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2. PRELIMINARY WEIGHT ESTIMATION
2.1 Background
The basic mission specifies that an airplane be designed to carry N P
passengers at a
cruising speed of V miles per hour over a range of R miles using turbojet or turbofan
engines. 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 the
capital 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 a
function 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 as
WF , 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 for
each 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 k is a constant which is generally
set by the operator based upon experience and includes the weight of the typical
passenger and accompanying baggage. Values for this factor k 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 dependent
upon the priorities placed on cargo by different airline operators. Therefore the payload in
the 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. Then
the additional payload due to freight can be included in the refined weight estimate.
2.2 Weight Components
The 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 the
airplane 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 therefore
necessary 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
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 factor k that was used for the passengers. Different values of k
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 fuel
necessary 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 for WTO in Eq. (2-1) may be solved for WE 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 WPLC is the
anchor point for the design of the airplane. All the possible results for WE radiate out
from the point ( 0, -WPLC ) and depend upon the coefficient of the WTO term.
Figure 2-2 Mission profile showing the 11 flight stages for a domestic flight
( R <3000 nm). International flights have an additional segment between 10 and 11
calling for a 30 minute hold at 15,000 ft altitude and segment 6 is calculated at
10% of the normal cruise time, rather than a blanket 1 hour.
These rules have been used in setting out the additional flight segments mentioned
previously. To calculate the portion of fuel used and the portion of fuel kept in reserve we
note that the former is given by
,
, ,
F USED
F USED FINAL F RES
TO
W
M M M
W
Then the nominal landing weight fraction is
,
,
LAND NOM
FINAL F RES
TO
W
M M
W
The latter term is given by
5 9
,
,
(^1 1 )
F RES (^) i i
F RES
TO i^ i i i
W W W
M
W W W
(^)
The total fuel, it will be recalled, is
FUEL FINAL
FINAL
TO TO
W W
M
W W
Recall that the normalized maximum fuel load is given by
, ,
, ,
F USED F RES
FUEL F USED F RES
TO
W W
M M M
W
1 2 3
4
5 6
7
8
9
1
0
11
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:
TO E PLC E PLC
FUEL
TO TO
W W W W W
M
W W
Data using his approximation is shown in Fig. 2-3 along with a trend line given by MFUEL
= 0.0048 R
1/
. 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 for
the 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 2000 4000 6000 8000 10000 12000
Range (miles)
1 - (We+Wpl)/Wto
1-(We+Wpl)/Wto = 0.0048R^0.
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 an
approximate 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 representative
values for these weight fractions for all stages except the cruise stage are given in Ref. 2-
2 and appear in the Table 2-2.
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
E TO
W W. A database that has been compiled here for 45 operational transports
provides the results shown in Fig. 2-5 which support this simplified result.
0 100 200 300 400 500
Gross Weight (000 lbs)
Climb Weight Fraction
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 W 4
/ W
3
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 of
commercial 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, the
scale 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
e to
to
W W
W
is shown to fit the actual data better than the simple approximation
e
to
W
W
0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.
Take-off weight, Wto (klbs)
Empty weight, We (klbs)
Actual weights
logWe=(logWto - A)/B
We=0.5Wto
Figure 2-5 Empty weight versus take-off weight for 45 operational transports
0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.
Take-off weight, Wto (klbs)
Empty weight fraction,
We/Wto
We/Wto = 0.82/(Wto)^.
Figure 2-6 Variation of the empty weight fraction We/Wto with take-off weight
Wto 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 consideration
one 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 W E
vs. W TO
plot. Those points, which
represent 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.
from the market survey aircraft to improve the estimates for these values.
2.4 Selection of Cruise Performance Characteristics
The cruise speed V should be as high as is reasonable, remembering that the drag rises
with 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 the
Mach 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 in
Appendix J. Typical cruise Mach numbers are in the range of 0.76< M <0.86 and the
actual values for the market survey aircraft may be used as a guide for the present design.
Similarly, the cruise value of the specific fuel consumption should be as low as possible,
but should be in keeping with existing or planned engine characteristics. Current turbofan
technology has provided cruise specific fuel consumptions in the range 0.5< Cj <0.6 in the
units of pounds of fuel per hour per pound of thrust. Again, published data for the engines
used by the market survey aircraft can provide a guide for representative values to be
used for the current aircraft design. It should be noted that some engine data shows values
for take-off specific fuel consumption which are down around 0.3 to 0.4 pounds of fuel
per hour per pound of thrust, but this applies only to take-off conditions and should not
be used for cruise calculations. For example, in the cost estimating procedure given in
Appendix J, the Air Transportation Association suggests 15 minutes for ground maneuver
time, including 1 minute for take-off. As indicated in Table 2-1, Roskam suggests W 3 /
W 0 =.99.99.995=0.9752. Then, for a 300,000 lb take-off weight the fuel consumed is
7,440 lb and therefore the fuel consumption rate is 29,760 lbs/hr. For a typical take-off
thrust to weight ratio of ( T / W ) to =0.3, the take-off thrust is Tto =90,000 lb and the effective
TSFC= 29,760/90,000= 0.33, which is roughly equivalent to the take-off value of about
0.35 that will often be seen to be quoted. To repeat, the value of TSFC for cruise is
considerably larger, namely 0.5 to 0.6.
The lift to drag ratio L/D represents the aerodynamic efficiency of the airplane and should
be as high as possible. Current commercial jetliners have lift-to-drag ratios in the range
of 14< L/D <19, with the higher values associated with long-range versions. The actual L/
D for the design aircraft will ultimately be calculated so it is wise, as usual, to try to make
reasonable estimates at every stage of the design. Though the cruise lift for an aircraft is
easily determined since it is merely equal to the weight of the aircraft at any stage of the
cruise, the drag is not easily determined. Indeed the drag is a closely guarded secret of the
aircraft manufacturer and great efforts are expended to continually reduce the drag of
new designs. The techniques used for reduced drag designs are quite sophisticated and
beyond the scope of this handbook. Thus the lift-to-drag ratios to be determined later in
the design process will not be as high as achieved in current practice, so it is advisable to
be somewhat conservative in the choice of the cruise lift-to-drag ratio, 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 additional
length 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 to
the 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 have L /
D =18, like the B 767-200. Other wide-body airliners, like the older Lockheed L 1011-
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 and
contemporaneous 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-
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 and
landing at sea level is also shown.
2.5 Fuel Characteristics
Jet 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 and
that 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
aircraft will not be drainable from the tanks and therefore is unusable. The weight of this
that MTFO be estimated using the value of MFUEL calculated and an approximate value for
WTO based on the values for the market survey aircraft.
2.6 Estimation of the Take-off and Empty Weights
Equipped with a small set of reasonable performance estimates for the design aircraft a
number of design lines can be entered on the WE vs WTO plot. The vicinity of the
confluence of the design lines, the historical data correlation, and the market survey data
correlation is the design region and this is illustrated in Fig. 2-10. It is within this design
region that the design choice exists and it must be finally be specified. That choice will
be one which best defines the initial estimate of the empty weight and the take-off weight
of the design aircraft. These weights will influence the subsequent development of the
design and if they are chosen poorly may require substantial alteration and iteration later
on. Nevertheless a choice must be made and the major result of this chapter of the design
report is the design plot of Fig. 2-10 with all its information and the final values for W E
and WTO and the associated assumed performance data.
Figure 2-10 General design curve illustrates the manner in which the design
region is determined. The final choice for WE and WTO is set by the
appropriate values of V , Cj , and L/D for the proposed aircraft.
The design lines for the different sets of Cj , V , and L / D should appear and be identified on
the design chart as should the market survey aircraft points. The design point for your
aircraft must be clearly shown and a discussion illustrating the criteria by which this
choice was made is to be included in the report. In addition, a weight breakdown table
showing the relevant data for the market survey aircraft and for the design aircraft should
W E
0
-W PLC
Design curves for various values of V , C j
, and L/D
W TO
Historical Correlation
W E
=0.5W TO
Market survey aircraft
Design region
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 Reduction
The 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 to
composite 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 issues
surrounding 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 this
regard 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 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 in
taxiing 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 a
turbofan 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 to
consider 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 are
moving 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.
Table 2-4 Weight Fractions for the Mission Segments for Turboprop Aircraft
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.
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
