# Investigation of Vehicle Stability with Consideration of
## 3 Investigation of the Factors Affecting the Vehicle Stability  
### Road Description  
Records of the actual Lithuanian road microprofile were used in modeling the vehicle stability tasks. Records were generated by road surface measurements performed using the DYNATEST 5051 RSP (Dynast A/S, Ballerup, Denmark) profilometer mounted on the VW Transporter [18; 49]. Whereas road profile records are characterized by exception and span-specific properties, the possibilities for formalization of the road microprofile description were analyzed by identifying the typical features of road surfaces of different quality. During formalization of the road description, the discrete nature and large interval of the road microprofile records, was considered. For example, the information on the micro-irregularity height within a single established line is recorded every 0.147 m under the IRI calculation methodology and every 1 m when spatial road microprofile is recorded. Road microprofile records contain road surface data on the two longitudinal lines that correspond to the vehicle wheel rolling surface, and the longitudinal distance between the data is 0.147 m. Analysis of available records confirmed that essential differences can be assessed using generalized data of the road span microprofile for an even asphalt pavement, uneven asphalt pavement (in service), and gravel road surfaces. The microprofile records of the road spans were analyzed using classic methodology by calculating the dispersion of unevennesses \(\sigma_{q}^{2}\) and correlation function \(R_{q}\):  
\[\sigma_{q}^{2}=\lim_{L_{q}\rightarrow\infty}\frac{1}{L_{q}}\int_{0}^{L_{q}}q_{ 0}^{2}(x)dx,\ R_{q}(x_{s})=\frac{1}{L_{q}\sigma_{q}^{2}}\int_{0}^{L_{q}}q_{0} ^{2}(x)q_{0}^{2}(x-x_{s})dx \tag{11}\]  
where \(L_{q}\) is the span length; \(q_{0}\) is the microprofile height with the \(y\)-coordinate of the midline equal to zero interval \(x_{s}\). Road surface roughness data were used for an accurate assessment of the effect of the road surface and investigation of the equalization function of the tire. The data reflect the roughness of the road surface on a single line every 2.5 mm. Data from three different road surfaces were used for the investigation: relatively even (I), medium (II) and very rough (III). These microprofile records are fairly accurate, and the effect of roughness on the road surface was considered in addition. The road surface roughness span data was distributed in the microprofile according to the principle of a random number generator. These measures enabled the authors to fairly accurately reflect the key characteristics of the road surface. The data on the microprofile and road surface roughness characteristics of the investigated road spans are presented in Table 1. The characteristic wavelengths were revised by harmonic analysis involving identification of the lengths of maximum amplitude waves \(R_{i}=\sqrt{a_{i}^{2}+b_{i}^{2}}\) for Equation (12):  
\[q(x)=\frac{x_{0}}{2}+\sum_{i=1}^{\infty}a_{i}\cos(i\omega x)+\sum_{i=1}^{ \infty}b_{i}\cos(i\omega x) \tag{12}\]The waviness of the road surface and its amplitudes were determined following harmonic analysis of typical road microprofile fragments. The maximum amplitude waves were longer than 12 m in the cases analyzed. Only a few longer waves were found. The number of shorter waves was higher, but the amplitude of the shorter waves was very small at 0.3 to 1 mm depending on the microprofile evenness. It should be emphasized that short wavelength unevenness amplitudes were clearly dependent on the road surface type. For modeling using a flat model, the effect of the road surface was assessed by analyzing the microprofile points on a single longitudinal line. The correlation functions of the road surface roughness are presented in Figure 4. It was noticed that waviness with waves shorter than those of the microprofile was characteristic of rough road surfaces.