MAE 1202: AEROSPACE PRACTICUM

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MAE 1202 AEROSPACE PRACTICUM

• Review and Introduction to Aircraft Performance
• April 13, 2009
• Mechanical and Aerospace Engineering Department
• Florida Institute of Technology
• D. R. Kirk

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MAE 1202 COMMENTS

• Only 3 lectures left
• 1.5 lectures on airplane performance
• 1.5 lectures on aircraft structures
• 2 more lecture-based homework assignments
• 1 extra homework assignment (replace lowest
  homework grade or extra credit)
• This week in laboratory Team Challenge 2
• Rocket launch contest on April 25
• Directions to Palm Bay site will be posted online
• Receive materials in laboratory this week
• Final rocket presentations in laboratory on April
  23 or April 24
• Remainder of class is pretty easy

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READING AND HOMEWORK ASSIGNMENTS

• Reading Introduction to Flight, by John D.
  Anderson, Jr.
• For this weeks lecture Chapter 6, Sections 6.1
  - 6.17
• Lecture-Based Homework Assignment
• Problems 5.21, 5.22, 5.23, 5.25, 5.26, 5.27,
  5.30
• DUE Wednesday, April 22, 2009 by 11 AM
• Turn in hard copy of homework
• Also be sure to review and be familiar with
  textbook examples in Chapter 5

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ANSWERS TO LECTURE HOMEWORK

• 5.21 Induced Drag 139.4 N
• 5.22 Induced Drag 1,200 N
• Note The induced drag at low speeds, such as
  near stalling velocity, is considerable larger
  than at high speeds, near maximum velocity.
  Compare this answer with the result of Problem
  5.20 and 5.21
• 5.23 CL 0.57, CD 0.027
• 5.25 e 0.913, a0 0.0678 per degree
• 5.26 VStall 19 m/sec 68.6 km/hour
• 5.27 cl 0.548, cl 0.767, cl 0.2
• 5.30 CL/CD 34.8

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AIRPLANE PERFORMANCE
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READING AND HOMEWORK ASSIGNMENTS

• Reading Introduction to Flight, by John D.
  Anderson, Jr.
• For this weeks lecture Chapter 6, Sections 6.1
  - 6.17
• For next weeks lecture Chapter 6
• Lecture-Based Homework Assignment
• Problems 6.1, 6.3, 6.9, 6.12, 6.16, 6.20
• DUE Wednesday, April 29, 2009 by 11 AM
• Turn in hard copy of homework
• Also be sure to review and be familiar with
  textbook examples in Chapter 6

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HOMEWORK SOLUTION

• 6.1 TR 5,174 N, TR 3,690 N
• 6.3
• Part a See plot on next page
• Part b 295 m/s
• Part c See plot on next page
• Part d 290 m/s
• 6.9 7.29 miles
• 6.12 Range 719 miles, Endurance 8.1 hours
• 6.16 Take-Off Distance 452 meters
• 6.20 Radius 305 meters, w 0.367
  radians/second

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SOLUTION FOR PROBLEM 6.3 SEA LEVEL
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SOLUTION FOR PROBLEM 6.3 5 km ALTITUDE
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FLIGHT MECHANICS LECTURE OUTLINE

• Behavior of entire airplane
• How fast can this airplane fly?
• How far can this airplane fly on a single tank of
  fuel?
• How long can this airplane stay in the air on a
  single tank of fuel?
• How fast and how high can it climb?
• How does it perform?

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4 FORCES ACTING ON AIRPLANE

• Model airplane as rigid body with four natural
  forces acting on it
• Lift, L
• Acts perpendicular to flight path (always
  perpendicular to relative wind)
• Drag, D
• Acts parallel to flight path direction (parallel
  to incoming relative wind)
• Propulsive Thrust, T
• For most airplanes propulsive thrust acts in
  flight path direction
• May be inclined with respect to flight path
  angle, aT, usually small angle
• Weight, W
• Always acts vertically toward center of earth
• Inclined at angle, q, with respect to lift
  direction
• Apply Newtons Second Law (Fma) to curvilinear
  flight path
• Force balance in direction parallel to flight
  path
• Force balance in direction perpendicular to
  flight path

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GENERAL EQUATIONS OF MOTION (6.2)
Free Body Diagram
Apply Newtons 2nd Parallel to flight path
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GENERAL EQUATIONS OF MOTION (6.2)
Free Body Diagram
Apply Newtons 2nd Parallel to flight path
Perpendicular to flight path
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STATIC VS. DYNAMIC ANALYSES

• Examine two forms of these equations
• Static Performance Zero Accelerations (dV/dt
  0, V2/rc 0)
• Maximum velocity
• Maximum rate of climb
• Maximum range
• Maximum endurance
• Dynamic Performance Accelerating Flight
• Take-off and landing characteristics
• Turning flight
• Accelerated flight and rate of climb

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LEVEL, UNACCELERATED FLIGHT
L
T
D
W

• JSF is flying at constant speed (no
  accelerations)
• Sum of forces 0 in two perpendicular directions
• Entire weight of airplane is perfectly balanced
  by lift (L W)
• Engines produce just enough thrust to balance
  total drag at this airspeed (T D)
• For most conventional airplanes aT is small
  enough such that cos(aT) 1

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LEVEL, UNACCELERATED FLIGHT

• TR is thrust required to fly at a given velocity
  in level, unaccelerated flight
• Notice that minimum TR is when airplane is at
  maximum L/D
• L/D is an important aero-performance quantity

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THRUST REQUIREMENT (6.3)

• TR for airplane at given altitude varies with
  velocity
• Thrust required curve TR vs. V8

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PROCEDURE THRUST REQUIREMENT

• Select a flight speed, V8
• Calculate CL

Minimum TR when airplane flying at (L/D)max

• Calculate CD

• Calculate CL/CD
• Calculate TR

This is how much thrust engine must produce to
fly at selected V8 Recall Homework Problem 5.6,
find (L/D)max for NACA 2412 airfoil
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THRUST REQUIREMENT (6.3)

• Different points on TR curve correspond to
  different angles of attack

At b Small q8 Large CL (or CL2) and a to support
W D large
At a Large q8 Small CL and a D large
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THRUST REQUIRED VS. FLIGHT VELOCITY
Zero-Lift TR (Parasitic Drag)
Lift-Induced TR (Induced Drag)
Zero-Lift TR V2 (Parasitic Drag)
Lift-Induced TR 1/V2 (Induced Drag)
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THRUST REQUIRED VS. FLIGHT VELOCITY
At point of minimum TR, dTR/dV80 (or dTR/dq80)
CD,0 CD,i at minimum TR and maximum
L/D Zero-Lift Drag Induced Drag at minimum TR
and maximum L/D
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HOW FAST CAN YOU FLY?

• Maximum flight speed occurs when thrust
  available, TATR
• Reduced throttle settings, TR lt TA
• Cannot physically achieve more thrust than TA
  which engine can provide

Intersection of TR curve and maximum TA defined
maximum flight speed of airplane
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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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POWER AVAILABLE (6.6)
Jet Engine
Propeller Drive Engine
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POWER REQUIRED (6.5)
PR vs. V8 qualitatively (Resembles TR vs. V8)
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POWER REQUIRED (6.5)
PR varies inversely as CL3/2/CD Recall TR
varies inversely as CL/CD
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POWER REQUIRED (6.5)
Zero-Lift PR
Lift-Induced PR
Zero-Lift PR V3
Lift-Induced PR 1/V
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POWER REQUIRED
At point of minimum PR, dPR/dV80
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POWER REQUIRED

• V8 for minimum PR is less than V8 for minimum TR

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WHY DO WE CARE ABOUT THIS?

• We will show that for a piston-engine propeller
  combination
• To fly longest distance (maximum range) we fly
  airplane at speed corresponding to maximum L/D
• To stay aloft longest (maximum endurance) we fly
  the airplane at minimum PR or fly at a velocity
  where CL3/2/CD is a maximum
• Power will also provide information on maximum
  rate of climb and altitude

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POWER AVAILABLE AND MAXIMUM VELOCITY (6.6)
Propeller Drive Engine
PA
PR
1 hp 550 ft lb/s 746 W
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POWER AVAILABLE AND MAXIMUM VELOCITY (6.6)
Jet Engine
PA TAV8
PR
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ALTITUDE EFFECTS ON POWER REQUIRED AND AVAILABLE
(6.7)
Recall PR f(r8) Subscript 0 denotes
seal-level conditions
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ALTITUDE EFFECTS ON POWER REQUIRED AND AVAILABLE
(6.7)Propeller-Driven Airplane
Vmax,ALT lt Vmax,sea-level
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RATE OF CLIMB (6.8)

• Boeing 777 Lift-Off Speed 180 MPH
• How fast can it climb to a cruising altitude of
  30,000 ft?

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RATE OF CLIMB (6.8)
Governing Equations
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RATE OF CLIMB (6.8)
Vertical velocity
Rate of Climb
TV8 is power available DV8 is level-flight power
required (for small q neglect W) TV8- DV8 is
excess power
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RATE OF CLIMB (6.8)
Jet Engine
Propeller Drive Engine
Maximum R/C Occurs when Maximum Excess Power
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EXAMPLE F-15 K

• Weapon launched from an F-15 fighter by a small
  two stage rocket, carries a heat-seeking
  Miniature Homing Vehicle (MHV) which destroys
  target by direct impact at high speed (kinetic
  energy weapon)
• F-15 can bring ALMV under the ground track of its
  target, as opposed to a ground-based system,
  which must wait for a target satellite to overfly
  its launch site.

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GLIDING FLIGHT (6.9)
To maximize range, smallest q occurs at (L/D)max
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EXAMPLE HIGH ASPECT RATIO GLIDER
q
To maximize range, smallest q occurs at
(L/D)max A modern sailplane may have a glide
ratio as high as 601 So q tan-1(1/60) 1
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RANGE 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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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 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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EXAMPLES OF GROUND EFFECT
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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