2.1 Hypersonic vehicles

The state of hypersonic vehicles today is such that there are no publicly acknowledged hypersonic vehicles in operation. This may soon be changing with the introduction of the X-60A, which recently passed the conceptual design review. The X-60A is designed as an expendable small-scale hypersonic flight regime test platform. Overall, the significance of hypersonic test vehicles is noted by the number and complexity of past-to-present U.S. research projects, see Table 1.

Table 1

Significant past and present U.S. hypersonic projects and programs^{(Reference Chudoba, Coleman, Oza, Gonzalez and Czysz2)}

Enabling operational hypersonic systems will allow for both rapid response and unpredictability from the military, as well as new commercial opportunities such as rapid overseas passenger or cargo transport. Additionally, as envisioned with the National Aero-Space Plane (NASP) program (cancelled in 1993), hypersonics represents a key technology that may one day enable cheap and reliable access to Low Earth Orbit (LEO). Examining Table 1, it is evident that a large number of hypersonic test platforms have been investigated, ranging from demonstration vehicles, proposed operational vehicles, and military weapons platforms. Regardless of the specifics of the hypersonic project, the vast majority require some type of air-carrier or air-launch platform, whether that has been a missile-derived booster, or a commercial or military aircraft adapted as an airdrop platform. Reviewing the major hypersonic projects also reveals the common trend of overly ambitious research objectives. Several programs have been flawed from the outset by incorporating too many simultaneous advances in propulsion, aerodynamics, and materials into the design, thereby increasing overall risk, schedule delays, and cost escalation.

2.2 Air-carrier vehicles

Air-carrier launched flight test experiments have been ongoing since the late 1940s, beginning with the Bell X-1 in the U.S. Fig. 1 chronicles past-to-present air-launch carrier vehicles and the project vehicles they have carried. The first three project vehicles to conduct captive carry tests used modified variants of the B-29 and B-50B bombers. These project vehicles have launched from the underside of former bombers. The heaviest project vehicle carried during this time has been the X-2 at 11,300kg (24,910lb). From the early 1960s to its retirement in 2004, the NB-52A/B operated as the primary carrier vehicle for project vehicle flight tests. The NB-52 launched renowned project vehicles such as the X-15, HL-10, X-24B, X-38, and X-43 from a wing pylon designed to carry just over 22,680kg (50,000lb)^{(Reference Lockett3)}. The heaviest vehicle launched has been the X-15A-2, with a weight of 24,090kg (53,100lb). Another special carrier aircraft operating since the late 1970s was the Boeing 747 shuttle carrier aircraft, which carried the Space Shuttle Orbiter (SSO) on the top of its fuselage. This modified Boeing 747-100 aircraft carried the 106,590kg (235,000lb) orbiter. The carrier retired in 2012 with the completion of the Space Shuttle (STS) program.

Figure 1.

Historical operation of carrier/carried vehicles.

Today, there are five operational aircraft that are used as carrier vehicles. These are the B-52H, the Northrop Grumman L-1011 Stargazer, the NASA C-20A, the Virgin Orbit B747-400 Cosmic Girl, and Scaled Composites Stratolaunch. The B-52H has been used to carry the D-21 in the late 1960s and more recently the X-51 from 2010 to 2013. The B-52H is similar to the NB-52B in that it carries the project vehicle on a wing pylon, but its pylon is only able to hold a maximum weight of 11,340kg (25,000lb)⁽⁴⁾. The L-1011 Stargazer is the carrier vehicle for the Pegasus and Pegasus XL launch vehicles. The Stargazer has a bottom fuselage carry configuration. It can launch a 23,190kg (50,990lb) Pegasus XL. The NASA C-20A has the capability to carry a payload under the fuselage or on a wing pylon. It has been used for the GOLauncher1 turned X-60A project vehicle.

The Virgin Orbit B747-400 Cosmic Girl is another wing pylon carry configuration launcher, which has a maximum pylon payload weight of 38,555kg (85,000lb). Its primary payload is the Virgin Orbit LauncherOne space launch vehicle, which has a maximum weight of 25,855kg (57,000lb). Finally, the Stratolaunch aircraft is a high wing pylon carry configuration where the maximum pylon carry weight is 247,210kg (545,000lb)^{(Reference Corda, Longo and Krevor5)}. It is designed to launch large hypersonic testbed vehicles such as the Stratolaunch Systems’ proposed Hyper-Z Mach 10 concept.

While the project vehicles in Fig. 1 are air launched, two additional launch approaches include ground and sea. A common practice is to launch from either ground or sea using ballistic missile-derived platforms. There has been other hypersonic project test vehicles that have been ground or sea launched using a ballistic missile derived launch vehicle (e.g. the Minotaur IV missile from the Minuteman II and Peacekeeper ICBMs, or the Strategic Targets System (STARS) booster stack from the Polaris ballistic missile). The hypersonic missile projects are included in Table 1 with the other project vehicle studies to remind that there is a potential for air launch carrier platform commonality between the military branches and other government agencies for in-flight hypersonic research.

Currently, the U.S. government does not have a dedicated common carrier vehicle platform for in-flight hypersonic research. The following sections summarise the fundamental constraints associated with selecting an air-launch carrier or booster carrier vehicle.

Figure 2.

Relative project vehicle length and weight characteristics.

2.3 Air launch carrier vehicle constraints

This study focuses only on subsonic launch carrier aircraft. Previous horizontal launch-to-orbit studies have identified that a supersonic/hypersonic carrier vehicle with a payload of 6,800kg (15,000lb) would require development of a new aircraft, which is cost prohibitive for their presumed six flights per year^{(Reference Bartolotta, Wilhite, Schaffer, Huebner, Voland and Voracek6)}. The DARPA/NASA study in Ref. (Reference Bartolotta, Wilhite, Schaffer, Huebner, Voland and Voracek6) also considered a horizontal launch system which could be used commercially for profit, whereas the test vehicles in this study would not be able to generate any revenue for the program.

In order to select an air carrier vehicle, the constraints of the carrier vehicle on the test vehicle solution space have to be established. Fundamentally, the carrier vehicle constrains the test vehicle’s take-off gross mass (TOGM) and maximum size in terms of length, width, and height. Figures 2-4 show the relationships between vehicle weight and geometry. The figures give a notional indication of how project vehicles tend to grow in size with increasing weight. Note that the weight and geometry data in these plots are normalised to the X-51A, with a weight, length, wingspan, and height of 4,000lb, 25ft., 4.6ft., and 2ft., respectively. Awareness of vehicle growth and subsequent payload capacity requirements for a launch system is critical for a future proof or application robust launch system.

Figure 3.

Relative project vehicle wingspan and weight characteristics.

Figure 4.

Relative project vehicle height and weight characteristics.

Table 2

Fundamental carrier constraints on test vehicles

The carrier vehicle constraints depend on the overall air-carry vehicle configuration. The test vehicle may be launched from the top of the fuselage (e.g. the NASA shuttle carrier aircraft 747-100), the bottom of the fuselage (e.g. the L-1011 Stargazer), or a pylon on the wing (e.g. the NB-52B). Note that other launch configurations have been investigated in Refs (Reference Sarigul-Klijn, Sarigul-Klijn, Hudson, McKinney, Voss, Chapman, Morgan, Tighe, Kramb, Doyle, Quayle and Brown7,Reference Sarigul-Klijn and Sarigul-Klijn8) for launch to orbit applications, such as towed carry and internal carry. Those launch configurations have not been considered in the present context.

Table 2 has been created in order to investigate the (a) geometric and (b) structural loading constraints. These constraints can be readily assessed for making decisions about test vehicle and carrier vehicle compatibility in the context of this study. Table 2 provides a breakdown of the various constraints for each of the three air-carry configuration types, whether on the top, bottom, or on a wing pylon. The second column of the table establishes the characteristics of the air carrier, consisting of maximum pylon carry weight, wing ground clearance, or fuselage length. The third column establishes whether these characteristics of the aircraft are readily known. The dimensions of most commercial aircraft are available in airport planning documents (e.g. see Refs. 9,10). However, geometry and weight data for military aircraft are not readily available.

Next, the fourth column states the test vehicle characteristics that are constrained by the air-carrier vehicle constraints such as the maximum width, height, and weight of the test vehicle. The geometric constraints can further be subdivided into the test vehicle characteristics that are required in order to determine if both vehicles are compatible. For instance, the maximum length of the test vehicle for a pylon launch will depend on the test vehicle’s stack length, axial center of gravity (CG) location, and its wingspan or horizontal tail span. Since the test vehicle will be positioned on the pylon based on its CG location, there is not a definitive maximum length criterion that can be measured on the air-carrier vehicle. However, if the CG is known, then the maximum length of the test vehicle can be determined from the jet wake geometry or other considerations like the motion of the flaps during take-off/landing. Finally, the last column identifies which test vehicle design characteristics are known and not known.

It is of first order or highest importance to correctly determine which air carrier vehicles are physically compatible with a selected test vehicle. However, there are other important considerations when making the selection. These are of operational nature such as flight rate desired for the test vehicle, growth potential for the test vehicle, launch location restrictions, cost of air carrier vehicle purchase and modifications, air carrier vehicle availability, maximum flight speed, and maximum ceiling. The next three subsections discuss the applicable constraints for the three air-carry configurations and how they affect air-carrier aircraft selection.

2.4 Bottom carry configuration

There have been four carrier aircraft examples with the fuselage bottom carry configuration. These are the EB-29, EB-50, L-1011 Stargazer, and C-20A. This carry configuration geometrically constrains the maximum height, width, and length of the test vehicle. The only consistent constraint across different aircraft models for the bottom carry configuration is the maximum test vehicle height.

For the maximum test vehicle height, the minimum landing gear height of each air carrier vehicle is used as a maximum allowable height for the test vehicle, see Fig. 5. The rear landing gear separation distance of the carrier aircraft is used as the maximum allowable width of the test vehicle. To constrain the length of the test vehicle, the distance between the nose gear and the rear gear of the carrier aircraft is used. Note that these width and length constraints are not hard constraints due to their dependence on the CG location and attachment point on the carrier aircraft. For instance, the test vehicle’s max wingspan may not cross where the landing gear of the carrier aircraft is located. For the length constraint, if the landing gear is not modified, the rear landing gear of the carrier aircraft will constrain the maximum length of the test vehicle if the carrier aircraft has a fuselage retracting landing gear like the B747-400. Smaller aircraft like the B737-900 do not have a fuselage retracting landing gear; they have wing landing gear that retracts into the fuselage. This length constraint does not consider the longitudinal static stability effects of placing the test vehicle too far forward on the carrier aircraft. The gear separation distance (from port to starboard) can be used as a rough estimate of the maximum width, see Fig. 5. In addition, as shown in Table 2, the maximum weight that the bottom of the fuselage can carry is not known, but the structural payload of the aircraft is used as a first order estimate.

Figure 5.

Bottom carry constraints.

As noted in Ref. (Reference Sarigul-Klijn and Sarigul-Klijn8), advantages to the bottom carry configuration include proven and easy separation from the carrier aircraft, attachment points are on the top of the test vehicle (as opposed to the underside thermal protection system, TPS, of the test vehicle), and the wing used for separation can be sized smaller^{(Reference Sarigul-Klijn and Sarigul-Klijn8)}. Disadvantages are primarily the restrictions in height and cost of modification to the carrier aircraft^{(Reference Sarigul-Klijn and Sarigul-Klijn8)}.

2.5 Top carry configuration

As shown in Table 2, the two primary carrier aircraft examples with the top carry configuration are the Lockheed SR-71A (with the D-21) and the Boeing 747-100 SCA (with the Space Shuttle Orbiter). This configuration is geometrically constrained only in the length direction. The distance between the fuselage nose and the leading edge of the vertical tail of the air carrier is used as the maximum allowable length. Figure 6 shows an example of how close the Space Shuttle Orbiter is getting to the maximum test vehicle length provided by the B747-100 fuselage. If the test vehicle is aft heavy due to a large booster, it may need to be shifted more towards the nose of the carrier aircraft. Furthermore, as the test vehicle may increase in size over the duration of the research program, the total drag and vertical CG location of the combined carrier/test vehicle combination needs to be considered.

Figure 6.

Space Shuttle Carrier Aircraft. Reproduced from Ref. (11).

Like the bottom carry configuration, the structural payload is used as an initial estimate for the maximum weight that the fuselage can handle for the top carry configuration. The Space Shuttle Orbiter provides an example of a maximum top fuselage payload of 106,590kg (235,000lb).

The top carry configuration’s primary advantage is the ability to carry large test vehicles. For example, a 2011 hypersonic test vehicle study^{(Reference Chudoba, Coleman, Oza, Gonzalez and Czysz2)} found that the pylon launch configuration of the B-52H is not big enough to geometrically accommodate five of the six air launched demonstrator vehicles the study considered. The disadvantages of this configuration are the hard point attachments on the TPS side (bottom) of the test vehicle and the associated high modification costs of the carrier aircraft^{(Reference Sarigul-Klijn and Sarigul-Klijn8)}. It also requires active aerodynamic controls and a test vehicle wing sized for the separation manoeuver from the carrier aircraft^{(Reference Sarigul-Klijn and Sarigul-Klijn8)}. According to Ref. (Reference Bartolotta, Wilhite, Schaffer, Huebner, Voland and Voracek6), the top carry configuration is also demanding a minimum separation distance between the carrier aircraft and the test vehicle before igniting any booster engines on the test vehicle.

2.6 Wing pylon carry configuration

The wing pylon carry configuration has been the most popular carry configuration since the introduction of the NB-52A/B in 1959 with the X-15 program. Like the bottom carry configuration, this configuration also constrains the maximum width, height, and length of the vehicle. The width is constrained by three carrier aircraft factors. These are the distance between the fuselage and inner engine nacelle, the geometry of the jet wake, and the distance between the carrier aircraft main landing gear and the engine nacelle. Figure 7 shows the jet wake, ground clearance, and fuselage/engine nacelle constraints that have been presented during the configuration development study for the X-24C test vehicle.

Figure 7.

NB-52 pylon carry constraints. Reproduced from Ref. (Reference Combs, Campbell, Cassidy, Sumpter, Seitz, Kachel, James, Walters, Love and Passon12).

The maximum height of the vehicle is constrained by the carrier aircraft wing ground clearance. A maximum length constraint for the pylon configuration is estimated for this study based on several known vehicles such as the X-24C and LauncherOne. The maximum length constraint for pylon configurations is also dependent on test vehicle CG location. For example, the LauncherOne rocket is aft heavy, so its CG location requires the vehicle to be moved forward. The test vehicle’s nose extends to around 23ft. past the pylon leading edge of the B747-400 wing. A hard constraint cannot be defined at this point. To do so would require knowledge of the test vehicle’s CG location and placement underneath the wing.

As discussed earlier, the NB-52A/B has been able to carry a maximum of 22,680kg (50,000lb). The pylon launcher Cosmic Girl has been designed to launch a maximum payload of 38,555kg (85,000lb) from the pylon. The current B-52H capability is around 11,340kg (25,000lb), but proposed B-52J upgrades are considering to upgrade the pylons to support the carry of multiple 9,071kg (20,000lb) weapons^{(4,Reference Trevithick13)} . These known pylon weight limits are used to estimate maximum pylon weight limits for the test vehicles in this study.

2.7 Vertical launch configuration considerations

Vertical launch platforms (e.g. Minotaur IV Lite) are advantageous to hypersonic test programs in that they can eliminate the need of an additional booster system (see booster arrangement on the X-43A and X-51 in Fig. 8). Additionally, vertical launch platforms are simplifying fueling routines whilst enabling the use of more exotic sub-chilled cryogenic propellants due to the use of ground support equipment and the relatively fast time from launch to operational conditions of the test vehicle. Vertically launched experimental tests tend to offer extended test times and higher test Mach numbers.

Figure 8.

X-43 and X-51 hypersonic test vehicles. Courtesy of NASA/USAF.

A disadvantage of the vertical launch system is that reusability is not necessarily implied. For systems that could be reusable like the Falcon 9 or future New Glenn, it’s unclear whether the booster is able to handle separation loads at the typical dynamic pressures of a hypersonic vehicle at flight conditions from 1,000 to 2,000 PSF^{(Reference Ruttle, Stork and Liston14)}. If it is not possible to survive these conditions, either extra development effort has to strengthen the reusable boosters, or the hypersonic vehicle design has to schedule a sub-orbital trajectory and achieve the required flight conditions upon reentry. Sub-orbital operation adds additional design constraints to the test vehicle such as additional non-aerodynamic controls and added thermal protection for reentry conditions.

Additional operational penalties for vertical launch systems include launch facility dependability and possible weather-related delays. Note that super-heavy carrier aircraft might have similar drawbacks where they are limited to only the largest runways and are still take-off/landing constrained due to local weather conditions.

4.1 Trade studies

The selection of concepts from the trade matrix, as introduced previously, require several logical eliminations. The following four considerations have guided towards a reduced and therefore manageable trade matrix. First, the common goals and desires described in the technology development timelines stem from NASA and the USAF. Second, the mission and operational requirements of past test vehicle programs. Third, selecting elements that are compatible with multiple air-carrier/booster vehicle options. Lastly, the availability of math models to analyse the composed vehicles. The logical deductions result in four basic and representative vehicle configurations with multiple mission and operational trades for each.

4.1.1 Trade studies: baseline vehicle definition

In selecting appropriate geometry configurations, the all-body (AB) and the wing-body (WB) type are selected as they are expected to form the boundaries of the feasible solution space. That is, a blended-body (BB) design point will fall within the bounds of the wing-body and all-body solutions. As such, the blended-body is not a necessary design trade. The baseline vehicles considered for the all-body and wing-body types are the FDL-7MC^{(Reference Goetsch19)} or McDonnell Douglas Model-176 and the USAF AFRL Generic Hypersonic Vehicle (GHV^{(Reference Ruttle, Stork and Liston14)}), respectively. The GHV represents a current system of study that is well documented for the Mach 5-6 range. It shares many features with the HIFiRE flight 6 and 8 vehicles^{(Reference Dolvin18)}. The GHV has previously been studied by the Aerospace Vehicle Design (AVD) Laboratory in 2015-16^{(Reference Gonzalez20)} which formally verified the AVD Laboratory synthesis system. The Model-176 all-body configuration has been selected as it represents a high-performance (high-L/D) and high Mach number range capable (Mach 12+) geometry, where the original design was intended for high down-range and cross-range space reentry capability. This all-body configuration has been thoroughly analysed by McDonnell Douglas throughout the relevant disciplines due to its NASP era origins^{(Reference Czysz21)}. Due to the highly integrated nature of hypersonic flight vehicles (specifically air-breathing vehicles), both of these baseline configurations open up a pragmatic path to modify and accommodate either a closed fuselage and rocket (GHV) or an integrated underslung 2D scramjet (Model-176). The emerging vehicle perturbations based on both baseline geometries open a representative spectrum by incorporating both near-term to mid-term propulsion systems.

Figures 9 and 10 below visualise the original baseline air-breathing GHV and the modified rocket-powered GHV respectively. The adapted GHV geometry has its fuselage closed and faired off into a semi-cylindrical body. The resultant adapted geometry has higher volumetric efficiency and is better suited to carrying pressurised propellant tanks. Other aspects of the geometry remain the same, with identical wing and tail surfaces. Although the removal of the Busemann intake and flow path does require a re-derivation of the wave-rider wing arrangement, this configuration is representative of what a WB configuration can achieve.

The Model-176 has been modified to incorporate an underslung 2D scramjet with the scramjet integration modeled after the X-51 test vehicle. Visualised in Figs 11 and 12 are the original baseline rocket-powered Model-176 and the modified air-breathing Model-176 respectively. The Model-176 derived configuration retains a deployable scissor wing for low-speed glide and landing considerations, see also previous sizing studies^{(Reference Chudoba, Coleman, Oza, Gonzalez and Czysz2,Reference Chudoba and Gonzalez22)} . These studies show that the blended-body and all-body configurations result in high wing-loadings, overall constraining the resulting vehicles for the horizontal unpowered landing.

Figure 10.

Rocket modified GHV.

Figure 11.

Original rocket-powered Model-176.

Figure 12.

Scramjet modified Model-176.

4.1.2 Trade studies: mission definition

This study considers two mission scenarios. The two missions are distinguished by whether an external booster is used or not for the vehicle’s climb and acceleration to the primary mission start condition. The air-breathing configuration is limited to the expendable rocket booster scenario. The non-air breathing rocket configurations are not limited; they are applied to both mission launch scenarios (i.e. external expendable boost system and internal reusable boost system). All scenarios start with an airdrop condition at Mach 0.8 and 30kft, a final endurance cruise condition at Mach 6, and a horizontal gliding recovery at a landing site. The two scenarios are discussed in more detail below.

The external expendable booster profile is illustrated in Fig. 13. For ease of comparison and relevance, a mission with a similar performance specification, stemming from the original GHV study^{(Reference Ruttle, Stork and Liston14)}, is used. The vehicle is airdropped, boosted to the starting condition, accelerates at constant altitude until it reaches the design Mach number, then executes a constant Mach endurance cruise segment, and finally performs a power-off gliding descent to the horizontal landing point.

Figure 13.

Mission: expendable vehicle boost with acceleration climb to cruise altitude.

The major change, compared to the original GHV mission, is the elimination of the secondary maneuvering flight additions, as their inclusion does not significantly change the size of the vehicle. This mission configuration assumes an expendable booster sized to place the test vehicle at 75kft with a Mach number of 4.5, which corresponds to the lower end of the GHV scramjet dynamic pressure range of 1,000 PSF. After staging the booster, the vehicle then accelerates to Mach 6, with an upper dynamic pressure of 1,864 PSF, followed by the specified endurance cruise and a gliding descent segment to landing approach.

In the second all-rocket scenario, as illustrated in Fig. 14, the test vehicle is accelerated to its cruise condition by an integrated onboard rocket system. The test vehicle is its own accelerator. The main engine powers acceleration and cruise. That is, this mission sizes the vehicle to include the propulsive capacity previously provided by the external booster. In this regard, the all-rocket vehicles are fully reusable. Given that the vehicle is launched at subsonic conditions, this flight scenario is limited to only rocket-powered vehicles. Having identified and described the mission flight segments, the following section addresses the primary hardware and capability trades.

Table 4

Hardware and mission trade study summary

Figure 14.

Mission: internal rocket vehicle boost with acceleration climb to cruise altitude.

4.2 Sizing logic

A synthesis methodology includes analysis methods for each design discipline and a process logic to integrate the methods into a cohesive analysis environment. A conceptual design of a flight vehicle system is generated via the coordination of the analysis sequence through a total system convergence process. This section provides an overview of the fundamental synthesis process logic applied.

The study sizing methodology (derived from Hypersonic Convergence^{(Reference Czysz21)}) is illustrated in Fig. 15. The sizing process involves a series of modeling routines, starting with a vehicle geometry definition. At this point, a baseline vehicle and mission profile has already been selected (sections 4.1.1 and 4.1.2). The vehicle slenderness parameter ( $\tau = {V_{tot}}/S_{pln}^{1.5}$ ) is held constant for each convergence cycle and is fed as an input into the geometry method, thereby setting the rest of the geometric outputs for the configuration. With a geometric definition in place, the discipline specific analysis modules execute sequentially, in the following order: aerodynamics, propulsion, performance, and finally weight and volume. The aerodynamic and propulsion modules generate the aerodynamic and propulsion maps for the vehicle at different operating conditions. The performance module utilises the aerodynamic and propulsion data to analyse the vehicle’s trajectory and determine performance parameters including required weight ratio along the flight path. This methodology is detailed by Coleman^{(Reference Coleman23)}. The weight and volume module calculates and updates the weight and volume of the vehicle based on the previous module’s output. On completion of a sequence of disciplinary module execution, the instance of analysis is complete. However, the overall vehicle has not necessarily converged.

Figure 15.

Hypersonic convergence sizing process.

After the discipline module execution sequence, the objective functions are tested for solution convergence. Two objective functions are minimised simultaneously, see Equations (1)-(2) ^{(Reference Gonzalez20,Reference Czysz21,Reference Coleman23)} . The first objective function, Equation (1), is a function of operating weight empty by weight analysis ( ${{OW}}{{{E}}_{{W}}}$ ) and operating weight empty by volume analysis ( ${{OW}}{{{E}}_{{V}}}$ ). The second objective function, Equation (2), is a function of wing loading ( $W/{S_{pln}}$ ), planform area ( ${{{S}}_{{{pln}}}}$ ), and take-off gross weight ( ${{TOGW}}$ ). The convergence process is complete when each cost function equates to zero. In other words, the total vehicle is said to be converged when its solution point is mathematically acceptable because weight and volume converge with ${{OW}}{{{E}}_{{W}}} = {{OW}}{{{E}}_{{V}}}$ and $ (W/{S_{pln}} ) = TOGW/{S_{pln}}$ . If the objective functions are not satisfied, the planform area and wing loading are iterated and the sequence repeats, until both cost functions are minimised simultaneously. For a more detailed discussion of this process, see Refs. (Reference Gonzalez20,Reference Czysz21).

Objective function 1:

(1) \begin{equation}{\rm{OWE}}_{\rm{W}} - {\rm{OWE}}_{\rm{W}} = 0 \end{equation}

Objective function 2:

(2) \begin{equation}\left( \frac{\rm{W}}{\rm{S}_{\rm{pln}}} \right) - \frac{\rm{TOGW}}{{\rm{S}}_{\rm{pln}}} = 0 \end{equation}

Each baseline vehicle definition represents a separate synthesis code or CMDS. Each CMDS in turn is generated quickly and consistently by utilising a synthesis system generating software. For more detailed information on this synthesis tool, see Refs. (Reference Rana, McCall, Haley, Gonzalez, Omoragbon, Oza and Chudoba15,Reference Gonzalez20,Reference Omoragbon24).

After solving for each vehicle design point, the locus of vehicle solutions can be mapped onto a solution space plot, where the available solution space is identified within the consideration of both technical and operational constraints. Solution space screening implies an overall focus on visualising multi-disciplinary design interactions and trends, while consistently comparing individual converged minimum-size vehicle point designs with each other.