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In this work, a model for the analytical solution of the differential equation of motion of a model rocket that describes a vertical trajectory in an upward movement is described. The solutions for velocity, v(t), and altitude, y(t), are compared with a numerical solution using Euler's method. To test these models and compare the methods for obtaining v(t) and y(t), the experimental flight of the Epsilon-8 model rocket, with a solid propellant engine, from the Carl Sagan rocketry group of the Federal University of Paraná (UFPR). In the analytical solution, an approximate model is considered in which the total mass of the mini rocket is constant during the propellant burn time. Numerical and analytical predictions for v(t) and y(t) can be obtained, using physical parameters related to the mini rocket, the drag force and the experimental curves for the thrust, T(t). T(t) curves of four engines manufactured by the Carl Sagan group were used, similar to the one used in the experimental flight of the Epsilon-8. Although the analytical method is satisfactory, the numerical method returns values of speed and altitudes closer to the experimental flight of the Epsilon-8. [ABSTRACT FROM AUTHOR]

This work describes the differential equations of motion and the respective solutions for speed v(t) and altitude y(t) as a function of time, relative to a rocket that follows a vertical trajectory in an upward motion were described. Four models are considered: in the first, the drag force of the air is neglected; in the second it is considered a linear drag force with speed; in the third and fourth models it is considered that the drag force is proportional to the square of the speed. The third model is distinguished by considering the total mass of a rocket constant. In the fourth model, a complete solution is presented, considering that the mass decreases linearly with time. To test these models, the experimental flight of the Epsilon-8 model rocket from the UFPR Carl Sagan Rocket Group was used. Experimental parameters related to the thrust curve as a function of the Epsilon-8 time (static test) were used, in which from the model rocket mass variation rate it was possible to obtain the rate of exhaust of the gases expelled in the engine. The third and fourth models, since they are more realistic, were used to adjust the experimental curve for v(t) and y(t). The third model, although it has an approximate solution, proves to be reasonable in the prediction of the peak, with an error of 8.6%. The fourth model, being the most complete, predicts the peak with an error of only 1.5% precisely in the time of the experimental peak. [ABSTRACT FROM AUTHOR]