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Ice Deformation Explains Curling Stone Trajectories

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Abstract

Friction forces explain why the velocity and angular velocity of a curling stone cease at the same time, but cannot explain why the curl distance is approximately independent of initial angular speed. Forces that can lead to this puzzling independence include asymmetric normal force, radial force, and center of mass drag force. The mechanisms that generate these forces depend upon asymmetries in the distribution of grit or ice fragments under the stone or upon the scratches made by the stone on the pebbled ice surface. Several current models of curling stone behavior are specific cases of the general mechanisms presented here; their applicability is discussed. Pebble wear influences curling behavior.

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Notes

  1. It is the case quite generally that a single force in a plane is equivalent to an equal force through an arbitrary point—here the CM—and a couple [19].

  2. This number is from Lozowski et al (2015) and is equivalent to an area density of \(\sigma =3300-33,000~\text {m}^{-2}\). Ewasko (2017) places the optimum density at 6–8 pebbles in\(^{-2}\) or \(9300-12,400~\text {m}^{-2}\). Mielke (2015) and Minnaar (2007) both state that pebbling requires 3 liters of water per sheet of ice which for Extra Fine pebble size (see Table 1) is equivalent to 7600 pebbles \(\text {m}^{-2}\).

  3. We have assumed that if the stone is raised by a protruding pebble, then that pebble supports half the stone weight.

  4. Thus a conical protrusion of height and width \(\delta h\) will present a projected area of \(\frac{1}{2}\delta h^2\) to the ice. RB asperities are characterized by a width s that is much greater than depth d (see Nyberg et al. 2013) so that the projected area is \(\frac{1}{2}sd\). Thus for a protrusion that is a RB asperity \(\delta h=\sqrt{sd}\) is the median scratch width scale.

  5. A recent paper suggesting that scratches caused by directional sweeping can influence stone transverse motion also supports the idea of a scratch mechanism origin of curling behavior [42].

References

  1. Harrington, E.L.: An experimental study of the motion of curling stones. Trans. R. Soc. Can. 18, 247–258 (1924)

    Google Scholar 

  2. Macaulay, W.H., Smith, G.E.: Curling. Nature 127, 60 (1931)

    Article  Google Scholar 

  3. Walker, G.T.: The physics of sport. Math. Gaz. 20, 172–177 (1936)

    Article  Google Scholar 

  4. Armstrong, K.S.: The physics of curling. Phys. Teach. 9, 384 (1971)

    Article  Google Scholar 

  5. Allen, J.: Friction on the ski slopes. Phys. World 10(3), 17 (1997)

    Article  Google Scholar 

  6. Shegelski, M., Niebergall, R., Walton, M.: Curl guide. Phys. World 10(6), 19 (1997)

    Article  Google Scholar 

  7. Denny, M., Robinson, H.: The last word. Phys. World 10(7), 20 (1997)

    Article  Google Scholar 

  8. Green, D.: Curling black label. Phys. World 10(9), 20 (1997)

    Article  Google Scholar 

  9. Lozowski, E., Shegelski, M.R.A., Hawse, M., et al.: Comment on “A scratch-guide model for the motion of a curling rock’’. Tribol. Lett. 68, 2 (2020). https://doi.org/10.1007/s11249-019-1242-z

    Article  Google Scholar 

  10. Penner, A.R.: Reply to the comment on “A scratch-guide model for the motion of a curling rock’’. Tribol. Lett. 68, 1 (2020). https://doi.org/10.1007/s11249-019-1243-y

    Article  Google Scholar 

  11. Lozowski, E., Shegelski, M.R.A.: Comment on “Improved pivot-slide model of the motion of a curling rock’’. Can. J. Phys. 99, 202–203 (2021)

    Article  CAS  Google Scholar 

  12. Mancini, G., de Schoulepnikoff, L.: Reply to the comment by Lozowski and Shegelski on “Improved pivot-slide model of the motion of a curling rock’’. Can. J. Phys. 99, 204–205 (2021)

    Article  CAS  Google Scholar 

  13. Wikipedia: Curling. https://en.wikipedia.org/wiki/Curling. Accessed 4 Jan 2022

  14. Denny, M.: Curling rock dynamics. Can. J. Phys. 76, 295–304 (1998)

    CAS  Google Scholar 

  15. Shegelski, M.R.A., Niebergall, R.: The motion of rapidly rotating curling rocks. Austral. J. Phys. 52, 1025–1038 (1999)

    Article  Google Scholar 

  16. Johnston, G.W.: The dynamics of a curling stone. Can. Aeronaut. Space J. 27, 144–161 (1981)

    Google Scholar 

  17. Maeno, N.: Assignments and progress of curling stone dynamics. Proc. Inst. Mech. Eng. (2016). https://doi.org/10.1177/1754337116647241

    Article  Google Scholar 

  18. Kameda, T., Shikano, D., Harada, Y., et al.: The importance of the surface roughness and running band area on the bottom of a stone for the curling phenomenon. Sci. Rep. (2020). https://doi.org/10.1038/s41598-020-76660-8

    Article  Google Scholar 

  19. Symon, K.R.: Mechanics, p. 230. Addison-Wesley, Reading (1960)

    Google Scholar 

  20. Maeno, N.: Curl mechanism of a curling stone on ice pebbles. Bull. Glaciol. Res. 28, 1–6 (2010)

    Article  Google Scholar 

  21. Lozowski, E., et al.: Comparison of IMU measurements of curling stone dynamics with a numerical model. Procedia Eng. 147, 596–601 (2016)

    Article  Google Scholar 

  22. Lozowski, E., Shegelski, M.R.A.: First principles pivot-slide model of the motion of a curling rock: Qualitative and quantitative predictions. Cold Regions Sci. Technol. 146, 182–186 (2018)

    Article  Google Scholar 

  23. Denny, M.: Comment on “On the motion of an ice hockey puck,’’ by K Voyenli and E Eriksen [Am. J. Phys. 53 (12), 1149–1153 (1985)]. Am. J. Phys. 74, 554–556 (2006)

    Article  Google Scholar 

  24. Shegelski, M.R.A., Niebergall, R., Walton, M.A.: The motion of a curling rock. Can. J. Phys. 74, 663–670 (1996)

    Article  CAS  Google Scholar 

  25. Penner, R.A.: The physics of sliding cylinders and curling rocks. Am. J. Phys. 69, 332–339 (2001)

    Article  Google Scholar 

  26. Maeno, N.: Dynamics and curl ratio of a curling stone. Sports Eng. 17, 33–41 (2017)

    Article  Google Scholar 

  27. Ivanov, A.P., Shuvalov, N.D.: One the motion of a heavy body with a circular base on a horizontal plane and riddles of curling. Regular Chaotic Dyn. 17, 97–104 (2012)

    Article  Google Scholar 

  28. Minnaar, J.: Scottish Ice Curling Group (Reports) https://scottishcurlingicegroup.org/reports.html (2007). Accessed 4 Jan 2022

  29. Lozowski, E.P., Szilder, K., Maw, S., et al: Towards a first-principles model of curling ice friction and curling stone dynamics. In: Proc. 25th International Ocean and Polar Engineering Conference, Kona, Big Island, Hawaii, USA, June 21–26 (2015)

  30. Ewasko, G.: CurlManitoba (Rocks-Pebble-Scraping) https://curlmanitoba.org/wp-content/uploads/2017/06/Rocks-Pebble-Scraping.pdf. Accessed 19 Jan 2022

  31. Mielke, J.: Curling Baron (Pebble/Nip) https://curlingbaron.wordpress.com/making-ice/. Accessed 19 Jan 2022

  32. Poirier, L., Lozowski, E.P., Thompson, R.I.: Ice hardness in winter sports. Cold Regions Sci. Technol. 67, 129–134 (2011)

    Article  Google Scholar 

  33. Kim, E., Gagnon, R.E.: A preliminary analysis of the crushing specific energy of iceberg ice under rapid compressive loading. In: 23rd IAHR International Symposium on Ice, Ann Arbor, Michigan, May 31–June 1(2016)

  34. Blackford, J.R.: Sintering and microstructure of ice: a review. J. Phys. D 40, R355 (2007)

    Article  CAS  Google Scholar 

  35. Denny, M.: Curling rock dynamics: Towards a realistic model. Can. J. Phys. 80, 1005–1014 (2002)

    Article  CAS  Google Scholar 

  36. Nyberg, H., Alfredson, S., Hogmark, S., et al.: The asymmetrical friction mechanism that puts the curl in the curling stone. Wear 301, 583–589 (2013)

    Article  CAS  Google Scholar 

  37. Maeno, N.: Curling. In: Braghin, F., Cheli, F., Maldifassi, S., et al. (eds.) The Engineering Approach to Winter Sports, pp. 327–347. Springer, New York (2016)

    Chapter  Google Scholar 

  38. Lozowski, E., Shegelski, M.R.A.: Pivot-slide model of the motion of a curling rock. Can. J. Phys. 94, 1305–1309 (2016)

    Article  Google Scholar 

  39. Penner, A.R.: A scratch-guide model for the motion of a curling rock. Tribol. Lett. 67, 35 (2019). https://doi.org/10.1007/s11249-019-1144-0

    Article  Google Scholar 

  40. Mancini, G., de Schoulepnikoff, L.: Improved pivot-slide model of the motion of a curling rock. Can. J. Phys. 97, 1301–1308 (2019)

    Article  CAS  Google Scholar 

  41. Honkanen, V., Ovaska, M., Alava, M.J., et al.: A surface topography analysis of the curling stone curl mechanism. Sci. Rep. (2018). https://doi.org/10.1038/s41598-018-26595-y

    Article  Google Scholar 

  42. Balsdon, M., Wood, J.: Comparing broom conditions in curling: Measurements using ice topography. In: Proc. 13th Internat. Sports Eng. Conference, June 22–26 (2020)

  43. Lozowski, E., Shegelski, M.R.A.: Null effect of scratches made by curling rocks. J. Sports Eng. Technol. 233, 370–374 (2018)

    Google Scholar 

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Acknowledgements

The author is grateful to Martin Ziegler for renewing his interest in this puzzling problem.

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    Mark Denny

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Denny, M. Ice Deformation Explains Curling Stone Trajectories. Tribol Lett 70, 41 (2022). https://doi.org/10.1007/s11249-022-01582-7

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