Preliminary Weight Estimation 08-05

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2. PRELIMINARY WEIGHT ESTIMATION

2.1 Background

The basic mission specifies that an airplane be designed to carry NP passengers at a

cruising speed of V miles per hour over a range of R miles using turbojet or turbofanengines. This specification actually contains all the major economic information which

will decide whether or not a particular commercial design will be successful. The

airplane itself will have an empty weight WE that we shall see is proportional to thecapital cost of the airplane. Thus this weight component is an important driver in

determining the purchase price of the airplane to a prospective buyer. The operating cost,

i.e. the expense incurred by the operator in flying the airplane, is made up of several parts

including fuel expense, crew expense, and maintenance expense. The first item is afunction of airplane design and engine performance while the last two items are

influenced by FAA requirements and tend to be dependent on the size of the airplane.

Therefore major attention will be paid to the amount of fuel necessary to operate the

airplane in accomplishing the mission specification. This factor is readily expressed asWF, the weight of fuel which must be carried by the airplane. Finally, there is the positive

factor of income generation by the airplane which is accomplished by charging a fee foreach passenger. This illustrates the importance of the payload: it is that portion of the

take-off weight WTO which contributes revenue and is proportional to the number of

passengers. Thus the payload weight WPL=kNP where kis a constant which is generally

set by the operator based upon experience and includes the weight of the typicalpassenger and accompanying baggage. Values for this factork range between 205 and

215 pounds per passenger (Torenbeek, Ref. 2-1, p.79).This value considers an average

passenger weight of 170lbs and an average luggage weight per passenger of 35lbs (short-hail flights) to 40lbs (long-haul flights. Revenue may also be produced by cargo carried

as part of the payload, but this is difficult to specify in the initial design, being dependentupon the priorities placed on cargo by different airline operators. Therefore the payload inthe initial design phase will be set by the passenger load alone as described previously.

Once the fuselage design is accomplished the volume available in the cargo hold, over

and above that necessary to accommodate the checked luggage, can be estimated. Thenthe additional payload due to freight can be included in the refined weight estimate.

2.2 Weight ComponentsThe take-off weight of the airplane is defined as WTO = WOE+ WF+ WPL where all terms

have been defined previously except for the operating empty weight of the airplane, WOE= WE + WTFO + WCREW. The operating empty weight of the airplane is the weight of theairplane in a condition ready to fly, but with no fuel or payload yet taken on board. It

therefore includes the empty weight of the airplane, WE, the weight of the trapped fuel

and oil (that is, the fuel and oil left in lines and at the bottom of tanks, etc., and thereforenecessary but unusable), WTFO , and the weight of the crew, WCREW . This last term

includes the weight of the flight crew, the flight attendants, and all their baggage. The

number of crew members is usually set by the operator with minima stipulated by the

FAA while the baggage allowance is set by the operator. Torenbeek gives a chart for

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estimating the number of passengers per flight attendant, a portion of which is given in

Table 2-1. When the number of crew members is determined, their total weight may be

found by using the weight factorkthat was used for the passengers. Different values ofk

for the flight crew and the flight attendants may be used in later design iterations, but for

preliminary design purposes it is sufficient to use the same average weight for all persons

on board, whether they are flight crew members, flight attendants, or passengers.Consideration of additional payload in the form of cargo freight will be considered

subsequently, as discussed in Section 2.1.

Table 2-1 Standard Flight Attendant Schedule

Average number of passengers per flight attendant

First Class Mixed Tourist

International Flights 16 21 31

U.S. Domestic Flights 20 29 36

The total usable fuel weight, WF, may be considered to be made up of two parts, the fuelnecessary for the mission of R miles WF,USED and the fuel reserve WF,RES . Again, the latter

is generally set by the operator within the requirements posted by the FAA. The take-off

weight may then be expressed as follows:

WTO = WE + WTFO + WPLC+ WF,USED + WF,RES (2-1)

Note the following definitions:

MTFO = WTFO/WTO

WF = WF,USED + WF,RES

MFUEL = WF/WTO

WPLC= WPL + WCREW

This expression forWTO in Eq. (2-1) may be solved forWE and the result written as

WE = (1 MTFO MFUEL)WTO WPLC (2-2)

Thus, the equation for the empty weight is that for a straight line, i.e., WE = aWTO + b.

This result is shown schematically in Fig. 2-1 where it is seen that the quantity WPLCis the

anchor point for the design of the airplane. All the possible results forWEradiate outfrom the point (0, -WPLC) and depend upon the coefficient of the WTO term.

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The remaining problem in the weight estimation process is the determination of the

coefficient of the take-off weight in the equation for empty weight. That is, the slope of

the line given by a = 1 (MTFO + MFUEL), where the term MFUEL clearly depends upon theamount of fuel used in carrying out the mission specification including the reserve

requirements. The total weight of fuel actually used is WF = WTO WFINALand

WF/WTO = 1 WFINAL/WTO = 1 - MFINAL (2-3)

This means that the fraction of take-off weight that is usable fuel is given by MFUEL = 1 -

MFINAL. The fuel fraction MFUEL may be found by applying a chain product of n stage

weight fractions as follows:

11

10 1

nFINAL i

FINAL

iTO i

W WWM

W W W=

= = = (2-4)

Figure 2-1 Empty weight as a function of take-off weight

Here we are using eleven stages to the mission: engine start and warm-up, taxi, take-off,

climb, cruise to full range, one hour additional flight at cruise conditions, descent to

destination and refused landing, climb, diversion to alternate airport 200nm distant,descent, landing. These stages are numbered and appear in the Fig. 2-2 and Table 2-1.

The normal flight plan calls only for stages 1 through 5 plus stages 10 and 11 while

stages 6 through 9 represent possible flight diversions due to poor weather or other suchsituations. These extra stages require the use of the reserve fuel which must always be

carried by the aircraft. Operational rules for determining fuel reserve requirements are set

out by the Air Transportation Association of America and are described in Appendix I.

WE

0

-WPLC

Increasing(1 M

TFO- M

FUEL)

WTO

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Figure 2-2 Mission profile showing the 11 flight stages for a domestic flight

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For purposes of illustration, this term may be approximated using information on empty

weights and numbers of passengers quoted in the literature for 41 operational jet airliners

as follows:

1TO E PLC E PLC FUEL

TO TO

W W W W W M

W W

+ = (2-10)

Data using his approximation is shown in Fig. 2-3 along with a trend line given by MFUEL= 0.0048R1/2. Note that for very long range aircraft the total fuel fraction approaches half

the take-off weight. This information provides a check on the estimates being made forthe fuel requirements of the aircraft being designed.

The eleven general mission stages are described in the Table 2-1, along with Roskam's(Ref. 2-2) suggestions for applicable average weight fractions. Note that stages 6 through

9, inclusive, are typical of FAA reserve requirements and that the normal flight includes

only stages 1 through 5, plus 10 and 11. The terms used in the table are explained more

fully later in this chapter.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2000 4000 6000 8000 10000 12000

Range (miles)

1-(We+Wpl)/Wto

1-(We+Wpl)/Wto = 0.0048R^0.5

Figure 2-3 The total fuel fraction MFUEL as a function of range as estimated from

available information on 41 jet operational airliners. The solid line is anapproximate curve fit to the data shown.

The ratio of the weight of the aircraft at the end of stage i to the weight at the start of

stage i (i.e. the end of the previous stage) is Wi/Wi-1. Compilations of representativevalues for these weight fractions for all stages except the cruise stage are given in Ref. 2-

2 and appear in the Table 2-2.

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Table 2-2Weight Fractions for the Various Mission Segments

Stage Description Wi/Wi-1

1 Engine start and warm-up 0.990

2 Taxi 0.990

3 Take-off 0.995

4 Climb 0.980

5 Cruise to full range exp [-RCj/V(L/D)]

6 One hour additional flight at cruise conditions exp [-Cj/(L/D)]

7 Descent to destination and refused landing 0.990

8 Climb 0.980

9 Diversion to alternate airport 200n.m. distant exp [-230Cj/V(L/D)

10 Descent 0.990

11 Landing 0.992

Obviously it is during the cruise stage that the major portion of the fuel weight will be

consumed and therefore the details of the aircraft operating performance must be

considered. It may be noted that once the characteristics of the airplane are known ingreater detail it will be possible to more accurately determine the weight of fuel used

during climb and descent and this would be carried out in order to obtain more refined

weight estimates. For example, Fig. 2-4 shows the ratio of the weight at the end of climb

to that at the start of climb as a function of the weight at start of climb; that is, the ratioW4/W3 in Table 2-2. The values shown are taken from Shevell (Ref. 2-3), and refer to the

fuel to climb for the Douglas DC-10-10 airliner; in particular, the data for the case of

climb to 35,000 ft was used. In Table 2-2 Roskam's generic value, W4/W3=0.98, isspecified, and this is reasonably close to the more accurate values in Fig. 2-2. A

discussion of the climb and descent segments of the mission profile is presented in

Chapter 8.

Our objective is to estimate the empty weight of the design aircraft and in order to obtain

an appreciation of where the value of WE for the new design should lie within theradiating fan of lines in Fig. 2-1 it is instructive to see what historical precedents apply.

Roskam (Ref. 2-2) has collected a substantial database on existing aircraft and hasgenerated curve fits describing the relationship between WE and WTO. These resultssuggest a correlation equation of the form

( )10 10log log /E TOW W A B= (2-11)

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In Eq. (2-11) the values of A and B are constants that are different for different classes of

aircraft. For jet transport aircraft Ref. 2-2 offers A = 0.0833 and B = 1.0383, which is

actually very close to a straight line and may be approximated by the equation

0.5E TO

W W= . A database that has been compiled here for 45 operational transportsprovides the results shown in Fig. 2-5 which support this simplified result.

0.964

0.966

0.968

0.97

0.972

0.974

0.976

0.978

0 100 200 300 400 500

Gross Weight (000 lbs)

ClimbWeightFraction

Figure 2-4 The ratio of the weight at the end of climb to that at the start of climb

as a function of the gross weight at start of climb; that is, the ratio W4/W3 of Table

2-1. The values shown are taken from Shevell (Ref. 2-3), for the Douglas DC-10-

10 airliner; in particular, the data for the case of climb to 35,000 ft was used.

It must be kept in mind that this simple correlation is based on wide variety ofcommercial aircraft built over a fairly long period of time and the scatter, though

appearing small on Fig. 2-5, is in the range of up to tens of thousands of pounds. When

the focus is narrowed to the particular class of market survey aircraft considered, thescale of the graph of WE vs. WTO will be larger and the deviations from the historical

curve more evident. The utility of a correlation of this type is in its ability to provide a

guideline for the development of a new design.

There is a slight nonlinearity in the relationship of empty weight to take-off weight that is

not apparent in Fig. 2-5, but is made clearer in Fig. 2-6. There the correlation

0.079

0.821000

e to

to

W W

W

=

(2-12)

is shown to fit the actual data better than the simple approximation 0.5e

to

W

W= .

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0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400. 0

Take-off weight, Wto (klbs)

Emptyweight,We(klbs)

Actual weights

logWe=(logWto - A)/B

e=0.5Wto

Figure 2-5 Empty weight versus take-off weight for 45 operational transports

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0

Take-off weight, Wto (klbs)

Emptyweightfraction,

We/Wto

We/Wto = 0.82/(Wto)^.079

Figure 2-6 Variation of the empty weight fraction We/Wto with take-off weightWto for the 45 transports of Fig. 2-4 illustrating the slight nonlinearity of the

relationship between the empty weight and the take-off weight.

As an additional indicator of the design range for the new aircraft under considerationone may make use of the characteristics of the three or four market survey aircraft that

have a similar mission. Since the empty and take-off weights are known for these aircraft

they may be represented as discrete points on a WE vs. WTO plot. Those points, whichrepresent the aircraft most like the design aircraft, serve to further limit the probable

region of the design plot where the new aircraft will fall. This is shown in Fig. 2-7.

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Figure 2-7 Estimation of empty weight using empirical weight relations and

characteristics of market survey aircraft which are shown as circular symbols

2.3 Fuel Consumption in Cruise

A discussion of the Breguet range equation suitable for this stage of the investigation is inChapter 8 and it may be written as follows:

4

5

loge

j

WV LR

C D W

= (2-13)

This form is applicable to aircraft powered by turbofan or turbojet engines; here R is the

range, Vis the cruise speed, L/D is the lift to drag ratio, and Cj is the thrust specific fuel

consumption. All the variables in the equation are to be evaluated under cruise

conditions. The fuel weight fraction expended during cruise may be obtained from theabove equation in the following form:

1

5

4

expj

W V LR

W C D

=

(2-

14)

In this equation the units must be consistent, for example, R in miles, Vin miles per hour,and Cj in pounds fuel per hour per pound of thrust, so that the argument of the

exponential function is dimensionless. One may now determine a value for W5/W4,W6/W5, and W9/W8 and therefore MF for the prescribed range if one picks a set of values

forV, Cj, and L/D. A range of representative values for some of these parameters may be

WE

0

-WPLC

WE=aW

TO+b

WTO

WE=0.504W

TO

Market survey aircraft

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found in Refs. 2-1 and 2-2. Of course, wherever possible, it is preferable to use

information from the market survey aircraft to improve the estimates for these values.

2.4 Selection of Cruise Performance Characteristics

The cruise speed Vshould be as high as is reasonable, remembering that the drag riseswith the square of the speed and the engines selected later on in the design process must

provide the thrust to overcome this drag. At the speeds considered for jet transports it is

preferable to consider the cruise Mach number since the drag is a strong function of theMach number. Furthermore, the commercial jet transports considered here generally

cruise in the stratosphere where the atmospheric temperature, and therefore the speed of

sound, is approximately constant, so it is also convenient to work with the cruise Mach

number. Standard atmospheric profiles may be used in the design process, as shown inAppendix J. Typical cruise Mach numbers are in the range of 0.76


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probably confining the maximum value to 16.

Loftin (Ref. 2-4) discusses the estimated L/D for the Boeing B-707 and the Douglas DC-

8, which he gives as 19.0-19.5 and 17.9, respectively. He suggests that the additionallength of the DC-8 fuselage increases the total wetted area of the airplane and therefore

the profile drag coefficient CD,0, thereby bringing down L/D. The Boeing 767-200 is said

to have L/D=18. Once, again, the reduction from the 19 or so of the B-707 is attributed tothe fact that the ratio of wetted surface area to wing planform area, Swet/S, is larger for the

B 767-200, although S is comparable for both. The Boeing B-747 is estimated to haveL/D=18, like the B 767-200. Other wide-body airliners, like the older Lockheed L 1011-200 and the McDonnell-Douglas MD 10-30 are estimated to have L/D values between 17

and 17.5. Heffley and Jewell (Ref. 2-5) present data on the characteristics of a number of

aircraft in cruise, as well as in power approach and landing configurations. A particular

case is that of the Convair CV-880, a medium size four jet airliner, similar to andcontemporaneous with the B 707 and DC-8 airplanes. The L/D and ML/D behavior with

Mach number is shown in Fig. 2-8. Note that although the L/D drops quite rapidly with

Mach number, the more important quantity for the range equation, ML/D ~ VL/D, drops

much more slowly.

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1

Mach Number

Power approach

Landing

Convair CV-880

L/D

ML/D

35 kft

23 kft

35 kft

23 kft

Figure 2-8 Data from Heffley and Jewell (Ref. 2-5)shows L/D and ML/D for the

Convair CV-880 jetliner at two altitudes. The L/D for power approach andlanding at sea level is also shown.

2.5 Fuel CharacteristicsJet fuel is a hydrocarbon fuel composed primarily of paraffin (approximately 70%) and

aromatic (approximately 20%) petroleum compounds. Some characteristics are shown in

Table 2-3 as taken from Ref. 2-6. The most commonly used fuel in the U.S. is Jet A andthat fuel will be used in developing the aircraft design. Fuel density is variable and fuel is

sold on a volumetric rather than a weight basis, so for it will be considered sufficient to

use the standard density shown. Some of the fuel (and lubricating oil) carried on the

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aircraft will not be drainable from the tanks and therefore is unusable. The weight of this

component has been denoted by WTFO and we need an estimate of this value to calculate

the term MTFO used in the relation between WE and WTO used to generate Fig. 2-7.Torenbeek (Ref. 2-1, p. 292) provides an expression for the weight of trapped fuel and oil

in terms of the volume of the fuel tanks on the aircraft. That expression can be converted

into an expression involving the weight of the fuel by using the value for the density ofJet A in Table 2-3. Using Torenbeeks approach on the database of 41 operational

airliners results in the data shown in Fig. 2-9, for which the following curve fit applies:

2 / 3 1/ 30.227

TFO FUEL TOM M W (2-15)

Table 2-3 Characteristics of Commonly Used Jet Fuels

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 400,000 800,000 1,200,000 1,600,000

Take-Off Weight (lbs)

Mtfo

Mtfo=0.227(Mfuel)^2/3(Wto)^-1/3

Figure 2-9 Application of Torenbeeks expression for trapped fuel and oil (Ref 2-

1, p.292) to the commercial airliner database and a curve-fit to the results

This expression forMTFO depends upon WTO (in pounds) while in the equation for WE it

was assumed that it is a constant. However, it is expected that MTFO will be small, and it

GeneralDesignation

U.S.Commercial

Designation

U.S.Military

Designation

Densityat

15C in

lb/gal

FreezingPoint in

degrees C

EnergyContent

Btu/lb

EnergyContent

Btu/gal

Wide cut

gasoline

Jet B JP-4 6.36 -50 to -58 18,720 119,000

Kerosene Jet A,

Jet A-1

JP-8 6.76 -40 to -50 18,610 125,800

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can be demonstrated that it lies in the range 0.001


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showing the relevant data for the market survey aircraft and for the design aircraft should

be provided. Of course, all of the work carried out must be described in the narrative of

the chapter.

2.7 New Materials for Weight ReductionThe need to reduce aircraft weight has manufacturers on a quest for new materials that

can outperform conventional airplane construction materials at lower weight. There is

extensive work underway to incorporate ever-greater percentages of aircraft structure tocomposite materials in particular and they are being assiduously pursued in the new 555

passenger Airbus A380 and the proposed Boeing 7E7, among others. There is still

concern about material lifetime, particularly with regard to fatigue, as well as to the

ability to affordably accommodate repair and maintenance work. There are other issuessurrounding the use of composite regarding porosity, environmental robustness, effect of

lightning strikes, and the like. A chart indicated the rapidly growing use of composites in

aircraft with the A380 using it for around 25% of total airframe weight and Boeing

proposing to use up to 50% in the B7E7. Military aircraft are leading the way in thisregard with the Bell Boeing V-22 and the Eurofighter already using composites for about

75% of the airframe weight and the F/A-22 and F/A-18E/F using between 50% and 60%.The material of choice for the Airbus A380 is glass fiber reinforced aluminum while that

for the Boeing 7E7 is carbon fiber reinforced plastic, known as CFRP. See Refs. 2-7 and

2-8.

2.8 Weight Estimation for Turboprop Powered Aircraft

The recent rapid rise in fuel prices has forced a revaluation of turboprop powered aircraft,particularly for regional airline service. For short range applications the cruise speed is

not as important in keeping travel time brief as it is for longer range flight. This becomes

apparent when one considers that most of the time in a short range flight is spent intaxiing from the gate, climbing, descending, and once again taxiing to the gate. The best

time advantage for a turbofan compared to a turboprop may be assumed to be in the ratio

of the cruise speeds, that is, about 500mph/350mph =1.43, a 90 minute flight in aturbofan would be about a 2 hour flight in a turboprop. Of course, a transcontinental

flight would be quite different, with a 6 hour flight becoming a 9 hour flight. Thus for

ranges of up to 500 or 600 miles the turboprop can deliver its good fuel economy with

relatively little passenger inconvenience. In general, the public has been moved toconsider jet aircraft to be the preferred mode of travel, even foe regional distances, so that

the question remains as to how much emphasis will be placed on returning turboprops to

a major role in airline service. At the moment the high and uncertain fuel prices aremoving airline operators to seriously consider asking aircraft manufacturers for advanced

design turboprop aircraft. The weight estimation procedures in Section 2 are still

applicable with some minor changes specific to turboprop engines. In particular, Table 2-2 showing the weight fractions for different mission segments is modified for turboprop

applications as given by Roskam (Ref. 2-2) and is shown in Table 2-4.

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Table 2-4 Weight Fractions for the Mission Segments for Turboprop Aircraft

Stage Description Wi/Wi-1

1 Engine start and warm-up 0.990

2 Taxi 0.995

3 Take-off 0.995

4 Climb 0.985

5 Cruise to full range exp [-RCp/375 p(L/D)]

6 One hour added flight at cruise conditions exp [-RCpV/375 p(L/D)]

7 Descent to destination and refused landing 0.985

8 Climb 0.985

9 Diversion to alternate airport 200n.m. distantexp [-200Cp/375 p(L/D)

10 Descent 0.990

11 Landing 0.995

The correlation between empty weight and take-off weight given by Eq. (2-12) is still

appropriate so that the only factors to deal with are the two new variables, Cp and p,appearing in Table 2-4. The quantity Cp is the specific fuel consumption of the turboprop

engine in the units of pounds of fuel per hour per shaft horsepower (lbs/hr-hp) and the

quantity p is the propeller efficiency and is dimensionless. Note that the range R is stillin miles and the velocity Vis the cruise velocity in miles per hour. The cruise speed of

turboprop commercial aircraft are in the range of 300mph to 350mph while lift to dragratios while lift to drag ratios are in the range of 14 to 18. Propeller efficiencies are in therange of 82% to 92% while specific fuel consumption is in the range of 0.5 to 0.7 lbs/hp-

hr. The procedure for estimating the take-off and empty weights follows that given

previously for turbofan aircraft.

2.8 References

2-1 Torenbeek, E.: Synthesis of Subsonic Airplane Design, Kluwer Academic

Publishers, Dordrecht, The Netherlands, 1982.

2-2 Roskam, J.: Rapid Sizing Method for Airplanes, Journal of Aircraft, Vol. 23,

No. 7, July 1986, pp. 554-560.

2-3 Shevell, R.: Fundamentals of Flight, Prentice-Hall, Englewood Cliffs, NJ, 1989

2-4 Loftin, K.: Quest for Performance The Evolution of Modern Aircraft, NASASP-468, 1985

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2-5 Heffley, R.K. and Jewell, W.F.: Aircraft Handling Qualities Data, NASA CR-

2144, December, 1972

2-6 Chevron Products Company: Aviation Fuels Technical Review, FTR-3, Chapter

2, 2000, www.chevron.com/products/prodserv/fuels/aviationfuel/toc.shtm

2-7 Aviation Week and Space Technology, April 26, 2004, p.59

2-8 National Research Council, et al: New Materials for Next-Generation

Commercial Transports, National Academy Press, 1996, on-line at

www.nap.edu/openbook/0309053900/html/R1.html

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http://www.chevron.com/products/prodserv/fuels/aviationfuel/toc.shtmhttp://www.nap.edu/openbook/0309053900/html/R1.htmlhttp://www.nap.edu/openbook/0309053900/html/R1.htmlhttp://www.chevron.com/products/prodserv/fuels/aviationfuel/toc.shtmhttp://www.nap.edu/openbook/0309053900/html/R1.html

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Preliminary Weight Estimation 08-05