# Modeling and Analysis of Noise Emission Using Data from Flight Simulators
## 2 Methods of Noise Modeling
In accordance with Doc 29, a linear interpolation is used between tabulated power settings, whereas a logarithmic interpolation is used between tabulated distances. After defining the area of observers with one of them in each node of the created grid, preliminary results of a noise map can be generated. However, because the values acquired from NPD data sets are only baseline, uncorrected noise levels, the model needs to account for a variety of effects that are specific to the nature of sound propagated from the aircraft. All of the corrections and adjustments are based on numerous simplifications by means of semi-empirical equations introduced in Doc 29, which were created through many years of preceding research in this field. The adjustments include, but are not limited to, the effect of engine installation in relation to the fuselage (i.e., are the engines mounted under the wingsor near the empennage) or the bearing of the observer relative to the temporary position of the aircraft, which allows us to mimic the lobed pattern of jet exhaust during the take-off run. The calculations are carried out individually for each of the thousands of observers in the defined grid, for a given position of the aircraft, thus producing a value of a desired noise metric (\(L_{Amax}\) or \(SEL\)) for a single segment of the aircraft's trajectory: \(L_{Amax}^{seq}\) or \(SEL^{seq}\). This is performed by simply adding up all the values of the previously described adjustments to the baseline NPD values:  
\[L_{Amax}^{seq}=L_{Amax}^{NPD}+AI+EI-LA+DIR \tag{1}\]  
\[SEL^{seq}=L_{SEL}^{NPD}+AI+EI-LA+DIR+DUR+NF \tag{2}\]  
The calculations are repeated for each of hundreds of segments yielding a multi-million-celled matrix of noise values corresponding to each observer and each segment of  
Figure 2: Simplified overview of single-event noise calculation. the aircraft's trajectory. Through appropriate calculations, the final values of \(L_{Amax}\) and \(SEL\) for each observer can be obtained:  
\[L_{Amax}=\max\left(L_{Amax}^{seg}\right) \tag{3}\]  
\[SEL=10\cdot\log\left(\sum 10^{0.1\cdot SEG^{out}}\right) \tag{4}\]  
Validation of the model with the default data from Doc 29 Vol. 3 App. A, which is shown in Figure 3, shows encouraging results as the compliance is on a satisfactory level. This and all of the following noise maps present a top-down view of the aircraft's trajectory, with the axis system attached to the threshold of the departure runway with the X-axis aligned with the runway track. No measurements or experiments in real-life conditions were performed for the needs of validation of the created model as it was created in accordance with the guidelines of ECAC.CEAC Doc 29, which are themselves based on the experimental and semi-empirical basis. A quantitative determination of substances generated as a result of aviation fuel combustion during flight operations is based on empirically determined emission factors. These factors are developed for each type of engine and depend on the operating phase (e.g., a different emission factor during climb compared to taxiing). Basic data regarding the analyzed aircraft in this project are available in the ICAO Engine Exhaust Emissions Databank in the form of the unit of mass of the emitted substance per unit of mass of burned jet fuel, e.g., grams of \(CO_{2}\) per kilograms of Jet A-1 [36]. This document, however, does not provide the emission index for \(CO_{2}\), and hence, the standard value of 9.75 kg \(CO_{2}\) per US gallon was used. It is assumed that the density of Jet A-1 is constant and is equal to 3.04 kg per one US gallon.