# A Practical Approach to Modeling and Performance Analysis of a Turboshaft Engine Using Matlab
## 4 Conclusions  
This study presents a model of a turboshaft engine with a free power turbine, developed based on key geometric parameters determined through design-point calculations and performance characteristics of the compressor and turbine, enabling performance analysis across a range of engine operating conditions. The model was implemented in the Matlab 2024b environment. A significant feature of this model is its use of the compressor map, along with the turbine minimum cross-sectional area and turbine pressure ratio calculated at the design point, to establish the operating line for turbine-compressor interaction. This line, defined in corrected parameters, is used in further engine calculations and recalculated based on engine settings and varying environmental conditions. The addition of a free power turbine map allows the model to simulate this component's operation across a wide range of performance parameters.  
For model validation, available data for the PZL-3W engine were used. However, this did not allow for a complete assessment of the model accuracy due to the limited availability of engine manufacturer data and discrepancies between the data presented in various publications. Additionally, the characteristics of the compressor and turbine maps did not originate directly from the modeled engine (as they are not available) but were instead selected from the literature. The results that could be verified indicate an estimation error of up to 4%. However, it is hard to distinguish whether this error stems from the proposed calculation methodology or, for instance, from discrepancies in the incorporated component maps.  
Calculations were performed under varying engine settings, as well as changes in ambient parameters. The results show that the model accurately reflects the engine behavior under the tested operating conditions. It demonstrated the model's extensive applicability for simulating both the effects of the environment and the engine operating conditions,  
Figure 14: Engine performance calculation against ambient temperature to maintain constant output shaft power. (**a**) Output shaft power (blue line) and compressor rotational speed (red line) as a function of ambient temperature, (**b**) SFC as a function of ambient temperature.  
which in this case depend on the HP shaft operating state as well as the load on the free power turbine. This confirms the model's suitability for analyzing and simulating free power turbine engine performance under diverse operating conditions.  
Conceptualization, [PERSON] and P.J.; methodology, [PERSON] and P.J.; software, [PERSON]; validation, [PERSON] and P.J.; formal analysis, [PERSON] and P.J.; investigation, [PERSON] and P.J.; resources, [PERSON]; data curation, R.J.; writing--original draft preparation, [PERSON] and P.J.; writing--review and editing, [PERSON]; visualization, R.J.; supervision, P.J.; project administration, R.J.; funding acquisition, R.J. All authors have read and agreed to the published version of the manuscript.  
The research leading to these results received funding from the commissioned task entitled \"VIA CARPATIA Universities of Technology Network named after the President of the Republic of Poland [PERSON]\", under a special purpose grant from the Minister of Science, contract no. MEiN/2022/DPI/2578 action entitled \"In the neighborhood--inter university research internship and study visits\".  
Not applicable.  
Data Availability Statement: Data available on request.  
The authors declare no conflicts of interest.