## Abstract

The rolling resistance (RR) of a tire depends on three factors: (i) the energy loss of rubber and reinforcements due to the cyclic deformation of the rolling tire, (ii) frictional energy in the contact area and (iii) the air resistance of the tire.

## Supplementary material

## References

- 1.Annual European community greenhouse gas inventory 1990–2006 and inventory report 2008, Technical Report No 6/2008, European Commission, DG Environment, European Environment Agency, May 2008Google Scholar
- 2.Japan Automobile Tyre Manufacturers Association,
*Guideline for Tyre Labeling to Promote the Use of Fuel Efficient Tyres (Labeling System)*. Available at: http://www.jatma.or.jp/english/labeling/outline.html - 3.European Union,
*On the Labelling of Tyres with Respect to Fuel Efficiency and Other Essential Parameters*, REGULATION (EC), No. 1222/2009 (Official Journal of the European Union, 2009)Google Scholar - 4.National Highway Traffic Safety Administration,
*Tire Fuel Efficiency Consumer Information Program*, Docket No. NHTSA-2010-0036 (2010)Google Scholar - 5.Yokohama Rubber (ed.),
*Study on Vehicle Tires (in Japanese)*, Sankaido (1995)Google Scholar - 6.Bridgestone,
*Bridgestone Environmental Report 2002*Google Scholar - 7.D.E. Hall, J.C. Moreland, Fundamentals of rolling resistance. Rubber Chem. Technol.
**74**(3), 525–539 (2001)CrossRefGoogle Scholar - 8.Tires and Passenger Vehicle Fuel Economy: Informing Consumers, Improving Performance. Technical Report 286, Committee for the National Tire Efficiency Study, Transportation Research Board, Board on Energy and Environmental Systems (2006)Google Scholar
- 9.D.J. Schuring, The rolling loss of pneumatic tires. Rubber Chem. Technol.
**53**(3), 600–727 (1980)CrossRefGoogle Scholar - 10.D.J. Schuring, S. Futamura, Rolling loss of pneumatic highway tires in the eighties. Rubber Chem. Technol.
**63**(3), 315–367 (1990)CrossRefGoogle Scholar - 11.Society of Automotive Engineers,
*Stepwise Coast-down Methodology for Measuring Tire Rolling Resistance*, SAE J2452 (2009)Google Scholar - 12.Z. Shida et al., A rolling resistance simulation of tires using static finite element analysis. Tire Sci. Technol.
**27**(2), 84–105 (1999)MathSciNetCrossRefGoogle Scholar - 13.Bridgestone (ed.),
*Fundamentals and Application of Vehicle Tires (in Japanese)*(Tokyo Denki University Press, 2008)Google Scholar - 14.T.C. Warholic, Tire rolling loss prediction from the finite element analysis of a statically loaded tire, Mater Thesis, University of Akron (1987)Google Scholar
- 15.J.R. Luchini et al., Tire rolling loss computation with the finite element method. Tire Sci. Technol.
**22**(4), 206–222 (1994)CrossRefGoogle Scholar - 16.J. Terziyski, R. Kennedy, Accuracy, sensitivity, and correlation of FEA-computed coastdown rolling resistance. Tire Sci. Technol.
**37**(1), 4–31 (2009)CrossRefGoogle Scholar - 17.K. Akutagawa et al.,
*Application of Non-linear FEA to Tyre Rolling Resistance Simulation*(ECCMR, London, UK, 2003)Google Scholar - 18.W.W. Klingbeil,
*Theoretical Prediction of Test Variable Effects, Including Twin-rolls, on Rolling Resistance*, SAE Paper, No. 800088 (1988)Google Scholar - 19.M.K. Chakko, Analysis and computation of energy loss in radial tires. Tire Sci. Technol.
**12**(1–4), 3–22 (1984)CrossRefGoogle Scholar - 20.D.S. Stutts, W. Soedel, A simplified dynamic model of the effect of internal damping on the rolling resistance in pneumatic tires. J. Sound Vib.
**155**, 153–164 (1992)CrossRefGoogle Scholar - 21.K. Yamagishi, J.T. Jenkins, The circumferential contact problem for the belted radial tire. J. Appl. Mech.
**47**, 512–518 (1980)zbMATHGoogle Scholar - 22.J.R. Luchini et al., Tread depth effects on tire rolling resistance. Tire Sci. Technol.
**29**(3), 134–154 (2001)CrossRefGoogle Scholar - 23.T.B. Rhyne, S.M. Cron, A study on minimum rolling resistance. Tire Sci. Technol.
**40**(4), 220–233 (2012)Google Scholar - 24.T. Akasaka et al., Analysis of the contact deformation of tread blocks. Tire Sci. Technol.
**20**(4), 230–253 (1992)CrossRefGoogle Scholar - 25.S. Futamura, Effect of material properties on tire performance characteristics—Part II, Tread material. Tire Sci. Technol.
**18**(1), 2–12 (1990)Google Scholar - 26.A. Abe et al., Optimum young’s modulus distribution in tire design. Tire Sci. Technol.
**24**, 204–219 (1996)CrossRefGoogle Scholar - 27.J.R. Luchini,
*Test Surface Curvature Reduction Factor for Truck Tire Rolling Resistance*, SAE Paper, No. 821264 (1982)Google Scholar - 28.S.K. Clark,
*Rolling Resistance Forces in Pneumatic Tires*, U.S. Department of Transportation, TSC Rep. No. DOT-TSC76-1 (1976)Google Scholar - 29.T. Freudenmann et al., Experimental determination of the effect of the surface curvature on rolling resistance measurements. Tire Sci. Technol.
**37**(4), 254–278 (2009)CrossRefGoogle Scholar - 30.L.W. DeRaad,
*The Influence of Road Surface Texture on Tire Rolling Resistance*, SAE Paper, No. 780257 (1978)Google Scholar - 31.A.N. Gent, J.D. Walter,
*The Pneumatic Tire*(NHTSA, 2005)Google Scholar - 32.H. Sakai,
*Tire Engineering (in Japanese)*, Guranpuri-Shuppan (1987)Google Scholar - 33.D.J. Schuring et al., Power requirements of tires and fuel economy. Tire Sci. Technol.
**2**(4), 261–285 (1974)CrossRefGoogle Scholar - 34.U. Peckelsen, F. Gauterin, Influence of real operating conditions on total rolling resistance. ATZ Worldwide
**115**, 54–59 (2013)Google Scholar - 35.D.J. Schuring, Energy loss of pneumatic tires under freely rolling, braking, and driving conditions. Tire Sci. Technol.
**4**(1), 2–15 (1976)Google Scholar - 36.E. Mogi et al.,
*Study on Contribution of Tire Driving Stiffness to Vehicle Fuel Economy*, SAE Paper, No.2012-01-0794 (2012)Google Scholar - 37.W.V. Mars, J.R. Luchini, An analytical model for transient rolling resistance behavior of tires. Tire Sci. Technol.
**27**(3), 161–175 (1999)CrossRefGoogle Scholar - 38.J.R. Luchini, J.A. Popio, Modeling transient rolling resistance of tires. Tire Sci. Technol.
**35**(2), 118–140 (2007)CrossRefGoogle Scholar - 39.L. Nielsen, T. Sandberg,
*A New Model for Rolling Resistance of Pneumatic Tires*, SAE Paper, No. 2002-01-1200 (2002)Google Scholar - 40.S.C. Burgess, J.M.J. Choi, A parametric study of the energy demands of car transportation: a case study of two competing commuter routes in the UK. Transport. Res. D
**8**, 21–36 (2003)CrossRefGoogle Scholar - 41.Michelin,
*The Tyre: Rolling Resistance and Fuel Saving*, Societe de Technologie Michelin, 2003. http://www.dimnp.unipi.it/guiggiani-m/Michelin_Tire_Rolling_Resistance.pdf - 42.F. An, M. Ross,
*A Model of Fuel Economy and Driving Patterns*, SAE Paper, No. 930328 (1993)Google Scholar - 43.Transportation Research Board, Tires and passenger vehicle fuel economy—informing consumers, improving performance. Transport. Res. Board Special Report 286 (2006)Google Scholar
- 44.P.S. Grover, S.H. Bordelon,
*New Parameters for Comparing Tire Rolling Resistance*, SAE Paper, No. 1999-01-0787 (1999)Google Scholar - 45.D.J. Schuring, J.S. Redfield,
*Effect of Tire Rolling Loss on Fuel Consumption of Trucks*, SAE Paper, No. 821267 (1982)Google Scholar - 46.C.R. Bradley, A. Delaval, On-road fuel consumption testing to determine the sensitivity coefficient relating changes in fuel consumption to changes in tire rolling resistance. Tire Sci. Technol.
**41**(1), 2–20 (2013)Google Scholar - 47.T.J. LaClair, R. Truemner,
*Modeling of Fuel Consumption for Heavy-Duty Trucks and the Impact of Tire Rolling Resistance*, SAE Paper, No. 2005-01-3550 (2005)Google Scholar - 48.A VL Cruise v3.1—Fuel Economy Simulation SoftwareGoogle Scholar
- 49.M. Guillou, C. Bradley,
*Fuel Consumption Testing to Verify the Effect of Tire Rolling Resistance on Fuel Economy*, SAE International, No. 2010-01-0763 (2010)Google Scholar - 50.T. Nakamura et al., Improvement of fuel efficiency in case of reduction in tire rolling resistance, in
*Proceedings of the JSAE Conference*, No. 20145714 (2014)Google Scholar - 51.K. Holmberg et al., Global energy consumption due to friction in passenger cars. Tribo. Int.
**47**, 221–234 (2012)CrossRefGoogle Scholar - 52.J. Barrand, J. Bokar,
*Reducing Tire Rolling Resistance to Save Fuel and Lower Emissions*, SAE Paper, No. 2008-01-0154 (2008)Google Scholar - 53.N. Nakate et al., The loss evaluation method to predict tire influences on fuel consumption of mode driving, in
*Proceedings of the JSAE Conference*, No. 20125663 (2012)Google Scholar - 54.H. Suzuki et al., Research on rolling resistance measurement with higher accuracy—validity of temperature correction to rolling resistance coefficient at low rolling resistance tires, in
*Proceedings of the JSAE Conference*, No. 20125688 (2012)Google Scholar - 55.R. Ookubo, K. Oyama, Effects of tyre tread temperature under actual driving on tyre characteristics. Trans. JSAE
**44**(2), 499–504 (2013)Google Scholar - 56.A. Kobayakawa et al.,
*A Study on Tire Aerodynamics*, JSAE Paper, No. 90-20135310 (2013)Google Scholar - 57.K. Kato et al., Enhancement of tire durability by considering air flow field. Tire Sci. Technol.
**37**(2), 103–121 (2009)CrossRefGoogle Scholar - 58.M. Koishi, Application of the simulation to elevate the product value (in Japanese). JSME J.
**116**(1131), 101–103 (2013)Google Scholar - 59.I. Kuwayama et al.,
*Development of Next Generation Ecology Tire Technology*, JSAE Paper, No. 90-20135154 (2013)Google Scholar - 60.I. Kuwayama et al., Expansion of ologic technology for eco-friendly vehicles. Tire Sci. Technol.
**45**(4), 288–306 (2017)CrossRefGoogle Scholar - 61.H. Kaga et al., Stress analysis of a tire under vertical load by a finite element method. Tire Sci. Technol.
**5**(2), 102–118 (1977)CrossRefGoogle Scholar - 62.Y. Nakajima, Application of computational mechanics to tire design—yesterday, today, and tomorrow. Tire Sci. Technol.
**39**(4), 223–244 (2011)CrossRefGoogle Scholar - 63.C. Hoever et al., Investigation of stress-distribution in a car tyre with regards to rolling resistance, in
*Proceedings of the ISMA 2010*(2010)Google Scholar - 64.M. Fraggstedt, Power dissipation in car tyres, Ph.D. Thesis, Royal Institute of Technology (2006)Google Scholar
- 65.C. Hoever, The influence of modelling parameters on the simulation of car tyre rolling losses and rolling noise, Ph.D. Thesis, Chalmers University of Technology (2012)Google Scholar
- 66.M.H.R. Ghoreishy,
*Rolling resistance simulation*(Tire Tech. Int, Annual Review, 2013), pp. 84–86Google Scholar - 67.R.W. Ogden,
*Non-linear Elastic Deformations*(Ellis Horwood Limited, 1984)Google Scholar - 68.A. Suwannachit, U. Nackenhorst, A novel approach for thermomechanical analysis of stationary rolling tires within an ALE–kinematic framework. Tire Sci. Technol.
**41**(3), 174–195 (2013)Google Scholar - 69.D. Whicker et al.,
*The Structure and Use of the GMR Combined Thermo-Mechanical Tire Power Loss Model*, SAE Paper, No. 810164 (1981)Google Scholar - 70.D. Whicker et al., A thermomechanical approach to tire power loss modeling. Tire Sci. Technol.
**9**(1), 3–18 (1981)CrossRefGoogle Scholar - 71.C.K.L. Davies et al., Characteriza-tion of the behaviour of rubber for engineering design purposes. 1. Stress-strain relations. Rubber Chem. Technol.
**67**, 716–728 (1995)CrossRefGoogle Scholar - 72.G. Kraus,
*In Reinforcement of Elastomers*(Wiley Inter-Sci, New York, 1965)Google Scholar - 73.J.D. Ulmer, Strain dependence of dynamic mechanical properties of carbon black-filled rubber compounds. Rubber Chem. Technol.
**69**, 15 (1996)CrossRefGoogle Scholar - 74.Y. Nakajima et al., Theory of optimum tire contour and its application. Tire Sci. Technol.
**24**, 184–203 (1996)CrossRefGoogle Scholar - 75.Y. Nakajima,
*New Tire Design Procedure Based on Optimization Technique*, SAE Paper, No. 960997 (1996)Google Scholar - 76.Y. Nakajima, Technology development to decrease rolling resistance of tire by optimization technology (in Japanese). JARI Res. J.
**21**, 305–313 (1999)Google Scholar - 77.A. Tamano, Technology to decrease RR (in Japanese). Nippon Gomu Kyokaishi
**69**(11), 749–756 (1996)CrossRefGoogle Scholar - 78.T.T. Diller et al.,
*Development of the Texas Drayage Truck Cycle and its use to determine the Effects of Low Rolling Resistance Tires on the NO*_{x}*Emissions and Fuel Economy*, SAE Paper, No. 2009-01-0943 (2009)Google Scholar - 79.Y. Nakajima et al., Application of neural network for optimization of tire design. Tire Sci. Technol.
**27**(2), 62–83 (1999)CrossRefGoogle Scholar - 80.Y. Nakajima et al., Surface shape optimization of tire pattern by optimality criteria. Tire Sci. Technol.
**31**(1), 2–18 (2003)CrossRefGoogle Scholar - 81.Y. Uemura, S. Saito, Reduction of rolling resistance under high inflation pressure—electric vehicle tyre. Kautsch. Gummi Kunstst.
**48**, 515–520 (1995)Google Scholar - 82.J.R. Cho et al., Numerical estimation of rolling resistance and temperature distribution of 3-D periodic patterned tire. Int. J. Solid Struct.
**50**, 86–96 (2013)Google Scholar - 83.J.R. Cho et al., Finite element estimation of hysteretic loss and rolling resistance of 3-D patterned tire. Int. J. Mech. Mater. Des.
**9**, 355–366 (2013)CrossRefGoogle Scholar - 84.Y. Uemura, S. Suzuki, New tire and technology (in Japanese). The Tire Monthly Co. (1994), pp. 58–65Google Scholar
- 85.A. Tamano, Technology to decrease rolling resistance of tire (in Japanese). Nippon Gomu Kyokaishi
**69**(11), 749–756 (1996)CrossRefGoogle Scholar - 86.Y. Nakajima, Current status and future of tire technology (in Japanese). Nippon Gomu Kyokaishi
**85**(6), 178–182 (2012)CrossRefGoogle Scholar - 87.Y. Ikeda, A. Kato, S. Kohjiya, Y. Nakajima,
*Rubber Science: A Modern Approach*(Springer, Heidelberg, 2017)Google Scholar - 88.F. Koutny, A method for computing the radial deformation characteristics of belted tires. Tire Sci. Technol.
**4**(3), 190–212 (1976)CrossRefGoogle Scholar

## Copyright information

© Springer Nature Singapore Pte Ltd. 2019