Speed-dependent directivity patterns of road-traffic vehicles Open Access

Acoustic immisions in urban environments are dominated by road traffic noise, such as emissions from passenger cars, motorcycles, buses, and trucks. Vehicle exterior noise consists of speed-dependent contributions from tire/road, powertrain, and aeroacoustic noise, each of those contributing to overall sound emission by characteristic directivity patterns. However, directivity pattern extraction of moving sound sources is a complex measurement problem, as discussed in the following. Therefore, noise mapping is based on simple analytical models, neglecting speed effects or further segment-specific emission characteristics of road-traffic sound sources. From a metrological point of view, simultaneous sound measurement in all radiation directions of a moving sound source is challenging and only possible by conventional methods if inherent measurement errors are acceptable:

1. The speed-dependent sound radiation of the tire/road noise and load-dependent engine sound components can be computed from separate measurements using a roller-type chassis dynamometer. The obtained results neglect advective wave propagation effects due to aerodynamic flow around the vehicle chassis.

2. A separate measurement of the stationary passenger car chassis in a wind tunnel is used to record the speed-dependent aeroacoustic radiation pattern. A disadvantage of this method arises from the positioning of the microphone capsules outside the flow so that the received signals are distorted by measuring through the moving medium. In order to avoid distortions in the capsule microphone placement is limited to positions outside the flow in wind tunnel measurements. Furthermore, the shape of measured directivity itself is distorted due to advection (Helfer, 2013).

Striving to eliminate these metrological limitations, this work presents a method to compute speed-dependent directivity patterns of road-traffic vehicles from stationary hemi-circular microphone array signals. Subsequently, the recorded time signals are post-processed by applying time-variant wave backpropagation in order to reconstruct the emission signals on a virtual spherical surface around the moving sound sources.

The following considerations are important in order to develop the measurement setup and its conditions in such a way that the measurement procedure is representative. The most recent knowledge on vehicle exterior noise and sound generation mechanisms is extensively compiled in Chapters 86 (tire/road noise), 87 (aeroacoustic noise), and 120 (engine noise and prediction) of Crocker's Handbook of Noise and Vibration Control (Crocker, 2007). Focusing on the tire/road noise component as shown in Table I, Ullrich (1984) derived proportional relationships for dominant physical tire parameters with regard to their individual influences on resulting sound power P.

From the data, it can be approximated that tire/road noise varies in a level range of about 40 dB depending on a rolling speed between 10 and 150 km/h. Tire/road noise depends on the combination of both surface textures. Theoretically, a variation potential in the sound pressure level of 7 dB can be associated with the vehicle and 9 dB associated with the pavement (Li, 2018). Therefore, depending on the specific tire/road combination the dynamic range can vary by ≈15 dB (Beckenbauer, 2013), thus increasing the overall dynamic range of tire/road noise to ≈55 dB. Focusing on a tire/road noise emission relationship with vehicle speed v, a proportional increase in about 30 to 35 times log(v) can be experimentally observed, although a very wide range in the multiplier has been reported in the literature. In addition to overall levels, the effects of case-specific tire/road interactions on directivity patterns are not discussed in the literature.

As stated in the final report of the Harmonoise (2004) project (Har), information on directivity patterns and sound power of road-traffic sound sources is rare in the literature. Therefore, it includes generic formulae for horizontal and vertical directivities. Assuming omnidirectionality in the lower frequency range $f≤1250$ Hz, for higher frequencies $f≥1600$ the horizontal directivity corresponds to a symmetric cardioid pattern that is constricted perpendicular to the direction of travel level and shows a level reduction of 5 dB compared to the maximum radiation in the direction of travel. Similar to the vertical directivity, the minimum of a symmetric cardioid pattern is vertically above the sound source. Depending on frequency and point source (PS) height, its level of attenuation varies between 2 and 8 dB (Jonasson, 2007). For a critical evaluation, the following section compares the computational directivity pattern results to the analytical patterns of category 1 (cars) from the Harmonoise catalogue as a reference. The Harmonoise model, which is used in common noise mapping procedures, describes cars by two vertically distributed source points with source heights 0.01 and 0.3 m, respectively. Each of those is attributed to a specific pattern in eight octave bands between 50 Hz and 10 kHz. Both, horizontal and vertical directivity patterns are plotted in Fig. 1. Important to note that the directivity patterns do not depend on the vehicle speed except from an overall level scaling factor.

Emphasized as balloon plots in Fig. 2, the formulae for the lower source describe four different spatial shapes in four frequency ranges:

1. Omnidirectionality is assumed for very low frequencies up to 80 Hz;

2. In the range of low mid-frequencies between 100 and 1250 Hz, the omnidirectional characteristic is increasingly attenuated above the vehicle for higher frequencies in order to simulate the shadowing of the tire/road noise by the vehicle body;

3. In the high mid-frequency range above 1600 Hz, an azimuthal component is added, which represents the amplified sound radiation through the horn effect;

4. In the range of high frequencies above 3150 Hz, only the azimuthal component remains, which describes a dipole that is reduced by 5 dB orthogonally to the direction of travel compared to the level in the direction of travel. The vertical level deflection is reduced (compared to lower frequency ranges), leading to an increase of about 4 dB.

However, as a data resource, the document refers to a conference paper abstract lacking any data, so these models are not independently reproducible. The most elaborated approach for modeling road-traffic vehicle directivities was published by Tsukui (1998) by approximating the directivities of three types of road vehicles at a fixed speed of 40 km/h in three octave bands around 500, 1000, and 2000 Hz in the horizontal and vertical planes. For this specific vehicle speed, similar directivities for all three vehicles in shapes of the vertically compressed hemisphere are reported with the A-weighted sound pressure levels in the upward direction being 9–10 dB(A) lower than lateral ones. Moreover, an asymmetrical drift of the horizontal directivity according to an elevation angle of $θ≈9°$ towards the backward direction can be observed for higher frequencies. At the current state of research, no speed-dependent directivities have been reported. However, details on the measured vehicles as well as a description of the precise post-processing steps are not well documented in any of the reviewed models. Furthermore, the equalization of the receiver characteristics has been neglected too.

Apart from directivities, two approaches for the determination of the sound power of a single vehicle have been described in the literature. On the one hand, Tachibana established a measurement procedure in a reverberant tunnel in order to practically apply the diffuse field method (Tachibana , 1981). On the other hand, assuming a line source approximation, the sound power of vehicle flow can be estimated as a function of average speed and traffic flow rate (Rey Gozalo , 2020).

In summary, the analytical road-traffic emission models developed in the Harmonoise project are referenced in this work by means of their wide integration with noise prediction simulation tools. However, this model is limited in terms of lacking drivetrain variability and neglecting the influence of driving speed on resulting directivity patterns.

This work focuses on speed-dependent directivity patterns of multiple vehicle classes with conventional internal combustion engine (ICE), hybrid, and electric drivetrains. Necessary data are obtained from an inverse measurement method, described in Sec. III. The presented method accounts for including the complex wave propagation effects into a far-field directivity pattern that neither can be simulated—even with elaborated numerical methods—nor directly obtained from wind tunnel or roller-type chassis dynamometer measurements. The following effects are part of the resulting directivity patterns: Advection due to the object's speed and the laminar flow around the moving object, refraction due to turbulent flow at body cavities, and diffraction due to object geometry. The generated data can be used for calibrated auralizations according to the procedure described in (Dreier and Vorländer, 2024). Beyond the scope of previously published research, this work presents the following novelty aspects:

• A technique to extract free-field radiation characteristics of moving sound sources.

• A supplementary directivity pattern database using the OpenDAFF (Ope) (OpenDAFF, 2024) and Spatially Oriented Format for Acoustics (SOFA) (Majdak , 2022) format conventions.¹

• Sound power computations based on single vehicle measurements (in opposite to established diffuse field or traffic flow-based line source measurement approaches).

This paper is structured as follows: Sec. II introduces the methodology for in situ directivity pattern measurements using a pass-through microphone array. The subsequent signal postprocessing chain using time-variant wave backpropagation and according to uncertainty considerations is presented in Sec. III. In Sec. IV, the considered vehicle classes as well as the actual measurement procedure are defined. The results by means of speed-dependent directivity patterns and according sound power levels are presented and compared to results from the analytical Harmonoise model in Sec. V. Finally, the results are discussed in Sec. VI.

The general experimental approach is briefly presented in the following with further details in Sec. III. In order to obtain a directivity pattern with quasi-freefield properties, the original source signals are recorded using a pass-through array. The recorded signals are post-processed for extraction of several outdoor sound propagation effects (see Fig. 4). As shown in Fig. 3, the wave backpropagation can be interpreted as a projection of signals recorded at a two-dimensional microphone array onto a three-dimensional reconstruction grid around a vehicle's center point. The term time-variant wave backpropagation emphasizes the inversion problem to be not only depending on distance but on emission and immision angles too. Technically, as illustrated in Fig. 3, the inversion process accounts for equalizing the angle-dependent measurement microphone response (cf. Sec. II B), the Doppler shift, a reflection from the ground, the geometrical distance law-dependent loss (Sec. III A) and the air absorption between the measurement point and the virtual directivity hull of the moving object. Finally, the directivity patterns are exported to the widely used data formats OpenDAFF (Ope) and SOFA (Majdak , 2022) in third-octave band magnitude spectra that are provided as an additional database.

The microphone array is conceptualized for in situ measurements during a pass-through procedure. The microphone array consists of 30 microphones that are placed on a hemi-circular arc with a radius of r = 3 m (Fig. 5).

An NTI Audio M2230 (NTi Audio, Schaan, Liechtenstein) measurement microphone (Class 1 according to IEC 61672; see IEC, 2012) was installed flat on the ground, while omnidirectional Sennheiser KE4 microphones (Sennheiser, Wedemark, Germany) installed on the remaining 29 positions on the hemi-circular arc. All microphones were connected to an RME Octamic XTC audio interface (RME Audio, Haimhausen, Germany), set to $fs=$ 96 kHz sampling rate and $NADC=$ 24 bit depth. The microphones were equipped with windshields to avoid aeroacoustic distortion.

Each array microphone including its mounting using a threaded rod was individually equalized for the elevation range $0°<Θ<90°$ with a resolution of $10°$⁠. The frequency responses were measured in the hemi-anechoic chamber of the Institute for Hearing Technology and Acoustics (IHTA, RWTH Aachen University) using the substitution method according to IEC 61094-8:2012 (IEC, 2012) by placing the receivers in the center of a hemi-circular measurement arc (Fig. 6, left). Both, individual directivity patterns in the frontal hemi-circle with a resolution of $δθ=10°$ as well as transducer sensitivities in V/Pa were measured with sweep excitation and subsequent post-processing for reflection removal. The signal-to-noise ratio (SNR) of the measurement chain, i.e., including preamplifiers, cables, and analog-to-digital converters, were $≈85$ dB for all channels.

The ideal sensor for the purpose of time-variant backpropagation would have spatially omnidirectional and spectrally flat properties. The microphone capsules are packaged in a custom-made cylinder (Fig. 6, right), which contains the electronics and XLR cable connector. The combination of the packaging with the threaded rod mounting causes a local diffraction of the sound field and therefore influences the overall frequency response. Therefore, the directivities of all microphones used in the measurement array were individually measured by measuring the transfer functions on an equiangular grid with a 2.5° × 2.5° resolution.

For example, the measurement result (Fig. 7) shows the transfer functions of a single Sennheiser KE4 array microphone including threaded rod mounting over different incidence angles θ in the frequency range 2 kHz $<f<$ 20 kHz.

In this plot, a perfectly omnidirectional receiver would appear as a spectrally flat transfer function at 0 dB. However, the result shows for off-axis positions the directivity pattern is approximately omnidirectional only in the frequency range f < 2 kHz. For higher frequencies f > 2 kHz, the result indicates higher sensitivity and directionality. A maximum gain of 4.5 dB can be observed at 20 kHz for incident waves approaching from the off-axis direction. The same trend applies to all microphones in the measurement setup and is individually equalized in the measured data. Finally, striving for an angle-dependent equalization of the recorded data, the resulting equalization filters are obtained by spectral inversion.

In the case of cars, the distribution of partial sources can be approximated by a finite line (FL) of uncorrelated broadband sources. This implies the sound pressure p to decay dependent on lateral distance $dlat$⁠, i.e., horizontally perpendicular to the driving direction, in a range between $p∝1/dlat2$ and $p∝1/dlat$ (see Fig. 9).

By using the backpropagation method, an inherent error $ΔBP$ occurs in the $Adiv$ compensation term in Eq. (1). This error is due to compensating spreading loss by an analytical decay, whereas the real-world sound source is distributed and neither a PS nor a FL source. However, the choice of a spreading loss type affects the overall sound pressure level reconstruction. To estimate the resulting error regarding the directivity pattern and sound power, both decays are compared to a simulated baseline emission of a simplified car. It consists of four incoherent PSs representing the tire/road noise emission on an acoustically hard surface. A wheelbase of 2.8 m with a width of 2.6 m is assumed. First, the directivity pattern of the simplified model is numerically calculated and referenced to a baseline of 0 dB in Fig. 10. Second, pass-through signals at a virtual receiver array are simulated using the auralization software VA. Third, the simulated data are backpropagated to a single coordinate in the center of the four PSs by using the same algorithm described in Sec. III. The backpropagation is performed twice, on the one hand assuming spreading loss of a PS and on the other hand assuming spreading loss of a FL source. Finally, both resulting backpropagation levels are referenced to the baseline level. The horizontal sound pressure level error depends on the azimuth angle and can be estimated to a remaining error range between $−1.3<ΔBP,FL<+1.8$ dB and $+3.0<ΔBP,PS<+5.0$ dB, respectively. By means of sound power, FL compensation overestimates the baseline by about 1.4 dB_SWL, whereas PS compensation is 5.7 dB_SWL higher.

The smaller error of $ΔBP,FL$ motivates the selection of the FL source compensation for $Adiv$ in case of cars. Nevertheless, without further knowledge of the exact locations of all contributing sound sources of a car, the remaining error cannot be further reduced. Compared to this, all other uncertainties related to microphone calibration and humidity and temperature measurements are negligible.

The range of characteristics of noise emissions is as broad as the multitude of variables in the vehicle configuration. For this reason, the following chapter compares noise emissions using reference cases of the most relevant road vehicle classes and also examines the influence of driving speed. Specifically, this experiment investigates six passenger cars from four different classes and a motorcycle (Fig. 13), according to the ISO 3833:1977 (ISO, 1977) classification scheme. Their individual specification regarding tire and fuel type, engine, and power is compiled in Table II.

The in situ measurements took place at the Institute for Automotive Engineering (IKA) test track, Aachen, Germany.² The test track consists of a straight asphalt road with a length of 450 m and a turning circle with a diameter of 95 m, in which the vehicles accelerate. The test track is surrounded on one side by agricultural fields and warehouses on the other side, from which no noticeable background noise distorts the acoustic measurements.

Clearly visible as light gray-shaded area in Fig. 11 (right), the area confines a certified asphalt layer with a length of 50 m, which is used for acoustic measurements of vehicle noise. The asphalt layer complies with the ISO 10844:2021-12 standard (ISO 10844:2021; ISO, 2021). The standard describes requirements for asphalt roads for the purpose of noise emission measurements of road vehicles and their tires. According to the standard, the asphalt of the road section is subject to a maximum sound absorption of 8% in each one-third octave band between 315 Hz and 1600 Hz, a maximum grain size of 8 mm and an average tread depth of 0.5 mm with 0.2 mm tolerance. As indicated by the orange line in Fig. 11 (right), the pass-through microphone array is placed in the center of the ISO-compliant asphalt area (see Fig. 12).

After accelerating the vehicle in the turning circle and turning onto the straight track, a constant vehicle speed was controlled by the driver with the assistance of a GPS-based feedback or the vehicle's integrated speed control. In the case of vehicles with ICE, the engagement of the speed-typical gear was controlled by automatic transmission. Aiming to center the vehicle through a measurement array, a non-transparent adhesive strip was placed on the windshield in such a way that the driver's subjective perception corresponded with the center strip of the test track. For each vehicle, measurements with three repetitions were taken at discrete vehicle speeds between 10 and 120 km/h with 10 km/h steps. See Fig. 13. The atmospheric conditions (temperature, relative humidity, and atmospheric pressure) were measured individually for each vehicle by using a digital thermo-hygrometer, type TFA Klima Bee 30.5036 (TFA Dostmann, Wertheim, Germany). By passing through the array, the sound emissions of the sources, such as cars or motorcycles, are recorded from multiple angles. The vehicle speed was externally validated by the placement of two light barriers at both ends of a trajectory with length L = 50 m. The passing trajectory for the backpropagation is ±25 m to both sides of the array, thus limiting the elevation angle to a minimum of $θmin=6.84°$⁠.

The results of the time-variant backpropagation are then reconstructed in the form of one-third octave band spectra at discrete grid points (Fig. 8) for each vehicle and speed and averaged for three measurement repetitions (as introduced in Sec. IV C). In the following, notable results are discussed by using two-dimensional (2D) projections and three-dimensional (3D) directivity patterns. The complete data are available in the accompanying database using two directivity exchange formats, OpenDAFF (Ope) and SOFA (Majdak , 2022) by means of both, normalized magnitude spectra (for use in auralizations) and third-octave sound pressure levels (for noise mapping applications). We start, however, with the results for the radiated sound power.

Based on the actual backpropagated measurement data, the speed-dependent sound power level L_W of each vehicle is computed using the procedure described in ISO 3745:2012 (ISO, 2012) by using the angular segments from the backpropagated data. According to the standard, the sound power is derived by summing the area-weighted sound intensities from each grid point. The latter in turn are obtained as the ratio of the squared effective sound pressures and the acoustic free-field impedance. The result is shown in Fig. 14 in comparison to sound power levels from the Harmonoise model (Jonasson, 2007).

The values calculated in this work agree with the models in terms of magnitude. Individual dips in the curves can be explained by the gear engaged: In the range of dominating powertrain noise contributions (at low speeds), a decrease in sound level can be observed for increasing driving speeds when the engine's contribution to the sound diminishes from high levels (due to high engine speed in low gear) to lower levels at higher driving speeds (due to lower engine speed in a higher gear). As expected, the noise emissions of electrified vehicles (VW Golf GTE and BMW i4) are lower than those with a combustion powertrain, with reductions up to 10 dB_SWL at low driving speeds. The obtained sound power level difference between motorcycles and passenger cars aligns with the predictions made by Harmonoise. For an average passenger car (category I) compared to a motorcycle (category IV.a), propulsion noise emissions of motorcycles are approximately 5–20 dB_SWL higher.

As mentioned in Sec. III, the backpropagated time signals are discretized by slicing and subsequent mapping to the sampling grid points. In the following, exemplary analyses by means of 3D balloon plots as well as 2D cross-sectional plots are presented. Shown using a normalized logarithmic scale (i.e., in decibels, referenced to the maximum emission value), each balloon plot shows the spatial emission of a single third-octave band (cf. Fig. 15), cross-sectional plot shows multiple third-octave bands in a single plane (cf. Fig. 16). The complete set of directivity patterns is compiled in additional material.

Without exception, the main sound radiation for all measured passenger cars can be observed along the vehicle axis. This finding supports the assumptions of the Harmonoise model in Fig. 2. However, changes in speed have a complex influence on the directivity patterns. In general, the individual emissions of all four wheels are visible in the directivity patterns by local main lobes in the horizontal patterns, such as in Fig. 16.

Vehicles with hybrid powertrains, such as the VW Golf GTE in this study, are advantageous for an isolated analysis of partial sound contributions to the overall emission and therefore exemplarily presented in the following. The aeroacoustic noise significantly contributes to the overall emission for higher speeds v > 80 km/h. The VW Golf GTE was measured in two different powertrain modi, with ICE, and in electric mode (with activated Acoustic Vehicle Alerting System, AVAS). For higher speeds v > 30 km/h, the AVAS component is deactivated in electric drivetrain mode, with remaining road/tire and aeroacoustical noise sources. Accordingly, the difference between the results of the two drivetrain modi can be attributed to the engine. Each modus is represented in the following by balloon plots in four different third-octave bands. The yellow arrow indicates the driving direction, the white arrow shows vertically upwards.

Clearly visible at high speeds in electric powertrain mode, the median and sagittal cross-sectional plots [Fig. 16(b)] indicate the aeroacoustic noise contribution—occurring with high sound levels, being dominant by > 10 dB in the lowest octave band—which is emitted obliquely upwards to the rear.

Focusing on inter-object differences between cars at a constant driving speed, Fig. 17 compares multiple third-octave band directivity patterns in the horizontal, median, and sagittal plane. The higher the frequency band, the smoother the directivity pattern. Moreover, no clear dominancy of a certain vehicle throughout all frequency bands can be observed. Rather than levels, the broadness of the main radiation lobes correlates to a specific car. Furthermore, the median plane patterns show symmetry to a large extent, whereas the sagittal plane patterns are more directional.

In contrast, Fig. 18 focuses on intra-object differences by comparing the patterns for a single car at multiple driving speeds. A comparison therefore refers to the speed dependency. Considering that the plot covers a wide level range of 70 dB, it is clear that the directivity patterns are speed-dependent.

In contrast to those of cars, the directivity pattern of the motorcycle is rather directed to the sides and depends less on speed. Particularly at low speeds, the directivity patterns between 10 and 50 km/h are very similar, which could be explained due to the highly dominant sound emission by the engine. The spectrally narrow-band and highly directed sound emission by the exhaust (which is physically mounted upwards with an elevation angle of $θex=50°$⁠) is clearly visible in the 3D balloon plot in Fig. 19.

Figure 20 shows the comparison of constant driving conditions with variation of the engaged gear. In the case of a motorcycle, the resulting patterns for gears 2 and 3 at a constant speed of 70 km/h differ significantly in low-frequency bands. Furthermore, the sound power level emitted with gear 2 engaged is about 2 dB_SWL higher than with gear 3 engaged.

Some general trends can be observed from the motorcycle directivity patterns. In the high-frequency range f > 4 kHz, slightly more energy is radiated to the driver's left side cf. horizontal and median plane plots in Fig. 21, due to chain noise. Furthermore, the gear selection has a major impact on the directivity patterns especially in low octave bands. The level decay in the sagittal directivity pattern plot reveals a steeper amplitude increase in the high frequencies at increasing speeds, and therefore at higher speeds, compared to low frequencies.

An open-access database containing directives and sound power of seven street vehicles at ten speeds was created. The results document the great variety of directivity patterns between different vehicle class segments and speeds. First and foremost, from the obtained data it can be concluded that the directivity patterns of road-traffic vehicles depend on driving speed. This sheds new light on the numerical pattern descriptions of commonly used sound source models, such as the Harmonoise model, which merely scale the overall level according to vehicle speed. Most influential on a resulting pattern is the driving condition of the vehicle, in particular the engine speed (as a result of the gear engaged). In general, no clear dominancy of a certain vehicle throughout all frequency bands can be observed—meaning that the mixture of contributing engine, tire/road, and aerodynamic sound sources is highly dependent on the particular vehicle. Rather than levels, broadness of the main radiation lobes correlates to a specific car. Furthermore, the median plane patterns show symmetry to a large extent, whereas the sagittal plane patterns are more directional. It is clear from the obtained results that future road-traffic models should distinguish between the powertrain type, such as electric cars or those with ICE. Not only differences in the directivity patterns themselves but also the sound power level reductions up to 10 dB_SWL should be taken into account. It is known from the literature that the level effect due to applied torque during acceleration causes variations up to 8 dB (depending on the tire design and on the applied torque), as well as increases by about 2 to 3 dB for partial versus full throttle (Crocker, 2007). Therefore, future work should evaluate if a variation in directivity patterns due to acceleration and load can be observed too. Furthermore, it should be evaluated if the tire-pavement combination is influencing the directivity patterns. Generally, powertrain noise does not show a constant relationship to vehicle speed, rather being a function of the gear selection. During the experiment presented, only the driver sat in the vehicle, therefore future work should evaluate if the emitted sound power levels significantly change in cases of more passengers and/or full trunk. For further discovering perceptual aspects, future work should evaluate the audibility of speed-dependent directivity patterns using auralizations for listening tests. The results can be applied to urban noise auralizations, in which urban planning measures are evaluated by using audio examples.

This research was supported by the HEAD-Genuit Foundation under project Grant No. P-22/02-W. The authors would like to thank Simon Kamps and Lars Heinrichs for their support during the measurements and simulations.

The authors have no conflicts to disclose.

The data that support the findings of this study are openly available in the Database for speed-dependent road-traffic vehicle directivity patterns at http://doi.org/10.5281/zenodo.14142914.