## 3 Materials and Methods  
The analysis outlined in this paper was derived from empirical experiments carried out by the authors following the RDE procedure. Specifically, the utilized measurement results consisted of emissions of selected pollutants, engine fuel consumption and the parameters that influence the above quantities. The vehicle used was fitted with an on-board measuring system, including exhaust emission analyzers, the Semtech DS (Camarillo, CA, USA) and the TSI 3090 EEPSTM (Engine Exhaust Particle SizerTM) Spectrometer (Shoreview, MN, USA). The road tests involved a passenger car with a spark-ignition engine. This type of vehicle corresponds well to European preferences and also applies to Polish conditions, as almost half of all vehicles used in Poland have spark-ignition engines. The vehicle was equipped with an exhaust after-treatment system that meets the Euro 6 emission standard, featured an automatic transmission and had 235/55R19-size tires. The vehicle had a mileage of 30,000 km and was serviced according to the manufacturer's schedule. Detailed parameters of the vehicle and its drive system are given in Table 1.  
The vehicle fuel was standard gasoline with an ethanol content of up to 10%. Air conditioning was utilized throughout the tests, since the ambient temperature recorded at the start was 26 \({}^{\circ}\)C and increased to 28 \({}^{\circ}\)C by the end of the test. Exhaust emission measurements were performed in Poznari in normal road traffic conditions, during the working day, and started at 11:00 a.m. The test route (Figure 1) complied with the requirements for RDE procedures and was divided into three phases: urban, rural and motorway. The urban part constituted about 33% of the entire route, was 22 km long and lasted about 60 min. Approximately 30% of the route consisted of the rural part, which was 20 km long and lasted about 25 min. The motorway part covered about 37% of the route, was 24 km long and lasted about 15 min. The temperatures of vehicle fluids at the beginning of the test were equal to the ambient temperature (the vehicle was conditioned for 24 h prior to the test). The total mass of the test equipment was about 100 kg, including batteries. The parameters that determined exhaust emissions and fuel consumption included the engine operating states, defined as follows:  
* Engine control;
* Engine rotational speed;
* Engine load, which can be represented by engine torque (or effective power);
* Engine thermal state, described by a set of temperatures of engine components and engine consumables (coolant, lubricating oil, etc.). In dynamic conditions, the engine operating properties, including pollutant emissions and fuel consumption, depend on the engine operating states, while the latter are determined by the velocity of the tested vehicle. The parameters investigated in this paper were as follows:  
* Engine control--s(t);
* Engine rotational speed--n(t);
* Engine relative torque--T\({}_{r}\)(t);
* Effective power--P\({}_{r}\)(t);
* Emission intensity of pollutant X--E\({}_{X}\) (carbon monoxide--CO; carbon dioxide--CO; nitrogen oxides--NO\({}_{x}\); hydrocarbons--HC);
* Particle number intensity--E\({}_{PN}\);
* Fuel consumption mass intensity--FC. The relative engine torque was defined as follows:  
\[\mathrm{T}_{r}(\mathrm{n})=\frac{\mathrm{T}(\mathrm{n})}{\mathrm{T}_{\mathrm{ ext}}(\mathrm{n})}, \tag{1}\]  
where n is the engine rotational speed, T is the engine torque and T\({}_{\mathrm{ext}}\) is the engine torque corresponding to the maximum engine control setting (based on external characteristics). The relative effective power was defined as follows: