Special issue article Proc IMechE Part D: J Automobile Engineering 2017, Vol. 231(9) 1274–1286 A drag coefficient for application Ó IMechE 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav to the WLTP driving cycle DOI: 10.1177/0954407017704784 journals.sagepub.com/home/pid Jeff Howell, David Forbes and Martin Passmore Abstract The aerodynamic drag characteristics of a passenger car have, typically, been defined by a single parameter: the drag coefficient at a yaw angle of 0°. Although this has been acceptable in the past, it does not provide an accurate measure of the effect of aerodynamic drag on fuel consumption because the important influence of the wind has been excluded. The result of using drag coefficients at a yaw angle of 0° produces an underprediction of the aerodynamic component of fuel consumption that does not reflect the on-road conditions. An alternative measure of the aerodynamic drag should take into account the effect of non-zero yaw angles, and a variant of wind-averaged drag is suggested as the best option. A wind-averaged drag coefficient is usually derived for a particular vehicle speed using a representative wind speed distri- bution. In the particular case where the road speed distribution is specified, such as for a driving cycle to determine fuel economy, a relevant drag coefficient can be derived by using a weighted road speed. An effective drag coefficient is deter- mined with this approach for a range of cars using the proposed test cycle for the Worldwide Harmonised Light Vehicle Test Procedure, WLTP. The wind input acting on the car has been updated for this paper using recent meteorological data and an understanding of the effect of a shear flow on the drag loading obtained from a computational fluid dynamics study. In order to determine the different mean wind velocities acting on the car, a terrain-related wind profile has also been applied to the various phases of the driving cycle. An overall drag coefficient is derived from the work done over the full cycle. This cycle-averaged drag coefficient is shown to be significantly higher than the nominal drag coefficient at a yaw angle of 0°. Keywords Drag coefficient, wind-averaged drag, driving cycle, wind environment, car aerodynamics Date received: 28 June 2016; accepted: 22 February 2017 Introduction The current test procedure used to derive fuel econ- omy in Europe is based on the Extra Urban Driving Fuel economy is a major concern for car owners Cycle (EUDC). The EUDC was introduced in 1996 to according to surveys of customer satisfaction. In addi- replace the earlier Euromix cycle which has been discre- tion, car owners are particularly concerned that, when dited. As current test procedures for the fuel economy cars are driven in the real world, they do not meet the are considered inadequate, an ambitious project is fuel economies predicted by manufacturers. Most man- under way to replace those in use around the world ufacturers inform customers in the car handbook that with a common worldwide test procedure, namely the these figures are obtained under ‘ideal’ conditions and Worldwide Harmonised Light Vehicle Test Procedure warn them not to expect the same. However, the gap (WLTP), based on a common test cycle, the Worldwide between the test results for the fuel consumption and Harmonized Light Vehicle Test Cycle (WLTC). The the real-world performance has increased from 8% in WLTP requires that the aerodynamic wind tunnel drag 2001 to around 40% in 2014.1 The difference can no longer be explained by the fact that original equipment manufacturers (OEMs) optimise the car performance Loughborough University, Loughborough, UK within the flexibility allowed by the rules, or by the poor representation of real-world conditions, including Corresponding author: Jeff Howell, Loughborough University, Epinal Way, Loughborough LE11 the exclusion of realistic wind effects, and has led to 3TU, UK. concerns over possible cheating. Email: [email protected] Howell et al. 1275 Figure 1. Increases in the drag coefficients with increasing yaw angle for (a) one-box multi-purpose vehicles, (b) two-box small hatchbacks, (c) two-box sport utility vehicles and (d) three-box saloons and fastbacks. MPV: multi-purpose vehicle; SH: small hatchback; SUV: sport utility vehicle; NB: notchback. data which are applied to the WLTC must be obtained which arises from the yaw created by considering a in a moving-ground wind tunnel, with very low levels typical distribution of the steady natural wind using of freestream turbulence (FST) and at a yaw angle of application of the wind-averaged drag technique. A 0°. Although the detailed requirements generate precise wind-averaged drag coefficient is typically determined data, the data obtained are not necessarily what is for a fixed vehicle speed; however, for application to a required. Conventional five-belt moving-ground simu- driving cycle, a wide range of vehicle speeds must be lations do not allow the rotating-wheel drag component considered. to be measured, the low levels of turbulence potentially The wide variation in the drag coefficient with yaw underestimate the car drag in the real world, and the angle is shown for a range of cars of different shapes effects of the natural wind on the drag are not included. and sizes. The concept of wind-averaged drag is dis- The resistance of the baseline configurations with the cussed and updated with recent meteorological data highest drag and the lowest drag can, as an option, be and a brief study of the effect of a sheared crosswind derived from coastdown testing, which reduces the flow on drag is made. The influence of vehicle speed on issues from wheel rotation, but these have to be con- the wind-averaged drag coefficient is analysed for a ducted in low-wind conditions that do not represent the range of mean wind speeds. An appropriate terrain- on-road environment. The aerodynamic drag compo- related mean wind speed is applied to each of the four nent input to the WLTC is therefore usually an under- phases of the WLTP driving cycle. The variation in estimate of the aerodynamic resistance experienced by wind-averaged drag, weighted by the velocity distribu- the car in the real world. tion, is then determined for the whole cycle. From the This paper does not address all the issues which lead power required to overcome the aerodynamic drag to an underestimate of the aerodynamic drag but inves- through the cycle, an appropriate overall drag coeffi- tigates only the effects of including a drag component cient is derived. 1276 Proc IMechE Part D: J Automobile Engineering 231(9) Table 1. Drag coefficients CD0 at a yaw angle of 0° for all cars. Car CD0 Car CD0 Car CD0 Car CD0 MPV 1 0.341 SH 1 0.336 SUV 1 0.407 NB 1 0.293 MPV 2 0.322 SH 2 0.334 SUV 2 0.381 NB 2 0.313 MPV 3 0.320 SH 3 0.333 SUV 3 0.390 NB 3 0.294 MPV 4 0.313 SH 4 0.330 SUV 4 0.394 NB 4 0.301 MPV 5 0.374 SH 5 0.338 SUV 5 0.408 NB 5 0.270 MPV 6 0.392 SH 6 0.334 SUV 6 0.354 NB 6 0.278 MPV 7 0.353 SH 7 0.323 SUV 7 0.349 NB 7 0.296 MPV: multi-purpose vehicle; SH: small hatchback; SUV: sport utility vehicle; NB: notchback. Drag coefficient at yaw minimum drag condition. This becomes unrepresentative of the drag experienced by a car when there is a natural The increase in drag coefficient with increasing yaw wind present, which is almost all the time. A wind- angle can vary considerably for cars of similar shape as averaged drag coefficient was proposed to account for this well as for cars of different types. Figure 1 demonstrates effect. Although relatively common in the field of truck this for a range of cars in the multi-purpose vehicle, the aerodynamics (see, for example the paper by Cooper3), it small hatchback and compact sport utility vehicle and has not been adopted for passenger cars. In part, this is the saloon (notchback) car categories, which represent because trucks tend to travel long distances at relatively one-box shapes, two-box shapes and three-box shapes steady speeds and they have drag characteristics which respectively. The data are obtained for 28 vehicles in show a very large increase with increasing yaw angle. the four categories and is the same data set as used by In the past, there have been reservations regarding Howell.2 the use of the wind-averaged drag approach as it can- The principal dimensions (length, width, height and not be used for information on any specific journey but frontal area) of the cars for which aerodynamic data represents the expected drag coefficient in an average are presented are given in Table 7 in Appendix 2. A national wind environment. These concerns, however, wide range of vehicle sizes are covered. The lengths are less important when related to a global emissions vary from 3.85 m to 5.07 m, the widths from 1.68 m to problem, such as carbon dioxide (CO ), and the analy- 1.90 m, the heights from 1.39 m to 1.86 m and the fron- 2 sis can be applied to all cars of a particular model dis- tal areas from 2.06 m2 to 2.80 m2. tributed across a country or region, and covering many All the cars were tested in the MIRA full-scale wind different journeys over the life of the vehicle.