Allen Guzik Trajectory
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Transcript of Allen Guzik Trajectory
AAE 450 Spring 2008
Allen GuzikTrajectory
Trajectory Optimization 1/25
AAE 450 Spring 2008
Delta V at Each Latitude Initial Assessment
– Only looks at Velocity gained from the rotation of the Earth
– Assume Launched Vertically and directly East
Trajectory Optimization 2/25
AAE 450 Spring 2008
Location and Wind Average Wind Velocities
– 4 m/s– 5 m/s– 7 m/s
Launch Locations– Federal– Commercial
(Already Approved)
– Proposed
Trajectory Optimization
Map Provided From www.googgle.com, Edited by Allen Guzik
3/25
AAE 450 Spring 2008
Backup Slides Wind Data Source: Brian Budzinski found the
data. (http://www.windstuffnow.com/main/wind_charts.htm)
Trajectory Optimization 4/25
AAE 450 Spring 2008
Backup Slides FAA Launch Locations Source: Kyle Donohue gathered the data
(www. faa.gov)
Trajectory Optimization
Federal Locations
Name of Facility Loacation
Vandenburg AFB Southern California
Edwards AFB Southern California
White Sands Missile Range New Mexico
Wallops Flight Facility Wallops Island, Virgina
Cape Canaveral Spaceport Cape Canaveral, Florida
Commercially Approved Locations
Name of Facility Loacation
Kodiak Launch Complex Kodiak Island, Alaska
California Spaceport Lompoc, California
Virgina Space Flight Center Wallops Island, Virgina
Florida Space Authority Cape Canaveral, Florida
Sea Launch Platform Equatorial Pacific Ocean
Mojave Civilian Test Flight Center Mojave, California
Southwest Regional Spaceport Upham, New Mexico
Proposed Locations
Name of Facility Loacation
Spaceport Washington Moses Lake, Washington
Nevada Test Site Nye County, Nevada
Utah Spaceport Wah Wah Valley, Utah
Great Falls Spaceport Montana
South Dakota Spaceport South Dakota
Oklahoma Spaceport Burns Flat, Oklahoma
Gulf Coast Regional Brezoria County, Texas
Wisconsin Spaceport Sheboygan, Wisconsin
Spaceport Alabama Baldwin county, Alabama
South Texas Spaceport Willacay County, Texas
West Texas Spaceport Pecos County, Texas
5/25
AAE 450 Spring 2008
Backup Slides Earth Help Basic Calculation
Trajectory Optimization 6/25
AAE 450 Spring 2008AAE 450 Spring 2008
Sample Airplane Launch
Trajectory Optimization
Trajectory Code Can Now Predict Orbits From an Aircraft Launch
Ascent Trajectory
Launch Site
Initial Height of 12,200 m
7/25
AAE 450 Spring 2008AAE 450 Spring 2008
ΔV Drag Comparison Purpose
– Attempt to validate how the trajectory code estimates drag
– Compare vehicle mass to Δv drag– Compare drag from different
launching configurations
Trajectory Optimization
Airplane, Balloon, Ground, Drag ΔV Comparison
Launch Type
GLOW [kg]
With Atmosphere Model No Atmosphere Model
ΔV Drag ΔV Total% ΔV Drag of
TotalΔV Drag ΔV Total
Airplane 29,023 75 9,918 0.76% 0 9,876
Airplane 5,593 215 11,295 1.90% 0 10,447
Balloon 5,593 14 2,911 0.48% 0 2,895
Ground 29,023 359 9,271 3.87% 0 10,677
Ground 5,593 932 10,154 9.18% 0 9,982
Assumptions– Same initial steering law
conditions– Orbit obtained is not considered– Same dimensions
Conclusions– Lighter Vehicle Increases Δv drag– Airplane and Balloon Launches decrease Δv drag– Trajectory Code handles drag appropriately, however the magnitude of the results
need to be verified.
8/25
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides
Trajectory Optimization
Sample Affect of Atmosphere on Ascent– Both Cases are for a GROUND LAUNCH
With Atmosphere No Atmosphere
9/25
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides
Trajectory Optimization
Sample Balloon Ascent
30,500 m
10/25
AAE 450 Spring 2008AAE 450 Spring 2008
Ψ3 Effect on Trajectory
Trajectory Optimization 11/25
Purpose– Attempt to understand how changing
steering angles affects the resulting trajectory.
– Feasibility of spin stabilization of third stage– Will be used to know how to get into orbit
for different vehicles.– Help write code for a better trajectory
model prediction.– Aid in understanding other launch systems
(i.e. plane and balloon)
Assumptions– Only Change Ψ3
– Hold Ψ1 and Ψ2 constant (-15˚, -30˚).
– 3 Stage Vehicle (Juno I Inputs)– Ground launch– Payload (5 kg)
AAE 450 Spring 2008AAE 450 Spring 2008
Other Plots
Trajectory Optimization
Conclusions– Best Results occur at the previous steering angle– Spin stabilized third stage is feasible.
12/25
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides
Trajectory Optimization 13/25
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides
Trajectory Optimization 14/25
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides
Trajectory Optimization 15/25
AAE 450 Spring 2008AAE 450 Spring 2008
Airplane Trajectory Results
Trajectory Optimization 16/25
Conclusions- Good airplane launch trajectories are possible
- Airplane launches can be cheaper than balloon launches
- Unfortunately D&C cannot control trajectory’s prescribed path
Airplane Trajectory Results
Model Name CostComparable Balloon Cost
Delta V[m/s]
Perigee[km]
Apogee[km]
Eccentricity
SA-SA-DT-DT $2,107,448 $2,157,403 8,988 400.7 1,030.5 0.0444
MA-SA-DA-DA $2,247,287 $2,524,942 8,765 398.1 2,448.6 0.1315
LA-SA-DA-DT $2,487,533 $2,752,318 8,987 406.8 1,742.8 0.0897
Too Aggressive for D&C
Example Orbit
Bradley Ferris
Junichi Kanehara
AAE 450 Spring 2008AAE 450 Spring 2008
Ψ3 Error Sensitivity
Trajectory Optimization
Conclusions- Perigee is greatly effected by Ψ3 error (1˚ ~= 10% error)
- If there is error, best case is for the error to be more negative
17/25
Purpose– Find how sensitive the orbit is from an error in Ψ3
– D&C needs this for their controller
Model Used for Analysis– LB-SA-DA-DA
Perigee Percent Error
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Per
cen
t E
rro
r
Sensitivity of Perigee to Psi3
0
50
100
150
200
250
300
350
400
450
500
550
-24 -20 -16 -12 -8 -4 0 4Psi3 Angle Change from the Nominal [degree]
Peri
gee [
km
]
Perigee
Nominal Value
Requested Orbit
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides
Trajectory Optimization 18/25
Eccentricity Percent Error
0%
5%
10%
15%
20%
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Pe
rce
nt
Err
or
Sensitivity of Eccentricity to Psi3
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Ec
ce
ntr
icit
y
Eccentricity
Nominal Value
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides
Trajectory Optimization 19/25
Apogee Percent Error
0%
5%
10%
15%
20%
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Per
cen
t E
rro
r
Sensitivity of Apogee to Psi3
6,000
6,500
7,000
7,500
8,000
8,500
9,000
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Ap
og
ee [
km]
Apogee
Nominal Value
AAE 450 Spring 2008AAE 450 Spring 2008
Presentation Slides: Ψ3 Effect on Trajectory and Resulting Orbit
Trajectory Optimization 20/25
Purpose– Attempt to understand how changing
steering angles affects the resulting trajectory.
– Feasibility of spin stabilization of third stage– Will be used to know how to get into orbit
for different vehicles.– Help write code for a better trajectory
model prediction.– Aid in understanding other launch systems
(i.e. plane and balloon)
Assumptions– Only Change Ψ3
– Hold Ψ1 and Ψ2 constant (-15˚, -30˚).
– 3 Stage Vehicle (Juno I Inputs)– Ground launch– Payload (5 kg)
Angle of Ψ2 Conclusions– Best Results occur at the previous steering
angle– Spin stabilized third stage is feasible.
AAE 450 Spring 2008AAE 450 Spring 2008
Presentation Slides: Ψ3 Error Sensitivity
Trajectory Optimization
Conclusions- Perigee is greatly effected by Ψ3 error (1˚ ~= 10% error)
- If there is error, best case is for the error to be more negative
21/25
Purpose– Find how sensitive the orbit is from an error in Ψ3
– D&C needs this for their controller
Model Used for Analysis– LB-SA-DA-DA
Perigee Percent Error
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
110%
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Per
cen
t E
rro
r
Sensitivity of Perigee to Psi3
0
50
100
150
200
250
300
350
400
450
500
550
-24 -20 -16 -12 -8 -4 0 4Psi3 Angle Change from the Nominal [degree]
Peri
gee [
km
]
Perigee
Nominal Value
Requested Orbit
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides (If needed)
Trajectory Optimization 22/25
Eccentricity Percent Error
0%
5%
10%
15%
20%
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Pe
rce
nt
Err
or
Sensitivity of Eccentricity to Psi3
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Ec
ce
ntr
icit
y
Eccentricity
Nominal Value
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides (If Needed)
Trajectory Optimization 23/25
Apogee Percent Error
0%
5%
10%
15%
20%
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Per
cen
t E
rro
r
Sensitivity of Apogee to Psi3
6,000
6,500
7,000
7,500
8,000
8,500
9,000
-24 -20 -16 -12 -8 -4 0 4
Psi3 Angle Change from the Nominal [degree]
Ap
og
ee [
km]
Apogee
Nominal Value
AAE 450 Spring 2008AAE 450 Spring 2008
Backup Slides (If Needed)
Trajectory Optimization 24/25
AAE 450 Spring 2008AAE 450 Spring 2008Trajectory Optimization 25/25
Backup Slides (If Needed)