1. AAE450 Senior Spacecraft Design Goppert, 1 James Goppert Week 8: March 8 th, 2007 Aerodynamics: Reentry Optimization Dynamics and Control: Communication Satellite Orbits Comm. Sat. Delta V’s Atmospheric Flight (Entry/Ascent)

2. AAE450 Senior Spacecraft Design Goppert, 2 Comm. Sat. Delta V’s Gangale Parameters –Inclination 4.5 [deg] –Lead/Lag Angle 8 deg –Earth parking orbit 500 km –Fly by altitude 500 km Gangale Results –Insertion 5.2 [km/s] (Leading) 5.5 [km/s] (Lagging) –Station-keeping 30 [m/s /yr] Mars Geostationary Parameters –Earth parking orbit 500 km Mars Geo. Results –Insertion 30 [km/s] –Station-keeping Est. 60 [m/s /yr]

3. AAE450 Senior Spacecraft Design Goppert, 3 Entry /Ascent Entry Delta V from Orbit –50 [m/s] –Employs drag of atmosphere Burn Location –Latitude: 0 [deg] –Longitude: -166.2 [deg] –Altitude: 300 [km] HMO –Heading: 78.54 [deg] Time of Flight –6 [hrs] –Treatment of Parachute/ Hover Phase Seperately (Last Presentation) Escape Tower Assumptions –10 g’s max from launch vehicle –15 g’s max sustainable –5 launch vehicle radii away at end of burn Results –Total mass 2 [mt] –Thrusters 3 Required 400 [kN] each –Burn Time 2.8 sec

4. AAE450 Senior Spacecraft Design Goppert, 4 Backup Slides James Goppert Week 8: March 8 th, 2007

5. AAE450 Senior Spacecraft Design Goppert, 5 Gangale Insertion Analysis Vector Diagram at Fly-by p z imim VmVm V - t2 V - ∞/m V + ∞/m δ Δ V eq V + t2 Δ V req V gt igig α1 α2 β

6. AAE450 Senior Spacecraft Design Goppert, 6 Ballistic Landing Approach Landing Site Fortran Generated Ground Track

7. AAE450 Senior Spacecraft Design Goppert, 7 Ballistic Landing Approach

8. AAE450 Senior Spacecraft Design Goppert, 8 Spherical Planet EOM’s kinematic equations dr = V*sin(gam) dtheta = V*cos(gam)*cos(psi)/(r*cos(phi)) dphi = V*cos(gam)*sin(psi)/r dynamic equations dV = Ft/m-g*sin(gam)+w_e**2*r*cos(phi)*(sin(gam)*cos(phi)-& cos(gam)*sin(psi)*sin(phi)) dgam = (Fn*cos(sig)/m-g*cos(gam)+V**2*cos(gam)/r+2*w_e*V*cos(psi)*& cos(phi)+w_e**2*r*cos(phi)*(cos(gam)*cos(phi)+& sin(gam)*sin(psi)*sin(phi)))/V dpsi = (Fn*sin(sig)/m/cos(gam)-v**2*cos(gam)*cos(psi)*tan(phi)/r+& 2*w_e*V*(tan(gam)*sin(psi)*cos(phi)-sin(phi))-& w_e**2*r*cos(psi)*sin(phi)*cos(phi)/cos(gam))/V Source: Optimal Trajectories in Atmospheric Flight, Vinh, 1981

9. AAE450 Senior Spacecraft Design Goppert, 9 Atmospheric Trajectory FORTRAN Input Example 3396.19e3 :semi-major axis of planet [km] 0.1083:eccentricity of mars oblate spheroid model [] 0. -2.9 300000 :initial geodetic pos.[rad,rad,m] (lat.,long.,alt.) 3092.96 0. 0.2:velocity(NED), flight path angle, heading[m/s,rad,rad] 9.80665 :earth grav. accel [m/s^2] 10.:maximum g load [g's] 4.283e13:mu for planet [m^3/s^2] 7.07764e-5:angular velocity of planet [rad/s] 1.:output time step [s] 0.:start time [s] 20000.:stop time [s] 1.e-8:ivprk variable step rk4 error tolerance 4000.:isp for hover motor [m/s] 100000. :total initial vehicle mass [kg]

10. AAE450 Senior Spacecraft Design Goppert, 10 Atmospheric Trajectory FORTRAN Output Output text file generated by FORTRAN –Echo’s input for record of case run –Output’s relavent state’s for plotting Matlab used to plot data from generated file –Capable of generating movies –Animated trajectory plots –All relavent quantities plotted

11. AAE450 Senior Spacecraft Design Goppert, 11 Escape Tower Analysis Assume –Ac = 15 g’s (max. acceleration of capsule) –An = 10 g’s (maximum accel. of launch veh.) –Isp = 2500 m/s –Theta = 17.5 deg (thrust angle of attack) –Mc = 8 mt (mass of capsule) –Structural Efficiency of 0.5 (high for truss structure and engine) Equations –X = ½(ac-an)*tb^2 –dm = Fr/Isp = 490 kg/s –Fc = Mc*Ac = 1.18e+6 N –Fr = Fc/cos(Theta) = 1.23e+6 N Results –tb = 2.8 sec –M = 2 mt (mass of escape tower/ structure and propellant)

12. AAE450 Senior Spacecraft Design Goppert, 12 Escape Tower Geometry