thesis defense presentation, maxwell fagin
TRANSCRIPT
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