1. Junichi (Jun) Kanehara 03/06/2008 Trajectory The Winner of the Balloon, 5[kg] case (LB-HA-DA-DA_v125) & New Version of Trajectory 3-D Plots
AAE 450 Spring 2008

2. 3D-Plots Payload Mass= 5.0 [kg] GLOW= 6,295 [kg] eccentricity: 0.0025
periapsis: [km]
apoapsis: [km] (from the surface of the Earth)
Max Acceleration: 5.22 G
deltaV Thrust-total : 11,853 [m/s]
deltaV required: 9,354 [m/s]
Plots generated by the version 2.0 of “AAE450_Trajectory_Plots.m” modified by Jun Kanehara
AAE 450 Spring 2008
Trajectory

3. June Solstice Trajectory AAE 450 Spring 2008
Plots generated by the version 2.0 of “AAE450_Trajectory_Plots.m” modified by Jun Kanehara
AAE 450 Spring 2008
Trajectory

4. December Solstice Trajectory AAE 450 Spring 2008
Plots generated by the version 2.0 of “AAE450_Trajectory_Plots.m” modified by Jun Kanehara
AAE 450 Spring 2008
Trajectory

5. Steering Law
AAE 450 Spring 2008

6. Model Name: LB-HA-DA-DA Delta V = 11,313
Stage 2
Prop Mass = 1, [kg]
Inert Mass = [kg]
Engine Mass = [kg]
Thrust (vac) = 15,256.9 [N]
Burn Time = [s]
Mass Flow Rate = [kg/s]
Exit Area = [m^2]
Exit Pressure = 11, [Pa]
Length = [m]
Diameter = [m]
Stage 3
Prop Mass = [kg]
Inert Mass = [kg]
Engine Mass = 8.56 [kg]
Thrust (vac) = [N]
Burn Time = [s]
Mass Flow Rate = [kg/s]
Exit Area = [m^2]
Length = [m]
Diameter = [m]
Model Name: LB-HA-DA-DA
Delta V = 11,313
Delta V Percentages = [ ]
Inert Mass = [ ]
Stage 1
Prop Mass = 4, [kg]
Inert Mass = [kg]
Engine Mass = [kg]
Thrust (vac) = 75,073.2 [N]
Burn Time = [s]
Mass Flow Rate = [kg/s]
Exit Area = [m^2]
Exit Pressure = 2, [Pa]
Length = [m]
Diameter = [m]
AAE 450 Spring 2008
Trajectory

7. Case ID: LB_HA_DA_DA_v125.txt Orbital Parameters Period: 6038.7878 [s]
Semi-major axis: [km]
eccentricity:
periapsis: [km]
apoapsis: [km]
Linear Tangent Steering Parameters:
a1 =
b1 =
a2 =
b2 =
a3 = e-019
b3 =
Flight Path Angle = 0.1 [deg].
at t=0[s]:
Altitude: h=30000 [m] (Initial Condition)
Radial (Vertical) Speed: Vr=0 [m/s]
Thrust
1st stage: [kN]
2nd stage: [kN]
3rd stage: [kN]
Max Acceleration
Max Stage= 28.5 [m/s^2]
Max Stage= 2.90 G
Max Stage= 51.2 [m/s^2]
Max Stage= 5.22 G
Max Stage= 39.0 [m/s^2]
Max Stage= 3.97 G
Max Stage= 3.8 [m/s^2]
Max Stage= 0.38 G
AAE 450 Spring 2008
Trajectory

8. (first 10.00 [s] is vertical flight) 2nd Stage: 212.96[s]
Burn Times
1st Stage: 175[s]
(first [s] is vertical flight)
2nd Stage: [s]
3rd Stage: [s]
Times at the end of each stage
End of first stage: [s]
End of second stage: [s]
End of third stage: [s]
Constant Mass Flow Rates
1st Stage: [kg/s]
2nd Stage: [kg/s]
3rd Stage: [kg/s]
Constant Exit Pressures
1st Stage: [kPa]
2nd Stage: 11.45[kPa]
3rd Stage: [kPa]
Altitudes
at the end of the vertical part of flight: 30,112.44[m]
at t= 0 [s]: [km]
at the end of the first stage: [km]
at the end of the second stage: [km]
at the end of the third stage: [km]
from AAE450_Delta_V.m
Delta_V_Thrust_1st= [m/s] (29.4 %)
Delta_V_Thrust_2nd= 4775 [m/s] (40.3 %)
Delta_V_Thrust_3rd= 3592 [m/s] (30.3 %)
Delta_V_Thrust_Total (what we get)= 11,853 [m/s]
Delta_V_Leo= ,727 [m/s]
Delta_V_Grav= ,034 [m/s]
DeltaV_drag= [m/s]
Delta_V_Earth_assist= [m/s]
Delta_V_Total (what we need)= 9,354 [m/s]
Delta V required to circularize: [m/s]
AAE 450 Spring 2008
Trajectory

9. Current Design: LB-HA-DA-DA_v125
Balloon ICs
Aircraft ICs with Vertical Vi
r_dot_i = [m/s] hi = 15,000 [m]
r_dot_i = 0.0 [m/s] hi = 30,000 [m]
Delta_V_Leo= ,727 [m/s] Delta_V_Grav= ,084 [m/s] DeltaV_drag= [m/s] Delta_V_Earth_assist= [m/s] Delta_V_Total (w/o circ) = ,422 [m/s] Delta V required to circularize= [m/s] Delta_V_Total_ (w/ circ) = ,968 [m/s] e: rp: [km] ra: [km]
Delta_V_Leo= ,727 [m/s] Delta_V_Grav= ,034 [m/s] DeltaV_drag= [m/s] Delta_V_Earth_assist= [m/s] Delta_V_Total (w/o circ) = ,354 [m/s] Delta V required to circularize= [m/s] Delta_V_Total_ (w/ circ) = ,922 [m/s] e: rp: [km] ra: [km]
Delta_V_savings = 46 [m/s]
AAE 450 Spring 2008
Trajectory