The atmospheric arc of a space trajectory has a strong path constraint due to the aerodynamic lateral loads on the structure. This forces the trajectory to follow a path with a zero angle of incidence (gravity turn trajectory). This chapter introduces analytical formulae for the gravity turn of the launcher. These formulas are useful to evaluate the variation of velocity loss due to gravity and to provide an estimate of the launcher performance. A simple generalisation of the well-known Tziolkowski formula for the rapid evaluation of launcher capability is introduced, which allows a more accurate estimate of the payload mass that a launcher can place in orbit. The analytical estimate is compared with the highly accurate numerical model of the ascent trajectory in the atmosphere, which is derived in detail. The different phases of the launcher trajectory are analysed: vertical ascent, pitch manoeuvre, pitch over, gravity turn. The general equations of motion of a launcher in the atmosphere are derived. The guidance parameters of the trajectory in the atmosphere are introduced and it is shown that the main parameter influencing the atmospheric arc is the duration of the pitch manoeuvre that the launcher has to perform after the vertical ascent.
Ascent Trajectories: Atmospheric Arc
Springer Aerospace Techn.
2024-12-27
43 pages
Article/Chapter (Book)
Electronic Resource
English
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