Multibody System Dynamics

, Volume 32, Issue 3, pp 337–356 | Cite as

Simulation of rowing in an optimization context

  • Robert Pettersson
  • Arne Nordmark
  • Anders Eriksson


Competitive rowing requires efforts close to the physiological limits, where oxygen consumption is one main aspect. The rowing event also incorporates interactions between the rower, the boat and oars, and water. When the intention is to improve the performance, all these properties make the sport interesting from a scientific point of view, as the many variables influencing the performance form a complex optimization problem. Our aim was to formulate the rowing event as an optimization problem where the movement and forces are completely determined by the optimization, giving at least qualitative indications on good performance. A mechanical model of rigid links was used to represent rower, boat and oars. A multiple phase cyclic movement was simulated where catch slip, driving phase, release slip and recovery were modeled. For this simplified model, we demonstrate the influence of the stated mathematical cost function as well as a parameter study where the optimal performance is related to the planned average boat velocity. The results show qualitatively good resemblance to expected movements for the rowing event. An energy loss model in combination with case specific properties of rower capacities, boat properties, and rigging was required to draw qualitative practical conclusions about the rowing technique.


Optimal control Biomechanics Boat-oar-water interaction Multiple phase optimization 



The authors gratefully acknowledge financial support from the Swedish National Center for Research in Sports (CIF) and from the Swedish Research Council (VR).


  1. 1.
    Volianitis, S., Secher, N.H.: Rowing, the ultimate challenge to the human body—implications for physiological variables. Clin. Physiol. Funct. Imaging 29(4), 241–244 (2009) CrossRefGoogle Scholar
  2. 2.
    Nolte, V.: Rowing Faster, 2nd edn. Human Kinetics, Champaign (2005) Google Scholar
  3. 3.
    Hofmijster, M.J., Landman, E.H.J., Smith, R.M., van Soest, A.J.K.: Effect of stroke rate on the distribution of net mechanical power in rowing. J. Sports Sci. 25(4), 403–411 (2007) CrossRefGoogle Scholar
  4. 4.
    Tachibana, K., Yashiro, K., Miyazaki, J., Ikegami, Y., Higuchi, M.: Muscle cross-sectional areas and performance power of limbs and trunk in the rowing motion. Sports Biomech. 6(1), 44–58 (2007) CrossRefGoogle Scholar
  5. 5.
    Nozaki, D., Kawakami, Y., Fukunaga, T., Miyashita, M.: Mechanical efficiency of rowing a single scull. Scand. J. Med. Sci. Sports 3, 251–255 (1993) CrossRefGoogle Scholar
  6. 6.
    Izquierdo-Gabarren, M., de Txabarri Expósito, R., de Villarreal, E., Izquierdo, M.: Physiological factors to predict on traditional rowing performance. Eur. J. Appl. Physiol. 108(1), 83–92 (2010) CrossRefGoogle Scholar
  7. 7.
    Shimoda, M., Fukunaga, T., Higuchi, M., Kawakami, Y.: Stroke power consistency and 2000 m rowing performance in varsity rowers. Scand. J. Med. Sci. Sports 19(1), 83–86 (2009) CrossRefGoogle Scholar
  8. 8.
    Caplan, N., Gardner, T.: A fluid dynamic investigation of the big blade and macon oar blade designs in rowing propulsion. J. Sports Sci. 25(6), 643–650 (2007) CrossRefGoogle Scholar
  9. 9.
    Leroyer, A., Barré, S., Kobus, J.M., Visonneau, M.: Experimental and numerical investigations of the flow around an oar blade. J. Mar. Sci. Technol. 13, 1–15 (2008) CrossRefGoogle Scholar
  10. 10.
    Sliasas, A., Tullis, S.: Numerical modelling of rowing blade hydrodynamics. Sports Eng. 12, 31–40 (2009) CrossRefGoogle Scholar
  11. 11.
    Leroyer, A., Barré, S., Kobus, J.M., Visonneau, M.: Influence of free surface, unsteadiness and viscous effects on oar blade hydrodynamic loads. J. Sports Sci. 28(12), 1287–1298 (2010) CrossRefGoogle Scholar
  12. 12.
    Ĉerne, T., Kamnik, R., Munih, M.: The measurement setup for real-time biomechanical analysis of rowing on an ergometer. Measurement 44(10), 1819–1827 (2011) CrossRefGoogle Scholar
  13. 13.
    Sliasas, A., Tullis, S.: Modelling the effect of oar shaft bending during the rowing stroke. Proc. Inst. Mech. Eng., Part P: J. Sports Eng. Technol. 225, 265–270 (2011) Google Scholar
  14. 14.
    Hofmijster, M., De Koning, J., van Soest, A.J.: Estimation of energy loss at the blades in rowing: common assumptions revisited. J. Sports Sci. 28(10), 1093–1102 (2010) CrossRefGoogle Scholar
  15. 15.
    Cabrera, D., Ruina, A., Kleshnev, V.: A simple 1+ dimensional model of rowing mimics observed forces and motions. Hum. Mov. Sci. 25, 192–220 (2006) CrossRefGoogle Scholar
  16. 16.
    Serveto, S., Barré, S., Kobus, J.M., Mariot, J.P.: A three-dimensional model of the boat-oars-rower system using ADAMS and LifeMOD commercial software. Proc. Inst. Mech. Eng., Part P: J. Sports Eng. Technol. 224(1), 75–88 (2010) CrossRefGoogle Scholar
  17. 17.
    Rongère, F., Khalil, W., Kobus, J.M.: Dynamic modelling and simulation of rowing with a robotics formalism. In: 16th International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 260–265 (2011) Google Scholar
  18. 18.
    Pettersson, R., Nordmark, A., Eriksson, A.: Free-time optimization of targeted movements based on temporal FE approximation. In: Proceedings of the Tenth International Conference on Computational Structures Technology. Civil-Comp Press, Kippen (2010) Google Scholar
  19. 19.
    Pettersson, R., Nordmark, A., Eriksson, A.: Optimization of multiple phase human movements. Multibody Syst. Dyn. (2013). doi: 10.1007/s11044-013-9349-8 MathSciNetGoogle Scholar
  20. 20.
    Eriksson, A.: Temporal finite elements for target control dynamics of mechanisms. Comput. Struct. 85, 1399–1408 (2007) CrossRefMathSciNetGoogle Scholar
  21. 21.
    Eriksson, A., Nordmark, A.: Temporal finite element formulation of optimal control in mechanisms. Comput. Methods Appl. Mech. Eng. 199(25–28), 1783–1792 (2010) CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Baudouin, A., Hawkins, D.: A biomechanical review of factors affecting rowing performance. Br. J. Sports Med. 36(6), 396–402 (2002) CrossRefGoogle Scholar
  23. 23.
    Jones, J.A., Allanson-Bailey, L., Jones, M.D., Holt, C.A.: An ergometer based study of the role of the upper limbs in the female rowing stroke. In: Procedia Engineering, vol. 2, pp. 2555–2561 (2010) Google Scholar
  24. 24.
    O’Sullivan, F., O’Sullivan, J., Bull, A.M.J., McGregor, A.H.: Modelling multivariate biomechanical measurements of the spine during a rowing exercise. Clin. Biomech. 18(6), 488–493 (2003) CrossRefGoogle Scholar
  25. 25.
    Kornecki, S., Jaszczak, M.: Dynamic analysis of rowing on Concept II type C ergometer. Biol. Sport 27(3), 187–194 (2010) CrossRefGoogle Scholar
  26. 26.
    Kaphle, M., Eriksson, A.: Optimality in forward dynamics simulations. J. Biomech. 41(6), 1213–1221 (2008) CrossRefGoogle Scholar
  27. 27.
    Erdemir, A., McLean, S., Herzog, W., van den Bogert, A.J.: Model-based estimation of muscle forces exerted during movements. Clin. Biomech. 22, 131–154 (2007) CrossRefGoogle Scholar
  28. 28.
    Ding, J., Wexler, A.S., Binder-Macleod, S.A.: A predictive model of fatigue in human skeletal muscles. J. Appl. Physiol. 89, 1322–1332 (2000) Google Scholar
  29. 29.
    Gill, P.E., Murray, W., Saunders, M.A.: User’s guide for SNOPT version 7: software for large-scale nonlinear programming. Tech. rep, Stanford, CA, USA (2006) Google Scholar
  30. 30.
    van Soest, A.J.K., Hofmijster, M.J.: Strapping rowers to their sliding seat improves performance during the start of ergometer rowing. J. Sports Sci. 27(3), 283–289 (2009) CrossRefGoogle Scholar
  31. 31.
    Zajac, F.E.: Muscle and tendon: properties, models, scaling and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17, 359–411 (1989) Google Scholar
  32. 32.
    Pennestrì, E., Stefanelli, R., Valentini, P.P., Vita, L.: Virtual musculo-skeletal model for the biomechanical analysis of the upper limb. J. Biomech. 40(6), 1350–1361 (2007) CrossRefGoogle Scholar
  33. 33.
    Eriksson, A., Nordmark, A.: Activation dynamics in the optimization of targeted movements. Comput. Struct. 89(11–12), 968–976 (2011) CrossRefGoogle Scholar
  34. 34.
    Kosterina, N., Westerblad, H., Eriksson, A.: History effect and timing of force production introduced in a skeletal muscle model. Biomech. Model. Mechanobiol. 11(7), 947–957 (2012) CrossRefGoogle Scholar
  35. 35.
    Consiglieri, L., Pires, E.B.: An analytical model for the ergometer rowing: inverse multibody dynamics analysis. Comput. Methods Biomech. Biomed. Eng. 12(4), 469–479 (2009) CrossRefGoogle Scholar
  36. 36.
    Bull, A.M.J., McGregor, A.H.: Measuring spinal motion in rowers: the use of an electromagnetic device. Clin. Biomech. 15(10), 772–776 (2000) CrossRefGoogle Scholar
  37. 37.
    Hase, K., Andrews, B., Zavatsky, A., Halliday, S.: Biomechanics of rowing. JSME Int. J. 45(4), 1082–1092 (2002) CrossRefGoogle Scholar
  38. 38.
    Baudouin, A., Hawkins, D.: Investigation of biomechanical factors affecting rowing performance. J. Biomech. 37, 969–976 (2004) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Robert Pettersson
    • 1
  • Arne Nordmark
    • 1
  • Anders Eriksson
    • 1
  1. 1.KTH MechanicsRoyal Institute of TechnologyStockholmSweden

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