MAE 1202: AEROSPACE PRACTICUM

1
MAE 1202 AEROSPACE PRACTICUM

• Review of Flight Performance
• Introduction to Aerospace Structures
• April 20, 2009
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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PROJECT COMMENTS

• Save receipts for any purchases up to about 15
  dollars
• Get all receipts to me in a single envelope by
  April 27
• Rocket Construction QA email Mr. Greg Peebles
  peebles_at_fit.edu
• Project Requirements
• Presentation
• In lab on Thursday/Friday April 24/25
• See next charts
• Launch Contest
• Saturday, April 25, 2009
• 9 am 2pm
• Final Report
• Due by Monday, May 4, 2009 by 5pm
• Report criteria located on project description
  document

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ORAL PRESENTATION REQUIREMENTS

• Presentation Length 20-30 minutes
• Everyone on team should present
• Potential Outline
• Overview (brief, no need to repeat requirements
  document)
• Calculations ? altitude and motor choice
• Weight, area, Cg vs. Cp, drag
• Rocket design
• ProEngineer drawings
• What you plan to do if
• Rocket goes too high
• Rocket goes too low
• Lots of wind on contest day
• Design Summary
• 1 Slide How to make MAE 1202 project better
• However, be creative and use your own judgment on
  how to make an excellent presentation!

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DIRECTIONS TO PALM BAY LAUNCH SITE

• Launch Contest Date
• This Saturday, April 25, 2009
• 9am 1pm
• Directions
• Palm Bay road West past I-95 to Minton Road.
• Take Minton south until it dead ends into
  Jupiter.
• Turn right (west) on Jupiter
• Make 2nd left onto Degroodt
• Travel south on Degroodt until you reach
  Bombardier
• (On southeast corner is Bayside High School)
• Turn Right onto Bombardier (West)
• Stay on Bombardier until it ends you will see us

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AIRPLANE PERFORMANCERANGE AND ENDURANCE

• How far can we fly?
• How long can we stay aloft?
• How do answers vary for propeller-driven vs.
  jet-engine?

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AIRPLANE POWER PLANTS

• Two types of engines common in aviation today
• Reciprocating piston engine with propeller
• Average light-weight, general aviation aircraft
• Rated in terms of POWER
• Jet (Turbojet, turbofan) engine
• Large commercial transports and military aircraft
• Rated in terms of THRUST

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THRUST VS. POWER

• Jets Engines (turbojets, turbofans for military
  and commercial applications) are usually rate in
  Thrust
• Thrust is a Force with units (N kg m/s2)
• For example, the PW4000-112 is rated at 98,000 lb
  of thrust
• Piston-Driven Engines are usually rated in terms
  of Power
• Power is a precise term and can be expressed as
• Energy / time with units (kg m2/s2) / s kg
  m2/s3 Watts
• Note that Energy is expressed in Joules kg
  m2/s2
• Force Velocity with units (kg m/s2) (m/s)
  kg m2/s3 Watts
• Usually rated in terms of horsepower (1 hp 550
  ft lb/s 746 W)
• Example
• Airplane is level, unaccelerated flight at a
  given altitude with speed V8
• Power Required, PRTRV8
• W N m/s

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POWER AVAILABLE (6.6)
Jet Engine
Propeller Drive Engine
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RANGE AND ENDURANCE

• Range Total distance (measured with respect to
  the ground) traversed by airplane on a single
  tank of fuel
• Endurance Total time that airplane stays in air
  on a single tank of fuel
• Parameters to maximize range are different from
  those that maximize endurance
• Parameters are different for propeller-powered
  and jet-powered aircraft
• Fuel Consumption Definitions
• Propeller-Powered
• Specific Fuel Consumption (SFC)
• Definition Weight of fuel consumed per unit
  power per unit time
• Jet-Powered
• Thrust Specific Fuel Consumption (TSFC)
• Definition Weight of fuel consumed per unit
  thrust per unit time

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PROPELLER-DRIVEN RANGE AND ENDURANCE

• SFC Weight of fuel consumed per unit power per
  unit time

• ENDURANCE To stay in air for longest amount of
  time, use minimum number of pounds of fuel per
  hour

• Minimum lb of fuel per hour obtained with minimum
  HP
• Maximum endurance for a propeller-driven airplane
  occurs when airplane is flying at minimum power
  required
• Maximum endurance for a propeller-driven airplane
  occurs when airplane is flying at a velocity such
  that CL3/2/CD is a maximized

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PROPELLER-DRIVEN RANGE AND ENDURANCE

• SFC Weight of fuel consumed per unit power per
  unit time

• RANGE To cover longest distance use minimum
  pounds of fuel per mile

• Minimum lb of fuel per hour obtained with minimum
  HP/V8
• Maximum range for a propeller-driven airplane
  occurs when airplane is flying at a velocity such
  that CL/CD is a maximum

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PROPELLER-DRIVEN RANGE BREGUET FORMULA

• To maximize range
• Largest propeller efficiency, h
• Lowest possible SFC
• Highest ratio of Winitial to Wfinal, which is
  obtained with the largest fuel weight
• Fly at maximum L/D

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PROPELLER-DRIVEN RANGE BREGUET FORMULA
Structures and Materials
Propulsion
Aerodynamics
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PROPELLER-DRIVEN ENDURACE BREGUET FORMULA

• To maximize endurance
• Largest propeller efficiency, h
• Lowest possible SFC
• Largest fuel weight
• Fly at maximum CL3/2/CD
• Flight at sea level

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JET-POWERED RANGE AND ENDURANCE

• TSFC Weight of fuel consumed per thrust per unit
  time

• ENDURANCE To stay in air for longest amount of
  time, use minimum number of pounds of fuel per
  hour

• Minimum lb of fuel per hour obtained with minimum
  thrust
• Maximum endurance for a jet-powered airplane
  occurs when airplane is flying at minimum thrust
  required
• Maximum endurance for a jet-powered airplane
  occurs when airplane is flying at a velocity such
  that CL/CD is a maximum

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JET-POWERED RANGE AND ENDURANCE

• TSFC Weight of fuel consumed per unit power per
  unit time

• RANGE To cover longest distance use minimum
  pounds of fuel per mile

• Minimum lb of fuel per hour obtained with minimum
  Thrust/V8
• Maximum range for a jet-powered airplane occurs
  when airplane is flying at a velocity such that
  CL1/2/CD is a maximum

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JET-POWERED RANGE BREGUET FORMULA

• To maximize range
• Minimum TSFC
• Maximum fuel weight
• Flight at maximum CL1/2/CD
• Fly at high altitudes

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JET-POWERED ENDURACE BREGUET FORMULA

• To maximize endurance
• Minimum TSFC
• Maximum fuel weight
• Flight at maximum L/D

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SUMMARY ENDURANCE AND RANGE

• Maximum Endurance
• Propeller-Driven
• Maximum endurance for a propeller-driven airplane
  occurs when airplane is flying at minimum power
  required
• Maximum endurance for a propeller-driven airplane
  occurs when airplane is flying at a velocity such
  that CL3/2/CD is a maximized
• Jet Engine-Driven
• Maximum endurance for a jet-powered airplane
  occurs when airplane is flying at minimum thrust
  required
• Maximum endurance for a jet-powered airplane
  occurs when airplane is flying at a velocity such
  that CL/CD is a maximum
• Maximum Range
• Propeller-Driven
• Maximum range for a propeller-driven airplane
  occurs when airplane is flying at a velocity such
  that CL/CD is a maximum
• Jet Engine-Driven
• Maximum range for a jet-powered airplane occurs
  when airplane is flying at a velocity such that
  CL1/2/CD is a maximum

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EXAMPLES OF DYNAMIC FLIGHT PERFORMANCE

• Take-Off Distance
• Turning Flight

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TAKE-OFF AND LANDING ANALYSES (6.15)
Rolling resistance mr 0.02
s lift-off distance
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NUMERICAL SOLUTION FOR TAKE-OFF
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USEFUL APPROXIMATION (T gtgt D, R)
sL.O. lift-off distance

• Lift-off distance very sensitive to weight,
  varies as W2
• Depends on ambient density
• Lift-off distance may be decreased
• Increasing wing area, S
• Increasing CL,max
• Increasing thrust, T

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TURNING FLIGHT
Load Factor
R Turn Radius
w Turn Rate
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EXAMPLE PULL-UP MANEUVER
R Turn Radius
w Turn Rate
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V-n DIAGRAMS
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STRUCTURAL LIMITS
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INTRODUCTION TO AEROSPACE STRUCTURES
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READING AND HOMEWORK ASSIGNMENTS

• Reading Assignment Introduction to Flight
• For this weeks lecture Chapter 10, Sections
  10.1-10.6
• For next week No Reading
• Lecture-Based Homework Assignment
• Problems 10.1, 10.2, 10.3, 10.4, 10.5
• DUE Monday, May 4 by 5 pm
• Turn in hard copy of homework
• Last homework assignment will count for extra
  credit
• Also be sure to review and be familiar with
  textbook examples in Chapter 10

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HOMEWORK SOLUTIONS

• 10.1
• AM-350 Stainless Steel Rod Dl 6.586 x 10-3 ft
• 2024 Aluminum Rod Dl 1.785 x 10-2 ft
• Aluminum rod will elongate most, by a factor of
  2.71
• 10.2 8,836 lb
• 10.3 Nose Gear 1,091 lb/in2, Main Gear 304.2
  lb/in2
• 10.4 2,940 lb/in2
• 10.5 33,320 lb/in2

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MOTIVATION WHERE HAVE WE ALREADY SEEN STRUCTURES?

• Nov. 12, 2001 crash of American Airlines Flight
  587 was world's worst single-plane crash in a
  decade
• Government pointed to pilot error as one possible
  cause, but new report says Airbus A300-600's
  composites, material that makes up tail, could
  have been culprit
• In theory, airplane should be able to withstand a
  sudden yaw, yet it is well known that severe and
  dangerous horizontal gust loads can be imposed on
  vertical stabilizers under some flight
  conditions. That is why they have computer
  monitoring of airspeed so as to reduce limit of
  rudder movement, on modern airliners  because
  structural limits of vertical stabilizer can be
  exceeded if rudder throw is too great when
  accompanied by a severe side loading
• http//www.ntsb.gov/events/2001/AA587/default.htm

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MOTIVATION WHERE HAVE WE ALREADY SEEN STRUCTURES?

• How thick should we make tank walls?
• Cannot burst from propellant pressure but must be
  light weight
• How to design Orbiter forward and aft attachment
  brackets?

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PHYSICS OF SOLID MATERIALS BASIC DEFINITIONS

• When external force is applied to a solid ? shape
  or size of solid tends to change
• Molecules within solid resist this change as an
  internal force
• Internal force per unit area is called stress
  (ex. N/m2, same units as pressure)
• 3 general classes of stress
• (a) Compression
• (b) Tension
• (c) Shear

Compressive and Tensile Stresses (s) act
perpendicular to cross-sectional area, A
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PHYSICS OF SOLID MATERIALS BASIC DEFINITIONS
Rod can compress
Rod can buckle
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COMPLEX BUCKLING
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PHYSICS OF SOLID MATERIALS BASIC DEFINITIONS

• When an external force is applied to a solid,
  shape or size of solid tends to change
• Molecules within solid resist this change as an
  internal force
• Internal force per unit area is called stress
  (ex. N/m2, same units as pressure)
• 3 general classes of stress
• (a) Compression
• (b) Tension
• (c) Shear

Shear Stress (t) act tangentially to
cross-sectional area, A
F
F
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DESIGN FOR SHEAR?

• Engine/wing attachment pins are designed to shear
• In event of a massive engine breakup, pins shear
  allowing engine to fall away from plane before it
  can destroy wing

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PHYSICS OF SOLID MATERIALS BASIC DEFINITIONS

• When compressive or tensile stresses act on
  material, material tends to change shape and size
• Example compressive or tensile stress act on rod
  ? length of rod changes

• Change in length per unit length is called
  strain, e
• For most materials (up to a certain limiting
  value of stress, called yield stress), stress is
  directly proportional to strain
• Equation is called Hookes law
• Proportionality constant, E is called modulus of
  elasticity or Youngs modulus

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PHYSICS OF SOLID MATERIALS BASIC DEFINITIONS

• When shear stresses act on material, material
  tends to change shape and size

• Equal and opposite shear stresses, t, act on
  vertical sides of segment, set up C.C.W. moment
• For equilibrium, equal and opposite moment must
  be set up by induced shear, ti, on top and bottom
  sides of segment
• Measure of deformation is angle, q, called
  shearing strain (given in units of radians)
• Up to a certain limit, shear stress is
  proportional to strain
• Proportionality constant, G, is called shear
  modulus or modulus of rigidity

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SUMMARY TENSION AND COMPRESSION

• Compressive and Tensile Stresses (s) act
  perpendicular to cross-sectional area, A
• Change in length per unit length is called
  strain, e
• For most materials (up to a certain limiting
  value of stress, called yield stress), stress is
  directly proportional to strain
• Equation is called Hookes law
• Proportionality constant, E is called modulus of
  elasticity or Youngs modulus

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ADDITIONAL EXAMPLES CANTILEVERED BEAM

• Many examples involve combinations of
  compressive, tensile and shear stress
• Consider cantilevered beam in neutral position,
  no forces act (neglecting weight (gravity))
• Beam is bent upward by applied load, F
• Top surface ? compressive stress
• Bottom surface ? tensile stress
• These stresses are transferred to wall junction
• At wall shear stress exists due to upward applied
  load
• Wall must be able to handle all stresses caused
  by upward applied load

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EXAMPLE LIFT DISTRIBUTION
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EXAMPLE NASA HELIOS

• Helios Proof-of-concept solar-electric flying
  wing, designed to operate at extremely high
  altitudes for long duration, remotely piloted
  aircraft
• Helios Prototype designed to fly at altitudes of
  up to 100,000 feet on single-day atmospheric
  science and imaging missions, as well as perform
  multi-day telecommunications relay missions at
  altitudes from 50,000 to 65,000 feet.
• Helios Prototype set world altitude record for
  winged aircraft, 96,863 feet, during a flight in
  August 2001
• Flight at 100,000 ft. is quite similar to that
  expected in the Martian atmosphere, so data
  obtained from the record altitude flight will
  also help to build NASA's technical and
  operational data base for future Mars aircraft
  designs and missions

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NOMINAL FLIGHT

• Wingspan 247 ft, Chord 8ft, Wing Thickness 12
  of Chord, Wing Area 1,976 ft2
• Airspeed 19 to 27 MPH cruise at low altitudes,
  up to 170 MPH at extreme altitude
• Altitude Up to 100,000 ft., typical endurance
  mission at 50,000 to 70,000 ft.
• Aspect Ratio 30.9

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EXAMPLE NASA HELIOS
This view of the Helios Prototype from a chase
helicopter shows abnormally high wing dihedral of
more than 30 feet from wingtip to the center of
the aircraft that resulted after the Helios
entered moderate air turbulence on its last test
flight. The extreme dihedral caused aerodynamic
instability that led to an uncontrollable series
of pitch oscillations and over-speed conditions,
resulting in structural failures and partial
breakup of the aircraft.
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EXAMPLE NASA HELIOS, JUNE 26, 2003
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MATERIAL TESTING

• Consider tests of various wires made of same
  material
• Measure applied load, and corresponding
  deformation

P
L
LDL
P
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HOW DO WE MEASURE?
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LOAD-DISPLACEMENT CURVES

• Consider same test on several different size
  wires made of same material

1
3
2
A1
A2
A3
lt
lt
Not very convenient as a design tool need a
different graph for each different size wire
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STRESS (s) STRAIN (e) CURVE

• Plot data from previous wire example using
  definitions of stress and strain

? Results of testing from any one wire can be
generalized to describe response of all wires
made of same material!
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STRESS-STRAIN CURVES

• Note data on previous page only considered
  relatively small loads
• Typical stress-strain curve showing response up
  to failure is more complex

From N. E. Dowling, Mechanical Behavior of
Materials, 2nd ed., Prentice-Hall, 1999
52
STRESS-STRAIN DIAGRAM
stu
s ? Ee
sty
s Ee
When stress is relieved material will return to
original shape No permanent structural deformation
When stress is relieved Material does not return
to original shape Permanent structural deformation
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CHARACTERIZATION

• Elastic Modulus, E
• Slope of initial linear region
• Yield Strength, sty
• Point where stress-strain behavior deviates from
  linearity
• Permanent deformation
• Ultimate Strength, stu
• Maximum stress at any point of curve

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SIMPLE EXAMPLE

• A 24-inch long rod is made from an aluminum
  material has following properties
• Modulus of Elasticity, E 11x106 psi
• Tensile yield strength, sty 47x103 psi (end of
  linear region)
• Ultimate tensile strength, stu 68x103 psi
  (rupture)
• Aluminum rod has a cross-sectional area, Acs, of
  0.25 in2 and supports a force P in tension as
  shown below

24 inches
P
P

• Questions
• Given P 8 kip 8,000 lb, find stress in rod?
• Given P 8 kip, find elongation of rod, DL?
• If P is increased to 16 kip 16,000 lb, can
  elongation of rod be determined from given
  information?

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SIMPLE EXAMPLE
24 inches
P
P

• Question 1
• Given P 8 kip 8,000 lb, find the stress in
  the rod?
• Note s lt sty (linear region. sty 47,000 psi)

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SIMPLE EXAMPLE
24 inches
P
P
Question 2 Given P 8 kip, find elongation of
rod, DL?
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SIMPLE EXAMPLE
24 inches
P
P

• Question 3
• If P is increased to 16 kip 16,000 lb, can
  elongation of rod be determined from given
  information?
• No we cannot determine elongation of rod
• Now in inelastic range where our linear formula
  (s Ee) does NOT hold

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STRENGTH How much load a structure can support
without breaking (rupture)?

• Some key questions
• What sort of wire should we use?
• How big should it be?

Help Me!
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QUICK EXAMPLE
Shark
1.2 mm
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SATISFACTORY APPROACH?

• Living on the edge
• No allowances for
• Imprecision in weight
• Defects in material, deviation from tested value
• Unknown unknowns

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FACTOR OF SAFETY

• Buffer in design to allow for variations in
  loading, strength of material
• Specified by governing agency (e.g. FAA, etc.)
• May be different values for different aspects of
  design
• Some typical values
• Bridges 3
• Mechanical Systems 2
• Airplanes 1.5
• Some missiles/drones 1.25
• Some useful Definitions
• Limit Load Largest loads actually expected in
  service
• Ultimate Load (Design loads)
• Ultimate Load Limit Load x Factor of Safety

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QUICK EXAMPLE INCLUDING F.S.
1.7 mm

• Other trade-offs
• Cost, availability, standard sizes versus custom
  made, weight, etc.

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STRESS-STRAIN CURVES
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AXIAL TENSION EXAMPLE
P
P

• ¼ ? ¾ balsa wood bar in simple tension
• Given tensile ultimate strength ?tu 1,500 psi
• Force to break Pu ?tu A
• Pu 1,500 psi (0.1875 in2) 281 lb
• Can you break it?

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STRUCTURAL LIFE

• Suppose a sample of material is loaded in
  following way
• Can we do this forever without breaking part?
• ? Probably Not
• Cyclic loading tends to reorganize internal
  defects, eventually collecting them together to
  form cracks, which continue to grow until they
  eventually weaken structure enough that it fails
• ? Called Fatigue

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FATIGUE S-N CURVES

• Plot shows number of cycles of loading required
  for failure for various stress levels

Ultimate yield stress Material breaks in 1 cycle
As maximum stress is made small than
ultimate stress, material can go through more
cycles before breaking

• Plot shows data for joints and splices for
  7075-76 aluminum alloy

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HIGH CYCLE FATIGUE (HCF) IN GAS TURBINE ENGINES

• HCF results from vibratory stress cycles at
  frequencies which can reach thousands of cycles
  per second and can be induced from various
  aeromechanical sources
• Widespread phenomenon in aircraft engines that
  leads to premature failure of major engine
  components (fans, compressors, turbines) and in
  some instances has resulted in loss of total
  engine and aircraft.

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ADDITIONAL EXAMPLES THERMAL STRESSES

• Beam constrained by two unmovable walls
• Heat added at some location
• When material gets hotter, volume expands
  (thermal expansion)
• But no room for body to move since constrained by
  both walls
• Compressive stress is induced in material to
  produce a strain that cancels thermal expansion
• If body is locally cooled ? thermal contraction ?
  induced tensile stress

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EXAMPLE OF THERMAL STRESSES
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AEROTHERMODYNAMIC HEATING

• Concern
• At high Mach numbers, is aerothermodynamic
  heating of vehicle a concern?
• Evaluation Approach
• Simplest explanation of aerothermodynamic heating
  is derived from concept of stagnation, or total,
  temperature
• Stagnation value is value temperature reaches in
  an adiabatic flow decelerated to zero speed
• Stagnation temperature provides estimate of
  heating
• Governing Equations

Mach Number is dependent on ambient air
temperature At Sea Level a (1.4287300)1/2
350 m/s At h 10 km a (1.4287200)1/2 283
m/s For same V, M increases with altitude due to
T decrease Total temperature is a function of
M2 Rises very rapidly with increasing M As
altitude increases, T decreases and helps heating
71
Tt vs. M0 at SEA LEVEL
72
IMPLICATIONS HIGH SPEED AERODYNAMICS

• Total temperature rises rapidly with increasing
  Mach number
• For M0 up to about 3.2 aerothermodynamic heating
  not be a major issue
• Phoenix air-to-air missile (Mach 5)
• Launched at higher altitude, say T150 K, missile
  feels Tt 900 K
• X-15, M6, Tt 1230 K at altitude
• Consider rocket car land speed record, M1.02
  No-over-heating problems
• An important parameter is geometry of nose
• Basic result of high-speed aerodynamics shows
  that heat transfer at nose is inversely
  proportional to radius of nose
• For speeds M lt 2.2 aluminum may be used
• For speeds M gt 2.4 skin temperatures get so hot,
  titanium must be used

73
AERODYNAMIC IMPLICATIONS
M8 3
M8 20

• At very high Mach numbers, nose is more rounded
  than ideal low-drag shape in order to spread high
  temperatures over a larger area and prevent nose
  from melting
• Note that structures and aerodynamics are
  inherently linked in this example

74
EXAMPLE SR-71 (YF-12)

• SR-71107 feet 5 inches long and can fly at Mach
  3 at altitudes of 80,000 feet
• After landing it is too hot to be touched for
  about 30 minutes
• SR 71 is several inches longer after flight than
  at takeoff
• In some places skin is corrugated, not smooth.
  Thermal expansion stresses of smooth skin would
  result in aircraft skin splitting or curling. By
  making surface corrugated, skin allowed to expand
  vertically and horizontally without overstressing
• Due to great temperature changes in flight,
  fuselage panels were essentially loose. Proper
  alignment only achieved when airframe warmed up
  and airframe then expanded several inches

75
AIRPLANE STRUCTURAL ELEMENTS
76
AIRPLANE STRUCTURAL ELEMENTS
77
WING BOX EXAMPLE
78
EXAMPLE WING STRUCTURE
Main Spar
Weight Savings
79
REFERENCES

• http//www.nasa.gov/centers/dryden/history/pastpro
  jects/Erast/helios.html
• http//www.nasa.gov/centers/dryden/news/FactSheets
  /FS-068-DFRC.html
• http//www.big-boys.com/articles/oknowwhat.html