## 1 Introduction
Other authors [16; 17] have focused on evaluating thrust measurement uncertainty without assessing its effect on total impulse determination. Another article [10] evaluates the uncertainties associated with thrust values obtained during these tests for two different configurations of measurement chains, using the theories of combined and expanded uncertainties. The results indicated that using signal amplifiers increased the measurement uncertainty in the analyzed chain. Similarly, [PERSON] et al. [17] detailed the uncertainty analysis for calculating the specific impulse of rocket motors, carried out at the NASA Lewis Research Center. The measured and calculated parameters were listed, including their nominal values, precision errors, degrees of freedom, and uncertainties expressed as percentages. The analysis revealed that the test facility could measure specific impulse with an uncertainty of 1.30%. [PERSON] and [PERSON] [18] presented the possibilities of utilizing the integrated LabVIEW environment to evaluate the uncertainty of measurement results in direct measurements. They also discussed the possibilities of presenting and visualizing the uncertainty of measurement results in a convenient and user-friendly form, and this methodology could be applied to acquisition programs. The studies mentioned in this part of the manuscript, such as those by [PERSON] et al. [2], [PERSON] et al. [3], and [PERSON] et al. [4], highlight significant advancements in propulsion technologies, ranging from electric solid propellants to innovative fuel grain geometries and machine learning applications. However, these works focus on developing new technologies and materials without addressing the uncertainty analysis in measuring critical parameters, such as thrust and total impulse. Similarly, studies like those by [PERSON] et al. [12] and [PERSON] et al. [13] address thrust measurement but do not consider the propagation of uncertainty along the measurement chain or the impact of signal oscillations on the accuracy of the results. These limitations in previous studies underscore the need for a more comprehensive and robust approach, as proposed in this study. The main objective of this work is to fill this gap by proposing a robust methodology for determining the uncertainty in the estimation of total impulse, considering the propagation of uncertainty in thrust measurement through numerical integration using the trapezoidal method. Additionally, this study aims to evaluate the impact of signal oscillations on the accuracy of the results, offering a more complete and reliable approach for uncertainty analysis in static tests of rocket motors. This methodology improves metrological reliability and provides a foundation for future research and practical applications in the defense industry. Thus, the present study contributed to this field by focusing on determining the uncertainty in total impulse estimation, considering the propagation of thrust measurement uncertainty in numerical integration using the trapezoidal method, and the impact of signal oscillation on the accuracy of the results. Thrust measurement uncertainty is one of the main sources of error in determining total impulse. To improve metrological reliability, adopting a robust approach to uncertainty propagation was essential. This approach allowed for a more precise and comprehensive assessment of total uncertainty, considering the uncertainties associated with each thrust measurement point over time. Previous studies addressing thrust measurement and total impulse calculation partially dealt with the problem of uncertainty propagation but did not perform a complete analysis of the expanded uncertainty involved in this process. These works did not explore in detail the oscillations of the acquired digital signal or the impact of post-processing on accuracy and metrological reliability. In this context, the present article fills an important gap in the literature, offering a more robust and comprehensive approach.