3.2.1 Empty Weight

The empty weight fraction of subsonic airliners varies roughly between 0.65 for short‐range aircraft and 0.45 for long‐range aircraft. An empty weight prediction based on statistics can be made as soon as the fuel weight fraction is known [4]. However, early empty weight estimations of an SCT generation may suffer from inaccuracies of at least 10%, resulting in considerable problems during the more advanced stages of the development. An extreme example of weight growth during the design development phase is the Concorde, whose MTOW increased from about 60,000 kg in the early design stage to 185,000 kg for the final production version. Remarkably, Concorde's empty weight fraction turned out to be only 0.44, a statistically normal percentage regarding its large total fuel weight of approximately 50% of the MTOW.

The decomposition of the OEW is based on the assumption that the DPL, the MTOW, and the installed take‐off thrust are the principal components affecting the empty weight as follows:

(3.2)

including the following three components:

• The first bracketed term, denoted as the body group, represents the fuselage weight, which is determined primarily by the fuselage dimensions and the maximum number of seats in the passenger cabin. Other components belonging to this category are the weight of cabin furnishings and equipment, and operator items. Since the vertical tail size is determined primarily by the fuselage geometry and the cabin configuration, its structure weight is also classified as a body group weight component¹. The factor for subsonic single‐deck airliner fuselages depends primarily on the number of seats abreast in the main cross‐section. Typical (approximate) values for narrow‐ and wide‐body subsonic transport are and , respectively.
• The second term – referred to as the airframe weight – summarizes components that are sized mainly to the MTOW defining the critical loading condition, . The wing structure and the landing gear typically belong to this category since their weights are considered functionally and statistically proportional to the MTOW. The wing structure weight fraction of subsonic airliners varies typically between 0.09 and 0.13, and if a horizontal tail or a fore‐plane is present its weight can be assumed to be proportional to the wing structure weight. Concorde's wing structure weight fraction of not more than 0.074 can be ascribed to the low aspect ratio, high inertia relief due to fuel, and the absence of complex high‐lift devices. Similar to subsonic transports, Concorde's twin‐leg main landing gear has a weight fraction of 0.039. However, due to the plane's high thrust/weight ratio, its power plant weight fraction of 0.13 is much higher than the typical 0.08 for subsonic jetliners.

  Statistics indicate that for present‐day subsonic jetliners is between 0.20 and 0.22. Taking into account that Concorde was designed during the 1960s, its airframe weight fraction is considered to be fairly low.

• The third term represents the installed power plant weight, which amounts to typically 30% of the total installed thrust; hence .
• The factor allows for on‐board power systems such as the environmental control system, hydraulic generation and distribution, electrical generation, distribution, and flight controls. The use of this term indicates that the system weight depends on the cabin capacity as well as the MTOW. Design studies from the past suggest that may be considered as a realistic guess for a supersonic airliner.
• The term represents a nominal weight of items present in all passenger aircraft, independent of their size and flight speed: flight deck crew and its accommodation and instrumentation. From statistical information it is concluded that this component depends mainly on the cabin cross section. Calibration of the method for subsonic airliners indicated that for single‐deck jetliners  kg. This weight component forms a small fraction of the OEW for large airliners but a significant component for and executive aircraft, whereas according to [10] the complex variable geometry nose has no given weight problem.

Calibration of the factors of proportionality in Equation (3.2) is hampered by the fact that the available SCT information database is very small. Only the Concorde and the TU‐144 have actually flown, whereas most of the information available on the SST projects developed in the USA during the 1960s has not been validated by prototype product information and flight performance. Indeed, the scarce data available on SCT development during the 1960s has become obsolete and needs to be updated in order to become useful for a future design.

It is worth noting that an expression similar to Equation (3.2) was discussed by Küchemann in [1] where he introduced “structural factors” with similar definitions and numerical values as and . He used the following values available for Concorde: and . However, the definitions of these terms are not unambiguous and Küchemann commented that the structural factors are rather conservative values based on present technology and we should be able to achieve and in a decade or two. This information is in accordance with the present text.

3.3.1 Mission Fuel

Since the conditions for quasi‐stationary cruising flight are valid for subsonic as well as supersonic flight, Bréguet's generalized range equation can be used for computing the range in cruising flight (index cr):

(3.3)

Equation (3.3) applies to a flight with constant Mach number and angle of attack. The calorific value of fuel per unit of mass is incorporated in (Equation 3.3) in the form of a reference range for kerosene fuel and the aircraft gross weight for the initial and end conditions of the flight are and , respectively. The range parameter is identical to the flight efficiency which was introduced in Chapter 2 and prediction of the aerodynamic efficiency will be treated in Chapter 7. Although Bréguet's equation represents the theoretical condition for the maximum range in quasi‐steady flight, long‐range flights are mostly executed with a stepped cruise/climb schedule.

According to [4] the fuel fraction required for such a sub‐optimum flight can be approximated as follows:

(3.4)

It is worth noting that the factor 0.5 in the denominator of Equation (3.4) stems from a Fourier series approximation of the natural logarithm, indicating that the average specific range is assumed to be equal to the nominal specific range when 50% of the cruise fuel has been consumed. Since the cruising flight is treated as a quasi‐steady motion, is considered to be constant and equal to its initial value. For a typical HSCT cruise fuel fraction = 0.40, the Bréguet range according to Equation (3.3) is 2% longer than the range obtained from Equation (3.4).

The reduced specific range during non‐cruising flight sectors is accounted for by adding lost fuel, which is primarily determined by the plane's energy height at the top of the climb and by the reduced specific range at low flight speeds and altitudes. The lost fuel and the additional fuel required for maneuvering are taken into account by increasing the range in cruising flight by the lost range . The fuel required to fly the design mission is thus obtained by replacing the cruise range in Equation (3.4) by the equivalent all‐out range , resulting in

(3.5)

The difference between cruising and off‐design flight conditions can have a significant effect on the equivalent all‐out range, in particular for short flights. An approximation for the lost range derived in [9] leads to the suggestion to use for a long‐range SCT mission.

3.3.2 Reserve Fuel

Accurate computation of the reserve fuel weight can be as cumbersome as computing the mission fuel weight. Fortunately, the early design stage of a subsonic airliner does not require such an effort since statistics indicate that reserve fuel weight is mostly between 4% and 5% of the MTOW and it is suggested to estimate the reserve fuel from

(3.6)

The subsonic flight conditions of SCT are, however, quite different from those during supersonic cruising and reduced flight efficiency values must be used for reserve fuel prediction. For Concorde this resulted in a reserve fuel weight of 6.5% of the mission fuel, not much different from its maximum payload fraction. This subject is associated with the discrepancy between cruise conditions and off‐design flight conditions of an SCT and it is likely that an optimized supersonic configuration featuring variable geometry will not suffer from Concorde's exceptional reserve fuel fraction.

3.5.1 MTOW Sensitivity

The basic weight weight distribution is derived by inserting the following educated guesses into Equation (3.7):

• Fuselage group weight: 150% of the volumetric payload; hence, .
• The wing structure weight is sensitive to the parameters affecting the aerodynamic efficiency, in particular the MTOW and the wing planform geometry. Since wing geometry is the most influential component for optimizing the vehicle's configuration, its structure weight fraction is treated as a selection variable.
• The power plant weight is based on a typical take‐off thrust/weight ratio of 0.35, an engine dry weight/thrust ratio of 0.20 and an additional 30% for engine accessories, intakes and engine mounts, resulting in an installed weight fraction of 0.091.
• The undercarriage weight fraction of 0.044 is assumed for a three‐leg main gear.
• The reserve fuel fraction is midway between subsonic airliners and Concorde.
• The on‐board power systems weight equals 12% of the payload‐dependent as well as the MTOW‐dependent OEW components. Hence, .

These assumptions yield a structural factor and, for a lost range , the equivalent all‐out range amounts to 10,870 km. The zero‐fuel weight (ZFW) is obtained from summation of the previous items,

(3.10)

and the take‐off gross weight required to comply with the above mentioned requirements is found by substitution of the structural factors into Equation (3.7),

(3.11)

As an example of a conservative design we assume a “year 2000 feasible” aerodynamic efficiency and an overall propulsive efficiency which yields a range parameter . For an assumed wing structure weight fraction of 0.10, the MTOW required to realize the mission equals 365,000 kg. The corresponding payload fraction is about 15% higher than Concorde's payload fraction. This performance must be considered as unsatisfactory for next‐generation SCT and it is necessary to investigate technological advancements required to increase the range parameter and/or design models leading to reduced wing structure weight. Figure 3.1 depicts the MTOW as a function of the wing structure weight fraction and the range parameter in cruising flight . It shows that, due to the high fuel weight fraction, the MTOW is more sensitive to the range parameter than to the wing weight fraction – a typical property of long‐range aircraft designed for supersonic cruising. In this initial weight study we therefore focus on improving the range parameter. For instance, a realistic aim for advanced future second generation SCT could be the achievement of according to Figure 2.4; that is, 33% higher than Concorde's range parameter. For a wing structure weight fraction of 0.10 the MTOW predicted according to Equation (3.11) amounts to 304,000 kg, corresponding to an OWE fraction 0.42 and a total fuel weight fraction of 0.49. The resulting payload fraction of 0.09 is one third higher than Concorde's payload fraction, which was achieved with . Achieving  = 4.50 will, however, require a major effort from the aerodynamic designers involved in the development of an advanced second generation CST with similar stringent top level requirements as assumed for this example.

The weight sensitivity of the design cycle is further clarified by assuming that downstream in the more detailed design process the wing structure weight appears to be 10% heavier then initially predicted. In that case the MTOW increases by 5.5% to 385,000 kg, whereas in the case of a 10% reduction of the range parameter the MTOW would increase by 20% to 440,000 kg. If, on the other hand, the aerodynamic and the propulsive efficiencies could both increase by 10%, the MTOW would decrease by a sensational 24% to 277,000 kg. The message is that fairly modest future improvements in the structural, aerodynamic, and propulsion characteristics compared to values which were considered realistic in the year 2000 may lead to a substantial weight reduction for a next‐generation advanced SCT design.

3.6.1 Range for Maximum Productivity

The achievable productivity for a specified MTOW is proportional to the product of the (maximum) payload fraction and the harmonic range . Referred to as the productivity parameter this figure of economic merit amounts to

(3.13)

The dimensionless productivity is computed for various values of the range factor according to Equation 3.2 for the example second generation SCT treated in Section 3.5. The result depicted on Figure 3.3 is explained by the fact that for short ranges the increasing range is dominating, whereas for long ranges the decreasing payload fraction dominates. Since the curves exhibit a shallow optimum the conclusion can be drawn that, from the point of view of conceiving an airliner with flexible operational capabilities, the preferred design range should be longer rather than shorter than this optimum. The maximum is achieved for . The “advanced future design” introduced previously, for which , is sized for a range of 10,000 km, thereby accurately satisfying this condition for maximum productivity. It is interesting that the Concorde, for which , the maximum productivity is achieved for a range of 6500 km, which is actually Concorde's maximum range. These results may be compared with present‐day long‐range airliners having a typical range parameter , for which the condition for maximum productivity leads to a theoretical optimum design range according to Figure 3.3 of 16,000 km.

3.6.2 Energy Efficiency

The fuel energy efficiency of a passenger transport is traditionally defined as the seat‐kilometer production per unit of fuel volume consumed during a given distance traveled,

(3.14)

A similar characteristic is the payload fuel efficiency, specifying the payload‐range productivity per unit of fuel weight consumed,

(3.15)

Applied to a given period of commercial operations, the total seat‐kilometer or payload‐kilometer produced represents the income potential, whereas the total amount of fuel consumed forms a large proportion of the operational expenses. Interpreted as a basic cruising flight performance, the energy efficiency can be defined alternatively as the ratio of transport work produced and fuel energy required to deliver this work. Applied to the instantaneous cruise performance, the momentary energy efficiency is proportional to the specific range :

(3.16)

where denotes the specific mass of fuel and is the distance flown per amount of fuel volume consumed. Equation 3.16 defines a dimensionless energy efficiency and, hence, one might be tempted to compare this with the usual definition of a mechanical or thermodynamic efficiency. This would, however, be an erroneous interpretation of the term “transportation work” since the energy level of the payload is not changing during (quasi‐)stationary flight. Combination of Equations 3.16 and 3.17 yields the FEE rewritten in terms of the range parameter and the payload fraction,

(3.17)

where denotes the aircraft momentary gross weight. For a typical payload weight per seat of 95 kg and a fuel energy density  MJ , we find seat‐kilometer per liter.

A more adequate criterion is the fuel energy efficiency referred to the mission fuel burnt per seat in relation to the range . Applying this criterion to hypothetical “advanced future SCT” with and a mid‐cruise payload fraction of 0.115, and combining it with the computed mission fuel of 134,000 kg according to Section 3.3, we find an FEE of 18 seat‐kilometers per liter. Equation (3.17) results in an average 17.6 seat‐kilometers per liter fuel for the complete mission – 3% below the instantaneous FEE in mid‐cruising flight. Although this compares favorably with Concorde's (estimated) FEE of 7.3 seat‐kilometers per liter it is worth noting that a modern subsonic jetliner with the same payload‐range productivity produces a typical 50 seat‐kilometers per liter. This makes it clear that the SCT, in spite of its much higher block speed, will have a substantial problem in being competitive on the commercial market.

3.6.3 Conclusion

The early weight prediction method exposed in this chapter and its application to second generation HSCT suggest that, compared to Concorde's performances, the payload‐range production can be improved considerably, provided the flight efficiency in high‐speed flight can be increased by at least 50%, making future advanced SCT carrying 250 passengers over the 10,000 km range at Mach 2.0 an attractive alternative for flying trans‐Pacific routes. Compared to present‐day subsonic airliners with similar payload‐range production, such an airliner would offer a block time reduction of up to 50%, leading to a productivity increase of 100% with 2.4 times Concorde's FEE. Since this figure of merit is (at least to a considerable extent) under the control of the advanced design team, the FEE may be considered as a prime candidate to be used as a figure of merit for optimizing the design.

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