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Numerical analysis of dynamic stability of falling maple samaras

自由下落枫树翼果的动稳定性分析

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Abstract

Due to autorotation, samaras can fly efficiently and stably to be dispersed over a great distance under various weather conditions. Here, we provide a quantitative analysis of the dynamic stability of free-falling maple samara (Acer grosseri Pax) and verify whether they are dynamically stable as observed. Morphological and kinematic parameters were obtained based on the existing experimental data of the maple seed. Then the linearized equations of motion were derived, and the stability derivatives were calculated by a computational fluid dynamics method. The techniques of eigenvalue and eigenvector analysis were also used to examine the stability characteristics. It is found that there are five natural modes of motion of the maple seed: one stable oscillatory mode, one fast subsidence mode, one slow subsidence mode, and two neutral stable modes. The two neutral modes are manifested as the seed moving horizontally at a low speed under disturbance. Results show that the maple seed has dynamic stability in sustaining the steady autorotation and descent, exhibiting a minor horizontal motion when disturbed. These findings can be applied to biomimetic aircraft.

摘要

自转的翼果可以在各种天气条件下高效稳定地被传播到很远的地方. 本文我们对自由下落的枫树翼果(Acer Grosseri Pax)的 动态稳定性进行了定量分析, 并验证了它们是否像观察到的那样动态稳定. 本文基于已有的枫树翼果的自由落体实验数据, 获得了 它们的形态学和运动学参数; 然后推导了线化的运动方程组, 并通过计算流体力学方法计算了枫树翼果的稳定性导数. 特征值和特 征向量分析法被用来求解枫树翼果的动稳定性. 本文研究结果发现, 枫树翼果有五个特征模态: 一个振荡收敛模态，一个快衰减模 态, 一个慢衰减模态, 以及两个中性稳定模态. 两种中性稳定模态表现为, 翼果受扰后在水平方向上以很小的速度运动. 因此本文得 到结论, 枫树翼果在维持稳定的自转和下降过程中具有动态稳定性, 在受到干扰后表现出较小的水平运动. 枫树翼果的动稳定性结 果可以为仿翼果飞行器的设计和控制带来一些启发.

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References

  1. D. F. Greene, and E. A. Johnson, Long-distance wind dispersal of tree seeds, Can. J. Bot. 73, 1036 (1995).

    Article  Google Scholar 

  2. R. Nathan, G. Perry, J. T. Cronin, A. E. Strand, and M. L. Cain, Methods for estimating long-distance dispersal, Oikos 103, 261 (2003).

    Article  Google Scholar 

  3. G. Planchuelo, P. Catalán, J. A. Delgado, and A. Murciano, Estimating wind dispersal potential in Ailanthus altissima: The need to consider the three-dimensional structure of samaras, Plant BioSyst.-An Int. J. Dealing All Aspects Plant Biol. 151, 316 (2017).

    Article  Google Scholar 

  4. R. Nathan, G. G. Katul, H. S. Horn, S. M. Thomas, R. Oren, R. Avissar, S. W. Pacala, and S. A. Levin, Mechanisms of long-distance dispersal of seeds by wind, Nature 418, 409 (2002).

    Article  Google Scholar 

  5. D. S. Green, The terminal velocity and dispersal of spinning samaras, Am. J. Bot. 67, 1218 (1980).

    Article  Google Scholar 

  6. S. Minami, and A. Azuma, Various flying modes of wind-dispersal seeds, J. Theor. Biol. 225, 1 (2003).

    Article  MATH  Google Scholar 

  7. R. Å. Norberg, Autorotation, self-stability, and structure of single-winged fruits and seeds (samaras) with comparative remarks on animal flight, Biol. Rev. 48, 561 (1973).

    Article  Google Scholar 

  8. C. K. Augspurger, Morphology and dispersal potential of wind-dispersed diaspores of neotropical trees, Am. J. Bot. 73, 353 (1986).

    Article  Google Scholar 

  9. A. Azuma, Flight of seeds, flying fish, squid, mammals, amphibians and reptiles, Flow Phenom. Nature 1, 88 (2007).

    Google Scholar 

  10. D. Lentink, W. B. Dickson, J. L. van Leeuwen, and M. H. Dickinson, Leading-edge vortices elevate lift of autorotating plant seeds, Science 324, 1438 (2009).

    Article  Google Scholar 

  11. E. J. Lee, and S. J. Lee, Effect of initial attitude on autorotation flight of maple samaras (Acer palmatum), J. Mech. Sci. Technol. 30, 741 (2016).

    Article  Google Scholar 

  12. I. Lee, and H. Choi, Scaling law for the lift force of autorotating falling seeds at terminal velocity, J. Fluid Mech. 835, 406 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Rabault, R. A. Fauli, and A. Carlson, Curving to fly: Synthetic adaptation unveils optimal flight performance of whirling fruits, Phys. Rev. Lett. 122, 024501 (2019).

    Article  Google Scholar 

  14. K. Varshney, S. Chang, and Z. J. Wang, The kinematics of falling maple seeds and the initial transition to a helical motion, Nonlinearity 25, C1 (2011).

    Article  MATH  Google Scholar 

  15. F. Farvardin Ahranjani, and A. Banazadeh, Applied flight dynamics modeling and stability analysis of a nonlinear time-periodic mono-wing aerial vehicle, Aerospace Sci. Tech. 108, 106381 (2021).

    Article  Google Scholar 

  16. S. Jameson, K. Fregene, M. Chang, and N. Allen, in Lockheed Martin’s samarai nano air vehicle: Challenges, research, and realization: Proceedings of the 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Tennessee (2012).

  17. B. H. Kim, K. Li, J. T. Kim, Y. Park, H. Jang, X. Wang, Z. Xie, S. M. Won, H. J. Yoon, G. Lee, W. J. Jang, K. H. Lee, T. S. Chung, Y. H. Jung, S. Y. Heo, Y. Lee, J. Kim, T. Cai, Y. Kim, P. Prasopsukh, Y. Yu, X. Yu, R. Avila, H. Luan, H. Song, F. Zhu, Y. Zhao, L. Chen, S. H. Han, J. Kim, S. J. Oh, H. Lee, C. H. Lee, Y. Huang, L. P. Chamorro, Y. Zhang, and J. A. Rogers, Three-dimensional electronic microfliers inspired by wind-dispersed seeds, Nature 597, 503 (2021).

    Article  Google Scholar 

  18. G. K. Nave Jr., N. Hall, K. Somers, B. Davis, H. Gruszewski, C. Powers, M. Collver, D. G. Schmale Iii, and S. D. Ross, Wind dispersal of natural and biomimetic maple samaras, Biomimetics 6, 23 (2021).

    Article  Google Scholar 

  19. S. Patnaik, in Design optimization of monoblade autorotating pods to exhibit an unconventional descent technique using Glauert’s modeling: Proceedings of ASME International Mechanical Engineering Congress and Exposition, (American Society of Mechanical Engineers, 2021).

  20. D. Sufiyan, L. S. T. Win, S. K. H. Win, G. S. Soh, and S. Foong, Joint mechanical design and flight control optimization of a nature-inspired unmanned aerial vehicle via collaborative co-evolution, IEEE Robot. Autom. Lett. 6, 2044 (2021).

    Article  Google Scholar 

  21. S. Thomas, D. Ho, A. Kerroux, L. Lixi, N. Rackham, and S. Rosenfeld, Concept and design of a biomimetic single-wing MAV, Int. J. Unmanned Syst. Eng. 2, 16 (2014).

    Article  Google Scholar 

  22. E. R. Ulrich, D. J. Pines, and J. S. Humbert, From falling to flying: The path to powered flight of a robotic samara nano air vehicle, Bioinspir. Biomim. 5, 045009 (2010).

    Article  Google Scholar 

  23. S. Win, L. Win, D. Sufiyan, G. Soh, and S. Foong, in Concurrent optimization of mechanical design and control for flapless samara-inspired autorotating aerial robot: Proceedings of 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), (IEEE, Boston, 2020).

    Book  Google Scholar 

  24. S. K. H. Win, L. S. T. Win, D. Sufiyan, and S. Foong, Design and ontrol of the first foldable single-actuator rotary wing micro aerial vehicle, Bioinspir. Biomim. 16, 066019 (2021).

    Article  Google Scholar 

  25. A. M. El Makdah, K. Zhang, and D. E. Rival, On the robust autorotation of a samara-inspired rotor in gusty environments, Bioinspir. Biomim. 17, 044001 (2022).

    Article  Google Scholar 

  26. B.T. Flood, Development and analysis of an autorotating, disposable micro air vehicle for tactical surveillance, UNSW Canberra ADFA J. Undergrad. Eng. Res. 7 (2015).

  27. C. Pandolfi, and D. Izzo, Biomimetics on seed dispersal: survey and insights for space exploration, Bioinspir. Biomim. 8, 025003 (2013).

    Article  Google Scholar 

  28. J. Mitchell, and J. A. Marshall, Design of a novel auto-rotating uav platform for underground mine cavity surveying. Queen’s Adaptive Technol. Cent. (2017).

  29. A. Azuma, and K. Yasuda, Flight performance of rotary seeds, J. Theor. Biol. 138, 23 (1989).

    Article  Google Scholar 

  30. D. Kremer, R. JURIŠIĆ GRUBEŠIĆ, and T. Dubravac, Morphometric research of samaras of North American ash species from Croatian plantations, Periodicum Biologorum 112, 333 (2010).

    Google Scholar 

  31. K. Yasuda, and A. Azuma, The autorotation boundary in the flight of samaras, J. Theor. Biol. 185, 313 (1997).

    Article  Google Scholar 

  32. D. F. Greene, and E. A. Johnson, The aerodynamics of plumed seeds, Funct. Ecol. 4, 117 (1990).

    Article  Google Scholar 

  33. S. J. Lee, E. J. Lee, and M. H. Sohn, Mechanism of autorotation flight of maple samaras (Acer palmatum), Exp. Fluids 55, 1718 (2014).

    Article  Google Scholar 

  34. C. W. McCutchen, The spinning rotation of ash and tulip tree samaras, Science 197, 691 (1977).

    Article  Google Scholar 

  35. M. Rao, D. C. Hoysall, and J. Gopalan, Mahogany seed—a step forward in deciphering autorotation. Curr. Sci. 106, 1101 (2014).

    Google Scholar 

  36. B. J. W. Chen, X. Wang, Y. Dong, H. J. During, X. Xu, and N. P. R. Anten, Maternal environmental light conditions affect the morphological allometry and dispersal potential of acer palmatum samaras, Forests 12, 1313 (2021).

    Article  Google Scholar 

  37. T. De Bellis, I. Laforest-Lapointe, K. A. Solarik, D. Gravel, and S. W. Kembel, Regional variation drives differences in microbial communities associated with sugar maple across a latitudinal range, Ecology e3727 (2022).

  38. B. G. Kwon, and M. H. Sohn, Effects of the CG positions on the autorotative flight of maple seeds, Int. J. Aeronaut. Space Sci. 23, 241 (2022).

    Article  Google Scholar 

  39. E. Salcedo, C. Treviño, R. O. Vargas, and L. Martínez-Suástegui, Stereoscopic particle image velocimetry measurements of the three-dimensional flow field of a descending autorotating Mahogany seed (Swietenia macrophylla), J. Exp. Biol. 216, 2017 (2013).

    Google Scholar 

  40. M. H. Dickinson, F. O. Lehmann, and S. P. Sane, Wing rotation and the aerodynamic basis of insect flight, Science 284, 1954 (1999).

    Article  Google Scholar 

  41. M. H. Sohn, and D. K. Im, Flight characteristics and flow structure of the autorotating maple seeds, J. Vis. 25, 483 (2022).

    Article  Google Scholar 

  42. B. Etkin, and T. Teichmann, Dynamics of Flight: Stability and Control (Wiley, New York, 1982).

    Google Scholar 

  43. G. K. Taylor, and A. L. R. Thomas, Dynamic flight stability in the desert locust Schistocerca gregaria, J. Exp. Biol. 206, 2803 (2003).

    Article  Google Scholar 

  44. V. M. Ortega-Jimenez, N. S. W. Kim, and R. Dudley, Superb auto-rotator: Rapid decelerations in impulsively launched samaras, J. R. Soc. Interface. 16, 20180456 (2019).

    Article  Google Scholar 

  45. R. Fang, Y. Zhang, and Y. Liu, Aerodynamics and flight dynamics of free-falling ash seeds, World J. Eng. Technol. 5, 105 (2017).

    Article  Google Scholar 

  46. R. Fang, Aerodynamics and Flight Dynamics of Free-Falling Samara Seeds. Dissertation for Master’s Degree, (Beihang University, Beijing, 2018).

    Google Scholar 

  47. M. Sun, J. Wang, and Y. Xiong, Dynamic flight stability of hovering insects, Acta Mech. Sin. 23, 231 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  48. M. H. Sohn, in Effects of the configuration characteristics on the motion parameters of autorotating flight of plant seeds, Proceedings of 5th International Conference on Experimental Fluid Mechanics, Munich, 2018.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11832004). We thank Rui Fang for the experimental data on the maple seed, Yanpeng Liu, Yanlai Zhang, and Jianghao Wu for their helpful suggestions, and Mao Sun for his constructive comments. The work was carried out at National Supercomputer Center in Tianjin, and the numerical calculations were performed on TianHe-1 (A).

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  1. Ministry-of-Education Key Laboratory of Fluid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing, 100083, China

    Tiantian Chen  (陈甜甜) & Shilong Lan  (兰世隆)

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  1. Tiantian Chen  (陈甜甜)
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  2. Shilong Lan  (兰世隆)
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Correspondence to Tiantian Chen  (陈甜甜).

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Tiantian Chen and Shilong Lan proposed the research topic and figured out the framework to solve the problem. Tiantian Chen processed the experimental data, conducted the numerical calculation and all other calculations, and analyzed the results. Tiantian Chen wrote the first draft of the manuscript and made all the figures and tables in the manuscript. Shilong Lan supervised the project, revised and edited the final version, and received the funding.

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Chen, T., Lan, S. Numerical analysis of dynamic stability of falling maple samaras. Acta Mech. Sin. 38, 322111 (2022). https://doi.org/10.1007/s10409-022-22111-x

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