## 3 The New Approach
### Relations and Model Definition  
The standardised vehicle models and freely available vehicle databases very often represent an idealized vehicle, which in its dimensions covers approximately 85% of the fleet of the same or similar type of vehicle or vehicles defined by national standards [21]. Common practice for passability assessments is to use the garbage truck model. However, due to significant differences in the dimensions and characteristics of the vehicle swept path during cornering, this leads to a situation where the vehicles that play the most crucial role in saving lives are omitted. Therefore, during the project, a simplified model of an FRS ladder truck was created and subsequently used to the assessment. Figure 6 shows the resulting simplified model defined in the AutoCad Vehicle Tracking software. For the purposes of model creation, it was necessary to determine not only the characteristic dimensions of the vehicle but also the actual turning radius, wheel angle, etc. The characteristic dimensions were determined with photogrammetric and geodetic measurements. Figure 7 shows the captured images of the ladder truck, reconstructed spatial model, and dimensions of the selected parts of the truck (length, height, ladder dimensions, etc.). Figure 5: Photo of a fire engine ladder truck [5,6]. Figure 8 shows the differences between the garbage truck model and FRS ladder truck. In order to obtain a real swept path of the reference FRS vehicle, a research experiment was conducted with an FRS vehicle (Figure 9). In this experiment, the full turn of the FRS vehicle at maximum wheel travel was monitored by drone. The speed of the vehicle was determined based on the FRS experience at approx. 5-10 km/h. The footage was subsequently rectified to enable direct identification of wheels trajectory and the vehicle contours. Thus, it was possible to determine the actual turning radius and wheel angle. Figure 8: Technical parameters of the fire engine ladder truck and the garbage truck. Figure 6: Final digital model of a fire engine ladder truck created in AutoCad Vehicle Tracking. Figure 7: Photogrammetric measurements of the characteristic dimensions of the FRS ladder truck in Photomodeler Scanner. [PERSON]'s steering geometry was subsequently used for verification of the model validity, specifically by calculating the steering angle. The principle is based on a fixed axle where only the wheels rotate and is shown in Figure 10[22]. \[\alpha_{i}=tan^{-1}\left(\frac{L}{R-\frac{T}{2}}\right) \tag{1}\]  
\[\alpha_{0}=tan^{-1}\left(\frac{L}{R+\frac{T}{2}}\right) \tag{2}\]  
By substituting the observed turning radius into the equation, a value for the wheel angle was obtained and compared with the experimentally measured value for the wheel angle. This verified that the determined vehicle turning radius corresponded to the real vehicle. The resulting simplified model showed that vehicles that are very similar to firefighting vehicles in terms of their parameters (length, width, and height) actually have significantly different trajectories. Figure 11 shows a comparison of the swept paths of a municipal waste vehicle (blue) and a fire engine ladder truck (red). This difference in their manoeuvrability is closely related to the different turning radius or steering angle of the wheels. The different behaviour can be seen especially in the initial phase of the turning manoeuvre, due to the greater body overhang of the fire engine ladder truck compared to a conventional truck. Figure 10: [PERSON]’s steering geometry [22]. Figure 9: An example of a calibration experiment of the swept path for vehicle model design. By using digital models of firefighting equipment and a digital model of the area, it was possible to verify the passage through the selected area in the current layout; this enabled to define the critical locations where potential bottlenecks may occur and which require subsequent structural modifications. These basic outputs became the basis for subsequent comprehensive research outputs.