AE 2350 Lecture Notes

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AE 2350 Lecture Notes 9

• May 10, 1999

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We have looked at..

• Airfoil aerodynamics (Chapter 8)
• Sources of Drag (Chapter 8, 11 and 12)
• Look at the figures on Chapter 11 and 12
• Induced Drag on finite wings (Chapter 9)
• Wave Drag, Profile Drag, Form drag, Interference
  Drag
• Airfoil and Aircraft Drag Polar
• High Lift Devices (Read Chapter 14)

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AERODYNAMIC PERFORMACE

• Performance is a study to see if the aircraft
  meets the all requirements.
• Level Flight (Is there enough thrust?)
• Climb Performance (Will it meet the requirement
  that the aircraft can gain altitude at a required
  rate given in feet/sec?)
• Range (How far can it fly without refueling?)
• Takeoff and Landing Requirements
• Others (e.g. Turn radius, Maneuverability)
• Read Chapter 15

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Your Fighter Has Certain Requirements

• Level Flight at a Maximum Speed of Mach 2 at
  30,000 feet altitude.
• Range (1500 Nautical Mile Radius with 45 Minutes
  of Fuel Reserve)
• Takeoff (6000 foot Runway with a 50 foot obstacle
  at the end)
• Landing (6000 foot Runway)
• Will your fighter do the job?

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Level Flight Performance

• You are doing this in Homework 5
• Steps
• Select a cruise altitude. Compute the speed of
  sound a?
• Select a set of M? 0.4, 0.6, 0.8.2.0
• Find Aircraft Speed M ? times a?
• Assume maximum gross weight GW is given or known.
• Find CL GW / (1/2 r? V?2 S)
• Find CD CD,0 CL2/(p AR e) Use a CD,0 of
  0.01 below M? 0.8, CD,0 of 0.02 at M? 1.2, 0.03
  at M? 1.6. Interpolate CD,0 linearly at other
  M?. .
• The quantity e is Oswald efficiency factor. Use
  0.9.
• Find Thrust required CD (1/2) r? V?2 S
• Plot Thrust Required vs. Speed
• Plot Thrust Available for your Engine at this
  altitude and Speed (Supplied by Engine
  Manufacturer)
• Where these two curves cross determines maximum
  and minimum cruise speeds

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Level Flight Performance
Thrust Required
Thrust Available with all engines
Drag (lbs)
Excess Thrust
Aircraft Speed (Knots)
Best speed for longest endurance flights since
the least amount of fuel is burned
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Maximum Rate of Climb
Drag (lbs)

• Find Excess Thrust from previous figure.
• Excess Power Excess Thrust times Velocity
• This power can be used to increase aircraft
  potential energy or altitude
• Rate of ClimbExcess Power/GW

Excess Thrust
Aircraft Speed (Knots)
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Cruise Speed for Maximum Range
V? L/D
Speed for maximum range
Aircraft Speed (Knots)
From your level flight performance data plot V?
L/D vs. V? As will be seen later, the speed at
which V? L/D is maximum gives maximum range.
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Factors that Affect Range
We assume that a cruise Mach number and altitude
has been selected. For your fighter design, you
may choose the cruise Mach number to be whatever
you want it to be, between 0.8 and 1.6, since it
was not given. Transport aircraft designers
usually select the Mach number that maximizes
range as the cruise Mach number. Older fighters
F-15, F-14 etc. cruise at or below Mach 0.8, to
keep the wave drag small, and keep the V? L/D
high. F-22 and the Eurofighter can cruise at
Mach 1.6 without using afterburners. This is
called Supercruise. While such a high cruise
speed is attractive, other aspects of performance
suffer. You may end up with a small AR wing to
keep wave drag small. A small aspect ratio wing
will have excessive induced drag, have a low
CLmax, and long takeoff and landing distances.
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Calculation of Range
We have selected a cruise V?. Over a small
period of time dt, the vehicle will travel a
distance equal to V? dt The aircraft weight will
decrease by dW as fuel is burned. If we know the
engine we use, we know the fuel burn rate per
pound of thrust T. This ratio is called
thrust-specific fuel consumption (Symbol used
sfc or just c). dt Change in the aircraft
weight dW/(fuel burn rate) dW / (Thrust
times c) dW/(Tc) Distance Traveled during
dtV?dW/(Tc) V? W/T(1/c) dW/W
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Calculation of Range (Contd)

• From previous slide
• Distance Traveled during dtV?W/T(1/c) dW/W
• Since TD and WL, W/T L/D
• The aircraft is usually flown at a fixed L/D.
• The L/D is kept as high as possible during
  cruise.
• Distance Traveled during dt V?L/D(1/c) dW/W

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Calculation of Range (Contd)

• From previous slide
• Distance Traveled during dt V?L/D(1/c) dW/W
• Integrate between start of cruise phase, and end
  of cruise phase. The aircraft weight changes from
  Wi to Wf.
• Integral of dx/x log (x) where natural log is
  used.
• Range V?L/D(1/c) log(Wi/Wf)

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Breguet Range Equation
Structures Weights Group/ Designer
Responsibility to keep Wf small.
Propulsion Group/ Designer Responsibility to
choose an engine with a low c
Aerodynamics Group/ Designer Responsibility to
maximize this factor.
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Estimating Fuel Weight in Cruise

• Given the range, engine fuel consumption c (in
  lb mass of fuel per hour per lb force of thrust),
  and V? L/D we can find Wi/Wf
• Use V? L/D at the cruise speed you selected. Use
  L GW, D is found from the level flight
  performance chart you prepared, at this speed.
• Assume Wi 99 of GW since some fuel is used
  during takeoff.
• After you have found Wf, compute Wi-Wf.
• This is the amount of fuel used in cruise.

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Estimating Fuel Reserve

• Use Breguet range equation again.Use
  Range/V? 0.75 hours
• Use for Wi, the value Wf at the end of cruise.
• Find Wf. Wi - Wf is the reserve fuel.

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Total Fuel Weight

• Total fuel weight is the sum of fuel burned
  during take-off( 1 of GW), cruise and reserve.
• In the previous slides we found fuel burned
  during cruise, and fuel needed as reserve.
• Add these three up to get the total fuel weight.

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Improved GW Estimate

• Until now we only had a guess for GW from
  historical data.
• We can improve this guess, as follows.
• Assume a empty weight Ks A (GW)B
• Use A 1.605, B0.916 if T/GW gt 0.9
• Use A 0.911, B0.947 if T/GW lt 0.9
• T Maximum Engine Thrust, with afterburners.
• This curve fit is from existing data.
  http//www.aoe.vt.edu
• Ks Technology factor. Use 0.75. A lower value
  means improved light weight technology (e.g. all
  composite construction).
• Improved GW estimate Empty Weight Fuel Weight
  Crew Weight Payload
• Use this GW to revise steady flight performance,
  fuel weight etc.
• Iterate Correct the fuel and empty weight that
  depend on GW.