The takeoff-mass of a two-stage-to-orbit Rocket-Based Combined Cycle Engine-Rocket (RBCC-RKT) launch vehicle is a crucial factor in its comprehensive performance. This paper optimizes the takeoff-mass together with the trajectory by reformulating it to a nonlinear optimal control problem. The range of the second stage rocket mass is considered as a process constraint. When the scopes of initial and terminal states are specified, the problem can be solved by using the Gauss pseudo-spectral method (GPM). In order to reduce the convergent difficulty caused by using table data, the data in different stages are utilized by employing an integrated interpolation strategy through the optimization. Simulation results show that the mass can be effectively optimized to meet the inertia mass ratio constraint of the first-stage, and the separation of Mach number and altitude can be optimized at the same time.

This study defined the body weight/length relationship and an equation for body mass estimation using morphometric measurements on Amazonian manatees Trichechus inunguis (Mammalia: Sirenia). Total length (TL), maximum girth (MG) and body mass (M) were obtained from 91 captive Amazonian manatees (46 males and 45 females) of different ages, and TL and M were obtained from eight free-ranging Amazonian manatees (6 males and 2 females). The data were analysed by linear and multiple linear regressions. The maximum length and mass measured were 266.5 cm and 379.5 kg, respectively. The equation for body weight/length relationship was M = 0.00001070 * TL3.122 (r2 = 0.984) (Equation I) and no differences between sexes and between captive and free-ranging animals were found (P > 0.05). We calculated two more equations for mass estimation (Equation II: M = 0.00003284 * TL1.857 * MG1.106, r2 = 0.992; and Equation III: M = 1.506 + 0.00003477 * TL * MG2, r2 = 0.995), and the best equation (high correlation coefficient and low percentage of residues) was Equation III. Equation I provides the body condition of manatees, whereas Equation III is more accurate for estimating body mass. Both equations are important tools for management of captive and free-ranging Amazonian manatees.