Propulsion and launching analysis of variable-mass rockets by analytical methods

Abstract

In this study, applications of some analytical methods on nonlinear equation of the launching of a rocket with variable mass are investigated. Differential transformation method (DTM), homotopy perturbation method (HPM) and least square method (LSM) were applied and their results are compared with numerical solution. An excellent agreement with analytical methods and numerical ones is observed in the results and this reveals that analytical methods are effective and convenient. Also a parametric study is performed here which includes the effect of exhaust velocity (C e ), burn rate (BR) of fuel and diameter of cylindrical rocket (d) on the motion of a sample rocket, and contours for showing the sensitivity of these parameters are plotted. The main results indicate that the rocket velocity and altitude are increased with increasing the C e and BR and decreased with increasing the rocket diameter and drag coefficient.

Analytic approach to determine optimal conditions for maximizing altitude of sounding rocket: Flight in standard atmosphere

“…The air density of a standard atmosphere is not a constant but changes with altitude, which means that the drag parameter K also changes with altitude. The aerodynamic drag coefficient is usually increases sharply near the Mach number of unity and decreases gradually with the Mach number after then [18,26,27]. Some preliminary numerical experiments showed that this model caused serious numerical oscillations especially when the velocity parameter is near to speed of sound, which seems due to the abrupt change of the drag coefficient around the Mach number of unity.…”

“…The basic model to simulate the effect of the Mach number is the one used by Ganji [18]. However the basic model showed some unstable behaviors near the Mach number of one.…”

“…An approximate solution can be obtained with neglecting drag force but it contains serious errors especially near ground. There are also approximate solutions with the Taylor series expansion, the perturbation method or the least square method [18], but they are complex and do not give information about the optimal conditions. Analytic solutions, on the contrary to numerical ones, are exact without numerical errors, give insights to understand the behavior of the system, show critical parameters, and lead to ways to determine the optimal conditions.…”

A novel instantaneous frequency estimation method for operational time-varying systems using short-time multivariate variational mode decomposition

“…Many real-life structures show time-varying (TV) properties under working conditions, such as traffic-excited bridges with time-varying mass (Bao et al 2009), launch vehicles with varying fuel mass (Ganji et al 2013), and hypersonic vehicles with time-varying stiffness and damping due to aerodynamic heating (Wang 2017). Modal parameters (natural frequency, mode shape, and modal damping) are functions of these structures' physical properties (mass, damping, and stiffness).…”

Analisis Uji Peluncuran Roket Air Berbasis Carbon Fiber Menggunakan Sistem Telemetri

“…Rocket technology is an important application in aeronautical or space technology. In everyday use, rocket technology mostly uses chemical propellants or chemical-based combustion [1]. This requires very complicated operations, expensive technology, spends a lot of time preparing for launch and security aspects also need to be considered.…”