thesis defense presentation, maxwell fagin

Optimization of

Supersonic Retropropulsive Flight for

Human Class Missions to Mars  

Maxwell H. Fagin Advisor: Professor Michael J. Grant

Purdue University, School of Aeronautics and Astronautics Thursday, December 10, 2015

Since 1960, 13 spacecraft have made it to the top of Mars’ atmosphere…

…and 5 of them were destroyed trying to get to the surface.

Mars 2 Mars 3 Mars 6 Viking 1 Viking 2

Pathfinder Polar Lander Spirit Opportunity Beagle

Phoenix Curiosity

“Space is hard, but landing on Mars is harder.”

Background: History

Two phases of entry, descent and landing (EDL):

Background: History

Terminal Phase High Energy Phase Altitude Range 150 km – 10 km 10 km – Surface  

Velocity Range   Mach 30 – Mach 1.5   Mach 1.5 – 0  

Critical Tasks  Dissipate orbital energy

Survive atmospheric heating Survive g-loads  

Reach target site Reconfigure for landing Achieve soft touchdown

Background: History

Altitude (Potential Energy)

Velocity (Kinetic Energy)

Touchdown

β    >  200    

β  =  100    

β  =  50  

β =m

CD ⋅A

Ballistic Coefficient Entry Interface

Background: History

Figure: Braun and Manning, 2012  

β =m

CD ⋅A

Background: History

64  

90  

146  62  

65  

Apollo 330  

Figure: Schoenenberger et. al, 2009, Images: NASA  

Only occurs here.  All of this…  Not useful during high energy phase.  

?

Modern Developments: IADs

β =m

CD ⋅AInflatable Aerodynamic Decelerators.  

Modern Developments: SRP

1)  A  method  to  dissipate  energy  without  compromising  on  targe6ng  2)  Mass  penal6es  significant,  but  may  be  the  only  way  

SRP: Historical Research

Mo6va6on:  Change  the  way  the  vehicle  flies  by  changing  the  shape  of  the  airflow  around  it,  WITHOUT  changing  the  shape  of  the  vehicle    Discoveries  that  an  axial  jet  can:  -­‐Displace  the  bow  shock  -­‐Negate  all  drag  -­‐Reduce  heat  load  (bow  shock  radia6on,  enthalpy  effects)  -­‐Discovery  that  a  peripheral  jet  can:  -­‐Displace  the  bow  shock  -­‐Enlarge  the  bow  shock  -­‐AUGMENT  DRAG  ON  THE  VEHICLE  (show  plot)  -­‐“Acts  as  a  force  mul6plier  for  the  engine”  

SRP: Modern Research

Focus:  CFD  Reproduc6on  of  wind  tunnel  data  CFD  studies  of  nozzle  placement  and  cant  angle    The  SRP  Envelope:  Discussion  of  limits  and  why  they  are  there  Introduce  Concept  of  op6mal  C_T  Falcon  9  Flight  video  

Thesis Background Mo6va6on  

 -­‐We  know  how  to  solve  this  problem.  We  did  it  for  the  moon.    -­‐Engines  at  high  enough  C_T  negate  aerodynamics    -­‐All  propulsive  lunar-­‐esque  landings  possible  (show  plot)    -­‐Cost  prohibi6ve,  TMI  mass  prohibi6ve  

 Aerodynamic  decelera6on  is  free,  propulsive  decelera6on  is  not.  But  we  need  a  propulsion  system  for  landing  accuracy.  

 -­‐As  long  as  we’ve  GOT  a  propulsive  system,  how  best  to  use  it?    -­‐Use  it  as  lible  as  possible  and  s6ll  land    -­‐Thrus6ng  full  through  the  SRP  envelope  is  throwing  away  free  decelera6on.  Why  not  

throble  back  and  use  it?    Gravity  losses  

Thesis Background Goal  

 -­‐What  kind  of  vehicle  would  this  imply?  How  heavy?    -­‐For  what  landing  requirements  is  this  strategy  beneficial?    -­‐How  big  are  the  gravity  losses?  Are  they  offset  by  other  factors?    -­‐What  other  design  tradeoffs  are  required?  

Study Details: Planet Planet  

 -­‐Proper6es    -­‐MOLA  

Study Details: Atmosphere Planet  

 -­‐Proper6es    -­‐MOLA  

Study Details: Equations of Motion

V =Velocityh = Altitudes = Downrangeγ = Flight Path Angle

dVdt

= −FDm− g ⋅sin(γ )

dγdt=FLmV

− gcos(γ )

dhdt=V ⋅sin(γ )

dsdt=V ⋅cos(γ )

F!"

Drag

g

γ

α

h^

F!"

Lift

s^

V!"

For non-propulsive 2D motion over a flat planet…  

Equations of Motion  

Study Details: Equations of Motion

T!" D

!"

V!"

!sγ

α

!h

ε

εvect

!L

ω p

V =Velocityh = Altitudes = Downrangeγ = Flight Path Angle

dγdt=

FLmV

⋅cos(σ ) + − gcos(γ ) +Vrcos(γ ) + 2wp cos(φ)cos(ψ) +

Study Details: Equations of Motion

dVdt

= −FDm

+ − g ⋅sin(γ )

Coriolis

w2prvcos(φ) cos(γ ) ⋅cos(φ)+ sin(γ ) ⋅sin(φ) ⋅sin(ψ)[ ]Centrifugal

(Planet’s Rotation)

Centrifugal (Vehicle’s motion)

dψdt

=FLmvsin(σ )cos(γ )

+ −Vrcos(γ )cos(ψ)tan(φ) + 2wp tan(γ )cos(φ)sin(ψ)− sin(φ)( )+

Gravity Aerodynamics

Aerodynamics Centrifugal

(Vehicle’s motion) Coriolis

−w2

prv ⋅cos(γ )

⋅ sin(φ) ⋅cos(φ) ⋅cos(ψ)[ ]Centrifugal (Planet’s Rotation)

Transform for 3D motion over a flat planet…  

Study Details: Spacecraft

Orion  aerodynamics    -­‐Propulsion  system    -­‐LOX-­‐Methane  vs.  hypergolic,  why  later  is  more  likely  for  first  crew.  

Study Details: Trajectory

Keplerian  Ballis6c  Pull  Up  Level  Flight  SRP  envelope  behavior  Review  Each  Phase  and  Cri6cal  Aspects  

Results: Drag Preservation Model

Overview  of  p(C_T)  law  Deriva6on  of  op6mal  throbling  law  

Results: Optimal Throttling

Review  SRP  envelope,  and  C_T  driven  throble  law  sec6on  

Results: Propellant Savings vs. L/D

Design  curves  from  thesis,  and  interpreta6on.  Likely  L/D  for  vehicle  to  fly.  

Results: Downrange vs. L/D

Design  curves  from  thesis,  and  interpreta6on.  Extent  of  range  control  possible.    Spend  extra  6me  on  these  slides,  emphasize  results.  

Future Work: Indirect Optimization

GPOPS,  path  constraints,  contour  following  controls  

Future Work: Lifting Body, HL20

Discussion  of  Kshi6j+Cordell,  agbody  thrust  op6on  

Future Work: Extended SRP envelope

Stall  speed  as  Mach  number  limit  to  SRP  envelope.  Benefits  to  entering  envelope  from  Mach  number  limit  Expected  small  gravity  losses  

Summary

Restatement  of  goals,  and  answer  of  ques6ons:    -­‐What  kind  of  vehicle  would  this  imply?  How  heavy?  

 -­‐For  what  landing  requirements  is  this  strategy  beneficial?    -­‐How  big  are  the  gravity  losses?  Are  they  offset  by  other  factors?    -­‐What  other  design  tradeoffs  are  required?  

References and Questions