Mathematical Modeling of Aerodynamic Space -to - Surface Flight with Trajectory for Avoid Intercepting Process for Safety and Security Issues

Dissertation has been made for research project of mathematical modeling of aerospace system “Space-to-Surface” for avoid intercepting process by flight objects “Surface-to-Air”. The dissertation includes Introduction, the 3 Chapters, and Conclusion. The research has been completed and created mathematical models which used for research and statistical analysis. In mathematical modeling has been including a few models: Model of atmosphere, Model of speed of sound, Model of flight head in space, Model of flight in atmosphere, Models of navigation and guidance, Model and statistical analysis of approximation of aerodynamic characteristics. Modeling has been created for a Space-to-Surface system defined for an optimal trajectory for targeting in terminal phase. The modeling includes models for simulation atmosphere, aerodynamic flight and navigation by an infrared system. The modeling simulation includes statistical analysis of the modeling results. Analysis and Introduction The analysis of the current scientific results of mathematical modeling in aerospace field and analysis of requirements for software support in aerospace industry opening the research tasks for creating the models of aerodynamic flights. The aerodynamic flight in atmosphere required safety and security issues for different humanitarian missions and civil actions. The flight in atmosphere with international standards must be secured and safety. According these requirements the research and software simulation in this dissertation created the new aerodynamic trajectory and technical parameters of flight for avoid intercepting process for safety and security. In dissertation has been created the aerodynamic trajectory and found the parameters, mathematical algorithm for navigation for safety landing. The requirements for trajectory have been made for safety landing, with minimization of error of landing and with minimization of flight timeframe. Analysis of research tasks initiated the creating models for avoid intercepting process for (different missions) and provide recommendations for aerospace industry. In research work has been used the research tools and methods of mathematical modeling, systems analysis, software computer simulation, statistical analysis and used theory of the probability. Chapter I Modeling has been made for a “Space-to-Surface” system for creating an optimal trajectory for targeting in terminal phase with avoids an intercepting process. The modeling includes models for simulation atmosphere, speed of sound, aerodynamic flight and the navigation by an infrared system. The modeling and simulation includes statistical analysis of the modeling results. In dissertation has created modeling and simulation of aerodynamic flight. The flight has an optimal trajectory for targeting and may be used for research missions. [1-4]. The scenario, which uses the unmanned vehicle of the “Space-to-Surface” system with optimal trajectory, includes: · Launching the vehicle from a space orbit with an altitude of (H=250-300km) by pulse from a space platform. In addition, the vehicle may be launched from an aircraft in the “Space-toSurface” mission during space flight. · After making the pulse from the space platform the vehicle enters the atmosphere. In next phase, it maneuvers in the atmosphere taking on horizontal flight. While in horizontal flight the vehicle is searching for the target by the infrared guidance system. Automatic control of the flight has the following conditions of altitude: Maneuver in atmosphere made with radius R=35-40km. ̈ Horizontal flight must have altitude H= 33-40 km for searching safety landing. The time for space flight is T=15-20 min until the time the vehicle enters the atmosphere. The time T=15-20 min is needed for the flight from space to enter to atmosphere with angle of attack A=3-4°. Trajectory of the vehicle in the atmosphere includes four phases: 1. Aerodynamic flight with the included entrance to the atmosphere with an angle of attack A=3-4°. This part of the trajectory has an altitude of H=90-100 km and a velocity of V=7.6 km/sec. 2. Maneuver in atmosphere from H=80-90 km to H=30-40 km in altitude. The velocity in this phase is V=5-7.6 km/sec. 3. Landing is searching while in horizontal flight. The velocity in this phase is V=3-5 km/sec. 4. The terminal phase, navigation and deployment of the landing process. The velocity in this phase is V=2.8-3 km/sec. All phases of the flight simulation include automatic control of the flight using parameter U. The mathematical model includes differential equations with parameter U integrated in four phases of flight. In the first phase it has been used for was gravitational flight: 1. U = cosθ, where θangle between horizontals and vector of vehicle velocity. In second phase it has been used for the maneuver in atmosphere with radius R=45 km: 2. U = V2/gR + cosθ, where Vvelocity of vehicle. In third phase it has been used for when the flight takes on horizontal flight with searching landing: 3. U = k(H-Y) + cosθ, where k – proportional coefficient, H=35 km, Y –current altitude. In fourth terminal phase it has been used for the infrared guidance to the landing: 4. U = k , where angle between vehicle and landing place. In terminal phase the design of vehicle may include the engine and make accelerating of velocity on final phase of flight. The vehicle in terminal phase may make maneuvers for avoid intercepting processing. The time for flight in the atmosphere with an altitude of H=100 km to deploy the landing is T=60-90 sec with a horizontal range of X=520-625 km. The vehicle, searching for the landing, starts in phase 3 by the infrared guidance system or may using the GPS for targeting. This simulation has been created by the integration of differential equations and includes modeling of the vehicle flight; searching, guidance, and automatic control and deploys the landing. As stated the modeling includes models of atmosphere, speed of sound, for automatic control of flight and for an infrared guidance. The simulation has been created in the programming language FORTRAN. The modeling includes statistical analysis of the modeling results. The simulation produced results with high probability of targeting inaccuracy (with an range error of R=8-10m). The simulation of the vehicle is used with a few parameters: · Weight m=1450-1550 kg · Aerodynamic coefficient K=Cy/Cx~2 · Wing area S~2m2 Gravitational flight, maneuver in the atmosphere, horizontal flight, searching, guidance and deployment the landing are defined in the models differential equations. All parameters (X, Y, Z, V, T, U, A) of the flight are integrated, where: · X, Y, Zcoordinates of vehicle; · T-time of flight; · Vvelocity of vehicle; · U-parameter of automatic control; · A-angle of attack. In modeling of atmosphere has been used the function the speed of sound Vs depends of altitude H, and made the linear approximation: If altitude H>80 km, the speed of sound is Vs=272, 6 m/sec; If altitude in 54 km<H<80 km, the Vs=330, 8-2*(H-54) m/sec; If altitude is 45, 5 km<H<54 km, the Vs=330, 8 m/sec; If altitude is 25 km<H<45, 5 km, the Vs=295, 1 + 1, 8(H-25) m/sec; If altitude is 11 km <H < 25 km, the Vs=295, 1 m/sec; If H < 11 km, the Vs = 340, 28-4, 1*H m/sec. Aerodynamic parameter CX had approximation: Cx = C(I,1)*M*M + C(I,2)*M + C(I,3), Where M –Mach number, I = 1, 2, 3 and C(I) have: C(1,1) = 1, 37 C(2,1) = -6 C(3,1) = 0, 01416 C(1,2) = 0, 2 C(2,2) = 12 C(3,2) = -0, 16993 C(1,3) = 0, 2 C(2,3) = 5 C(3,3) = 0, 51679 The atmosphere as function of altitude: p(H) = p*exp(-K*H) The differential equations for vehicle “Space-to-Surface” have definition: dV/dt =-Cx*p(H)*V*S*V/2*m*g – g*sinθ; dθ /dt= g/V*(n – cosθ); dZ/dt= -V cosθ sinW; dX/dt=V cosθ cosW; dY/dt=Vsinθ; dn/dt=(U-n)/T; dW/dt=gn/Vcosθ Where, V –current speed of vehicle; θangle between horizontals and vector of vehicle velocity; X, Y, Zcoordinates of vehicle; g= 9, 080665m/sec2; U-parameter of automatic control; In mathematical modeling of flight vehicle have been used and integrated the differential equations: Analysis modeling results after computer software simulation declared in horizontal range X= 615000m: T (sec) V (m/sec) θ X (m) H (m) U 0 7873 -0,0442 0 84109 0 10 7872 -0,0556 78617 74127 0 20 7870 -0,0691 157160 69169 0 30 7862 -0,0815 235596 63241 0 40 7834 -0,0939 313791 56362 0 50 7743 -0,1064 391361 48564 0 60 7451 -0,1192 467111 39984 0 70 6756 -0,1484 537382 31005 -6,406 80 4225 -0,3814 591596 17874 -13,413 9