## 2 Model Development
### Emission Module  
The emission module describes the emitted sounds of an individual passenger car. Its structure is depicted in Figure 2. As described above, the acoustical emission of the passenger car is assumed to consist of the two contributions: tire noise and propulsion noise. Their corresponding emission signals are denoted as \(s_{\text{tire}}\) and \(s_{\text{prop}}\), respectively.  
Tire noise strongly depends on tire type [22; 24], road surface type [18; 21; 22; 25] and vehicle speed [18; 21; 22; 23]. Further, the horn effect mainly determines the horizontal directivity of tire noise [21; 23; 26]. To model these effects, the tire noise contribution is assumed to depend on the road and tire type, as well as on vehicle speed \(v\) and the emission angle \(\varphi\). Section 2.2.1 shows how the signals \(s_{\text{tire}}\) are calculated based on these input parameters.  
Figure 2: Simulation flowchart of the auralization of accelerating passenger cars. The input variables marked by a * are time dependent.  
In current noise prediction models, propulsion noise is commonly calculated as a function of vehicle speed, acceleration and road inclination [18; 21; 27]. This is due to the fact that these models are developed and used in cases for which the engaged gear is not known. The gear, however, strongly influences the sound of propulsion [23]. For a given speed, acceleration and road inclination, by changing the gear, the engine speed, as well as the engine load change. From an engine's viewpoint, it is these two parameters that are sufficient to fully describe the engine condition. Section 2.2.2 explains how in the auralization model, engine speed \(n\) and engine load \(\Gamma\) are calculated by simulating the driving dynamics of the vehicle. These simulations require information on the vehicle and the driving style, the road inclination \(\alpha\) and the vehicle speed \(v(t)\) as a function of time \(t\). Further, propulsion noise features a directivity [23], which is also taken into account in the auralization model. Section 2.2.3 shows how, based on \(n\), \(\Gamma\) and the emission angle \(\varphi\), the signal \(s_{\text{prop}}\) is calculated.  
The audible emission signals \(s_{\text{tire}}\) and \(s_{\text{prop}}\) are generated artificially by two digital sound synthesizers. The synthesizers are based on a combination of additive and subtractive synthesis. In additive synthesis, the signal is constructed by the sum of sinusoids, each having a time-varying amplitude and phase [28; 29; 30]. On the other hand, subtractive synthesis uses filters to shape a more complex source signal, e.g., a sawtooth wave or white noise [28; 29]. The combination of both techniques is known as spectral modeling synthesis [30; 31; 32]. However, in contrast to the applications presented in [31] and [32], in the presented model, the sounds are not synthesized using the short-time Fourier transform (STFT), but directly in the time domain. The structure of the synthesizer is similar to the one recently published for wind turbine sounds [6].  
The signal of propulsion noise, \(s_{\text{prop}}\), is fully attributed to the upper point source S2. However, the sound power of the tire noise contribution is attributed to the point sources by 80%/20% [21]. This translates to a ratio of 2:1 of their respective sound pressure signals. The conditions of incoherent signals and energy conservation yield a normalization factor of \(1/\sqrt{5}\). Thus, the sound pressure source signals are:  
\[s_{2}(t) = \frac{1}{\sqrt{5}}\cdot s_{\text{tire,2}}(t)+s_{\text{prop}}(t) \tag{1}\] \[s_{1}(t) = \frac{2}{\sqrt{5}}\cdot s_{\text{tire,1}}(t) \tag{2}\]  
at reference distance \(r_{0}=1\) m for source positions S2 and S1, respectively. Indices 2 and 1 indicate that different, uncorrelated signals for the sound of tires are generated for the two source positions.