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Content
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Guidance
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Reasoning
Aircraft weight, and its accurate prediction, is critical asit affects all aspects of performance, manufacturingcosts, selling price and all other items.
Designer must keep weight to a minimum as far aspractically possible.
Preliminary estimates possible for take-off weight,empty weight and fuel weight using basic requirement,
specification (assumed mission profile) and initialconfiguration selection.
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Glossary
5
AFM: Aircraft flight manualMTOW: Maximum takeoff weight
MEW: Manufacturers empty weight
MZFW: Maximum zero-fuel weight
MLW: Maximum landing weight
BOW: Basic operating weight
FAR: Federal Aviation Regulation
L/D: Lift-to-drag ratio
WTO: Weight at takeoff
WPL: Payload weight
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Some Tasks in the Conceptual Design
6
Sensitivity study (Wto to Wpl,We, R, S.F.C(Cj), and L/D)
Estimating
T/W, W/S
Configuration
selection
Design of cockpit and
the fuselage
Design of the
wing
Landing gear design
Cost prediction
Selection Integration
of the Propulsion
system
Design of stabilizers
and control
surfaces
Estimation of cg
variation and
airplane inertias
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Structural layout
Preliminary drag and
weight estimation (CD0,
We,Wto,Wf)
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This course material is concerned with
7
Sensitivity study (Wto to Wpl,We, R, S.F.C(Cj), and L/D)
Estimating
T/W, W/S
Configuration
selection
Design of cockpit and
the fuselage
Design of the
wing
Landing gear design
Cost prediction
Selection Integration
of the Propulsion
system
Design of stabilizers
and control
surfaces
Estimation of cg
variation and
airplane inertias
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Structural layout
Preliminary drag and
weight estimation (CD0,
We,Wto,Wf)
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Manufacturers Empty Weight:
Weight of the structure, powerplant, furnishings, systems and other items of
equipment that are an integral part of a particular aircraft configuration. It is
essentially a dry weight, including only those fluids contained in closed
systems.
Includes:
- airframe, systems
- closed system fluids
- seats, seat belts
- seller-furnished emergency equipment
- fire extinguishers
Does not include:- galley structure, ovens, inserts, etc.
- escape slides
- life rafts, life vests
- portable oxygen bottles
- fluids like engine oil, trapped fuel, potable water
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Standard Items:Equipment and system fluids which are not considered an integral
part of a particular aircraft configuration, are not included in the
MEW, but which do not normally vary for aircraft of the same type.
Standard items may include, but are not limited to:- unusable fuel, oil, and engine injection fluids
- unusable drinking and washing water
- first aid kits, flashlights, megaphone, etc
- emergency oxygen equipment
- galley/bar structure, inserts, ovens, etc.
- electronic equipment required by the operator
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Operational Items:
Personnel, equipment and supplies necessary for a particular
operation but not included in theBasic Empty Weight. These items
may vary for a particular aircraft and may include, but are not
limited to:
- flight and cabin crew plus their baggage- manuals and navigation equipment
- removable service equipment:
cabin (blankets, pillows, literature, etc.)
galley (food, beverages, etc.)- usable drinking and washing water
- toilet fluid and chemical
- life rafts, life vests, emergency transmitters
- cargo containers, pallets, and/or cargo tiedown equipment if used.
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Weight Definitions
disposable load =payload+useable fuel (+any necessary ballast)
Where
Payload= the revenue earning load
Maximum ramp weight:MTOW +start, taxi, and run-up fuel
Maximum ramp weight is that approved for ground maneuver
Maximum landing weight:maximum weight approved for touchdown
Maximum zero fuel weight: Maximum weight allowed before usable fuel mustbe loaded in defined sections of the aircraft. Any weight added above the MZFW
must be only due to fuel.
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APS weight (aircraft prepared for service), which is the same as the basic emptyweight, i.e. fully equipped operational, without crew, usable fuel or payload (the
load that generates revenue, income).
AUW, Wo The all-up (gross) weight is the maximum weight at which flight
requirements must be met.
Maximum to take-off weight = gross (all-up) weight = MTOW
= operating empty weight+ disposable load
in which operating empty weight and disposable load are built up as follow
Basic empty weight =Manufactures weight +standard items
Operating empty weight= basic empty weight+ operational items
(From an equipment standpoint, the airplane is ready for operation.)
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The maximum allowable weights that can legally be used by agiven airline are listed in the AFM, and Weight and Balance
Manual; these are called the airplanes Certified Weight Limits:
Maximum weights chosen by the airline
Some airlines refer to these as the purchased weights Certified weight limits are often below the structural limits
Airlines may buy a certified weight below structural capability
because many of the airport operating fees are based on the airplane's
AFM maximum allowable weight value. Typically the purchase priceis a function of the certified weight bought
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The maximum allowable Operational Takeoff Weight may belimited to a weight which is lower than the Certified Maximum
Weightby the most restrictive of the following requirements:
Airplane performance requirements for a given altitude and
temperature:
- Takeoff field length available
- Tire speed and brake energy limits
- Minimum climb requirements
- Obstacle clearance requirements
Noise requirements Tire pressure limits
Runway loading requirements
Center of gravity limitations
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Weight Definitions
Take-off weight (WTO)(Roskam method)
WTO= WOE+ WF+ WPL
where:
WOE(or WOWE) = operating weight empty
WF = fuel weight
WPL = payload weight
Note that other methods (e.g. Raymer) use slightly different
terminology but same principles.
(1)
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Weight Definitions
Operating weight empty may be further broken down
into:
WOE= WE+ Wtfo + Wcrew
where:
WE = empty weight
Wtfo = trapped (unusable) fuel weightWcrew = crew weight
(2)
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Weight Definitions
Empty weight sometimes further broken downinto:
WE= WME+ WFEQ
where:
WME = manufacturers empty weight
WFEQ = fixed equipment weight
(includes avionics, radar, air-conditioning, APU, etc.)
(3)
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Weight Figures for Transport Aircraft
Aircraft MTOW (tones) MLW(tones) Basic Operating
Weight (tones)
BOW/MTOW
Jet Airliners/Transports
Airbus A319 75.5 62.5 40.6 0.537
Airbus A380 560 386 276.8 0.494
ERJ-145LR 22 19.3 12.114 0.550
Embraer 170ER 37.2 32.8 20.94 0.563
Embraer 190LR 50.3 43 27.72 0.551
Boeing 747-400ER 412.769 295.742 180.985 0.438
Boeing 767-400ER 204.117 158.758 103.1 0.505
Boeing 777-200 (HGW, GE
Engines)286.9 206.35 137.05 0.478
Boeing 777-200LR 347.452 223.168 145.15 0.418
Boeing 777-300ER 351.534 251.3 167.83 0.477
Boeing 727-200ADV 95.1 73.1 45.72 0.480
Boeing 757-200 115.65 95.25 62.10 0.537
Boeing 737-900 79.15 66.36 42.56 0.536
Boeing 787-8 219.539 167.829 114.532 0.522
Business Jets
Cessna Citation X 16.14 14.425 9.73 0.603
Dassault Falcon 50 EX 18.498 16.2 9.888 0.535
Embraer Legacy 600 22.50 18.5 13.675 0.600
Cessna Encore 7.634 6.895 4.763 0.624
Gulfstream G350 32.160 29.937 19.368 0.602
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Weight Figures for Transport Aircraft (cont.)
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Weight Figures for Fighter Aircraft
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Overview
All textbooks use similar methods wherebycomparisons made with existing aircraft.
In Roskam (Vol.1, p.19-30), aircraft classified into oneof 12 types and empirical relationship found for logWEagainst log WTO.
Categories are: (1) homebuilt props, (2) single-engine props, (3) twin-
engine props, (4) agricultural, (5) business jets, (6) regional
turboprops, (7) transport jets, (8) military trainers, (9)fighters, (10) military patrol, bombers & transports, (11)flying boats, (12) supersonic cruise.
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Overview (Cont.)
Most aircraft of reasonably conventional designcan be assumed to fit into one of the 12
categories.
New correlations may be made for new
categories (e.g. UAVs).
Account may also be made for effects of modern
technology (e.g. new materials)method
presented in Roskam Vol.1, p.18.Raymer method uses Table 3.1 & Fig 3.1 (p.13).
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RoskamsEmpty Weight Estimation Method
Category 7 Category 8
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RaymersEmpty Weight Fraction Estimation Equation
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This workflow addresses a higher fidelity approach for weight estimation!
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Process begins with guess of take-off weight.
Payload weight determined from specification.
Fuel required to complete specified mission then
calculated as fraction of guessed take-off weight.Tentative value of empty weight then found
using:
WE(tent)= WTO(guess)WPL - Wcrew - WF - Wtfo(4)
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Values of WTOand WEcompared with appropriate
correlation graph.
Improved guesses then made and process iterateduntil convergence.
Note that convergence will not occur if specification is
too demanding.
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Initial Guess of Take-off Weight
Good starting point is to use existing aircraft with similar
role and payload-range capability.
An accurate initial guess will accelerate the iteration
process.
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Payload Weight & CrewWPLis generally given in the specification and
will be made up of:
passengers & baggage; cargo; military loads (e.g.
ammunition, bombs, missiles, external stores, etc.).
Typical values given in Roskam Vol.1 p8.
Specific values for some items (e.g. weapons)
may be found elsewhere.
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Mission Fuel Weight This is the sum of the fuel used and the reserve
fuel.
WF = WF(used) + WF(res)
Calculated by fuel fraction method. compares aircraft weights at start and end of
particular mission phases.
difference is fuel used during that phase (assuming no
payload drop).
overall fraction is product of individual phase
fractions.
(5)
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1. Start & warm-up2. Taxi3. Take off4. Climb5. Cruise6. Loiter7. Descend8. Taxi
Fuel fractions for fuel-intensive phases (e.g. 4, 5 & 6 above)
calculated analytically.
Non fuel-intensive fuel fractions based on experience and
obtained from Roskam (Vol I, p12), Raymer, etc.
civil jet
transport
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Reference: Roskam Vol. I - Table 2.1Prof. Bento S. de Mattos
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Using Roskamsmethod/data for a transport jet
(Vol.I, Table 2.1):
W1/WTO= 0.99
W2/W1= 0.99
W3/W2= 0.995
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For piston-prop a/c:
For jet a/c:
where:
Ecl= climb time (hrs), L/D = lift/drag ratio, cjis sfc for jet a/c
(lb/hr/lb), cpis sfc for prop a/c (lb/hr/hp), Vcl= climb speed(mph), p= prop efficiency, W3& W4= a/c weight at start and
end of climb phase.
3
4
1lncl
clj cl
WLE
c D W
3
4
1375 ln
p
cl
clcl p cl
WLE
V c D W
(6a)
(6b)
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Initial estimates of L/D, cjor cp, pand Vcl
made from Roskam or Raymer databases for
appropriate a/c category. Alternatively, use
approximations, e.g. from
Roskam Vol.1, Table 2.1
(W4/W3=0.98 for jettransport, 0.96 to 0.9 for
fighters).
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Phase 5 (cruise)
Weight fraction calculated usingBreguet range
equations.
For prop a/c:
For jet a/c:
These give the range in miles.
(7a)
(7b)
4
5
1375 lnpcrclcl p cr
L WRV c D W
4
5
lncrclj cr
V L WR
c D W
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For jet a/c, range maximised by flying at 1.32 x
minimum drag speed and minimising sfc.
Wing operates at about 86.7% of maximum L/D value. Cruise-climbing can also extend range.
For prop a/c, range maximised by flying at minimum
drag speed and sfc.
Wing operates at maximum L/D value.
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Initial Estimates of Lift/Drag Ratio (L/D)
Using Roskam (Table 2.2selected values):
cruise loiter
Homebuilt & single-engine 8 - 10 10 - 12
Business jets 1012 12 - 14
Regional turboprops 1113 1416
Transport jets 1315 14 - 18
Military trainers 810 10 - 14
Fighters 47 69
Military patrol, bombers & transports 1315 1418
Supersonic cruise 4 - 6 79
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Jet Airplane Airplane fitted with propeller
1ln i
fj
L WR
Wc D
ln ifj
V L WE
Wc D
ln ifj
V L WR
Wc D
1ln i
fj
L WE
Wc D
In order to obtain a better estimation for the L/D ratio we shall
consider the Breguet equations for range (R) and endurance (E):
(6b) (6a)
(7a)(7b)
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2
0D D LC C kC
Considering that he TSFC does not vary with speed and that thedrag polar can be written as
After inserting into the preceding Breguet equations the above
drag polar, we obtain the L/D ratio for maximum range and
maximum endurance for a jet airplane deriving the resulting
equations and equaling them to zero:
max range 0
1 3
4 D
L A e
D C
max endurance 0
1
2 D
L A e
D C
with1
kAe
(8a) (8b)
(9a) (9b)
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with
2
0 2
0
L L L
D D
LD
D
C C CLC C
CAe D CC
Ae
Using
Diff
Differentiating with respect to CLand setting to zero
2
0
2
022
0
2
0
L L L
D L
D
L D
LL
D
C C Cd C C
C Ae AeC C Ae
dC CC
Ae
Therefore, the CDfor this condition is
0 0 01
2D D D DC C C Ae C Ae
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Specific Fuel Consumption
Jet aircraft - Initial estimates of cj (lb/hr/lb)
Using Raymer (Table 3.3):
Roskam Vol.1 Table 2.2 (p.14) gives a/c
category-specific values (see next slide).
cruise loiter
Turbojet 0.9 0.8
Low-bypass turbofan 0.8 0.7
High-bypass turbofan 0.5 0.4
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Specific Fuel Consumption
Jet aircraft - Initial estimates of cj (lb/hr/lb)
Using Roskam (Table 2.2):
cruise Loiter
Business & transport jets 0.5 - 0.9 0.4 - 0.6
Military trainers 0.5 - 1.0 0.4 - 0.6
Fighters 0.6 - 1.4 0.6 - 0.8
Military patrol, bombers,
transports, flying boats
0.50.9 0.4 - 0.6
Supersonic cruise 0.71.5 0.6 - 0.8
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Specific Fuel Consumption
Using Raymer (Table 3.4):
Take propeller efficiency (p) as 0.8 or 0.7 for
fixed-pitch piston-prop in loiter.
cruise loiter
Piston-prop (fixed pitch) 0.4 0.5
Piston-prop (variable
pitch)
0.4 0.5
turboprop 0.5 0.6
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Specific Fuel Consumption
Using Roskam (Table 2.2):
Cruise loiter
Single engine 0.50.7, 0.8 0.50.7, 0.7
Twin engine 0.50.7, 0.82 0.50.7, 0.72
Regional turboprops 0.40.6, 0.85 0.50.7, 0.77
Military trainers 0.40.6, 0.82 0.40.6, 0.77
Fighters 0.50.7, 0.82 0.50.7, 0.77
Military patrol, bombers &
transports
0.40.7, 0.82 0.50.7, 0.77
Flying boats, amphibious 0.50.7, 0.82 0.50.7, 0.77
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Specific Fuel Consumption
Better estimation for
Engine Thrust and
fuel flow
Java code and applet can be obtained @http://www.grc.nasa.gov/WWW/K-12/airplane/ngnsim.html
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Fuel fraction (W6/W5) found from appropriateendurance equation as in Phase 4.
For jet a/c, best loiter at minimum drag speed
(maximum L/D value); for prop a/c at minimumpower speed.
W7/W6= 0.99
W8/W7= 0.992
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Mission fuel used (WF(used))
8 7 6 5 34 2 1
7 6 5 4 3 2 1
ff
TO
W W W W W W W WM
W W W W W W W W (10)
(11) ( ) 1F used ff TOW M W
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WFthen found from equation (5), by adding
reserve fuel (WF,res).
This then allows for tentative value for WE(tent)
to
be found, from eq. (4).
This may be plotted with WTOon appropriate a/c
category graph to check agreement with fit.
If not, then process must be iterated untilsatisfactory.
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Two other possible mission phases may need to be
considered for certain aircraft:
maneuvering
payload drop
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Breguet range equation may be used with
range covered in turn (Rturn) from perimeter
length of a turn (Pturn) multiplied by number
of turns (Nturn).
For manoeuvre under load factor of n:
turn turn turnR N P
2
22
1turn
VP
g n
(12a)
(12b)
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Payload Drop
Treated as separate sortie phase with change intotal weight but no fuel change.
Fuel fraction taken as 1 but subsequent phases
corrected to allow for payload drop weight change.
Roskam Vol.1 pp.63-64 gives details.
e.g. if W5and W6are weights before and after
payload drops:5 34 2 1
54 3 2 1
TOTO
W WW W W
W WW W W W W
(13a)
(13b)6 5 PLW W W
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Worked Example Jet Transport
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Worked ExampleJet Transport
(Roskam Vol.1, p55)
Specification
Payload: 150 passengers at 175 lb each & 30 lb
baggage each.
Crew: 2 pilots and 3 cabin attendants at 175 lb eachand 30 lb baggage each.
Range: 1500 nm, followed by 1 hour loiter, followed
by 100 nm flight to alternate and descent.
Altitude: 35,000 ft for design range.
Cruise speed: Mach number = 0.82 @ 35,000 ft.
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Worked Example Jet Transport
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Worked ExampleJet Transport
(Roskam Vol.1, p55)
Specification (Cont.)
Climb: direct climb to 35,000 ft at max WTO.
Take-off & landing: FAR 25 field-length of 5,000 ft.
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WPL= 150 x (175 + 30) = 30,750 lb
Wcrew= 1,025 lb
Initial guess of WTOrequired, so compare with
similar aircraft:
Boeing 737-300 has range of 1620 nm for payload
mass of 35,000 lbWTO= 135,000 lbs.
Initial guess of 127,000 lb seems reasonable.
Now need to determine a value for WF, using
the fuel fraction method outlined above.
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As in earlier example, for a transport jet:
W1/WTO= 0.99
W2/W1= 0.99
W3/W2= 0.995
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Phase 4 (climb)
W4/W3= 0.98
The climb phase should also be given credit in
the range calculation. Assuming a typical climb rate of 2500 ft/min at
a speed at 275 kts then it takes 14 minutes to
climb to 35,000 ft.
Range covered in this time is approximately
(14/60) x 275 = 64 nm.
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Cruise Mach number of 0.82 at altitude of
35,000 ft equates to cruise speed of 473 kts.
Using eq. (7b):
Assumptions of L/D = 16 and cj= 0.5 lb/hr/lb
with a range of 150064 (=1436 nm) yield avalue of:
W5/W4= 0.909
4
5
lncrclj cr
V L WRc D W
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Using eq. (6b):
Assumptions of L/D = 18 and cj= 0.6 lb/hr/lb.
No range credit assumed for loiter phase.
Substitution of data into eq. (6b) yields:
W6/W5= 0.967
3
4
1lncl
clj cl
WLE
c D W
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No credit given for range.
W7/W6= 0.99
May be found using eq. (6b) again.
Cruise will now take place at lower speed and
altitude than optimumassume cruise speed of
250 kts (FAR 25), L/D of 10 and cjof 0.9 lb/hr/lb.
Gives: W8/W7= 0.965
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No credit given for range.
W9/W8= 0.992
found from eq. (8) (with additional term for
W9/W8)
= 0.992x0.965x0.99x0.967x0.909x0.98x0.995x0.99x0.99= 0.796
Using eq. (9), WF= 0.204 WTO= 25,908 lb
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Using eq. (4):
WE(tent)= WTO(guess)WPL - Wcrew - WFWtfo
WE(tent)= 127,00030,7501,02525,908 - 0
= 69,317 lb
By comparing with Roskam Vol. 1, Fig. 2.9, it is
seen that there is a good match for these values ofWEand WTO, hence a satisfactory solution has
been reached.
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Specification / design requirements often re-
evaluated and refined at this stage, using above
method.
Examples include:
Effect of a range increase/decrease on MTO. Effect of payload mass change on MTO.
Effect of using composite materials instead of
aluminium alloys. More details and examples in Raymer p.28-31 and
Ch.19.
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Essentially Roskamsversion (Vol.1, p.68) ofRaymerstrade studies detailed above.
Sensitivity of MTOis investigated with changes tothe following typical set of parameters:
Empty weight (WE), payload (WPL), range (R),
endurance (E), lift/drag (L/D), specific fuel consumption
(cjor cp) and propeller efficiency (p).
Sensitivity to general parameter y expressed by:
Regression constants used in equations are relevant
to particular a/c category.
TOW
y
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Estimating Cruise Fuel Consumption
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g p
Performance
Max operating Mach number 0.83
Max operating altitude 41,000 ft (cabin altitude: 8,000 ft)
Take-off field lenght 6,500 ft (SL / ISA + 15
C / MTOW)
Landing field 5,000 ft (SL / MLW = 90% of MTOW)
Range with max payload 2,200 nm (overall fuel volume for 3,200 nm version)
External noise FAR 36 Stage IV minus 15 db
IPET7 Airliner
Estimating Cruise Fuel Consumption
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67
g p
41000 ft
0,150
0,170
0,190
0,210
0,230
0,250
0,270
0,290
0,40 0,50 0,60 0,70 0,80 0,90
Mach
SR
[nm/kg]
MTOW 90% MTOW 80% MTOW
Long Range MMO
SR vs. Mach number 41000 ft
0,00
2,00
4,00
6,00
8,00
10,00
12,00
14,00
0,40 0,50 0,60 0,70 0,80 0,90
Mach
M*L/D
MTOW 90% MTOW 80% MTOW
Mach*L/D vs. Mach number
The number of Mach for maximum specific range (SR) is not the same as that for
maximum M*L/D because sfc increases with speed
IPET7IPET7
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TASSR
Fuel flow
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