Arabian Journal for Science and Engineering

, Volume 43, Issue 9, pp 4957–4975 | Cite as

Development of a Novel Characterisation Methodology for the Aerodynamic Coefficients of a Tractor–Trailer Unit Based on Relative Flow Angles and Vehicle Dimensions

  • Vihar Malviya
  • Taimoor Asim
  • Isuru Sendanayake
  • Rakesh Mishra
Open Access
Research Article - Mechanical Engineering


Tractor–trailer units are integral part of the heavy commercial vehicle industry, used globally for goods transportation. Manufacturers have been trying to design aerodynamically efficient tractor–trailer units to reduce ever increasing fuel costs. In order to investigate the aerodynamic response of tractor–trailer units, the aerodynamic forces and moments have to be determined accurately, especially under crosswind conditions. In the present study, a computational fluid dynamics-based solver has been employed to simulate the flow field around a tractor–trailer with a view to quantify the effects of side wind and size variations on aerodynamic force moment system acting on tractor–trailer combination. It has been shown that the aerodynamic forces are significantly influenced by both the geometrical and flow characteristics. The drag, lift and side forces acting on a tractor–trailer unit are highest at relative flow angles of \(15{^{\circ }}\), \(30{^{\circ }}\) and \(90{^{\circ }}\), respectively. Aerodynamic forces and coefficients have been enumerated for these geometrical and flow conditions, and have been used to develop novel semi-empirical correlations for the aerodynamic coefficients for the tractor–trailer unit. These correlations have been shown to predict the aerodynamic coefficients for various vehicle dimensions under a range of flow conditions with reasonable accuracy.


Heavy commercial vehicle (HCV)  Computational fluid dynamics (CFD)  Computer-aided design (CAD)  Computer-aided engineering (CAE)  Aerodynamic coefficients 

List of symbols


Drag coefficient vehicle (–)

\(C_{\mathrm{L }}\)

Lift coefficient of the vehicle (–)


Side coefficient of the vehicle (–)


Coefficient of pressure (–)


Length of the vehicle (m)


Height of the vehicle (m)


Width of the vehicle (m)


Static gauge pressure (Pa)


Flow velocity magnitude (m/s)

Greek symbols

\(\infty \)

Free stream

\(\mu \)

Dynamic viscosity of air (N-s/m\(^{2}\))

\(\rho \)

Density of air (kg/m\(^{3}\))

\(\psi \)

Angle of the flow relative to the vehicle (rad, \({^{\circ }}\))


  1. 1.
    Baker, C.J.; Reynolds, S.: Wind-induced accidents of road vehicles. Accid. Anal. Prev. 24(6), 559–575 (1992)CrossRefGoogle Scholar
  2. 2.
    Hucho, W.: Aerodynamics of Road Vehicles, 4th edn. Society of Automotive Engineers (SAE), New York (1998)Google Scholar
  3. 3.
    Asim, T.; Sendanayake, I.; Mishra, R.;, Zala, K.; Ubbi, K.: Effects of moving boundary layer control (MSBC) on the drag reduction in heavy commercial vehicles. In: 40th National Conference on Fluid Mechanics and Fluid Power, NIT Hamirpur, pp. 12–14 , Paper No. 154 (Dec. 2013)Google Scholar
  4. 4.
    Malviya, V.U.: Effects of a novel aerodynamic intervention for heavy commercial vehicles on fuel saving and stability. Ph.D. Thesis, University of Huddersfield (2011)Google Scholar
  5. 5.
    Rose, M.J.: Commercial vehicle fuel economy—the correlation between aerodynamic drag and fuel consumption of a typical tractor. Wind Eng. Ind. Aerodyn. 9(1–2), 89–100 (1981)CrossRefGoogle Scholar
  6. 6.
    Calkins, D.E.; Su, W.; Chan, W.T.: A design rule-based tool for automobile systems design. SAE Technical Paper 980397 (1998)Google Scholar
  7. 7.
    Singh, R.: Automated aerodynamic design optimization process for automotive vehicle. SAE Technical Paper 2003-01-0993 (2003)Google Scholar
  8. 8.
    Malviya, V.U.; Mishra, R.; Fieldhouse, J.: Enhanced analytical vehicle stability model. In: 12th EAEC European Automotive Congress, Bratislava (29 June–1 July 2009)Google Scholar
  9. 9.
    Malviya, V.U.; Mishra, R.: Development of an analytical multi-variable steady-state vehicle stability model for heavy road vehicles. Appl. Math. Model. 38(19–20), 4756–4777 (2014)CrossRefGoogle Scholar
  10. 10.
    Malviya, V.U.; Mishra, R.; Fieldhouse, J.: CFD investigation of a novel fuel-saving device for articulated tractor–trailer combinations. Eng. Appl. Comput. Fluid Mech. 3(4), 587–607 (2009)Google Scholar
  11. 11.
    Berta, C.; Tacca, T.; Zucchelli, A.: Aerodynamic study on vehicle shape with the panel method: an effort to calculate the influence of shape characteristics on aerodynamic performance. SAE Technical Paper 801401 (1980)Google Scholar
  12. 12.
    Calkins, D.E.; Chan, W.T.: CDaero—a parametric aerodynamic drag prediction tool. SAE Technical Paper 980398 (1998)Google Scholar
  13. 13.
    Koromilas, C.; Harris, C.; Sumantran, V.; Pachon, L.; Zeng, S.: Rapid aerodynamic development of two-volume vehicle shapes. SAE Technical Paper 2000-01-0488 (2000)Google Scholar
  14. 14.
    Rho, J.H.; Ku, Y.C.; Lee, D.H.; Kee, J.D.; Kim, K.Y.: Application of modelling function design method to road vehicle aerodynamic optimization in initial design stage. SAE Technical Paper 2009-01-1166 (2009)Google Scholar
  15. 15.
    Baker, C.J.: A simplified analysis of various types of wind-induced road vehicle accidents. J. Wind Eng. Ind. Aerodyn. 22, 69–85 (1986)CrossRefGoogle Scholar
  16. 16.
    Baker, C.J.: Measures to control vehicle movement at exposed sites during windy periods. J. Wind Eng. Ind. Aerodyn. 25(2), 151–161 (1987)CrossRefGoogle Scholar
  17. 17.
    Baker, C.J.: High sided articulated road vehicles in strong cross winds. J. Wind Eng. Ind. Aerodyn. 31(1), 67–85 (1988)CrossRefGoogle Scholar
  18. 18.
    Coleman, S.A.; Baker, C.J.: High sided road vehicles in cross winds. J. Wind Eng. Ind. Aerodyn. 36(2), 1383–1391 (1990)CrossRefGoogle Scholar
  19. 19.
    Baker, C.J.: Ground vehicles in high cross winds part I: steady aerodynamic forces. J. Fluids Struct. 5(1), 69–90 (1991)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Baker, C.J.: Ground vehicles in high cross winds part II: unsteady aerodynamic forces. J. Fluids Struct. 5(1), 91–111 (1991)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Baker, C.J.: Ground vehicles in high cross winds part III: the interaction of aerodynamic forces and the vehicle system. J. Fluids Struct. 5(2), 221–241 (1991)CrossRefGoogle Scholar
  22. 22.
    Coleman, S.A.; Baker, C.J.: The reduction of accident risk for high sided road vehicles in cross winds. J. Wind Eng. Ind. Aerodyn. 44(1–3), 2685–2695 (1992)CrossRefGoogle Scholar
  23. 23.
    Baker, C.J.: The behaviour of road vehicles in unsteady cross winds. J. Wind Eng. Ind. Aerodyn. 49(1–3), 439–448 (1993)CrossRefGoogle Scholar
  24. 24.
    Baker, C.J.: The quantification of accident risk for road vehicles in cross winds. J. Wind Eng. Ind. Aerodyn. 52, 93–107 (1994)CrossRefGoogle Scholar
  25. 25.
    Allen, J.W.: Aerodynamic drag and pressure measurements on a simplified tractor–trailer model. J. Wind Eng. Ind. Aerodyn. 9(1–2), 125–136 (1981)CrossRefGoogle Scholar
  26. 26.
    Modi, V.J.: Moving surface boundary-layer control: a review. J. Fluids Struct. 11(6), 627–663 (1997)CrossRefGoogle Scholar
  27. 27.
    Regert, T.; Lajos, T.: Description of flow field in the wheelhouses of cars. Int. J. Heat Fluid Flow 28(4), 616–629 (2007)CrossRefGoogle Scholar
  28. 28.
    Singh, S.N.; Rai, L.; Puri, P.; Bhatnagar, A.: Effect of moving surface on the aerodynamic drag of road vehicles. Proc. Inst. Mech. Eng. D: J. Automob. Eng. 219, 127–134 (2005)CrossRefGoogle Scholar
  29. 29.
    Yabin, L.; Tan, L.; Hao, Y.; Xu, Y.: Energy performance and flow patterns of a mixed-flow pump with different tip clearance sizes. Energies 10(2), 191 (2017)CrossRefGoogle Scholar
  30. 30.
    Tan, L.; Zhu, B.; Wang, Y.; Cao, S.; Gui, S.: Numerical study on characteristics of unsteady flow in a centrifugal pump volute at partial load condition. Eng. Comput. 32(6), 1549–1566 (2015)CrossRefGoogle Scholar
  31. 31.
    Asim, T.; Mishra, R.: Optimal design of hydraulic capsule pipeline transporting spherical capsules. Can. J. Chem. Eng. 94(5), 966–979 (2016)CrossRefGoogle Scholar
  32. 32.
    Asim, T.; Mishra, R.: Computational fluid dynamics based optimal design of hydraulic capsule pipelines transporting cylindrical capsules. Int. J. Powder Technol. 295, 180–201 (2016)CrossRefGoogle Scholar
  33. 33.
    Asim, T.; Mishra, R.; Abushaala, S.; Jain, A.: Development of a design methodology for hydraulic pipelines carrying rectangular capsules. Int. J. Press. Vessels Pip. 146, 111–128 (2016)CrossRefGoogle Scholar
  34. 34.
    Agarwal, V.C.; Mishra, R.: Optimal design of a multi-stage capsule handling multi-phase pipeline. Int. J. Press. Vessels Pip. 75, 27–35 (1998)CrossRefGoogle Scholar
  35. 35.
    Mishra, R.; Singh, S.N.; Seshedri, V.: Velocity measurement in solid–liquid flows using an impact probe. Flow Meas. Instrum. 8(3–4), 157–165 (1998)CrossRefGoogle Scholar
  36. 36.
    Mishra, R.; Singh, S.N.; Seshedri, V.: Improved model for the prediction of pressure drop and velocity field in multi-sized particulate slurry flow through horizontal pipes. Powder Handl. Process. 10, 279–287 (1998)Google Scholar
  37. 37.
    Mishra, R.; Palmer, E.; Fieldhouse, J.: An optimization study of a multiple-row pin-vented brake disc to promote brake cooling using computational fluid dynamics. Proc. Inst. Mech. Eng. D: J. Automob. Eng. 223(7), 865–875 (2009)Google Scholar
  38. 38.
    Versteeg, H.K.; Malalasekera, W.: An Introduction to Computational Fluid Dynamics. Longman Scientific and Technical, London (1995)Google Scholar
  39. 39.
    Cebeci, T.; Shao, J.P.; Kafyeke, F.; Laurendeau, E.: Computational Fluid Dynamics for Engineers. Horizons Publishing, New York (2005)Google Scholar
  40. 40.
    Lomax, H.; Pulliam, T.H.; Zingg, D.W.: Fundamentals of Computational Fluid Dynamics. Springer, Berlin (2001)CrossRefzbMATHGoogle Scholar
  41. 41.
    Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. Am. Inst. Aeronaut. Astronaut. 32(8), 1598–1605 (1994)CrossRefGoogle Scholar
  42. 42.
    Lasdon, L.S.; Fox, R.L.; Ratner, M.W.: Nonlinear optimization using the generalized reduced gradient method. RAIRO Oper. Res. 8(V3), 73–103 (1974)MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Vihar Malviya
    • 1
  • Taimoor Asim
    • 1
  • Isuru Sendanayake
    • 1
  • Rakesh Mishra
    • 1
  1. 1.University of HuddersfieldHuddersfieldUK

Personalised recommendations