brad ferris - engineering.purdue.edu

Brad Ferris01/24/0801/24/08

Trajectory AnalystModeling ThrustModeling Thrust

Assistance Provided by Daniel Chua

AAE 450 Spring 2008

ModelingA tiAssumptions– Constant mass flow rate, exit velocity– No flow separation

New code structure– Call a function to get thrust at a given time– Apply Thrust Equationpp y q

T = m_dot * ve + ( pe – pa) * Ae

AAE 450 Spring 2008Group Name (i.e.Trajectory Optimization)

ResultsVelocity at 320 km circular orbit: 7 715 km/sVelocity at 320 km, circular orbit: 7.715 km/sVelocity at 320 km w/o pressure thrust: 5.296 km/sVelocity at 320 km w/ pressure thrust: 6 911 km/sVelocity at 320 km w/ pressure thrust: 6.911 km/sVelocity difference due to pressure thrust: 1.615 km/s

C l i d F t W kConclusions and Future WorkCode can now model thrust more accuratelyCode can now model thrust more accuratelyIncorporate data from Propulsion group


Velocity Plots–Without Pressure ThrustRadial Velocity Tangential Velocityy g y

Blue – Simulation VelocityGreen – Circular Orbit Velocity


Trajectory Plots–Without Pressure ThrustAltitude Trajectoryj y

Red – Simulation AltitudeGreen – Circular Orbit Altitude


Velocity Plots–With Pressure ThrustRadial Velocity Tangential Velocityy g y

Blue – Simulation VelocityGreen – Circular Orbit Velocity


Trajectory Plots–With Pressure ThrustAltitude Trajectoryj y

Red – Simulation AltitudeGreen – Circular Orbit Altitude


Brad Ferris02/07/08

Trajectory AnalystEffect of Varying Vehicle Parameters

AAE 450 Spring 2008

Nominal OrbitN i l C ditiNominal Conditions– Jupiter C Vehicle Model

3 Stage Ground– 3 Stage, Ground Launch

– 1 kg Payload Massg y

Orbit Parameters– Eccentricity: 0.650Eccentricity: 0.650

(0 for a circular orbit)– Periapsis: 95 km

Image by: Brad Ferris

AAE 450 Spring 2008Trajectory Optimization

Image by: Brad FerrisTraj. Code by: Traj. Group

Eff t f V i P tEffects of Varying ParametersChange Effect Effect of Varying Parameters on Orbit Shape

0 8

0.9

1

Change EffectIncrease 1st

Stage Prop M

Less Eccentric

0.4

0.5

0.6

0.7

0.8

Ecce

ntri

city 1st Stage Prop Mass

1st Stage Burn Time1st Stage Thrust

MassIncrease 1st

Stage Burn Time

More Eccentric

0

0.1

0.2

0.3

65 75 85 95 105 115 125 135

ETime

Increase 1st

Stage ThrustMore Eccentric

65 75 85 95 105 115 125 135

Percent Nominal Value

Increase Payload Mass

Less Eccentric Chart and Data by: Brad Ferris

Traj. Code by: Traj. Group


V i P l d MVarying Payload MassEccentricity v. Payload Mass

0.6

0.7

0.3

0.4

0.5

Ecc

entri

city

0

0.1

0.2

E

00 2 4 6 8 10 12

Payload Mass (kg)

Chart and Data by: Brad Ferris


Chart and Data by: Brad FerrisTraj. Code by: Traj. Group

Brad Ferris02/21/0802/21/08

Trajectory AnalystModeling DragModeling Drag

Assistance provided by Jayme Zott, Kyle Donohue

AAE 450 Spring 2008

ModelingA tiAssumptions:– Atmosphere molecular weight is constant– Angle of Attack is zero

Speed of Sound: a = [γRT]1/2

Use Mach Number to get CD

Apply Equation for DragApply Equation for DragD = CD * q * S


V lid tiValidationDrag Force v. Mach NumberWith

20000

25000

W/O F ti

function, notice drag

15000ra

g (N

)W/O FunctionCd Function

behaviorOver most M h

5000

10000DMach numbers, drag

00 1 2 3 4 5

Mach Number

drag without function is


higher Figure by Brad Ferris

Orbit parametersWithout Function With F tiWithout Function– 762 / 232710 km

(periapsis / apoapsis)

With Function– 807 / 232477 km

(periapsis / apoapsis)(p p p p )– Eccentricity: 0.942– Delta V Drag: 461 m/s

(periapsis / apoapsis)– Eccentricity: 0.942– Delta V Drag: 384 m/s

– Delta V Total: 10760 m/sSteering Angles:

g– Delta V Total: 10672

m/sSt i A l– Steering Angles:

6,-28,-28 deg.– Steering Angles:

6,-28,-28 deg.


D d TiDrag and TimeDrag v. Time

20000

25000

15000

rag

(N)

W/O FunctionCd Function

5000

10000Dr

00 50 100 150 200 250

Time (s)


Figure by Brad Ferris

Brad Ferris03/06/08

Trajectory AnalystEffect of Launch Angle

AAE 450 Spring 2008

DescriptionS tSetup– Case: V125, 200 g (SB-HA-DA-DA)– Constant Steering Law : 26, -2, -2 (deg.)

Method– Vary Launch Angle– Examine Effect on Orbit Obtained


C iComparisonsP i i & A i L h A l

As launch angle decreases

Periapsis & Apoapsis v. Launch Angle

2500

3000

apoapsisperiapsisdecreases,

orbit becomes more eccentric 1500

2000

eigh

t (km

)

p p300 (km)

As launch angle decreases

500

1000 He

decreases, total ΔV required d

07980818283848586878889

Launch Angles (deg.)

Figure by: Brad Ferris


decreases Figure by: Brad Ferris

ΔV T t l C iΔV Total ComparisonsΔV Total v. Launch Angle

9180

9190

9150

9160

9170

otal

(km

/s)

9120

9130

9140

ΔV

To

91107980818283848586878889

Launch Angle (deg.)



E t i it C iEccentricity ComparisonsEccentricity v. Launch Angle

0.14

0.16

0.08

0.1

0.12

entri

city

0.02

0.04

0.06 Ecc

07980818283848586878889

Launch Angle (deg.)



Brad Ferris03/27/08

Trajectory AnalystForces, Equations of Motion

AAE 450 Spring 2008

Free Body DiagramForcesForces

Thrust (T)Drag (D)Weight (W)

AnglesAnglesFlight path angle (γ)Thrust offset (α΄)

Figure by Brad Ferris


Modeling ForcesDrag (D)g ( )• D = CD * q * S• Speed of sound: a = [γRT]1/2Speed of sound: a [γRT]• CD - function on Mach number (Aerothermal

group)g p)Thrust (T)• T = m dot * ve + ( pe – pa) * AeT m_dot ve ( pe pa) Ae

• Topt= m_dot * ve, pe, Ae (Propulsion group)Weight (W=m(t)*g)


Weight (W m(t) g)

ee

Vector BasesBasesBases

ei frame: Earth fixedEarth fixedai frame: rotates along ez by θ(longitude)b frame:bi frame: rotates along ay by Φ


y y(latitude) Figure by Amanda Briden

Equations of Motion

Given in body-fixed unit vectors (bi)


brad ferris - engineering.purdue.edu

Documents