bergen, pp. 1–9. IEEE.Google Scholar
Kushleyev, A., Mellinger, D., Powers, C. & Kumar, V. 2013 Towards a swarm of agile micro quadrotors. J. Auton. Robots 35, 287300.CrossRefGoogle Scholar
Langelaan, J. 2007 Long distance/duration trajectory optimization for small UAVs. AIAA Paper 2007-6737.CrossRefGoogle Scholar
Langelaan, J.W. & Bramesfeld, G. 2008 Gust energy extraction for mini- and micro- uninhabited aerial vehicles. J. Guid. Control Dyn. 32 (2), 464473.CrossRefGoogle Scholar
Laurent, K., Fogg, B., Ginsburg, T., Halverson, C., Lanzone, M., Miller, T., Winkler, D.W. & Bewley, G.P. 2021 Turbulence explains the accelerations of an eagle in natural flight. Proc. Natl Acad. Sci. USA 118 (23), e2102588118.CrossRefGoogle ScholarPubMed
Lissaman, P. & Patel, C. 2007 Neutral energy cycles for a vehicle in sinusoidal and turbulent vertical gusts. AIAA Paper 2007-863.CrossRefGoogle Scholar
Mackowski, A.W. & Williamson, C.H.K. 2011 Developing a cyber-physical fluid dynamics facility for fluid–structure interaction studies. J. Fluids Struct. 27 (5), 748757.CrossRefGoogle Scholar
Mahmoudzadeh, S., Powers, D. & Yazdani, A. 2016 Differential evolution for efficient AUV path planning in time variant uncertain underwater environment. arXiv:1604.02523.Google Scholar
Mallon, J.M., Bildstein, K.L. & Katzner, T.E. 2015 In-flight turbulence benefits soaring birds. Auk 133 (1), 7985.CrossRefGoogle Scholar
Maxey, M.R. 1987 a The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441465.CrossRefGoogle Scholar
Maxey, M.R. 1987 b The motion of small spherical particles in a cellular flow field. Am. Inst. Phys. 30 (7), 1915.Google Scholar
Maxey, M.R. & Corrsin, S. 1986 Gravitational settling of aerosol particles in randomly oriented cellular flow fields. J. Atmos. Sci. 43 (11), 11121134.2.0.CO;2>CrossRefGoogle Scholar
Maxey, M.R. & Riley, J.J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883889.CrossRefGoogle Scholar
Mordant, N., Crawford, A.M. & Bodenschatz, E. 2004 Experimental Lagrangian acceleration probability density function measurement. Physica D 193 (1), 245251.CrossRefGoogle Scholar
Morelli, E.A. & Smith, M.S. 2009 Real-time dynamic modeling: data information requirements and flight-test results. J. Aircraft 46 (6), 18941905.CrossRefGoogle Scholar
Morelli, P. 2003 Why microlift soaring? In XXVII OSTIV Congress, Leszno, Poland.Google Scholar
Norberg, U.M. 1996 Avian Energetics and Nutritional Ecology. Springer.Google Scholar
Nourani, E. & Yamaguchi, N. 2017 The effects of atmospheric currents on the migratory behavior of soaring birds: a review. Ornithological Sci. 16, 515.CrossRefGoogle Scholar
Patel, C. & Kroo, I. 2006 Control law design for improving UAV performance using wind turbulence. AIAA Paper 2006-231.CrossRefGoogle Scholar
Patel, C.K., Lee, H.-T. & Kroo, I.M. 2009 Extracting energy from atmospheric turbulence with flight tests. Tech. Soaring 33 (4), 100108.Google Scholar
Pennycuick, C. 2008 Soaring behaviour and performance of some east african birds, observed from a motor-glider. IBIS 114, 178218.CrossRefGoogle Scholar
Pennycuick, C.J. 2002 Gust soaring as a basis for the flight of petrels and albatrosses (Procellariiformes). Avian Sci. 2, 112.Google Scholar
Porta, A., Voth, G., Crawford, A., Alexander, J. & Bodenschatz, E. 2000 Fluid particle accelerations in fully developed turbulence. Nature 409, 10171019.CrossRefGoogle Scholar
Pozorski, J. & Rosa, B. 2019 The motion of settling particles in isotropic turbulence: filtering impact and kinematic simulations as subfilter model. In Direct and Large-Eddy Simulation XI (ed. Salvetti, M.V. et al. ), ERCOFTAC Series, vol. 25, pp. 215220. Springer.CrossRefGoogle Scholar
Preiss, J., Honig, W., Sukhatme, G. & Ayanian, N. 2017 Crazyswarm: a large nano-quadcopter swarm. In IEEE International Conference on Robotics and Automation (ed. Okamura, A. et al. ), pp. 32993304. IEEE.Google Scholar
Quinn, D., Kress, D., Chang, E., Stein, A., Wegrzynski, M. & Lentink, D. 2019 How lovebirds maneuver through lateral gusts with minimal visual information. Proc. Natl Acad. Sci. USA 116 (30), 1503315041.CrossRefGoogle ScholarPubMed
Reddy, G., Celani, A., Sejnowski, T.J. & Vergassola, M. 2016 Learning to soar in turbulent environments. Proc. Natl Acad. Sci. USA 113 (33), E4877E4884.CrossRefGoogle ScholarPubMed
Rosa, B., Parishani, H., Ayala, O. & Wang, L.-P. 2016 Settling velocity of small inertial particles in homogeneous isotropic turbulence from high-resolution DNS. Intl J. Multiphase Flow 83, 217231.CrossRefGoogle Scholar
Shakhatreh, H., Sawalmeh, A.H., Al-Fuqaha, A., Dou, Z., Almaita, E., Khalil, I., Othman, N.S., Khreishah, A. & Guizani, M. 2019 Unmanned aerial vehicles (UAVs): a survey on civil applications and key research challenges. IEEE Access 7, 4857248634.CrossRefGoogle Scholar
Teets, E.H. Jr. & Carter, E.J. 2002 Atmospheric conditions of stratospheric mountain waves: soaring the Perlan aircraft to 30 km. In 10th Conference on Aviation, Range, and Aerospace Meteorology (ed. T. Glickman). American Meteorological Society.Google Scholar
Tom, J. & Bragg, A. 2019 Multiscale preferential sweeping of particles settling in turbulence. J. Fluid Mech. 871, 244270.CrossRefGoogle Scholar
Tooby, P.F., Wick, G.L. & Isaacs, J.D. 1977 The motion of a small sphere in a rotating velocity field: a possible mechanism for suspending particles in turbulence. J. Geophys. Res. 82 (15), 20962100.CrossRefGoogle Scholar
Voth, G.A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49 (1), 249276.CrossRefGoogle Scholar
Wang, L.-P. & Maxey, M.R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 2768.CrossRefGoogle Scholar
Watkins, S., Abdulrahim, M., Thompson, M.A., Shortis, M., Loxton, B., Segal, R., Bil, C. & Watmuff, J. 2012 An overview of experiments on the dynamic sensitivity of MAVs to turbulence. Aeronaut. J. 114 (1158), 485492.CrossRefGoogle Scholar
Watkins, S., Mohamed, A., Fisher, A., Clothier, R., Carrese, R. & Fletcher, D.F. 2015 Towards autonomous MAV soaring in cities: CFD simulation, EFD measurement and flight trials. Intl J. Micro Air Veh. 7 (4), 441448.CrossRefGoogle Scholar
White, C., Watkins, S., Lim, E.W. & Massey, K. 2012 The soaring potential of a micro air vehicle in an urban environment. Intl J. Micro Air Veh. 4 (1), 113.CrossRefGoogle Scholar
Wood, R.J. 2007 Design, fabrication, and analysis of a 3DOF, 3 cm flapping-wing MAV. In IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1576–1581. IEEE.CrossRefGoogle Scholar
Yang, H., Jing, D., Tarokh, V., Bewley, G.P. & Ferrari, S. 2021 Flow parameter estimation based on on-board measurements of air vehicle traversing turbulent flows. AIAA Paper 2021-0380.CrossRefGoogle Scholar
Yokoyama, N. 2011 Path generation algorithm for turbulence avoidance using real-time optimization technique. AIAA Paper 2011-6957.CrossRefGoogle Scholar