Skip to main content
SpringerLink
Log in

Simulation of the trajectory of a punted rugby ball taking into account the asymmetrical pressure distribution caused by the seams

  • Regular Paper
  • Published:
Journal of Visualization Aims and scope Submit manuscript

Abstract

This paper describes the effect of the seams of a rugby ball on the side force and the flight trajectory of the punted kick. Measurement of the aerodynamic force on a non-spinning rugby ball reveals that the side force coefficient depends on the position of the seam as well as the angle of attack. It was found from pressure-sensitive paint measurements that the seam of the ball is the trigger for initiating low pressure when the seam is situated around 60° from the stagnation point. The flight trajectory of the fluctuating ball can be obtained by numerically integrating the six degree-of-freedom non-linear equations of motion. It was shown that a slower spinning ball fluctuates from side to side during flight because of the asymmetrical pressure distribution on the sides of the ball.

Graphical Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

C Y :

Side force coefficient

D :

Drag (N)

g :

Gravitational acceleration (m s−2)

I L :

Moment of inertia of the ball on its longitudinal axis (kg m2)

I T :

Moment of inertia of the ball on its transverse axis (kg m2)

L :

Lift (N), or rolling moment (Nm)

(L a , M a , N a ):

(x b , y b , z b ) Components of the aerodynamic moment (Nm)

M :

Pitching moment (Nm)

m b :

Mass of the ball, 0.42 (kg)

m ij :

Euler-angle transformation matrix

N :

Yawing moment (Nm)

(P, Q, R):

(x b , y b , z b ) Components of the angular velocity vector (s−1)

(U, V, W):

(x b , y b , z b ) Components of the velocity vector (m s−1)

\( \vec{V} \) :

Velocity vector (m s−1)

V b :

Volume of the ball, 4.8 × 10−3 (m3)

Y :

Side force (N)

(X a , Y a , Z a ):

(x b , y b , z b ) Components of the aerodynamic force (N)

(X E , Y E , Z E ):

Inertial coordinate system (m)

(x b , y b , z b ):

Body-fixed coordinate system (m)

\( \left( {\hat{x}_{b} ,\hat{y}_{b} ,\hat{z}_{b} } \right) \) :

(x b , y b , z b ) Components of the unit vector in the body-fixed coordinate system

α :

Angle of Attack (°)

Θ:

Pitch angle (°)

θ wt :

Angle between \( \vec{V} \) and \( \hat{x}_{b} \) (°)

ρ:

Air density (kg m−3)

Φ:

Roll angle (°)

Ψ:

Yaw angle (°)

\( \vec{\omega } \) :

Angular velocity vector (revolutions per second)

(χ, ξ, η, ζ):

Quaternion parameters

( )0 :

initial conditions

References

  • Bell JH, Schairer ET, Hand LA, Mehta RD (2001) Surface pressure measurements using luminescent coatings, Annu. Rev Fluid Mech 33:155

    Article  Google Scholar 

  • Brancazio PJ (1987) Rigid-body dynamics of a football. Am J Phys 55:415–420

    Article  Google Scholar 

  • Holmes C, Jones R, Harland AR, Petzing JN (2006) Ball launch characteristics for elite rugby union players. Eng Sport 6(1):211–216

    Google Scholar 

  • Kato K, Ohya A, Karasawa K (1999) Stability and control of airplanes, vol 11. University of Tokyo Press, Tokyo (in Japanese)

    Google Scholar 

  • Puklin E, Carlson B, Gouin S, Costin C, Green E, Ponomerev S, Tanji H, Gouterman M (2000) Ideality of pressure-sensitive paint. I. Platinum tetra (pentafluoropheny) porphine in fluoroacrylic polymer. J Appl Poly Sci 77:2795–2804

    Article  Google Scholar 

  • Seo K, Kobayashi O, Murakami M (2004) Regular and irregular motion of a rugby football during flight. Eng Sport 5(1):567–573

    Google Scholar 

  • Seo K, Kobayashi O, Murakami M (2006) Flight dynamics of the screw kick in rugby. Sports Eng 9:49–58

    Article  Google Scholar 

  • Stevens BL, Lewis FL (2003) Aircraft control and simulation, 2nd edn. Wiley, New York, pp 25–34

    Google Scholar 

  • Yamashita T, Sugiura H, Nagai H, Asai K, Ishida K (2007) Pressure-sensitive paint measurement of the flow around a simplified car model. J Vis 10:289–298

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by Grant-in-Aid for Young Scientists (A).

Author information

Authors and Affiliations

  1. Faculty of Education, Art and Science, Yamagata University, Yamagata, Japan

    Kazuya Seo

  2. Department of Aeronautics and Astronautics, Tokai University, Hiratsuka, Japan

    Osamu Kobayashi

  3. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan

    Masahide Murakami

  4. Department of Aerospace Engineering, Tohoku University, Sendai, Japan

    Daisuke Yorita, Hiroki Nagai & Keisuke Asai

Authors
  1. Kazuya Seo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Osamu Kobayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masahide Murakami
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Daisuke Yorita
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hiroki Nagai
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Keisuke Asai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kazuya Seo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Seo, K., Kobayashi, O., Murakami, M. et al. Simulation of the trajectory of a punted rugby ball taking into account the asymmetrical pressure distribution caused by the seams. J Vis 13, 97–105 (2010). https://doi.org/10.1007/s12650-009-0019-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12650-009-0019-0

Keywords

Search

Navigation