The ascending trajectories performance and control to minimize the heat load for the transatmospheric aero-space planes

The paper discusses the performance and control of ascending trajectories for Transatmospheric Vehicles (YAW) using air-breathing propulsion. The work looks to minimize the heat load per unit area near the stagnation point. The vehicle is modelled as a point variable mass with drag polar and variable thrust. The earth is assumed spherical with exponential atmosphere. The research is structured in two parts. The first part is an analytical and seeks the two controls (aerodynamic and thrust) which are necessary to transfer this TAV from one specified state(e.g. h₁ ≈ 20 km, 5, Q₁ ≈ 5 kj/cm²… etc.) to a second specific state (e.g. h₂ ≈ 63 km, M₂ ≈ 25, Q₂ ≈ 300 kj/cm²… etc.) while satisfying given equality constraints such as constant dynamic pressure, and constant rale of climb. Certain algebraic relations among the state variables u, ŋ, γ, and Q and a feedback for aerodynamic and thrust controls have been derived a closed form solutions. The heat load can be Q 350kj/cm² for rc > 35 m/sec, q ≤ 0.2 atm., 0≤ τ_ant 0 τ 1. This analytical approach was helpful in the numerical approach in the second part. The second part was carried out by using extensive numerical optimization algorithms. The control laws which minimize the total heat load were found as combinations of some state variables in a parametric way which give the heat load Q ≈ 300 kj/cm² for the two controls;τ_nt = a₁, + a₂u² + a₃ T), and λ_n1 = b₁, + b₂ u² + b₃ ŋ. A numerical example was worked out for i llustration, and in general all the constraints were satisfied.