A novel technique to determine free-stream velocity from ground-based anemometric measurements during track tests.
A novel method was developed to predict the free-stream velocity experienced by a traveling vehicle based on track-side anemometric measurements. The end objective of this research was to enhance the reliability of the prediction of free-stream conditions in order to improve the accuracy of aerodynamic drag coefficient ([C.sub.D]) assessments from track tests of surface vehicles. Although the technique was applied to heavy-duty vehicles in the present work, it is equally applicable to any vehicle type. The proposed method is based on Taylor's hypothesis, a principle applied in fluid mechanics to convert temporal signals into the spatial domain. It considers that the turbulent wind velocity fluctuations measured at one point are due to the "passage of an unchanging pattern of turbulent motion over the point". The method is applied to predict the wind velocity that the vehicle will experience as it encounters a wind pattern detected earlier by an anemometer located upwind. The proposed technique has the potential to enhance the accuracy of free-stream velocity predictions aimed at calibrating a vehicle-mounted anemometer. A sensitivity analysis highlights the errors on the predicted free-stream speed and yaw angle that result from errors in the evaluation of the terrestrial wind speed and direction. Moreover, considering that a surface vehicle travels through the atmospheric boundary layer, it is demonstrated that using track-based anemometers to calibrate a vehicle-mounted anemometer installed at a different height leads to incoherency and can cause substantial errors in the evaluation of free-stream conditions. It is recommended that all ground-based anemometers be installed at the same reference height relative to local ground, as the vehicle-mounted anemometer.
CITATION: Tanguay, B., "A Novel Technique to Determine Free-Stream Velocity from Ground-Based Anemometric Measurements During Track Tests," SAE Int. J. Commer. Veh. 9(2):2016, doi: 10.4271/2016-01-8023.
In the framework of a research collaboration with Environment Canada (1), the Aerodynamics Laboratory of the National Research Council of Canada (NRC) conducted aerodynamic experiments on two tractor-trailer combinations at Ford Motor Company's Arizona Proving Ground (APG). The experiments were conducted in June 2011 in the midst of the Environmental Protection Agency's (EPA) test campaign for the development of the Phase-I regulations to curtail greenhouse gas emissions and fuel consumption of mediumand heavy-duty vehicles (HDV), which led to the Phase-I rules in the USA  and in Canada . The experiments and the ensuing analysis conducted by the author were documented in three technical reports (2). The present article is derived from this research which led to the development of ideas, techniques and procedures aimed at enhancing the accuracy and reducing the uncertainty of free-stream wind predictions and aerodynamic drag assessments from track tests, applicable to any vehicle type.
The Phase-I regulations  introduced by the EPA relied on coastdown testing as the primary technique to determine the aerodynamic drag coefficient ([C.sub.D]) of test vehicles with the possibility of using alternative methods (wind tunnel testing or CFD (3)) correlated to coast-down results. The required use of a track-side anemometer during coast-down tests, following recommended practice SAE J1263 (4) , was only aimed at determining whether the mean wind speed was below the admissible limit of 16 km/h but this anemometric data was not utilized in the analysis. Thus, the Phase-I regulations focused on the "zero-yaw drag coefficient" without ascertaining that the yaw angle was effectively zero. The proposed phase-II rule  introduces the use of a vehicle-mounted anemometer with the intent of taking into account the variation of [C.sub.D] with yaw angle ([[PSI].sub.[infinity]]), from which a wind-averaged drag coefficient ([C.sub.Dwa]) is derived by combining with the results from one of the alternative methods. The proposed test procedure is akin to SAE recommended practice J2263  whereby wind velocity measurements from one or several track-based anemometers are utilized to correct the readings of the vehicle-mounted anemometer for "vehicle blockage". However, one major deviation of the proposed rule from standard J2263 is that the terrestrial wind velocity measured by track-based anemometers at vehicle mid-height is used to "calibrate" the vehicle-mounted anemometer sensing the apparent wind at a different height. The soundness of this approach will be evaluated herein by considering intrinsic properties of the terrestrial wind, which constitutes the operational environment for such tests.
The aerodynamic drag coefficient of HDVs is typically charac-terized by a pronounced rise with yaw angle. The assessment of the yaw-sensitivity of [C.sub.D] from track tests requires testing in windy conditions producing large enough free-stream yaw angles to enable the calculation of [C.sub.Dwa'] the wind-averaged drag coefficient. This characterization is important to enable the evaluation of fuel consumption in various wind conditions. In this respect, the pioneering work of Buckley, Walston et al.   who developed procedures and analysis methods for coast-down testing in windy conditions has provided valuable insight for the present work. The subsequent work by Buckley  has contributed towards the development of SAE recommended practice J2263. Notwithstanding, the methods proposed in reference , in SAE standard J2263  and in the proposed phase-II rule  to name a few, rely on assumptions that do not take into consideration the turbulent nature of the terrestrial wind for the calibration of a vehicle-mounted anemometer. For instance, one such assumption was exemplified by Buckley :
"The analysis rests on the assumption that the spatial averages of the wind speed and direction along a common section of test track are the same during two successive vehicle passes back and forth along the track ..."
Likewise, many studies aimed at determining the drag coefficient from track tests (e.g. ) do not consider the inherent property of the terrestrial wind in ground vicinity, which is characterized by spatiotemporal, turbulent fluctuations with correlation length scales not exceeding several metres , In a specific example pertaining to HDVs , the terrestrial wind speed and direction measured in proximity of the test track midpoint are used as reference values to calibrate the onboard anemometer readings taken during the same time interval, irrespective of the vehicle's position along the track. This method rests on the assumption that the terrestrial wind velocity at the vehicle location is equal to the wind velocity measured at the track midpoint during the same time interval, suggesting that the wind is spatially uniform and characterized by temporal variations only.
The first portion of the present paper considers free-stream wind conditions in the context of a surface vehicle traveling through the near-ground turbulent boundary layer and the errors that result from an improper free-stream correction of the apparent wind measured onboard a traveling vehicle. A detailed review and analysis of the turbulent winds experienced by a surface vehicle traveling through the atmospheric boundary layer was presented by Cooper and Watkins , emphasizing the large variability of turbulent wind conditions that a vehicle can experience. More recently, McAuliffe  reported experimental results characterizing the turbulent environment experienced specifically by heavy-duty vehicles, corroborating the wide range of turbulent wind conditions associated with the surrounding terrain or the presence of nearby vehicles, among other things. In the present work, a novel technique is proposed to predict the free-stream wind velocity from track-based anemometric measurements using "Taylor's hypothesis", a useful approximation first proposed by British physicist Geoffrey Ingram Taylor , This analysis technique is applied to correct the onboard anemometric measurements to free-stream conditions. Moreover, the consideration that a surface vehicle travels through the atmospheric boundary layer is treated analytically to evaluate the effect of the vertical position of a vehicle-mounted anemometer on the prediction of free-stream velocity. Finally, some procedural guidelines are then proposed, to maximize the accuracy and reliability of track tests aimed at characterizing vehicle aerodynamic performance.
The experimental campaign conducted in the framework of the present project was the first such field test carried out by the NRC Aerodynamics Laboratory, contrasting with its primary activity of wind tunnel testing. The experience and the aerodynamic data gathered during these tests motivated the examination of the challenges associated with aerodynamic measurements in the field and the development of ideas having the potential to improve the accuracy and reliability of aerodynamic experiments conducted in an uncontrollable, unsteady environment. This first implementation of the proposed methods is illustrated by applying them to the limited data set acquired during these experiments. Further testing with optimized experimental arrangements would enable the improvement and refinement of the proposed techniques.
CONTEXT AND EXPERIMENTAL ARRANGEMENT
The experimental campaign was commissioned by the EPA in the context of the development of its Phase-I regulations for limiting GHG emissions from medium- and heavy-duty vehicles . In the midst of this test program, NRC was granted access to two tractors each coupled to a 28-foot trailer (5) to conduct a distinct set of aerodynamic experiments involving the measurement of static pressure distributions on the tractors and trailers. NRC conducted constant-speed runs to acquire static pressure signals using its own on-board instrumentation system and coast-down runs for evaluating the vehicles' aerodynamic drag. The static pressure experiments will be the focus of a separate publication.
The experiments were conducted at Ford's Arizona Proving Ground located in Wittmann, approximately 65 kilometres north-west of Phoenix, Arizona. A satellite view of the test track is shown in Figure la. The lower plot displays in red the itinerary followed by one of the test vehicles during several runs, as acquired by the onboard GPS receiver. Two propeller-vane anemometers were installed on the windward side of the straightaway to measure the wind speed and direction, at positions prescribed by the EPA. They are labelled [AN.sub.1] and [AN.sub.2] in Figure 1b. A measurement station was also located next to anemometer [AN.sub.1] to record the barometric pressure, temperature and humidity of the air required for calculating the density and viscosity of the ambient air. The data from both sites were recorded with two GPS data loggers at a rate of 10 samples per second. Each vehicle tested was equipped with a similar propeller-vane anemometer protruding 2.4 metres ahead of the vehicle nose at the end of a boom, sensing the wind speed and angle that were also recorded by an onboard GPS data logger. Details on the characteristics and accuracies of the instrumentation used are provided in the Appendix.
The GPS latitudes and longitudes were converted to orthogonal cartesian coordinates by using the equations defining the WGS84 ellipsoid  as an approximation to the earth's shape, the standard representation used on current GPS devices. As shown in the lower plot of Figure 1. the north end of the southern hairpin was defined as the origin of the test track (X, Y) = (0, 0) (labelled 'O'), whereas the south end of the northern hairpin was defined as the end of the track (labelled '[E/OE]"). Based on the GPS data, the useful track length, i.e. distance, is approximately 3.078 km. The results from a survey of the straightaway indicates a maximum elevation difference of approximately 64 millimetres over a distance of more than 3 km, as determined from a set of 100 measurement points. The flatness of this track ensured that gravitational loads could be neglected in a coast-down analysis. The track consisted of a single lane (6) that was traveled back and forth in both directions. The flatness of the land surrounding the track with a minimal number of obstacles was favourable in terms of wind conditions. The long fetch over which the wind profile develops with minimal obstruction is indeed conducive to stabler winds.
ON THE CRITICAL IMPORTANCE OF FREE-STREAM CONDITIONS
The coefficient of aerodynamic drag [C.sub.D] is the ratio of the drag force D experienced by a traveling vehicle to the force that would result from applying a pressure differential equal to the free-stream dynamic pressure [q.sub.[infinity]] across a surface of area A, typically the vehicle frontal area:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
The accuracy in quantifying [C.sub.D], the measure of a vehicle's aerodynamic efficiency, depends critically on the ability to determine the approach flow conditions 'at infinity ([infinity])', that is, sufficiently far, in the free-stream zone where the flow field is unperturbed by the vehicle's presence. In a wind tunnel, where the flow conditions are controlled, the flow field around the test vehicle is distorted by the tunnel-specific configuration (7), when compared to operating conditions in 'open air'. The associated challenge is to predict the corresponding free-stream values by applying empirical blockage-corrections. To reduce the implicit errors, it is advisable to minimize these approximate corrections by combining a vehicle model with a wind tunnel test section producing a minimal area ratio A/C while satisfying the minimum Reynolds number constraint [Re.sub.[infinity]] > [Re.sub.min]., as achieved with the experimental configuration described in  for testing HDV models.
The analogous challenge for aerodynamic experiments on test tracks is distinct. In this case, unlike in a wind tunnel simulation, the flow conditions are realistic, but the zone where perturbation-free wind conditions exist is too far from the vehicle nose for probing with a conventional boom-mounted anemometer, typically sensing the apparent wind velocity within a few metres forward of the nose of a HDV. This phenomenon was demonstrated by means of a wind tunnel experiment (8) whereby the PIV (9) technique was applied to measure the flow field forward of the nose of a generic HDV model in a horizontal plane at model mid-height. The results are schematized in Figure 2. An anemometer sensing the wind velocity forward of the vehicle at point a measures a wind speed that is lower than the unperturbed wind speed [U.sub.[infinity]] and a wind angle larger than [[PSI].sub.[infinity]] by virtue of the presence of the solid obstacle downwind distorting the flow field. Relying on this information to determine the drag coefficient can lead to significant errors:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
Equation 3. which was obtained by differentiating equation 1. indicates that the relative error on [C.sub.D] is twice the relative error on [U.sub.[infinity]] Walston et al.  reported that an anemometer located 3 metres forward of the nose of a 1970 's HDV measured a speed approximately 10% lower than the free-stream value. Based on equation 3. this would result in an overestimate of [C.sub.D] of the order of 20%. The impact on the curve [C.sub.D]( [[PSI].sub.[infinity]]) of a biased measurement of the velocity [[??].sub.[infinity]] within the perturbed zone ahead of the vehicle is depicted in Figure 3. At zero degrees of yaw, the bias in the measured wind speed causes a vertical shift of [C.sub.D] from point A to point B. For non-zeeo yaw angles, the [C.sub.D] shift is accompanied by a yaw angle bias (e.g. from point C to point D) resulting in the observed vertical shift and flattening of the [C..sub.D] ([[PSI].sub.[infinity]]) curve.
In the context of quantifying the aerodynamic drag coefficient of a surface vehicle on a road, the determination of the free-stream speed [U.sub.[infinity]] and yaw angle [[PSI].sub.[infinity]] presents a major challenge. The general concept consists in calculating the vectorial difference between the vehicle velocity [??] and the unperturbed terrestrial wind velocity [??] experienced by the vehicle to produce the free-stream velocity vector [[??].sub.[infinity]]. These values are then used to apply a "free-stream calibration" to the anemometric data sensed by a boom-mounted anemometer measuring the biased apparent wind at point a (see Figure 2). The technical challenge is related to the fact that the terrestrial wind measurement is made at a single specific point in space, some distance away from the vehicle trajectory. Thus, the spatial resolution is non-existent. However, the 100 ms temporal resolution of the anemometers used in the present study, is small relative to the time scales of the turbulent motions. This will be capitalized on in the analysis to follow.
A schematized plan view of the zone of interaction between a traveling vehicle and the measured terrestrial wind is shown in Figure 4. The track-based anemometer (labeled AN), located a distance L from the centreline of the vehicle's trajectory, measures the terrestrial wind velocity vector [??](t) which is oriented at angle [gamma](t) relative to the vehicle travel direction. An important consideration is that the height of the anemometer sensing point relative to the local ground must be the same as the height of the vehicle-mounted anemometer above the test track, as will be demonstrated below. The anemometric information measured at point AN propagates over a distance F (the fetch) to reach point c some time after the measurement was made. The measured 'wind front' and the vehicle's boom-mounted anemometer meet at point c at a unique instant in time. The vectorial difference between the terrestrial wind and vehicle velocities at that precise space-time instant yields the sought free-stream velocity vector [[??].sub.[infinity]]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
By expressing this vectorial equation in terms of magnitude and direction, we obtain the free-stream wind speed (10) and direction:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
Examining Figure 4, the position of the weather station on the windward side of the track is conducive to a prediction of the unperturbed terrestrial wind velocity that will combine with the instantaneous vehicle velocity at point c to yield the free-stream wind velocity experienced by the vehicle at the instant it crosses that point. However, if the wind direction were shifted 180[degrees], with the weather station now located on the leeward side of the track, the anemometer would then be located downwind of point c and consequently, it would sense some wind velocity originating from point c at some time after the passage of the vehicle through that point. This wind velocity is not equal to the unperturbed terrestrial wind velocity experienced by the vehicle at point c. Instead, it is a perturbed wind velocity corresponding to the "signature" of the vehicle's passage at point c. The utilization of a wind velocity sensed by an anemometer installed on the leeward side of a test track to calculate the free-stream wind velocity experienced by a traveling vehicle introduces a bias in the aerodynamic analysis.
Examples of suggested configurations for terrestrial wind measurements are shown in Figure 5. Under conditions of a prevailing wind direction whereby the same side of the track is consistently to windward (Figure 5b), then all available anemometers would be installed on that side (11). This situation is optimal since all anemometers provide useable wind data at all times, from which a substantial database of calibration points can be created with efficiency. On the contrary, when the wind direction is unpredictable and can alternate on either side of the track in the course of a test campaign, then a pair of anemometers should be installed at each measurement station, one on either side of the track, as shown in Figure 5a. In this case, only the anemometric data from the windward anemometers is used for the calculations, so half as much valid data as in the former case will be collected per unit of time.
COASTING THROUGH THE ATMOSPHERIC SURFACE LAYER
The schematics of Figures 2 and 4 only portray a simplified bird's eye view of the conditions that a vehicle is subjected to during a track experiment. It is important to recognize that the vertical distribution of the terrestrial wind velocity has a fundamental impact on the flow field that a traveling vehicle experiences and consequently on the approach used to evaluate the reference wind velocity vector [[??].sub.[infinity]]. The "natural wind" has fundamental characteristics that may affect the aerodynamic loads experienced by a travelling vehicle, as shown by Watkins and Cooper . One such characteristic is the variation of the wind velocity with elevation. The atmospheric surface layer (ASL) is defined as the layer of air in the immediate vicinity of the earth's surface within which the mean wind speed increases monotonically from zero at ground level to an outer value at the edge of the layer. This layer is turbulent, that is, the velocity at any point in space fluctuates relative to the local mean, with velocity variations in all three spatial directions. In general, it can be said that the time and length scales associated with these fluctuations are a function of the height z, of the topology and roughness of the surrounding terrain (see reference ) and of the external forcing by temperature and pressure gradients, among other things.
Turbulent boundary layers have been studied extensively in laboratory wind tunnels but the ASL has received less attention, due to the technical challenges involved. However, recent experiments conducted at the SLTEST research facility in Utah   have confirmed the similarity between the structure of the near-neutral (12) ASL and canonical, zero-pressure-gradient boundary layers studied in wind tunnels. The results of these investigations are consistent with Von Karman's "law of the wall" (see reference ). a logarithmic function relating the mean velocity distribution to the shear stress ([TAU]) at the solid boundary. In particular, it was shown in  that the validity of the "law of the wall" spans the lower 15% of the near-neutral ASL, which is reported to have a thickness of 80 [+ or -] 8 metres. Hence, any surface vehicle is totally immersed within the logarithmic wind velocity profile that extends up to about 12 metres from the ground. The "law of the wall" for a fully developed turbulent boundary layer on a flat plate is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
Where [U.sub.[tau]] is the skin friction velocity, [KAPPA] is the Von Karman constant ([kappa] [approximately equal to] 0.4) and B is a parameter characterizing the roughness of the boundary. In practice, for the atmospheric surface layer, an equivalent and more practical relationship (e.g. in ) is used to capture the surface roughness effects, as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
Where [z.sub.o] is an empirical constant called the "characteristic roughness height" whose value has a large impact on the mean velocity distribution, [z.sub.o] is not a direct measure of the height of terrain roughness, rather a measure of its capacity to withdraw momentum from the flow near the ground. Its value is obtained through field experiments. For the present analysis, it was more practical to rewrite equation 9 in terms of the value of the mean wind speed [W.sub.ref] prevailing at the reference height (13) [z.sub.ref]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
Figure 6 presents two mean wind velocity profiles for the lower 6 metres of the ASL, based on equation 10. The fuller profile ([z.sub.o] = 5 * [10.sup.-4] m) corresponds to the ASL developing over a flat desert whereas the other mean speed distribution ([z.sub.o]=5 * [10.sup.-2] m) is characteristic of the wind blowing over a field with tall grass. These empirical parameters were obtained from reference , Both profiles were calculated for a consistent mean wind speed of 25 km/h at the vehicle mid-height point ([z.sub.ref] = 2.057 metres for a typical tractor-trailer) depicted by the bull's eye symbol. This value is within the limits prescribed in the SAE recommended practice J2263 for coast-down testing . The figure emphasizes the marked variation of mean wind speed with height and the dramatic effect of terrain roughness on the velocity gradient.
For a given wind direction [gamma] and vehicle speed V, one can calculate the variation in apparent mean wind speed and yaw angle as a function of height z by applying equations 4 to 7 and 10. Figure 7 depicts the apparent wind profiles that a vehicle would experience when traveling at 60 and 120 km/h in the presence of a terrestrial wind characterized by equation 10 and blowing at [W.sub.ref] = 25 km/h, at 30 degrees from the travel direction, for both terrain roughness conditions. The upper two plots (a, b) correspond to the vehicle traveling against a headwind and emphasize the speed deficit in the near-ground region and the mono tonic increase of free-stream speed and yaw angle with height. For the rougher terrain and a vehicle speed of 120 km/h, the yaw angle increases from about 6[degrees] to 10[degrees] between heights z = 0.5 m and z = 4 m. The corresponding lower plots (c, d) display the profile for the vehicle traveling in the opposite direction, with a tailwind blowing at [gamma] = -150[degrees]. In this case, because the tailwind component reduces the magnitude of [??], the yaw angle variations are exacerbated, with a rise from approximately 4[degrees] to 9[degrees] between the same heights of 0.5 and 4 metres. It is noteworthy that the apparent wind speed increases monotonically towards the ground level, in this case. The distinct shapes of these velocity profiles indicate that coast-down runs in opposite directions in the presence of terrestrial winds are different in character and ought to be treated as distinct objects of analysis. Besides, the variation of velocity with height warrants special attention with respect to prescribing the height at which the vehicle-mounted anemometer measures the apparent wind.
The plots presented in Figure 8 were created to investigate the effect of varying the vertical position [z.sub.an] of the vehicle-mounted anemometer on the correspondence between the apparent wind speed [U.sub.an] measured at that height and the speed [U.sub.ref] that would be sensed if the anemometer were positioned at the reference height [z.sub.ref] The control parameters are shown in the inset of Figure 8a, with [z.sub.ref] corresponding to the mid-height of a typical HDV. The data was produced by varying the vehicle speed V, much like during a coast-down run. As expected from the previous examination of the velocity profiles, if the anemometer is positioned above the reference height, then [U.sub.an] exceeds [U.sub.ref] for the headwind run whereas the converse is true for the tailwind run. For example, for a speed of [U.sub.ref] =60 km/h and the anemometer located 3 metres above the reference position, i.e. [z.sub.an] =[z.sub.ref] + 3 m=5.057 m, the measured speed is about 12% higher than [U.sub.ref] for the headwind run. On the contrary, for the tailwind run, [U.sub.an] is approximately 8% lower than the reference speed [U.sub.ref'] an overall difference of 20% between headwind and tailwind runs with the same value of [U.sub.ref] When the test anemometer is positioned below [z.sub.ref'] the trend is reversed.
The corresponding information regarding the yaw angle is presented in Figure 9. Similarly, major discrepancies are observed with the yaw angle measurement. Let us consider the difference [DELTA][PSI] in yaw angles measured at [z.sub.an]= 5.057 m and at the reference height at [T.sub.ref]=+10 [degrees] for the headwind run and at [[PSI].sub.ref]=-10[degrees] for the tailwind run. In the case of the headwind run, [DELTA][PSI] [approximately equal to] +1.5[degrees] whereas for the tailwind run, this value becomes [DELTA][PSI] [approximately equal to] -3.3[degrees].
Finally, the influence of the terrestrial wind speed [W.sub.ref] on the correspondence between wind measurements at z=[z.sub.ref]=2.057 m and at z = 5.5 m is presented in Figure 10. It is striking to see the pronounced effect of a change in the terrestrial wind speed on the relationship between measurements at both heights. For the same apparent wind [U.sub.ref] of say 60 km/h combined with a terrestrial wind speed of [W.sub.ref]=20 km/h, the differences between the sensed wind speeds and yaw angles for headwind and tailwind runs are about 8% and 4[degrees] respectively.
In summary, positioning the vehicle-mounted anemometer at a height [z.sub.an] [not equal to] [z.sub.ref] leads to a conundrum whereby for a fixed value of the reference apparent wind speed [U.sub.ref'] the speed ratio [U.sub.an] /[U.sub.ref] and the yaw angle difference [[PSI].sub.an]-[[PSI].sub.ref] change with the value of the terrestrial wind speed [W.sub.ref] and with the travel direction. It is argued that such a configuration is not conducive to providing reliable data for calibrating a vehicle-mounted anemometer to free-stream conditions, a critical prerequisite for calculating reliable drag coefficient curves [C.sub.D]([[PSI].sub.[infinity]]). It must be noted that at any point (X, 7), any instantaneous wind profile W(z, t) at time t will not have the same shape as the mean wind profile [??](z) which has been the focus of this section. However, any instantaneous turbulent profile is an instantaneous deviation from the trend curve that constitutes the mean wind profile [??](z). The trend is that the wind speed increases with height and this fact must be taken into account.
The analytical exploration conducted here on the basis of the knowledge of the documented shape of the ASL velocity profile, reveals the criticality of placing the vehicle-mounted anemometer forward of the vehicle and at a reference height most representative of the oncoming flow field to which the vehicle is subjected. Furthermore, for the purpose of correcting the vehicle-mounted anemometer readings to free-stream conditions, all track-side anemometers should be sensing the terrestrial wind velocity at the same reference height. It is common practice to set the reference height to the vehicle mid-height point, e.g. in SAE recommended practice J2263 . As stated above, the measurement height is relative to the local ground or track, for the ground-based and vehicle-mounted anemometers respectively. In light of the shape of the apparent wind profiles displayed in Figure 6, the author argues that setting the reference measurement height to vehicle mid-height is an arbitrary choice. Indeed, it can be shown that the height of the centroid of the dynamic pressure distribution (14) varies with the wind conditions and that a measurement height different than h/2 might be more representative of typical operational conditions. This topic will be addressed in a future publication. As will be seen in the following two sections, the proposed configuration, combining vehicle-based and track-side anemometric measurements made at a common reference height, is conducive to the application of a novel technique for predicting the free-stream velocity used to 'calibrate' the vehicle-based velocity measurement to free-stream conditions.
Considering the repercussions of an improper account of wind conditions on the assessment of vehicle aerodynamic performance, the calibration of the biased wind velocity readings sensed by a vehicle-mounted anemometer using track-side anemometric measurements is a pivotal step. In order to achieve this, one must predict the relative wind velocity experienced by the vehicle on the basis of a local wind measurement made some distance away from the vehicle trajectory, as depicted previously in Figure 4.
The approach adopted here is expected to enhance the reliability of the prediction of the free-stream velocity [[??].sub.[infinity]]. The method is based on Taylor s hypothesis  which considers the unsteady wind fluctuations (i.e. the turbulence) measured at one point in space as a frozen spatial pattern advected past that point at the locally-measured mean flow velocity:
"If the velocity of the air stream which carries the eddies is very much greater than the turbulence velocity, one may assume that the sequence of changes in U at a fixed point are simply due to the passage of an unchanging pattern of turbulent motion over the point. "
Taylor's hypothesis is also referred to as the "frozen turbulence" hypothesis, in which fields of "frozen eddies" are advected by the local flow at the advection speed [W.sub.a], as schematized in the diagram of Figure 11. This approximation has played a major role in turbulence research since it allowed the spatial structure of turbulent motions to be inferred from temporal measurements made at one point.
In the present context, the advection of a turbulent signal from its measurement point [??]AN to a point [[??].sub.c] downwind is schematized in Figure 12. A velocity signal [??](t) arriving at point c was measured by the anemometer located upwind at point AN some time earlier. The time [T.sub.a] that is necessary for the information to propagate between these two points is proportional to the distance traveled (the fetch F) at the advection speed [W.sub.a]. This is expressed mathematically as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
Taylor s hypothesis has recently undergone extensive scrutiny and several studies dispute the idea that turbulent eddies are advected at the mean speed of the flow, arguing that the advection speed depends on the frequency and wavenumber of the turbulent eddies   , New light is being shed on this phenomenon, especially since the advent of spatial measurement techniques such as Particle-Image Velocimetry (PIV) in wind tunnels , direct numerical simulations of turbulent flows ,  and the use of arrays of ultrasonic wind sensors  and LiDARs (15)  for field measurements in the atmospheric surface layer. These techniques provide time-resolved measurements of a flow field over some spatial extent, against which Taylor s hypothesis was examined. The dominant issue highlighted by these studies pertains to the advection speed of the turbulent eddies whose value may differ from the local mean speed. For instance, in two experimental studies   involving field measurements in the ASL using arrays of ultrasonic anemometers, the ratio of the advection speed to the mean speed [W.sub.a] / [??] was reported to lie between 1 and 1.2.
Another important consideration in the present context is the persistence of a turbulence pattern as it propagates downwind. In accordance with the well-know 'turbulent energy cascade' , turbulent kinetic energy is transferred from the large scales of motion to the small ones, until they dissipate. This could lead to a degradation of the signature of a detected pattern, as it advects downwind (a detrimental effect for predictive purposes). A recent field study using a Doppler LiDAR  confirmed that the smaller scale structures are the least persistent:
"The applicability of Taylor's frozen turbulence hypothesis is strongly dependent on the scale of the turbulent structures... Atmospheric structures larger than the measurement height tend to be especially long lived and the best candidates for the applicability of Taylor's hypothesis "
This reassuring discovery provides a strong level of confidence for the application at hand since the turbulent energy is dominated by scales larger than the two-metre reference measurement height (for HDVs). A similar result had already been obtained by Powell and Elderkin  in the early 1970s:
APPLICATION OF TAYLOR'S HYPOTHESIS
The main unknown in the application of Taylor's approximation is the advection speed which is not easily measurable. The approach adopted here is based, among others, on recent experiments  investigating mixing layers with PIV. Consistent with the results of that study, the smaller (higher frequency) eddies will be considered as being entrained by the larger flow structures, at the local mean speed [??]. Contrary to laboratory experiments in wind tunnels where flow conditions are under control, the atmospheric surface layer is undergoing perpetual change, posing specific challenges relating to the determination of a proper "mean wind speed". For the present purpose of estimating wind conditions at point c downwind of an anemometer, we are considering that the dominant, larger scales of the flow having characteristic length [??]T are the "propagators" of the anemometric information. Consequently, the speed [W.sub.a] was determined by averaging the wind speed measured by the anemometer over that length scale. The characteristic length scale of the flow, [??]T, was calculated using the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
Where S(f)is the normalized power spectral density. Figure 13a shows an example of a spectrum computed from the anemometric data acquired during the aerodynamic experiments. The corresponding spectral information expressed in terms of wavelength (Figure 13b) encompasses flow scales ranging from less than a metre to 200 metres. The spectra were calculated from signal excerpts of sufficient duration to enable the capturing of low frequencies corresponding to a wavelength of the order of 100 metres, typically 0.01 Hz. Once the length scale [??]T is obtained, the time-evolving advection speed is determined by the following steps:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)
Where [T.sub.[tau]](t) is the integration time and [W.sub.a]* (t) is the preliminary estimate of the advection speed given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
Where K is the ratio of advection speed to mean speed. In the absence of a direct measurement of [W.sub.a], the value [kappa] = 1 was used for the present work. Combining equations 14 and 15 yields the following implicit equation for the integration time [T.sub.[tau]](t), which must be solved iteratively:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)
The advection velocity vector [[??].sub.a] is then obtained by averaging the wind velocity vectorially over the time span [T.sub.[tau]]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
The advection speed [W.sub.a] and direction [[phi].sub.a] are finally obtained by considering that:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)
With the advection velocity vector [[??].sub.a] (t) defined and the vehicle trajectory known, it is straightforward to calculate using Taylor's approximation (equation 11). the arrival time [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and position [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of the wind pattern at crossing point c on the vehicle trajectory (see Figure 4) And since the vehicle position [[??].sub.v] (t) is known from the GPS data, the vehicle's position at time [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] enables the separation [delta] between the vehicle's anemometer and point [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to be calculated:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)
The final position and time ([[??].sub.c], [t.sub.c]) for one crossing between the wind pattern measured at point [[??].sub.an] and the vehicle-mounted anemometer are obtained by an iterative process leading to the minimization of the separation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Finally, the calibration point is obtained by calculating the vectorial average, over a short time interval [DELTA]t, of both the vehicle velocity and the wind velocity, as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)
The free-stream velocity vector used to calibrate the vehicle-mounted anemometer is then obtained by applying equation 4:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)
Considering that for a vehicle speed of, say 100 km/h, the 14-metre long vehicle crosses point c from bumper to tail in approximately 500 ms, it was decided to set [DELTA]t to 500 ms.
The iterative computations were performed with an in-house program written in the Matlab[R] (16) computer language. The experimental data were post-processed after test completion, but they could be processed onboard and live, if a wireless data communication system enabled the transmission of the track-based measurements to the vehicle. This would allow anomalies to be detected swiftly. With an efficient computer code, these iterative calculations converge rapidly. To maximize the quality of the calibration, it is advisable to acquire as much data as possible covering the widest possible range of wind conditions, both during the vehicle warm-up phase and the ensuing coast-down or constant-speed runs.
To illustrate the relevance of the proposed method, let us consider a specific example of anemometric data acquired during the present project. Figure 14 presents a 30-second excerpt of anemometric measurements recorded by anemometer [AN.sub.1] For the terrestrial wind speed (black trace), an advection speed of [W.sub.a] [congruent to] = 4.4 m/s was calculated, at a mean advection angle of [[gamma].sub.a] [congruent to] = 150[degrees]. The unsteadiness of the turbulent wind, both in magnitude and direction, is manifest in this graph. Considering a distance (17) of L = 8 m from the anemometer to the vehicle trajectory, then the fetch is F = 16 m, so that a wave measured by the anemometer will require about 3.7 seconds to reach the vehicle trajectory. During that period, a vehicle traveling at 100 km/h has moved 103 metres, experiencing significantly different wind conditions. Another perspective is obtained by inspecting points A and B in Figure 14. Here, we assume that the terrestrial wind velocity used for calibration is sampled at the moment (time [t.sub.A]) when the vehicle's anemometer is nearest to station [AN.sub.1] (at distance L - see Figure 4) and that the measured wind speed is [W.sub.A] (point labeled A on the plot). The problem is that [W.sub.A] was actually measured about 3.7 seconds earlier than the vehicle's arrival. The best estimate of the wind velocity sensed by the vehicle-mounted anemometer is to use the value [W.sub.A] that was recorded about 3.7 second before the vehicle's arrival, corresponding to point B in the graph. In this specific example the bias would be [W.sub.A] -[W.sub.B] [congruent to] = 2.3 m/s.
Another view of this data set is shown in the polar plot of Figure 15a highlighting the combined variations in wind speed and direction. Each of the 60 points on the polar plot represents a 500 ms average of the wind angle [??].5 and speed [??].5, consistent with the calculation procedure exposed above. This polar plot emphasizes the variability of the wind velocity within the 30-second period. In Figure 15b, each point indicates the range of values of [??] 5 and W.5 within contiguous 5-second data segments, a period comparable to the advection time reported above. One observes variations on the order of [DELTA]W [approximately equal to] 1.5 m/s and [DELTA][gamma] [approximately equal to] 30[degrees] or more during these segments. Such variability illustrates the importance of determining the closest time when a detected wind pattern crosses the vehicle path. The fundamental question is to determine the effect of such differences on the values of the free-stream speed [U.sub.[infinity]] and yaw angle [[PSI].sub.[infinity]].
To answer this question, the sensitivities of equations 5 and 6 to variations in W and [gamma] were derived using partial derivatives. The details of the derivation are provided in the Appendix. The absolute error on [U.sub.[infinity]] resulting from independent, uncorrected errors on W and [gamma] was approximated by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)
with the relative error in free-stream speed defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)
The contour plots of Figure 16 delineate the relative error on [U.sub.[infinity]] and the absolute error on [PSI].sub.[infinity] resulting from biases [DELTA]W and [DELTA][gamma] from the 'true' values of wind speed and direction. To exemplify the variations observed and presented in Figure 15, the bull's eye symbol represents combined biases of [DELTA]W=l m/s and [DELTA][gamma]=15[degrees], well within the variations highlighted in Figure 15. The plots indicate that these deviations induce errors of about 8% on [U.sub.[infinity]] and 4.5[degrees] on [[PSI].sub.[infinity]] . Errors of this magnitude are significant and are conducive to a 'cloud-like' set of calibration points with a low level of correlation. It is postulated that taking into account the physical phenomenon of advection using Taylor's hypothesis reduces the bias of each calibration point, even for relatively short distances L between an anemometer and the vehicle trajectory.
Figure 16 shows error levels corresponding to the specific conditions of the previous example. The variation in error sensitivity with wind angle y is noteworthy. This behaviour is depicted in the two graphs of Figure 17. Similar graphs would be obtained with other parameters, albeit with different amplitudes. In the upper graph, the relative error on [U.sub.[infinity]] due to error [[member of].sub.w] on wind speed reaches maxima of about 7% error on [U.sub.[infinity]] per m/s of error on W at [gamma] = 0[degrees] and 180[degrees], indicating that the high-sensitivity zone for [U.sub.[infinity]]-errors due to errors on W is at shallow wind angles in the vicinity of [[PSI].sub.[infinity]] = 0. This is to be expected, when examining equation 37 of the appendix and assigning a small yaw angle by setting | cos [gamma]| [right arrow] 1. This implies that for obtaining a reliable estimate of [C.sub.Do], the accuracy in determining the terrestrial wind speed W is paramount. It is noteworthy that the sensitivity [[member of].sub.w] vanishes in the vicinity of 100[degrees]. Inspecting equation 34 of the Appendix, this happens at the angle [gamma]* = [cos.sup.-1] (-[sigma]) which in this case corresponds to about 104[degrees], as shown. The trend for the sensitivity to errors in [gamma] ([[member of].sub.[gamma]]) is reversed, with a maximum sensitivity at [gamma] = [gamma]* reaching about -5% per 10[degrees] of error on [gamma] whereas this sensitivity vanishes at both extremes, indicating a non-sensitivity of [U.sub.[infinity]] to [gamma]-errors at the extremes. In Figure 17b, the trend in the curves is interchanged between [gamma] and W. In this case, the errors on [[PSI].sub.[infinity]] due to error on [gamma], with a maximum at [gamma] = 0[degrees] of approximately 0.45[degrees] per degree of error on [gamma] is relatively forgiving. On the other hand, errors on W affect the yaw angle at a rate of approximately 5[degrees] per m/s at wind angle [gamma] =90[degrees].
The observed sensitivities are schematized in general form in Table 1. highlighting the main features for shallow wind angles in the vicinity of [gamma] = 0[degrees], 180[degrees] and for winds near-normal to the track, [gamma] [approximately equal to] 90[degrees]. The black circles point to a high sensitivity to a parameter whereas white circles indicate insensitivity. Between these extremes however and irrespective of the wind angle, combined errors in W and [gamma] will propagate into errors on free-stream velocity [[??].sub.[infinity]], confirming the importance of a reliable wind prediction technique.
During the experimental campaign, eight coast-down and eight constant-speed runs were acquired for each of the two test vehicles. Since two anemometers were installed on the windward side of the track, these tests provided 32 data points per vehicle, to calibrate the boom-mounted anemometer. A major difference between the example provided above, is that the anemometers were installed much further from the track, namely with distances L of 37.4 m and 29.4 m for anemometers [AN.sub.1]se and [AN.sub.2] respectively. These positions are far from ideal from the perspective of wind predictions whereby the fetch F should be minimized to reduce the stream-wise signature degradation of the advected wind patterns. The purpose of these anemometers for the EPA was solely to determine whether the mean wind speed was below the admissible limit of 16 km/h for testing. Notwithstanding, this anemometric data was used to test the proposed method, recognizing that these conditions are a challenging test of the technique. A summary of typical conditions that were measured during the tests is provided in Table 2. The characteristic length scales of the wind were of the order of 50 metres and beyond and the corresponding averaging times [T.sub.T] to calculate the mean advection speed were of the order of 20 seconds.
A more detailed view of the wind predictions afforded by applying Taylor's hypothesis to the readings of anemometer [AN.sub.1] is presented in the three plots of Figure 18. It displays the 32 predictions made for one of the test vehicles during constant-speed and coast-down runs. The upper plot, Figure 18a shows the predicted advection speeds, fetch and length scale. As expected, the fetch, which exceeds 40 metres, is substantial. The advection times, Taylor averaging times and the turbulence intensity are shown in the middle graph. Finally, Figure 18c highlights in red the difference between the vehicle arrival time at crossing point c and the arrival of the advected wind pattern measured some 20 seconds earlier by anemometer [AN.sub.1] The differences [[DELTA]t.sub.c] are all lower than the sampling time interval of 100 ms, confirming the convergence of the solutions. Although these results are encouraging, it was impossible to verify how close to reality the velocities predicted at crossing times [t.sub.c] were. Such a validation would require a sophisticated set-up consisting of an array of anemometers, comparable to the arrangements utilized in the studies discussed earlier. The only verification that was achievable here was to inspect the quality of the calibration of the vehicle-mounted anemometer readings to free-stream conditions.
CALIBRATION OF THE VEHICLE-MOUNTED ANEMOMETER
The choice of a proper calibration function to represent the response of an anemometer located forward of a traveling vehicle must rest on some knowledge of aerodynamics theory. By virtue of kinematic similarity and the underlying principle of dimensional analysis, the steady flow field forward of a vehicle exposed to a uniform approach flow characterized by the free-stream speed [U.sub.[infinity]] must satisfy the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)
Where [??] is a spatial coordinate, L is the characteristic dimension of the vehicle (e.g. its width) and [??] is the velocity vector measured at point [??]. Equation 25 indicates that anywhere within the flow field of interest, the normalized velocity vector [??]/[[??].sub.[infinity]] is independent of the value of the free-stream velocity [U.sub.[infinity]]. Indeed, for the purposes of the present application, it is argued that the effect of Reynolds number [Re.sub.[infinity]] on the flow field is confined to a narrow zone surrounding the vehicle fore-body, whose [Re.sub.[infinity]]-dependent thickness is negligible relative to the distance where the anemometer senses wind velocity. This implies that the yaw angle [[PSI].sub.b] sensed by the boom-mounted anemometer must be a sole function of the free-stream yaw angle, independent of [U.sub.[infinity]]. Further, for a symmetrical vehicle (18), the yaw angle [[PSI].sub.b] must be an odd function of the free-stream yaw angle, that is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)
This also means than when [[PSI].sub.[infinity]] = 0, the anemometer yaw angle is also given by [[PSI].sub.b] = 0. Note that [[PSI].sub.b] is a corrected value of the as-measured yaw angle [[PSI].sub.b.sup.(m)] from which the angle offset [[DELTA][PSI].sub.b] was removed to make [[PSI].sub.b] = 0 when the free-stream yaw angle [[PSI].sub.[infinity]] =0:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)
Although the form of function [[PSI].sub.[infinity]] ([[PSI].sub.b]) it is not known a priori, inspection of the data revealed that a function of proportionality modelled the data properly. Thus, the function used to calibrate the yaw angle was defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)
Where [C.sub.[PSI]] is the single parameter to be determined by regression. It can be shown with similar arguments that the wind speed [U.sub.b] sensed by the boom-mounted anemometer must be an even function of the yaw angle [[PSI].sub.[infinity]], that is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)
The analysis also reveals that [U.sub.[infinity]] depends upon both the yaw angle and wind speed measured by the anemometer. This can be explained as follows. Consistent with equation 25. for a fixed free-stream speed [U.sub.[infinity]], changing the free-stream yaw angle alters the flow field and consequently, both the value of [U.sub.b] and [[PSI].sub.b] must change. Considering the requirement that [U.sub.b] is an even function of [[PSI].sub.[infinity]] (and therefore of [[PSI].sub.b]), implying that both [U.sub.[infinity]] and [U.sub.b] must reach maxima or minima at [[PSI].sub.[infinity]] = 0, the following ansatz was used:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)
Where [C.sub.uo] and [C.sub.u] are parameters to be determined from a regression analysis. The [sin.sup.2] term was chosen to account for the expected non-linear variation of [U.sub.b]/[U.sub.[infinity]] with [[PSI].sub.b] while keeping the function even. The values of the calibration constants derived from the data obtained by applying Taylor's hypothesis are listed in Table 3. An example of a straight proportionality fit of the data for one of the vehicles is presented in Figure 19. They indicate they the apparent wind speed sensed by the vehicle-mounted anemometer is about 9% lower than the sought free-stream value and the measured yaw angle is close to twice as large as [[PSI].sub.[infinity]] . This trend is consistent with the results of Walston et al.  and confirms the critical importance of correcting these readings to free-stream conditions. The calibration functions defined in equations 28 and 30 and are plotted in Figure 20 for both vehicles tested, emphasizing the disparity between the calibration curves. For vehicle 1, both the speed and yaw angle deviate more substantially from the free-stream values than for vehicle 2, from which it can be inferred that the flow fields forward of these two vehicle configurations are distinct. The differences observed confirm that a distinct anemometer calibration is required for each vehicle configuration tested.
The results obtained indicate that despite the less-than-optimal position of the track-side anemometers causing advection times [T.sub.a] beyond 20 seconds and fetches F reaching up to 50 metres between the anemometer measurement station and the encounter point (c) with the vehicle, the application of Taylor's hypothesis enabled the calibration of the vehicle-mounted anemometer to free-stream conditions, notwithstanding the limited data set of 32 calibration points per vehicle.
Unlike aerodynamic evaluations conducted in wind tunnels or computational environments where the flow conditions are carefully controlled and repeatable, corresponding experiments on test tracks are plagued by wind conditions characterized by perpetual change, posing specific challenges with respect to determining a proper reference free-stream wind velocity from which the coefficient of aerodynamic drag ([C.sub.D]) depends. Despite their consistency, the wind tunnel and CFD computations only provide a repeatable simulation or approximation of the operating conditions that vehicles experience. On the contrary, the test track offers realistic conditions but their reliable quantification is a major challenge. The dominant hurdle is effectively the determination of the free-stream velocity that vehicles experience in the natural operating environment. It was shown that a 10% error in the speed [U.sub.[infinity]] leads to a 20% error on [C.sub.D]. This is the typical error level associated with wind measurements with a conventional boom-mounted anemometer sensing the perturbed flow field forward of a HDV.
SAE recommended practice J2263  prescribes the use of a vehicle-based anemometer located at vehicle mid-height to determine the wind conditions experienced by the test vehicle. The standard stipulates that the readings of one or several track-based anemometers shall be used to correct for the vehicle 'blockage effect' but the proposed correction technique is vague and rests on the assumption that "the wind during each pair of runs is constant". This statement does not take into account the physics of the turbulent wind, characterized by spatio-temporal fluctuations that can have large amplitudes. More recently, the EPA has proposed a new regulation  prescribing that the vehicle-mounted anemometer be installed one metre above the leading edge of a HDV trailer and that it shall be calibrated against track-based anemometric readings taken at vehicle mid-height.
The present work addressed specifically the issue of predicting the free-stream velocity from ground-based anemometric measurements, with the end objective of enhancing the reliability and accuracy of the prediction of free-stream conditions, in order to improve the accuracy of [C.sub.D] assessments from track tests of any vehicle type. A novel method to predict the free-stream velocity experienced by a traveling vehicle based on track-side anemometric measurements, was developed. The proposed method is based on Taylor's hypothesis which considers that the turbulent wind velocity fluctuations measured at one point are due to the "passage of an unchanging pattern of turbulent motion over that point". The technique was applied to experimental data acquired by the NRC Aerodynamics Laboratory on the APG straightaway.
The novel technique relies on the well established fact that a turbulent wind pattern sensed by an anemometer is advected downwind while maintaining the essence of its 'signature' for a sufficiently long time and distance, thereby enabling the prediction of a velocity at some point downwind. It was shown that the proposed technique has the potential to improve the accuracy of wind predictions compared to current methods, by calculating the meeting point and time between a wind pattern measured some time earlier upwind, and the vehicle-mounted anemometer, thereby enabling the correction of its biased readings to free-stream conditions. This experiment constitutes the first exercise whereby Taylor's hypothesis was applied to predict free-stream velocity, albeit with an experimental arrangement that was provided to NRC but could not be optimized for the task at hand. Future experiments should be designed with the following consideration in mind: The fetch F should be minimized by installing each anemometer at a strategic position, as close as possible to the vehicle trajectory while ensuring that the anemometer readings are not perturbed by the vehicle passage at the instant when the wind pattern is detected.
As part of this work, the effect of the vertical position of a vehicle-based anemometer on the ability to establish a reliable correspondence with track-based wind measurements made at the reference height (19) was examined analytically. The purpose of this examination was to determine the impact on the predicted free-stream conditions, of positioning the vehicle- and track-based anemometers at different heights. This analysis relies on the knowledge that the test vehicle is travelling through the atmospheric surface layer which is characterized by a logarithmic mean velocity profile known as 'the law of the wall'. The results indicate that installing the vehicle-based anemometer at a height different than the vehicle reference measurement height would lead to unreliable and unrepeatable correspondence between ground-based and vehicle-based anemometric data. This is because both the vertical distribution of apparent wind speed and yaw angle are modified by parameters such as: reference terrestrial wind speed ([W.sub.ref]) direction of travel and height difference between the boom-mounted and track-based anemometers. The only configuration where these discrepancies vanish is when both anemometers are measuring the wind at the same reference height. In light of the shape of the apparent wind profiles to which a vehicle is exposed, the author argues that setting the reference measurement height to vehicle mid-height is an arbitrary choice. Indeed, it can be shown that the height of the centroid of the dynamic pressure distribution, the source of the aerodynamic drag, varies with the wind conditions and that a measurement height different than h/2 might be more representative of typical operational conditions. This topic will be addressed in a future publication.
The following major practical recommendations should be applied to improve free-stream velocity predictions using the proposed method, in order to calibrate a vehicle-mounted anemometer:
1. Only the anemometric data from anemometers located on the windward side of the test track should be used for predictive purposes.
2. Each track-side anemometer should measure the wind at a height relative to the local ground equal to the reference height above the track of the vehicle-mounted anemometer (typically one half the vehicle height).
3. Each track-side anemometer should be installed as close as possible to the track, but outside of the range where the readings will be perturbed by the passage of the vehicle.
4. The vehicle-mounted anemometer should be measuring the apparent wind directly in front of the vehicle nose, at a point centred laterally and located at the reference height above the track (typically one half the vehicle height).
5. A distinct calibration of the vehicle-mounted anemometer to free-stream conditions is required for each vehicle or vehicle configuration, due to differences in the perturbed flow field forward of each specific vehicle configuration.
The novel method proposed herein has the potential to improve the reliability and accuracy of the prediction of free-stream velocity from ground-based anemometric measurements, with the concomitant improvement of the accuracy of drag coefficient assessments. This work constitutes the first application of the proposed concepts to track testing and was verified with a limited number of test points. Notwithstanding, the results obtained are encouraging but more comprehensive tests with an optimized experimental arrangement, in particular regarding anemometer placement, will allow the technique to be refined and further tested. One key element to consider is the advection velocity which, in the present work, was assumed to be equal to the mean wind velocity, the customary approximation in fluid mechanics. Ideally, this quantity should be measured directly with a dedicated instrument in order to further improve the reliability of the prediction of free-stream velocity.
[1.] U.S. Environmental Protection Agency and U.S. Department of Transportation. "Greenhouse Gas Emissions Standards and Fuel Efficiency Standards for Medium- and Heavy-Duty Engines and Vehicles." US Federal Register 76(179):57106-57513, 2011.
[2.] Environment Canada. "Heavy-duty Vehicle and Engine Greenhouse Gas Emission Regulations." Canada Gazette Part II 147(6):450-572, 2013.
[3.] SAE Surface Vehicle Recommended Practice, "Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques," SAE Standard J1263, Rev. Mar. 2010.
[4.] U.S. Environmental Protection Agency and U.S. Department of Transportation. "Greenhouse Gas Emissions Standards and Fuel Efficiency Standards for Medium- and Heavy-Duty Engines and Vehicles - Phase 2." US Federal Register 80(133):40137-40766, 2015.
[5.] SAE Surface Vehicle Recommended Practice, "Road Load Measurement Using Onboard Anemometry and Coastdown Techniques," SAE Standard J2263, Rev. Dec. 2008.
[6.] Walston, W., Buckley, F., and Marks, C, "Test Procedures for the Evaluation of Aerodynamic Drag on Full-Scale Vehicles in Windy Environments," SAE Technical Paper 760106, 1976, doi: 10.4271/760106
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(1) Now "Environment and Climate Change Canada"
(2) These reports published in 2011, 2012 and 2013 contain proprietary information and consequently may not be used as references in this paper. Notwithstanding, the author is making their non-confidential content available for the benefit of the readers
(3) Computational Fluid Dynamics
(4) Note that SAE Recommended practices Jl 263 and J2263 are not heavy-duty vehicle testing standards. In this paper, reference to these two reecommended practices is made because they are currently the only two SAE standards covering road load measurement with the coast-down technique
(5) 28-foot trailers were used because the same tractor-trailer combinations were previously tested in the NRC 9m x 9m Wind Tunnel which cannot accommodate larger vehicles in its test section
(6) The facility has since been upgraded with the addition of a separate second lane
(7) e.g. solid boundaries for closed test section wind tunnels and nozzle-collector configuration for open-jet wind tunnels
(8) This research conducted by the author was documented in an NRC laboratory technical report containing proprietary information
(9) Particle Image Velocimetry
(10) Throughout this paper, the word "velocity" (e.g. V ) refers to a vector whereas "speed" (e.g. V) refers to the magnitude (scalar) of the velocity.
(11) This was the case for the present experiments
(12) In a neutrally-stable ASL, shear-driven turbulent energy production overwhelms buoyancy-driven production caused by thermal gradients
(13) Here, the reference hight [z.sub.ref] is defined as the height above ground at which both the terrestrial wind and the apparent wind velocities should be measured. It is common practive (e.g. in SAE J2263 to set [z.sub.ref]=h/2, the vehicle mid-height
(14) The dynamic pressure distribution q(z) is the source of aerodynamic drag. The centroid of this distribution might be a more suitable reference
(15) A LzDAR-anemometer makes use of lasers to illuminate airborne particles. The doppler shift of the back-scattered light detected by the collection optics is a measure of the wind velocity entraining the particles.
(16) Matlab is a registered trademark of The Mathworks, Inc.
(17) * This distance is provided as an example to illustrate the appropriateness of the method for short fetches. In the present experiments, the anemometers were much farther from the track.
(18) Here, we are assuming the presence of asymmetric mirrors does not affect the symmetry of the flow field sensed by the boom-mounted anemometer located 2.4 m forward of the vehicle nose.
(19) Here, the reference height [z.sub.ref] is defined as the height above the local ground or track at which both the terrestrial wind and the apparent wind velocities should be measured. It is common practice (e.g. in SAE standard J2263) to set [z.sub.ref]=h/2, the vehicle mid-height
National Research Council Canada
Dr. Bernard Tanguay, Senior Researcher
National Research Council Canada Aerodynamics Laboratory Ottawa, Canada
This work was made possible thanks to the financial and logistic support of Environment Canada* and the contribution of the U.S. Environmental Protection Agency. The author is thankful to his NRC colleagues Jason Leuschen and Yves Cronier who were wholly engaged with the author in the preparation and execution of these experiments. As well, the support staff of the NRC 9 m x 9 m Wind Tunnel was instrumental in the success of this test campaign. The courteous and helpful interactions with the staff at Ford's Arizona Proving Ground contributed towards an enjoyable and productive experience. Finally, the kind support of Mr. Lin Farmer, Vice-President of Automotive Testing and Development Services, inc. and his staff, is gratefully acknowledged.
AMBIENT CONDITIONS AND AIR PROPERTIES
v - kinematic viscosity of air
[rho] - density of air
FLOW CONDITIONS AND AERODYNAMICS
[U.sub.[infinity]] - free-stream air speed
[q.sub.[infinity]] - free-stream dynamic pressure, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[Re.sub.[infinity]] - free-stream Reynolds number based on vehicle width w
[Re.sub.min]. - minimum value of [Re.sub.[infinity]] for [C.sub.D] invariance
V - vehicle speed relative to ground
W - terrestrial wind speed measured at vehicle mid-height
w'- standard deviation of the terrestrial wind speed W
[[PSI].sub.[infinity]] - free-stream yaw angle
q - dynamic pressure (generic)
D - aerodynamic drag
[C.sub.D] - coefficient of aerodynamic drag
[C.sub.D] - coefficient of aerodynamic drag at zero yaw angle
[C.sub.Dwa] - wind-averaged coefficient of aerodynamic drag
[sigma] - ratio between wind speed W and vehicle speed V
[gamma] - angle between the terrestrial wind velocity vector [??] and the vehicle velocity vector [??]. -180[degrees] < [gamma] [less than or equal to] 180[degrees].
[[gamma].sub.a] - angle between the advection wind velocity vector [[??].sub.a] and the vehicle velocity vector [??] -180[degrees] < [[gamma].sub.a] [??] 180[degrees].
[[PSI].sub.b.sup.(m)] - wind angle, as-measured by boom-mounted anemometer
[[DELTA][PSI].sub.b] - angular offset making [[PSI].sub.b] = 0 when [[PSI].sub.[infinity]] = 0
[[PSI].sub.b] - corrected wind angle boom-mounted anemometer (offset [[DELTA][PSI].sub.b] removed)
[U.sub.b] - wind speed sensed by the boom-mounted anemometer
[phi] - wind angle sensed by a track-side anemometer
[tau] - shear stress at the solid boundary
[U.sub.[tau]] - skin friction velocity, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
B - constant term of the logarithmic profile ("law of the wall")
Z - vertical coordinate (z =0 at track level)
[Z.sub.0] - characteristic roughness height
D - Distance between the anemometer and the vehicle at the instant the "wind front" is detected
[D.sub.adm] - Admissible value of D to avoid perturbation of anemometer readings.
F- The fetch, i.e. the distance between the anemometer and the point at which the detected "-wind front" crosses the vehicle trajectory
[L.sub.T] - characteristic length scale of the turbulent wind measured at reference height
[T.sub.T] - Taylor integration time corresponding to length scale [L.sub.T] advected from the anemometer to point c
[W.sub.a] - advection speed of the wind
[T.sub.a] - the time required for the "wind pattern " to be advected from the anemometer to point c
[KAPPA] - ratio between advection speed and mean wind speed [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[delta] - distance between the vehicle anemometer and crossing point c when the advected "wind pattern " reaches that point.
VEHICLE AND TEST TRACK CHARACTERISTICS
A - vehicle frontal area (reference area)
l - vehicle overall length
w - vehicle width
h - vehicle overall height
G - longitudinal distance separating the vehicle-mounted GPS receiver from the boom-mounted anemometer
[d.sub.f]- distance from vehicle nose to the boundary where free-stream conditions exist
X- X-coordinate of vehicle position relative to track origin 'O'. X positive towards EAST
Y - Y-coordinate of vehicle position relative to track origin 'O'. Y positive towards NORTH
L - lateral distance (normal to trajectory) between a ground-based anemometer and the vehicle travel direction
[theta] - angle between geographical north and the vehicle trajectory
[??] - unit vector identifying the X-direction
[??] - unit vector identifying the Y-direction
[??] - unit vector identifying the direction of the mean terrestrial wind velocity
[??] - unit vector identifying the vehicle travel direction
[??] - position vector [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[[??].sub.v] - vehicle position
[[??].sub.c] - position of crossing point c
[[??].sub.AN] - position of track-based anemometer
[??] - terrestrial wind velocity vector (general)
[??] - vehicle velocity
[[??].sub.[infinity]]- free-stream velocity
SUBSCRIPTS AND SUPERSCRIPTS
[infinity] - refers to free-stream conditions i.e. 'far enough' forward of the vehicle
c - point of intersection between a line identifying the mean wind direction measured by a weather station and the vehicle trajectory.
ref - refers to the reference height for anemometric measurements, i.e. vehicle mid-height
an - refers to the height at which the vehicle-mounted anemometer measures the local apparent wind.
wa - wind-averaged
T - refers to Taylor integration time or length scale
a - refers to the advection of the "wind front" at speed [W.sub.a]
v - refers to the vehicle under test
adtn - admissible value, e.g. [F.sub.adm] is the maximum allowable fetch
min - designates the minimum value of a variable
max - designates the maximum value of a variable
b - refers to boom-mounted anemometer
AN - refers to track-side anemometer
1 - refers to track-side anemometer [AN.sub.1]
2 - refers to track-side anemometer [AN.sub.2]
x' - the apostrophe (') refers to the standard deviation of x
cal - refers to a quantity used as calibration reference for the vehicle-mounted anemometer
t - time
z - vertical coordinate
f (x) - a function of variable x
[??] - time-average of x(t)
C - cross-sectional area of wind tunnel test section
[DELTA]x - absolute error level of variable x - OR an increment or differential in x (contextual)
[member of](x) - relative error level of variable x
S (f) - normalized power spectral density function
ASL - Atmospheric Surface Layer
AL - Aerodynamics Laboratory
NRC - National Research Council of Canada
EC - Environment Canada
EPA - Environmental Protection Agency
APG - Ford Motor Company's Arizona Proving Ground
ATDS - Automotive Testing and Development Services, inc.
CFD - Computational Fluid Dynamics
CHARACTERISTICS OF THE INSTRUMENTATION USED
Both anemometric stations [AN.sub.1] and [AN.sub.2] were equipped with R.M. Young R model 5103V propeller-vane anemometers, each mounted atop a sturdy tripod. The height of the rotational axis of the anemometer propellers was measured to be approximately 2.07 m above local ground, that is, close to one half of the overall vehicle height. A third such anemometer was mounted at the end of the vehicle-mounted boom, with its rotational axis also positioned at vehicle mid-height point. The key performance characteristics of the R.M. Young anemometer are provided in Table 4.
Table 4. Characteristics of R.M. Young[R] 5103V anemometer. Characteristic Values Wind speed range 0 to 360 km/h accuracy the greater of [+ or -]1 km/h or [+ or -]1% of reading detection threshold 3.6 km/h Wind angle range 0[degrees] to 360[degrees] accuracy [+ or -]3[degrees] detection threshold 4 km/h
In order to ensure the synchronization of data originating from three distant locations, GPS data loggers were utilised for both weather stations and for the onboard measurements. The acquisition devices were VBOX[R] data loggers, model VBSS10, made by the British firm Racelogic[R]. Besides receiving standard GPS information (time, position, speed, heading, ...) every 100 millisecond, each data logger sampled analogue signals from the anemometers and weather instruments at the same rate and streamed the data to an SD-card. The pertinent characteristics of these data loggers are presented in Table 5. The designation 95% CEP indicates that there is a 95% probability that the GPS position is within a circle of 1.8 m diameter centered on the actual position.
Table 5. Accuracy and resolution of Racelogic[R] GPS dataloggers quantity units accuracy resolution Time s 0.01 0.01 Velocity km/h 0.10 0.01 X, Y position m < 1.8 (**) 0.01 Heading degrees 0.1 0.01 (**) 95 % CEP (Circle of Error Probable)
DERIVATION OF THE ERROR ESTIMATE ON THE PREDICTED FREE-STREAM VELOCITY VECTOR
To evaluate the error levels in the free-stream speed [U.sub.[infinity]] and yaw angle ^ derived from ground-based anemometric measurements of the terrestrial wind speed W and direction y, we first recall the definitions of the former two variables given earlier by equations 5 to 7:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (31)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (32)
The absolute error on [U.sub.[infinity]] resulting from independent, uncorrected errors on W and [gamma] is approximated by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (33)
The partial derivatives are obtained by differentiating equation 31:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (34)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (35)
Substituting equations 34 and 35 into equation 33 yields:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (36)
And the relative error e on [U.sub.[infinity]] is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (37)
It is important to note that in all equations involving [[DELTA].sub.[gamma]], this quantity MUST be expressed in radians ! Applying the same treatment to equation 32 to determine the error level in the prediction of [[PSI].sub.[infinity]], we obtain:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (38)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (39)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (40)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (41)
Table 2. Examples of variables measured by [AN.sub.1] and [AN.sub.2] Variable [AN.sub.1] [AN.sub.2] [??] [m/s] 2.99 2.38 w' [m/s] 0.85 0.88 [L.sub.T] [m] 72.6 49.2 [T.sub.t] [s] 24.3 20.7 [??][[degrees]] 287.2 283.0 [??]'[[degrees]] 23.3 27.1 Table 3. Calibration parameters for both vehicles Parameter: [[DELTA][[PSI].sub.b]] [[degrees]] C.sub.[PSI] Vehicle 1 363.30 0.548 Vehicle 2 4.78 0.690 Parameter: [C.sub.uo][-] [C.sub.u][-] Vehicle 1 0.905 -1.62 Vehicle 2 0.935 -1.86
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|Publication:||SAE International Journal of Commercial Vehicles|
|Date:||Oct 1, 2016|
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