aae 450 spring 2008 allen guzik trajectory trajectory optimization 1/25

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


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)


AAE 450 Spring 2008

Backup Slides FAA Launch Locations Source: Kyle Donohue gathered the data

(www. faa.gov)


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


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


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


AAE 450 Spring 2008AAE 450 Spring 2008

Sample Airplane Launch


Trajectory Code Can Now Predict Orbits From an Aircraft Launch

Ascent Trajectory

Launch Site

Initial Height of 12,200 m

7/25


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


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


Backup Slides


Sample Affect of Atmosphere on Ascent– Both Cases are for a GROUND LAUNCH

With Atmosphere No Atmosphere

9/25


Backup Slides


Sample Balloon Ascent

30,500 m

10/25


Ψ3 Effect on Trajectory


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)


Other Plots


Conclusions– Best Results occur at the previous steering angle– Spin stabilized third stage is feasible.

12/25


Backup Slides



Airplane Trajectory Results


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


Ψ3 Error Sensitivity


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


Backup Slides


Eccentricity Percent Error

0%

5%

10%

15%

20%

-24 -20 -16 -12 -8 -4 0 4


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


Ec

ce

ntr

icit

y

Eccentricity

Nominal Value


Backup Slides


Apogee Percent Error

0%

5%

10%

15%

20%

-24 -20 -16 -12 -8 -4 0 4


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


Ap

og

ee [

km]

Apogee

Nominal Value


Presentation Slides: Ψ3 Effect on Trajectory and Resulting Orbit


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.


Presentation Slides: Ψ3 Error Sensitivity


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


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


Backup Slides (If needed)


Eccentricity Percent Error

0%

5%

10%

15%

20%

-24 -20 -16 -12 -8 -4 0 4


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


Ec

ce

ntr

icit

y

Eccentricity

Nominal Value


Backup Slides (If Needed)


Apogee Percent Error

0%

5%

10%

15%

20%

-24 -20 -16 -12 -8 -4 0 4


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


Ap

og

ee [

km]

Apogee

Nominal Value

AAE 450 Spring 2008AAE 450 Spring 2008Trajectory Optimization 25/25


aae 450 spring 2008 allen guzik trajectory trajectory optimization 1/25

Documents

v dragairplane

drag comparisonpurposeattempt

balloon launches

data www

dragtrajectory code

resulting trajectory

changing steering angles

totalv dragv totalairplane29