_______________________________________ © The author(s) and/or their employer(s), 2014

Real world drag coefficient – is it wind averaged drag? S Windsor Aerodynamics, Jaguar Land Rover, UK

ABSTRACT Drag reduction of road vehicles continues to be the holy grail of aerodynamicists with renewed importance of aerodynamics as OEMs strive to reduce CO2 and improve fuel economy. New legislation such as Worldwide harmonized Light vehicles Test Procedure (WLTP) is increasing the emphasis on real world boundary conditions (with moving ground wind tunnel testing) and vehicle configurations, in an effort to obtain more realistic fuel consumption figures. However, WLTP in common with all other drive cycles used in the automotive sector is based on zero-yaw aerodynamic measurements. This implicitly assumes conditions vehicles rarely see: the onset wind vector is at zero yaw, the atmosphere is still and undisturbed by other road users. This paper will show that many modern cars (particularly low drag saloon cars) have noticeable drag coefficient (CD) minima at zero yaw, with some having up to 10% increase in CD for relatively small yaw angle changes around zero. The concept of wind averaged drag ( ) will be discussed as a means of assessing real world aerodynamic performance. Three methods of calculating CDW are investigated and the MIRA method is preferred for application to passenger cars. This demonstrates that including yaw angle effects via provides a significantly different perspective on the aerodynamic contribution to fuel economy. 1. INTRODUCTION Modern wind tunnels, with their moving ground and quasi turbulence generators, are being designed and built to achieve an experimental set up that is getting closer and closer to the real world. But the wind tunnel still only partially simulates on road conditions and it is very difficult to quantify each of the known errors that exist between the wind tunnel and the real world as in Figure 1. Generally, an automotive wind tunnel provides an environment with low levels of turbulence, a floor boundary layer approaching 0 mm and most often used at zero yaw. However, road vehicles spend very little time being driven in conditions where the ambient wind is either stationary and/or at 0° yaw to the vehicle’s direction and in low levels of turbulence, yet the de facto drag coefficient (CD) is measured (and quoted) assuming the ambient wind is 0 kph and/or at 0° to the vehicle’s direction. Measuring a vehicle’s CD with this assumption is both repeatable and quick to compute in both the wind tunnel and CFD codes but the aerodynamicist knows that in the “real world” ambient conditions and vehicle set-up must, or at least should, be taken into account when calculating the vehicle’s true CD.

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Figure 1 A vehicle in its real environment (based on Hucho [1])

Automotive wind tunnels were designed to be able to yaw the vehicle to simulate crosswinds but even now, nearly 60 years later, it is uncommon for any data of CD at yaw to be published or quoted. Yet it is the change in CD with yaw angle that is of particular interest in understanding its effect on real world fuel economy as well as stability etc. The concept of wind averaged drag takes a range of CD at yaw and calculates the vehicle’s drag coefficient in the real world environment; essentially it “characterizes” a vehicle’s aerodynamic drag behaviour. 2. NOTATION The relative velocity and wind direction of a vehicle travelling at velocity VV with the ambient wind velocity VW is shown in Figure 2 below. The resultant velocity is termed VRES at a yaw angle of Ψ.

Figure 2 Relative Wind Velocity and Direction

VV = vehicle velocity (kph) VW = wind velocity (kph) VRES = relative wind velocity (kph) Ѳ = wind direction relative to the vehicle Ψ = relative yaw angle CDΨ = drag coefficient at yaw angle Ψ CDW = wind averaged drag coefficient for wind velocity VW

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3. WIND TUNNEL TEST RESULTS A range of SUV, saloon and sports cars (as shown in Table 1) were tested in the MIRA Full Scale Wind Tunnel (FSWT) to measure their aerodynamic characteristics. All the vehicles were tested at standard loading conditions, and measurements were taken over the yaw range ±5° in 1° increments and ±30° in 5° increments. The test results were left unedited and so positive and negative yaw data may not be symmetrical.

Table 1 Vehicle Data Sets

SUV and 2 Box Vehicles Audi Q3 SUV Audi Q5 SUV Audi Q7 SUV BMW X1 SAV BMW X3 SUV BMW X5 SUV BMW X6 SAV Ford Grand C-Max (for shape) MPV Ford S-Max MPV Honda CR-V SAV Hyundai iX35 SUV Jeep Compass SUV Kia Sorrento SUV Land Rover Discovery 3 SUV Land Rover Freelander 2 SUV Lexus RX-450h SUV Mazda CX-5 SUV Mercedes B-Class (for shape) 2-Box Mercedes ML SUV Nissan Qashqai SUV Porsche Cayenne GTS SUV Range Rover Evoque 5-Door SUV Range Rover 10MY SUV Range Rover 12MY SUV Range Rover LWB 14MY SUV Range Rover Sport 10MY SUV Range Rover Sport 14MY SUV Volvo XC60 SUV VW Touareg SUV

The test results from these vehicles are anonymised in all of the subsequent Figures and Tables. It was noted that many vehicles, particularly low drag saloons, had a noticeable drag coefficient minima at 0° yaw (see Figure 3). This yaw response is not as common on SUVs but still evident on some vehicles. The percentage increase in CD with yaw from straight ahead for a selection of saloons and SUVs is shown in Figures 3 and 4 respectively. In many cases the vehicles which have low CD at 0° yaw are far more likely to have a greater increase in CD with yaw. What is unclear though is whether this yaw response is as a result of overall vehicle drag reduction or a particular body feature, for example front bumper planform. Front bumper planform can be used very

Saloons and Sports Cars Audi A3 5-Door Wagon Audi A5 Sportback Saloon Audi A6 Saloon Audi A8 Saloon BMW 320d Eff Dyn Saloon BMW 535 Saloon BMW 740 Saloon Ford Mondeo 4-Door Saloon Jaguar F-Type Coupe Sports Jaguar F-Type Convertible Sports Jaguar XF 10MY Saloon Jaguar XF Sportbrake Wagon Jaguar XJ 10MY Saloon Jaguar XK Coupe 10MY Sports Jaguar XK Convertible 10MY Sports Lexus GS-450h Saloon Mercedes C250 Saloon Mercedes E350 Saloon Mercedes S350 Saloon Porsche Panamera Saloon Vauxhall Insignia 08MY Saloon Vauxhall Insignia 12MY Saloon

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effectively to control flow separation at small yaw angles [1] but this can be disadvantageous at large yaw angles. Figure 3 shows that for Saloons A to F, drag coefficient increases between 5 and 11% over the range 0-5°. Saloon G shows that this trend is not typical for all vehicles in this sector, with an increase of less than 5% over the same yaw angle.

Figure 3 Saloon Car Yaw Response

Results in Figure 4 show that SUVs are less likely to show the exaggerated minima of the saloon vehicles, but where this response is evident the magnitude is much less. In Figure 4, SUVs A and B show marked minima at 0° but only have a 6-7% rise in CD at 5° yaw with the other vehicles having more parabolic yaw responses. In the case of SUVs A and B, they are not vehicles with class leading low CD at 0° yaw.

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Figure 4 SUV Yaw Response

4. WIND AVERAGED DRAG METHODS Having identified that some vehicles have large increases in CD at small yaw angles it would be useful to be able to quantify the effect of the wind on CD for a given road speed and to compare vehicle to vehicle. Wind averaged drag (CDW) is one approach that allows this comparison to be made. There are 3 commonly known and documented methods for calculating ‘wind averaged’ drag coefficient: MIRA [2], SAE J1252 [3] and TRRL Report 392 [4] and these documents should be referred to for full derivation of their methods. Each of these methods is very similar in their general calculation but they differ in how a weighting is applied to the results as outlined below. The MIRA method (see Appendix 1) assumes a fixed vehicle velocity and then uses 7 different ambient wind velocities from 2kph - 26kph (1.2mph – 16.2mph) with a weighting factor applied to each velocity. The wind averaged drag coefficient is then calculated using 133 data points and averaged over the range ±180°. A worked example of the MIRA method can be found in Appendix 4, and in this case study the vehicle measured CD= 0.272 in the wind tunnel and CDW = 0.289 by calculation. The SAE J1252 method (see Appendix 2) assumes a fixed vehicle velocity and a fixed ambient wind velocity of 11.3kph (7mph). In this method it is assumed that the wind approaches the vehicle with equal probability from any direction. CDW is then calculated using 12 data points, 6 in both yaw directions.

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The TRRL method (see Appendix 3) is similar to the SAE method in that it too assumes a fixed vehicle velocity and a fixed ambient wind velocity of 11.3kph (7mph). However the TRRL method applies a weighting factor to the wind direction over the range ±180°. CDW is then calculated using 12 data points, 6 in both yaw directions. All of the methods use the following simplified derivation in their calculation: The relative wind velocity is given by equation (1):

2 2 2RES V W V WV V V V V Cos (1)

And the yaw angle by equation (2):

1 sintancos

W

V W

VV V

(2)

The wind averaged drag coefficient CDW can now be defined, assuming longitudinal vehicle symmetry, by equation (3) where CDΨ is determined using wind tunnel data.

2

0

1 RESDw D

V

VC C dV

(3)

The integral in equation (3) cannot obviously, or simply, be evaluated by finding an indefinite integral so numerical techniques were employed in its calculation, namely the mid-point and trapezium rules. A synopsis of the calculations can be found in the Appendix. 5. WIND AVERAGED DRAG RESULTS The wind averaged drag coefficient (CDW) for all of the vehicles was calculated using the three methods described above and compared to the CD as measured at the MIRA FSWT, and the results are shown in Table 2. A fixed vehicle speed of 70 mph, maximum speed for cars on UK motorways, was used on the calculations. It should be noted that many of the vehicles were not “eco” or low drag variants; many were fitted with high powered engines and sports kit with wide tyres. The SAE method [3] for calculating CDW is the simplest of the three methods, in that a notional average wind speed is assumed to be equally probable from all directions relative to the vehicle. The MIRA method [2] gives a weighting to the wind velocity and the TRRL method [4] gives a weighting to the wind direction distribution for the UK. It is of no surprise that the SAE and TRRL methods give essentially the same result as they use a similar approach. The SAE method averages 12 data points to calculate the CDW, and the TRRL method uses the same 12 data points but then uses a weighted average of 6 averages and thereby avoiding Simpson’s Paradox. The MIRA method is the more comprehensive of the three methods as it uses a much larger data set of 19 yaw angles and 7 wind speeds, and therefore is the preferred method in this paper to calculate CDW.

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Table 2 Difference Between the Wind Averaged Drag Methods and MIRA FSWT Results

6. DISCUSSION Comparing the results from the three methods in Table 2, for the saloon cars the method range is within 0.005 and an average of 0.002, and it is similar for the SUV and 2-box cars with a maximum range of 0.006 and an average of 0.003. The maximum and minimum CDW for the sports and saloon cars is +0.018 and -0.002 respectively with an average of CDW= 0.009. For the SUV vehicles the maximum and minimum CDW is +0.017 and -0.004 respectively with an average of CDW= 0.010 and no obvious anomalies. From the full scale wind tunnel tests some vehicles have pronounced CD minima at 0° yaw and it was thought that this type of yaw response would have a large effect on CDW. Before the CDW calculations were made it was considered that vehicles with smaller drag rise at yaw would have lower “real world” drag. This hypothesis is not particularly obvious in Table 2, but if the sensitivity of CDW is extracted from the wind tunnel data in Figure 5, the evidence becomes more apparent. For saloons and sports cars the sensitivity of wind averaged drag, taken as (CDW - CD), becomes more pronounced as CD decreases. From Figure 5, for example those vehicles with a 0° yaw drag coefficient of CD= 0.290 fall into two distinct groups depending on their CD yaw response. Vehicles with a parabolic response show a CDW increase between 0.004 and 0.006, whereas those with a pronounced minima show a CDW increase between 0.010 and 0.015. It is clear that CDW should be calculated on an individual basis.

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Figure 5 Sensitivity of Wind Averaged Drag (CDW) for Saloons

and Sports Cars It is the value of CDW that, potentially, most accurately reflects the performance of the vehicle in the real world. The truck industry in North America has been aware of the need to characterize a vehicle’s behaviour in the natural environment for many years [4] [5], as the rate of change of drag with yaw is approximately ten times that of saloon cars. More recently Cooper [6] and Leuschen [7] describe how some aerodynamic devices are sub-optimal because the effect of turbulence and wind direction has been ignored. SAE recommends that CDW at vehicle highway speed is used for vehicle performance and economy predictions. From Table 2 it can be seen that CDW is between 3-5% higher than CD measured at straight ahead. A 5% increase in CD is equivalent to approximately only a 0.5% increase in fuel consumption on the New European Driving Cycle (NEDC); but the NEDC only considers that the vehicle will be travelling above 70 kph (19 m/s) for a short period of the cycle. The NEDC is supposed to represent typical car usage in Europe and is used to assess the emissions levels of cars. It consists of four urban driving cycles and an extra urban driving cycle as shown in Figure 6. The mean speeds in the urban cycle are low and therefore the aerodynamic forces are not overly significant. It is not until the last third of the NEDC, the extra urban cycle, where aerodynamic drag becomes an important consideration as speed rises above 70kph. But even in this part of the cycle the vehicle only travels at speeds >70kph for 215s, which is only 18% of the total NEDC test.

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Figure 6 NEDC Drive Cycle

Real World fuel economy should ideally be calculated from a drive cycle that represents the full range of driving speeds and nearer to real world scenarios. In 1994 BMW published data [8] for their vehicles based on annual distances driven (Figure 7), and this showed that on average their cars spent 70% of their annual mileage on motorways or national highways and only 30% in the city. On this data, aerodynamic drag is very significant in affecting real world fuel economy and even more so in Germany where the motorway speeds are higher than in the UK. In the case of the BMW 7 Series it spends nearly 50% of its annual mileage on motorways and one could safely assume at speeds regularly in excess of 160kph.

Figure 7 BMW Press Information 1994 [8]

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The United Nations is currently developing a proposal for a new global technical regulation on the Worldwide harmonized Light vehicles Test Procedure (WLTP) which aims to provide a harmonized method to determine pollutants and CO2 emissions. This new procedure takes into account higher vehicle speeds in the drive cycle (see Figure 8), but still only over a short period, and stipulates the need for wind tunnels that better replicate the real world with moving ground and rotating wheels. However the vehicles continue to be tested in turbulence levels of <1% and more importantly the effect of CD increase with yaw angle is overlooked.

0 200 400 600 800 1000 1200 1400 1600 1800

Time (s)

Figure 8 Proposed WLTP Drive Cycle

7. CONCLUSIONS In the “real world”, ambient conditions and vehicle set-up must be taken into account when calculating the vehicle’s CD. The measured CD, either from wind tunnel tests or from CFD, is certainly not the CD experienced by the customer. The real world drag coefficient needs to allow for ambient wind strength and direction (wind averaged drag), vehicle loading (or attitude), trim level differences and wind tunnel set up. The suggested method to calculate wind averaged drag coefficient (CDW) is the MIRA method as it is more appropriate than the SAE or TRRL methods. It uses a wider range of ambient wind speeds and yaw angles rather than a single wind speed at 6 yaw angles. For the computation, yaw data is required over the yaw range ±5° in 1° increments and at ±10°and ±15°. CDW was calculated for a range of vehicles using a sample set of 51 sports, saloons, 2-box and SUVs, and the average increase was CD= +0.007 to +0.010. Two saloon cars had an increase of more than CD= +0.015 over their CD at 0° yaw. Therefore it is important to either use this delta, or the actual CDW for the vehicle in question, when calculating real world fuel economy. It should be remembered that drag coefficients obtained from wind tunnel tests and CFD are highly idealized. The vehicles are set at a predetermined trim height, with

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a particular wheel and tyre combination, with the wind at 0° yaw and tested in low turbulence all of which vary in the real world. ACKNOWLEDGEMENTS I thank Jaguar Land Rover for permission to publish this paper. I am also grateful to colleagues past and present for their encouragement and discussion over its contents. The views expressed are the author’s own and do not necessarily represent company policy. REFERENCES 1. Hucho, W-H., Aerodynamics Of Road Vehicles, Fourth Edition 2. MIRA Aerodynamic Wind Tunnel Facilities Users’ Handbook 3. SAE J1252 JUL2012, SAE Wind Tunnel Test Procedure for Trucks and Buses 4. Ingram, K.C. The Wind Averaged Drag Coefficient Applied to Heavy Goods

Vehicles, Transport and Road Research Laboratory (TRRL) Supplementary Report 392, 1978

5. Buckley, F. and Sekscienski, W., Comparisons of Effectiveness of Commercially Available Devices for the Reduction of Aerodynamic Drag on Tractor-Trailers, SAE Technical Paper 750704, 1975

6. Cooper, K., Truck Aerodynamics Reborn - Lessons from the Past, SAE Technical Paper 2003-01-3376, 2003

7. Leuschen, J. and Cooper, K., Full-Scale Wind Tunnel Tests of Production and Prototype, Second-Generation Aerodynamic Drag-Reducing Devices for Tractor-Trailers, SAE Technical Paper 2006-01-3456, 2006

8. BMW Techniktag ’94 (annual in-house Engineering Conference) APPENDICES Calculation of Wind Averaged Drag Coefficients Appendix 1 MIRA Method Notation

VV = vehicle velocity (kph) VW = wind velocity (kph) VRES = relative wind velocity (kph) Ѳ = wind direction relative to the vehicle Ψ = relative yaw angle CDΨ = drag coefficient at yaw angle Ψ CDW = wind averaged drag coefficient for wind velocity VW

Calculations

2 2 2RES V W V WV V V V V Cos (1)

1 sintancos

W

V W

VV V

(2)

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2

0

1 RESDw D

V

VC C dV

(3)

Where: VV= 110kph

The following values of VW were used with the weighting factor as indicated.

VW (kph)

Weighting Proportion

2 0.210 6 0.330 10 0.250 14 0.130 18 0.055 22 0.020 26 0.005

Yaw data is required at 0, 1, 2, 3, 4, 5, 10, 15° in both positive and negative directions. Appendix 2 SAE J1252 Method Notation

VV = vehicle velocity (kph) VW = wind velocity (kph) VRES = relative wind velocity (kph) Ѳ = wind direction relative to the vehicle Ψ = relative yaw angle CDΨ = drag coefficient at yaw angle Ψ CDW = wind averaged drag coefficient for wind velocity VW

Calculations

1 sintancos

W

V W

VV V

(1)

2 2 2RES V W V WV V V V V Cos (2)

2

1 2. .W Wi

V V

V VM CosV V

(3)

30 15i i (4)

6

6

16DW D ii

C C M

(5)

Where: VV= 110kph

VW= 11.3kph (7mph) i = 1 to 6 in increments of 1

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Yaw data is required at 0, 1, 2, 3, 4, 5, 10, 15° in both positive and negative directions. It is assumed that the wind approaches the vehicle with equal probability from any direction. Appendix 3 TRRL Method Notation

VV = vehicle velocity (kph) VW = wind velocity (kph) VRES = relative wind velocity (kph) Ѳ = wind direction relative to the vehicle Ψ = relative yaw angle CDΨ = drag coefficient at yaw angle Ψ CDW = wind averaged drag coefficient for wind velocity VW

Calculations

2 2 2RES V W V WV V V V V Cos (1)

1 sintancos

W

V W

VV V

(2)

2

0

1 RESDw D

V

VC C dV

(3)

Where VV= 110kph and VW= 11.3kph (7mph) The following values of Ѳ were used with the probability / weighting factor as indicated.

Wind Direction(Ѳ°) Probability p(Ѳ)

166-15 0.155 16-45 0.168 46-75 0.170 76-105 0.169 106-135 0.171 136-165 0.167

Yaw data is required at 0, 1, 2, 3, 4, 5, 10, 15° in both positive and negative directions.

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Appendix 4 MIRA Method Worked Example Measured data from MIRA:

Wind Averaged Drag Calculation:

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