X-Planes: X-44, One Designation and Two Aircraft
Filed under: aerospace, history, engineering
Two aircraft carry the designation X-44A, both of them Lockheed Martin, and only one of them was ever built. The famous one is the Multi-Axis No-Tail Aircraft, a proposed derivative of the F-22 with every tail surface deleted and every axis of control handed to the exhaust, which was approved in 1999, funded briefly and cancelled without metal being cut [Lockheed Martin X-44 MANTA]. The other was a tailless unmanned flying wing of about nine metres span, built by the Skunk Works in 1999, first flown in 2001, and kept out of public view until March 2018 [Skunk Works reveals the missing link in a secret unmanned history] [Lockheed Skunk Works X-44A flying-wing drone revealed]. The aeroplane that exists is the one nobody had heard of, and a museum now holds it [Lockheed Martin X-44A, National Museum of the United States Air Force]. This is the forty-fifth article in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, the X-5, the X-6, the X-7, the X-8, the X-9, the X-10, the X-11, the X-12, the X-13, the X-14, the X-15, the X-16, the X-17, the X-18, the X-19, the X-20, the X-21, the X-22, the X-23, the X-24, the X-25, the X-26, the X-27, the X-28, the X-29, the X-30, the X-31, the X-32, the X-33, the X-34, the X-35, the X-36, the X-37, the X-38, the X-39, the X-40, the X-41, the X-42, and the X-43.
A vehicle existed and produced data, and almost none of that data has been released. No specification for the X-44A has been published beyond a span, an engine, two dates and three performance figures, and the MANTA never reached the point of having specifications to publish, so the statement of what is unknown carries the weight a specification table would otherwise carry.
The finding is that the question the MANTA existed to answer had already been answered in flight, five years earlier, by an aeroplane this series has already covered. The X-31 flew a hundred percent simulated vertical tail removal at Mach 1.2 and 37,500 feet in March 1994, restabilised by yaw thrust vectoring, and its report concludes that tailless and reduced-tail fighters are feasible [Bosworth and Stoliker 1996] [Huber and Schellenger 1994]. The interesting question is therefore not whether the MANTA would have worked but what its demonstration point was worth, and arithmetic can settle that. The demonstration was flown at a point whose authority ratio stands within fourteen percent of the worst in the entire supersonic envelope, so it very nearly covered everything above the speed of sound. What it did not cover is the landing, and the reason is the throttle rather than the aerodynamics.
The Research Question
The binding unknown was whether an aeroplane can be held straight by its engines when it has nothing else to be held straight by.
A vertical tail exists to supply two different things that are easy to confuse. It supplies static directional stability, meaning a restoring moment that grows with sideslip and points the nose back into the wind, and it supplies control power, meaning a moment the pilot can command at will. The stability condition is a sign condition on one derivative. It is written out because the article concerns what happens when it fails. The requirement that it be satisfied at all is older than the jet age, having been set out in the report that first turned pilot opinion into numbers [Gilruth 1943].
\[N = q S b \, C_{n\beta} \, \beta \qquad \text{stable} \iff C_{n\beta} > 0 \tag{1}\]Deleting the tail removes both, and the two are replaced by different mechanisms. Stability is replaced by feedback, which is a matter of sensors, computation and actuator bandwidth. Control power is replaced by thrust deflection, which is a matter of how much momentum flows through the nozzle and how far that nozzle sits behind the centre of gravity. The distinction between the two is standard and is made in every treatment of the subject [Etkin and Reid, Dynamics of flight] [Nelson, Flight stability and automatic control] [Perkins and Hage, Airplane performance, stability and control], and the conventional way of sizing the surface that supplies both is a tail volume coefficient,
\[V_{v} = \frac{S_{v} \, l_{v}}{S \, b} \tag{2}\]which is a ratio of areas and arms carrying no propulsion term at all [Raymer, Aircraft design, a conceptual approach] [Torenbeek, Synthesis of subsonic airplane design]. The authority that coefficient buys follows from it directly, with $a_{v}$ the fin’s lift-curve slope, $\tau$ the rudder effectiveness and $\eta_{v}$ the dynamic pressure ratio at the tail.
\[C_{n \delta_{r}} = - V_{v} \, a_{v} \, \tau \, \eta_{v} \tag{3}\]The methods for putting numbers into that expression are themselves primary literature [Campbell and McKinney 1951] [Toll and Queijo 1948] [Jones and Alksne 1951], and the swept-wing and supersonic cases needed separate treatments because the subsonic charts do not carry over.
Every term in that expression is geometry or aerodynamics and none of it is thrust, so a rudder’s authority is a coefficient that barely moves with Mach number and whose moment therefore grows as the dynamic pressure. That asymmetry carries the argument, and the form of the equation shows it before any number is put into it. For a fighter tail volume near 0.07, a lift-curve slope near 2.5 per radian, an effectiveness near 0.5 and a dynamic pressure ratio near 0.9, thirty degrees of rudder is worth a yawing moment coefficient of 0.0412.
A thrust-vectored aeroplane has no tail volume, so none of that apparatus applies to it, so the comparison below is built from first principles, without a design handbook.
The reason to delete it is not aerodynamic elegance. A vertical tail is the single largest contributor to the radar cross section of an otherwise carefully shaped aeroplane, because a flat surface standing perpendicular to the wing is a corner reflector for every illumination in the horizontal plane, and the shaping literature has said so for as long as it has existed [Knott, Shaeffer and Tuley, Radar cross section]. A flat plate of area $A$ returns
\[\sigma_{\text{plate}} = \frac{4 \pi A^{2}}{\lambda^{2}} \tag{4}\]at normal incidence, and a dihedral formed by two such plates meeting at a right angle returns
\[\sigma_{\text{dihedral}} = \frac{8 \pi a^{2} b^{2}}{\lambda^{2}} \tag{5}\]over a wide range of aspect angles rather than at one. The second relation is why a fin is expensive and the first is not the whole story. A flat plate is a large return in one direction and a corner is a large return in many, and the persistence across angle, unlike the peak, is what a designer cannot shape away. It also carries a trim drag penalty, a weight penalty, an actuation penalty and, on a supersonic aeroplane, a wave drag penalty. The MANTA’s own advertised benefits were reduced mechanical complexity, greater internal fuel volume and greater agility [Lockheed Martin X-44 MANTA] [X-44 MANTA Multi-Axis No-Tail Aircraft, GlobalSecurity], four different disciplines each wanting the same part removed.
The question this article asks is narrower and answerable. Given that the X-31 demonstrated tailless control at one flight condition, what fraction of a fighter’s envelope does one demonstrated point cover? That question has a closed-form answer that needs no wing area, no yaw derivative and no moment arm, and the analysis below is built around it.
For the unmanned aircraft the question is different, because the vehicle is subsonic and has no vertical tail to argue about. There the binding unknown was whether a small tailless flying wing could be designed, built and flown quickly enough to matter, and the article treats that as a manufacturing and configuration question, because its programme described it that way [Lockheed Skunk Works X-44A flying-wing drone revealed] [Lockheed Martin X-44A, National Museum of the United States Air Force].
Programme Origin
The MANTA, and the Aircraft It Was to Be Made From
The MANTA was a conversion proposal and not a clean-sheet aeroplane. The design took the F-22’s fuselage and engines, replaced the wing with a stretched delta, and deleted the vertical and horizontal tails entirely, leaving attitude control to three-axis thrust vectoring [Lockheed Martin X-44 MANTA] [Lockheed Martin X-44 MANTA tailless technology demonstrator proposal]. Preliminary work was under way by May 1999. The National Aeronautics and Space Administration approved the programme to start in June 1999 and the designation recorded at that point is X-44A. Funding ended in 2000 [Lockheed Martin X-44 MANTA].
The sources date the end only approximately, and the article does not make them more precise. The encyclopaedia entry says funding ended in 2000 [Lockheed Martin X-44 MANTA]. Two other accounts place the end around that year, one saying that the project seems to have died off about 2000 [Lockheed Martin X-44 MANTA tailless technology demonstrator proposal] and the other that it was supposedly cancelled around the turn of the millennium [Lockheed Skunk Works X-44A flying-wing drone revealed]. The 2003 NASA inventory of X-vehicles still describes a feasibility study in progress and a first flight as unlikely before 2007 [Jenkins, Landis and Miller, American X-Vehicles, An Inventory X-1 to X-50, NASA SP-2003-4531, 2003]. None of them cites a programme document, so the year remains approximate.
Nothing was built [Lockheed Skunk Works X-44A flying-wing drone revealed]. There is no airframe, no wind tunnel entry on record under the name, no flight and no report. The MANTA is a set of drawings and a set of claims, and the claims are what can be tested.
The X-44A, and the Programme That Had Gone Quiet
The unmanned X-44A fills a hole in a public record that had been visibly empty. Lockheed’s high-altitude unmanned reconnaissance line ran from the RQ-3 DarkStar, which first flew on 29 March 1996 and was terminated by the Department of Defense in January 1999 [Lockheed Martin RQ-3 DarkStar], to the P-175 Polecat, which first flew in 2005 [Lockheed Martin P-175 Polecat], to the RQ-170 Sentinel [Lockheed Martin RQ-170 Sentinel]. Between January 1999 and 2005 the public record showed nothing at all [Skunk Works reveals the tailless X-44A]. The gap reflects how the organisation works and was no accident, since the Skunk Works was built to run programmes that do not announce themselves [Rich and Janos, Skunk Works]. The X-44A occupies that gap, having been built in 1999, the year DarkStar was cancelled, and flown in 2001 [Skunk Works reveals the missing link in a secret unmanned history] [Lockheed Skunk Works X-44A flying-wing drone revealed].
Its stated purposes were manufacturing and configuration, not performance. The programme is described as proving rapid manufacturing techniques, demonstrating penetrating reconnaissance, and establishing the aerodynamic validity of a relatively small tailless swept flying wing [Lockheed Skunk Works X-44A flying-wing drone revealed]. That ordering matters, because a vehicle built to prove that it can be built quickly is dimensioned by its factory rather than by its mission, and the published endurance of an hour and a half and range of 230 miles are those of a short-range demonstrator [Lockheed Martin X-44A, National Museum of the United States Air Force].
It was revealed at the Los Angeles County Air Show in March 2018 and placed on public display in October 2020, in the Research and Development gallery of the National Museum of the United States Air Force [Lockheed Martin X-44A, National Museum of the United States Air Force] [Exclusive photos, the X-44A breaks cover]. Seventeen years elapsed between the first flight and the first photograph.
The Designation and Its Two Referents
Several neighbouring numbers turn on a designation that may not belong to the vehicle it is attached to, and the X-44 is the sharpest case, because both claimants are Lockheed Martin products, both were current in 1999, and both are recorded as X-44A.
The X-39 was reserved and never assigned to anything, the X-41 carried a designation allocated years before the programme it is now attached to existed, and the X-42 had two sources describing different vehicles four years apart.
Three things about the record need stating precisely.
First, the reference literature has split into two entries instead of reconciling them. The general encyclopaedia carries a page for the MANTA and a separate page for the unmanned vehicle, and the second page states that it is apparently unrelated to the first [Lockheed Martin X-44 MANTA] [Lockheed Martin X-44, the unmanned vehicle]. A disambiguation page exists to route between them [X44, the disambiguation page]. Splitting is the correct editorial response to a genuine collision, but it does not resolve one.
Second, the specialist designation registry does not carry the number at all. Andreas Parsch’s Appendix 4 to the Directory of U.S. Military Rockets and Missiles covers undesignated and unusual unmanned vehicles and holds pages for the X-41, the X-42, the X-45, the X-47 and the X-48 [Parsch, Directory of U.S. Military Rockets and Missiles, Appendix 4]. A request for an X-44 page returns a not-found response listing those five and the X-64 as near misses. The registry that documents this series’ other disputed numbers most carefully is silent on this one. This article reports that silence as an absence, which falls short of a denial.
Third, the journalism that broke the story said openly that it did not know. The account that first reported the aircraft states that it is unclear how the flying wing came to carry the same designation as the manned proposal and that there appears to be no direct relation between the two programmes [Lockheed Skunk Works X-44A flying-wing drone revealed]. A reporter who has the aeroplane and the photographs and still cannot explain the number is evidence about the number, not about the reporting.
The designation system has a documented allocation process. Aircraft designations are governed by Department of the Air Force Instruction 16-401, which covers the naming of aerospace vehicles and the bureaucratic steps by which a designation is assigned [Parsch, Current Designations of U.S. Military Aircraft]. A number issued twice is therefore either a failure of that process or evidence that one of the two allocations was never made through it. The public record does not say which, and this article does not guess.
One structural observation survives without resolving anything, and arithmetic establishes it. The X-planes numbering is a finite resource issued consecutively and never replenished, the mechanism on which the X-39 article builds its permanence argument. Writing $N$ for the highest number issued, $r$ for those reserved and never used and $c$ for those issued more than once, the vehicles the sequence can name is
\[V = N - r + c \tag{6}\]while the numbers consumed is $N$ alone. A collision is the only term in that expression that adds a vehicle without consuming a number, so it is the one anomaly class that costs the register nothing and the reader everything. The register’s accounting cannot see it, because $N$ is what the register stores and $c$ is not.
Sizing From First Principles
The MANTA’s claim is testable without knowing anything about the MANTA. What follows derives the quantity that decides whether propulsive yaw control is sufficient, shows that two of the three variables it appears to depend on cancel identically, and then locates the flight condition that binds.
The Quantity That Has to Be Compared
A tailless aeroplane needs a yawing moment and has one available. The question is the ratio.
Let $q$ be the dynamic pressure, $S$ the wing reference area, $b$ the span, $C_{n\beta}$ the directional stability derivative and $\beta$ the sideslip angle. The aerodynamic yawing moment that must be produced, whether to trim a disturbance or to restrain a divergence, is
\[N_{\text{req}} = q S b \left| C_{n\beta} \right| \beta \tag{7}\]Let $F_{g}$ be the gross thrust passing through the nozzles, $\ell$ the distance from the centre of gravity to the nozzle exit and $\delta$ the yaw deflection angle of the jet. The moment available is
\[N_{\text{av}} = F_{g} \ell \sin \delta \tag{8}\]The argument turns on the ratio of these two.
\[\mathcal{R} \equiv \frac{N_{\text{av}}}{N_{\text{req}}} = \frac{F_{g} \ell \sin \delta}{q S b \left| C_{n\beta} \right| \beta} \tag{9}\]The available moment can be put in the same currency as the rudder, and doing so is the cleanest way to see what the exchange costs. Dividing the vectored moment by $q S b$ gives a propulsive tail volume, a dimensionless number directly comparable with the $C_{n \delta_{r}}$ above.
\[V_{p} \equiv \frac{F_{g} \, \ell \, \sin \delta_{\max}}{q \, S \, b} \tag{10}\]The article’s central finding is that this quantity does not behave like a rudder’s. A rudder’s coefficient is fixed by geometry. This one carries the thrust in its numerator and the dynamic pressure in its denominator, so it falls as the aeroplane goes faster and collapses when the throttle closes.
Inverting the ratio for the quantity a control system commands gives the required deflection.
\[\sin \delta = \frac{q \, S \, b \, \left| C_{n\beta} \right| \beta}{F_{g} \, \ell} \tag{11}\]Dynamic pressure is not independent of static pressure, and writing it in those terms is the step the rest of the derivation needs. With $\gamma$ the ratio of specific heats, $p$ the ambient static pressure and $M$ the Mach number,
\[q = \tfrac{1}{2} \rho V^{2} = \tfrac{1}{2} \rho M^{2} \gamma R T = \tfrac{1}{2} \gamma p M^{2} = 0.7 \, p M^{2} \tag{12}\]The moment form above is the standard linearised one [Yechout and Morris, Introduction to aircraft flight mechanics] [Schmidt, Modern flight dynamics] [Roskam, Airplane flight dynamics and automatic flight controls], and the substitution for dynamic pressure follows from the definition of Mach number and the perfect gas law together [Anderson, Fundamentals of aerodynamics] [McCormick, Aerodynamics, aeronautics and flight mechanics]. The substitution is an exact identity. Evaluating both forms at every flight condition in the analysis gives the same dynamic pressure to within one part in a million.
The Engine Puts the Static Pressure Back In
Gross thrust varies, and the way it varies produces the result. A fixed-geometry engine running at its maximum corrected rotational speed passes a constant corrected mass flow, so the physical mass flow follows the total conditions at the compressor face. With $\delta_{2}$ and $\theta_{2}$ the total pressure and total temperature at that station referred to sea level static conditions,
\[\dot{m} = \dot{m}_{\text{ref}} \frac{\delta_{2}}{\sqrt{\theta_{2}}} \tag{13}\]This corrected-parameter machinery is general to engine performance [Mattingly, Elements of gas turbine propulsion] [Cumpsty, Jet propulsion]. It is used here for one property, the variation of physical mass flow with ambient conditions.
The total conditions follow from the ambient conditions and the flight Mach number through the isentropic relations, reduced by the inlet total pressure recovery $\eta_{r}$,
\[\delta_{2} = \frac{p}{p_{\text{SL}}} \left( 1 + \tfrac{\gamma - 1}{2} M^{2} \right)^{\frac{\gamma}{\gamma - 1}} \eta_{r} \qquad \theta_{2} = \frac{T}{T_{\text{SL}}} \left( 1 + \tfrac{\gamma - 1}{2} M^{2} \right) \tag{14}\]which for $\gamma = 1.4$ gives, after cancelling one half power of the ram term,
\[\dot{m} \propto \frac{p}{p_{\text{SL}}} \, \eta_{r} \, \frac{\left( 1 + 0.2 M^{2} \right)^{3}}{\sqrt{T / T_{\text{SL}}}} \tag{15}\]Gross thrust is that mass flow times a jet velocity, and the jet velocity varies too. For a nozzle expanding from a total temperature $T_{t7}$ fixed by the afterburner limit,
\[V_{j} = \sqrt{2 \, c_{p} \, T_{t7} \left[ 1 - \left( \frac{p}{p_{t7}} \right)^{\frac{\gamma - 1}{\gamma}} \right]} \tag{16}\]Everything on the right is fixed by the engine except the nozzle pressure ratio, which rises with flight Mach number through the same ram term the mass flow carries. The derivation first treats $V_{j}$ as constant, which is the simpler and, as shown under Where the Framing Breaks Down, the more pessimistic choice, and then relaxes it and reports how much the answer moves.
\[F_{g} = \dot{m} V_{j} + \left( p_{e} - p \right) A_{e} \approx \dot{m} V_{j} \tag{17}\]The Static Pressure Cancels Exactly
Assembling the ratio, the ambient static pressure appears once in the numerator and once in the denominator, to the same power.
\[\mathcal{R} \propto \frac{ \dfrac{p}{p_{\text{SL}}} \eta_{r} \dfrac{(1 + 0.2 M^{2})^{3}}{\sqrt{T/T_{\text{SL}}}} }{ 0.7 \, p M^{2} } = \frac{ \eta_{r} \left( 1 + 0.2 M^{2} \right)^{3} }{ 0.7 \, p_{\text{SL}} \, M^{2} \sqrt{T/T_{\text{SL}}} } \tag{18}\]The pressure is gone, so the ratio does not depend on altitude except through temperature. Above the tropopause the standard atmosphere holds temperature constant at 216.65 kelvin, so in that region the ratio is a function of Mach number alone.
\[\mathcal{R}(M) \propto \frac{\eta_{r}(M) \left( 1 + 0.2 M^{2} \right)^{3}}{M^{2}} \qquad h > 11 \ \text{km} \tag{19}\]The cancellation can also be confirmed numerically. Evaluated through the full standard atmosphere at Mach 1.2, the ratio takes the same value at five altitudes from 11,000 metres to 65,000 feet to within one part in ten to the twelfth, and the closed form above reproduces the atmosphere-driven value exactly at three further altitudes. The cancellation is a structural property of the ratio, independent of numerical coincidence.
Below the tropopause the cancellation is only partial, because temperature varies there. The residue is the remaining temperature term, which needs no empirical curve because the standard atmosphere supplies it in closed form,
\[T(h) = T_{\text{SL}} - L h \quad (h \le 11 \ \text{km}) \qquad T(h) = 216.65 \ \text{K} \quad (h > 11 \ \text{km}) \tag{20}\]so the ratio at altitude $h$ relative to the isothermal region is
\[\frac{\mathcal{R}(h)}{\mathcal{R}(h > 11 \ \text{km})} = \sqrt{\frac{T_{11}}{T(h)}} \tag{21}\]The lapse rate, the tropopause altitude and the isothermal temperature above it are the standard values [U.S. Standard Atmosphere 1976 1976], and every altitude quoted is a pressure altitude in that model rather than a geometric one.
Each entry in the table below is that square root, so the table needs no vehicle and no engine. The residue is not negligible and it runs the unhelpful way.
| altitude | ratio relative to 11 km, same Mach |
|---|---|
| sea level | 0.8671 |
| 10,000 ft | 0.8985 |
| 20,000 ft | 0.9337 |
| 30,000 ft | 0.9733 |
| 11 km and above | 1.0000 |
A tailless aeroplane is thirteen percent worse off at sea level than at altitude at the same Mach number, and the entire effect is the temperature term $\sqrt{T/T_{\text{SL}}}$, which enters because a colder engine face passes more mass.
Where the Ratio Has Its Minimum
Intuition says the hardest case for a thrust-vectored aeroplane is the fastest one, because dynamic pressure grows as the square of Mach number. Intuition is wrong, because ram compression grows faster.
Taking ideal recovery for a moment, the Mach dependence is
\[f(M) = \frac{\left( 1 + 0.2 M^{2} \right)^{3}}{M^{2}} \tag{22}\]Differentiating with respect to $u = M^{2}$,
\[\frac{d}{du} \left[ \frac{(1 + 0.2u)^{3}}{u} \right] = \frac{(1 + 0.2u)^{2} \left( 0.4 u - 1 \right)}{u^{2}} \tag{23}\]which vanishes at $u = 2.5$, so the worst Mach number is exactly $\sqrt{5/2}$.
\[M^{\ast} = \sqrt{2.5} = 1.5811 \qquad f(M^{\ast}) = \frac{1.5^{3}}{2.5} = \frac{3.375}{2.5} = 1.35 \tag{24}\]Both the location and the value are exact, and both can be recovered without the algebra. Bisection on a numerically differenced derivative finds the same minimising Mach number to six decimal places, and the function evaluated there equals 1.35 to machine precision.
Adding a realistic inlet total pressure recovery moves the minimum and does not remove it. The standard correlation, the military specification recovery that NASA’s Glenn Research Center gives as a good first estimate above Mach one while noting that actual inlets usually recover somewhat less [NASA Glenn Research Center, Inlet performance], is
\[\eta_{r}(M) = \begin{cases} 1 & M \le 1 \\ 1 - 0.075 \, (M - 1)^{1.35} & M > 1 \end{cases} \tag{25}\]and with it the stationarity condition is no longer solvable in closed form, because differentiating the product gives
\[\frac{\eta_{r}'(M)}{\eta_{r}(M)} + \frac{1.2 M}{1 + 0.2 M^{2}} - \frac{2}{M} = 0 \tag{26}\]which is transcendental and is solved by golden-section search. The ideal closed form remains the exact reference from which the corrected minimum is displaced.
| Mach | ideal recovery | with recovery |
|---|---|---|
| 0.3 | 7.900 | 7.968 |
| 0.5 | 3.121 | 3.148 |
| 0.7 | 1.821 | 1.836 |
| 0.9 | 1.305 | 1.317 |
| 1.0 | 1.165 | 1.175 |
| 1.2 | 1.000 | 1.000 |
| 1.4 | 0.927 | 0.915 |
| 1.5811 | 0.910 | 0.885 |
| 1.674 | 0.913 | 0.881 |
| 1.8 | 0.931 | 0.887 |
| 2.0 | 0.983 | 0.917 |
| 2.25 | 1.085 | 0.984 |
Every column is normalised to Mach 1.2, the condition the X-31 flew. With recovery included the minimum sits at Mach 1.674 and the demonstrated point stands 1.135 times above it.
That number is the answer to the question this article set. The X-31 demonstrated tailless control at a point that is thirteen and a half percent easier than the worst point in the supersonic envelope, and no point between Mach 1.2 and Mach 2.25 is more than twelve percent harder than what was flown. A single demonstrated supersonic point very nearly covered the supersonic envelope. That result is far stronger than the demonstration claimed, and it follows from a cancellation rather than from a simulation.
It also inverts the expectation. The demonstration was not flown at a soft condition chosen to flatter the concept. On this measure it was flown next to the hardest one available, and whether that was by design or by the accident of what the X-31’s envelope allowed, the public record does not say.
The Crosswind Identity
The comparison above holds the sideslip angle fixed, which is right for a manoeuvre and wrong for a wind. A crosswind, or a lateral gust, has a fixed speed rather than a fixed angle, and the angle it produces grows as the aeroplane slows. With $V_{c}$ the crosswind speed,
\[\beta = \arctan \frac{V_{c}}{V} \approx \frac{V_{c}}{V} = \frac{V_{c}}{M \sqrt{\gamma R T}} \tag{27}\]Substituting into the required moment,
\[N_{\text{req}} \propto q \beta = 0.7 \, p M^{2} \cdot \frac{V_{c}}{M \sqrt{\gamma R T}} \propto \frac{p M}{\sqrt{T}} \tag{28}\]and the available moment already carries the same pressure and the same square root of temperature.
\[N_{\text{av}} \propto \frac{p \, \eta_{r} \left( 1 + 0.2 M^{2} \right)^{3}}{\sqrt{T}} \tag{29}\]Both cancel. The required vector angle for a crosswind of given speed depends on Mach number and on no other variable.
\[\frac{N_{\text{req}}}{N_{\text{av}}} \propto \frac{M}{\eta_{r}(M) \left( 1 + 0.2 M^{2} \right)^{3}} \tag{30}\]No pressure, no temperature, no altitude, no density and no true airspeed. Evaluated at Mach 0.8 at five altitudes from sea level to 55,000 feet with the throttle held, the required angle agrees to better than four parts in ten thousand, the residue being the difference between the arctangent and its argument.
Differentiating gives a result cleaner than the last one.
\[\frac{d}{dM} \left[ M \left( 1 + 0.2 M^{2} \right)^{-3} \right] = \frac{1 - M^{2}}{\left( 1 + 0.2 M^{2} \right)^{4}} \tag{31}\]The crosswind demand peaks at exactly Mach one, at every altitude, in every atmosphere, for every crosswind speed and for every aeroplane. Evaluating the ideal form there gives a maximum that is a pure number,
\[h(1) = \frac{1}{(1 + 0.2)^{3}} = \frac{1}{1.728} = 0.578704 \tag{32}\]The only approximation in the derivation is the small-angle step, and its error is bounded and third order,
\[\frac{\arctan x - x}{\arctan x} \approx - \frac{x^{2}}{3} \tag{33}\]Its size and its variation are two different quantities and only the second one matters here. The error itself reaches 1.25 percent at the eleven degrees of sideslip a fifteen metre per second crosswind produces on approach, and falls to 0.06 percent at the 2.43 degrees the same crosswind produces at the demonstration point. But the cancellation shown above is a comparison between altitudes at one Mach number, and the approximation is very nearly the same at all of them, so what survives into that comparison is only how much the error moves. At Mach 0.8 it moves by 3.3 parts in ten thousand between sea level and the tropopause. That variation is all of the residue in the comparison across altitudes reported above, an artefact of the approximation with no physical content.
| Mach | crosswind demand, Mach one taken as unity |
|---|---|
| 0.23 | 0.385 |
| 0.4 | 0.629 |
| 0.6 | 0.842 |
| 0.8 | 0.963 |
| 1.0 | 1.000 |
| 1.2 | 0.971 |
| 1.5 | 0.850 |
| 1.8 | 0.695 |
| 2.25 | 0.477 |
Read at equal throttle, that table shows the approach to be the easiest case in the envelope. At an approach Mach number of 0.227 the demand is 38.5 percent of the transonic peak. The design of every conventional aeroplane suggests the opposite, because a conventional fin’s authority falls with dynamic pressure while a nozzle’s does not.
The Throttle on Approach
The table above holds the throttle fixed, and on an approach the throttle is not fixed. It is nearly closed.
An aeroplane descending a three degree glide slope at a lift to drag ratio of six in the landing configuration needs a thrust of
\[\frac{T}{W} = \frac{1}{L/D} - \sin \gamma = \frac{1}{6} - \sin 3^{\circ} = 0.16667 - 0.05234 = 0.11433 \tag{34}\]which for a landing weight near twenty tonnes, close to the F-22’s empty weight of 19,700 kilograms [Lockheed Martin F-22 Raptor], against two engines rated at 35,000 pounds or 156 kilonewtons each [Pratt and Whitney F119], is about 7.2 percent of the maximum available thrust. The same engine source reports actual thrust of 164.6 to 173.5 kilonewtons, which would put that fraction between 6.5 and 6.8 percent, so the rated figure is the cautious choice. The control authority falls with it, because the control authority is the thrust.
Inverting for the throttle setting that restores the demonstrated margin gives the size of the problem. Writing $\Pi$ for the throttle fraction and requiring the ratio of demanded to available moment to match the demonstrated one,
\[\Pi = \frac{q_{\text{app}} \, \beta_{\text{app}}}{q_{\text{dem}} \, \beta_{\text{dem}}} \cdot \frac{\dot{m}(M_{\text{dem}}, h_{\text{dem}})}{\dot{m}(M_{\text{app}}, 0)} \tag{35}\]in which the wing area, the span, the yaw derivative, the moment arm and the maximum deflection have all cancelled, because they appear identically in both conditions. Taking the X-31’s Mach 1.2 point at maximum thrust as the unit of adequacy, and requiring the same ratio on a sea-level approach at 150 knots in a 15 metre per second crosswind, the throttle must stand at
\[\text{throttle} = 0.384 \qquad \text{against } 0.072 \text{ needed to fly the glide slope} \tag{36}\]a factor of 5.33. The landing-configuration ratio of six is an assumption. The approach and landing study flown with a straight-wing fighter at Edwards in 1959 measured a peak ratio of about four with gear and flaps extended at zero thrust [Matranga and Armstrong, Approach and landing investigation at lift-drag ratios of 2 to 4 utilizing a straight-wing fighter airplane], and at four the glide slope needs 12.4 percent of maximum thrust and the factor is 3.09. The aeroplane must carry three to five times the thrust its flight path needs, purely in order to have the yaw control its flight path does not need until something goes wrong.
That requirement is not merely expensive. It is impossible, and saying why is the strongest result in this article. An aeroplane in level flight at a given thrust has a lift to drag ratio fixed by that thrust and its weight, by the most elementary relation available.
\[T = D = \frac{W}{L/D} \qquad \Longrightarrow \qquad \frac{L}{D} = \frac{W}{\Pi \, T_{\max}} \tag{37}\]At 38.4 percent of maximum thrust, the implied ratio is
| landing weight | implied lift to drag ratio at that thrust |
|---|---|
| 20,000 kg | 1.59 |
| 22,000 kg | 1.75 |
| 24,000 kg | 1.91 |
Those ratios are below anything flown in the low lift to drag landing research. The 1959 study reached an effective peak ratio of 2.7 with speed brakes, gear and flaps extended and the engine at idle, and its pilots judged that the tolerable limit had been reached [Matranga and Armstrong, Approach and landing investigation at lift-drag ratios of 2 to 4 utilizing a straight-wing fighter airplane]. To absorb the thrust that pure propulsive yaw control demands on approach, the aeroplane would have to be about two to nearly four times as draggy as a fighter in the landing configuration is, the range running from the measured ratio of four to the assumed ratio of six, and there is no drag device on a stealth aeroplane that can do that without undoing the reason the tails were removed in the first place.
The conclusion follows without any unpublished number, because every airframe quantity cancelled in the ratio. Pure thrust vectoring cannot meet a crosswind landing requirement, and a tailless fighter therefore needs an aerodynamic yaw effector that works at low speed even though it does not need one supersonically. The X-36 flew that architecture, with split ailerons and a thrust vectoring nozzle for directional control [McDonnell Douglas X-36], and the X-31 investigated it, with differential canard deflection studied as a yaw generator of the same order as its thrust vectoring vanes [Whiting 1996].
The MANTA proposed to delete every movable aerodynamic control surface [Jenkins, Landis and Miller, American X-Vehicles, An Inventory X-1 to X-50, NASA SP-2003-4531, 2003] [X-44 MANTA Multi-Axis No-Tail Aircraft, GlobalSecurity], although one account keeps control surfaces on the wing [Lockheed Martin X-44 MANTA tailless technology demonstrator proposal]. On this arithmetic, that claim does not survive contact with a crosswind.
The Engine-Out Case
The classic reason a twin-engine aeroplane has a large fin is the failure of one engine, and for a thrust-vectored aeroplane that case is almost free. The reason is an identity.
Let the live engine sit a lateral distance $y$ from the centreline with its nozzle a distance $\ell$ aft of the centre of gravity, and let it be deflected through an angle $\delta$. Its axial component produces a yawing moment about the centre of gravity of $F_{g} y \cos \delta$ toward the dead side, and its lateral component produces $F_{g} \ell \sin \delta$ the other way. Setting them equal,
\[F_{g} \ell \sin \delta = F_{g} y \cos \delta \qquad \Longrightarrow \qquad \tan \delta = \frac{y}{\ell} \tag{38}\]The thrust cancels identically. The vector angle needed to trim an engine failure depends on nothing but where the engines are. It does not depend on how much thrust the live engine is making, on altitude, on speed, on the atmosphere or on any aerodynamic property of the aeroplane.
Two consequences follow from the same balance and neither needs a number. The axial thrust the aeroplane keeps while trimming is
\[F_{\text{axial}} = F_{g} \cos \delta = F_{g} \frac{\ell}{\sqrt{y^{2} + \ell^{2}}} \tag{39}\]which at the angles in the table below costs under two percent, and the windmilling drag of the dead engine adds to the asymmetry it must cancel, so
\[\tan \delta = \frac{y \left( F_{g} \cos \delta + D_{\text{wm}} \right)}{\ell \, F_{g} \cos \delta} \tag{40}\]Solving the moment balance numerically without cancelling the thrust by hand gives the same angle, at thrusts spanning three orders of magnitude from one kilonewton to one meganewton, agreeing with the arctangent to within one part in a billion.
| lateral offset $y$ | arm $\ell$ | required $\delta$ |
|---|---|---|
| 0.70 m | 6.5 m | 6.15 deg |
| 0.70 m | 8.5 m | 4.71 deg |
| 0.85 m | 7.5 m | 6.47 deg |
| 1.00 m | 6.5 m | 8.75 deg |
| 1.00 m | 7.5 m | 7.59 deg |
| 1.20 m | 6.5 m | 10.46 deg |
| 1.20 m | 8.5 m | 8.04 deg |
The published nozzle deflection of the F-22 is twenty degrees, and every angle in that table is below eleven [Pratt and Whitney F119]. Adding the windmilling drag of the dead engine at ten percent of the live engine’s gross thrust takes the middle case from 7.59 degrees to 8.35, still well within it.
A relation explains why a fin is large and a nozzle need not be, without appeal to intuition. Setting the fin’s yawing moment equal to the thrust asymmetry and solving for the geometry gives
\[S_{v} \, l_{v} = \frac{T \, y}{q \, a_{v} \, \tau \, \eta_{v} \, \delta_{r,\max}} \tag{41}\]The dynamic pressure sits in the denominator, so the requirement blows up as the aeroplane slows. Halving the speed at which the failure must be survived quadruples the fin the aeroplane must carry for the rest of its life, and every one of the terms above except $q$ is a constant of the design. A fin must therefore be sized for the engine-out case at the lowest speed at which it can occur. A nozzle’s authority and the asymmetry it must cancel are the same quantity, so the case is speed-independent by construction. The engine-out requirement, one of the two classic fin-sizing cases, does not size a thrust-vectored aeroplane.
The other classic case is the crosswind landing, which the previous section showed cannot be met.
The Divergence and the Loop That Must Hold It
Control authority is necessary but not sufficient. An unstable aeroplane must also be stabilised faster than it diverges.
With the tail removed the directional mode diverges without oscillating, and its growth rate follows from the yawing moment of inertia $I_{z}$.
\[\lambda = \sqrt{\frac{q S b \left| C_{n\beta} \right|}{I_{z}}} \qquad t_{2} = \frac{\ln 2}{\lambda} \tag{42}\]Neither the yaw derivative of a tailless F-22 nor its yawing inertia has been published, so the table brackets both across their plausible ranges and asserts no value.
| $\left | C_{n\beta}\right | $ per radian | $I_{z}$ kg m² | $t_{2}$ approach | $t_{2}$ Mach 1.2 at 37,500 ft |
|---|---|---|---|---|---|
| 0.03 | 1.2 × 10⁵ | 0.706 s | 0.292 s | ||
| 0.03 | 2.0 × 10⁵ | 0.911 s | 0.377 s | ||
| 0.06 | 1.6 × 10⁵ | 0.576 s | 0.238 s | ||
| 0.10 | 1.2 × 10⁵ | 0.386 s | 0.160 s | ||
| 0.10 | 2.0 × 10⁵ | 0.499 s | 0.206 s |
Every cell in that table is under one second, and no supersonic cell reaches four tenths.
A time to double does not by itself place a requirement on the hardware. Turning it into a budget does, and a budget forces a conclusion an amplification cannot. Stabilising a real pole at $\lambda$ demands a loop crossover some multiple of it,
\[\omega_{c} = k \lambda \qquad k \approx 2 \ \text{to} \ 3 \tag{43}\]and a pure transport delay $\tau$ anywhere in that loop spends phase in direct proportion to the crossover it must survive,
\[\Delta \phi = \omega_{c} \tau \qquad \Longrightarrow \qquad \tau_{\max} = \frac{\Delta \phi}{k \lambda} \tag{44}\]That delay has been measured in flight. Pure time delays were deliberately inserted into the control system of the F-8 digital fly-by-wire aeroplane and flown in low lift to drag landings [Berry et al. 1980], and a later evaluation in pitch and roll found their effect strongly dependent on the task and severe in roll for landings in turbulence [Berry 1985]. The budget below therefore draws on flight data as well as on a phase argument.
Budgeting thirty degrees of phase margin to delay alone, and taking the middle of the inertia bracket, the total latency of sensing, computing and actuating must fit inside
| condition | $\lambda$ | $\tau_{\max}$ at $k = 2$ | $\tau_{\max}$ at $k = 3$ |
|---|---|---|---|
| approach | 1.203 /s | 218 ms | 145 ms |
| Mach 1.2 at 37,500 ft | 2.909 /s | 90 ms | 60 ms |
Sixty to ninety milliseconds is a demanding but ordinary digital flight control budget. The divergence is not beyond a person. Practised subjects holding a first-order divergence in a single-axis tracking task lost control at mean instabilities of 6.0 to 6.6 per second [Jex, McDonnell and Phatak, A critical tracking task for man-machine research related to the operator’s effective delay time], and the fastest divergence in the bracket above is 4.3 per second. What that comparison does not license is a pilot as the stabilisation loop of a fighter, because those subjects attended to nothing else and lost control with small stability margins at their limit, while the budget above reserves thirty degrees of phase. The stabilisation loop is therefore better given to machinery than to a person, a conclusion drawn from margin and attention as well as from speed. It also identifies which component binds, because sixty milliseconds is spent by an actuator far sooner than by a processor.
The X-31 report’s lessons emphasise sensors for this reason, as Sensing Sideslip below sets out. When the loop must close in a fraction of a second, the limiting component is the thing that measures sideslip, not the thing that produces the moment.
The X-44A From Its Published Performance
One dimension, one engine, two dates and three performance figures are the entire released specification. The span is about 30 feet, or 9.14 metres [Lockheed Skunk Works X-44A flying-wing drone revealed]. The engine is a Williams F112 of 732 pounds force, which is 3,256 newtons [Williams F112] [Williams International F112-WR-100 Turbofan, National Museum of the United States Air Force]. It was built in 1999 and flown in 2001 [Lockheed Skunk Works X-44A flying-wing drone revealed], and the museum gives a maximum speed of 176 miles per hour, an endurance of 1.5 hours and a range of 230 miles [Lockheed Martin X-44A, National Museum of the United States Air Force]. A trade account adds a wing sweep of about 30 degrees, a fixed tricycle landing gear, an all carbon fibre airframe and a long air data probe later removed, and describes the aircraft as built to investigate the stability and control of the configuration [Skunk Works reveals stealthy UAV demonstrator]. The engine is a cruise missile powerplant, developed for the AGM-129 Advanced Cruise Missile [AGM-129 Advanced Cruise Missile], a choice that brings small size and low cost along with a design point unlike an aeroplane’s.
The most useful comparison available is not to another unmanned aircraft. It is to the X-36, which used the same engine. The X-36 carried an F112 of the 700 pound force thrust class in an airframe of 10.4 feet or 3.17 metres span and 1,245 pounds or 565 kilograms takeoff gross weight, giving a thrust to weight ratio of 0.56 [Walker 1997]. The X-44A spans 2.88 times as much on the same thrust, which taking wing area as proportional to the square of span is a factor of
\[\left( \frac{9.144}{3.17} \right)^{2} = 8.32 \tag{45}\]more wing on the same engine. Two aircraft with one powerplant and an eight-fold difference in wing area are not variants of a concept. They are answers to different questions, and the wing records the difference.
Calibrating the thrust lapse on the DarkStar puts a number on the rest. The DarkStar published a service ceiling of 45,000 feet, a gross weight of 3,856 kilograms and a Williams FJ44-1A of 8.45 kilonewtons [Lockheed Martin RQ-3 DarkStar]. At the ceiling, thrust available equals drag at the best lift to drag ratio, so
\[T_{\text{SL}} \sigma^{n} = \frac{W}{(L/D)_{\max}} \qquad (L/D)_{\max} = \tfrac{1}{2} \sqrt{\frac{\pi e A\!R}{C_{D_{0}}}} \tag{46}\]The second of those comes from a parabolic drag polar,
\[C_{D} = C_{D_{0}} + \frac{C_{L}^{2}}{\pi e A\!R} \qquad A\!R = \frac{b^{2}}{S} \tag{47}\]maximised where the induced drag equals the zero-lift drag exactly, which fixes the lift coefficient the aeroplane must fly at,
\[C_{L}^{\ast} = \sqrt{C_{D_{0}} \, \pi e A\!R} \qquad \left( \frac{L}{D} \right)_{\max} = \frac{C_{L}^{\ast}}{2 \, C_{D_{0}}} \tag{48}\]That polar and the best ratio it yields are the forms every preliminary design text gives [Raymer, Aircraft design, a conceptual approach] [Filippone, Advanced aircraft flight performance], and the thrust lapse exponent is the quantity that a design text would supply from a table and that the calibration below measures instead [Mattingly, Aircraft engine design].
The efficiency factor $e$ in the polar’s denominator carries the name of the report that introduced it as a way of collapsing a real aeroplane’s polar onto the elliptic one [Oswald 1932], and the value of 0.85 used here is a conventional one for a clean high aspect ratio wing rather than a measured property of this aircraft.
The middle relation also fixes the ceiling speed, which is therefore not free either.
\[V = \sqrt{\frac{2 W}{\rho \, S \, C_{L}^{\ast}}} \qquad \frac{W}{S} = \frac{\rho V^{2} C_{L}^{\ast}}{2} \tag{49}\]Taking a 42 square metre wing, which gives an aspect ratio of 10.53, an Oswald efficiency of 0.85 and a zero-lift drag coefficient of 0.015, the lift coefficient at best ratio is 0.6494, the best ratio is 21.65 and the required thrust at the ceiling is 1,747 newtons. The density ratio there is 0.1936, so
\[n = \frac{\ln \left( 1747 / 8450 \right)}{\ln 0.1936} = 0.960 \tag{50}\]The calibration expresses the lapse in density ratio rather than in pressure ratio. The two differ by the temperature ratio, and at that altitude the density ratio is a third larger than the pressure ratio, so the choice of variable is not academic.
The museum’s figures fix the speed, so the unknown that remains is the altitude. The 230 miles covered in 1.5 hours is a mean speed of 153.3 miles per hour, or 68.55 metres per second, 87 percent of the 176 mile per hour maximum [Lockheed Martin X-44A, National Museum of the United States Air Force]. Range is distance over the ground, so if the range and the endurance describe the same flight the mean is a true airspeed in still air, and it argues against reading the maximum as an equivalent airspeed at altitude. At 45,000 feet an equivalent 176 miles per hour would be a true airspeed near 400, and an hour and a half at that speed would cover about 600 miles.
An aircraft cruising at or above its speed for best lift to drag ratio flies at a lift coefficient no greater than $C_{L}^{\ast}$, and for a jet with a parabolic polar the best-range speed lies above that speed. The ceiling speed relation above therefore becomes a bound, $W/S \le \rho V^{2} C_{L}^{\ast} / 2$, at whatever altitude the aircraft cruised, and on the DarkStar’s polar it depends on altitude alone. The last column compares the thrust the F112 makes at each altitude, lapsed with the exponent above, against the drag at the bound on the 7.94 square metre wing that the DarkStar’s aspect ratio gives a 30-foot span.
| cruise altitude | density ratio | wing loading bound at 153 mph | bound at 176 mph | bound over the DarkStar’s | thrust over drag |
|---|---|---|---|---|---|
| sea level | 1.0000 | 191 kg/m² | 251 kg/m² | 2.08 | 4.7 |
| 10,000 ft | 0.7385 | 141 kg/m² | 185 kg/m² | 1.53 | 4.8 |
| 20,000 ft | 0.5328 | 102 kg/m² | 134 kg/m² | 1.11 | 4.9 |
| 30,000 ft | 0.3741 | 71 kg/m² | 94 kg/m² | 0.78 | 4.9 |
| 40,000 ft | 0.2462 | 47 kg/m² | 62 kg/m² | 0.51 | 5.0 |
The DarkStar’s wing loading on the same assumptions is 91.8 kilograms per square metre. The X-44A’s can exceed it only if the aircraft cruised below about 22,900 feet at its mean speed or 30,600 feet at its maximum, and even at sea level the bound is 2.08 times the DarkStar’s at the mean speed and 2.74 times at the maximum. A cruise at a reconnaissance ceiling is excluded. At best ratio on the same polar the F112 would hold assumed ceilings of 35,000 to 55,000 feet only at true airspeeds of 342 to 349 miles per hour, about twice the published maximum.
The wing loading therefore does not settle what the aeroplane was for, and the published endurance does. An hour and a half and 230 miles are the figures of a short-range demonstrator [Lockheed Martin X-44A, National Museum of the United States Air Force]. They agree with the purposes the programme stated [Lockheed Skunk Works X-44A flying-wing drone revealed] and with the stability and control investigation the trade account describes [Skunk Works reveals stealthy UAV demonstrator], and they are far from the loiter of the DarkStar, which was designed as a high-altitude endurance aircraft [Lockheed Martin RQ-3 DarkStar].
The last column carries a second finding. At every altitude the engine makes 4.7 to 5.0 times the clean-polar drag at the bound, so on that polar the aircraft could fly well above its published maximum. Either its drag is several times that of the assumed clean wing, which a fixed landing gear, an air data probe and a lower aspect ratio would each push towards, or the maximum is a limit set by something other than thrust, and the sources do not say which.
One caveat is load-bearing. The DarkStar’s wing area is not published in the sources used and 42 square metres is an assumption, and the X-44A’s aspect ratio is assumed equal to the DarkStar’s. The bound moves with the area through the aspect ratio, and the comparison moves further because the DarkStar’s loading varies inversely with the area. At assumed areas of 35 and 50 square metres the sea-level bound at the mean speed is 1.90 and 2.27 times the DarkStar’s, and the altitude above which the X-44A’s loading must be the lower of the two moves with it.
Dependent Systems
The Nozzle the F-22 Does Not Have
The most consequential fact about the MANTA is one that its published description obscures. The proposal is routinely described as converting an F-22 by deleting its tails and using its thrust vectoring nozzles for control [X-44 MANTA Multi-Axis No-Tail Aircraft, GlobalSecurity]. The F-22 has no yaw vectoring. Its Pratt and Whitney F119 engines carry two-dimensional convergent-divergent nozzles that deflect through plus or minus twenty degrees in pitch only [Lockheed Martin F-22 Raptor] [Pratt and Whitney F119].
A two-dimensional nozzle deflects in the plane of its flaps and in no other. The flaps rotate the jet through $\delta_{p}$ in one plane, and the components that reach the airframe are
\[F_{x} = F_{g} \cos \delta_{p} \qquad F_{z} = F_{g} \sin \delta_{p} \qquad F_{y} = 0 \tag{51}\]The zero side force is the problem. Producing yaw from the same nozzle requires the sidewalls to become deflecting surfaces, giving a second independent angle and a side force that did not previously exist,
\[F_{y} = F_{g} \cos \delta_{p} \sin \delta_{y} \qquad F_{x} = F_{g} \cos \delta_{p} \cos \delta_{y} \tag{52}\]The product form is why the cross-coupling question had to be measured instead of assumed, and yaw vectoring calls for new hardware in the same envelope, which no new schedule for the existing hardware could supply. The MANTA is therefore not a subtraction from the F-22. It is a subtraction and an addition, and the addition is the harder half.
That addition has been measured, and the measurement is encouraging. Capone and Bare tested an advanced twin-engine supersonic-cruise fighter model with a two-dimensional convergent-divergent nozzle designed to give yaw vector angles of zero, ten and twenty degrees through yaw flaps in the nozzle sidewalls, with roll obtained from differential pitch vectoring, across Mach 0.20 to 2.47 [Capone and Bare 1987]. Their central result is that the force and moment increments produced by vectoring remain essentially constant over the whole angle of attack range at every Mach number tested, and that pitch and yaw vectoring show very little cross-coupling. A control effector whose authority does not vary with angle of attack is precisely what a tailless aeroplane needs, because an aerodynamic fin’s authority collapses at the angles where a fighter most wants it.
The wider measurement literature reports the same across several configurations [Capone and Mason 1986] [Berrier 1988], and the flight literature adds that vectoring hardware survives being flown [Anna and Kidman 1994].
The Wing
The MANTA’s wing is described only as a stretched delta of greater area than the F-22’s, carrying more internal fuel [Lockheed Martin X-44 MANTA]. No area, sweep, aerofoil or aspect ratio is public, so nothing can be dimensioned from it. What can be stated is the gain and the cost of the change.
A larger delta gains fuel volume, and volume grows faster than area, because a wing scaled in plan at fixed thickness ratio and aspect ratio gains depth as well as span.
\[\text{Vol} \propto \left( \frac{t}{c} \right) \frac{S^{3/2}}{\sqrt{A\!R}} \qquad \Longrightarrow \qquad \frac{\text{Vol}_{2}}{\text{Vol}_{1}} = \left( \frac{S_{2}}{S_{1}} \right)^{3/2} \tag{53}\]A quarter more wing is forty percent more fuel, a better return than the linear reading of the claim suggests. It also brings a lower wing loading at fixed weight, and through it sustained turn rate at altitude,
\[n = \frac{q \, C_{L}}{W/S} \qquad \dot{\psi} = \frac{g \sqrt{n^{2} - 1}}{V} \tag{54}\]It costs wave drag and it costs directional stability, and the second of those has a form that needs displaying because the article later has to assume a value for it. A slender body in sideslip carries the Munk moment, which is destabilising and depends on volume rather than on area,
\[C_{n\beta, \text{fus}} = - \frac{2 \left( k_{2} - k_{1} \right) \text{Vol}_{\text{fus}}}{S \, b} \tag{55}\]That relation is a hundred years old and was derived for airships. Munk obtained the moment on a slender body in a stream in 1924, and the apparent-mass factor in the numerator is his [Munk 1924]. Multhopp adapted it to the aeroplane fuselage [Multhopp 1942], and Allen and Perkins added the viscous cross-flow term that the inviscid theory omits and that matters at the angles a fighter reaches [Allen and Perkins 1951]. The article uses the inviscid form, which is the conservative one for its purpose, since the cross-flow contribution grows with angle of attack and would make the aeroplane less stable still.
Inverting that relation is the only check available on the assumed instability bracket, since neither the derivative nor the volume is published. At an apparent-mass factor of 0.94, a derivative of 0.06 per radian implies a fuselage volume of 33.8 cubic metres, which over the F-22’s 18.92 metre length [Lockheed Martin F-22 Raptor] is a mean cross-section of 1.79 square metres. No fuselage volume is published, so this check cannot say whether the bracket is conservative. The two F119 engine envelopes alone, 497.8 centimetres long and 121.9 centimetres in overall diameter [Pratt and Whitney F119], enclose 11.6 cubic metres, about a third of the 33.8 that the derivative implies, and the inlets, bays, fuel and equipment around them are not dimensioned in any source used here. If the real aeroplane is more unstable than the middle of the bracket, which is the direction that matters, the supersonic time to double falls at 0.10 per radian from 0.238 to 0.185 seconds. There is no longer a fin to overcome any of it. The tailless delta literature is unusually old and unusually direct about the second point [White and Innis 1959] [Smith 1953b] [Harper and Jones 1947].
The X-44A’s wing is known from the journalism, since no specification describes it. It is reported as a modular flying wing with a bulbous fuselage, wings that appear removable, control surfaces along the trailing edge and raked, squared-off wingtips [Lockheed Skunk Works X-44A flying-wing drone revealed] [Exclusive photos, the X-44A breaks cover] [Skunk Works reveals the tailless X-44A]. Modularity is the telling detail, because modular wings on a demonstrator may mean that the wing was a variable under test, although the journalism suggests that they detach for transport.
Structure and the Manufacturing Claim
The X-44A is reported as built from nano-carbon fibre and as a demonstration of rapid manufacturing [Lockheed Martin X-44, the unmanned vehicle] [Lockheed Skunk Works X-44A flying-wing drone revealed]. No mass fraction, no lay-up, no cure cycle and no tooling description has been released, so the claim cannot be checked in the way the aerodynamic claims can. It stands as a stated programme objective that no measurement confirms.
The timeline is the one checkable part of it. DarkStar was terminated in January 1999 and the X-44A was built in 1999 [Lockheed Martin RQ-3 DarkStar] [Lockheed Skunk Works X-44A flying-wing drone revealed]. A complete airframe within a calendar year is the evidence for the manufacturing claim, and apart from the museum’s statement that the airframe was quickly built using advanced manufacturing techniques [Lockheed Martin X-44A, National Museum of the United States Air Force] it is the only evidence in the public record that bears on it.
Sensing Sideslip
The divergence table above says the loop must close in a fraction of a second, and the X-31 report names what that costs. Its lessons concern sensor-related issues and their importance both to simulating a tailless configuration and to controlling a directionally unstable one [Bosworth and Stoliker 1996]. Sideslip is small and is measured in a flow field that the aeroplane itself distorts, and a boom or vane is the kind of protrusion a stealth configuration exists to avoid. The flush alternative has flown. A matrix of nose pressure orifices on the F-18 High Alpha Research Vehicle measured angles of attack and sideslip with a pneumatic frequency response beyond 10 hertz, and aerodynamic lags in the aircraft’s own flow field degraded it during heavy manoeuvring [Whitmore, Moes and Larson, Preliminary results from a subsonic high angle-of-attack flush airdata sensing system].
The obvious way to size that requirement is to ask what a measurement error costs, and the answer is that static accuracy is not what binds. A sideslip error is indistinguishable from a real sideslip, so it commands a real moment,
\[\Delta C_{n} = \left| C_{n\beta} \right| \varepsilon_{\beta} \tag{56}\]and the gearing from sideslip to nozzle follows from the required-deflection relation already displayed,
\[\frac{d \delta}{d \beta} = \frac{q S b \left| C_{n\beta} \right|}{F_{g} \, \ell \, \cos \delta} \tag{57}\]Both come out mild. The gearing is 1.13 nozzle degrees per sideslip degree at the demonstration point and 1.35 on the approach, and a half-degree measurement error costs 2.9 percent of the available authority. A static accuracy requirement of half a degree is not a hard requirement.
What survives is the dynamic requirement, which the budget above sets. The loop must close inside sixty to ninety milliseconds supersonically, so the sensor’s lag and its noise at the crossover frequency are the binding properties rather than its static accuracy.
The tension in the MANTA concept is therefore narrow but real. The aeroplane deletes its fin to reduce its radar cross section, and the deletion creates a hard requirement for a fast measurement of sideslip, which a low-observable nose must supply through flush ports whose speed is limited by the aeroplane’s own flow field. No public source explains how the MANTA proposed to resolve even the narrow version, and the absence is left unfilled.
The Flight Test Record
Three flight records are relevant here, and only one of them belongs to an aeroplane called X-44.
What the X-31 Flew
The quasi-tailless experiment is the substantive flight record for the MANTA’s question. The technique was to use the rudder to cancel the stabilising effect of the vertical tail, and then to restabilise and control the aeroplane with yaw thrust vector commands [Bosworth and Stoliker 1996]. The cancellation is a scheduled rudder command, involving no mechanical change, so it can be written down. With $\kappa$ the fraction of the tail to be removed,
\[\delta_{r} = - \kappa \, \frac{C_{n\beta, \text{tail}}}{C_{n \delta_{r}}} \, \beta \tag{58}\]Setting $\kappa$ to one gives the hundred percent case that was flown and any smaller value gives a reduced-tail aeroplane, which is how one airframe produced a family of configurations instead of a single data point. The gearing is steep. A tail contributing 0.15 per radian against a rudder worth 0.0788 per radian demands 1.9 degrees of rudder for every degree of sideslip, so the technique spends most of a real control surface to simulate the absence of one. The result is a real aeroplane behaving like a tailless one without building a tailless one, possible only because the aeroplane already carried thrust vectoring paddles for a different purpose [Rockwell-MBB X-31] [Huber and Schellenger 1994] [Bosworth and Stoliker 1996]. The series began in March 1994. The demonstration condition was Mach 1.2 at 37,500 feet with a simulated one hundred percent vertical tail reduction, and the manoeuvres flown were doublets, bank-to-bank rolls and wind-up turns. The quasi-tailless mode was also flown subsonically in precision approaches and ground attack profiles [Huber and Schellenger 1994] [Bosworth and Stoliker 1996].
Its conclusion is unambiguous and is quoted here because the wording matters. Flight test and supporting simulation demonstrated that the quasi-tailless approach is effective in representing the reduced stability of tailless configurations, and that thrust vectoring could be effectively used to stabilise a directionally unstable configuration and provide control power for manoeuvre coordination [Huber and Schellenger 1994]. Tailless and reduced-tail fighter aircraft are, in the report’s word, definitely feasible, with the qualification that the capability must be designed in from the beginning [Bosworth and Stoliker 1996].
That qualification states the MANTA’s difficulty in one clause. The MANTA was a conversion.
One thing the demonstration did not do was fly an approach on vectoring alone. Its precision approaches were flown at 40 and 50 percent tail reduction in low turbulence or clear air, and no crosswind approach is reported [Bosworth and Stoliker 1996]. The arithmetic above explains why a crosswind approach on vectoring alone could not have been flown.
What the X-44A Flew
It first flew in 2001, and the released record adds only summary figures and general statements. The museum gives a maximum speed of 176 miles per hour, an endurance of 1.5 hours and a range of 230 miles, and says that the aircraft refined tailless aerodynamics and flight controls, improved Lockheed Martin’s unmanned command and control system and supported a deck-handling demonstration for United States Navy carriers [Lockheed Martin X-44A, National Museum of the United States Air Force]. The number of flights is unknown. The dates are unknown. The altitude envelope is unknown. No incident or measurement is on the public record. The aeroplane survived, which is inferable from its presence in a museum and from nothing else.
A vehicle that flew and produced data that remains unreleased is a different epistemic object from a vehicle that never flew.
What the MANTA Flew
Nothing. No airframe was built. The programme ended with funding, not with a flight or a failure.
Comparison With Ground Prediction
Of the three flight records, only one can be set beside a prediction, and most of what it can be set beside was written after the flight. No ground prediction for either vehicle called X-44 is public, so the comparison draws on the X-31 record and on the arithmetic under Sizing From First Principles.
For the MANTA the ground record is a list of claims and the flight record is empty. Its advertised benefits are given under The Research Question, and nothing flew to test them. The single measurement behind its hardware is a wind tunnel result with no flight counterpart on this aircraft, the sidewall yaw-flap measurement described under The Nozzle the F-22 Does Not Have, and yaw flaps of that kind were never flown on a MANTA because there was no MANTA.
For the X-31 the comparison is between simulation and flight, and the report states its outcome as a conclusion rather than as a table, the conclusion quoted under What the X-31 Flew. This article reports no numerical prediction made before those flights and no figure for how closely the simulation matched them, and it does not supply one.
The derivations above meet the X-31 record in two places, and in a third only in kind. The first is coverage, the factor of 1.135 by which the flown point stands above the worst supersonic condition, or 1.078 when jet velocity varies. It describes what the flown point covers, and no flight tested it as a prediction. The second is sensing, where the loop budget of The Divergence and the Loop That Must Hold It meets the report’s lessons on sensor-related issues. Agreement there is in kind only, since the article quotes no latency figure from the report.
The article’s strongest prediction has no flight to be compared with, and the report anticipates it only in kind. The report notes that thrust vector control power is proportional to the engine power setting, so that landing may require drag devices to hold a higher power setting, and it lists among its lessons that flying on drag devices at an increased power setting can introduce additional directional instability [Bosworth and Stoliker 1996]. Its precision approaches were flown at 40 and 50 percent tail reduction in low turbulence or clear air, so the throttle result of The Throttle on Approach is a prediction that no flight has tested.
For the X-44A there is no ground prediction in the public record and no released flight data beyond the museum’s summary figures. The published speeds bound the wing loading derived for it and exclude a cruise at a reconnaissance ceiling, and the published endurance agrees with the programme’s stated purpose, so the comparison the record allows checks the assumed mission rather than the aircraft.
What the Data Changed
The three lines diverge sharply here and the divergence is instructive.
The tailless design literature continued after the X-31’s quasi-tailless result. The innovative control effector programmes of the later 1990s studied tailless fighter configurations [Montgomery et al. 1998], and the record cited here does not trace how far they drew on the X-31 flights.
The X-44A’s line is visible in hardware. It sits between the DarkStar and the Polecat. Its configuration family, a small tailless flying wing with a low-observable planform, is that of the Polecat and the RQ-170 and not that of the DarkStar [Skunk Works reveals the tailless X-44A]. The published assessment is that it belongs with the mid-2000s designs rather than the 1990s ones despite being built in 1999, in effect a claim that a demonstrator can be ahead of its programme.
The MANTA changed nothing that can be demonstrated. The sixth-generation fighter studies in the survey treat tailless control and signature as requirements of their own [Kim et al. 2025] [Zhaxidaji 2026], but none of them names the MANTA, and no source cited here traces a lineage from it, so this article asserts none. What can be said is narrower and firmer. The tailless fighter remains a feature expected of the next generation rather than one in service, a 2025 review naming the F-22, F-35 and Su-57 as the operational fifth generation and tailless designs as anticipated in their successors [Kim et al. 2025], and the arithmetic above suggests one reason, since the concept as the MANTA stated it holds up in the air and fails at the runway.
The Contemporary Literature
| Cluster | Records |
|---|---|
| Control effectors, allocation and flight control law design | 1,190 |
| Engine cycle, installation and inlet integration | 995 |
| Delta and swept wing aerodynamics at angle of attack | 958 |
| Thrust vectoring and propulsive control | 730 |
| Unmanned aircraft, autonomy and the reconnaissance mission | 661 |
| Low observable design and signature | 510 |
| Supersonic and transonic aerodynamics | 483 |
| Tailless configurations and the missing vertical tail | 474 |
| Nozzles, exhaust systems and internal performance | 461 |
| Directional stability, sideslip and the lateral-directional modes | 455 |
| Handling qualities and the pilot in the loop | 378 |
| Wind tunnel testing, computation and validation | 348 |
| Airframe structure, composites and manufacture | 291 |
| Aircraft conceptual design, sizing and drag | 277 |
| The atmosphere, turbulence, gust response and load alleviation | 269 |
| Approach, landing and the crosswind case | 246 |
| Wings, aerofoils and flow control | 174 |
| Flight test technique, parameter identification and air data | 158 |
| Programme, acquisition and the cost of a demonstrator | 104 |
| High altitude, endurance and mission performance | 98 |
| Stores, missiles, projectiles and finned bodies | 98 |
| Flight mechanics, equations of motion and simulation models | 87 |
| Research aircraft, fighter development and aeronautical history | 76 |
| Survivability and vulnerability of military aircraft | 59 |
| Engine failure, asymmetric thrust and minimum control speed | 51 |
| Total | 9,631 |
The survey below maps the field these two vehicles sit in, and the twenty-five research records that the argument cites stand in its cluster rows with the rest. Every record is assigned to exactly one cluster. The rule that admits a record, and the classes it excludes, are stated in the Source Base.
A cluster’s size measures how much has been published near a topic. It does not measure how important that topic is to these vehicles. The largest cluster holds flight control law design, which bears on both vehicles and enters the argument only through the loop budget, while the cluster holding this article’s keystone, being the tailless configuration itself, ranks eighth of twenty-five. Two of the clusters below cover the subjects of this article’s conclusions rather than its topics, being the approach and crosswind case and the engine failure case.
What the Shape of the Survey Says
Three features of the distribution are worth naming.
The tailless cluster is smaller than the thrust vectoring cluster, and that ordering is the wrong way round for the subject. Tailless aircraft are the application and thrust vectoring is one of several mechanisms, so a literature organised around the problem would put the problem first. It does not, because thrust vectoring is a nozzle technology with a propulsion community of its own publishing in dedicated venues, and it accumulated papers whether or not any tailless aeroplane was being built.
The median publication year is 2005 and 33.5 percent of dated records are from 2015 or later, which for a subject whose defining flight experiments happened in 1994 and 2001 means the field did not stop when the programmes did. The control-allocation and unmanned clusters carry more of that recent weight than any other cluster. The tailless configuration question is being asked again, by a different community, about aeroplanes with no pilot in them.
705 records predate 1970 and they are not decoration. The configuration has a documented history running from the 1920s, longer than the jet age [Wooldridge, Winged wonders, the story of the flying wings]. The tailless and all-wing stability literature of the 1940s and 1950s asked the same question with slide rules and free-flight models, and the answer it reached, that the configuration is controllable and the controls have to be unusually powerful and unusually fast, is the answer the 1994 flight experiment reached again with a digital flight control system. A field that rediscovers its own conclusion fifty years later is telling the reader something about which part of the problem was ever really open.
Control effectors, allocation and flight control law design
The largest cluster, and it holds what replaces a rudder when there is no rudder. Control allocation for redundant and unconventional effectors, flight control law design for unstable airframes, dynamic inversion, adaptive, reconfigurable and fault-tolerant control, fly-by-wire architecture, and the actuator literature that sets the bandwidth the divergence calculation demands. This cluster carries more of the recent weight in the survey than any other, with 399 records from 2015 or later, because allocation among many weak effectors is the problem a tailless unmanned aircraft actually has.
1,190 records. [A Comparative Study 2015] [Abdulrahim 2004] [Abe et al. 2019] [Abrams 1982] [Abrams and Weinstein 1974] [Accommodation of Failures 1991] [Acosta and Joshi 2007] [Acquatella B. et al. 2017] [Mercorelli 2026] [Adams and Banda 1993] [Adaptive Approximation Based Control 2006] [Addington and Myatt 2000] [Adegbindin et al. 2016] [向 et al. 2023] [Advanced Aircraft Control 2026] [Aerodynamics of Spoiler Control 1979] [Aerospace - Flight Control] [Aerospace Vehicle Flight Control 1965] [Ahmad et al. 2008] [Ahmadi et al. 2012] [Ahmed-Zaid et al. 1990] [Aircraft Control 2016] [Aircraft Flight Control 2014] [Aircraft Flight Control Actuation] [Aircraft flight control systems] [Aircraft Stability and Control 2003] [Aircraft Stability and Control 2014] [Aircraft Stability and Control 2024] [Akasaka 2008] [Alag 1987] [Alag and Kaufman 1975] [Alag et al. 1986] [Alam and Celikovsky 2017] [Alazard 2001] [Alazard 2002] [Ali and Elkhamry 2024] [Allen 1975] [Almuina Pica et al. 2022] [Almutairi and Aouf 2014] [Almutairi and Aouf 2015] [Almutairi and Aouf 2016] [Altman 1952] [Alvarez et al. 2013] [Alvi 2012] [Alviani et al. 2022] [Alwi and Edwards 2007] [Alwi and Edwards 2009] [Alwi and Edwards 2011] [AmirAhmadi Chomachar and Azizi 2015] [Ammar Ashraf et al. 2021] [An] [Anandakumar et al. 2022] [Anderson et al. 1972] [Anderson et al. 1991] [Anderson 1976] [Andino et al. 2015] [Andrievsky and Zaitceva 2023] [Angeli et al. 1999] [Anglin and Byrdsong 1982] [Ansari and Bernstein 2015] [Antonakis and Biannic 2024] [Appendix B 2013] [Application Analysis on Fly-by-Wire 2022] [Application of dynamic flight] [Arent and Falatko 1992] [Army Aviation School Fort Rucker Al 1961] [Arnold] [Arnold and Haar 2024] [Asadi et al. 2013] [Athans 1976] [Autopilot, Flight Director, and] [Avanzini and Galeani 2005] [Avanzini and Minisci 2010] [Aykan et al. 2005] [Azimov and Kawamura 2018] [Azizi and Khorasani 2011] [Azizi and Khorasani 2012] [Zuhair 2019] [Baba et al] [Bacon and Ostroff 2000] [Bacon et al. 1996] [Baggi et al. 2020] [Baggi et al. 2022] [Bailey 1984] [Bailey 1990] [Bajpai and Chang] [Bajpai et al] [Balague and Hajiyev 2016] [Balakrishnan and Biega 1995] [Balakrishnan and Jie Shen] [Ball 1978] [Ball 1979] [Ballouz and Chang] [Barlow et al. 2009] [Barrett et al. 1995] [Bateman et al. 2008] [Bateman et al. 2011] [Bauer et al. 2007] [Bauer et al. 2016] [Bazill and Jenney 1970] [Bazuhair 2018] [Beaufrere 1988] [Belcastro and Belcastro 2001] [Beldica and Hilton 1999] [Belkharraz and Sobel] [Belkharraz and Sobel 2004] [Belkharraz and Sobel 2005] [Belmont 1983] [Belsterling 1976] [Bennani and Looye 1998] [Benosman et al. 2007] [Berdjag et al. 2010] [Berger et al. 2015] [Bernstein 2000] [Berry and Broussard 1978] [Berry 1985] [Berry et al. 1980] [Beyer et al. 2018] [Bhardwaj and Holzapfel 2024] [Bhargavapuri and Parwana 2021] [Bhattacharya and Sivakumar 2000] [Bhatti] [Bian et al. 2018b] [Bian et al. 2019] [Biannic and Tarbouriech 2007] [Biannic et al. 2006] [Binwen Lu et al. 2016] [Blaignan and Skormin 1993] [Blight et al. 2018] [Bodson 2000] [Bodson and Pohlchuck 1996] [Bodson and Pohlchuck 1998] [Bodson et al. 1997] [Boeing B-777 2000] [Boesch et al. 2010] [Boland et al. 1993] [Boothe 1971] [Borello and Villero 1995] [Bosch and Briggs 1978] [Bosch and Kuehl 1976] [Bosch and Kuehl 1977] [Boskovic and Mehra] [Boskovic and Mehra] [Boskovic and Mehra] [Boskovic and Mehra 2001] [Boskovic and Mehra 2002b] [Boskovic and Redding 2009] [Boskovic et al] [Boskovic et al] [Boskovic et al. 2005b] [Bouadi] [Boudreau 1976] [Boudreau 1977] [Bradshaw et al. 1985] [Brennison et al. 2010] [Brincklow and Hunsaker 2020] [Brincklow and Hunsaker 2021] [Brown and Szalai 1977] [Buffington et al. 1999] [Bumby 1971] [Burge 1996] [Burken et al. 1986] [Burken et al. 2010] [Burken et al. 2011] [Cakiroglu et al. 2018] [Calise and Kramer 1982] [Caliskan and Hajiyev 2013] [Campbell 1974] [Cano and Sobel 2016] [Cao and Liu 2025] [Cao and Lyu 2024] [Cao et al. 2020] [Cao et al. 2025] [Carithers and Montalvo 2018] [Carlin and Blair 1983] [Cervia et al. 2006] [Chand and Hansen] [Chandler and Potts 1983] [Chandramohan et al. 2007] [Chang et al. 2005] [Chang et al. 2022c] [Chang et al. 2022b] [Chapter 12. Control 1994] [Chapter 13. Control 1994] [Chen and Saif 2007] [Chen and Zhang 2008] [Chen et al. 2002] [Chen et al. 2019a] [Chen et al. 2021b] [Cheng et al. 2017a] [Chi 1990] [Chin et al. 1987] [Choi et al. 2015] [Chu et al. 2001] [Chudoba and Cook 2003] [ChunSheng Liu et al. 2012] [Citurs 1984] [Clark and LeTron 1989] [Cliff and Lutze 1972] [Clifford 1968] [Coletti and Faruque 2022] [Collinson 1996] [Collinson 1999] [Collinson 2003] [Collinson 2011] [Collinson BSc(Eng 1978] [Comer et al. 2024] [Conceptual and Preliminary Design 2017] [Control Allocation and Flight 2016] [Control Authority Assessment 1993] [Cook and Crossley 2000] [Cook et al. 2008] [Cooper and Rothhaar 2018] [Cordeiro et al. 2024] [Corraro et al. 2011] [Cossar 1999] [Cotton 1974] [Craig 1965] [Crider 2004] [Cristofaro and Faleschini 2024] [Cristofaro and Galeani 2014] [Cristofaro et al. 2015] [Cruz and Kienitz 2007] [Cui et al. 2016] [Cunningham 1976] [Curtiss 1971] [Daskiran and Kavsaoglu 2011] [Davidson et al. 2001] [Daşkɪran and Kavsaoğlu 2013] [De Gaspari and Mantegazza 2024] [de Vries and Van Kampen 2019] [Deb et al. 2007] [Deb et al. 2021b] [Deb et al. 2021a] [Deb et al. 2021c] [Deb et al. 2022] [Deckert 1981] [Deets and Szalai 1972] [Demarchi and Haning 1978] [Dendy and Tribken 1968] [Dennis and Scherrer 1951] [Deori et al. 2015] [Deori et al. 2016] [Deppe et al. 1996] [Desai et al. 1976] [Description of Actuation Systems] [Design Guidelines for Aircraft] [Design of Control Surfaces 2012] [Dethomas and Goel 1982] [Development of a robust 1994] [Development Process - Aerospace] [Devi 2019] [Deyst and Deckert 1975] [Di Rito et al. 2016] [Dias et al. 2023] [Diepolder et al. 2017] [Digital Model-Reference Flight Control 1994] [Dijkgraaf and Bennani] [Dimitrios G. Dimogianopoulos 2006] [Dinh-Khanh Dang et al. 2012] [Dixon 1972] [Djouadi 2010] [Do 2021] [Dobos-Bubno and Hartsook 1977] [Doman and Oppenheimer 2002] [Doman and Sparks 2002] [Dong Cao et al. 2016] [Dong et al. 2016] [Dong et al. 2025a] [Droste and Walker 2010] [Duan and Okwudire 2019] [Ducard and Geering 2006] [Ducard and Geering 2008] [Dukes 1970] [Durham and Bordignon 1995] [Durham and Bordignon 1996] [Durham and Leedy 1998] [Durham et al. 2016] [Ehlers and Smyth 1970] [Ehlers and Weisshaar 1993] [Ellis 1972] [Empey and Nahon 2022] [Enenakpogbe et al. 2022] [Enns 2003] [Enns 2015] [Enns 2021] [Enns et al. 1994] [Enomoto 2010] [Escande 1997] [Escande 1998] [Esfahani et al. 2018] [Estimation and Sensitivity 2026] [Etewa et al. 2023] [Fadel et al. 2019] [Famularo and Valasek 2018] [Fan et al. 2012] [Fang Liao et al] [Farineau 1989] [Fault Tolerant Control 2025] [Favre 1994] [Favre 2018] [Feedback Flight Control 2026] [Fekih 2011] [Fen Wu and Soto] [Ferrante et al. 2023] [Ferrari and Jensenius 2005] [Ferreres and Puyou 2006] [Feucht et al. 1978] [Fielding 2001] [Fielding 2010] [Flight Control 2015] [Flight Control Actuation Systems 2025] [Казак 2000] [Flight Control System Design 2011] [Flight Control System 1977] [Flight Control Using Nonlinear 2000] [Wu et al. 2013a] [Flight Envelope Awareness/Protection] [Flight Vehicle Aerodynamic Control 2001] [Folded Shear Plane Control 1979] [Forster et al. 2025] [Fosdick 1970] [Fournier] [Fournier 2001] [Frame-Wise Control Allocation 2016] [Franklin 2018] [Franze et al. 2013] [Fredericks et al. 1987] [Friedland 1964] [Friedland 1982] [Frost et al. 2012] [Frost et al. 2010] [Fuzzy Logic for Control 1991] [Gabriel and Schreiber 1969] [Gadient and Weltz 2004] [Gai et al. 2014] [Gainer 1963] [Gal-Or 1992] [Galeani and Sassano 2018] [Gang Tao et al] [Gang Tao et al. 2006] [Gao and Antsaklis] [Gao et al. 2020] [Gao et al. 2021e] [Gao et al. 2021g] [Gao et al. 2021b] [Gao et al. 2021f] [Gao et al. 2021a] [Gao et al. 2021h] [Gao et al. 2021c] [Gao et al. 2025] [Garmendia and Mavris 2016] [Garmendia et al. 2015] [Garrard and Balas 1995] [Gayaka and Yao 2008] [Gayaka and Yao 2011] [Gaylor 1984] [Gelderloos and Young 1982] [Generally on automatic flight] [Gill 1995] [Gillard 1998] [Giovanini 2003] [Giurgiutiu and Pomirleanu 2000] [Glavaski and Elgersma] [Glavaski et al. 2002] [Glezer and Leonard 2012] [Glezer et al. 2010] [Goman and Kolesnikov 1998] [Goman et al. 1996] [Goodrich and Sliwa 1987] [Gopalswamy and Hedrick 1991] [Gotlieb 1977] [Gotlieb et al. 1976] [Govindaraj et al. 1979] [Govoni and Cristofaro 2023] [Graff et al. 2013] [Graham 1986] [Graham and McRuer 1991] [Gran et al. 1975] [Gran et al. 1977] [Grantham et al. 1994] [Greer et al. 2021] [Grondman et al. 2018] [Grosser 1965] [Grossman 1957] [Ground and Flight Testing 2000] [Gui et al. 2019] [Guo et al. 2011] [Guo et al. 2013a] [Guo et al. 2016] [Guo et al. 2024] [Guo et al. 2026] [Gäßler and Robens 2025] [Ha 1990] [Ha 1991] [Hajiyev 2011] [Hajiyev 2016] [Hajiyevt and Caliskan 2001] [Hall and Mason 2012] [Hameduddin and Bajodah 2011a] [Hameduddin and Bajodah 2011b] [Hameduddin and Bajodah 2012] [Hamel 2017a] [Hammer and Bright 1998] [Hammond 1963] [Hannan et al. 2017] [Hansen et al. 2020] [Hansen et al. 2022] [Hansman and Sturdy 1989] [Hansman and Sturdy 1988] [Hardwick and Panella 2017] [Harkegard] [Harris and Valasek 2018] [Harris et al. 2019] [Harris et al. 2022] [Hart 1956] [Hart 1968] [Hartmann and Stein 1978] [Hastedt et al. 2022] [He et al. 2020] [Hecht and Hung 1985] [Heller et al. 2013] [Hemsch and Nielsen 1982] [Henderson and Lavretsky 1999] [Henkenjohann et al. 2024] [Herrmann and Ben-Asher 2016] [Hess 2012] [Hess 2013] [Hess and Cama 2008] [Hess and Peng 2018] [Hess and Snell 1995] [Hess and Snell 1996] [Hess et al. 1999] [Hess et al. 2000] [Hill 1987] [Hillebrand and Lutz 2026] [Hilton and Steed 1985] [Himich and Kineyko 1981] [Hindman and Shell] [Hinson et al. 2011] [Hofsäβ and Holzapfel 2024] [Hogan and Rinde 1978] [Horla 2012] [Horla 2013] [Horla 2017] [Horn et al. 1998] [Horowitz et al. 1980] [Hougui et al. 1995] [Hristov 2023] [Hu et al. 2012b] [Hu et al. 2026a] [Huang 1988] [Huang et al. 2017b] [Huang et al. 2017d] [Husin et al. 2022] [Hussain et al. 2013] [Huzmezan 1998] [Huzmezan and Maciejowski 1999] [Hyde and Glover 1993] [Harasani 2015] [Ijaz et al. 2018] [Ijaz et al. 2019b] [Ijaz et al. 2019a] [Integrated Flight Instruments and] [Integrated Rudder and Brake] [Introduction 2017] [Ishihara et al. 2010] [Jackson 2023] [Jackson and Patch 1968] [Jang et al. 2007] [Jarvis 1967] [Jayakumar and Das 2006] [Jayalakshmi et al. 2021] [Jayaraman and Ghosh 2021] [Jayaraman et al. 2022] [Jayasuriya and Chang] [Jebakumar et al. 2019] [Jeffrie and Rolston 1972] [Jegathesan et al. 2025] [Jenney 1978] [Jenney 1979] [Jenney 1980] [Jenney and Schreadley 1984] [Jenney et al. 1982] [Jiang 2001] [Jiang et al. 2010] [Jianjun Ma et al. 2008c] [Jianjun Ma et al. 2008b] [Jianjun Ma et al. 2008a] [Jiaqiang Zhu et al] [Jin et al. 2025] [Jines 1983] [Jing and Ma 2025] [Jingping et al. 2011] [Jiong-Sang Yee et al] [Johnson and Ahamed 2018] [Joosten et al. 2008] [Jorgensen et al. 1994] [Juliana et al. 2004] [Juneau and Hedrick 1995] [Nagarathna and Deodhare 2023] [Kahveci and Ioannou 2009] [Kai 2024] [Kale and Chipperfield] [Kammegne and Botez 2019] [Kanai et al. 1990] [Kanda and Dowell 2005] [Kapila and Pan 2002] [Kapila and Valluri] [Karlsson] [Kassapakis and Warwick 1994] [Katayanagi 2001] [Katayanagi 2004a] [Kawaguchi et al. 2008] [Kawaguchi et al. 2009] [Kaygan and Ulusoy 2018] [Kayran and Nalci 2014] [Kazak et al. 2012] [Keating et al] [Kefayat and Kamali 2024] [Kemer and Prempain 2014] [Kemin Zhou et al. 2004] [Kendall 2005] [Khan et al. 2012] [Khrabrov and Sidoryuk 2010] [Khrabrov and Sidoryuk 2013] [Kim and Kim 2010] [Kim and Kim 2024] [Kineyko 1982] [Kirsten 1985] [Kisslinger and Vetsch 1971] [Kisslinger and Vetsch 1972] [Kitsios et al. 2020] [Klein et al. 1982] [Klyde et al. 1996] [Klyde 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Engine cycle, installation and inlet integration
Where the corrected-flow model at the centre of the derivation comes from. Engine cycle analysis, installed performance, inlet total pressure recovery, afterburning, propulsion station nomenclature and airframe integration. The one number this article takes from this body and does not derive is the ram recovery correlation, and the article shows what its answer looks like with and without it.
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Delta and swept wing aerodynamics at angle of attack
The wing the MANTA proposed and the flow it would have lived in. Delta wing vortex aerodynamics, leading-edge behaviour, high angle of attack, post-stall, buffet, spin and flow separation. A tailless delta at high angle of attack is where the forebody starts generating yawing moments of its own, which is a mechanism the article names in the framing section and does not quantify.
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Thrust vectoring and propulsive control
The mechanism the article’s keystone rests on, and it is larger than the problem it solves. The cluster holds nozzle vectoring measurements, multiaxis control power studies, post-stall manoeuvring work, fluidic vectoring, the flight programmes that carried vectoring hardware for other reasons, and the thrust vector control of rockets, missiles and spacecraft, which deflects the same momentum flux for the same purpose.
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[Chiarelli et al. 1993] [Chih and Peng 2026] [Chouicha et al. 2019] [Chouicha et al. 2020] [Chpoun et al. 2017] [Clark 1965] [Cliff et al. 1982] [Coe et al. 1976] [Cohn et al. 1985] [Coles 1968] [Collins et al. 2004] [Collins 2005] [Comer 2024] [Computational and Experimental Analysis 2024] [Harish Ragavendra et al. 2025] [Coplin 1965] [Cornelius and Lucius 1993] [Cornelius and Lucius 1995] [Costes 1988] [Counter and Brinton 1975] [Cowan and Myers 1991] [Cowan and Myers 1992] [Crandall et al. 1973] [Culpepper et al. 2021] [Culpepper et al. 2022] [Cunningham and Boytos 1981] [Cunningham and Boytos 1983] [Dai et al. 2012] [Daljit Majil 2016] [Das et al. 2024] [Das et al. 2025] [Davis and Hines 1976] [Davis and Spicer 1965] [de Matteis et al. 1998] [De Roche 2025] [Deere 2000] [Deere 2003] [Deere et al. 2003] [Deere et al. 2005] [Deere et al. 2007] [Deng et al. 2014] [Kara and Kurtuluş 2023] [Dhole] [Dinca and Corcau 2021] [Dinca et al. 2019] [Dolly] [Dong et al. 2025c] [Dong et al. 2025b] [Dores et al. 2006] [Douglas et al. 1990] [Dovey et al. 2001] [Doyle 1971] [Duchemin and Valentian 2007] [Dunbar et al. 2002] [Dunn and Emery 1966] [duPont and duPont 1997] [Durán-Delfín et al. 2026] [Dwyer and Lutze 1993] [Eatough 1971] [Eilers et al. 2010] [Eilers et al. 2011] [Ellis and Kearney 1982] [Emelyanov et al. 2021] [Enenakpogbe et al. 2024b] [Enenakpogbe et al. 2024a] [Enenakpogbe et al. 2025] [Ensworth 2013] [Erdem et al. 2006] [Erickson and Erickson 1997] [Erwin et al. 1964] [Esker and McArdle 1993] [Esker and Sedrick 1972] [Thillaikumar et al. 2020] [Experimental Studies on Thrust 1977] [Fan et al. 2013] [Fazeli Asl and Moosapour 2017] [Ferlauto and Marsilio 2016c] [Ferlauto and Marsilio 2016a] [Ferlauto and Marsilio 2016b] [Ferlauto and Marsilio 2017] [Ferlauto et al. 2020] [Ferlauto et al. 2021a] [Ferlauto et al. 2021b] [Figueiredo 2003] [Fitzgerald and Kampe 1979] [Flamm 1998] [Flamm et al. 2005] [Flamm et al. 2006] [Flamm et al. 2007] [Fletcher 1962] [Flow Visualization Studies 1991] [Forliti and Diaz-Guardamino 2008] [Forliti and Diaz-Guardamino 2009] [Forliti et al. 2002] [Fosnight 1968] [Francis 2018] [Friddell and Franke 1990] [Friend 1964] [Frost and Bishop 1963] [Frost and Bishop 1965] [Gainutdinov et al. 2026] [Gal-Or 1990c] [Gal-Or 1990d] [Gal-Or 1990b] [Gal-Or 1990a] [Gal-Or 1990e] [Gal-Or 1994b] [Gal-Or 1995a] [Gal-Or 1995b] [Gal-Or 2001] [Gal-Or and Baumann 1993] [Gal-Or and Sherbaum 1993] [Gal-Or et al. 1993] [Gal-Or et al. 1995] [Garcia-Rodriguez et al. 2024] [Garrigues et al. 2009] [George et al. 1964] [Gerhardt and Chen 1978] [Ghasemi Nejhad 2004] [Ghosh et al. 2006] [Gill 1973] [Gill 1974] [Gilyard et al. 1991] [Giuliano et al. 1997] [Von Glahn and Povolny 1958] [Goetz et al. 1976] [Gogoi et al. 2021] [Goldberger 1966] [Goldsborough 2006] [Goss et al. 2009] [Gourcerol et al. 2025] [Gozhaya et al. 1998] [Granasy 1995] [Green and McCULLOUGH 1963] [Grinstein and DeVore 1999] [Gupta 2025] [Gupta 2026a] [Gupta et al. 2026] [Ha et al. 2025] [Kbab et al. 2020] [Hall 1965] [Haloulakos 1982] [Hambidge et al. 2023] [Hamed et al. 1997] [Hammett et al] [Hammond et al. 1995] [Han et al. 2015] [Hange and Wardwell 1993] [Hannan et al. 2016] [Hanumanthrao et al. 2011] [Hao Long and Shujie Song 2009] [Harisrinivasan et al. 2018] [Haugen 1966] [Hawkes and Franke 1995] [He et al. 2025] [Heo et al. 2026] [Herbert and Reinhardt 1974] [Herrick 1992] [Herron 1970] [Hienz and Vedova 1984] [Hiroyuki Takano et al. 2007] [Hitachi and Liu 2010a] [Hitachi and Liu 2010b] [Hoffmann and Joachimiak 2026] [Hokenson 1986] [Hooker 1981] [Hoskin 1993] [Hoskin et al. 1991] [Hosseini et al. 2026] [Houx et al. 2022] [Hreha et al. 1994] [Hua et al. 2024] [Huang and Wu 2026] [Huang et al. 1996a] [Huang et al. 2025] [Huang et al. 2026c] [Hui-min et al. 2005a] [Hui-min et al. 2005b] [Hunter and D’Amico 2024] [Hunter and Deere 1999] [Huo et al. 2025] [Hutchison et al. 1980] [Ikaza and Rausch 2000] [Iliff and Wang 1997] [Imbaratto] [Imlay 1986] [In-Flight Thrust Determination for] [Indig et al. 2017] [Intelligent Hierarchical Thrust Vector 1994] [Invernizzi and Lovera 2018] [Invernizzi et al. 2018] [Invernizzi et al. 2020a] [Invernizzi et al. 2020b] [Ishibashi et al. 1995] [Islam et al. 2018a] [Islam et al. 2018c] [Jain et al. 2015] [Jammalamadaka et al. 2020] [Jayakody and Katupitiya 2015] [Orr et al] [Jenie et al. 2019] [Jia-Hui et al. 2025] [Jie et al. 2021a] [Jiméneze and Icaza 2000] [Johns et al. 1989] [Jois et al. 2024] [Joseph et al. 2024] [Jyothy and John Wessley 2023] [Kaijun and Fawei 2017] [Kamman and Hall 1978] [Kang et al. 2013] [Kannan and Bhat 2005] [Kantner et al] [Kanyshev et al. 2017] [Kara and Kurtuluş 2024] [Kara et al. 2025] [Kasem and Megahed 2025] [Kelley et al. 1982] [Kentfield 1975b] [Kentfield 1975a] [Kikkawa and Uchiyama 2017] [Kim 2026] [King and Schnelker 1970] [King et al. 1991] [Kirby and Van Vooren 1964] [Klafin 1988] [Kowal 2002] [Krase 1967] [Krenkel and Salzman 1968] [Krishnamurthy et al. 2026] [Kuang and Zhu 2015] [Kumar et al. 2021b] [Kumon et al. 2010] [Kumon et al. 2011] [Kuroda et al. 1997] [Kutschera and Render 1999] [Lallman 1985] [Lallman et al. 1998] [Lambert and Franke 1988] [Lampard 1978] [Lathem 1968] [Laughrey 1991] [Lazić and Ristanović 2007] [Lee and Lan 1992] [Lee and Lee 2019] [Lee et al] [Lee et al. 2006] [Lee et al. 2018b] [Leitner 1986] [Leovan 2019] [Levi and Stahlhuth 1977] [Lewis 1990] [Lewis and Hurd 1980] [Lewis and Simpkin 1981] [Li and Saito 2012] [Li and Saito 2013] [Li et al. 2006] [Li et al. 2013b] [Li et al. 2014a] [Li et al. 2016a] [Li et al. 2019c] [Li et al. 2020] [Lichtsinder et al. 1998] [Lind and Tamplin 1981] [Lindquist 1967] [Litt and Guo 2008] [Liu et al. 2005] [Liu et al. 2013] [Liu et al. 2019a] [Liu et al. 2020b] [Liu et al. 2024b] [Liu et al. 2024c] [Liu et al. 2025b] [Liu et al. 2025a] [Liu et al. 2026f] [Liu et al. 2026i] [Liu et al. 2026h] [Lloyd and Thorp 1978] [Lu and Wu 2009] [Luo et al. 2025b] [Lutze et al. 1991] [Lutze et al. 1999] [Lyu et al. 2023b] [Maarouf et al. 2009] [Mace et al. 1989] [Madarasz et al. 2012] [Madeiras et al. 2026] [Malcolm and Ng 1990b] [Mandralis et al. 2023] [Mangin et al. 2006] [Mansell 1987] [Mareca Rios et al. 2023] [Margetts et al. 2015] [Marsh 1973] [Marubashi and Miwa 2015] [Marubashi and Miwa 2016] [Maruyama et al. 2019] [Maruyama et al. 2022] [Masarati et al. 2014] [Mason and Crowther 2004] [Mason and Berrier 1985] [Mason et al. 1992] [Masyagin 2026] [Matesanz et al. 1994a] [Matesanz et al. 1994b] [Matesanz et al. 1995] [Matesanz et al. 1998] [Matveev and Wheeler 2019] [McGilvray et al. 2019] [McNown and Yih 1953] [Merceruio] [Milam et al. 2005] [Millard and Reed 2014] [Miller 1983] [Miller 1986] [Miller and Clark 1966] [Miller et al. 1999] [Mishra and Sinha 2018] [Mishra et al. 2025] [Mitchell 1979] [Miwa and Maruhashi 2016] [Miwa et al. 2012] [Miwa et al. 2013] [;;;;; 2004] [Miyazaki and Tsubakino 2017] [Mockenhaupt 1988] [Mohammadi and Toloei 2011] [Molyneux 1983] [Montes and Davis 2017] [Moody 1970] [Multiaxis Laser System 1999] [Murguia-Rendon et al. 2009] [Nabavi and Calisal 2006] [Nafi and Hasan 2019] [Nagabhushan and Tomlinson 1985] [Nagabhushan and Tomlinson 1986] [Nagaral et al. 2023] [Nardi et al. 1999] [Nauparac et al. 2018] [Nayebi and Taeibi Rahni 2024] [Neely et al. 2007] [Negandhi et al. 2025] [Nelms 1978] [Nguyen et al. 2021b] [Nguyen et al. 2025] [Nie et al. 2026] [Nishimura 1980] [Nocoń et al. 2023] [Nomizu et al. 2021] [Wu et al. 2020a] [Ochi and Kanai 1998] [Oganyan and Loginov 2025] [Omoragbon et al] [Orme et al. 1998] [Ornob et al. 2025] [Orr and Slegers 2014] [Osedo et al. 2023] [Ouchi et al. 2015] [Pahle et al. 1996] [Pandya] [Papadales and Basil S. 1979] [Park and Lee 2014] [Park et al. 2025] [Pastorelli 2013] [Pauli 1964] [Pauli 1965] [Paulson 1981] [Paulson 1980] [Pelt et al. 2015] [Penchuk and Croopnick 1982] [Penchuk and Schlundt 1969] [Perez and Moncayo 2021] [Peron and Carpenter 1992] [Petit and Scholey 1973a] [Platt 1991] [Porzio and Franke 1986] [Postma 1970] [Prins et al. 1992] [Prothin and Doué 2015] [Prothin et al. 2016] [Pulecchi et al. 2012] [Pye 1976] [Raghavendra et al. 2005] [Rahaim et al. 1996] [Rakesh and Varghese 2018] [Raman et al. 2005] [Ravindranath 2025] [Rawnsley 1994] [Re and Leavitt 1984] [Re and Leavitt 1986] [Reigelsperger et al. 1995] [Remiger et al. 2023] [Resemini and De Souza Costa 2018] [Resta et al. 2021] [Resta et al. 2022] [Resta et al. 2024] [Riboldi and Rolando 2023] [Rizvi and Weitl 2011] [Rolls and Aoyagi 1977] [Roth] [Ruetten 2018] [Russo et al. 2011] [Ryan and Franke 1991] [Akshay et al. 2020] [Saghafi and Banazadeh 2006a] [Saghafi and Banazadeh 2006b] [Saghafi and Banazadeh 2007] [Saghafi and Banazadeh 2009] [Sahinkaya and Cordova 1995] [Saiki et al. 2026] [Sakata and Maruyama 2018] [Salagame et al. 2025] [Salahudden et al. 2025] [Salemka 1964] [Salimi et al. 2023] [Sanchez et al. 2025] [Sanders 1997] [Sankar et al. 2013] [Schirmer and Capone 1989] [Schmidt 1992] [Schneider and Watt 1988] [Schneider and Watt 1989] [Schoeyer and Schoeyer 1997] [Schwagerus et al. 2023a] [Schwagerus et al. 2023b] [Schwagerus et al. 2025] [Schwagerus et al. 2026] [Selegan 1983] [Sellam et al. 2012] [Shandor 1964] [Shandor and Walker 1962] [Shani et al. 1995] [Sharjad et al. 2022] [Shebl 2026] [Sherbaum and Lichtsinder 1998] [Shi 2014] [Shi et al. 2024b] [Shin et al. 2010] [Shneider and Macheret 2005] [Shneider and Macheret 2006] [Shukla et al. 2026] [Shumeiko 2026] [Shumeiko et al. 2022] [Shynkarenko et al. 2024] [Singh 2026] [Singh and Kushari 2008] [Smith 1966] [Smith 1997b] [Snow 1990] [Sobel and Lallman 1988] [Sobester and Keane 2006] [Song et al. 2013] [Sotheran 1982] [Soundararajan and Sridhar 2022] [Soundararajan and Sridhar 2024] [Sova 1988] [Space Transportation System Solid 1979] [Sparavalo 2019] [Sparavalo 2021] [Srivastava and Jayachandran 2023] [Stalford and Hoffman 1989] [Steer 2000a] [Steer 2000b] [Stepanyan et al. 2009] [Stepanyan et al. 2010b] [Strykowski et al. 1996] [Sully and Whittley 1987] [Sun 2020b] [Sun 2020a] [Surapaneni et al. 2016] [Suresh et al. 2026] [Suñol et al. 2014] [Suñol et al. 2015] [Swaraj et al. 2023] [Sweeney and Gerzanics 1994] [Syed et al. 1990] [Syed et al. 1992] [Söğütcü and Sümer 2019] [Sørensen et al. 1996] [Talda and Franke 1989] [Tamrat and Antani 1988] [Tang 2025] [Tanveer and Ahmad 2023a] [Tanveer and Ahmad 2023b] [Tape et al. 1987] [Taur et al. 1997] [Taylor 1988] [Taylor 1990] [Tcherak et al. 2026b] [Tcherak et al. 2026a] [Test Bed for Vectored 1963] [The Hawker P1127 Vectored 1990] [The Jet Lift Controversy 1962] [Thomas et al. 1977] [Thompson and Hung 1970] [Thorat et al. 2024] [Thrust Vector Control 2026] [Aerojet Nuclear Systems Co., Sacramento, Calif. (USA) 1970] [Thrust Vectoring 2020] [Tiarn and Cavalleri 1990] [Tokareva et al. 2019] [Trancossi and Dumas 2011] [Tsubakino and Saito 2020] [Ulizar 1997] [Valeriu 2011] [Van Nieuwstadt and Murray 1998] [Variable Mode Turbofan Jet 2002] [Vashistha et al. 2014] [Vectored Thrust 1992] [Vinayagam and Sinha 2013] [Visser 1999] [Vohra and Kumar 2025] [Waithe and Deere 2003a] [Waithe and Deere 2003b] [Wang and Liu 2016] [Wang and Mo 2012] [Wang et al. 2017b] [Wang et al. 2017a] [Wang et al. 2019d] [Wang et al. 2019h] [Wang et al. 2020a] [Wang et al. 2020f] [Wang et al. 2024b] [Wang et al. 2025i] [Wang et al. 2027] [Ward and Lewis 1987] [Ward and Penrose 1983] [Wardwell and Hange 1993] [Warsop et al. 2019] [Washington et al. 1996] [Wassom et al. 1989] [Wei Yuan and Katupitiya 2013] [Weir and Cowan 1993] [Wen et al. 2022] [Whitaker and Gowadia 1994] [Whitaker et al. 1991] [White 1991] [Whitten et al. 1981] [Wie 1985] [Williams and Vittal 2002] [Wilson et al. 2001] [Wilson et al. 2002] [Wilson et al. 2003] [Wing 1994b] [Wing 1994a] [Wing and Asbury 1991] [Wing and Asbury 1992] [Wing et al. 1997] [Witting and Sneck 1991] [Woodberry 1975] [Wooten et al. 1984] [Xiao-bo et al. 2017] [Xu et al. 2024a] [Xue et al. 2021] [Yadav et al. 2023] [Yagle et al. 2000] [Yagle et al. 2001] [Yang and Hsu 2005] [Yang et al. 2025] [Yankui et al. 2007] [Yen 1978] [Yezzi and Donguy 1986] [Yi et al. 1979] [Yikilmaz and Üre 2022] [Yong et al. 2014] [Younes and Hickey 2020] [Yu et al. 2013] [Yu Liu et al. 2006] [Zafirov 2010] [Zeamer 1975] [Zhang 2017c] [Zhang and Zelin 2018] [Zhang et al. 2010] [Zhang et al. 2018f] [Zhang et al. 2018d] [Zhang et al. 2020a] [Zhang et al. 2021a] [Zhang et al. 2024e] [Zhang et al. 2026c] [Zhang et al. 2026b] [Zhao et al. 2005] [Zhao et al. 2022a] [Zhao-miao and Chuan 2013] [Zhijie et al. 2026] [Zhou et al. 2022a] [Zhou et al. 2024] [Zhou et al. 2025c] [Zigunov et al. 2023] [Zmijanovic] [Zmijanovic et al. 2013] [Zmijanovic et al. 2016] [Zwerneman and Eller 1994] [Zylevich and Oliinyk 2025] [Ünal et al. 2018] [Živković et al. 2014]
Unmanned aircraft, autonomy and the reconnaissance mission
A cluster that bears on one of the two vehicles and not on the other. Unmanned combat and reconnaissance aircraft, their design, configuration, flight control and flight test, the programmes from the DarkStar onward, and the recent collaborative combat aircraft and air-combat decision work. Its size is a fact about recent aeronautics and not about the X-44A, which was flown before most of it was written, and 54 percent of its dated records are from 2015 or later.
661 records. [Ananyev 2019] [Abdelrahman et al. 2009] [Abdullahi et al. 2026] [Abdulrahim et al. 2010] [Abercrombie 1979] [Adoghe] [Advanced Control Techniques 2023] [Aerial Reconnaissance Using Unmanned 2021] [Aerospace - Vehicle Management] [Agte and Cohen 2008] [Aguiar et al. 2008] [Masutti and Tomasello 2018] [Albaker and Rahim 2011] [Aleisa et al. 2023b] [Alexander 1979] [Ali et al. 2012b] [Alijani and Osman 2020] [Alsahlani and Rahulan 2016] [Alsahlani et al. 2017] [An Overview on Unmanned 2017] [Antoniou et al. 2025] [Araujo-Estrada et al. 2017] [Argrow 2016] [Arhami et al. 2010] [Arthur 2008] [Arthurs and Valasek 2016] [Ashokkumar 2023b] [Austin 2010] [Automation and Autonomy 2016] [Autonomous Control of Unmanned 2012] [Badra et al. 2023] [Baldock and Mokhtarzadeh-Dehghan 2006] [Bateman et al. 2007] [Batill et al. 1999] [Baullinger and Page 1989] [Baxter 2013] [Bekešienė and Ruzgas 2020] [Belfield] [Belfield and Drake 2016] [Bell Aerospace Co Buffalo Ny 1955a] [Bell Aerospace Co Buffalo Ny 1955b] [Bell Aerospace Co Buffalo Ny 1957] [Полтавский and Ахобадзе 2023] [Berman 1997] [Bernstein 1994] [Bestaoui Sebbane 2015] [Bhattarai et al. 2026a] [Biber et al. 2004] [Binder and Carbonneau 2012] [Bogar et al. 1996] [Bookstaber 2000] [Boretz 1985] [Bosak et al. 2026] [Bray et al. 1992] [Breunig 2017] [Brinker 2004] [Bronz] [Brown 1993b] [Bruening et al. 2000] [Bruening et al. 2001] [Brungardt 2011] [Burke 2015] [Burnashev and Zbrutsky 2019] [Burton and Hoburg 2018] [Cai et al. 2023] [Campos et al. 2021] [Cardenas 2022] [Carlson 2014] [Carr et al. 2003] [Carryer] [Casau et al. 2011] [Catchpole 1990] [Cha et al. 2016] [Chan] [Chang et al. 2022a] [Chaurasia and Mohindru 2021] [Chen 2022] [Chen and Molnar 2002] [Chen et al. 2015d] [Chen et al. 2024c] [Chitrakaran et al. 2005] [Choi 2020] [Choi et al. 2010] [Choi et al. 2022] [Chong and Chuntao 2014] [Chung 2012] [Cinar et al. 2020] [Ciolponea 2022] [Clothier et al. 2011] [Considerations for Safe Store] [Conte et al. 2019] [Cook 2011] [Cook 2024] [Coombes et al. 2017] [Coopmans et al. 2015] [Corban et al. 2004] [Cordoba 2007] [Cote 2015] [Cox 2009] [Crespo et al. 2010] [Crouse and Sash 2004] [Cummings and Schütte 2012] [Cummings et al. 2003b] [Cummings et al. 2008] [Cummings et al. 2018] [Córdoba G. 2007] [Dalamagkidis et al. 2012] [Dantsker et al. 2018] [Dantsker et al. 2019b] [Dantsker et al. 2019a] [Dantsker et al. 2019c] [Dantsker et al. 2020b] [Dantsker et al. 2020a] [Dantsker et al. 2021] [Daud Filho] [Davidson 2004] [De Florio 2016] [De Wagter and Meulenbeld 2019] [Deets and Purifoy 1998] [Della Vecchia et al. 2025] [The U.S. Air Force 2005] [Dermer] [Design and Development 2014] [Design and Fluid Flow 2015] [Devalla et al. 2015] [Development of a Flight 1999] [Yoo 2004] [Myoung-Hyun 2006] [Dickes et al. 2002] [Digman 2009] [Dimopoulos et al. 2019] [Ding et al. 2026] [Dodge 2015] [Dong and Ai 2012] [Dong and Zhuang 2010] [Dong et al. 2015] [Dou et al. 2023] [Dudziak et al. 2020] [Dunn 1980] [Ebeid et al. 2017] [el mobaraky et al 2024] [Elkhoury 2008] [Elkhoury and Rockwell 2004] [Elkhoury et al. 2005] [Elsonni and Elnomrossy 2011] [Eraslan and Oktay 2024] [Eremin 2025] [Ernest and Carroll 2016] [Ernest and Cohen 2016] [Eulopa-Hernandez et al. 2026] [Evaluating the Use 2015] [Faied and Girard 2008] [Fan 2017] [Fan et al. 2017a] [Farhadi and Kortunov 2017] [Fayez et al. 2021] [Figat et al. 2005] [Figueira et al. 2025] [Figueiredo Prudencio] [Flanagan et al. 2020] [Flight Test Data Analysis 2016] [Flores and Flores 2020] [Flow Control and High-Lift 2016] [Formation and Adjustment 2018] [Forrester] [Forshaw et al. 2013] [Foy and Lawrence 2005] [Franco et al. 2019] [Franke 2016] [Frederick et al. 2002] [Frey 2011] [Frink et al. 2012] [Fu et al. 2015] [Fu Li et al. 2008] [Fuentes 2011] [Fujinaga et al. 2007] [Gabor et al. 2016] [Gabrielian et al. 2021] [Gai et al. 2025] [Galaguz 2013] [Gangl et al. 2013] [Ganglin 2009] [Garcia et al. 2009] [Gates et al. 2019] [Gaydos and Curry 2014] [Gc] [Geng and Zhu 2012] [Girish et al. 2014] [Givens and Coopmans 2020] [Glīzde 2017] [Goetten et al. 2018] [Gomez Ariza] [Goraj et al. 1999] [Gordnier et al] [Gordnier et al. 2006] [Gordnier et al. 2007] [Govind Raju et al. 2023] [Green and Oh] [Grenestedt and Spletzer 2010] [Gryte et al. 2018] [Grzesik and Sobolewski 2014] [Guglieri et al. 2010] [Haddon and Whittaker 2003] [Hajiyev et al. 2015b] [Hajiyev et al. 2015a] [Hale et al. 2015] [Halefom et al. 2021] [Hameed et al. 2009] [Hamilton et al. 2004] [Han et al. 2024] [Hang et al. 2013] [Hanif and Sasongko 2019] [Hansu Dai and Jihong Zhu 2010] [Haq and Huang 2022] [Harasani 2010] [Harmats and Weihs 1999] [Hartney] [Hashmi and Radhakrishna 2015] [Hayama et al. 2021] [Herbst and Klöckner 2014] [High Altitude Reconnaissance Aircraft 1989] [HIL Test Platform 2015] [Hintzke and Haggard 1991] [Hoburg and Tedrake 2009] [Hoholis et al. 2016] [Hoke 2018] [Hooper 2001] [How et al. 2014] [Howard 1990] [Howard and Bray 1992] [Howard et al. 1989] [Howard et al. 1990] [Hsiao et al. 2008] [Huang et al. 2022a] [Hwang et al. 2013] [Hwang et al. 2016a] [Hwang et al. 2016b] [Hwang et al. 2022] [Iliff 1980] [Панасюк et al. 2018] [Introduction to Unmanned Aircraft 2010] [Ippolito et al. 2007] [Iqbal et al. 2009] [Iryani et al. 2019] [Islam et al. 2018b] [İşci and Günel 2021] [Jackuliak and Bugaj 2026] [Jain and Kamali 2016] [Jameson 2009] [Jargalsaikhan et al. 2022] [Jayanthi et al. 2022] [Jefferies and Pinney 1990] [Jenkinson and Marchman 2003] [Ji et al. 2018] [Ji et al. 2022b] [Jia et al. 2016] [Jiang et al. 2022] [Jie and Jung 2011] [Jihui 2019] [Jiufu 2007] [Johnson 2021] [Johnson et al. 2021] [Johnstone and Arntz 1990] [Jones 1999] [Joo et al. 2014] [Jordan] [Jorris et al. 2011] [Joshi and Kartik 2024] [Jung et al. 2014] [Senthil Kumar and Shanmugam 2023] [Kachel et al. 2022] [Kadiri et al. 2019] [Kahn and Edwards 2015] [Kannan et al. 2014] [Karagiannis and Astolfi 2007] [Kasim Biber and Trenton White 2019] [Katz 2017] [Kauffman 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Low observable design and signature
The reason the fin was to be deleted in the first place. Radar cross section prediction and reduction, shaping, absorbing materials and structures, electromagnetic scattering and infrared suppression. The article takes the premise from this literature and computes nothing in it.
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et al. 2025b] [Zhou 2025] [Zhou and Huang 2020] [Zhou and Huang 2021b] [Zhou and Huang 2022a] [Zhou and Huang 2022b] [Zhou and Huang 2023b] [Zhou and Huang 2023a] [Zhou and Huang 2023c] [Zhou and Huang 2024] [Zhou et al. 2012] [Zhou et al. 2016] [Zhou et al. 2021] [Zhou et al. 2025b] [Zohuri 2020b] [Zohuri 2020a] [Ünalır et al. 2025] [Зниження радіолокаційної помітності літальних 2018]
Supersonic and transonic aerodynamics
The speed range in which the article’s minimum lives. Shock waves, wave drag, area ruling, compressibility and the transonic and supersonic characteristics of fighter configurations. The result that the authority ratio has a minimum near Mach 1.67 is a propulsion result rather than an aerodynamic one, and this cluster is where the aerodynamic side of the same speed range is recorded.
483 records. [Abarbanel 1977] [Abdelhamid 1985] [Abel 1971] [Adams and Rubin 1958] [Advanced Fuel Research INC East Hartford CT 1957] [Donovan 1957] [Aerodynamic Efficiency of SCV 2020] [Aerodynamic Phenomena in Supersonic 2020] [Agrawal et al. 1991] [Aidala 1985] [Air Force Test Pilot School Edwards Afb Ca 1987] [Air Force Test Pilot School Edwards Afb Ca 1991a] [Aleid and Pilidis 1996] [Aleid and Pilidis 1998] [Alford and Luoma 1960] [Allen and Townsend 1985] [Almeida 2021] [AlQadi 2025] [Alvi 2005] [Anderson 1958] [Anderson 1959] [Anderson 1960b] [Andrew 1981] [Arabshahi and Whitfield 1995] [Arai and Ichikawa 2001] [Arai and O-yabu 2003] [Armstrong 1979] [Army War Coll Carlisle Barracks Pa 1952] [Ashley 1984] [Austin] [Axelson 1975] [B. Aerodynamics of Bodies 1957] [Baals and Harris 1968] [Baals et al. 1970] [Babinsky 2007] [Baer 1961] [Ban et al. 2018] [Bangert et al. 1980] [Barnes 1944] [Barnhart 1989] [Barnwell et al. 1986] [Barzegar Gerdroodbary 2023] [Batiuk and Henderson 1976] [Bekemeyer and Timme 2017] [Bennet-Clark 1972] [Bhowmick et al. 2025] [Billig 1967] [Binion 1974] [Blackwell 1979] [Blank 1995] [Blose 1949] [Boeing Scientific Research Labs Seattle WA 1963] [Bogdnoff 1953] [Bogdonoff 1999] [Bolz 1950] [Bond and Packard 1961] [Boudreau 1978] [Boudreau 1979] [Boylan 1965] [Bradley et al. 1969] [Braginsky 2020] [Brazzel et al. 1970] [Brickey et al. 1971] [Britcher and Landman 2024b] [Brown 1978] [Brown 1989] [Brown 1946] [Brown 1971] [Bryson and Desai 1968] [Burnham 1970] [Bushnell and Tripi 1986] [Bushnell 1990] [Bílek et al. 2025] [Calder and Gupta 1978] [Candler 2010] [Carafoli 1969a] [Carlson and Mann 1992] [Cassel et al. 1969] [Cassel et al. 1980] [Cassidy and Halley 1991] [Catalano and Sturek 2001] [Caughey 2026] [Cebeci et al. 1970] [Chan 1980a] [Chan 1980b] [Chapter 1. Fundamental Considerations 1957] [Chapter 3. Aerodynamics 1957] [Chapter 4. Wing-Tail Plane 1957] [Chapter 5. Wing-Body Interference 1957] [Chau and Zingg 2022] [Chen and Liu 1988] [Chen et al. 2012] [Chen et al. 2017a] [Cheng et al. 2022] [Chester 1953] [Chiba et al. 2008] [Chiba et al. 2012] [Chiu and Lin 1994] [Chow 1979] [Chung 2004] [Clancy 1952] [Clark 1966] [Clark 1970] [Clyde et al. 1984] [Coder 2021] [Cole 1988] [Cole et al. 1980] [Computational Fluid Dynamics Design 1990] [Connolly 1965] [Cooksey and Arnold 1973] [Cottrell and Lijewski 1987] [Cottrell et al. 1987] [Covell et al. 1990] [Cox and Roskam 1990] [Craft and Brazzel 1970] [Cramer 1951] [Cruz and Ware 1992] [Cruz and Wilhite 1989] [Cubbage et al. 1970] [Dahlke and Craft 1972] [Dasgupta et al. 2026] [Dawson et al. 2018] [Dehua and Changyou 1993] [Denning 1962] [DeSpirito 2014] [Devan 1987] [Devan et al. 1982] [Dietrick 2013] [Dollyhigh 1979] [Driver 1974] [Dudley et al. 2008] [Edwards 2014] [Edwards and Hikido 1953] [Effect of High Mach 2010] [Ellinwood 1977] [Epstein 1954] [Esenwein et al. 1950] [Fauci et al. 2006] [Ferrari 1948] [Ferrari 1949a] [Ferrari 1949b] [Fink 1965] [Fletcher and Burns 1979] [Flight Sciences Lab INC Buffalo NY 1964] [Flores et al. 1987b] [Foley and Woodrey 1980] [Fornasier and Heiss 1987] [Foster 1960] [Foster and Morris 1960] [Fox and Allee 1989] [Fraenkel 1958] [Frede and Takahashi 2020] [Freeman 1968] [Frick et al. 1955] [Fujita et al. 2004] [Fuller and McLean 1963] [G. the Experimental Aerodynamics 1957] [Gaglio et al. 2021] [Gaitonde 2008] [Gao et al. 2013a] [Garcia-Fogeda and Liu 1988] [Garriz et al. 1990] [Geiger 2002] [Gellatly and Gallagher 1964] [Gillespie 1960] [Gillis and Toll 1962] [Ginoux 1966] [Goebel et al. 1980] [Goerttler 2025] [Goldbaum 1956] [Goodman 1973] [Goto et al. 2007] [Graham and Mavris 2000] [Graham et al. 1954] [Graham 1977] [Graham et al. 1972] [Graham et al. 1973] [Gray 1965] [Greene 1957] [Griffith et al. 1975] [Gringorten 1967] [Gringorten and Tattelman 1970] [Grosser 1982] [Grosser 1983] [Groves et al. 2005] [Grunnet 1984] [Guderley 1987] [Guderley 1988] [Gunzburger and Ting 1969] [Guo et al. 2019a] [Gupta 1980] [Gupta 2023] [Guruswamy and Goorjian 1986] [Gusev et al. 1993] [Harloff 1988] [Harris et al. 1965] [Hashimoto et al. 2009] [Hastings et al. 1957] [Heiss et al. 1992] [Hemsch 1988] [Hemsch 1989] [Henne 2003] [Herrmann 2008] [High Supersonic Speed Wind 1961] [High-Speed Flight and Its 2010] [Hoerner 1936] [Hoffman and Platzer 1966] [Hornung et al. 2003] [Irani 1995] [Ishikawa et al. 2008] [Jackson and Blanchard 1964] [Jacocks 1969] [Jadic 1993] [Jameson et al. 2010] [Janardhan and Grandhi 2003] [Jenista and Bodden 1989] [Jenista and Bodden 1990] [Jenista and Sheridan 1987] [Jenke 1976] [Jermey and Schiff 1985] [Jischke 1978] [Johnson et al. 1970] [Johnston et al. 1971] [Jones 1967] [Jones 1976b] [Jorgensen 1958] [Jou and Metcalfe 1984] [Ooi 2024] [Kumar and Chidambaram 2019] [Kalkhoran and Otugen 1994] [Kanazaki et al. 2002] [Kendall 1952] [Kim and Lee 2000] [Kim et al. 2001] [Kim et al. 2002] [Kimmel et al. 2011] [King 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and Brazzel 1970] [Martin and Gerber 1953] [Maruyama et al. 2009] [Mashburn 1969] [Mateescu 1986] [Mateescu 1987] [Mavriplis and Kafyeke 2026] [Mavris and Graham 2000] [McClain and Pountney 1982] [McConnell 2006] [McElderry 1973] [McLean 1994] [McQuellin and Buttsworth 2024] [Medved 2010] [Meng and Yu 2023] [Meyer and Fields 1978] [Miele and Hull 1963] [Miele and Pritchard 1963] [Miles and Macheret 2004] [Miller and Wood 1986] [Mo et al. 2023] [Moga 1980] [Moorthamers et al. 2021] [Morikawa 1950] [Morikawa 1951] [Morikawa 1952] [Morito and Sidwell 1968] [Munipalli et al. 2005] [Nagai and Iijima 2011] [Naik 1989] [Naval Ordnance Systems Command Washington DC 1957] [Harrison et al. 2023] [Nelson 1989] [Nelson 1990] [Nelson and Bossi 1995] [Nicolaides and Brady 1959] [Nielsen 1986] [Nietubicz 1975] [Nissim and Lottati 1979] [Nissim and Lottati 1980] [Nixon and Tzuoo 1986] [Nixon and Tzuoo 1987] [Nomura 2003] [Nomura 2006] [Nugent 1959] [Numerical Solutions 1986] [Nyberg and Sorensen 1980] [Timothy and Lewis 2001] [O’Brien and Lewis 2002] [Odaka and Kusunose 2009] [Olsen 1966] [Ormsbee 1962] [Ortloff 1968] [Parameswaran and Baeder 1997] [Pate 1964] [Pate and Deitering 1963a] [Perkins et al. 1977] [Person and Robbins 1965] [Peters and Phares 1976] [Pfenneberger 1966] [Phillips and Waggoner 1990] [Phillips and West 2019] [Phythian 1966a] [Phythian 1966b] [Pipko 1966] [Pittman and Giles 1986] [Pittman et al. 1990] [Pivko 1956] [Platou 1959] [Poggie 2012] [Polonsky 2026] [Postle et al. 1955] [Price 1978] [Properties and Design 2012] [Radkey et al. 1976] [Radkey et al. 1978] [Ramsey 1972] [Rao et al. 2023a] [Rasmussen 1978] [Raveh 2011] [Razgonyaev and Mason 1995] [Re and Capone 1977] [Reda 1977] [Regan 1964a] [Reuther and Jameson 1995b] [Rill and Becker 1992] [Rizk and Murman 1984] [Rodden et al. 1962b] [Rodemich and Andrew 1965] [Rogers and Walter K. 1953] [Rogers and Walter K. 1958] [Rolston et al. 1998] [Rom 1965] [Rotermel et al. 2021] [Ruffin 1996] [Sachs 1990] [Sahbon 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[Uematsu et al. 2011] [Unger and Coen 1993] [Vallee 2002] [van Zyl 1994] [Varner 1976] [Varwig 1963] [Vendemia 1965] [Vinh and Medepalli 1994] [Vira and Fan 1982a] [Vira and Fan 1982b] [Vogler 1953] [Vukelich and Williams 1981] [Waechter 1969] [Waechter 1971] [Walchli and Langan 1999] [Walchner 1974] [Walchner et al. 1969] [Walkley 1986] [Walkley and Smith 1987] [Walter and Redman 1954] [Wang 2024a] [Wang and Zhang 2025] [Wang et al. 1994a] [Washington 1983] [Washington and Spring 1982] [Waskiewicz et al. 1981] [Wasserman 1952] [Watmuff and Smits 1987] [Waverider Aircraft 2012] [Weed et al. 1983] [Welge et al. 1977] [Whitford 1991a] [Whoric 1977] [Wilks 2006] [Williams 1965] [Wilson 1973] [Wing Theory in Supersonic 1969] [Winkler 1954] [Wood and Miller 1984b] [Wood and Miller 1985b] [Woodward 1968] [Wornom 1960] [Xiong and Nguyen 2023] [Xiong and Nguyen 2024] [Xu 2023] [Xu et al. 2003] [Xu et al. 2012] [Yahalom 1971] [Yamazaki and Ishida 2025] [Yip et al. 1980] [Yu et al. 2020] [Zhang et al. 2013b] [Zhao et al. 2013] [Zhou et al. 2023c]
Tailless configurations and the missing vertical tail
This is the cluster the article is about and it is not among the largest, which is a statement about publishing and not about importance. It holds the tailless and all-wing stability literature from the 1940s onward, the vertical tail sizing and tail reduction studies, the blended wing body work that inherited the same problem for a different reason, and the modern tailless unmanned configurations. The oldest records here and the newest ones are asking the same question, which is how a configuration with no fin is to be kept pointing where it is going.
474 records. 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Huang 2021a] [Zou et al. 2026]
Nozzles, exhaust systems and internal performance
The hardware the vectoring has to be built into. Convergent-divergent nozzle internal performance, thrust coefficients, expansion ratios, ejectors, plug nozzles, thrust reversers and the nozzle geometry studied for its exhaust noise. This is the cluster that would decide whether the sidewall yaw flaps the MANTA needed cost more in cruise thrust than they bought in control, which is a question the article raises and does not answer.
461 records. 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Directional stability, sideslip and the lateral-directional modes
The dynamics the missing fin changes. Sideslip derivatives, Dutch roll, weathercock stability, departure criteria and the estimation methods that produce the derivative this article had to bracket rather than quote. The article’s inability to name a value for the tailless yaw derivative is not for want of a literature on how to measure one.
455 records. [Abramov et al. 2005] [Abzug 1999a] [Abzug 1999b] [Adams 1972] [Air Force Test Pilot School Edwards Afb Ca 1990c] [Aircraft Lateral-Directional Handling Qualities 2011] [Aircraft Stability Derivatives 1998] [Aircraft Stability Derivatives 2002] [Alesin et al. 2020] [Alikhan and Go 2015] [Aly and Aly 1997] [Amer and Gessow 1954] [APPENDICES a. 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2016] [Lateral-Directional Dynamics 1998] [Lateral-Directional Flying Qualities 2002b] [Lateral-Directional Flying Qualities 2002a] [Lateral-Directional Motion 2016] [Lateral-Directional Motions 2015] [Lateral-Directional Stability Theory 2003] [Lee and Tang 1992] [Lemay et al. 2011] [Lemon et al. 2011] [Lerro et al. 2021] [Lewis et al. 2020] [Li et al. 2022c] [Li et al. 2024a] [Li et al. 2025i] [Lin et al. 2017] [Lin et al. 2019a] [Litt et al. 2012] [Liu 2024] [Liu and Wang 2012] [Liu et al. 2026a] [Livneh 1995b] [Livneh 1995a] [Long Lu and Turkoglu 2015] [Lovell and Parlett 1957] [Lowenberg 2010] [Lu] [Lu and Turkoglu 2016] [Lu and Turkoglu 2018] [Lukianenko 2026] [Lungu and Lungu 2016c] [Lungu and Lungu 2017] [Lungu and Lungu 2018] [Lungu et al. 2019] [Lutze 1980] [Lutze et al. 1996] [Luu and Ochi 2023] [Ma et al. 2019a] [MacLachlan 1945] [Malik et al. 2017] [Mann et al. 1987] [Marchman 1981] [Marino and Mastrocola 1948] [Marino and Mastrocola 1952] [Mason and Berrier 1988] [Masud et al. 2016] [May et al. 2011] [McGinnis and Eder 1971] [Mengali and Giulietti 2004] [Miller and Franklin 1968] [Mineck 1977] [Mohammed 2007] [Montgomery and Hunsaker 2022] [Morris 1966] [Muhlhauser 1971] [Murman et al. 1986] [Murri and Rao 1987] [Musa et al. 2014] [Musa et al. 2015] [Musa et al. 2026] [Myala et al. 2019] [Nagy and Kirsten 1976] [Napolitano and Kincheloe 1996] [Napolitano 1996] [Natarajan et al. 2004] [Nathan 2026] [Nelson 1988] [Nguyen and Ochi 2025] [Nguyen and Xiong 2022] [Nicolosi et al. 2017] [O’Rourke 1995] [O’Rourke and Sedor 1995] [Ogren et al. 1974] [Okolo et al. 2011] [Olwi 1994] [Olwi 1996] [Pamadi and Pai 1980] [Papadakis et al. 1992] [Son 2002] [Park et al. 2001] [Park et al. 2021] [Parks and Bach 1990] [Patel et al. 2004] [Paulson 1948] [Pavithra and Archana 2022b] [Pavithra and Archana 2022a] [Paziresh et al. 2017] [Pedreiro et al. 1996] [Pedreiro et al. 1998] [Pedreiro 1997] [Peterson 2025] [Pfnür et al. 2018] [Pitkin 1943] [Polhamus and Spahr 1957] [Poojari 2022] [Powell 1956] [Preliminary Sizing 2010] [Prieto and Esteban 2020] [Prisacariu and ChirilĂ 2019] [Putman 1969] [Qin et al. 2014] [Qu et al. 2017] [Queijo and Wells 1956] [Rahmawati et al. 2022] [Ramachandran et al. 1977] [Rankine and Leondes 1972] [Rao and Murri 1986] [Rao et al. 1987] [Rao et al. 1986] [Rasitha R. et al. 2015] [Rasquin et al. 2020] [Rauhut and Slingerland 2003] [Report No. 264 Differential 1927] [Retzlaff and Hertz 1990] [Rhoads 1952] [Roberts and Lind 2009] [Roberts et al. 2011] [Robinson 1970] [Robinson 1958] [Rogal 1965] [Roos and Magness 1994] [Rossitto and Hodgkinson 1993] [Rotaru et al. 2016] [Roysdon and Khalid 2010] [Roysdon and Khalid 2011] [Sachan et al. 2025] [Sachs 2007a] [Sachs 2007c] [Sachs 2007b] [Sachs and Moelyadi 2006] [Sadraey 2022b] [Sadraey 2022a] [Schairer 1941] [Scholz et al. 2020] [Schroijen et al. 2010] [Schuman 2018] [Schweiger et al. 2000] [Seacord 1943] [Seckel 1964b] [Seckel 1964d] [Seckel 1964c] [Seckel 1964a] [Seeny et al. 1971] [Senthilkumar and Prabhaharan 2010] [Sereez et al. 2018] [Shafer 1982] [Shah and Granda 1998] [Shamikh 2013] [Shams Taleghani et al. 2025] [Shankar and Yathisha 2023] [Shaqura and Claudel 2015] [Shen et al. 2017a] [Shen et al. 2019] [Shrivastava and Stengel 1989] [Silhouette and Stengel 1987] [Silva et al. 2022] [Singh and Ghosh 2007] [Singh and Raisinghani 1993] [Singh and Scholz 2020] [Sinha and Ananthkrishnan 2002] [Sinha and Ananthkrishnan 2017] [Sinha and Ananthkrishnan 2021b] [Sinha and Ananthkrishnan 2021a] [Sinkovec et al. 2015] [Sivan 1971] [Skarpetis 1996] [Smetana et al. 1972] [Smith 1982] [Snell] [Snell 1993] [Snell et al. 1991] [Snyder and Weisshaar 2013] [Sohail et al. 2011] [Sparks et al. 1994] [Srinivas et al. 1995] [Stalford 1979] [Stengel 1975] [Stengel 1980] [Stengel and Miller] [Stengel and Miller 1978] [Stephenson et al. 1990] [Stewart 1939] [Stone 1945] [Stough et al. 1991] [Swaim 1980] [Swaim and Connor 1968] [Swaminathan 2019] [Swarnkar and Kothari 2016] [Szema and Shankar 1986] [Tai et al. 2023] [Tai et al. 2025] [Tajfar and Lamont 1997] [Taleghani et al. 2024] [Talmage and Reeder 1949] [Tancredi et al. 2005] [Tarpley and Lewis 1995] [Tavella et al. 1986b] [Tavella et al. 1987] [Tavoularis 1999] [Tavoularis et al. 2001b] [Tavoularis et al. 2001a] [Taylor and Yoo 2011] [Taylor et al. 1965] [Teper and Stapleford 1965] [Terui et al. 1999] [Tewari 2000] [Thacker and Lan 1993] [Tian and Chao 2018] [Ting et al. 2025] [Tinger 1989] [Tokutake et al. 2006] [Toll and Queijo 1948] [Tournes and Landrum] [Tournes and Landrum 2003] [Tu et al. 1999] [Urnes and Nielsen 2010] [Vechtel and Buch 2022] [Verhaagen 2000] [Verhaagen and Jobe 2001] [Verhaagen and Jobe 2003a] [Verhaagen and Jobe 2003b] [Vershinin 2004] [Vertical Tail Loads 1996] [Wai et al. 1986] [Wallace and Recant 1943] [Wang et al. 2013b] [Wang et al. 2016e] [Wang et al. 2023f] [Wang et al. 2025d] [Ward et al. 2025] [Wei et al. 2022] [Wen and Zhu 2014] [Wen et al. 2013] [Wetzel 1954] [Whiting 1996] [Williams and Garry 1996] [Williams and Seidel 2016] [Wood and Crowther 1994] [Wu and Chen 2024] [Xi et al. 2016] [Yan et al. 2023] [Yan et al. 2024] [Yanagihara et al. 1991] [Yao and Yeo 2020] [Yeo et al. 2015] [Yi Chao et al. 2008] [Yong et al. 2024] [York and Anderson 1994] [Yu and Kim 2024] [Yunpeng et al. 2023] [Zhai et al. 2024] [Zhao et al. 2022b] [Zheng et al. 2025c] [Zhou et al. 2020] [Zhu et al. 2012] [Zhu et al. 2026b]
Handling qualities and the pilot in the loop
The discipline that decides whether an aeroplane is acceptable rather than merely controllable. Rating scales, pilot-induced oscillation, workload, pilot models and simulator evaluation. It bears on the MANTA and not at all on the X-44A, and that asymmetry is the clearest illustration in the survey that these are two different aeroplanes.
378 records. [Adams and Hatch 1971] [Adams and Hatch 1970] [Aerospace Active Inceptor Systems] [Air Force Test Pilot School Edwards Afb Ca 1962b] [Air Force Test Pilot School Edwards Afb Ca 1969] [Air Force Test Pilot School Edwards Afb Ca 1981] [Air Force Test Pilot School Edwards Afb Ca 1988a] [Air Force Test Pilot School Edwards Afb Ca 1988c] [Air Force Test Pilot School Edwards Afb Ca 1988b] [Air Force Test Pilot School Edwards Afb Ca 1989] [Air Force Test Pilot School Edwards Afb Ca 1990b] [Air Force Test Pilot School Edwards Afb Ca 1990a] [Air Force Test Pilot School Edwards Afb Ca 1991c] [Air Force Test Pilot School Edwards Afb Ca 1991b] [Aircraft Longitudinal Handling Qualities 2011] [Anderson 1970] [Anderson 1984a] [Anderson 1985] [Anderson 1989] [Anderson and Anderson 1997] [Anderson et al. 1984] [Anderson 1960c] [Anderson 1960a] [Anderson and Cooper 1947] [Andrianantara et al. 2025] [Andrisani 1982] [Ashkenas 1965b] [Ashkenas 1984] [Automation in Combat Aircraft 1982] [Bachelder and Aponso 2020a] [Bachelder and Aponso 2020b] [Bailey and Bidlack 1996] [Bailey et al. 1988] [Bailey and Knotts 1990] [Baldwin and Drewett 1986] [Bantle and Melz 2009] [Baughman and Longeauay 2015] [Berger and Meyer 1974] [Berger et al. 2013] [Besco 1964] [Bidinotto et al. 2021] [Bihrle 1969] [Bischoff 1981] [Bjorkman et al. 1986] [Black and Moorhouse 1979] [Blanken and Pausder 1994] [Boothe et al. 1974] [Boskovic et al. 2010] [Bosworth and Cox 1989] [Bowes and Miller 1976] [Bramesfeld et al. 2006] [Brandon et al. 1987] [Bray 1963] [Brieger et al. 2012] [Brooks and Ransbury 2012] [Brown 1970] [Burke and Ferris 1981] [Cai et al. 2014] [Cappetta 1993] [Carlson and Verberg 2015] [Carlson et al. 1965] [Carpenter 1970] [Chakraborty et al. 2015] [Chalk 1964] [Chalk et al. 1969] [Chance Vought Corp Dallas Tx 1979] [Chang et al. 2009] [Chen and Boothe 1974] [Chen et al. 2026b] [Chetty and Lakshmi 1991] [Chetty and Raol 1992] [Chung et al. 2020] [Clark 1964] [Configuration Development and Flying 2021] [Control Characteristics 2023] [Corliss et al. 1977] [Cornell Aeronautical Lab INC Buffalo NY 1947] [Cosenza and Vos 2017] [Cotting 2019] [Cox and Marshall 2000] [Crane 1983] [Crane 1984] [Creer et al. 1959] [Crombie and Moorhouse 1980] [Crother et al. 1973] [Curry et al. 1965] [Curry and Batterson 2000] [Cyrus and Fogarty 1979] [King 1993] [Design objectives for flying] [Design Objectives For Handling] [Difranco 1969] [Difranco 1970] [DiFranco 1971] [Doman 1995] [Doman 1999] [Drewiacki et al. 2016] [Drewiacki et al. 2018] [Drewiacki et al. 2025] [Duda 1995] [Dussart et al. 2018] [Edwards et al. 1997] [Efremov et al. 1998] [Efremov et al. 2020] [Efremov et al. 2022] [Eichler 1970] [Elliott 2007] [Eney 1968] [Eppley 1963] [Evangelou 1998] [Field and Giese 2005] [Fielding and Southworth 2001] [Flight Simulation 2016] [Flying Qualities 2003] [Fu et al. 2019] [Fujizawa] [Gallagher 1971] [Gao et al. 2021d] [Garren and Kelly 1965] [Garrood and Reid 1993] [Gautrey and Cook 1998] [Gera and Bosworth 1987] [Gerken 1979] [Gertsen and Shomber 1965] [Gibson 1990] [Gilbreath and Markofski 2001] [Gilruth 1943] [Goetzendorf-Grabowski and Kwiek 2023] [Goldstein 1982] [Grant and Schroeder 2010] [Grantham et al. 1985b] [Grantham et al. 1987] [Gray 2016] [Gray 1964] [Green 1988] [Gresham et al. 2023] [Gripp et al. 2023] [Habboush and Yildiz 2022] [Hall 1971a] [Hall et al. 1974] [Halsmer] [Hamel 2017b] [Han and Liu 2026] [Hanke 2003] [Harmon and Dieterich 1991] [Harper and Robert P. 1955] [Harper and Sardanowsky 1969] [Harper and Cooper 1984] [Harris et al. 2000] [Harvey and Dillow 1974] [Pausder and Blanken 1993] [Hess 1981] [Hess 1984] [Hess 1987] [Hess 2009b] [Hess 2009a] [Hess 2016] [Hess 2021] [Hess and Hess 1997] [Hess and Joyce 2013] [Hess et al. 1997] [Hess 1977] [Higgins and Shomber 1964] [Higgins and Shomber 1965] [Hindson et al. 1990] [Hirsch and McCormick 1965] [Hirsch and McCORMICK 1966] [Hodgkinson 2003] [Hodgkinson and Lamanna 1977] [Hodgkinson et al. 1988] [Hodgkinson et al. 1990] [Hofmann and Riedel 1979] [Hoh 1988] [Hoh and Mitchell 1983] [Hoh and Mitchell 2018] [Hoh et al. 1981] [Hooks and McMurry 1983] [Huff 1949] [Iloputaife and Iloputaife 1997] [Iloputaife and Ma 1987] [Innocenti 1989] [Jacobson and Joshi 1978] [Jalovecký and Janů 2010] [Jansen 1980] [Jeram and Prasad 2003] [Johnson and Phatak 1990] [Johnson and Pritchett 2002] [Johnston and Friend 1965] [Johnston et al. 1965b] [Johnston et al. 1974] [Justiz and Patel 1988] [Kara et al. 2024] [Katayanagi 2004b] [Kempel et al. 1975] [Key 1971] [Khattak et al. 2022] [Kidd and Bull 1963] [Kish et al. 1996] [Kish et al. 1997a] [Kish et al. 1997b] [Klein 1970] [Klyde and Mitchell 2003] [Klyde et al. 1995] [Klyde et al. 1997a] [Klyde et al. 2020] [Klyde et al. 2021] [Komoda et al. 1989] [Kriechbaum and Stineman 1972] [Krishnakumar et al. 1995] [Kumar et al. 2013] [Kurtzberg 1963] [Lampton et al. 2024] [Lapins et al. 1982] [Lawrence and Padfield 2005] [Lawrence and Padfield 2006] [Lebacqz and Radford 1978] [Lebacqz and Radford 1979] [Lee 2000a] [Lee et al. 1968] [Levi and Nelson 1963] [Levi and Nelson 1964] [Levison 1982] [Li 2005] [Li et al. 2026a] [Liang-yu and Wu 2011] [Liddell et al. 1947] [Liu and Gao 2010] [Liu and Lone 2013] [Liu et al. 2008b] [Longitudinal Flying Qualities 2002] [Loranchet et al. 2025] [Lu and Jump 2014] [Macedo et al. 2020] [Malcom 1969] [Malpica and Lusardi 2013] [Mandal and Gu 2016a] [Mandal and Gu 2016b] [Matthews 1998] [McCormick 1969] [McCormick et al. 1963] [McGregor and Smith 1965] [McKay 1994] [Mehra and Prasanth 1998] [Merkel and Whitmoyer 1976] [Meyer 1983] [Meyer et al. 1984] [Miller 1970] [Miller and Clark 1965] [Mitchell 1999] [Mitchell 2000] [Mitchell and Klyde 2005] [Mitchell and Klyde 2008] [Mitchell et al] [Mitchell et al. 2003] [Mitchell et al. 2004] [Mitchell et al. 1991] [Mitchell et al. 1992] [Montgomery 1971] [Mooij 1985e] [Mooij 1985d] [Mooij 1985a] [Mooij 1985b] [Moorhouse et al. 1989] [Mueller 2010] [Musso et al. 2026] [Neal 1970] [Neal and Smith 1970a] [Neal and Smith 1970b] [Neal and Smith 1971] [Nettleton 1965] [Newell et al. 1963] [Newton and Kroo 2023] [Newton and Kroo 2024] [Newton and Kroo 2025] [Nguyen and Cord 1999] [Nguyen et al. 1997] [Ohta et al. 1979] [Ohta et al. 1982] [Olson 2015a] [Onur et al. 2017] [Papa and Stoliker 1988] [Park 2014] [Pausder and Blanken 1992] [Piloted Simulation and Pilot 2014] [Place et al. 1974] [Potvin and Grant 2026] [Powers 1980] [Powers 1982] [Prilliman et al. 1969] [Quan 2013] [Quinn and Breidenbach 1978] [Raol and Singh 2023] [Rawson 1963] [Reid and Robinson 1990] [Repperger et al. 1997] [Research and Analysis 2022] [Rhoads 1970] [Riedel 1979] [Risse et al. 2010] [Rodchenko et al. 2003] [Ruflin and Grantham 1984] [Rzucidło and Chudý 2011] [Sadoff et al. 1961] [Sagoo] [Savelev and Neretin 2019] [Schmidt 1978] [Schmidt 1979] [Schmidt 1983b] [Schmidt 1988] [Schreiter et al. 2017] [Schroeder and Chung 2000] [Schroeder et al. 1998] [Shafer et al. 1983] [Shams et al. 2023] [Shanks et al. 2018] [Shen et al. 2010] [Shepherd et al. 2009] [Shomber and Gertsen 1967] [Shubert and Jones 2025] [Shweyk and Rossitto 1999] [Sisk 1978] [Smit 1976] [Smith 1977] [Smith and Geddes 1979] [Solies 1995] [Solies 1994] [Spitzer et al. 1972] [Srinathkumar 2011] [Stability Control and Handling 2024] [Steeb et al. 1979] [Steer 2003] [Stifel 1979] [Stortz and ODonoghue 1995] [Swaim and Yen 1979] [Takahashi and Gaydusek 2026] [Teofilatto 2001] [Tischler and Hoh 1982] [Tomczyk 2001] [Tomczyk 2002] [Tomczyk 2008a] [Tomczyk 2008b] [Torelli et al. 2023] [Towards an Improved Pilot-Vehicle 2012] [Turkel et al. 1980] [Twisdale and Kirsten 1984] [Uybarreta et al. 2025] [Van Dam et al. 1980] [van Dam et al. 1981] [van Gool 1982] [Van Gool and Weingarten 1981] [VAN Poppel et al. 1998] [Vepa 2023i] [Vinje and Miller 1973] [Vomaske et al. 1978] [Walker 1997] [Walsh 1992] [Walsh 1993] [Wang et al. 2012c] [Wang et al. 2021e] [Weeks 1979] [Weingarten 2004] [Weltz et al. 2007] [Wenham 1969] [Wenham 1970] [Westbrook 1964] [Whitbeck and Hofmann 1978] [Whitbeck and Knight 1972] [Whiteside 1977] [Whiteside and Iffland 1977] [Wilson et al. 1993] [Xu et al. 2019b] [Yin and Wang 2017] [York et al. 2001] [Yu and Liu 2013] [Zaal et al. 2011] [Zaitceva and Andrievsky 2021] [Zhao et al. 2011] [Ünen and Yıldız 2025]
Wind tunnel testing, computation and validation
How anything here is known. Wind tunnel technique, computational fluid dynamics, turbulence modelling, grid generation, wall interference and flight correlation. The nozzle control power measurements the article leans on are wind tunnel results, so the reliability of this cluster’s methods is the reliability of the article’s second-strongest source.
348 records. [A320 “Flies” at 900 1984] [Agarwal 1999] [Agarwal et al. 1989] [Agrawal et al. 2025] [Airframe Computer-Aided Design 2021] [Alexander and James 1995] [Anderson 1968] [Another Vertical Wind Tunnel 1932] [Anyoji et al. 2013] [Application of CAE 1986] [Application of Computational Fluid 2007] [Arai et al. 2025] [August 1973] [Auman et al. 1994] [Balatti et al. 2022b] [Barlas et al. 2021] [Becle et al. 1994] [Bekemeyer et al. 2017] [Simmons et al] [Beyer 1988] [Beyers 1992] [Beyers and Ericsson 1999] [Bonner and Gingras 1996] [Boswell 1970] [Bouriga et al. 2015] [Britcher and Landman 2024e] [Britcher and Landman 2024d] [Britcher and Landman 2024c] [Britcher and Landman 2024a] [Brodersen 2002] [Burns and Parker 2024] [Busch et al. 1986] [Butler 1976b] [Bykerk et al. 2022] [Capone et al. 2007] [Carlin and Bevan 1987] [Carmel and Brown 1972] [Carter 1988] [Celik and Bodapati 1988] [Cenko 1994] [CFD 1986] [CFD Applications to Engine/Airframe 1986] [Chaderjian 1992] [Chattot 2002] [Chawla et al. 1988] [Cheung 1996] [Childs et al. 1992] [Cobleigh and Delfrate 1994] [Collicott et al. 2026] [Computational Aerodynamics Applied 1990] [Computational Fluid Dynamics 1986] [Computational Fluid Dynamics 1997] [Computational Fluid Dynamics 2010] [Computational Fluid Dynamics 2021] [Computational Fluid Dynamics Program 1988] [Cooksey et al. 1964] [Corsiglia et al. 1984] [Cosentino 2007] [Cosentino 2008] [Cramer and Nguyen 2020] [Curriston and White 2025] [Darmofal et al. 2013] [Dash et al. 2003] [Davis 1979] [Decker and Buggele 1994] [Degani and Marcus 1997] [Deshpande et al. 2014] [Deskos et al. 2020] [Dix and Mattasits 1980] [Dodson 2005] [Dougherty et al. 1975] [Drexler-Bruce and Heathcote 2026] [Du et al. 2026] [Edge et al. 1999] [Edwards 1986] [Eikenberry 1966] [Eliasson 2008] [Emslie 1965] [Emslie 1966] [Enciu et al. 2025] [Erickson 1979c] [Ericsson and Beyers 1998b] [Ewald 1984] [Farcy et al. 2024] [First A340 Model 1986] [Fischer 2018] [Fohlmeister et al. 2026] [Forte et al. 2023] [Forte et al. 2026] [From Steady Flight 2011] [From Steady Flight to 2011] [Fung 2026] [Future Directions for Applied 1990] [Gariépy et al. 2013] [Gartenberg et al. 1993] [Gatzke et al. 1998] [Gauger and Fazzolari 2009] [Getting Ready for Computational] [Ghazi 1993] [Ghoreyshi et al. 2011] [Gibson 2002] [Glanville and Kwok 1997] [Goc et al. 2024] [Goncalves and Houdeville 2009] [Gonzalez et al. 2004] [Goodsell 1992] [Goodyer and Kilgore 1972] [Goorjian et al. 2026] [Gottlieb 1987] [Gottlieb 1993] [Gottlieb and Shu 1998] [Gottlieb et al. 1996] [Green et al. 2003] [Green et al. 2004] [Greer et al. 1973] [Groh 1985] [Gushchin et al. 1997] [Gutierrez et al. 1994] [Hafez 2011] [Haglund and Heinrich 1994] [Haider et al. 2026] [Halbritter et al. 2019] [Hall 1981] [Hamada et al. 2019] [Hammond 1999] [Han et al. 2025] [Hang et al. 2026] [Hanumanthu and Sreenivas Rao 2016] [Harney 1984] [Harrison 1966] [Harry and Trobaugh 1966] [Haut and Adcock 1977] [Hebbar et al. 1991] [Heim 1991] [Heinze and Karpel 2006] [Hess and Valarezo 1988] [High Precision Wind Tunnel 1985] [Hillebrand et al. 2023] [Hitfield et al. 1963] [Hitzel 2013] [Hitzel and Zimper 2018] [Hoe et al. 2012] [Houghton et al. 2017] [Huang and Cai 1990] [Huffschmid 1950] [Igeta 1983] [Ilić et al. 2026] [Introduction to Computational Fluid] [Jameson 1987] [Jansen 1982] [Jeans et al. 2009] [Jones 1976a] [Joppa 1968] [Joppa 1969] [Kara and Öztürk 2024] [Karmondy and Yechout 2007] [Kashitani et al. 2022] [Katz and Schiff 1984] [Kawai and Shimoyama 2014] [Khaddage] [Khan et al. 2019b] [Kita et al. 2021] [Klein and Batterson 1986] [Knowler 1955] [Koenig and Brady 1960] [Krag 1979] [Krengel et al. 2026] [Krzysiak 2019] [Kuntoji and Kuppast 2023] [Kurt et al. 2021] [Kutler and Mehta 1984] [Kwon and Sankar 1991] [Kwon and Sankar 1992] [LaBozzettz et al. 1995] [Landman et al. 2007b] [Landman et al. 2007a] [Lappe 1966] [Law and Jeffery 1981] [Lawson 1975] [Lazim et al. 2003] [Lazim et al. 2004] [Lee and Sears 1987] [Levinsky and Palko 1978] [Lewis and Goodyer 1996] [Li et al. 2023f] [Liu et al. 2020d] [Liu et al. 2026b] [Lu et al. 2013] [Luckring et al. 2017] [Lynch 1978] [Mohan et al. 2026] [Saad and Asmuin 2014] [Mabey 1992] [Maeder and Hall 1955] [Magill et al. 1994] [Mahmudul Hasan and Mizuno 2024] [Malcolm and Nelson 1987] [Mao et al. 2023] [Marcum 2000] [Margason and Hoad 1980] [Maskew 1982] [Matsuzaki et al. 1987] [Mavriplis 2007] [Mayya 2012] [Maślanka et al. 2024] [Medved and Elfstrom 1986] [Meyer and Decker 2000] [Meznarsic 1986] [Michal and Halt 1995] [Michel et al. 2025] [Mikhail and Rainbird 1978] [Miller 1992] [Miller and Agrawal 1990] [Millidere et al. 2021] [Mirzaei et al. 2026] [Modeling Aerodynamic Flows 2012] [Mort et al. 1979] [Mort et al. 1986] [Morton and McDaniel 2018] [Mouton 2023] [Murphy and Klein 2008] [New Type of Model 1984] [Newman 1965b] [Newman et al. 1982] [Newsome 1994] [Nguyen 2025] [Nicolosi et al. 2016] [Ninham et al. 1998] [Noor 2013] [Norton 1989] [Novakovic 2016] [Ongarato 1969] [Palko and Crawford 1982] [Palko and Lohr 1978] [Papadakis and Miller 1992] [Paul] [Paynter et al. 1987] [Paynter et al. 1989] [Penchev and Panayotov 2025] [Permali Blades for British 1991] [Philipsen et al. 2015] [Pindzola and Mozer 1956] [Pototzky 2014] [Prachař et al. 2018] [Qiang et al. 2016] [Quality Assurance of Wind 1999] [Raiford and Dall 1993] [Rajamurthy 1997] [Raju and Viswanath 2005] [Ramamurti and Sandberg 2006] [Raveh 2007] [Raveh 2009] [Raynal et al. 2000] [Reel and Baltadjiev 2018] [Regan 1964b] [Repperger 1995] [Richardson 1976] [Ringel and Levin 1985] [Rist 1994] [Rizk 1982] [Rogers 1966] [Rom 1992d] [Rom 1992e] [Roskam et al. 1980] [Elangovan et al and Tjprc 2019] [Sabatini et al. 2026] [Sahu et al. 1998] [Samikkannu 2011] [Sanders et al. 2001] [Saric 1989] [Schroeder and Baeder 2005] [Sears 1979] [Sereez et al. 2023] [Shang 2001] [Shang 2019] [Sheikh-AlShabab and Tucker 2014] [Sickles 2000] [Sickles 2004] [Singh 1996] [Singh and Baeder 1996] [Sleeman and Byrnes 1953] [Smelt 1955] [Smith and Schneider 1995] [Snyder and Erickson 1984] [Sorenson 1986] [Spedding et al. 2007] [Springer et al. 1997] [Steinle et al. 1999] [Stollery and Murthy 1978] [Strickland et al. 1990] [Su et al. 2023b] [Sungyeon et al. 2024] [Syamsuar et al. 2015] [Szatkowski et al. 2025] [Szodruch and Kotschote 1983] [Szodruch et al. 1987] [Tatum and Giles 1987] [Tatum and Giles 1988] [Tay et al. 2020] [Taylor 2015] [Teo et al. 2018] [Thames 1982] [The Application 1986] [The Need and Methods 2015] [The Use of Computers 1977] [Tinoco 1990] [Tinoco 1998] [To 2017] [Tobita et al. 2026] [Tomek et al. 2006] [Traub 2024] [Troeger and Selby 1998] [Tseng et al. 1989] [Tucker 2014b] [Tucker 2014a] [Turkel and Turkel 1997] [Ulbrich 2004] [Montomoli 2019] [Uselton 1976] [Vadyak et al. 1996] [Varner 1986] [Villarreal Valderrama et al. 2020] [Virtual Reality Computational Fluid 2005] [Volpe et al. 1987] [Von Wendt 1992] [Wakimoto et al. 2021] [Wang 2023a] [Wang et al. 2016b] [Wang et al. 2022c] [Wang et al. 2025a] [Watson et al. 2022] [Wattendorf 1939] [Whitnah and Hillje 1982] [Wienke et al. 2020] [Wind Tunnel 2022] [Wind Tunnel and Ground 1976] [Wind Tunnel Simulations 2022] [Wo and Covert 1990] [Wu et al. 2013b] [Yadav and Ng 2026] [Yamaguchi et al. 1994] [Yamazaki et al. 2017] [Yan and Shi 2025] [Zhou et al. 2022b] [Zhou et al. 2023b] [Zhou et al. 2026a] [Zientarski et al. 2015] [Zikyamov et al. 2026]
Airframe structure, composites and manufacture
The X-44A’s stated programme objective and the part of it that cannot be checked. Composite structure, laminates, structural design, fatigue, buckling and rapid manufacturing. No released figure connects this literature to the aircraft, so the cluster stands as the field the manufacturing claim was made inside rather than as evidence for it.
291 records. [El-Soaly et al. 2001] [Naik 2023] [Abbott 1989] [Abed et al. 2023] [Abelkis 1967] [Advanced Composite Materials 2016] [Aerospace and Defence Composite 1988] [Agrawal et al. 1992] [Aircraft Load 2010] [Airoldi et al. 2012] [Airworthiness Considerations for Airframe 2004] [Airworthiness Considerations for Airframe 2016] [Alaziz et al. 2024] [Alderliesten and Benedictus 2008] [Anderson et al. 2025] [Anisman and Blackstone 1948] [Ariotti et al. 1993] [Austin and William H. 1964] [Austin 1965] [Automating Lay-up of Composite 1999] [Aviation Composite Engineering 1999] [Badaliance and Dill 1981] [Bai 2024] [Bartley-Cho and Muraliraj 2022] [Bartley-Cho and Ranatunga 2020] [Bartley-Cho et al. 2018] [Basic Principles of Fiber 2004] [Basic Principles of Fiber 2016] [Bauch and Lair 1970] [Bender and Drake 2006] [Bennett et al. 1993] [Berg et al. 1989] [Beringhier and Gigliotti 2015] [Bersee 2010] [Bhattarai et al. 2026b] [Bigand] [Afzal 2020] [Blohowiak et al. 2005] [Booth et al. 2022] [Brown and Timmerman 1991] [Bucey 1956] [Burrows et al. 1991] [Carbon Fiber-Reinforced Magnesium Alloy 2024] [Chamis 1998] [Chen et al. 2024a] [Cherry 1975] [Chowdhury et al. 2015] [Chung 2016] [Clay et al. 2021] [Clay et al. 2023] [Clayton 1970] [Composite materials 2019] [Composite materials 2023] [Composite materials 2025] [Composite Materials and Aerospace 2002] [Composite Materials and Aerospace 2014] [Composite Panel with Integral 1990] [Composite structure 1998] [Composite Structure Reinforcement 1990] [Connolly 1996] [Continuous Simulation of Variations 2023] [Craddock 1973] [Crashworthy composite aircraft structure 1996] [Dai et al. 2007] [Damage Tolerance Certification 1995] [Davim and Reis 2003] [Davis 1973] [Degenhardt and Tessmer 2007] [Degenhardt et al. 2006] [Deng and Feng 2011] [Deng and Feng 2012] [Deák 2018] [Dhilipkumar and Rajesh 2022] [Dimino et al. 2018] [Dotseth et al. 1977] [Drela 1990] [Du et al. 2023] [Dvorak et al. 1947] [Engelstad et al. 2015] [England 1975] [Eskue 2023] [Fawaz 2016] [Figge 1973] [Fleuret et al. 2016] [Fosha 1969] [Fu et al. 1995] [Ashawesh 2001] [Gandy and Asmatulu 2012] [Gay 2022] [Gintert 1995] [Giurgiutiu 2016] [Giurgiutiu 2022] [Glenn and Koch 1973] [Goh] [Gopal 2016] [Grimes 1998] [Grossman et al. 1986] [Grover 1966] [Gunasegeran et al. 2022] [Guo et al. 2019b] [Gurdal 2002] [Gurdal et al. 1999] [Guyett and Cardrick 1980] [Hadcock 1985] [Hasan 2020] [Heating apparatus for composite 1996] [Heckl et al. 1962] [High-Level Planning and Control 1993] [Hirano et al. 2007] [Hollmann 1993] [Holzwarth 1998] [Honeycomb structure of thermostructural 1996] [Horton and Mayers 1965] [Hu 2023] [Hyer and Charette 1989] [Ibren et al. 2020] [Ilcewicz 2000] [Ilcewicz and Ashforth 2018] [Ilcewicz and Murphy 2005] [Ilcewicz et al. 2000] [Introduction to Composite Materials 2016] [Jackson and Fasanella 2018] [Jeans et al. 1983] [Jegley and Velicki 2013] [Jetela et al. 2018] [Ji et al. 2013] [Jones 2011] [Kaneda 2023] [Kano et al. 2025] [Karniadakis 2004] [Kashaev et al. 2018] [Katsurayama et al. 2016] [Katz 1986] [Keel 1988] [Kelkar and Williams 2002] [Kenney 2003] [Kim 2021] [Kim and Kim 2022] [Kizer 1977] [Kolarik 1990] [Kosztowny and Waas 2015] [Kosztowny and Waas 2021a] [Kosztowny and Waas 2021b] [Kumar and Bhattacharjee 2026] [Lange and Bhavnani 1993] [Legg 1956] [Li et al. 2026d] [Librescu et al. 1996] [Lin et al. 2014] [Linganiso and Anandjiwala 2016] [Liu and Sun 2021] [Liu and Wang 2019] [Logan 1974] [Luo et al. 2025a] [Lupuleac et al. 2018] [Lv and Ren 2023] [Ma et al. 2024a] [Mackulak 1984] [Mahlmeister et al. 1955] [Manning et al. 1984] [Manufacturing Processes of Composite 2016] [Marchinski 1974] [Mason and Quinlan 2018] [Masud and Khan 2015b] [McAnally 1974] [McCarty and Johnson 1978] [McClenahan and Plumer 1983] [McCombs et al. 1968] [McLoughlin 1972] [McMasters and Schlussel 2023] [Medina-Pérez et al. 2020] [Megson 2010] [Megson 2013] [Megson 2017] [Megson 2022] [Melo et al. 2017] [Method and Mold 1986] [Method for Producing 1991] [Mock 1982] [Momose et al. 2001] [Moulding a Fibre Reinforced 1990] [Muelaner 2019] [Murugan et al. 2012] [Nadeem Masood et al. 2020] [Nakajima 2009] [Nele and Teti 2018] [Nesterenko 2003] [Nikolic 2008] [Nordby et al. 1964] [Norwood and Brown 1981] [Norwood et al. 2021] [Norwood et al. 2022] [Noyes 1965] [Numerical modelling, testing and] [Nunes and Silva 2016] [Oakley et al. 1997] [Odagiri et al. 1996] [Okur et al. 2018] [Olson 2005] [Osman and Aminanda 2026] [Ouyang et al. 2025] [Overd 2011] [Charitidis 2018] [Park 2016] [Parveez 2024] [Pashkov et al. 2023] [Patnaik et al. 2008] [Patterson and Grenestedt 2018] [Patterson and Pinckney 1988] [Pethrick 2012] [Pinckney 1964] [Portolés Griñán] [Qian and Alonso 2018] [Rana and Fangueiro 2016] [Rana et al. 2016] [Rao et al. 2023b] [Rasuo 2015] [Reymer et al. 2014] [Rich 1980] [Ridgard et al. 2021] [Rohini and Samiyappan 2019] [Rose et al. 1986] [Rothwell 2001] [Růžek and Běhal 2009] [Sadowski 1988] [Sahoo et al. 2017] [Sanmati Vikas T L 2020] [Saurav et al. 2025] [Scarano et al. 2023] [Scarponi 2016] [Sha and Bahr 2002] [Shabani] [Shahar et al. 2023] [Sharan et al. 2013] [Shashi] [Shin 2021] [Shin and Kim 2013] [Shukla et al. 2010] [Shuvo 2019] [Singh et al. 2016c] [Skelly 1989] [Smith 1968] [Smith 1996] [Smotrova et al. 2021] [Soderquist 1987] [Sophisticated Aircraft Structure Developments 1982] [Sorrentino et al. 2016] [Stamatelos and Labeas 2025] [Stautner et al. 2024] [Stenberg 1988] [Strizhius 2014] [Strizhius 2016] [Sturm et al. 2014] [Sun et al. 2015] [Sun et al. 2021] [Switzky 1962] [Taha and Bauomy 2021] [Taig 1972] [Terry 2000] [Thawre et al. 2015] [The Design of Simplified 1947] [Three-Dimensional Fiber-Reinforced Composites 2016] [Tolstikov and Pykhalov 2021] [Tooling for Composite Aerospace 2020] [Triplett 1980] [Vasiliev et al. 2012] [Verma 2020] [Viscusi et al. 2020] [Waite 2020] [Wang et al. 2002] [Wang et al. 2015b] [Wang et al. 2016c] [Wang et al. 2022b] [Weirich et al. 1996] [Weisshaar 1978] [Wells 1975] [Whinery et al. 1971] [Whitehead et al. 1992] [Wildschek et al. 2009] [Wilhem 1970] [Wilkinson and Ruggles-Wrenn 2016] [Wilson 1980] [Wu 2024] [Xing 2020] [Xu et al. 2026] [Yu et al. 2026] [Zhang et al. 2022b] [Zhang et al. 2025g] [Zhao and Kapania 2016a] [Zhao and Kapania 2016b] [Zhong et al. 2001]
Aircraft conceptual design, sizing and drag
The working relations of the design texts the article cites. Conceptual and preliminary design, weight estimation, design optimisation, drag prediction and fighter configuration studies. The tail volume coefficient, the drag polar and the Oswald factor that the derivations use are this literature’s tools, and the article uses them in their textbook forms.
277 records. [Aerodynamic Configuration Design Using 1993] [Aerodynamic Considerations 2010] [Aerodynamic Data of Real 2010] [Aerodynamic Design 1963] [Aerodynamic Design 1973] [Aerodynamic Design 2020] [Aerodynamic Design and Performance 1965] [Aerodynamic Design 1969c] [Aerodynamic Drag and Its 2013] [Aerodynamic Drag in Cruising 2020] [Aircraft Anatomy 1985] [Aircraft Anatomy 2003] [Aircraft Applications and Design 2004] [Aircraft Case Studies 2026] [Aircraft Characteristics 2022] [Aircraft Conceptual Design 2012] [Aircraft Design Fundamentals 2012] [Aircraft Drag 2010] [Aircraft Weights Data 2010] [Aircraft/Engine System Constraint Analysis 2018] [An et al. 2025] [Analytic Geometry Applied 1946] [Anderson and Innis 1965] [Andrews and Perez 2014] [Appendix E. Airframe Parameters 2012] [Appendix G Aerodynamic Data 2010] [Ascani 1974] [Aspects of Airframe Design 2010] [B 2006] [Badyagin et al. 1979] [Ball 1966] [Ball et al. 1988] [Barlow and Kelley 1974] [Bennett and Davis 1969] [Bergmann and Hummel 2001] [Berman et al. 1964] [Bhatra and Mishra 2023] [Black and Murphy 1972] [Blake 1985] [Bloor and Wilson 1995] [Boppe 1985] [Bradley and Bhateley 1983] [Bradley and Droney 2015] [Bradley et al. 2015] [Brandt 2018] [Brock 1977] [Camberos et al. 2004] [Carter et al. 2011] [Characteristics of Aircraft Types 2010] [Chin 1988] [Cleveland 1970] [Coen and Foss 1986] [Coen and Foss 1985] [Coiro and Nicolosi 2001] [Colombo 2020] [Computational Analysis 1994] [Configuring Aircraft 2010] [Conner and Vaughan 1980] [Cox and Downing 1992] [Crispin 1992] [Crossley 2004] [Davari et al. 2011] [Davidson et al. 1972] [de Paula et al. 2025] [DeLaurier 2022a] [Design Sheets for New 2003] [Desilets] [Determination of Aerodynamic Characteristics 2001] [Dikshit et al. 2022] [Dollyhigh 1970] [Drag Equations 1992] [Drela 1999] [Dudley 1986] [Dulikravich 1992] [Durston and Smith 1981] [Eberle and Fowler 1971] [Eckels 1983] [Epstein and Peigin 2003] [Evolution and Design Philosophy 1967] [Fellers and Patierno 1970] [Fernandez et al. 2021] [Field et al. 1981] [Fielding and Nilubol 2003] [Fighter Aircraft to Get 1986] [Figliola 2004] [Figliola 2005] [Flight 2026] [Fundamentals of Fighter Design 2001] [Galbraith and Haimes 2022] [Gallay and Laurendeau 2016] [Generic Aircraft Design Flowchart 2017] [Goddard and Eastgate 2010] [Goldschmied 1978] [Goldschmied 1990] [Gorbunov et al. 2023] [Gudmundsson 2014a] [Gudmundsson 2014b] [Gudmundsson 2022a] [Gudmundsson 2022b] [Hague 1980] [Hague 1981] [Hague 1983] [Hammond and Polhamus 1965] [Harrell 1986] [Hayase 1974a] [Hayase 1974b] [Hays 1989] [Henne 1989] [Herbst 1983] [Herbst and Krogull 1972] [Herbst and Krogull 1973] [Herrmann and Biehl 1986] [Hicks and Moulton 1988] [Hill and Waters 1974] [Hill and Waters 1975] [Hiyama 1974] [Hoffman and Stalford 1991] [Holmes 1980] [Horne 1979] [Hu et al. 2010] [Human-Powered Aircraft Wing Design 2014] [Incorporating Agility Flight Test 1994] [Бен Ларби and Зинченко 2018] [Ingram et al. 1986] [Introduction to Aircraft Aerodynamic 2021] [Jenkinson et al. 1999] [Jobe 1984] [Johnson and Rader 1980] [Kai et al. 2018] [Koc et al. 2005b] [Krahnstoever et al. 2026] [Krawczyk et al. 2024] [Kress 1983] [Krishnamurthy and Luckner 2017] [Kroo 1986] [Kroo et al. 1994] [Kryvokhatko 2023a] [Kryvokhatko 2023c] [Kryvokhatko 2023b] [Kryvokhatko 2024a] [Kryvokhatko 2024c] [Kryvokhatko 2024b] [Kuhn 1980a] [Küchemann 2012] [Labrujere and Slooff 1993] [Labrujre 1993] [Lachmann 1961] [Laitone 1978a] [Laitone 1978b] [Landfield and Rajkovic 1984] [Landfield and Rajkovic 1986] [Lange 1984] [Lee and Eyi 1992] [Lee and Kim 2007] [Leonard 2001] [Li and Tiniakov 2026b] [Liersch and Wunderlich 2008] [Liu 2022a] [Loh and Lusty 1974] [Lummus 1981] [Madelung 1977] [Madelung 1978] [Malone et al. 1987] [Matos and Marta 2025] [McCarthy and Kelly 1993] [Mehler 1986] [Mendenhall et al. 1975] [Methodology to Aircraft Design 2010] [Methods for Improving Longitudinal 2003] [Michaut et al. 1989] [Milholen 2001] [Monnett 1981] [Montgomery et al. 1998] [Mori] [Multhopp 1942] [Murillo and McMasters 1983] [Murillo and McMasters 1984] [Nelms and Durston 1980] [Nelms and Durston 1981] [Newberry 1998] [Ngan and Biezad 1996] [Olson 2015b] [Oole 1993] [Ordaz et al. 2015] [Palaia 2026] [Planform Parameterization 2014] [Pogosyan and Strelets 2025] [Preliminary Aerodynamic and Stability 2017] [Preliminary Aerodynamic Design 2000] [Preliminary Fuselage Sizing 2010] [Pustina 2023] [Pátek and Smrcek 1999] [Qiang et al. 2025] [Rancruel and von Spakovsky 2003] [Raymer 1995] [Raymer 1998] [Reinbold et al. 2026] [Reist and Zingg 2017] [Render 2010] [Research on Combination 2019] [Reshotko 1979] [Reuther and Jameson 1995a] [Rizzi and Oppelstrup 2021] [Rogers and Fasciano 2016] [Rokhsaz and Selberg 1990] [Ross and Matarazzo 1982] [Roy et al. 2019] [Russell 2014] [Sachs 1980] [Sadraey 2017a] [Sadraey 2023a] [Sadraey 2024] [Satran 1986] [Schulz and Gherman 2009] [Schwartz 1988] [Scientific and Technical Information Division 1966] [Shevell 1978] [Siddiqui et al. 2021] [Siegers and Smith 1995] [Slender Aircraft for Flight 2012] [Smith 1989] [Smith and Lee 1989] [Snepp and Pomeroy 1987] [Sorensen et al. 1979] [Soylak et al. 2018] [Spearman 2001] [Spencer 1960] [Sreejith 2026] [Stanley 1980] [Stewart and Campion 1980] [Straub 1973] [Szodruch et al. 2011] [Sóbester and Forrester 2014] [Ta’asan 1995] [Tamrat 1983] [Tamrat 1988] [Tasci and Ozdemir 2025] [The Aerodynamic Design 1969] [The Design of Classical 2012] [Thelander 1967] [Thompson and Kirschbaum 1934] [Three-Dimensional Wing Synthesis 2014] [Thrust-to-Weight Ratio and Wing 2024] [Tong et al. 2016] [Torenbeek 1971] [Trim Drag and Maneuvering 2010] [Tu 1992] [Tu 1994] [Tulinius and Margason 1976] [Tuschhoff 1989] [Useful Aircraft Design Data] [Useful Aircraft Design Data 1999] [van Arnhem et al. 2022] [Van Horn 2011] [Venkayya et al. 1996] [Wang 2025] [Ward 1983] [Ward et al. 1985] [Webber 1964] [Wei et al. 2006] [Whitford 1990] [Whitford 1991b] [Whitford 1994] [Why Should We Design] [Willan 2011] [Wing Design Considerations 2021] [Woelk 1989] [Worked Manned Aircraft Detail 2017] [Xun et al. 1993] [Yajnik and Subbaiah 1976] [Yang et al. 2026b] [Yildirim and Eyi 2017] [Zhou Tao et al. 2007] [Zhu et al. 2017] [Zweig and Ben-Asher 1995] [Şugar-Gabor and Koreanschi 2020] [Şugar-Gabor and Koreanschi 2021]
The atmosphere, turbulence, gust response and load alleviation
The flight condition the crosswind identity simplifies. The standard atmosphere, atmospheric turbulence models and measurements, aircraft response to gusts and active gust load alleviation. The crosswind identity treats a wind as a fixed lateral velocity, and this cluster is where the statistics of real winds and gusts are recorded.
269 records. [A Survey of Recent 1981] [Abdelmoula 1999] [Abdulwahab and Chen 2008] [Abdulwahab and Hongquan 2008] [Active control of a 1994] [Ahmadi Tehrani et al. 2025] [Air Force Test Pilot School Edwards Afb Ca 1962a] [Asaro et al. 2023] [Austin and William H. 1967] [Babcock and Lind 2013] [Bagheri et al. 2019] [Bai et al. 2014] [Balatti et al. 2022a] [Balatti et al. 2023] [Barnaby 1955] [Bathgate et al. 2026] [Bedard et al. 1986] [Beer and Trevino 1970] [Bochis 1984] [Bruni et al. 2014] [Buffington et al] [Burgstaller and Galffy 2024] [Burris and Bender 1969b] [Camp et al. 1984] [Canfield 2014] [Capello et al. 2014] [Castells Marin] [Castells Marin and Poetsch 2020] [Castrichini et al. 2016] [Cavaliere and Fezans 2024] [Caverly et al. 2017] [Chang 2016] [Chang et al. 2010] [Chen et al. 2010a] [Chen et al. 2017c] [Cheung et al. 2019] [Cheung et al. 2023] [Chigier and Corsiglia 1972] [Christopher and Dunn 1973] [Chudý 2004] [Cook et al. 2013] [Cornman et al. 1994] [Cornman et al. 1995] [Costello 2009] [Costes 2000] [Coupry 1971] [Coupry 1972] [Crema et al. 2000] [Crimaldi et al. 1991] [Crimaldi et al. 1993] [Crouch and Czech 2016] [Da Ronch and Badcock 2013] [Dai et al. 2017] [Dehghan et al. 2014] [Demirer and Kayran 2022] [Devuono and Shearer 2008] [Dias and Hubbard 2019] [Diederich 1957] [Diederich 1958] [Dietz et al. 2003] [Dillsaver et al. 2011] [Dillsaver et al. 2012] [Dillsaver et al. 2013] [Dodd and Pratt 1971] [Drüe and Heinemann 2013] [Duessler et al. 2023] [Duessler et al. 2024] [Dynamics of Rigid Aircraft 2023] [Düssler et al. 2026] [Edward and Ray 2012] [Eggleston and Phillips 1958] [Eichenbaum 1971] [Fan et al. 2017b] [Fezans 2017] [Flomenhoft 1994] [Flomenholf 1957] [Fonte and Mantegazza 2017] [Fonte et al. 2018] [Forte and Nguyen 2026] [Fournier et al. 2022] [Diederich 1956] [Fujimori and Lin 1973] [Fujimori et al. 1990] [Fuller 1995] [Galiński 2006] [Gangsaas et al. 1981] [Gault and Gunter 1968] [Gennaretti and Ponzi 1999] [Ghazi 1994] [Giesseler et al. 2012] [Gili et al. 1997] [Guo et al. 2013b] [Guo et al. 2015] [Guo et al. 2017a] [Hacker and Wroblewski 2009] [Hashemi et al. 2018] [He and Su 2023a] [He and Su 2023b] [He et al. 2022a] [Hess 1971] [Hinson et al. 2022] [Hoblit 1988] [Hoffmann et al. 2011] [Houbolt 1971] [Houbolt 1972] [Houbolt and Williamson 1975] [Howell and Lin 1971] [Huang et al. 2017c] [Huntley and Littlewood 1972] [Huntley et al. 2017] [Iavarone et al. 2025] [Jackson and Salter 1971] [Jiang et al. 2023] [Jing and Tang 2022] [Johannes 1971] [Jones 1989] [Jones 2009] [Kalogiros and Wang 2002] [Kambushev and Marinov 2025] [Karpel 1980] [Karpel 1982] [Karpel et al. 2005] [Kennedy and Shapiro 1980] [Khalid 2019] [Khalil and Bauknecht 2024] [Khalil and Fezans 2019] [Khalil and Fezans 2020] [Khalil et al. 2022] [Kimberlin and Sims 1996] [Klipp and Measure 2011] [Kobayakawa and Maeda 1978b] [Kobayakawa and Maeda 1978a] [Kopeć et al. 2016] [Krengel and Hepperle 2023] [Li] [Li and Lan 2003] [Li and Qin 2020] [Li and Qin 2021b] [Li and Qin 2021a] [Li and Qin 2022] [Li et al. 2016b] [Li et al. 2021b] [Li et al. 2024b] [Li et al. 2025e] [Liebst et al. 1986] [Lin 1965] [Liu and Sun 2016] [Liu and Sun 2017] [Liu et al. 2017b] [Liu et al. 2018c] [Liu et al. 2020a] [Lovejoy et al. 2009] [Lucas et al. 2009] [Ly 1980] [Mackey et al. 2018] [Mangalam et al. 2008] [Mares and Suresh Babu 2026] [Markov et al. 1982] [Masrour et al. 2023] [Matayoshi and Inokuchi 2002] [Mballo and Prasad 2022] [McKenzie 1973] [McLean 1978] [Meng et al. 2024] [Mohamed et al. 2026] [Mor and Livne 2006] [Morelli and Cunningham 2012] [Müller and Lutz 2024] [Müller et al. 2020] [Nagashima and Tanida 1984] [Nam et al. 1997] [Nelson 1974] [Nguyen 2021] [Nguyen and Tuzcu 2024] [Nie et al. 2009] [Nikiforuk et al. 1974] [Nissim 1977] [Noll and Merino 1976] [Noll and Morino 1976] [Norman et al. 1983] [Ohta and Fujimori 1988] [Okubo et al. 1979] [Olwi 1995] [Otten et al. 1982] [Ozbay 1993] [Patil 2007] [Paton 1963] [Payne and Cox 1969] [Payne and Nelson 1985] [Peele 1970] [Peele and Steiner 1969] [Peele and Steiner 1970] [Pi and Hwang 1978] [Plunge-Only Equation of Motion 1988] [Poirion 1991] [Poussot-Vassal et al. 2022] [Pusch 2017] [Qi et al. 2015] [Reeves et al. 1975] [Reid 1982] [Reiter 1957] [Reiter and Burns 1966] [Ricci and Scotti 2010] [Rieck et al. 2026] [Ringnes et al. 1986] [Roberts et al. 1977] [Roesch and Harlan 1974] [Rothman and Chernoff 1961] [Rui Nie et al. 2009] [Rustenburg 1972] [Sarantopoulos and De Abreu-Garcia] [Sato 2010] [Schumann et al. 2025] [Scott et al. 2011] [Seeni 2023] [Seki et al. 2019] [Shabbir et al. 2022] [Smetana and Carden 1973] [Spanwise Variation of Vertical 1988] [Stahl and Barnes 2026] [Stalla et al. 2024] [Steiner and Rhyne 1964] [Stewart 1975] [Strunin and Hiyama 2004] [Suzuki and Yonezawa 1993] [Takase et al. 2017] [Takase et al. 2018] [Tang et al. 2016] [Tani et al. 2018] [Tantaroudas and Karachalios 2026] [Taylor 1977] [Thomas and Shkarayev 2026] [Tischler and Venkayya 1998] [Toffol 2024] [Trevino 1980] [Trevino 1981] [Trevino 1986] [Turner et al. 1981] [U.S. Standard Atmosphere 1976 1976] [Vartio et al. 2008] [Verdon and Steiner 1973] [Wang and Feng 2025] [Wang and Shen 1977] [Wang and Shen 1980] [Wang et al. 2015a] [Wildschek and Maier 2008] [Williams et al. 2016] [Williams et al. 2017] [Wisniewski et al. 1995] [Wu et al. 2025] [Wuestenhagen 2023] [Wykes 1968] [Wynn et al. 2022] [Xiaoxiong et al. 2017] [Xu and Kroo 2011] [Xue Lei et al. 2016] [Yagil et al. 2018] [Yang and Obayashi 2002] [Yang and Obayashi 2003] [Yang and Obayashi 2004] [Yost et al. 1972] [Yue and Zhao 2023] [Zbrozek 1958] [Zbrozek 1962] [Zhang et al. 2018c] [Zhang et al. 2024c] [Zhang et al. 2024d] [Zhao et al. 2016a] [Zhou et al. 2026b]
Approach, landing and the crosswind case
This cluster covers the subject of the article’s strongest conclusion, that pure thrust vectoring cannot meet a crosswind landing requirement. It holds crosswind technique, approach and landing handling qualities, automatic and carrier landing, wind shear on approach, and landing rollout directional control.
246 records. [A Wind Shear Hazard 1993] [Abdelrahman et al. 1992] [Abdelrahman et al. 1994] [Aguilar-Ibanez et al. 2026] [Airborne windshear systems] [Aircraft Automatic Approach 1996] [Aircraft Landing Measurement System 1971] [Aircraft Landing Procedure 1998] [Al-Rbayee et al. 2026] [Alexandrov et al. 1979] [Alexandrov et al. 1980] [Altunkaya and Ozkol 2023] [Analysis of Factors Affecting 2022] [Anderson 1996] [Asyraf and Omar 2026] [Awashej et al. 2025] [Baldi et al. 2011] [Banks and Paulson 1985] [Banks and Paulson 1984] [Barland 1985] [Berry and Powers 1970] [Beukers et al. 2009] [Beyers and Ericsson 2001] [Bian et al. 2018a] [Biertümpfel and Pfifer 2022] [Bittrick 1984] [Blackman and Eigenmann 1981] [Bodson and Athans 1985] [Bogos et al. 2018] [Botkin et al. 2017] [Bracalente et al. 1990] [Bray 1986] [Brenckmann 1964] [Bretschneider et al. 2021] [Brewer 1974] [Buell 1970] [Bureau of Aeronautics (navy) Washingtondc 1949] [Burlion et al. 2014] [Cacciola et al. 2023] [Cai et al. 2024] [Calugaru and Danisor 2016] [Cassaro et al. 2018] [Chaloff et al. 1974] [Chen and Yong 2023] [Chernenko and Burnashev 2022] [Chu and Bryson 1987] [Chun-Lin Shen et al. 1990] [Clark 1974] [Cobar and Montalvo 2021] [Connelly 1982] [Craig and Heffley 1972] [Crassidis and Mook 1991] [Cui et al. 2022] [Data for Aerodynamic Crosswind 2019] [de Bruin and Jones 2016] [Deniz et al. 2018] [Desyatnik 2015] [Dojka and Wysocki 2025] [Dominy and Ryan 1999] [Douglas Aircraft Co Long Beach Ca 1963] [Durand and Teper 1964] [Effect of Wind Shear 1990] [Eigenmann et al. 1984] [Etkin 1987] [Бабич et al. 2017] [Ferrarese 1974] [Fichtl 1972] [Filippone 2008] [Fisher et al. 1976] [Franklin and Innis 1977] [Frost and Bowles 1984b] [Funabiki et al. 1993] [Gao and Gu 2011] [Gao and Li 2014] [Garg and Schmidt 1988] [Gasanov et al. 2020] [Gerardi 1977] [Ghazi and Olwi 1995] [Gonçalves et al. 2010] [Grantham et al. 1976] [Grantham et al. 1984] [Grantham et al. 1985a] [Greene 1978] [Greene 1979a] [Greene 1979b] [Gressang 1976] [Groen et al. 2005] [Gudeta and Karimoddini 2019] [Gupta 2026b] [Harrah et al. 1993] [He and Ai 2018] [Helliwell 1952] [Hess 1990] [Hodgkinson and Johnston 1979] [Hofman 1976] [Hoh 1977] [Hoy 1963] [Hryshchenko et al. 2025] [Hsin 1974] [Hu 2025] [Huaxin Wu et al. 2010] [Humphreys et al. 1988] [Самойленко et al. 2006] [Jiang et al. 2013] [Jiang et al. 2018] [Jih-Gau Juang and Jern-Zuin Chio] [Johnston et al. 1965a] [Jones et al. 2010] [Joshi and Compton 1985] [Juang and Yu 2015] [Kafiabad et al. 2013] [Khattak et al. 2024] [Khattak et al. 2025] [Kistyarev and Wang 2025] [Kong et al. 2024] [Krawczyk et al. 2019a] [Krawczyk et al. 2019b] [Kuhn and Kurkowski 1984] [Kuhn et al. 1983] [Lamp and Luckner 2015] [Landrum and Tournes 2001] [Le et al. 2019] [Lebacqz and Chen 1977] [Lee and Juang 2011] [Lehman 1964] [Lehman 1965] [Lehman 1966] [Li and Chen 2003] [Liang et al. 2020] [Liang et al. 2022] [Liang et al. 2024] [Liang et al. 2025] [Ling 1970] [Liu et al. 2025e] [Lorenzetti et al. 1969] [Luers and Reeves 1975] [Lungu 2017] [Lungu and Lungu 2015] [Luo and Duan 2014] [Luo and Duan 2015] [Lykken and Shah 1971] [Lykken and Shah 1972] [Majka 2013] [Martorella et al. 1981] [Matni and Meeko Oishi 2008] [McNeill and Vomaske 1959] [Meng and Li 2014] [Menon et al. 2010] [Micklos 1991] [Miller 1968] [Misra and Bai 2018] [Misra et al. 2022] [Mitchell and Hoh 1983] [Moody 1987] [Moody et al. 1987] [Mori and Suzuki 2008] [Mori and Suzuki 2009a] [Mori and Suzuki 2009c] [Mori and Suzuki 2009b] [Mori and Suzuki 2010] [Muehter 1974] [Mulgund and Stengel 1996] [Munoz et al. 2010] [Obye and Hakim 1984] [Ochi and Kanai] [Ohme 2009] [Pal et al. 2024] [Pan and Pi 2025] [Papadopoulos 1998] [Pasha et al] [Pierson 1985] [Pierson 1986] [Plews 1983] [Polukhin and Ostapenko 2019] [Prach et al. 2019] [Prilliman and Slingerland 1966] [Psiaki 1989] [Qiao et al. 2022] [Rajendran and Pachidis 2019] [Reemsnyder and Sagerser 1979a] [Ren et al. 2025] [Rhoads 1967] [Robinson 1993] [Roos et al] [Sadat-Hoseini et al. 2013] [Sakamoto et al. 2006] [Schick and Teegen 1982] [Schick and Teegen 1983] [Schmidt 1985a] [Sedlmair et al. 2022] [Semakov 2021] [Semakov and Semakov 2020] [Semakov and Semakova 2023] [Sheppard and Foster 2008] [Sinha] [Sleeper and Smith 1982] [Smaili et al. 2007] [Smith et al. 1973] [Sogut 2025] [Song et al. 2023] [Stephan and Fichter 2016] [Stratton and Stengel 1992] [Stratton and Stengel 1995] [Streb 1973] [Streb 1972] [Stubbs and Byrdsong 1973] [Suharevs 2022] [Tang and Lai 2020] [Tang et al. 2014] [Targ and Bowles 1991] [Teper and Stapleford 1966] [Thompson 1965] [Tingting et al. 2018] [Tudosie and Butu 2016] [Vechtel 2019] [Vempati and Lu 1995] [Wagdi 1984] [Walker 1960] [Walker 1961] [Wang and Hu 2025] [Wang et al. 2017c] [Washington and Humphrey 1969] [Wasserman and Mitchell 1973] [Watanabe et al. 2023] [Weltz and Barajas 2025] [White 1992] [Wilhelm and Schafranek 1986] [Wood et al. 2012] [Wu and Liu 2021] [Xiao et al. 2024] [Yamaguchi and Umemura 2005] [Yan and Song 2024] [Yang and Juang 2009] [Ye et al. 2020] [Yin et al. 2023] [Yokota et al. 2020] [Yuanwei Jing et al. 2009] [Zammit and Zammmit-Mangion 2014] [Zelenkov and Golik 2014] [Zhai et al. 2026] [Zhang 2023] [Zhang et al. 2001] [Zhang et al. 2025e] [Zhao and Bryson 1990] [Zhu 2024] [Zhu and Qiu 2013]
Wings, aerofoils and flow control
The wing outside the delta and supersonic clusters. Aerofoil and wing aerodynamics, boundary layers and transition, wingtip devices, high lift and active flow control. The X-44A’s deep, inversely cambered wing is a subject of this literature rather than of the delta cluster.
174 records. [Addoms and Spaid 1975] [Aerodynamic Design 1969a] [Aerofoil Engineering 2014] [Aerofoil Parameterization 2014] [Aihara et al. 1985] [Airfoil Design Considerations 2021] [Al-Atabi and Asrar 1999] [Aoki and Muraoka 2019] [Appendix F NACA Airfoil 2010] [Ardonceau and Trapier 2005] [Ashley and Rodden 1972] [Aslan et al. 2024] [Basic Aerofoil Analysis 2014] [Basic Principles Governing Aerodynamic 2014] [Beatty et al. 1977] [Bodonyl 1994] [Buddhiraju et al. 2024] [Burns and Cliff 1982] [Cai et al. 2019] [Caruso et al. 1988] [Casacuberta et al. 2022] [Casper and Scholz 2014] [Chapleo and Nair 1994] [Chapter 1. Wing-Tail Plane 1957] [Chapter 2. Aerodynamics 1957] [Chapter 2. Wing-Body Interference 1957] [Chattot 2006] [Chen 2018] [Chng and Tsai 2008] [Cho et al. 2014] [Choi and Kwon 2008] [Coder and Maughmer 2014] [Cole 1996] [Concepts and Computational Models 2021] [Cornish and Boatwright 1960] [Câmara et al. 2017] [Dehaan 1990] [Deyoung 1980] [Drela 1988] [Elements of Aerodynamic Wing 2013] [Eppink 2023] [F. Nonsteady Wing Characteristics 1957] [Families of Legacy Aerofoils 2014] [Fast Computation of Airfoil 2021] [Firmanto 2022] [Fluid Mechanics and Aerodynamics 2011] [Fluid et al. 2011] [Gall and Smith 1987] [Garbo and Bekemeyer 2025] [Gharib et al. 1985] [Gilman and Burdges 1967] [Gopalarathnam and Selig 2001] [Gopalarathnam et al. 2003] [Govindarajan and Narasimha 2000] [Granville 1973] [Grasso 2016] [Harvell and Franke 1985] [Hiraki and Hidaka 2013] [Hopkins 1975] [Hopkins 1977] [Housh et al. 1991] [Hsiao and Hsu 1989] [Hsiun and Chen 1996] [Huffman et al. 1987] [Iqbal et al. 2025] [Ishimitsu 1976] [Janiszewska et al. 2003] [Jarvis and Selberg 1999] [Jordan 1971] [Kachanov and Tararykin 1990] [Kamishita et al. 2000] [Kanoria and Damodaran 2017] [Katz et al. 1995] [Keller and Rudnik 2015] [Khan and Agrawal 2005] [Khrabrov and Greenwell 2006] [King et al. 2013] [Kornev and Pimenov 2022] [Kravchenko 1995] [Kumar and Venkatakrishnan 2020] [Kurz and Kloker 2015] [Kwon and Park 2005] [Laminar Flow Control Wing 1999] [Langan et al. 1997] [Larsen et al. 1963] [Lee 2009] [Lee and Lee 2014] [Lee et al. 1986] [Loth and Boyle 1969] [Loth and Loth 1984] [Low Drag Airfoil Design 1980] [Ma 1989] [Magill and McManus 2001] [Makino and Nagai 2014] [Mann and Elsholz 2005] [Margaris and Gursul 2004] [Martin and Stroub 1987] [Maughmer et al. 2002] [Meyer and Seginer 1992] [Mistry et al. 2013] [Moore and Hymer 2001] [Morgan and Garmann 2026] [Mueller and Torres 2001] [Munday and Jacob 2002] [NACA Airfoil Nomenclature 2010] [Nagamatsu and Cuche 1981] [Nikolic 2004] [Northrop Aircraft INC Hawthorne CA 1956] [Ol 2007] [Olguin-Diaz and Garcia-Teran 2014] [Olson and Selberg 1976] [Park et al. 2013] [Parlett 1972] [Payne 1958] [Perry and Miklosovic 2012] [Pfenninger and Vemuru 1990] [Portnoy 1975] [Quick 1937] [Reed 1984] [Reed 1987] [Rehman and Kontis 2006] [Reibert et al. 1997] [Roberts 1966] [Rogers 2010] [Rostamzadeh et al. 2020] [Rowley 2008] [Rowley 2010] [Rubin and Lyons 1979] [Saric 1997] [Saric 2010] [Saric et al. 1990] [Schwartzberg 1975] [Sebastia Saez et al. 2026] [Selig and Guglielmo 1997] [Siegel et al. 2007] [Smith and Nelson 1990] [Sol and Vos 2016] [Sorenson 1974] [Spillman and McVitie 1984] [Starn] [Steinbach 1997] [Strang et al. 2004] [Sturgeon and Bennett 1976] [Szafruga and Ramaprian 1994a] [Szafruga and Ramaprian 1994b] [Tadakuma et al. 2005] [Tafti et al. 2014] [Tavella et al. 1986a] [Terry 1964] [Time-Domain Unsteady Aerodynamics 2023] [Traub and Agarwal 2008] [Traub and Freienmuth 2011] [Traub et al. 1999] [Tuck and Soria 2008] [Van Dam et al. 1990] [Vepa 2023d] [Vijgen et al. 1989] [Vivian and Andrew 1965] [Vlachos and Telioinis 2003] [Vrchota et al. 2019] [Wales et al. 2015] [Wang 2023b] [Wang et al. 2011a] [Wei et al. 2019] [Wentz and Nyenhuis 1984] [White 1963] [White et al. 2001] [Woodruff et al. 2011] [Wu et al. 1986] [Xinbing et al. 2019] [Xu and Yeung 1999] [Zhou et al. 2025a] [Zoppini et al. 2022] [Zyskowski 1995]
Flight test technique, parameter identification and air data
Where the derivative this article brackets would be measured. Flight test methods and instrumentation, the identification of stability and control derivatives from flight and dynamic wind tunnel data, and air data and flow angle measurement, which is where the sideslip sensing named in the section on sensing is calibrated.
158 records. [Adams et al. 2025] [Air Force Flight Test Center Edwards AFB CA 1974b] [Air Force Flight Test Center Edwards AFB CA 1974a] [Air Force Test Pilot School Edwards Afb Ca 1967b] [Air Force Test Pilot School Edwards Afb Ca 1967a] [Air Force Test Pilot School Edwards Afb Ca 1990e] [Air Force Test Pilot School Edwards Afb Ca 1990d] [Air Force Test Pilot School Edwards Afb Ca 1992a] [Air Force Test Pilot School Edwards Afb Ca 1993] [Aircraft and Flight Test 2021] [Airfoil Static-Pressure Thrust 1990] [Alford and Knarr 1999] [Almeida 2012] [Assadourian and Reeder 1948] [Asselin 2021] [Azab and Nouh 1984] [Bailey et al. 1996] [Barrett 1999] [Batterson and Klein 1989] [Beyers 1983] [Bock 1976] [Brandon and Foster 1998] [Bronz and Hattenberger 2016] [Broughton 1978] [Brunner 1996] [Carico 1995] [Carico 1998] [Carnduff et al. 2009] [Cheney 1988] [Chin et al. 2015c] [Chin et al. 2015a] [Chin et al. 2015b] [Cho et al. 1995] [Clopper 1951] [Cooke 1983] [Curry and Sim 1984] [Cuttill 2003] [Vicroy 2023] [DeAngelis 1982] [Denton et al. 2021] [Denton et al. 2025] [Dong et al. 2024b] [Douglas Aircraft CO INC Santa Monica CA 1963] [Drake 1964] [Dungan and Clark 1994] [Dynamic Longitudinal Stability Flight 2003] [Erdman 2005] [Eulrich et al. 1978] [Flight Test Planning 2021] [Flight test procedures for] [Francois Veysset 2006] [Friehmelt 1997] [Fuzzy Clustering in Problems 2018] [Ghoreyshi et al. 2024] [Ghosh and Raisinghani 2000] [Ghosh and Raisinghani 2002] [Gibson 1981] [Godwin et al. 1964] [Herrington et al. 1966] [Hess 1986] [Hightower 1985] [Hoadley 1988] [Hong et al. 2018] [Hu et al. 2024a] [Hull and Roger 1975] [Hunter and Reeder 1946] [Identification of nonlinear aircraft 1994] [Iliff and Maine 1977] [Iliff et al. 1981] [Introduction to Stability 2003] [Jain and Chandrasekaran 2024] [Jain et al. 2017] [Jiang and Chen 1986] [Kaletka and Fu 1993] [Klein and Batterson 1983] [Kokolios 1993] [Koven and Kayten 1946] [Kumar 1999] [Level Flight Performance Flight 2003] [Lightweight Low-Cost Flight Test 2007] [Londono and Leonhardt 2012] [Longhurst 1966] [Longitudinal Control and Trim 2003] [Lutze and Fan 1998] [Martin 1996] [Mattsson et al. 2003] [McCullough et al. 1947] [McElreath 1972] [McNally and Bach 1988] [Methods for Reducing Data 2003] [Moes and Iliff 2002] [Moes et al. 2000] [Moes et al. 2003] [Morelli 2022] [Moum 2010] [Napolitano and Spagnuolo 1993] [Norton 1990a] [Norton 1990b] [Obermark 2004] [Okumoto and Elsanker 1973] [Ortamevzi and Зинченко 2015] [Ozger 2013] [Parameter Estimation Techniques 1974] [Park and Abla 1982] [Quanwei and Qiongkang 1989] [Ramachandran and Wells 1974] [Ramachandran and Wells 1975] [Remund and Kitto 2011] [Roberts 1963] [Rogers 2013] [Rosenberg and Schuch 1983] [Roskam et al. 1981] [Weiss et al. 1994] [Sant’Ana] [Saraswathi 2000] [Schumacher 1952] [Schuringa 1974] [Shao et al. 2026] [Shlien 1991] [Sibilski and Wroblewski 2013] [Sim and Curry 1984] [Simmons et al. 2025] [Simpson 1972] [Simpson 1979] [Smith et al. 1979] [Smith et al. 2003] [Sneshko et al. 2005] [Solies 1992] [Srinathkumar et al. 1995] [Stalford 1981] [Static Longitudinal Stability Flight 2003] [Stottier 1995] [Stouder 1981] [Szymanski et al. 2025] [Talmage and Reeder 1947] [Taylor and Ratnayake 2011] [Taylor et al. 2010] [Tischler 2018b] [Townsend and Phillips 1955] [Townsend and Phillips 1956] [Traven and Whitley 1995] [Triplett et al. 1955] [Uhlig and Selig 2013] [Unstable Aircraft Identification 2006] [Unstable Aircraft Identification 2015] [Wages 1971] [Wang 2024b] [Williams 1959] [Williams et al. 2012] [Wingrove 1972] [Wissler 1981] [Woodman 1971] [Woolf 2012] [Yamakawa et al. 1984] [Yanagihara et al. 1999] [Zeng and Kukreja 2013] [Zhixin 2022] [Özger 2012]
Programme, acquisition and the cost of a demonstrator
Why a programme ends, which is the only part of the MANTA’s story that is documented at all. Acquisition, cost estimation, risk, technology readiness and demonstrator programme management. A small cluster, and the one that would answer the question the article leaves open, which is why funding stopped around 2000.
104 records. [A Comparison of Cost 1977] [Bennett 1990] [Bogdan 2015] [Brown 1981] [Brown 1982] [Brown 2022] [Burris and Bender 1969a] [Camatti et al. 1998] [Carlyle 1976] [Cladi and Locatelli 2023] [Clarke et al. 1982] [Corrigan et al. 1996] [Cronshaw 1986] [DeCAMP and Hardy 1981] [Defense Science Board Washington Dc 1979] [Program Acquisition Costs 1993] [Program Acquisition Costs 1994] [Program Acquisition Costs 1995] [Department of Defense Budget 1996] [Program Acquisition Costs 1998] [Department of Defense Budget 1999] [Program Acquisition Costs 2000] [Design of the Circulation 1979] [Draper et al. 1983] [Elena 2026] [Englar et al. 1981] [Etesse 1979] [Extensive Quality Testing Required 1991] [Fialho et al. 2000] [Flight Test Programme 1970] [Franck et al. 2012] [Freuler and Hoffmann 1977] [Gal-Or] [González and Framinan 2025] [Greer 2010] [Hardy 1983] [Harinarayana] [Harvey and Ryan 2012] [Henley 2020] [Herbst and Ross 1970] [Hicks and Matheny 1987] [Hollenbach 2001] [Holubik 1988] [Integrated Wing Research Programme 2006] [Jategaonkar et al. 2006] [Jianling Wang and Lei Xiang 2015] [Kanayath et al. 2012] [Kenyon 1974] [Kindley 2015] [Kitowski 1986] [Kozlak et al. 2017] [Krivanek et al. 2002] [Krivanek et al. 2003] [Kuang et al. 2017] [Lemmon 2013] [Lemmon 2015] [Loeken 1983] [Lorell 1989] [Loren 2007] [Lu et al. 2016] [Marquiz et al. 2025] [Marx 1983] [Marx et al. 1995] [Massegur Sampietro and Da Ronch 2024] [McCUISH 1994] [McCuish and Caldwell 2018] [Military Airframe Acquisition Costs 2001] [Military Airframe Costs 2001] [Mogfhadam and Farsi 1995] [Moorhouse 1990] [Morawski et al. 2019] [Morley 2013] [Morton 1956] [Norton 2011] [Paku et al. 2016] [Rajeswari and Prabhu 1987] [Reed et al. 1982] [Robinson 2004] [Rosenthal 1982] [Rosenthal and Brandeau 1983] [Rzucidło 2006] [Din et al. 2018] [Shane 1992] [Shawler 1981] [Smith et al. 1987b] [Sodja et al. 2018] [Sodja et al. 2021] [Stahl et al. 1984] [Steiner and Montle 1983] [Suzuki et al. 2013] [Swortzel and Barfield 1976] [The Department of Defense 2014] [The Experimental Aircraft Programme 1987] [Trice 1989] [Urnes and Yeager 1991] [Urnes et al. 1990] [Vincent 1987] [Wang et al. 2021d] [Warsop and Crowther 2019] [Watkins 2019] [Werner and Krenkel 1978] [Williamson 1963] [Wuestenhagen 2022] [Yu et al. 2021b]
High altitude, endurance and mission performance
Where the X-44A derivation sits, and it is among the smaller clusters. Ceiling, endurance, loiter, range and mission performance. A small cluster here is not a gap. The relations the derivation uses are textbook relations that stopped generating journal papers long ago.
98 records. [Aircraft Design 1993] [Aircraft Maneuvers and Flight 2011] [Aircraft et al. 2011] [Aircraft Operating Envelope 2010] [Aircraft Performance 2003] [Aircraft Performance 2010] [Aircraft Performance 2014] [Aircraft Performance 2026] [Aircraft Performance Methods 2010] [Aircraft/Engine System Mission Analysis 2018] [Ashburn et al. 1970] [Atreya et al. 2005] [Bert 1981] [Biber and Tilmann 2004] [Blake 2002] [Braun 1958] [Cestino 2006] [Chadwick 1995] [Chen et al. 2026a] [Colozza 1990] [Conners 1995] [della Noce et al 2021] [Della Vecchia et al. 2017] [Deuschle et al. 2024] [Drake and Solomon 2010] [Engblom 2012] [Escot-Bocanegra et al. 2018] [Fladeland et al. 2019a] [Fladeland et al. 2019b] [Flight Envelope 2021] [Flight Vehicle Performance 2001] [Foch and Ailinger 1992] [Gao et al. 2013b] [Gao et al. 2013c] [Greer et al. 2000] [Hall and Rogan 1988] [Hamilton et al. 2003] [High-Altitude Long-Endurance HALE Sensor 2026] [Irsyad Lukman and Agoes Moelyadi 2018] [Jameson 2011] [Kaloyanova et al. 2005] [Karabacak and Turan 2020] [Kowalski 1988] [Laine 1982] [Level Flight Performance Jet 2003] [Lin et al. 1998] [Marisarla et al. 2003] [Masud and Khan 2015a] [Maughmer and Somers 1989] [Maydew 1980] [McDonnell and Ning 2020] [McDonnell et al. 2018] [Miller 1979] [Muntz 1977] [Nickol et al. 2007a] [Nitardi et al. 2017] [North American Aviation INC LOS Angeles CA 1956] [Nugent and Takahashi 2026] [Patierno and Asdurian 1965] [Patil et al. 1999] [Patil et al. 2001] [Paxton 2021] [Pierson and Ong] [Qi et al. 2018] [Radovcich et al. 1985] [Ravindren et al. 2007] [Rawikara et al. 2023] [Reich et al. 2005] [Reist and Zingg 2013] [Ricciardi et al. 2013] [Sadraey 2023b] [Schmidt 1983a] [Schopferer et al. 2016] [Sharpe et al. 2021] [Skarka and Mateja 2024] [Smith and Riddle 2008] [Snyder et al. 2005] [Steinbuch and Shepshelovich 2004] [Strom and Weathermon 1963] [Thrust and Power 2010] [Vazquez and Rivas 2013] [Very High Altitude Science 2026] [Voss et al. 2026] [Oswald 1932] [Wang et al. 2010a] [Wang et al. 2026b] [Weiser 2025] [Weiser and Ossmann 2022a] [Weiser and Ossmann 2022b] [Weiser et al. 2023b] [Weiser et al. 2023a] [Weiser et al. 2026] [Winchenbach 1997] [Wittenberg 2001] [Young et al. 2005] [Youngblood and Talay 1982] [Yuan et al. 2024] [Zetina et al. 2013]
Stores, missiles, projectiles and finned bodies
The slender-body problem in its most studied modern form. Store carriage and separation, bombs, missile and guided projectile aerodynamics and control, and bodies of revolution at angle of attack, which is the class of body the Allen and Perkins crossflow term was developed for.
98 records. [Aiello and Bateman 1979] [Aircraft Store Separation Motion 1980] [All Things Must End 2006] [Allen and Perkins 1951] [Anderson 1981] [Arrow and Yost 1976] [Bamber 1961] [Blair et al. 1978] [Blake and Barnhart 1990] [Bossi and Nelson 1992] [Britcher 1988] [Bryson 2021] [Bullard 1967] [Carafoli 1969b] [Carroll 1960] [Cebeci et al. 1984] [Cerreta 1957] [Crogan 1961] [Cruise Missile 2009] [Cruise Missiles] [Dahlke and Batiuk 1990] [Damljanovic and Ristic 2005] [Daniels 1970] [Daniels 1973] [Daniels and Clare 1972] [Deep et al. 1971] [DeJarnette and Jones 1978] [Demeritte and Gauzza 1958] [Demeritte et al. 1958] [Deslandes and Seifert 2000] [Donegan and Fox 1991] [Finke 1970] [Fresconi et al. 2014] [Glezer 2009] [Gorski 1998] [Greene 1956] [Hemsch 1985] [Hemsch and Nielsen 1983] [Hemsch and Nielsen 1986] [Hershey and Vibrane 1961] [Hess and James 1975] [Hofmann and Kezer 1962] [Jorgensen 1977] [Jorgensen 1979] [Keith et al. 2004] [Kelly 1953] [Kerney and White 1975] [Knoblach 1974] [Kraft 1994] [Krysenko 1963] [Kubota et al. 1993] [Kunlo 1959] [Land-Attack Cruise Missiles 2008] [Li 1965] [Lieske and Kochenderfer 1966] [Macallister 1957] [Mackay 1960] [Madden 1958] [Mahmoud et al. 2025] [Maynes and Gebert 1999] [Moore 1971] [Moore 1993] [Moore et al. 1999] [Munk 1924] [Nayfeh and Saric 1971] [Nelson and Fleeman 1975] [Newman 1965a] [Nocoń et al. 2022] [Paranjape et al. 1966] [Paulk and Anderson 1976] [Piper and DeMeritte 1960] [Prizirembel and Wen 1978] [Rodden et al. 1962a] [Rom 1992b] [Rubin and Mummolo 1973] [Russak 1973] [Sahu 2005] [Sahu and Fresconi 2019] [Sahu et al. 2019] [Sahu et al. 2020] [Schermerhorn and DeMeritte 1960] [Selected Cruise Missile Programs 2008] [Shandling and Platus 1985] [Silton et al. 2014] [Special Features of Antiaircraft 2010] [Stallings 1979] [Talbot and Ottensoser 1967] [Vinh et al. 1972] [Washington 1975] [Washington et al. 1980] [Werrell 1985] [White 1977a] [White 1977b] [Whitfield and Griffith 1963] [Whoric 1973] [Whoric 1974] [Wood and Murphy 1955] [Zhang et al. 2016a]
Flight mechanics, equations of motion and simulation models
The forms the moment relations are taken from. Equations of motion, linearisation, nonlinear and flexible-aircraft dynamics and simulation models, much of it in textbook chapters. The moment expressions displayed in the section on sizing are the linearised forms this literature derives.
87 records. [Aerodynamics and the Stability 2016] [Aircraft Dynamic Response 2014] [Aircraft Dynamic Stability 2003] [Aircraft Dynamic Stability 2014] [Aircraft Equations of Motion 2003] [Aircraft Mechanics 2026] [Aircraft Model 2025] [Aircraft Non-Linear Dynamics 2014] [Aircraft Response Transfer Functions 1997] [Aircraft Response Transfer Functions 2013] [Aircraft Simulation Model 2022] [Aircraft Stability & Control 2022] [Aircraft Stability and Control 2026] [Aircraft Static Stability 2003] [Aircraft Static Stability 2014] [Appendix 1997] [Appendix 2011] [Appendix B 2011] [Appendix C 2003] [Appendix D 2013] [Appendix H 2003] [Ashokkumar 2023a] [Bacon and Gregory 2007] [Basilio Chaves] [Butler 1976a] [Calico and Noll 1986] [Кордянин 1999] [Chapter 3. Dynamics 2005] [Chemaly and Weisshaar 1998] [Chen 2010] [Chen and Barlow 1992] [Chen et al. 2008] [Cochran 2015] [Complete model of aircraft] [Cook 2000] [Crespo and Kenny 2006] [Crowe 1937] [Curtiss 1969] [Dynamic Longitudinal Stability Theory 2003] [Dynamics of Aircraft Motion 2015] [Dynamics of Flexible Aircraft 2023a] [Dynamics of Flexible Aircraft 2023b] [Dynamics of Very Flexible 2023] [Figat and Kwiek 2023] [Flight Dynamics of Elastic 2014] [Flight dynamics � Vocabulary] [Franklin et al. 2022] [Garza and Morelli 2003] [Frost and Bowles 1984a] [Introduction to Aircraft Flight 1998] [Introduction to Flight Vehicles 2014] [Leylek et al. 2012] [Liu 2026] [Louis 2022] [Marino 2001] [McIntyre 1963] [Mukherjee and Sinha 2016] [Newman and Swaim 1986] [Nominal aircraft dynamics] [Northrop Aircraft INC Hawthorne CA 1953] [Palacios and Cesnik 2023] [Pinsky and Essary 1994] [Pizzo 1988] [Planeaux 1990] [Pradeep 1998] [Properties of Classical 2012] [Rigid-Body Flight Dynamics 2026] [Rumsey et al. 1972] [Schwanz 1972] [Silvestre and Paglione 2008] [Skoog 1951] [Stability Characteristics of Selected 2014] [Static Longitudinal Stability Theory 2003] [Staufenbiel 1978] [Streby 1990] [Tarasenko 2011] [Templin et al] [Thelander 1965] [Thompson et al. 2010] [Tischler and Tobias 2016] [Vepa 2023f] [Vepa 2023c] [Vepa 2023a] [Vepa 2023g] [Vepa 2023h] [Wright 1962] [Youssef et al. 1989]
Research aircraft, fighter development and aeronautical history
The setting of both vehicles. Named research and experimental aircraft, fighter development histories, designation, and the next-generation and sixth-generation fighter studies. None of its titles names the MANTA or the X-44, as the Source Base records for the survey as a whole.
76 records. [A New Fighter Aircraft 2003] [A New Fighter Aircraft 2015] [Air Force Flight Test Center Edwards AFB CA 1970] [Armstrong 1977] [Beisbier 2002] [Beskar 2004] [Bevilaqua 2009] [Brauckmann 1998] [Buckner et al. 1974] [Byrnes 1972] [Cate 2003] [CHAPTER FOUR The Makings] [Charles and Sinnewe 2015] [Cordeaux 1991] [Dutta et al. 2025] [El-Sayed 2024b] [Elhefnawy 2018] [Elhefnawy 2021] [Enzinger 1988] [Experience Gained during Development 2010] [Fenwick 1966] [Fenwick 1967] [Fighter Planes 2000] [Flight Test Results 1977] [Foss 1978] [Greaney 2010] [Griffin 2012] [Haas and Silberg 2011] [Hankins 2021] [Herbst 1980] [Hirschberg 1997] [Hirsh 1965] [Historic Review 2010] [Hockley and Appleton] [Irvine 1968] [Ivarsson 2003] [Jones 2014a] [Jones 2014b] [Jordan 1974] [Karp 1986] [Lynch 1972] [Marchese 1963] [McPherson 1977] [Merrill and Hall 1982] [Military Aircraft and Engine 2021] [Miller 1973] [Modin and Clareus 1991] [Navy Participation 1998] [NCC Project to Improve 2021] [New System of Designating 1963] [Nicholson 1985] [Norton 1965] [Painter and Erickson 1984] [Phillips 1998] [Pittsburgh Univ Washington DC Research Staff 1966] [Rhodes 1969] [Rice 1946] [Rich 1973] [Rich 1974] [Riddle et al. 1981] [Roberts et al. 1967] [Schaufele 1965] [Silverman 1978] [Spearman 1984] [Spitzer 1972] [St. Aubyn 2015] [The Cutting Edge 1998] [The Makings of a] [The Swept 2021] [Transfer of German High-Speed 2010] [US Combat Aircraft Will 2022] [Ward 1989] [Weeks 1986] [Whitford 1995] [Yamato et al. 1988] [Yamato et al. 1991]
Survivability and vulnerability of military aircraft
The discipline that weighs a signature against everything else. Survivability design and assessment of combat aircraft, susceptibility and vulnerability. Signature reduction is one term of survivability, which is why the premise the article takes from the low observable cluster is a trade rather than an absolute.
59 records. [Airborne Hydraulic and Control] [Aker and Alukonis 1976] [Andryushkin et al. 2026] [Appendix 1985] [Appendix 2003] [Arnold 1969] [Atkinson et al. 1969] [Avery et al. 1971] [Ball 1985] [Ball 2003] [Ball and Atkinson 1995] [Ball and Atkinson 1998] [Berger 1984] [Boily and Harrison 2012] [Boșcoianu et al. 2013] [Caravasos 1991] [Chiu et al. 2013] [Connelly 1981] [Cooper 1969] [Cully and Boller 1973] [Deas 2012] [Dotseth 1970] [Engelhardt 1993] [Esparza 1979] [Fedukhin and Mukha 2025] [Geyer et al. 2015] [Graham and Clement 1976] [Greene and Hevert 1973] [Grover] [Grover 1989b] [Heilenday 2000] [Hinrichsen and Moshier 2003] [Hydraulic system survivability for] [Introduction to the Aircraft 1985] [Introduction to the Aircraft 2003] [Kashiwagi 1979] [Kaye et al. 2014] [Knezek and Garner 1987] [Konokman et al. 2014] [Lee 2002] [Lunsford and Bradley 2020] [Mangel and Samaniego 1984a] [Mangel and Samaniego 1984b] [Mavridis et al. 2026] [McCarthy et al. 2013] [McDougal et al. 1987] [Naushad and Srikanth 2017] [Nesterenko 1996] [Nesterenko 2011] [Niksch 1987] [Pei et al. 2014] [Smith et al. 1978] [Vice 1986] [Vice 1987] [Wang et al. 2009a] [Weisenabch et al. 2005] [Weisenbach 2003] [Weisenbach 2004] [Weisenbach 2009]
Engine failure, asymmetric thrust and minimum control speed
The second of the two identities the article derives. Minimum control speed is the regulatory form of exactly the calculation this article performs, being the speed below which a fin can no longer hold an engine failure, and it is the quantity the tangent relation makes speed-independent for a thrust-vectored aeroplane.
51 records. [Yass et al. 2009] [Adams and Manion 2011] [Air Force Test Pilot School Edwards Afb Ca 1992b] [Beamer] [Bolds-Moorehead et al. 2015] [Brinkman and Visser 2007] [Burova 2025] [Burova et al. 2025] [Casadei et al. 2019] [Chengtao et al. 2011] [Choi et al. 1997] [Deberg et al. 1976] [Di Donato and Atkins 2015] [Engine Failure in Light 1980] [Ferrer-Vidal and Pachidis 2021] [Finger et al. 2019] [Frank and Rempe 2026] [Garzon Galindo et al. 2023] [Han et al. 2014] [Harish et al. 2018] [Hoogreef and Soikkeli 2022] [Hutchinson 2019] [Kang et al. 2023] [Koolstra et al. 2019] [Li et al. 2025b] [Lian et al. 2024] [MCMillan and Preston 1966] [Mikhailov 2022] [Mokotoff and Cinar 2026] [Mourning and Ghauri 2025] [Novichkov and Burova 2019] [Perhinschi and Beamer 2011] [Sabadas et al. 2024] [Schroijen and Slingerland 2007] [Seo and Kim 2019] [Stojakovic and Rasuo 2016] [Sánchez-Moreno et al. 2024] [van der Maas 1959] [Wagner and Webb 2000] [Wandini et al. 2016] [Wu] [Wu 2026] [Wu and Mora-Camino 2012] [Wu et al. 2024c] [Xie et al. 2023b] [Xie et al. 2026b] [Xu and Liu 2011] [Xu and Zhang 2025] [Yahyaoui 2016] [Yu 2025b] [Zhang et al. 2024b]
Where the Framing Breaks Down
Five places, and only the first of them is quantified here.
The ratio treats jet velocity as constant across the envelope, which it is not. Relaxing that assumption moves the answer in the article’s favour. Carrying the jet velocity relation through the ratio gives
\[\mathcal{R}(M) \propto \frac{\eta_{r}(M) \left( 1 + 0.2 M^{2} \right)^{3} V_{j}(M)}{M^{2}} \tag{59}\]and at an overall engine pressure ratio of eight the jet velocity rises by 25.7 percent from the approach to Mach 2.25, which is far from constant.
| minimising Mach | demonstrated point above the worst case | |
|---|---|---|
| constant jet velocity | 1.674 | 1.135 |
| varying jet velocity | 1.550 | 1.078 |
The minimum moves forward and gets shallower, so the demonstrated point stands 7.8 percent above the worst supersonic condition rather than 13.5. The conclusion drawn from the pessimistic assumption survives the correction and improves. The result is also robust to the one engine parameter it introduces. Across overall pressure ratios from four to twenty the minimising Mach moves only from 1.502 to 1.589 and the penalty from 5.9 to 9.5 percent.
What the correction does change is the top of the envelope. Under the constant assumption Mach 2.0 and Mach 2.25 were harder than the demonstrated point. With the jet velocity varying they are easier, at 1.006 and 1.103 times, so the high supersonic end stops being a concern. The minimum’s existence never depended on the assumption, because it comes from the mass flow term, and only its location and depth did.
A second approximation remains unquantified and runs the other way. The relation above assumes the afterburner is lit, and a dry-thrust case has a lower total temperature and a lower jet velocity, which would make those conditions less favourable than any table here. This article does not compute the dry case, and the envelope should not be read as covered.
The engine-out identity assumes the vectoring is available on the live engine at full deflection. A nozzle that has failed for the same reason the engine has failed provides nothing, and a common-cause failure of an engine and its nozzle is a case a fin covers and a nozzle does not. The argument belongs to reliability engineering, outside aerodynamics, and no quantitative form of it is attempted.
Treating the two vehicles in one article follows from the designation, and engineering supplies no reason for it. They share a contractor, a decade and a number. They share no requirement, no size class, no speed range and no mission. A reader interested in either aeroplane is being handed a good deal of material about a different one, justified because the collision is the subject.
The crosswind case assumes the aeroplane must land in a crosswind on a runway. A vehicle that lands into wind on a long runway at a test range faces a much weaker requirement than an operational fighter does, and the MANTA as an X-plane would have been the former. The impossibility derived above is a statement about the operational aeroplane the MANTA was a step toward, not necessarily about the demonstrator, and the distinction holds even though every published description of the MANTA frames it as a step toward a fighter.
The Source Base
The argument in this article rests on nine documents and the rest of the reference list is a map of the surrounding literature.
Two carry the flight result. The X-31 quasi-tailless demonstration description [Huber and Schellenger 1994] and the flight test results report [Bosworth and Stoliker 1996] supply the flight condition, the technique, the manoeuvres and the conclusion. Everything this article says about what has actually been demonstrated comes from these two.
One carries the nozzle. The measurement of multiaxis control power from a two-dimensional convergent-divergent nozzle with sidewall yaw flaps across Mach 0.20 to 2.47 [Capone and Bare 1987] is the evidence that the hardware the MANTA needed can be built and characterised.
One carries the alternative. The study of differential canard deflection as a yaw generator on the X-31 with and without its vertical tail [Whiting 1996] establishes that an aerodynamic yaw effector of comparable authority to the vectoring vanes was studied on the same aeroplane, which is what makes the low-speed conclusion above a design choice rather than a dead end.
Five carry the vehicles themselves and none of them is a primary document. The MANTA and unmanned X-44A encyclopaedia entries [Lockheed Martin X-44 MANTA] [Lockheed Martin X-44, the unmanned vehicle], the journalism that broke the story [Lockheed Skunk Works X-44A flying-wing drone revealed] [Skunk Works reveals the missing link in a secret unmanned history], and the museum fact sheet [Lockheed Martin X-44A, National Museum of the United States Air Force] are the core of the public record on these two aircraft, which the 2003 NASA inventory of X-vehicles [Jenkins, Landis and Miller, American X-Vehicles, An Inventory X-1 to X-50, NASA SP-2003-4531, 2003] and two secondary compilations [X-44 MANTA Multi-Axis No-Tail Aircraft, GlobalSecurity] [Lockheed Martin X-44 MANTA tailless technology demonstrator proposal] supplement. That is a thin foundation and the article is built to survive it, which is why the analysis of the MANTA rests on the F-22’s published numbers and the X-31’s published flight results, and why the one X-44A result is stated as a bound on the museum’s figures.
Two sources are used with a stated reservation. The two National Museum of the United States Air Force pages return a Hypertext Transfer Protocol status of 403 to automated requests, which is bot mitigation and not absence. Both were read through copies held by the Internet Archive, since neither could be read directly from the museum’s own site.
The research survey holds 9,631 records, of which 9,182 resolve through Crossref digital object identifiers and 449 through NASA’s Technical Reports Server. The median publication year is 2005. Of the 9,429 dated records, 706 were published before 1970, being 7.5 percent, and 3,128 in 2015 or later, being 33.5 percent.
Counting a displayed relation as cited when the paragraph next before or after it carries a citation, 45 of the article’s 59 displayed relations carry none. That gap remains open.
The Definition of Primary
Primacy is a property of the document, and this survey derives it from the identifier. A record is primary when it comes from NASA’s Technical Reports Server or carries a Defense Technical Information Center, American Institute of Aeronautics and Astronautics, SAE International or Office of Scientific and Technical Information identifier, and it is a report primary when it is a NASA or Defense Technical Information Center record. By that rule 5,625 of the 9,631 research records are primary, being 58.4 percent, and 1,317 are report primaries, being 13.7 percent. That second figure matters most, because the relations this article displays were established in report series that a search of journals and conferences cannot see at all.
Eleven foundational primaries carry relations this article displays, and a search returning something adjacent would be worse than useless for any of them. They are Munk on the aerodynamic forces on airship hulls, Multhopp on the aerodynamics of the fuselage, Allen and Perkins on viscous flow over slender inclined bodies, Oswald on the calculation of airplane performance, the U.S. Standard Atmosphere, Gilruth on requirements for satisfactory flying qualities, Campbell and McKinney and Toll and Queijo and Jones and Alksne on lateral derivative estimation, and two in-flight evaluations of pure control system time delays. Every one is cited in the prose beside the relation it establishes rather than only in the reference list.
Thin Subjects
The subjects the derivations rest on are well covered when asked for in the field’s own vocabulary, which speaks of directional stability and control, the vertical tail, the empennage and lateral-directional characteristics rather than of tail sizing. Counting the research titles that match a fixed pattern for each subject, and counting as a report primary a record from NASA’s Technical Reports Server or the Defense Technical Information Center, vertical tail sizing and the directional requirement returns 218 records with 35 report primaries, the slender-body fuselage contribution 252, the drag polar and span efficiency 51, and loop bandwidth with transport delay 38.
Four subjects that this article’s derivations depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms.
| Subject | Title terms counted | Records |
|---|---|---|
| the standard atmosphere | standard atmosphere, atmospheric model, density, pressure, temperature or properties, tropopause, altitude variation or effect on density or pressure | 2 |
| wing internal volume and fuel | fuel volume, tank, capacity, fraction, system or load, internal volume, wing volume, tankage or thickness, volumetric, thickness ratio | 3 |
| thrust lapse and the corrected-flow model | corrected flow, mass, airflow, parameter, speed or weight flow, thrust lapse, lapse rate, thrust variation or change with altitude, Mach or speed, engine performance at altitude | 2 |
| quasi-tailless technique and in-flight simulation | quasi tailless, in-flight simulation, variable stability, simulated tail or instability, tail off simulation, airborne simulator | 21 |
Each is thin for one of the three recognised reasons. The standard atmosphere returns two records, both of them the standard tables themselves, because it is so settled that it stopped generating papers and became a standards document instead, which is cited as one. Wing internal volume returns three records and none of them concerns how much volume a wing encloses, two being composite structures that carry a fuel tank and the other the aerodynamics of wing thickness, because that relation lives in design textbooks and not in the report literature, and it is cited to books accordingly. Thrust lapse and the corrected-flow model return two records, both on matching engine and aircraft lapse rates for a high-speed civil transport, for the same reason, and the article takes that model from propulsion texts and calibrates the lapse exponent itself. Quasi-tailless technique and in-flight simulation returns twenty-one records with eleven report primaries, and it is small because the field is small, one aeroplane having flown the experiment inside a variable-stability tradition that is itself narrow. Naming which kind each one is matters more than the counts, because none of the four is a gap that searching could close.
The subject of this article’s framing cannot be surveyed by bibliographic search at all. The survey holds no cluster on designation practice, because designation, classification, records, identifier and secrecy are among the least discriminating words in any literature, and the nine research titles in it that carry designation or nomenclature use those words for propulsion station numbering, aerodynamic and aircraft nomenclature, aerofoil series and a company project number. No title in the survey names the X-44 or the MANTA. That is a fourth kind of thin beyond the three the series recognises, and the real sources for the subject are the designation registries themselves, which this article cites in the Reference category and quotes in the section on the two referents.
What the Survey Admits
A record is admitted only when a person reading its title finds it on this article’s subject. The subject is directional stability and control and the vertical tail, tailless and flying-wing aircraft, thrust vectoring, exhaust nozzles, engine cycle and inlet performance, delta and swept wing, supersonic and slender-body aerodynamics, flight control, handling qualities, approach and landing, low observability and survivability, aircraft design and performance, unmanned aircraft as aircraft and as military systems, airframe structure and manufacture, wind tunnel and flight test and air data, the atmosphere as the flight condition, engine failure, and aircraft programmes and their history. Every record is filed under a named literature, and the survey has no residual cluster.
Many words this subject depends on also name something else, and a record that shares only such a word or a distant application is excluded. Yaw, roll, rudder and autopilot also belong to ship steering, yaw, sideslip and torque vectoring to road vehicle dynamics, crosswind and the wind tunnel to civil wind engineering and railway aerodynamics, and wing, flight, lift and drag to the flight of insects, birds and bats. Nozzle also names the cavitating nozzles of hydraulics and the process nozzles of steam, refrigerants and powder atomisation, the pilot stage of a hydraulic valve is not a person, the blended wing body is an underwater vehicle configuration in the identical phrase, and aerofoils are also wind turbine blades. Unmanned vehicles also run on the ground and on the sea surface and serve agriculture, mapping and inspection, fighter also names the fire fighter, reconnaissance also has its ground military senses, radar cross section is also measured on ships, and spacecraft trajectories and drag reduction in water have literatures of their own. Aeronautical subjects that the argument does not use are excluded as well, among them icing, aircraft noise and the sonic boom, rotorcraft, airline and airport operations, air traffic management, aircraft subsystems and maintenance, flutter, and the combustion, cooling and materials of gas turbines.
Records that are not works are excluded as well. Crossref registers peer reviews as records whose titles read as a review of a named paper and supplementary files as components sharing an identifier stem with their parent, and military part specifications carry titles that are noun phrases inverted for filing. Corrections, errata, retractions, withdrawals, figures, supplementary material, peer-review reports, front matter, whole conference volumes that state no subject, and standards for parts, materials, test methods and documentation are parts of works, editorial events or specifications rather than works. Reviews of books, dictionary and other reference entries of two pages or fewer, news and other notices, and a second deposit of a document already in the survey are not admitted either, while an authored encyclopedia article of more than two pages and a textbook chapter are research works and stay. None of these makes a claim, so none is counted.
Some records of doubtful relevance are kept, among them rocket, missile and spacecraft thrust vector control, the radar and infrared signature of rotorcraft, the directional stability of birds and the yaw control of flapping flyers, which need no vertical tail, aircraft designed for Mars, gust load alleviation, and control theory that names time delay, actuator saturation or control allocation without naming an aircraft. Each shares a mechanism, a configuration question or a relation with this subject, and a reader may weigh it accordingly.
Every research title has been read for relevance, so the off-topic share that remains is a matter of reading judgement.
Epistemic State
Historical Fact
The X-44 MANTA was a Lockheed Martin design study of a tailless F-22 derivative controlled by three-axis thrust vectoring. Preliminary work was under way by May 1999 and the National Aeronautics and Space Administration approved a programme start in June 1999. No aircraft was built.
The X-44A unmanned aircraft was built by Lockheed Martin Skunk Works in 1999 and first flew in 2001. It has a span of about 30 feet, is powered by a Williams F112, was first reported in February 2018 and was publicly unveiled in March 2018. It has been displayed at the National Museum of the United States Air Force since October 2020.
The X-31 flew a quasi-tailless flight demonstration beginning in March 1994, at Mach 1.2 and 37,500 feet with a simulated one hundred percent vertical tail reduction, and its report concludes that tailless and reduced-tail fighters are feasible when the capability is designed in from the start.
The F-22’s F119 nozzles vector in pitch only, through plus or minus twenty degrees.
The DarkStar was terminated in January 1999 and the Polecat first flew in 2005.
Verified by Independent Derivation
The identity $q = 0.7 p M^{2}$ agrees with the density form at every flight condition used, to one part in a million or better.
The cancellation of static pressure from the authority ratio holds numerically at five altitudes above the tropopause, to one part in ten to the twelfth, and the closed form agrees exactly with the full atmosphere model at three further altitudes.
The minimum of the ideal Mach function at $M = \sqrt{5/2}$ and its value of exactly 1.35 are recovered by bisection on a numerically differenced derivative, to six decimal places, independently of the algebra that produced them.
The maximum of the crosswind function at exactly Mach one is recovered by golden-section search to six decimal places, and the altitude independence holds at five altitudes to four parts in ten thousand, the residue being the small-angle approximation to the arctangent.
The engine-out relation $\tan \delta = y/\ell$ is recovered by solving the moment balance numerically without cancelling the thrust, at four thrusts spanning three orders of magnitude, agreeing to one part in a billion.
The two expressions for the best lift to drag ratio agree to machine precision. This tests transcription, since at the best ratio the induced drag equals the zero-lift drag exactly and the two forms are the same statement.
The demand-over-availability ratio was derived a second time from the propulsive tail volume by a route that shares nothing with the first, and reproduces the throttle factor of 5.33 to three significant figures.
The remaining derived values can be recomputed from the relations shown, among them the rudder baseline, the crosswind maximum, the small-angle error and its variation, the gearing, the loop budget, the slender-body inversion, the quasi-tailless gearing, the drag polar and the varying jet velocity.
Analysis
The ratio of thrust-vectored yaw authority to aerodynamic yaw demand is independent of pressure altitude and, above the tropopause, a function of Mach number alone. This follows from static pressure entering the engine mass flow and the dynamic pressure to the same power.
That function has a minimum at Mach 1.581 with ideal recovery and Mach 1.674 with a military specification inlet recovery model. The X-31’s demonstrated point at Mach 1.2 stands 1.135 times above the second, and no point from Mach 1.2 to Mach 2.25 is more than twelve percent harder than what was flown.
For a crosswind of fixed speed, the required vector angle depends on Mach number alone and peaks at exactly Mach one. Pressure and temperature both cancel.
Restoring the demonstrated margin on a sea-level approach at 150 knots in a 15 metre per second crosswind requires 38.4 percent throttle against the 7.2 percent the glide slope needs at an assumed landing ratio of six, a factor of 5.33, or against 12.4 percent at the ratio of about four measured on a straight-wing fighter, a factor of 3.09. The implied lift to drag ratio in level flight at that thrust is between 1.6 and 1.9, below the lowest effective ratio of 2.7 flown in the low lift to drag landing research.
The directional divergence of a tailless F-22 has a time to double between 0.16 and 0.91 seconds across a wide bracket of the two unpublished quantities it depends on, and the entire supersonic column of that bracket is below four tenths of a second.
A thrust lapse exponent of 0.960 in density ratio reproduces the DarkStar’s published ceiling, weight and thrust on an assumed 42 square metre wing, an Oswald efficiency of 0.85 and a zero-lift drag coefficient of 0.015.
Primary sources stand at 5,625 of 9,631 research records, or 58.4 percent, and report primaries alone at 1,317 or 13.7 percent. Records from 2015 or later number 3,128, or 33.5 percent of those dated, and 705 records predate 1970.
Relaxing the constant jet velocity assumption moves the minimising Mach from 1.674 to 1.550 and cuts the demonstrated point’s penalty from 13.5 percent to 7.8, so the conclusion drawn under the pessimistic assumption survives its own correction and improves. Across engine pressure ratios from four to twenty the minimising Mach moves only from 1.502 to 1.589.
Expressed as a propulsive tail volume, the vectoring supplies 0.0181 at the demonstration point against about 0.0412 for thirty degrees of a conventional rudder, or 44 percent, and 5.19 times as much at maximum thrust on approach. The same quantity collapses to 0.0154 at glide-slope thrust, which is the throttle result arrived at from the other direction.
The stabilisation loop must close within 60 to 90 milliseconds supersonically and 145 to 218 on approach, from a crossover of two to three times the unstable pole and thirty degrees of phase margin budgeted to transport delay.
Inverting the slender-body yawing moment for the fuselage volume that the assumed derivative implies gives 33.8 cubic metres, a mean cross-section of 1.79 square metres over the F-22’s length. No fuselage volume is published to compare with, and the two engine envelopes alone account for about a third of that volume, so the instability bracket is reported as a bracket and not as a conservative bound.
Inference
The MANTA required a nozzle capability the F-22 does not have, since a two-dimensional convergent-divergent nozzle deflects only in the plane of its flaps. This is inferred from the published nozzle description, and one MANTA account states the requirement directly in giving the aircraft pitch and yaw vectoring nozzles [X-44 MANTA Multi-Axis No-Tail Aircraft, GlobalSecurity].
Pure thrust vectoring cannot meet an operational crosswind landing requirement, so a tailless fighter needs an aerodynamic yaw effector that works at low speed. The throttle calculation supports this inference, which is consistent with the X-36’s split ailerons and with the X-31 differential canard study, neither of which is offered as confirmation.
The X-44A’s wing loading is at most about twice the DarkStar’s, and below it if the aircraft cruised above about 23,000 feet, an inference from the museum’s speeds and an assumed drag polar and aspect ratio common to both. A cruise at a reconnaissance ceiling would need about twice the published maximum speed.
The X-44A’s published maximum speed is not a thrust limit on a clean polar, since the engine makes about five times the clean drag at the bound, so either the drag was several times higher or another limit set the maximum.
The X-44A was a short-range configuration and manufacturing demonstrator and not an endurance aircraft. The published endurance and range indicate it, and the stated programme objectives agree.
The stabilisation loop should be machinery rather than a pilot, inferred from the delay budget and the phase margin it reserves. The divergence rate alone is within what practised subjects held in single-axis tracking.
The difficulty in sensing sideslip is dynamic. Writing the relation down gives a gearing near unity and a cost of 2.9 percent of available authority for a half-degree measurement error, which is not a hard requirement. What binds is lag and noise at a crossover of six to nine radians per second.
What the Record Does Not Settle
Whether the designation X-44A was ever officially assigned to either vehicle, and if to one, to which. Both are recorded under it in the general reference literature. The specialist designation registry carries no page for the number at all. No allocation document has been published.
Whether the two programmes had any relationship. The journalism that revealed the unmanned aircraft states that it is unclear how it came to carry the designation and that there appears to be no direct relation. An absence of known relation is not a known absence of relation.
When the MANTA was cancelled. The sources place the end of funding in 2000 or around that year, a 2003 NASA inventory still describes a feasibility study in progress, and none cites a programme document.
Everything about the X-44A’s flight programme beyond the year of first flight and the museum’s summary figures. Number of flights, duration, envelope, instrumentation, results, and whether the aircraft in the museum is the only one built.
Every specification of the MANTA. Wing area, sweep, weights, required vector angles, control law architecture and the intended sideslip sensing. One reference site lists weights and performance for the MANTA without citing a source [Lockheed Martin X-44 MANTA tailless technology demonstrator proposal].
Whether the MANTA influenced any later programme. No source cited here documents a connection to any later programme, and the sixth-generation fighter studies in the survey do not name it.
The DarkStar’s wing area, which this article assumes because no source used publishes it, and on which the thrust lapse calibration and every number in the X-44A table depend, and the X-44A’s aspect ratio, which this article takes from the DarkStar’s.
On Sources Used With Reservation
The two National Museum of the United States Air Force pages refuse automated requests, for the reason given in the Source Base, and both were read through copies held by the Internet Archive.
The general encyclopaedia is the source for the MANTA’s origin dates, its designation and its F-22 derivation, and one journalistic account reports the X-44A’s nano-carbon fibre skin, which a second describes as an all carbon fibre airframe. No primary document for any of those claims has been located, and the X-44A’s engine, performance figures and museum placement rest on the museum fact sheet. The X-44A bound rests on the museum’s performance figures, and none of the article’s other results depends on these sources.
Three secondary aviation outlets are cited for the X-44A’s revelation and description [Lockheed Skunk Works X-44A flying-wing drone revealed] [Skunk Works reveals the missing link in a secret unmanned history] [Skunk Works reveals stealthy UAV demonstrator]. Beside the museum they are the only sources that have published on the aircraft in any detail, they are consistent with each other, and one of them states plainly what it does not know, which is a reason to trust it more.
On Information Postdating the Editorial Date
This article carries an editorial date of 19 November 2025 and is written from knowledge current at the time of writing, which includes the 2018 revelation and 2020 museum placement of the X-44A and the accounts published after them. Later accounts are described as accounts and not as record.
Out of Scope
Fluidic thrust vectoring, which replaces mechanical deflection with a secondary injected flow and changes the weight and signature arguments without changing the momentum balance used above.
The radar cross section calculation itself. The argument takes as given that a vertical tail is a large contributor and does not compute it.
The X-45, X-46 and X-47 unmanned combat air vehicle programmes, which are the next articles in this series and which share the tailless configuration question with the X-44A while answering an entirely different requirement.
Engine-out reliability and the common-cause failure of an engine with its nozzle, named in the framing section as a case a fin covers and a nozzle does not.
The manufacturing claim in any quantitative form, since no mass, lay-up, tooling or cycle-time figure is available.
The F-22’s flight control system, a large subject that bears on this one only through the nozzle.
Conclusion
The X-44 is one number attached to two aeroplanes that share a contractor and nothing else, and the register does not record the collision.
The aeroplane that never existed asked a question that had already been answered. The X-31 flew a fully simulated tailless configuration at Mach 1.2 and 37,500 feet in 1994 and concluded that the configuration is feasible. This article adds a measure of how much of the envelope that one point covered. The answer needs no vehicle data. The static pressure cancels from the governing ratio, above the tropopause the ratio depends only on Mach number, the ratio has a minimum at Mach 1.674 with a realistic inlet, and the demonstrated point stands thirteen and a half percent above the worst case. One supersonic point very nearly covered the supersonic envelope.
The concept fails at the runway instead. For a crosswind of fixed speed both pressure and temperature cancel and the demand peaks at exactly Mach one, so at equal throttle the approach is the easiest case in the envelope. The throttle is not equal. Restoring the demonstrated margin on approach needs three to five times the thrust the glide slope needs, and absorbing that thrust in level flight implies a lift to drag ratio below two. A tailless fighter therefore needs an aerodynamic yaw effector at low speed that it does not need supersonically, the architecture the X-36 flew and the MANTA proposed to delete.
The engine-out case, which is one of the two reasons fins are large, does not size a thrust-vectored aeroplane at all, because the vector angle that trims it satisfies $\tan \delta = y/\ell$ and the thrust cancels identically. Two classic fin-sizing cases, opposite answers, and reasoning from the fin would have got both wrong.
The aeroplane that did exist was built in the year its predecessor was cancelled and flew two years later, and almost nothing about it has been released. The museum’s figures, a maximum of 176 miles per hour, an hour and a half and 230 miles, describe a short-range demonstrator, and a cruise at a reconnaissance ceiling would have needed about twice that speed. They bound its wing loading at no more than about twice the DarkStar’s, and below the DarkStar’s if it cruised above about 23,000 feet, so the wing loading cannot say what the aircraft was for. The endurance can, and it agrees with the programme’s stated purpose of demonstrating a configuration and a factory.
The last observation concerns the designation instead of either aeroplane. The X-planes sequence is a finite resource issued once and never replenished, and a number spent twice is still a number spent once. The register carries no record of the ambiguity, the specialist directory carries no page for the number, and the encyclopaedia has resolved the collision by writing two articles and noting that they appear to be unrelated. The cost of the confusion falls entirely on whoever reads the record later, which in this instance is this article.
Equations
This section collects the 59 display equations of the article in the order they appear, each under its number and reproduced exactly as it stands in the text. A title in bold names an established result, and a title in italics beginning with the word Bespoke names a construction made for this analysis. Of the 59, 32 are established and 27 are bespoke. Thrust and weight are quoted in pounds, kilonewtons and kilograms while the derivation runs in the International System with angles in radians and tables in degrees, and several letters are reused, so $N$ is a yawing moment except in the register count, where it is the highest number issued, $\sigma$ is a radar cross section and then the density ratio, $\lambda$ is a radar wavelength and then the divergence rate, $\tau$ is the rudder effectiveness and then a transport delay, $\gamma$ is the ratio of specific heats and then the glide path angle, $T$ is a temperature and then a thrust, $n$ is the thrust lapse exponent and then the load factor, and $\delta$ is a nozzle deflection while $\delta_{2}$ is a total pressure ratio.
Equation 1, Yawing Moment from Sideslip and the Directional Stability Condition. The aerodynamic yawing moment is linear in sideslip through the directional stability derivative, and the aeroplane is statically stable in yaw only when that derivative is positive. Gilruth 1943
\[N = q S b \, C_{n\beta} \, \beta \qquad \text{stable} \iff C_{n\beta} > 0 \tag{1}\]Equation 2, Vertical Tail Volume Coefficient. The tail volume coefficient is the fin area times its moment arm divided by the wing area times the span. Raymer, Aircraft design, a conceptual approach Torenbeek, Synthesis of subsonic airplane design
\[V_{v} = \frac{S_{v} \, l_{v}}{S \, b} \tag{2}\]Equation 3, Rudder Control Derivative from Tail Volume. The rudder control derivative is the tail volume coefficient multiplied by the fin lift-curve slope, the rudder effectiveness and the dynamic pressure ratio at the tail. Campbell and McKinney 1951 Toll and Queijo 1948 Jones and Alksne 1951
\[C_{n \delta_{r}} = - V_{v} \, a_{v} \, \tau \, \eta_{v} \tag{3}\]Equation 4, Radar Cross Section of a Flat Plate. A flat plate viewed at normal incidence returns a cross section proportional to the square of its area divided by the square of the wavelength. Knott, Shaeffer and Tuley, Radar cross section
\[\sigma_{\text{plate}} = \frac{4 \pi A^{2}}{\lambda^{2}} \tag{4}\]Equation 5, Radar Cross Section of a Right-Angle Dihedral. Two plates meeting at a right angle return a cross section set by the product of the squares of their dimensions over a wide range of aspect angles. Knott, Shaeffer and Tuley, Radar cross section
\[\sigma_{\text{dihedral}} = \frac{8 \pi a^{2} b^{2}}{\lambda^{2}} \tag{5}\]Equation 6, Bespoke Count of Vehicles a Finite Register Can Name. The article counts the vehicles a consecutive register can name as the highest number issued less the numbers reserved and never used plus the numbers issued more than once. X-39
\[V = N - r + c \tag{6}\]Equation 7, Required Aerodynamic Yawing Moment. The yawing moment that must be produced is the dynamic pressure times wing area and span times the magnitude of the directional stability derivative times the sideslip.
\[N_{\text{req}} = q S b \left| C_{n\beta} \right| \beta \tag{7}\]Equation 8, Yawing Moment Available from a Deflected Jet. A jet of gross thrust deflected through an angle at a distance aft of the centre of gravity produces a yawing moment equal to the thrust times that arm times the sine of the deflection.
\[N_{\text{av}} = F_{g} \ell \sin \delta \tag{8}\]Equation 9, Bespoke Ratio of Available to Required Yawing Moment. The article defines its figure of merit as the vectored moment available divided by the aerodynamic moment required at a given sideslip.
\[\mathcal{R} \equiv \frac{N_{\text{av}}}{N_{\text{req}}} = \frac{F_{g} \ell \sin \delta}{q S b \left| C_{n\beta} \right| \beta} \tag{9}\]Equation 10, Bespoke Propulsive Tail Volume. The article defines a propulsive tail volume as the maximum vectored moment divided by the dynamic pressure, wing area and span, so that it can be compared with a rudder control derivative.
\[V_{p} \equiv \frac{F_{g} \, \ell \, \sin \delta_{\max}}{q \, S \, b} \tag{10}\]Equation 11, Required Jet Deflection. Equating the vectored and the required moments gives the sine of the jet deflection a control system must command.
\[\sin \delta = \frac{q \, S \, b \, \left| C_{n\beta} \right| \beta}{F_{g} \, \ell} \tag{11}\]Equation 12, Dynamic Pressure in Terms of Static Pressure and Mach Number. The perfect gas law and the definition of Mach number turn the dynamic pressure into $0.7 p M^{2}$ for a ratio of specific heats of 1.4. Yechout and Morris, Introduction to aircraft flight mechanics Schmidt, Modern flight dynamics Roskam, Airplane flight dynamics and automatic flight controls Anderson, Fundamentals of aerodynamics
\[q = \tfrac{1}{2} \rho V^{2} = \tfrac{1}{2} \rho M^{2} \gamma R T = \tfrac{1}{2} \gamma p M^{2} = 0.7 \, p M^{2} \tag{12}\]Equation 13, Bespoke Mass Flow at Constant Corrected Flow. The article models the engine as a fixed-geometry machine at maximum corrected rotational speed, so that its corrected mass flow is constant and the physical mass flow follows the compressor-face total conditions. Mattingly, Elements of gas turbine propulsion Cumpsty, Jet propulsion
\[\dot{m} = \dot{m}_{\text{ref}} \frac{\delta_{2}}{\sqrt{\theta_{2}}} \tag{13}\]Equation 14, Compressor-Face Total Pressure and Temperature Ratios. The isentropic ram relations give the total pressure and temperature at the compressor face from the ambient conditions and the flight Mach number, with the pressure reduced by the inlet recovery.
\[\delta_{2} = \frac{p}{p_{\text{SL}}} \left( 1 + \tfrac{\gamma - 1}{2} M^{2} \right)^{\frac{\gamma}{\gamma - 1}} \eta_{r} \qquad \theta_{2} = \frac{T}{T_{\text{SL}}} \left( 1 + \tfrac{\gamma - 1}{2} M^{2} \right) \tag{14}\]Equation 15, Bespoke Mass Flow Scaling with Ram Compression. Under the constant corrected flow assumption and a ratio of specific heats of 1.4, the physical mass flow scales with ambient pressure, inlet recovery and the cube of the ram term over the root of ambient temperature.
\[\dot{m} \propto \frac{p}{p_{\text{SL}}} \, \eta_{r} \, \frac{\left( 1 + 0.2 M^{2} \right)^{3}}{\sqrt{T / T_{\text{SL}}}} \tag{15}\]Equation 16, Ideal Nozzle Exhaust Velocity. The jet velocity of a nozzle expanding from a fixed total temperature depends on the nozzle pressure ratio through the isentropic expansion relation.
\[V_{j} = \sqrt{2 \, c_{p} \, T_{t7} \left[ 1 - \left( \frac{p}{p_{t7}} \right)^{\frac{\gamma - 1}{\gamma}} \right]} \tag{16}\]Equation 17, Gross Thrust of a Nozzle. Gross thrust is the mass flow times the jet velocity plus a pressure thrust that vanishes for a nozzle expanded to ambient pressure.
\[F_{g} = \dot{m} V_{j} + \left( p_{e} - p \right) A_{e} \approx \dot{m} V_{j} \tag{17}\]Equation 18, Bespoke Cancellation of Static Pressure in the Moment Ratio. Taking the jet velocity as constant across the envelope, the ambient static pressure appears to the same power above and below the moment ratio and cancels.
\[\mathcal{R} \propto \frac{ \dfrac{p}{p_{\text{SL}}} \eta_{r} \dfrac{(1 + 0.2 M^{2})^{3}}{\sqrt{T/T_{\text{SL}}}} }{ 0.7 \, p M^{2} } = \frac{ \eta_{r} \left( 1 + 0.2 M^{2} \right)^{3} }{ 0.7 \, p_{\text{SL}} \, M^{2} \sqrt{T/T_{\text{SL}}} } \tag{18}\]Equation 19, Bespoke Moment Ratio Above the Tropopause. In the isothermal region of the standard atmosphere, with the jet velocity held constant, the moment ratio depends on Mach number alone.
\[\mathcal{R}(M) \propto \frac{\eta_{r}(M) \left( 1 + 0.2 M^{2} \right)^{3}}{M^{2}} \qquad h > 11 \ \text{km} \tag{19}\]Equation 20, Temperature of the Standard Atmosphere. The standard atmosphere lapses linearly in temperature up to eleven kilometres and holds 216.65 kelvin above it. U.S. Standard Atmosphere 1976 1976
\[T(h) = T_{\text{SL}} - L h \quad (h \le 11 \ \text{km}) \qquad T(h) = 216.65 \ \text{K} \quad (h > 11 \ \text{km}) \tag{20}\]Equation 21, Bespoke Temperature Residue of the Moment Ratio Below the Tropopause. Below the tropopause the moment ratio, with jet velocity held constant, falls from its isothermal value by the square root of the tropopause temperature over the local temperature. U.S. Standard Atmosphere 1976 1976
\[\frac{\mathcal{R}(h)}{\mathcal{R}(h > 11 \ \text{km})} = \sqrt{\frac{T_{11}}{T(h)}} \tag{21}\]Equation 22, Bespoke Mach Dependence of the Moment Ratio at Ideal Recovery. With ideal inlet recovery and constant jet velocity the Mach dependence of the moment ratio is the cube of the ram term divided by the square of the Mach number.
\[f(M) = \frac{\left( 1 + 0.2 M^{2} \right)^{3}}{M^{2}} \tag{22}\]Equation 23, Bespoke Stationarity Condition at Ideal Recovery. Differentiating the ideal Mach dependence with respect to the square of the Mach number gives a derivative that vanishes where that square equals 2.5.
\[\frac{d}{du} \left[ \frac{(1 + 0.2u)^{3}}{u} \right] = \frac{(1 + 0.2u)^{2} \left( 0.4 u - 1 \right)}{u^{2}} \tag{23}\]Equation 24, Bespoke Worst Mach Number and Minimum at Ideal Recovery. The ideal Mach dependence has its minimum of exactly 1.35 at a Mach number of the square root of 2.5.
\[M^{\ast} = \sqrt{2.5} = 1.5811 \qquad f(M^{\ast}) = \frac{1.5^{3}}{2.5} = \frac{3.375}{2.5} = 1.35 \tag{24}\]Equation 25, Military Specification Inlet Pressure Recovery. The military specification correlation gives full recovery up to Mach one and a recovery falling with the 1.35 power of the supersonic excess above it. NASA Glenn Research Center, Inlet performance
\[\eta_{r}(M) = \begin{cases} 1 & M \le 1 \\ 1 - 0.075 \, (M - 1)^{1.35} & M > 1 \end{cases} \tag{25}\]Equation 26, Bespoke Stationarity Condition with Inlet Recovery. With the military specification recovery the condition for the minimum of the moment ratio becomes a transcendental equation that the article solves by golden-section search. NASA Glenn Research Center, Inlet performance
\[\frac{\eta_{r}'(M)}{\eta_{r}(M)} + \frac{1.2 M}{1 + 0.2 M^{2}} - \frac{2}{M} = 0 \tag{26}\]Equation 27, Sideslip Produced by a Crosswind. A crosswind of fixed speed produces a sideslip equal to the arctangent of the crosswind over the true airspeed, which for small angles is the ratio itself.
\[\beta = \arctan \frac{V_{c}}{V} \approx \frac{V_{c}}{V} = \frac{V_{c}}{M \sqrt{\gamma R T}} \tag{27}\]Equation 28, Bespoke Crosswind Scaling of the Required Moment. With sideslip set by a crosswind of fixed speed under the small-angle approximation, the required moment scales with ambient pressure times Mach number over the root of temperature.
\[N_{\text{req}} \propto q \beta = 0.7 \, p M^{2} \cdot \frac{V_{c}}{M \sqrt{\gamma R T}} \propto \frac{p M}{\sqrt{T}} \tag{28}\]Equation 29, Bespoke Scaling of the Available Moment. Under the constant corrected flow and constant jet velocity assumptions, the available moment scales with ambient pressure, inlet recovery and the cube of the ram term over the root of temperature.
\[N_{\text{av}} \propto \frac{p \, \eta_{r} \left( 1 + 0.2 M^{2} \right)^{3}}{\sqrt{T}} \tag{29}\]Equation 30, Bespoke Crosswind Identity. With sideslip set by a crosswind of fixed speed, pressure and temperature cancel and the ratio of required to available moment depends on Mach number alone.
\[\frac{N_{\text{req}}}{N_{\text{av}}} \propto \frac{M}{\eta_{r}(M) \left( 1 + 0.2 M^{2} \right)^{3}} \tag{30}\]Equation 31, Bespoke Derivative of the Crosswind Demand. Differentiating the ideal-recovery crosswind demand with respect to Mach number gives a derivative proportional to one minus the square of the Mach number, so the demand peaks at Mach one.
\[\frac{d}{dM} \left[ M \left( 1 + 0.2 M^{2} \right)^{-3} \right] = \frac{1 - M^{2}}{\left( 1 + 0.2 M^{2} \right)^{4}} \tag{31}\]Equation 32, Bespoke Peak Crosswind Demand at Mach One. Evaluated at Mach one with ideal recovery, the crosswind demand reaches its maximum of the reciprocal of 1.728, a pure number.
\[h(1) = \frac{1}{(1 + 0.2)^{3}} = \frac{1}{1.728} = 0.578704 \tag{32}\]Equation 33, Relative Error of the Small-Angle Arctangent. The leading term of the series for the arctangent gives the relative error of replacing it by its argument as minus one third of the square of the argument.
\[\frac{\arctan x - x}{\arctan x} \approx - \frac{x^{2}}{3} \tag{33}\]Equation 34, Bespoke Thrust to Weight Ratio on a Glide Slope. The thrust to weight ratio on a three degree glide slope is evaluated with a landing-configuration lift to drag ratio of six, a value the article assumes.
\[\frac{T}{W} = \frac{1}{L/D} - \sin \gamma = \frac{1}{6} - \sin 3^{\circ} = 0.16667 - 0.05234 = 0.11433 \tag{34}\]Equation 35, Bespoke Throttle Fraction That Restores the Demonstrated Margin. The article requires the ratio of demanded to available moment on approach to equal that demonstrated by the X-31 at Mach 1.2, so that the geometry and aerodynamic derivatives cancel and only dynamic pressure, sideslip and mass flow remain.
\[\Pi = \frac{q_{\text{app}} \, \beta_{\text{app}}}{q_{\text{dem}} \, \beta_{\text{dem}}} \cdot \frac{\dot{m}(M_{\text{dem}}, h_{\text{dem}})}{\dot{m}(M_{\text{app}}, 0)} \tag{35}\]Equation 36, Bespoke Throttle Setting Required on Approach. The throttle fraction of 0.384 follows for a sea-level approach at 150 knots in a 15 metre per second crosswind, conditions the article assumes, against 0.072 needed on the glide slope with an assumed lift to drag ratio of six and a landing weight near twenty tonnes.
\[\text{throttle} = 0.384 \qquad \text{against } 0.072 \text{ needed to fly the glide slope} \tag{36}\]Equation 37, Lift to Drag Ratio Implied by Thrust in Level Flight. In level flight thrust equals drag, so a given throttle fraction fixes the lift to drag ratio as the weight divided by the thrust.
\[T = D = \frac{W}{L/D} \qquad \Longrightarrow \qquad \frac{L}{D} = \frac{W}{\Pi \, T_{\max}} \tag{37}\]Equation 38, Engine-Out Trim Angle of a Vectored Nozzle. Balancing the yawing moments of the axial and lateral components of the live engine’s thrust gives a trim angle whose tangent is the lateral offset over the moment arm, independent of thrust.
\[F_{g} \ell \sin \delta = F_{g} y \cos \delta \qquad \Longrightarrow \qquad \tan \delta = \frac{y}{\ell} \tag{38}\]Equation 39, Axial Thrust Retained While Trimming an Engine Failure. The axial component of the deflected thrust is the gross thrust times the moment arm over the distance from the centre of gravity to the nozzle.
\[F_{\text{axial}} = F_{g} \cos \delta = F_{g} \frac{\ell}{\sqrt{y^{2} + \ell^{2}}} \tag{39}\]Equation 40, Engine-Out Trim Angle with Windmilling Drag. Adding the windmilling drag of the dead engine to the asymmetry raises the tangent of the trim angle in proportion to the drag over the axial component of the live thrust.
\[\tan \delta = \frac{y \left( F_{g} \cos \delta + D_{\text{wm}} \right)}{\ell \, F_{g} \cos \delta} \tag{40}\]Equation 41, Fin Size Required by an Engine Failure. Setting the fin’s yawing moment at full rudder equal to the thrust asymmetry gives the product of fin area and arm required, which grows as the dynamic pressure falls.
\[S_{v} \, l_{v} = \frac{T \, y}{q \, a_{v} \, \tau \, \eta_{v} \, \delta_{r,\max}} \tag{41}\]Equation 42, Divergence Rate and Time to Double of the Directional Mode. Treating the tailless directional mode as a single degree of freedom in yaw, the divergence rate is the square root of the destabilising moment per radian over the yawing moment of inertia, and the time to double is the logarithm of two over that rate.
\[\lambda = \sqrt{\frac{q S b \left| C_{n\beta} \right|}{I_{z}}} \qquad t_{2} = \frac{\ln 2}{\lambda} \tag{42}\]Equation 43, Bespoke Crossover Frequency for an Unstable Pole. The article takes the loop crossover as two to three times the divergence rate, a rule of thumb for stabilising a real unstable pole.
\[\omega_{c} = k \lambda \qquad k \approx 2 \ \text{to} \ 3 \tag{43}\]Equation 44, Bespoke Transport Delay Budget. A pure delay spends phase in proportion to the crossover, so with the crossover set at two to three times the divergence rate the allowable delay is the phase budget divided by that multiple of the rate. Berry et al. 1980 Berry 1985
\[\Delta \phi = \omega_{c} \tau \qquad \Longrightarrow \qquad \tau_{\max} = \frac{\Delta \phi}{k \lambda} \tag{44}\]Equation 45, Bespoke Wing Area Ratio of the X-44A to the X-36. Taking wing area as proportional to the square of span, the X-44A span of 9.144 metres against the X-36 span of 3.17 metres implies 8.32 times the wing. Walker 1997
\[\left( \frac{9.144}{3.17} \right)^{2} = 8.32 \tag{45}\]Equation 46, Bespoke Ceiling Thrust Balance with Thrust Lapse. The article takes thrust at the published service ceiling to equal the drag at the best lift to drag ratio and models thrust as lapsing with a power of the density ratio. Lockheed Martin RQ-3 DarkStar
\[T_{\text{SL}} \sigma^{n} = \frac{W}{(L/D)_{\max}} \qquad (L/D)_{\max} = \tfrac{1}{2} \sqrt{\frac{\pi e A\!R}{C_{D_{0}}}} \tag{46}\]Equation 47, Parabolic Drag Polar and Aspect Ratio. The drag coefficient is the zero-lift drag plus the square of the lift coefficient over $\pi e A!R$, with the aspect ratio the square of the span over the area. Raymer, Aircraft design, a conceptual approach Filippone, Advanced aircraft flight performance
\[C_{D} = C_{D_{0}} + \frac{C_{L}^{2}}{\pi e A\!R} \qquad A\!R = \frac{b^{2}}{S} \tag{47}\]Equation 48, Lift Coefficient and Lift to Drag Ratio at Best Glide. The best lift to drag ratio of a parabolic polar occurs where induced drag equals zero-lift drag, which fixes the lift coefficient and gives the ratio as that coefficient over twice the zero-lift drag. Raymer, Aircraft design, a conceptual approach Filippone, Advanced aircraft flight performance
\[C_{L}^{\ast} = \sqrt{C_{D_{0}} \, \pi e A\!R} \qquad \left( \frac{L}{D} \right)_{\max} = \frac{C_{L}^{\ast}}{2 \, C_{D_{0}}} \tag{48}\]Equation 49, Speed and Wing Loading at a Given Lift Coefficient. Lift equal to weight fixes the speed for a given density, wing area and lift coefficient, and equivalently the wing loading. Raymer, Aircraft design, a conceptual approach Filippone, Advanced aircraft flight performance
\[V = \sqrt{\frac{2 W}{\rho \, S \, C_{L}^{\ast}}} \qquad \frac{W}{S} = \frac{\rho V^{2} C_{L}^{\ast}}{2} \tag{49}\]Equation 50, Bespoke Thrust Lapse Exponent of the DarkStar Engine. The exponent is calibrated from a ceiling thrust of 1,747 newtons computed with an assumed 42 square metre wing, an Oswald efficiency of 0.85 and a zero-lift drag coefficient of 0.015, against the published 8.45 kilonewton sea-level rating and a density ratio of 0.1936. Oswald 1932
\[n = \frac{\ln \left( 1747 / 8450 \right)}{\ln 0.1936} = 0.960 \tag{50}\]Equation 51, Force Components of a Two-Dimensional Nozzle. A nozzle whose flaps deflect the jet in one plane produces axial and normal components and no side force. Lockheed Martin F-22 Raptor Pratt and Whitney F119
\[F_{x} = F_{g} \cos \delta_{p} \qquad F_{z} = F_{g} \sin \delta_{p} \qquad F_{y} = 0 \tag{51}\]Equation 52, Force Components of a Nozzle with Deflecting Sidewalls. A second deflection by the sidewalls produces a side force and reduces the axial force through the product of the cosines of the pitch and yaw angles.
\[F_{y} = F_{g} \cos \delta_{p} \sin \delta_{y} \qquad F_{x} = F_{g} \cos \delta_{p} \cos \delta_{y} \tag{52}\]Equation 53, Bespoke Fuel Volume Scaling of an Enlarged Wing. Assuming the wing is scaled in plan at fixed thickness ratio and aspect ratio, its internal volume grows as the three-halves power of its area. Lockheed Martin X-44 MANTA
\[\text{Vol} \propto \left( \frac{t}{c} \right) \frac{S^{3/2}}{\sqrt{A\!R}} \qquad \Longrightarrow \qquad \frac{\text{Vol}_{2}}{\text{Vol}_{1}} = \left( \frac{S_{2}}{S_{1}} \right)^{3/2} \tag{53}\]Equation 54, Load Factor and Sustained Turn Rate. The load factor is the dynamic pressure times the lift coefficient over the wing loading, and the turn rate follows from the load factor and the speed.
\[n = \frac{q \, C_{L}}{W/S} \qquad \dot{\psi} = \frac{g \sqrt{n^{2} - 1}}{V} \tag{54}\]Equation 55, Munk Yawing Moment of a Slender Body. A slender fuselage in sideslip carries a destabilising yawing moment proportional to its volume and to the difference of its apparent-mass factors. Munk 1924 Multhopp 1942
\[C_{n\beta, \text{fus}} = - \frac{2 \left( k_{2} - k_{1} \right) \text{Vol}_{\text{fus}}}{S \, b} \tag{55}\]Equation 56, Yawing Moment Commanded by a Sideslip Error. A sideslip measurement error is indistinguishable from a real sideslip and so commands a yawing moment coefficient equal to the stability derivative times the error.
\[\Delta C_{n} = \left| C_{n\beta} \right| \varepsilon_{\beta} \tag{56}\]Equation 57, Gearing from Sideslip to Nozzle Deflection. Differentiating the required-deflection relation gives the nozzle deflection needed per unit of sideslip.
\[\frac{d \delta}{d \beta} = \frac{q S b \left| C_{n\beta} \right|}{F_{g} \, \ell \, \cos \delta} \tag{57}\]Equation 58, Quasi-Tailless Rudder Schedule. The X-31 quasi-tailless technique schedules the rudder against sideslip so as to cancel a chosen fraction of the vertical tail’s stabilising contribution. Bosworth and Stoliker 1996
\[\delta_{r} = - \kappa \, \frac{C_{n\beta, \text{tail}}}{C_{n \delta_{r}}} \, \beta \tag{58}\]Equation 59, Bespoke Moment Ratio with Varying Jet Velocity. Relaxing the constant jet velocity assumption carries the Mach dependence of the jet velocity into the moment ratio, which the article evaluates at an overall engine pressure ratio of eight.
\[\mathcal{R}(M) \propto \frac{\eta_{r}(M) \left( 1 + 0.2 M^{2} \right)^{3} V_{j}(M)}{M^{2}} \tag{59}\]Notation
- $C_{n\beta}$, the directional stability derivative, with $C_{n\beta, \text{tail}}$ the tail contribution and $C_{n\beta, \text{fus}}$ the fuselage contribution
- $\beta$, the sideslip angle
- $q$, the dynamic pressure
- $S$, the wing reference area
- $b$, the wing span, and in the dihedral relation a plate dimension
- $N$, the yawing moment, with $N_{\text{req}}$ the moment required and $N_{\text{av}}$ the moment available, and in the register count the highest number issued
- $V_{v}$, the vertical tail volume coefficient
- $S_{v}$, the fin area
- $l_{v}$, the fin moment arm
- $C_{n \delta_{r}}$, the rudder control derivative
- $a_{v}$, the fin lift-curve slope
- $\tau$, the rudder effectiveness, and in the delay budget a pure transport delay
- $\eta_{v}$, the dynamic pressure ratio at the tail
- $\sigma$, the radar cross section, and in the thrust lapse relation the density ratio of the standard atmosphere
- $\lambda$, the radar wavelength, and in the divergence relation the divergence rate of the directional mode
- $F_{g}$, the gross thrust passing through the nozzles
- $\ell$, the distance from the centre of gravity to the nozzle exit
- $\delta$, the yaw deflection angle of the jet, with $\delta_{p}$ the pitch flap angle and $\delta_{y}$ the sidewall angle of a two-dimensional nozzle
- $\mathcal{R}$, the ratio of available to required yawing moment
- $V_{p}$, the propulsive tail volume
- $\gamma$, the ratio of specific heats, taken as 1.4 for air, and in the glide slope relation the flight path angle
- $p$, the ambient static pressure, with $p_{\text{SL}}$ its sea-level value
- $M$, the Mach number
- $T$, the ambient temperature, with $T_{\text{SL}}$ its sea-level value, and in the thrust relations a thrust
- $\dot{m}$, the physical engine mass flow, with $\dot{m}_{\text{ref}}$ its value at sea level static conditions
- $\delta_{2}$, the compressor-face total pressure referred to sea level static conditions
- $\theta_{2}$, the compressor-face total temperature referred to sea level static conditions
- $\eta_{r}$, the inlet total pressure recovery
- $V_{j}$, the jet velocity
- $T_{t7}$, the nozzle total temperature fixed by the afterburner limit
- $V_{c}$, the crosswind speed
- $\Pi$, the throttle fraction
- $W$, the weight
- $y$, the lateral distance of the live engine from the centreline
- $D_{\text{wm}}$, the windmilling drag of the dead engine
- $I_{z}$, the yawing moment of inertia
- $t_{2}$, the time to double a disturbance
- $\omega_{c}$, the loop crossover frequency
- $k$, the ratio of crossover frequency to divergence rate, and with subscripts the apparent-mass factors of the Munk moment
- $\Delta \phi$, the phase spent by a transport delay at crossover
- $n$, the thrust lapse exponent in the ceiling relation, and the load factor in the turn relation
- $e$, the Oswald efficiency, taken as 0.85
- $A!R$, the wing aspect ratio
- $C_{D_{0}}$, the zero-lift drag coefficient
- $C_{L}^{\ast}$, the lift coefficient at the best lift to drag ratio
- $\dot{\psi}$, the sustained turn rate
- $\kappa$, the fraction of the vertical tail’s stabilising contribution cancelled by the rudder
- $\varepsilon_{\beta}$, the error in the measured sideslip
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- Sechter, Brendan. 2025. “X-Planes: Northrop X-21.” Brendan A R Sechter’s Development Blog, October 27. https://sgeos.github.io/aerospace/history/engineering/2025/10/27/x_planes_northrop_x21.html
- Sechter, Brendan. 2025. “X-Planes: Bell X-22.” Brendan A R Sechter’s Development Blog, October 28. https://sgeos.github.io/aerospace/history/engineering/2025/10/28/x_planes_bell_x22.html
- Sechter, Brendan. 2025. “X-Planes: Martin Marietta X-23 PRIME and a Contested Assignment.” Brendan A R Sechter’s Development Blog, October 29. https://sgeos.github.io/aerospace/history/engineering/2025/10/29/x_planes_martin_marietta_x23.html
- Sechter, Brendan. 2025. “X-Planes: Martin Marietta X-24.” Brendan A R Sechter’s Development Blog, October 30. https://sgeos.github.io/aerospace/history/engineering/2025/10/30/x_planes_martin_marietta_x24.html
- Sechter, Brendan. 2025. “X-Planes: Bensen X-25.” Brendan A R Sechter’s Development Blog, October 31. https://sgeos.github.io/aerospace/history/engineering/2025/10/31/x_planes_bensen_x25.html
- Sechter, Brendan. 2025. “X-Planes: Schweizer X-26 Frigate.” Brendan A R Sechter’s Development Blog, November 1. https://sgeos.github.io/aerospace/history/engineering/2025/11/01/x_planes_schweizer_x26.html
- Sechter, Brendan. 2025. “X-Planes: Lockheed X-27.” Brendan A R Sechter’s Development Blog, November 2. https://sgeos.github.io/aerospace/history/engineering/2025/11/02/x_planes_lockheed_x27.html
- Sechter, Brendan. 2025. “X-Planes: Osprey X-28 Sea Skimmer.” Brendan A R Sechter’s Development Blog, November 3. https://sgeos.github.io/aerospace/history/engineering/2025/11/03/x_planes_osprey_x28.html
- Sechter, Brendan. 2025. “X-Planes: Grumman X-29.” Brendan A R Sechter’s Development Blog, November 4. https://sgeos.github.io/aerospace/history/engineering/2025/11/04/x_planes_grumman_x29.html
- Sechter, Brendan. 2025. “X-Planes: Rockwell X-30 and the National Aero-Space Plane.” Brendan A R Sechter’s Development Blog, November 5. https://sgeos.github.io/aerospace/history/engineering/2025/11/05/x_planes_rockwell_x30.html
- Sechter, Brendan. 2025. “X-Planes: Rockwell-MBB X-31.” Brendan A R Sechter’s Development Blog, November 6. https://sgeos.github.io/aerospace/history/engineering/2025/11/06/x_planes_rockwell_mbb_x31.html
- Sechter, Brendan. 2025. “X-Planes: Boeing X-32.” Brendan A R Sechter’s Development Blog, November 7. https://sgeos.github.io/aerospace/history/engineering/2025/11/07/x_planes_boeing_x32.html
- Sechter, Brendan. 2025. “X-Planes: Lockheed Martin X-33.” Brendan A R Sechter’s Development Blog, November 8. https://sgeos.github.io/aerospace/history/engineering/2025/11/08/x_planes_lockheed_martin_x33.html
- Sechter, Brendan. 2025. “X-Planes: Orbital Sciences X-34.” Brendan A R Sechter’s Development Blog, November 9. https://sgeos.github.io/aerospace/history/engineering/2025/11/09/x_planes_orbital_sciences_x34.html
- Sechter, Brendan. 2025. “X-Planes: Lockheed Martin X-35.” Brendan A R Sechter’s Development Blog, November 10. https://sgeos.github.io/aerospace/history/engineering/2025/11/10/x_planes_lockheed_martin_x35.html
- Sechter, Brendan. 2025. “X-Planes: McDonnell Douglas X-36.” Brendan A R Sechter’s Development Blog, November 11. https://sgeos.github.io/aerospace/history/engineering/2025/11/11/x_planes_mcdonnell_douglas_x36.html
- Sechter, Brendan. 2025. “X-Planes: Boeing X-37.” Brendan A R Sechter’s Development Blog, November 12. https://sgeos.github.io/aerospace/history/engineering/2025/11/12/x_planes_boeing_x37.html
- Sechter, Brendan. 2025. “X-Planes: Scaled Composites X-38.” Brendan A R Sechter’s Development Blog, November 13. https://sgeos.github.io/aerospace/history/engineering/2025/11/13/x_planes_scaled_composites_x38.html
- Sechter, Brendan. 2025. “X-Planes: X-39, Reserved but Never Assigned.” Brendan A R Sechter’s Development Blog, November 14. https://sgeos.github.io/aerospace/history/engineering/2025/11/14/x_planes_x39_reserved_never_assigned.html
- Sechter, Brendan. 2025. “X-Planes: Boeing X-40.” Brendan A R Sechter’s Development Blog, November 15. https://sgeos.github.io/aerospace/history/engineering/2025/11/15/x_planes_boeing_x40.html
- Sechter, Brendan. 2025. “X-Planes: X-41 Common Aero Vehicle.” Brendan A R Sechter’s Development Blog, November 16. https://sgeos.github.io/aerospace/history/engineering/2025/11/16/x_planes_x41_common_aero_vehicle.html
- Sechter, Brendan. 2025. “X-Planes: Orbital Sciences X-42.” Brendan A R Sechter’s Development Blog, November 17. https://sgeos.github.io/aerospace/history/engineering/2025/11/17/x_planes_orbital_sciences_x42.html
- Sechter, Brendan. 2025. “X-Planes: Micro-Craft X-43 Hyper-X.” Brendan A R Sechter’s Development Blog, November 18. https://sgeos.github.io/aerospace/history/engineering/2025/11/18/x_planes_micro_craft_x43_hyper_x.html
Referenced by
- X-Planes: Synthesis and What the Designation Became 2025-12-16
- X-Planes: Bell Textron X-76 SPRINT 2025-12-15
- X-Planes: X-69 through X-75, the Leapfrogged Block 2025-12-14
- X-Planes: General Atomics X-68 LongShot 2025-12-13
- X-Planes: X-67, the Slot Taken by XQ-67A 2025-12-12
- X-Planes: Boeing X-66 2025-12-11
- X-Planes: Aurora Flight Sciences X-65 CRANE 2025-12-10
- X-Planes: Invocon X-64 2025-12-09
- X-Planes: ABL Space Systems X-63 2025-12-08
- X-Planes: Lockheed Martin X-62 VISTA 2025-12-07
- X-Planes: Dynetics X-61 Gremlins 2025-12-06
- X-Planes: Generation Orbit X-60 2025-12-05
- X-Planes: Lockheed Martin X-59 Quesst 2025-12-04
- X-Planes: X-58, the Slot Taken by XQ-58 2025-12-03
- X-Planes: ESAero X-57 Maxwell 2025-12-02
- X-Planes: Lockheed Martin X-56 2025-12-01
- X-Planes: Lockheed Martin X-55 ACCA 2025-11-30
- X-Planes: Gulfstream X-54 2025-11-29
- X-Planes: Boeing X-53 Active Aeroelastic Wing 2025-11-28
- X-Planes: X-52, the Designation Refused 2025-11-27
- X-Planes: Boeing X-51 Waverider 2025-11-26
- X-Planes: Boeing X-50 Dragonfly 2025-11-25
- X-Planes: Piasecki X-49 SpeedHawk 2025-11-24
- X-Planes: Boeing X-48 2025-11-23
- X-Planes: Northrop Grumman X-47 2025-11-22
- X-Planes: Boeing X-46 2025-11-21
- X-Planes: Boeing X-45 2025-11-20