A Drag Coefficient for Application to the WLTP Driving Cycle

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 distribution. 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 determined 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 economy 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. tunnel. This wind tunnel has a closed working section, In a typical case the wind-averaged drag is computed 7 m wide and 5 m high (35 m2 cross-section) and 15 m for a particular car speed and accounts for the probabil- long, with an open return. The wind tunnel has a fixed ity of wind speed and direction. The wind velocity dis- ground plane. The standard MIRA corrections for tribution is based on averaged meteorological data for blockage, based on the continuity and the pressure gra- a region, and an equi-probable wind direction is almost dient, were applied. The cars were set up in the wind always assumed. tunnel according to the European Aerodynamic Data Various forms of the wind-averaged drag coefficient Exchange standard, with the exception that the nom- exist, with different probabilities for wind speed and inal air speed for all testing was 27 m/s. direction and vehicle speed. Windsor4 reviewed three The vehicles display a wide range of increases in the forms of wind-averaged drag and preferred the method drag coefficient with increasing yaw angle. The increase used by MIRA5 (derived from the paper by Carr6). The DC in the drag coefficient as measured at a yaw D10 MIRA method was adopted as a starting point for the angle of 10°, where DC = C –C , ranges from D10 D10 D0 analysis in this paper. 0.023 to 0.128. The highest variation in the drag coeffi- The wind-averaged drag coefficient C at a vehicle cient with yaw angle is experienced by the one-box DW speed U is defined as multi-purpose vehicle shapes, whereas the lowest sensi- V tivity to the yaw angle is found for the three-box notch- 1808 Z 2 back cars. The drag coefficients CD0 at a yaw angle of 1 UR CDW = CD(c) df ð1Þ 0° are given for each car in Table 1. p UV 08

C Wind-averaged drag where D(c) is the drag coefficient at the yaw angle c and f is the wind angle relative to the vehicle axis. The The drag coefficient of a passenger car almost always resultant velocity UR and the yaw angle c are functions increases with increasing yaw angle, and therefore the of the car speed UV, the wind speed UW and the wind drag coefficient at a yaw angle of 0° is, typically, the angle f as shown in Figure 2 and are given by Howell et al. 1277

wind speed data are still issued by the Meteorological Office in knots (nautical miles/hour)), which is 16.5 km/h. This value, obtained at a height of 10 m, is adjusted for a sea level location and assumes an open terrain with a roughness height z0 of 0.03 m. This mean wind speed must be adjusted to account for a typical Figure 2. Velocity diagram. terrain and for a height relevant to passenger cars. As a boundary layer flow the wind speed is zero at the ground surface and varies with the height above the 2 2 1=2 ground. For the lower part of the boundary layer UR = U + U +2UVUW cos f ð2Þ VW (below 50 m), a power law for defining the variation in U sin f c = tan1 W ð3Þ the wind speed with the height is preferred, such that UV + UW cos f z a The wind direction is assumed to be equally probable, UW = UWG ð4Þ zG and the probability of a certain wind speed is obtained from a weighting function. where UW is the wind speed at a height z above ground, 6 As the wind data used by Carr were obtained many zG is the gradient height of the atmospheric boundary years ago, and the data available now are considerably layer at which the wind velocity is UWG and a is the more extensive, mainly because of the requirements of appropriate power. the wind power industry, the wind data relevant to the Typical wind velocity profiles, which are relevant to wind-averaged drag computation were reviewed and the study of building aerodynamics, were defined for updated. different terrains following the work by Davenport8 Equation (1) provides the wind-averaged drag coef- and Scruton9 and are shown schematically in Figure 3 ficient at a given vehicle speed but, if the distribution of (after Hucho10), with details given in Table 2. In high- the vehicle speeds is defined, as in the case of a particu- roughness terrains, such as town centres, this profile, lar driving cycle, it becomes possible to derive a wind- near the ground, is displaced upwards by a few metres11 averaged drag coefficient for that driving cycle. This and, at heights relevant to cars, the wind speed is very overall drag coefficient is derived in this paper and uncertain but takes the form shown in the detail added called a cycle-averaged drag coefficient. to Figure 3. It should be noted that there is a distinct lack of data Wind environment for the wind velocity at heights relevant to cars (i.e. z \ 2.0 m), in any conditions. Smith12 obtained velocity A car travelling along the road is in a constantly chang- profiles over 3.0 m at two open-terrain sites. The expo- ing environment, as a consequence of being immersed nent a at the two sites were approximately 0.10 and in the lowest region of the Earth’s atmospheric bound- 0.18. Wind statistics from Birmingham Airport ary layer. The natural wind is not steady in either velo- obtained at the standard height of 10 m were adjusted city or direction. It is also turbulent and sheared. for a 2 m height using an exponent of 0.17, which may The long-term 10 year average annual wind speed for explain the use of that exponent by Carr.6 Examples of the UK, for 2002–2011, according to Meteorological roadside wind profiles measured by Volvo in rougher Office7 data, is 8.9 knots (it should be noted that the terrains, presented by Go¨tz,13 had values of a from

Figure 3. Effect of the terrain on the wind velocity profile. 1278 Proc IMechE Part D: J Automobile Engineering 231(9)

Table 2. Wind characteristics for different terrains.

Terrain a zG z0 UW(0.6)/UW(10) REF (m) (m)

1 Open country 0.16 300 0.03 0.638 2 Rural (many hedges) 0.22 365 0.08 0.421 3 Suburban 0.28 430 0.20 0.273 4 City centre 0.40 560 1.00 0.112

Figure 4. Wind velocity profiles near the ground.

0.22 to 0.34. Wind data relevant to a low-rise building The wind profiles for these four terrain conditions, in open terrain have been obtained by Richards et al.14 close to the ground, are shown in Figure 4. The wind The data compared wind energy spectra at heights of velocities are relative to the mean velocity at a height of 1.0 m and below with data at heights of 10 m and 10 m for the reference terrain with an exponent a of showed that the von Ka´rma´n spectrum does not apply 0.16 and account for the increase in the gradient height close to the ground. The energy is biased to higher fre- of the boundary layer as a increases. quencies, reflecting the increase in smaller-scale eddies. The distribution of wind speeds over time is defined In the absence of sufficient useful wind data close to closely by the Weibull function. The probability distri- the ground in roadside conditions, the input required bution function, i.e. the probability of occurrence for a here is obtained by extrapolating the available meteoro- particular wind speed, is given by logical data. "# The wind speed at a different height and over a differ- k U k1 U k PUðÞ= W exp W ð5Þ ent terrain from the Meteorological Office reference data W c c c (z =10m;a =0.16;z0 = 0.03) is computed, following 15 Cooper, by generating the wind speed at the gradient where k is the shape factor and c is the scale factor. It height for the reference case (z = 300 m), by transferring G should be noted that the mean wind speed UWM is given this gradient wind speed to the gradient height for the ter- by rain required and by then calculating the wind velocity at 1 the new height using equation (4). Table 2 also gives the UWM = cG 1+k ð6Þ ratio of the wind speed at a height of 0.6 m for the different terrains to the wind speed at a height of 10 m for the where G is the gamma function. referencecase(a = 0.16) to illustrate the effect of differ- The factors k and c or UWM uniquely define any ent shear flows on the wind velocity close to the ground. particular site. Fru¨h16 has provided wind data from 72 In the MIRA5 computation of the wind-averaged drag, a sites distributed across Great Britain (i.e. excluding height of 1.0 m was assumed, but this height is shown in Northern Ireland), and a summary of his data, showing the next section of this paper, on an updated wind- k as a function of the mean wind velocity, is presented averaged drag, to be an overestimate, and a more realistic in Figure 5. It can be seen that there is a tendency for k typical height is considered to be approximately 0.6 m. to increase with increasing wind speed, but it is weak. Howell et al. 1279

Similarly, as also shown in the Department of Transport17 data, traffic density is geographically dependent, varying significantly in different regions of the country. The highest concentrations are around the motorway networks and, in particular, very heavy concentrations occur in the central ‘box’ area defined by the cities London, Bristol, Manchester and Leeds. The wind characteristics in this region are identified in Figure 5 as the data points denoted as Central, where it can be seen that the mean wind speed is reduced to 17.5 km/h, and the average value of k is increased slightly to 2.02. The range of k is from 1.77 to 2.23, and the wind speed range is from 15.0 km/h to 20.0 km/h with one very elevated site at 25.0 km/h. These wind velocity data are not adjusted and the mean wind velocity data, corrected to sea level and Figure 5. Weibull shape parameter versus mean wind speed open terrain for the central counties of the UK, are for Great Britain sites. taken from the work by Kosmina and Henderson,19 which gives 15.6 km/h. The mean wind speed increases with increasing elevation. For every 100 m above sea The average values over the whole country of both level, the velocity11 is increased by 10%. The average parameters are U = 19.6 km/h and k = 1.91. The WM elevation for the motorways in this central region is main range of k is from 1.6 to 2.2, with a solitary low approximately 100 m. value of 1.43, and the mean wind speed shows a wide variation from 15.0 km/h to 27.8 km/h. Wind speed values here are noticeably higher than the Meteorological Updated wind-averaged drag Office long-term average, but these data are not corrected for terrain or elevation. The wind-averaged drag is usually obtained at a fixed In this analysis, the considerable variation in the wind vehicle speed. In the past, MIRA issued wind-averaged speed during the year is not relevant as the long-term drag data in their published surveys at vehicle speeds of mean is of interest. The diurnal variation of the wind 50 km/h, 70 km/h, 90 km/h, 110 km/h and 130 km/h, speed should, however, be considered. Over land, wind with a single mean wind speed. For the purposes of this speeds are higher during the day than at night. The same paper, the wind-averaged drag data must be calculated is true for coastal sites when the wind is from over the for ranges of vehicle speeds and mean wind speeds. land. From Department of Transport17 data, almost all The MIRA wind data are presented as a weighted vehicle journeys are undertaken between 0700 hours and velocity distribution for a height above ground of 2200 hours, and between these times the mean wind 1.0 m. Howell and Panigrahi20 have shown that the speed can exceed the 24 h average by up to 10%, when mean wind speed for this case is 8.28 km/h and the averaged over the year. There is a seasonal variation in Weibull shape factor k = 1.79. It is now, with the pas- the diurnal effects, with the greatest variation in the sum- sage of time, unclear how this mean wind speed was mer months and the lowest variation in the winter. An derived, but it is consistent with a vehicle travelling in example of a 5% variation in the average is shown in rural conditions (a = 0.21) and could have been con- Figure 6 from Meteorological Office18 data. sidered appropriate at the time. The lower value of k obtained for the older data is partly explained by the use of cup anemometers, which tend to underestimate the contribution of low wind speeds. Using the data currently available, as developed in the preceding section and for the purposes of this paper, the mean wind speed over a reference terrain (a = 0.16) at the reference height of 10 m, which is adjusted for nominal elevation above sea level (+10%) and diurnal effects (+5%), is taken to be 18.1 km/h. The value of the Weibull shape factor k is taken to be 2.0. This is a special case of the Weibull function known as the Rayleigh distribution. This change in the shape factor modifies the weighting distribution as used in the MIRA method. The new weighting is shown in Table 3 Figure 6. Typical diurnal variation in the wind speed. compared with the MIRA weighting. 1280 Proc IMechE Part D: J Automobile Engineering 231(9)

Table 3. Weighting distributions for various wind speed ranges.

UW/UWM Weighting for the following k k = 1.79 (MIRA) k = 2.00

0–0.483 0.210 0.177 0.483–0.966 0.330 0.347 0.966–1.449 0.250 0.285 1.449–1.932 0.130 0.138 1.932–2.415 0.055 0.043 2.415–2.899 0.020 0.009 2.899–3.382 0.005 0.001

The wind-averaged drag data presented by Howell and Panigrahi20 used the MIRA weighting (k = 1.79) and a point of application at 1.0 m. Computing the Figure 7. Variation in CDW with UWM/UV for different vehicle wind-averaged drag coefficient for the same range of types. cars, using k = 2.00, but the same point of application, MPV: multi-purpose vehicle; HB: hatchback; SUV: sport utility vehicle; surprisingly showed an almost negligible difference. NB: notchback. The largest difference was found to be less than 2 counts (DCDW = 0.002) for the most sensitive car and at the highest wind speed. For most wind speeds and equal to the drag coefficient CD0 at a yaw angle of 0°. vehicles, the difference was less than 1 count. An assess- At higher ratios of the wind speed to the vehicle speed, ment was also made of the weighting distribution to see the wind-averaged drag coefficient increases approxi- whether the wind-averaged drag was influenced by mately linearly. increasing the number of steps in the distribution. For In the MIRA method it is assumed that the shear- the particular vehicle investigated, increasing the steps flow wind input is equivalent to a uniform crosswind, to 26 (from 7 in the MIRA method) for a bin size of 1 where the magnitude of the crosswind is equal to the km/h changed the wind-averaged drag coefficient by sheared wind velocity at a fixed height above the less than 1 count. ground. This height was chosen to be 1.0 m and was The wind-averaged drag coefficient was computed applied to all cars, but the justification is now for a range of vehicles, as follows. The drag characteris- unknown. (It should be noted that a similar fixed point tics for each vehicle at a yaw angle are made symmetri- of application was used by Cooper15 for trucks; in this cal by averaging the drag coefficient at each 6 yaw case the height was 3.0 m.) angle. This is not analytically essential, but it avoids Recent studies at Loughborough University by 21 taking the integration limits in equation (1) to 6180°. Howell et al. have provided a potential solution to Curve fitting of the drag data is achieved in two steps: a this uncertainty. Using computational fluid dynamics, fourth-order even polynomial is fitted to the data from the steady-state drag coefficient was computed for both 0° to 5° or 10°, and a fourth-order polynomial is applied fastback vehicle shapes and estate (squareback) vehicle from 5° or 10° to 25°. With such high-order polyno- shapes in a crosswind. The applied crosswind was mod- mials, any extrapolation is suspect, but the effect on the elled with a uniform velocity profile and a shear profile, overall wind average drag from larger yaw angles is neg- with the exponent a = 0.16. For comparison the shear ligible. The wind-averaged drag coefficient CDW is cal- flow input had the same mass flow over the height of culated using equation (1) and as detailed by Windsor.4 the car as in the uniform unsheared crosswind case. This assumes that all wind angles are equally probable, The drag coefficient and the vertical distribution of the but the modified weighted wind velocity distribution, drag coefficient were found to be almost identical in given above, is applied. CDW is calculated for vehicle the two cases. Table 4 shows the drag coefficients for speeds of 15 m/s, 30 m/s and 60 m/s (54 km/h, 108 km/ both car configurations at a yaw angle of 0° and at a h and 216 km/h), and mean wind speeds from 2.1 km/h yaw angle of 10° in a uniform crosswind and a sheared to 12.5 km/h to provide a range of values for the ratio crosswind. The yaw angle for the sheared crosswind UWM/UV of the wind speed to the vehicle speed. flow is defined by the mean crosswind velocity over the For any particular vehicle the wind-averaged drag is car height. The drag loading in the vertical plane is found to be a unique function of UWM/UV, although shown in Figure 8 for the two crosswind cases and at a technically this only applies if a constant weighting dis- yaw angle of 0° for the fastback shape. tribution for UW/UWM is applied. Typical examples for For equal mass flow over the height of the car, the four different vehicles are shown in Figure 7, but all mean velocity is the shear flow velocity at a height of vehicles show similar variations. When the mean wind approximately 0.4 times the height of the car, which speed is zero, the wind-averaged drag coefficient is suggests that this is the height at which the crosswind Howell et al. 1281

Figure 8. Drag coefficient distributions at a yaw angle of 10°, with and without shear.

Table 4. Drag coefficients in a sheared crosswind flow and a uniform flow.

Car CD0 CD10 Sheared flow Uniform flow

Estate 0.309 0.357 0.358 Fastback 0.257 0.335 0.333

Table 5. Speed details for the WLTC phases.

Phase Average speed Maximum speed Figure 9. WLTC. (km/h) (km/h)

Low speed 25.7 56.5 function of the time. The WLTC is divided into four Medium speed 44.5 76.6 parts defined as the low-speed phase, the medium-speed High speed 60.8 97.4 phase, the high-speed phase and the extra-high-speed Extra-high speed 94.0 131.3 phase. These divisions were originally described as the Overall speed 53.8 urban phase, the rural phase and the motorway phase (with the motorway phase divided into two high-speed sections). The basic speed details for each phase are velocity acting on the vehicle in a sheared flow is summarised in Table 5. The effects of stops are ignored. determined. The vehicle speed distribution, which is obtained Although this study was conducted for only two from the time spent at any given speed as a ratio of the vehicle types, one exponent and one yaw angle, it is felt total cycle time, excluding stops, for each phase of the that the result has more general application to other cycle is shown in Figure 10, left axis. The car speed data vehicle types. The wind velocity input for each vehicle are taken in steps (bins) of 5 km/h. is then taken to be the velocity at 40% of the vehicle For the purpose of calculating the wind-averaged height and is different for each car. For a typical vehi- drag, it is assumed that each phase operates in broadly cle height of 1.5 m, this height is 0.6 m. It does not vary different terrains. Thus, the low-speed phase is predo- significantly with increasing shear exponent. minantly city centre driving, and the extra-high-speed Using the mean wind speed of 18.1 km/h for open phase is mainly in open country. For the purposes of country terrain at 10 m established at the start of this this paper, the terrain categories 1 to 4 from Table 1 section, the mean wind speeds for the four terrain con- are applied to the four phases of the driving cycle, and ditions of Table 2 at 0.6 m are as follows: city centre, therefore a mean wind velocity can be ascribed for each 2.02 km/h; suburban, 4.95 km/h; rural, 7.61 km/h; open phase. As the wind-averaged drag coefficient CDW is country, 11.54 km/h. simply a function of UWM/UV, the variation in CDW over the driving cycle can be obtained, and an example for a small hatchback is shown for the four phases in Application to WLTC Figure 10, right axis. The WLTC is the test cycle that supports the WLTP The low wind speeds in the low-speed phase can still and is employed to generate fuel economy and emis- generate large yaw angles, because the vehicle speed is sions data. The vehicle speed is shown in Figure 9 as a low, but the aerodynamic resistance is also low. For 1282 Proc IMechE Part D: J Automobile Engineering 231(9)

To determine a cycle-averaged drag coefficient, the work done over the whole cycle with the wind-averaged drag coefficient CDW varying with the velocity ratio UWM/UV is equated to the work done when the drag coefficient remains constant. This constant drag coefficient is denoted by CDWC, the cycle-averaged drag coefficient. Thus, Ð T ÐCDWUV3 dt CDWC = ð8Þ T UV3 dt where T is the total time for the four phases of the test cycle, excluding the periods when the car is stationary.

Cycle-averaged drag coefficient Figure 10. WLTC velocity distribution and CDW. Following the process described in the preceding section the WLTC cycle-averaged drag coefficient was determined for each car in the 28-vehicle data set repre- this reason and because of the uncertainty in the flow senting four vehicle categories: one-box multi-purpose near the ground, as discussed in the section on the wind vehicles, two-box hatchbacks and compact sport utility environment, the drag coefficient is taken to be the drag vehicles, and three-box notchback and fastback shapes. coefficient at a yaw angle of 0°. In the other phases The values are plotted as a function of the drag coeffi- where the vehicle speed is low and the ratio UWM/UV is cient at a yaw angle of 0° in Figure 12. higher than 0.3, the wind-averaged drag coefficient is It can be seen that there is little correlation between capped at the value for U /U = 0.3 to avoid uncer- WM V the two. CDWC is typically about 5% higher than the tainties from over-extrapolation. This cap is arbitrary, drag coefficient at a yaw angle of 0°, but in the worst but adjusting the value from 0.25 to 0.5 produced a case it is 11.4% higher, whereas in the best case it dif- negligible variation in the overall cycle-averaged drag fers by only 2.2%. In both cases the vehicle is a multi- coefficient. purpose vehicle. For the purposes of this paper, the power required The increase DCDWC = CDWC–CD0 in the computed to overcome the aerodynamic drag during the test cycle cycle-averaged drag coefficient from the drag coeffi- must be evaluated. The power required PA is given by cient for a yaw angle of 0° is plotted in Figure 13 as a function of the increase DCD10 = CD10–CD0 in the drag CDWrUV3 A PA = ð7Þ coefficient at a yaw angle of 10°, as measured in the 2 wind tunnel. where r is the air density and A is the frontal area of Several OEMs use a similar drag coefficient increase the car. The distribution of the power required, as a as a target measure of the aerodynamic drag in the real function of the car velocity, is shown in Figure 11 for the four phases of the WLTC.

Figure 12. Cycle-averaged drag coefficient versus drag coefficient at a yaw angle of 0°. Figure 11. Distributions of the drag power over the cycle. MPV: multi-purpose vehicle; SUV: sport utility vehicle. Howell et al. 1283

Table 6. Breakdown of the phase contributions to the overall drag.

Phase Contribution

Low speed 0.02 Medium speed 0.09 High speed 0.26 Extra-high speed 0.63 Overall speed 1.00

employed here follows the MIRA method and has seven wind speed inputs (bins) to represent the Weibull wind distribution. The insensitivity of the wind- averaged drag coefficient to the value of k resolves one uncertainty. Some authorities in the field of wind Figure 13. Increase in the cycle-averaged drag coefficient power claim that k changes significantly with height, versus increase in the drag coefficient rise at a yaw angle of 10°. although most do not consider the effect. It can be MPV: multi-purpose vehicle; SUV: sport utility vehicle. ignored for this analysis. world, but it is given much less significance than the Effect of the reference wind speed drag coefficient at a yaw angle of 0°.Thecorrelation here is not good but it shows a general trend that the The wind-averaged drag coefficient and, as a conse- increase in the cycle-averaged drag tends to increase as quence, the cycle-averaged drag coefficient is, however, the drag rise with yaw angle increases. In this data set, sensitive to the choice of the wind speed. Although the long-term mean value of the natural wind at 10 m is there is a fourfold increase in DCDWC between those cars with the lowest sensitivity and those with the high- reasonably well understood, knowledge of the shear est sensitivity of the drag coefficient to the yaw angle. flows in the road environment experienced by passen- From a breakdown of the four phases of the driving ger cars is almost non-existent, and the choice of ter- cycle, the contribution of each phase to the overall rain applicable to the different phases of the test cycle, aerodynamic work done over the cycle can be obtained, as used in this analysis, must be considered arbitrary. which is the same as the contribution of each phase to The wind data used here are based on UK meteorologi- the cycle-averaged drag coefficient. The contributions cal data, and a similar mean wind speed is found across of each phase are essentially identical for all the cars most of northern Europe. In southern Europe, how- investigated and are shown in Table 6. ever, the wind speeds tend to be lower. Almost 90% of the drag arises from the high-speed There is, therefore, considerable uncertainty about phase and the extra-high-speed phase. The small contri- the correct wind speed values to apply in this analysis. butions from the low-speed phase and the medium- However, the sensitivity of the cycle-averaged drag speed phase suggest that the wind speed characteristics coefficient to changes in the mean wind speed can be 6 for these do not need to be very accurately defined, explored. The effect of a 10% change in the reference whereas much greater precision is required for the high- mean wind speed, which modifies the wind speed over speed phases. A corollary of this is that the driving cycle the whole cycle, is shown in Figure 14. A 10% change in the mean wind speed results in an increase of approx- in the high-speed phase must be appropriate and care- fully defined for the drag contribution to be accurate. imately 16% in the cycle-averaged drag coefficient over the drag coefficient at a yaw angle of 0°. Over the full range of vehicles in the data set, this variation repre- Discussion sents a change in the drag coefficient of between 2 and 6 counts (i.e. DCD = 0.00220.006), for cars with the Weibull shape factor lowest drag coefficient and the highest wind-averaged The Weibull shape factor k = 2.0 used in this paper drag coefficient respectively. and derived from a wide range of measurement sites across Great Britain was changed from that used in the MIRA method, which was k = 1.79. It was found, Drag input considerations however, that this change has almost no effect on the The aerodynamic data used in this analysis are based wind-averaged drag coefficient throughout the ranges on wind tunnel measurements, where the flow is uni- of wind speeds and vehicle speeds of interest in this form and has low turbulence. In the real world the paper. This seems a surprising result as the peak in the effects of the natural wind introduce unsteadiness. At wind distribution moves to a noticeably higher wind the low-frequency end of the spectrum the flow can be speed for the same mean wind speed. The weighting treated as quasi-steady, while changing in both the 1284 Proc IMechE Part D: J Automobile Engineering 231(9)

road speed, but they make a negligible contribution to the overall cycle-averaged drag coefficient. It can be shown that the value of CDWC is unchanged (to four decimal places) by setting the drag coefficient at yaw angles greater than 25° to the CD value at 25°. This is confirmed by a regression analysis that was applied to the wind-tunnel-derived data which shows that the cycle-averaged drag coefficient can be given by

CDWC =0:530CD0 +0:345CD5 +0:130CD10

+0:007CD15 ð9Þ

where CDc is the drag coefficient obtained in the wind tunnel at each yaw angle c from 0° to 15°. There is no physical reality to this expression, but the agreement is good and the differences from the derived values, are always less than 1 count. It can be considered as an Figure 14. Change in the cycle-averaged drag coefficient with engineering tool for determination of the proposed the mean wind speed. cycle-averaged drag coefficient. MPV: multi-purpose vehicle; SUV: sport utility vehicle. Drag measurement implications The principal component is the drag coefficient at a velocity and the direction. It has been shown theoreti- yaw angle of 0°, but C at a yaw angle of 5° is almost 22 D cally by Howell that this can introduce a significant as significant. The inputs from larger yaw angles have a unsteady drag component, which is dependent on the diminishing influence. The importance of the drag coef- drag rise with yaw angle. The high-frequency end of ficient at these small yaw angles suggests that drag data the flow unsteadiness spectrum can be considered as should be obtained between 0° and 5° and it should be free stream turbulence. In a review of the literature on noted that Windsor4 recommended measuring the drag 23 FST relevant to road vehicles, Howell et al. showed at 1° intervals between+5° and 25°. that, in general, the drag coefficient at a yaw angle of A further implication is that aerodynamics develop- 0° is increased by FST and the effect is vehicle specific, ment engineers should make as much effort to reduce but there are almost no published data on the effect of the drag coefficient at yaw angles up to 10°, or even FST on drag at a yaw angle for car shapes. 15°, as is currently devoted to reducing the drag coefficient at a yaw angle of 0° . Simplifications An increase in the applied drag coefficient to account for the effects of a natural wind, as proposed here, has The computation to derive the cycle-averaged drag an impact on the overall fuel economy, but the effect is coefficient CDWC is fairly complex, but some simplifica- small for many cars. Typically, the drag is increased by tions can be made. If, instead of a variable height (0.4 5%, which increases the fuel consumption by approxi- 3 car height), for the calculation of the wind speed, a mately 1%. However, for cars which are sensitive to the fixed height of 0.6 m is used, the deviation from the yaw angle, where, from examples given in this paper, correct result is less than 1 count (i.e. DCD = 0.001) for the increase in the drag coefficient can approach 12%, all the vehicles in the data set. It should be noted that the increase in the fuel consumption can be expected to this height is significantly less than the height of 1.0 m exceed 2%, which cannot be ignored. It is important used in the MIRA method. that all vehicle characteristics which influence the fuel An almost identical result for the cycle-averaged economy are represented appropriately. drag coefficient is found from the wind-averaged drag coefficient obtained at a single fixed ratio of the wind Conclusions speed to the vehicle speed: UWM/UV = 0.101. The difference from the correct result is also less than 1 count This paper is an attempt to generate a drag coefficient for all the cars investigated here. The cycle-averaged for application to the WLTC, using the principles of drag coefficient can, therefore, be derived with suffi- wind-averaged drag. The conclusions are as follows. cient accuracy by using the MIRA method with the unmodified wind distribution and a vehicle speed of 1. The wind-averaged drag coefficient, for a given 82.0 km/h. vehicle, is shown to be a unique function of the The wind tunnel data used as input were obtained at ratio of the wind speed to the vehicle speed if the yaw angles up to 630°,at5° intervals. These large yaw wind speeds have the same velocity distributions. angles are required to produce accurate wind-averaged 2. A typical terrain is ascribed to each phase of the drag coefficients at high ratios of the wind speed to the driving cycle so that an appropriate mean wind Howell et al. 1285

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Appendix 1 Appendix 2 Notation Vehicle dimensions c Weibull scale factor CD drag coefficient CD0 drag coefficient at a yaw angle of 0° Table 7. Vehicle dimensions. CDW wind-averaged drag coefficient Car L (m) W (m) H (m) A (m2) CDWC cycle-averaged drag coefficient k Weibull shape factor MPV 1 4.64 1.84 1.63 2.62 P probability MPV 2 4.28 1.75 1.63 2.41 PA aerodynamic drag power MPV 3 4.14 1.72 1.60 2.40 t time MPV 4 4.62 1.81 1.73 2.73 T total cycle time, excluding stops MPV 5 4.76 1.79 1.64 2.53 MPV 6 4.32 1.71 1.86 2.70 UR resultant velocity MPV 7 4.75 1.80 1.78 2.81 UV velocity of the vehicle SH 1 3.97 1.72 1.50 2.18 UW wind velocity SH 2 3.94 1.71 1.49 2.21 UWG wind gradient velocity SH 3 4.03 1.69 1.49 2.20 U mean wind velocity SH 4 4.05 1.72 1.46 2.16 WM SH 5 3.96 1.74 1.46 2.14 z height above the ground SH 6 3.85 1.70 1.51 2.20 zG gradient height of the atmospheric SH 7 3.97 1.68 1.46 2.09 boundary layer SUV 1 4.39 1.80 1.76 2.63 z0 roughness parameter of the terrain SUV 2 4.50 1.82 1.73 2.63 a wind profile exponent SUV 3 4.51 1.76 1.68 2.52 SUV 4 4.61 1.82 1.86 2.80 G gamma function SUV 5 4.58 1.78 1.71 2.55 f wind angle SUV 6 4.74 1.88 1.66 2.65 c yaw angle SUV 7 4.57 1.85 1.67 2.60 NB 1 4.92 1.87 1.46 2.30 NB 2 4.71 1.85 1.39 2.23 Abbreviations NB 3 5.07 1.90 1.48 2.48 FST free-stream turbulence NB 4 4.58 1.77 1.45 2.20 NB 5 4.83 1.86 1.50 2.37 SH small hatchback NB 6 4.47 1.74 1.42 2.06 MPV multi-purpose vehicle (people carrier) NB 7 4.73 1.81 1.43 2.17 NB notchback SUV sport utility vehicle MPV: multi-purpose vehicle; SH: small hatchback; SUV: sport utility WLTC Worldwide Harmonized Light Vehicle vehicle; NB: notchback. Test Cycle WLTP Worldwide Harmonized Light Vehicle Test Procedure