X-Planes: Boeing X-48

On 20 July 2007 an aeroplane weighing about as much as three passengers took off from Rogers Dry Lake, and the number that matters about it is 240. [Risch et al. 2009] The X-48B spans 20.4 feet. The aeroplane it was built to describe spans 240 feet, and every claim the programme made about that larger machine had to travel across a factor of 8.5 percent to get there [Regan 2008] [Boeing flies X-48C blended wing body research aircraft].

This is the forty-ninth 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, the X-43, the X-44, the X-45, the X-46, and the X-47.

One airframe flew 122 times over nearly six years, as two aeroplanes, and the record of those flights is extensive. The second X-48B flew 92 times and was then rebuilt as the X-48C, which flew 30 more [Second X-48B modified into X-48C configuration, NASA Dryden] [X-48 Research, All Good Things Must Come to an End, NASA]. It flew in two configurations, through envelope expansion, parameter identification, engine-out testing and deliberate approaches to the limit of controlled flight [X-48 Research, All Good Things Must Come to an End, NASA].

It is the first aeroplane in this series whose central question is about the instrument rather than the vehicle. The previous three articles were unmanned combat aircraft. This one is a transport configuration, and the interesting thing about it is not what it did but what its size permits anyone to conclude.

The Research Question

The blended wing body was never in doubt at cruise, and was entirely in doubt on approach. The configuration’s case is aerodynamic efficiency, and by the time the X-48 flew, the cruise argument had been made in analysis and in the tunnel [Liebeck 2004]. What no tunnel settles is whether a large tailless aeroplane with twenty trailing-edge surfaces and no horizontal tail can be flown safely at low speed by a line pilot, and where it stops being controllable.

A free-flight model answers that question, and it answers it by giving something up. A model cannot match every dimensionless group at once. Matching the ratio of inertial to gravitational force, which is the Froude number, makes the model move like the aeroplane. Matching the ratio of inertial to viscous force, which is the Reynolds number, makes the air behave around the model as it does around the aeroplane. At any scale below one, those two demands conflict, and the free-flight tradition resolves the conflict in favour of Froude [Chambers 2010].

This article asks what the X-48B’s scale factor bought and what it cost. The answer can be computed, and it bears directly on the most quoted result of the flight programme.

Programme Origin

Four scaled blended wing bodies preceded the answer, and two of them never flew. The designation record for the family is set out in the specialist directory [Parsch, Boeing X-48, Directory of U.S. Military Rockets and Missiles], and the general configuration has a literature of its own reaching back to the tailless transports of the 1940s [Wooldridge, Winged wonders, the story of the flying wings] [Blended wing body].

The first was the BWB-17, a 17-foot-span model weighing 120 pounds, built at Stanford University under the sponsorship of the National Aeronautics and Space Administration, abbreviated NASA, and flown on 29 July 1997 at El Mirage Dry Lake. It was dynamically scaled, carried an onboard computer for stability augmentation, and demonstrated good handling qualities within the normal envelope [Liebeck 2004].

The second was the X-48A. In 2000 NASA and Boeing began a 35-foot-span remotely piloted model, and the designation was allocated in late 2001 [Parsch, Boeing X-48, Directory of U.S. Military Rockets and Missiles]. It was described as a 14 percent scale vehicle of the 450-passenger study aircraft [X-48 Blended Wing Body, GlobalSecurity] [Parsch, Boeing X-48, Directory of U.S. Military Rockets and Missiles]. After about a year the programme was cancelled and NASA redirected its effort to a 12-foot-span free-flight model for the Langley Full-Scale Tunnel [Chambers 2010]. That redirection is the most consequential decision in this article, and the section on scaling prices it.

The third and fourth are the two X-48B airframes, of which only the second flew [Risch et al. 2009]. Boeing Phantom Works took the lead on the X-48B in 2006 with NASA and the Air Force Research Laboratory [Boeing Phantom Works to lead research on X-48B blended wing body concept] [X-48 Blended Wing Body, GlobalSecurity]. Two X-48B airframes were built by Cranfield Aerospace in the United Kingdom to Boeing’s specifications [Cranfield Aerospace Solutions] [Boeing X-48]. Ship 1 went to the Langley Full-Scale Tunnel for 250 hours of testing in May 2006, and Ship 2 became the flight vehicle [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090]. Ship 2 was later rebuilt as the X-48C [Second X-48B modified into X-48C configuration, NASA Dryden].

Sizing From First Principles

The Geometry Closes Exactly

Two numbers are published separately and their ratio is not approximate. NASA’s fact sheet and the flight-test papers give the X-48B a span of 20.4 feet and call it an 8.5 percent scale vehicle [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090] [Risch et al. 2009], and Boeing gives the full-scale aeroplane a span of 240 feet [Boeing flies X-48C blended wing body research aircraft]. Taking the ratio,

\[n = \frac{20.4\ \text{ft}}{240\ \text{ft}} = 0.085000 \tag{1}\]

which agrees with the published 8.5 percent to fourteen decimal places. The agreement establishes that the reference vehicle is a real design with a fixed span and that its span was no round number attached afterwards, and every relation below inherits that exactness.

What Froude Matching Does to Everything Else

Two dimensionless groups compete and only one can be held. The Froude number is the ratio of inertial to gravitational force and the Reynolds number is the ratio of inertial to viscous force,

\[Fr = \frac{V^{2}}{Lg}, \qquad Re = \frac{VL}{\nu} \tag{2}\]

Setting the model’s Froude number equal to the aeroplane’s fixes the speed ratio, and it does so without reference to the air at all,

\[\frac{V_m^{2}}{L_m g} = \frac{V_f^{2}}{L_f g} \implies r_V = \frac{V_m}{V_f} = \sqrt{\frac{L_m}{L_f}} = \sqrt{n} \tag{3}\]

The mass condition is a separate requirement, and it is usually forgotten. A dynamic model must also match the relative density factor, which compares the model’s mass to the air it displaces,

\[\sigma = \frac{m}{\rho l^{3}} \tag{4}\]

so that the weight ratio carries an atmospheric term,

\[r_W = \frac{n^{3}}{\sigma} \tag{5}\]

When the model and the aeroplane fly in the same air, $\sigma$ is one and the term disappears. The article returns to what happens when they do not.

Holding the Froude number and the relative density fixed determines every other ratio by dimensions alone. With $n$ the length ratio and the model flying in the same air as the aeroplane,

\[r_V = \sqrt{n}, \qquad r_t = \sqrt{n}, \qquad r_\omega = \frac{1}{\sqrt{n}} \tag{6}\] \[r_W = n^3, \qquad r_I = n^5, \qquad r_{Re} = n^{3/2} \tag{7}\]

The Reynolds ratio is not an independent choice but a consequence, being the product of the speed ratio already fixed by Froude and the length ratio,

\[r_{Re} = r_V \, r_L = n^{1/2} \cdot n = n^{3/2} \tag{8}\]

and that single line states the cost of the decision in full. Two further ratios follow the same way and both matter later. The dynamic pressure and the wing loading go as

\[r_q = \frac{\rho V_m^{2}}{\rho V_f^{2}} = r_V^{2} = n, \qquad r_{W/S} = \frac{n^{3}}{n^{2}} = n \tag{9}\]

The weight goes as the cube because it is a force and a force at matched Froude number scales as $\rho V^2 L^2$, which is $n \cdot n^2$. The underlying rigid-body equations are standard [Etkin and Reid, Dynamics of flight] [McCormick, Aerodynamics, aeronautics and flight mechanics]. The exponent of three halves in the Reynolds row comes from that product of the velocity and length ratios.

At $n = 0.085$ these evaluate to the following.

Quantity	Ratio	Value at 8.5 percent
Length	$n$	0.0850
Velocity	$n^{1/2}$	0.2915
Time	$n^{1/2}$	0.2915
Angular rate	$n^{-1/2}$	3.430
Weight and force	$n^{3}$	$6.141 \times 10^{-4}$
Moment of inertia	$n^{5}$	$4.437 \times 10^{-6}$
Reynolds number	$n^{3/2}$	0.02478
Thrust to weight	$1$	1.000

Two rows carry the argument. The model’s angular motions run 3.430 times faster than the aeroplane’s, and the model’s Reynolds number is 1/40.35 of the aeroplane’s.

The Pilot Does Not Scale

Time compression constrains the pilot as much as the aeroplane. Any interval scales as

\[t_m = t_f \sqrt{n} = 0.2915 \, t_f \tag{10}\]

so a motion that the full-scale aeroplane would develop over three seconds develops in the model in

\[t_m = 3 \times 0.2915 = 0.875\ \text{s} \tag{11}\]

and the angular rates that go with it are faster by the reciprocal,

\[r_\omega = \frac{1}{\sqrt{n}} = 3.430 \tag{12}\]

The aeroplane is on a dry lake bed and the pilot is in a ground station, and the pilot’s reaction time is not multiplied by 0.2915 to match. [Risch et al. 2009]

NASA’s account of dynamic model testing acknowledges the problem, noting that because a model’s angular motions are so much faster than the aeroplane’s, the models may be difficult to control, and that the response has often been to share the piloting task among more than one person [Chambers 2010].

This series has measured this before at a gentler scale. The X-36 was a 28 percent remotely piloted tailless demonstrator [X-36 Tailless Fighter Agility Research Aircraft, NASA], and the same relations give a time compression of 1.890 and a Reynolds penalty of 6.75. Against it,

\[\frac{r_t^{-1}(0.085)}{r_t^{-1}(0.28)} = 1.815, \qquad \frac{r_{Re}^{-1}(0.085)}{r_{Re}^{-1}(0.28)} = 5.979 \tag{13}\]

The X-48B’s pilot faced dynamics 1.815 times faster than the X-36’s, and its aerodynamics were 5.979 times further from full scale. The X-36 article argued that a scale factor is a statement about what an experiment is able to measure. The X-48B repeats that argument at nearly twice the severity.

Reynolds Number in Absolute Terms and at Altitude

A ratio of 40.35 does not locate either aeroplane on the Reynolds scale, and the absolute values decide whether the mismatch matters. Using a reference chord and the published maximum speed of 118 knots [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090] [Vicroy 2011],

\[Re = \frac{V c}{\nu}, \qquad c = \frac{S}{b} = \frac{100.5}{20.4} = 4.926\ \text{ft} \tag{14}\]

The programme’s correlation update supplies the wing area of 100.5 square feet [Vicroy 2011]. The ratio below does not depend on it, because the chord cancels.

At sea level, with $\nu_0 = 1.5723 \times 10^{-4}\ \text{ft}^2/\text{s}$,

\[Re_{\text{model}} = \frac{199.2 \times 4.926}{1.5723 \times 10^{-4}} = 6.24 \times 10^{6} \tag{15}\]

and the corresponding full-scale condition, at $V_f = V_m/\sqrt{n}$ and $c_f = c/n$,

\[Re_{\text{full}} = \frac{683.1 \times 58.0}{1.5723 \times 10^{-4}} = 2.52 \times 10^{8} \tag{16}\]

Both are above the range where a boundary layer is deciding whether to be turbulent at all, and they are two orders of magnitude apart.

The published speed also checks the scaling. Inverting the speed ratio on the model’s maximum,

\[V_f = \frac{118}{\sqrt{0.085}} = 404.7\ \text{kt} \tag{17}\]

a sensible cruise speed for a large subsonic transport, and a second piece of evidence for a real reference design.

The atmosphere then makes the mismatch worse, and nowhere else in this article does the standard atmosphere earn its keep. The model flew to a ceiling of 10,000 feet [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090] [Vicroy 2011], inside a working area that reached from the ground to 10,000 feet above mean sea level [Risch et al. 2009], while the full-scale aeroplane’s low-speed regime is near the ground. Kinematic viscosity rises with altitude,

\[\nu(h) = \frac{\mu(h)}{\rho(h)}, \qquad \frac{\nu(10{,}000)}{\nu(0)} = \frac{2.0135 \times 10^{-4}}{1.5723 \times 10^{-4}} = 1.281 \tag{18}\]

so a model tested at its ceiling against an aeroplane approaching at sea level suffers

\[P_{\text{effective}} = n^{-3/2} \times \frac{\nu(10{,}000)}{\nu(0)} = 40.35 \times 1.281 = 51.7 \tag{19}\]

The effective penalty therefore lies between 40.35 and 51.7, depending on the test altitude, and the larger figure applies to any manoeuvre flown high.

What Cancelling the X-48A Cost

The penalty is a function of span alone once the reference is fixed, since $n = b/b_{\text{ref}}$ gives

\[P(b) = \left(\frac{b_{\text{ref}}}{b}\right)^{3/2}, \qquad \tau(b) = \left(\frac{b_{\text{ref}}}{b}\right)^{1/2} \tag{20}\]

Evaluated against the X-48B’s 240-foot reference, the three spans NASA planned or flew price out as follows. The 12-foot model is the 5 percent free-flight model of the Langley Full-Scale Tunnel [Vicroy 2011].

Vehicle	Span	Scale	Time compression	Reynolds penalty
X-48A, planned and cancelled	35 ft	0.1458	2.619	17.96
X-48B, flown	20.4 ft	0.0850	3.430	40.35
Langley free-flight model	12 ft	0.0500	4.472	89.44

The cost of the substitution is a ratio of two such penalties and needs no other quantity,

\[\frac{P(20.4)}{P(35)} = \left(\frac{35}{20.4}\right)^{3/2} = 2.247, \qquad \frac{\tau(20.4)}{\tau(35)} = \left(\frac{35}{20.4}\right)^{1/2} = 1.310 \tag{21}\]

Cancelling the 35-foot aeroplane and flying the 20.4-foot one multiplied the Reynolds shortfall by 2.247 and made the aeroplane 31 percent quicker in its own time. Those two factors price the 2002 decision in the only units that can express it. The table holds the reference fixed, because the substitution posed that comparison. The X-48A itself was described as a 14 percent vehicle of the 450-passenger study aircraft, which implies a reference span of 250 feet, close to the 249 feet of the BWB-450 baseline, and against that reference its own time compression is 2.673 and its own Reynolds penalty 19.09 [X-48 Blended Wing Body, GlobalSecurity] [Liebeck 2004]. It is not an argument that the decision was wrong, since a 35-foot vehicle is a different programme in cost, airspace and risk, but it is the quantity the decision traded.

The Vehicle Implied by the Model’s Weight

A dynamically scaled model is weight-scaled, so the relation can be run backwards. Taking the maximum weight of 525 pounds given in the flight-test papers [Risch et al. 2009] [Regan 2008] and inverting the cube,

\[W_{\text{full}} = \frac{525\ \text{lb}}{n^3} = 8.549 \times 10^{5}\ \text{lb} \tag{22}\]

That figure assumes $\sigma = 1$, the term the earlier section set aside. Restoring it,

\[W_{\text{full}} = \frac{W_m}{n^{3}} \cdot \frac{\rho_f}{\rho_m} \tag{23}\]

and evaluating for three readings of where the model’s condition sits,

Model condition	$\rho_m/\rho_0$	Implied full-scale weight
same air as the aeroplane	1.0000	854,875 lb
Rogers Dry Lake, 2,300 ft	0.9344	914,885 lb
ceiling, 10,000 ft	0.7385	1,157,634 lb

The field reading takes the lake bed at about 2,300 feet [Rogers Dry Lake]. The figure of 854,875 pounds can serve only as a lower bound, and the article uses it as one.

No technical source consulted states the reference vehicle’s weight, so the figure is a derivation. A magazine account published before the first flight calls the X-48B a scaled-down model of a theoretical 500-ton, 240-foot-wide aircraft [Jacobs 2007, Thinking outside the tube, Wired]. Read as 1,000,000 pounds, that round figure lies inside the range above, and the three readings come to 0.855, 0.915 and 1.158 of it. The derivation can also be tested against a published design. Among the sources consulted, the only blended wing body design with both a published weight and a published span is Liebeck’s second-generation airliner, sized for 800 passengers, with a maximum takeoff gross weight of 823,000 pounds on a span of 280 feet [Liebeck 2004]. Scaling that design geometrically to a 240-foot span,

\[W(240) = 823{,}000 \times \left(\frac{240}{280}\right)^{3} = 518{,}274\ \text{lb} \tag{24}\]

gives a comparison of

\[\frac{W_{\text{full}}}{W(240)} = \frac{854{,}875}{518{,}274} = 1.649 \tag{25}\]

Geometric scaling holds the shape and lets the wing loading grow with span. Holding the wing loading instead makes weight follow the square of span,

\[W_{2}(240) = 823{,}000 \times \left(\frac{240}{280}\right)^{2} = 604{,}653\ \text{lb} \tag{26}\]

and the two laws differ by the factor 280/240, or 1.167. Against each,

Model condition	Over the cube law	Over the square law
same air as the aeroplane	1.649	1.414
Rogers Dry Lake, 2,300 ft	1.765	1.513
ceiling, 10,000 ft	2.234	1.915

so the vehicle implied by the model’s weight is between 1.414 and 1.649 times as heavy as the passenger design brought to the same span, and between 1.513 and 1.765 times as heavy on the field-elevation reading. The choice of scaling law changes the size of the excess by a sixth, and no reading brings the ratio near one.

The excess is large, and the programme’s description of the full-scale aeroplane accounts for its direction. Boeing describes the 240-foot aeroplane as a heavy-lift, subsonic airplane for military applications such as aerial refuelling and cargo missions [Boeing flies X-48C blended wing body research aircraft], and the Air Force’s stated interest was a multi-role, long-range, high-capacity military transport [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090]. A freighter is denser than an airliner of the same dimensions, as the conventional airlifter it would replace shows [Boeing C-17 Globemaster III], and the weight relations behind that comparison are the standard conceptual-design ones [Raymer, Aircraft design, a conceptual approach] [Torenbeek, Synthesis of subsonic airplane design] [Nicolai and Carichner, Fundamentals of aircraft and airship design]. The model’s weight therefore agrees with the heavy military vehicle the programme described and does not agree with a passenger design of the same span. The scale relations fix the size of that excess. They do not show how much of it payload density explains, and this article does not attempt that division.

Thrust Is Invariant Under Froude Scaling and This Model Does Not Match It

Thrust is a force, so it scales as $n^3$, and thrust to weight is therefore the same number for the model and the aeroplane. That makes it directly checkable, with the installed thrust of 54 pounds an engine from the flight-test papers [Risch et al. 2009] [Regan 2008] and the full-scale thrust from Liebeck’s design [Liebeck 2004].

\[\left(\frac{T}{W}\right)_{\text{model}} = \frac{3 \times 54\ \text{lbf}}{525\ \text{lb}} = 0.3086 \tag{27}\] \[\left(\frac{T}{W}\right)_{\text{full}} = \frac{3 \times 61{,}600\ \text{lbf}}{823{,}000\ \text{lb}} = 0.2245 \tag{28}\] \[\frac{(T/W)_{\text{model}}}{(T/W)_{\text{full}}} = \frac{0.3086}{0.2245} = 1.374 \tag{29}\]

The model carries 1.374 times the thrust to weight of the aeroplane it represents. Such a margin is no defect. A model that must take off from a lake bed, climb to a test altitude inside a small working area and go around from an approach needs margin the transport does not.

But it means the demonstration is tilted, and the direction is computable. Thrust to weight is one of the handful of ratios that fixes an aeroplane’s performance at all [Anderson, Aircraft performance and design].

The quantity that matters for engine-out is the asymmetric thrust carried as a fraction of weight, which for $N_e$ equal engines with one failed is

\[\frac{\Delta T}{W} = \frac{T}{W} \cdot \frac{1}{N_e} \tag{30}\]

Evaluating for the two models and for the full-scale trijet,

\[\left(\frac{\Delta T}{W}\right)_{B} = \frac{0.3086}{3} = 0.10286, \qquad \left(\frac{\Delta T}{W}\right)_{C} = \frac{0.3560}{2} = 0.17800 \tag{31}\] \[\left(\frac{\Delta T}{W}\right)_{\text{full}} = \frac{0.2245}{3} = 0.07485 \tag{32}\]

against which the two aeroplanes stand at

\[\frac{0.10286}{0.07485} = 1.374, \qquad \frac{0.17800}{0.07485} = 2.378, \qquad \frac{0.17800}{0.10286} = 1.731 \tag{33}\]

An engine-out yaw moment is a thrust asymmetry, so a model with 37 percent more thrust to weight produces a proportionally larger upset than the full-scale aeroplane would at the same flight condition. Engine-out control was a stated flight-test objective, specified at low speed, in the takeoff configuration and at minimum operating empty weight with an outboard engine failed [Risch et al. 2009]. In the first 39 flights it was evaluated at a benign condition, each engine in turn reduced to idle, and found satisfactory [Risch et al. 2009]. So the specified test is harder than the aeroplane will face, and a pass is conservative. The X-48C’s engine-out case is harder still, at 2.378 times the full-scale upset, because losing one engine of two removes half the thrust where losing one of three removes a third, and the C model’s thrust to weight is higher as well. This tilt errs on the comfortable side, the opposite of the tilt found in X-Planes: Lockheed Martin X-35.

The Two Aircraft

	X-48B	X-48C
First flight	20 July 2007	7 August 2012
Last flight	2010	9 April 2013
Flights	92	30
Span	20.4 ft	just over 20 ft
Gross weight	523 to 525 lb	about 500 lb
Engines	3 turbojets, 54 lbf installed each	2 turbojets, 89 lbf each, planned at 75
Thrust to weight	0.309	0.356
Vertical surfaces	winglets with rudders at the tips	twin tails moved inboard
Aft body	as designed	extended about 2 ft
Maximum speed	118 kt	about 140 mph
Ceiling	10,000 ft	10,000 ft
Endurance	30 to 40 min, 13 gal fuel	about 30 min

The figures in the table are from the fact sheet, the flight-test papers, the correlation update and the programme’s announcements [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090] [Risch et al. 2009] [Regan 2008] [Vicroy 2011] [X-48 Research, All Good Things Must Come to an End, NASA] [Boeing flies X-48C blended wing body research aircraft] [X-48 Blended Wing Body, GlobalSecurity]. The sources disagree about the C model’s engines and the disagreement is load-bearing. NASA’s fact sheet gives two engines of 89 pounds thrust, while the programme’s 2011 presentation gives two of 75 as planned [Vicroy 2011] [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090]. The later figure is more likely to describe what was fitted and the earlier to describe what was planned, and this article uses 89 while reporting both, because the engine-out arithmetic of the scaling section above depends on which is right. At 75 pounds the thrust to weight falls from 0.356 to 0.300 and the engine-out factor from 2.378 to 2.004, which moves the size of the conclusion and not its direction.

The C model was a noise aeroplane and its modifications were acoustic in intent. The winglets were relocated inboard next to the engine exhaust ducts, becoming twin vertical tails, and the aft deck was extended about two feet rearward, both to shield engine noise from the ground [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090] [Boeing flies X-48C blended wing body research aircraft]. The low-noise configuration descends from NASA’s Environmentally Responsible Aviation studies of aircraft two decades ahead [The Environmentally Responsible Aviation project, a technology development project].

Two of those changes work against the axis the programme had already named as weakest. Moving a vertical surface inboard on a swept planform moves it forward, shortening its moment arm about the centre of gravity, and the aft-deck extension recovers part of that arm rather than adding to it. Separately, the C model has two engines where the B model had three. NASA reports that the handling qualities of the C model differed from the B model and that new flight control limiters were written for it, the clearest published statement that the noise modification was not free [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090].

The X-48C Made the Weak Axis Weaker

The programme’s own stated hypothesis was that yaw control is poor throughout the flight envelope [Risch et al. 2009]. The noise modification then acted on that axis twice, in the same direction, and neither action was intended to. [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090]

The first is the engine count. The asymmetric thrust fraction computed above rises from 0.10286 to 0.17800, a factor of 1.731 against the B model.

The second is the moment arm. Directional authority from a vertical surface scales with the tail volume coefficient,

\[V_v = \frac{S_v \, l_v}{S \, b} \tag{34}\]

in which $l_v$ is the distance from the centre of gravity to the surface’s aerodynamic centre. On a swept planform, moving a surface inboard moves it forward, because the structure it attaches to sweeps aft with span,

\[\Delta l_v = \Delta y \, \tan \Lambda \tag{35}\]

The sweep angle of the X-48’s outer trailing edge is not published in any source consulted, so the shift appears here only as a sensitivity. Taking the winglets from the tip at $y = 10.2$ ft to a station near the exhaust ducts at roughly 2.5 ft, so $\Delta y = 7.7$ ft,

Assumed sweep	Forward shift	Net after the 2 ft aft-deck extension
30 degrees	4.45 ft	2.45 ft
35 degrees	5.39 ft	3.39 ft
40 degrees	6.46 ft	4.46 ft

The aft deck was extended about two feet rearward, which acts in the recovering direction [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090]. Against a tail arm of order ten feet on a twenty-foot aeroplane, a net loss of two to four feet is a reduction in $V_v$ of roughly a quarter to nearly a half, before any account is taken of the change in surface area or of the interference between a tail and an exhaust plume.

Both effects push the same way on the axis already named as weakest, and NASA records the consequence. The project team wrote flight control system modifications for the C model, including limiters to keep it inside a safe envelope, because its handling qualities differed from the B model’s [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090]. The arithmetic above is one reading of why.

Dependent Systems

Control Allocation Across Twenty Surfaces

The X-48B carries twenty individually actuated control surfaces along the trailing edge of the wing and the winglets, and those twenty provide all of its control power [Risch et al. 2009]. There is no horizontal tail, and the rudders sit on the winglets at the tips [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090]. Pitch, roll and yaw are produced by blending surfaces that each contribute to more than one axis, and the outboard elevons split into drag rudders for yaw in the manner of the B-2 [Liebeck 2004] [Northrop Grumman B-2 Spirit].

The test plan listed an assessment of the dynamic interaction of all twenty surfaces among its objectives [Risch et al. 2009], an unusual thing to have to schedule and a direct consequence of the configuration.

The Leading Edge, Flown Both Ways

Leading-edge slats were fitted to increase maximum lift for takeoff and landing, and the flight programme tested two leading-edge configurations, slats extended and slats retracted, bolted in place before each flight and interchangeable between flights [Risch et al. 2009] [Regan 2008]. By bracketing the leading edge, the programme hedged where the scaling is weakest, whether or not it was framed that way at the time.

The Ground Station

The aeroplane was flown from a ground control station using conventional stick, rudder and throttle, inside an irregular working area on the north side of Edwards Air Force Base whose longest straight dimension is about 5.5 nautical miles [Risch et al. 2009]. An aeroplane whose motions run 3.430 times fast, inside 5.5 nautical miles, is a demanding piloting task before any aerodynamics are considered.

The Flight Test Record

The programme flew 122 times, 92 as the X-48B and 30 as the X-48C [X-48 Research, All Good Things Must Come to an End, NASA]. The first 39 flights, from July 2007 to December 2008, which the progress paper describes as the first two phases of a planned three-phase programme, are documented in detail and are the basis for what follows [Risch et al. 2009].

Testing proceeded in blocks. Envelope expansion came first, then parameter identification, stalls and engine-out work. Three weight configurations were flown, with empty weights of about 395, 405 and 430 pounds, and three centre-of-gravity positions separated by four inches of mean aerodynamic chord. Typical flights lasted 30 to 35 minutes and were limited by a 13-gallon fuel capacity [Risch et al. 2009]. By the end of August 2009 the aeroplane had flown 58 flights, and the initial envelope expansion had reached 23 degrees angle of attack and 20 degrees of sideslip [Taylor 2009].

The approach to the limit of controlled flight was made in one-degree increments of angle of attack, descending at idle thrust, which the team judged the lowest-risk condition for probing uncontrollable flight. At each increment the pilot evaluated controllability in all three axes and performed a pitch-over recovery [Risch et al. 2009].

The flight programme did not stop at 39 flights and the fuller picture is better. The correlation update calls the six-block campaign to flight 80 its Phase I, the same six blocks the progress paper had divided into three phases, alternating slats extended and slats retracted and ending in departure limiter assaults [Risch et al. 2009]. Its summary of the phase reports the aeroplane as extremely manoeuvrable in roll, closely matching simulation for up-and-away flight and landing, and the flight control design as very robust [Vicroy 2011].

The stall results carry angles, and the difference between the two leading-edge configurations is large.

\[\alpha_{\text{stall}}^{\text{slats out}} = 24^\circ, \qquad \alpha_{\text{stall}}^{\text{slats in}} = 14^\circ, \qquad \Delta\alpha = 10^\circ \tag{36}\]

Slats extended, the aeroplane stalled successfully to 24 degrees and remained controllable three degrees beyond the angle of maximum lift. Slats retracted, it reached 14 degrees [Vicroy 2011]. Ten degrees is not a refinement. It gives the clearest available measure of how much the leading edge governs this configuration’s behaviour, which matters because the leading edge is where the Reynolds sensitivity lives.

The departure limiter assaults were, in the programme’s own words, highly successful [Vicroy 2011].

What they found earlier is still the article’s most quoted fact. Just below the predicted stall angle of attack the aeroplane became difficult to hold steady because of a sustained pitch bobble. At a limiting angle of attack the bobble subsided and the aeroplane departed in uncommanded wing roll-offs. The limiting angle was reached six times across three flights with three separate pilots in the slats-extended configuration, and twice with slats retracted. Every pitch-over recovery succeeded. One pilot described holding the aeroplane near the limit as attempting to balance it on the head of a pin [Risch et al. 2009].

One detail matters more than the rest. When a pilot attempted to counter the roll-off with lateral stick, the input slightly delayed the roll-off and then produced a more abrupt wing drop [Risch et al. 2009].

Comparison With Ground Prediction

The flight programme was flown against a body of prediction, and the record shows where the two met and where they did not. Before flight there were the design paper’s account of how the configuration should stall, the simulation, and a ground-test campaign of free-flight, rotary, forced-oscillation and high-Reynolds tunnel tests. Where the comparison closed, the programme says so. Its phase summary reports the aeroplane closely matching simulation for up-and-away flight and landing [Vicroy 2011], and the sustained pitch bobble appeared just below the predicted stall angle of attack [Risch et al. 2009], both as set out in the flight test record above. The subsections below take the design intent for the stall, the instrument that answered the Reynolds question, and the comparisons that were poor or never made.

The Flight Result and the Design Intent Disagree

Liebeck’s published account of the configuration states that separation is initiated in the kink region between the outboard wing and the centrebody, that the outer wing flow remains attached and provides lateral control into the stall regime, and that this is the ideal spanwise location for the stall to begin because the ailerons remain effective and pitch-up is avoided [Liebeck 2004].

The X-48B found uncommanded wing roll-off, and found that lateral control made it worse. [Risch et al. 2009] Those two statements are not compatible. The design intent is that the outboard wing keeps flying and the pilot keeps roll authority [Liebeck 2004]. The flight result is that the aeroplane rolls off uncommanded and that using roll authority sharpens the departure.

The Scale Factor Permits That Disagreement and Cannot Settle It

Separation onset and its spanwise progression are Reynolds-dependent phenomena. At a Reynolds number 1/40.35 of the full-scale value, the model’s separation may begin at a different station on the span and at a different angle of attack than the aeroplane’s. The disagreement between design intent and flight observation is therefore of the kind the scale factor permits, and further flying of the model cannot resolve it.

The limitation applies to the flight vehicle and not to the programme, and the rest of this section turns on that distinction.

The Programme Answered the Reynolds Question With a Different Instrument

The flight vehicle was never asked to carry the Reynolds-governed half alone.

The correlation update plots the ground-test campaign on axes of vehicle scale against chord Reynolds number, and the tests spread across it below the full-scale region of interest that the plot marks [Vicroy 2011]. Free-flight, forced-oscillation, rotary, large-angle and free spin and tumble tests sit at small scale and low Reynolds number. Static aerodynamic tests, the Arnold Engineering Development Center 16T tunnel and the National Transonic Facility sit at higher Reynolds numbers, the last reaching about 70 million against a region of interest that begins above about 90 million [Vicroy 2011]. The X-48B flight test occupies one point on that plane.

Dynamic fidelity and Reynolds number came from different instruments, and the programme ran both. A pressurised cryogenic tunnel buys Reynolds number and cannot fly. A free-flight model flies and cannot reach that Reynolds number. Neither substitutes for the other, and the correlation exercise joins them.

The verdict recorded on the free-flight method is favourable. The update reports that the free-flight test method provided good correlation with the observed one-g flight test limits [Vicroy 2011]. A subscale free-flight model, judged against the larger flight vehicle of the same configuration, predicted the limits well, a narrower and better-supported claim than the one usually made for the X-48, and one the record contains.

The Poor Comparison Was Somewhere Else Entirely

Asked where the ground-to-flight comparisons were poor, the programme does not name the stall. It names the pitching moment, with a cause unrelated to scaling, and an engine model that early analysis showed needed improving [Vicroy 2011].

The magnitude of the support interference effect on pitching moment was much larger than anticipated [Vicroy 2011]. The same configuration measured on a three-inch post with a pitch link and on a 1.2-inch bent sting in the Langley 14 by 22 foot tunnel gave materially different pitching-moment curves. The defect lies in how the model was held, not in how it was scaled, and on a tailless aeroplane trimmed by its own trailing edge the pitching moment is the quantity least able to absorb an error.

A second lesson is administrative, and the programme states it without qualification. Ground-to-flight correlation is difficult without a central repository of wind tunnel, flight, computational and simulation data [Vicroy 2011]. The finding concerns data management rather than aerodynamics, and only a programme running seven kinds of test on one configuration is in a position to reach a conclusion of that kind.

The programme also names what it could not compare. Transonic behaviour, held only in the National Transonic Facility and 16T data, and post-departure modes such as the falling leaf, the spin and the tumble, held only in large-angle, rotary and free spin and tumble data. Neither has a flight comparison at all [Vicroy 2011], and that absence is the precise form of the concern this article raises.

What the Data Changed

The comparisons changed the reading of the result and left the result itself alone. The flights and their recoveries stand as reported. What moves is how far each finding can be carried from a 20.4-foot aeroplane to a 240-foot one, and the dimensionless group that governs each finding settles it, as the scaling derivation established.

What Transfers and What Does Not

The division is clean and it follows from which group is matched.

Froude-governed and transferable. The character of the departure as a motion, the number of cycles it takes to develop, whether a pitch-over recovery works, the control law’s ability to hold the aeroplane, and the handling qualities of the whole low-speed envelope. These are dynamics, and the model was built to reproduce dynamics. The programme’s claim to have proved low-speed controllability throughout the envelope rests here and is sound [X-48 Research, All Good Things Must Come to an End, NASA].

Reynolds-governed and not transferable without further argument. The angle of attack at which the roll-off begins, the spanwise station at which separation starts, the maximum lift coefficient, and whether the slat is required. These are the properties of a boundary layer [Schlichting and Gersten, Boundary layer theory], and a model at 1/40.35 of the aeroplane’s Reynolds number is not evidence about them. That maximum lift rises with Reynolds number over this range is a standard result [Hoerner and Borst, Fluid-dynamic lift].

The objective list asks for both. One objective is to determine, via flight manoeuvres and dynamic-scaling relationships, the full-scale low-speed flight characteristics and departure onset boundaries [Risch et al. 2009]. The first transfers from the flight vehicle alone and the second does not, and the scale factor’s entire content lies in the difference between them.

The programme did not confuse the two and its test campaign is the evidence. The criticism that survives is narrower and is about repetition rather than about method. The flight vehicle alone is easily read as having proved the configuration’s low-speed behaviour, when what it proved is the dynamic half, and the Reynolds half was pursued separately in higher-Reynolds tunnels that approached the full-scale value without reaching it [Vicroy 2011]. A short account of the X-48 tends to lose that distinction, and the distinction decides what the result means.

What the X-48 Validated

The X-48 validated a control system and a recovery technique for a configuration, on an aeroplane whose departure boundary is its own rather than the full-scale vehicle’s. The flight vehicle is usually credited with more, but this smaller claim is the more defensible one, and the programme as a whole claims more than the flight vehicle does, correctly, because it ran the tunnels that the aeroplane could not be.

What remained unknown in 2000 was whether a control system could keep a large tailless transport inside its envelope and recover it from the edge. The flight vehicle answered that, and answered it at a scale where the recovery had to run three and a half times quicker than on the aeroplane. The result is durable and does not need the departure boundary to be true.

The Contemporary Literature

Cluster	Records
Aerodynamics of the configuration	1,174
Blended and hybrid wing body configurations	636
Stall, departure and the uncommanded roll-off	541
Reynolds number, scale effect and the transfer to full scale	523
Flight control law design and envelope protection	500
Aircraft noise, shielding and the quiet configuration	462
Tailless stability and control, and directional authority	397
Transport aircraft design, sizing and fuel efficiency	314
Parameter identification and flight test technique	309
Propulsion, airframe integration and installed performance	288
High-lift devices, slats and separation control	213
Remotely piloted operation and the ground station	207
Control allocation and redundant control effectors	193
Dynamic scaling, similitude and what a subscale model can answer	189
Structures, materials and the airframe	174
Rotorcraft, V/STOL and powered lift	86
Aeroelasticity, flutter and flight vibration	82
Flight test instrumentation, air data and test data processing	69
Flight test programmes, organisations and their history	61
The atmosphere and the flight condition	60
Flight mechanics and aircraft performance	57
Unconventional wings, joined, oblique, swept forward, morphing and flexible	44
Flight simulation and simulators	43
Total	6,622

Aerodynamics of the configuration

The flow the vehicle lives in. Lift, drag, vortex behaviour, boundary layers, computation, wind tunnel technique and the effect of ice on the wing. The X-48’s aerodynamic question is a low-speed one, which is unusual in this series, because the cruise case was never in doubt and the approach and the stall were.

1,174 records. 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McDevitt 1964] [Leylek et al. 2010] [Lhopiteau et al. 2025] [Li 1965] [Li and Leschziner 2007] [Li and Polak 1966] [Li et al. 2000b] [Li et al. 2024d] [Lian and Shyy 2005] [Lifshitz et al. 1996] [Liguore and Pitt 2004] [Lijewski 1978] [Lin and Wang 1993] [Lin et al. 1997] [Lindqvist et al. 2001] [Liu 2022] [Liu et al. 2009c] [Liu et al. 2016a] [Livingston 1965] [Lizak 1960] [Lo 1970] [Lo 1972] [Lo 1988] [Lo and Glassman 1975] [Lo and Oliver 1970] [Lo and Ulbrich 1991] [Lock 1963] [Lockheed-California Co Burbank 1964] [Lombardi 1995] [Lombardi and Morelli 1994] [Lombardi et al. 1996] [Lombardi et al. 1997] [Lorber et al. 2018] [Lori et al. 2007] [Losada Costoso et al. 2024] [Lovell 1999] [Lowry et al. 2001] [Loya et al. 2020] [Luce 1949] [Luchuk et al. 1982] [Luckring 1979] [Luckring 2004] [Luckring 2015] [Lund 2000] [Lupo et al. 1998] [Lv et al. 2022] [Ma et al. 2015] [Ma et al. 2016] [MacCormack 2007] [Macha and Buffington 1989] [Mack 1952] [Mack et al. 2009] [Mack 1999] [MacMaster 2016] [Macwilkinson et al. 1974] [Madsen et al. 2003] [Maeder and Hall 1955] [Magness et al. 1989] [Makino et al. 2003] [Malfa et al. 1991] [Malmuth 1984] [Malmuth and Cole 1984] [Malone and Sankar 1985] [Maniet 2001] [Manor and Wentz 1985] [Manuilovich 2021] [Marcum 2000] [Mark and Dehart 1976] [Martin 2008] [Martin et al. 1976] [Martin et al. 2008] [Martin et al. 1993] [Martinz et al. 1997] [Maryland Univ College Park 1962] [Maseland et al. 2006] [Maslov et al. 2008] [Matalanis et al. 2011] [Mateescu 1986] [Matheny and Panageas 1981] [Matheson 1987] [Maxworthy and Cheng 1989] [May and Vatistas 2006] [McClinton et al. 1998] [McCormick 1956] [McDowell and Williamson 1982] [McInville and Moore 1994] [McNally and Bach 1988] [Measurements of Discrete Vortex 1976] [Medved and Elfstrom 1986] [Merz 1968] [Methel et al. 2022] [Methods for Drag Determination 2003] [Metkowski and Maughmer 2021] [Meznarsic 1986] [Meznarsic and Gross 1980] [Mialon et al. 2010] [Mickle et al. 2012] [Mignosi et al. 1986] [Mikhail and Rainbird 1978] [Miles 1948] [Miller 1976] [Miller 1992] [Miller and Wood 1983] [Miller et al. 2022] [Moellmann and O’Connor 1967] [Mohamed et al. 2021a] [Mokry 1972] [Mokry 1989] [Mokry 2001] [Mokry and Khalid 2000] [Molyneux 1972] [Moore and Frei 1983] [Moore and Inville 1995] [Moore et al. 1993] [Morelli and Klein 1995] [Morelli and DeLoach 2003] [Morgan and Caster 1965] [Mori et al. 2024] [Morino et al. 1989] [Popov et al. 2010] [Morse 1956] [Mort et al. 1986] [Moul and Taylor 1980] [Murali et al. 2024] [Murawski 1999] [Murillo and McMasters 1983] [Murman 1979] [Murman 1982] [Murphy and Klein 2003] [Murphy and Schmidt 1953] [Murphy et al. 2004] [Murphy et al. 2016] [Murphy and Klein 2011] [Murri et al. 1984] [Murthy and Wedemeyer 1990] [Myatt and Blake 1999] [Nafroni et al. 2023] [Nagel and Thomas 1965] [Nakamura et al. 1993] [Nambu et al. 2012] [Nangia et al. 2003] [NASA Wake Vortex Research 1993] [Nastase 2008] [Naval Ordnance Systems Command Washington DC 1957] [Nazeer et al. 2021] [Neal 1970] [Nelson 1974] [Nesterov 1963] [Neville and Stephens 1993] [Newman et al. 1982] [Newman et al. 2014] [Nguyen and Urnes 2012] [Ni et al. 2024] [Nicolaides 1952] [Nicolaides 1971] [Nicolaides et al. 1967] [Nicolosi et al. 2015] [Niedling 1980] [Nietubicz 1975] [Nikolic 2005] [Nixon and Farshchi 1987] [Noise Radiation from Turbulent 1976] [Nonweiler 1955] [Norris et al. 1989] [Null and Shkarayev 2005] [Nyberg and Sorensen 1980] [O’Donnell and Mohseni 2018] [Obara and Lamar 2009] [Obayashi et al. 1993] [Obayashi et al. 1995] [Ocokoljić et al. 2017] [Olejnik et al. 2021] [Olsen 1965] [Olsen 1966] [Olwi and Ghazi 1991] [Ongarato 1968] [Orlik-Ruckemann 1983] [Oruganti and Narsipur 2020] [Othman and Kanazaki 2015] [Oudheusden et al. 2004] [Ozger 2007] [Paglino and Beno 1971] [Pagliuca and Timme 2016] [Palko and Crawford 1982] [Palko and Lohr 1978] [Pallister et al. 1992] [Pamadi et al. 2000] [Panagiotou et al. 2015] [Pandya and Aftosmis 2001] [Pankhurst 1958] [Park and Rokhsaz 2003] [Park et al. 2021] [Parkinson 1986] [Pate 1980] [Patil and Navrátil 2024] [Patterson 1967] [Paul] [Payne and Henry E. 1961] [Peake] [Peigin and Epstein 2007] [Peitzman 1978] [Peng et al. 2024] [Perkins et al. 1977] [Pershing 1986] [Persoon et al. 1980] [Pesch and Hess 2019] [Petoshin and Chasovnikov 2011] [Petrov 1993] [Pettit et al. 1994] [Petty 1975] [Pfaff 1965] [Pfeiffer and King 2012] [Pfnür and Breitsamter 2019] [Phillips and Waggoner 1988] [Phillips et al. 1970] [Phythian 1966] [Piat and Estève 2002] [Pindzola and Chew 1960] [Pindzola and Lo 1969] [Pindzola and Mozer 1956] [Platou 1968] [Polhamus 1983] [Poll 1986] [Poole and Cromack 1970] [Popov et al. 2009] [Potapczuk and Bidwell 1990] [Pounds 1972] [Pounds and Walker 1980] [Prasannakumar et al. 2024] [Presas et al. 2024] [Prizirembel and Wen 1978] [Putman et al. 1977] [Qin 2012] [Quanwei and Qiongkang 1989] [Quast et al. 1990] [Quick 1937] [Quitter et al. 2021] [Radespiel 1989] [Rae 1967] [Rae and Shojiro 1977] [Rahmani et al. 2022] [Rakshith et al. 2015] [Rambacher and Bons 2023] [Rambacher et al. 2024] [Rao et al. 2023] [Rasuo 2000] [Rathert et al. 1949] [Ratvasky et al. 2003] [Razgonyaev and Mason 1995] [Redd et al. 1979] [Reed and Saric 2001] [Reichenbach et al. 2011] [Reimer et al] [Reubush 1978] [Reubush 1979] [Revell et al. 1975] [Reynolds 1963] [Reynolds 1995] [Rich 1973] [Richardson 1976] [Rife et al. 1992] [Rill and Ganzer 1988] [Rinehart 1970] [Ringenbach 1989] [Rinoie et al. 2004] [Risse et al. 2014] [Rist 1994] [Rittenhouse 1959] [Rizk and Lovell 1986] [Rizk et al. 1988] [Robins and Delisi 1989] [Rock et al. 1999] [Rodgers 1963] [Roger et al. 2023] [Rogers 1966] [Rogers 2013] [Rom 1992b] [Rooney et al. 1977] [Rose et al. 1982] [Roskam et al. 1980] [Ross et al. 1987] [Rossow 2001] [Rowley 2008] [Roy and Mukherjee 2020a] [Rubio and Ballard 1967] [Rudenko and Ryzhkova 1968] [Rueger and Crites 1992] [Rumsey and Lee-Rausch 2015] [Runyan and George-Falvy 1979] [Ruo and Sankar 1988] [Ruyten 1999] [Ruyten 2004] [Srinivasan et al. 2020] [Saadeh et al. 2026] [Sabatino et al. 2023] [Sacks et al. 1963] [Sakakibara et al. 2021] [Din et al. 2018] [Saltzman and Ayers 1981] [Saltzman and Ayers 1982] [Saltzman et al. 1999] [Santos and Mattos 2009] [Santos et al. 2026] [Saric 1989] [Saric 2010] [Sarkar and Panneerselvam 1998] [Sarkar et al. 2000] [Sarkar et al. 2009] [Sarkar et al. 2011] [Sarohia and Massier 1978] [Satran et al. 1985] [Savin 2017] [Savin 2019] [Schmit 2012] [Schmitt et al. 1983] [Schneider and Collicott 1997] [Schuelein 2008] [Schuman 2018] [Schwartz et al. 2024] [Schweikhard 1966] [Schütte and Hummel 2025] [Scott et al. 2015] [Secco and Martins 2018] [Segall and Gajdjis 1991] [Seiff 1954] [Seiff and Sandahl 1951] [Seraj and Martins 2023] [Serovy et al. 1979] [Serpieri and Kotsonis 2015] [Shahid 2025] [Shan et al. 2011] [Shang 2007] [Shankar and Malmuth 1982] [Shantz 1953] [Sheporaitis 1972] [Sheridan 1978] [Shih and Ding 1996a] [Shirley et al. 2014] [Shizawa et al. 1996] [Signor and Borst 1986] [Silva et al. 2006] [Sim 1976] [Sims and Carter 1981] [Simulation by Vortex Rings 1976] [Sinacori and Lange 1961] [Sinha 2007] [Sirbaugh 1983] [Slotnick 2014] [Smeltzer et al. 1983] [Smith 1949] [Smith 1953] [Smith 1974] [Smith 1989] [Smith and Parsons 1970] [Smith and Shaw 1975] [Snyder and Erickson 1984] [Sobieczky 1998] [Song and Lv 2011] [Song et al. 1995] [Sowyrda 1961] [Spadão et al. 2026] [Spaid 1987] [Spaid 1990] [Spedding et al. 2007] [Spillman 1992] [Spurlin and Lueck 1984] [Squire 1975] [Squires and Warmbrodt 1983] [Srivathsan and Rauleder 2023] [Stahara and Spreiter 1979] [Stahara and Spreiter 1980] [Stallings and Hartman 1981] [Stallings and Lamb 1981] [Staples and Nagati 1990] [Stargill 1983] [Stefko and Jeracki 1988] [Stefko et al. 1987] [Steimle et al. 2012] [Steinle et al. 1999] [Stengel 1983] [Stewart 1985] [Stoican et al. 2018] [Stone 1945] [Strand 1972] [Strand and Levinsky 1969] [Stringfield 1984] [Study on the Ground 2022] [Sun et al. 2018] [Sundaram and Wu 1983] [Sutcliffe and Rennie 2016] [Sutton 1982] [Sutton et al. 1982] [Swamy et al. 1978] [Symington 1940] [Szodruch 1991] [Tabatabaei et al. 2021] [Tafti et al. 2014] [Tai 1990] [Tai et al. 2024] [Takahashi et al. 2023] [Tan and Hattori 2026] [Tang et al. 2000] [Tayman and Walden 1998] [Telionis 1990] [Terry 1964] [Tetrault et al. 2000] [Tetrault et al. 2001] [The Airscrew 1983] [The Stability of Two-Phase 1997] [The Swept 2021] [Theodorsen 1960] [Theodorsen and Nomicos 1961] [Thomas 1967] [Thomas and Lan 1991] [Tidbury 1945] [Tijdeman et al. 1979b] [Tijdeman et al. 1979a] [Torii and Matsuzaki 1992] [Tran-Luu and Solomon 2005] [Transonic Flight Test 1994] [Transonic Wind Tunnel Wall 1982] [Traub 2009] [Trimmer and Clark 1963] [Triplet 1983] [Triplett 1984] [Trolinger and O’Hare 1970] [Tsatsas et al. 2025] [Tu 1992b] [Tu 1992a] [Tu 1994] [Tucker 1990] [Tucker and Quinn 1944] [Tuncer and Platzer 1998] [Turner 1982] [Ueki et al. 2020] [Ueno et al. 2004] [Ulbrich 2010] [Ulbrich and Boone 1998] [Ulbrich and Boone 2004] [Ulbrich and Steinle 1994] [Ulbrich et al. 2014] [Ulbrich 1998] [Ustinov 2001] [Vaganov et al. 2018] [Valenti and Yukish 2022] [van Arnhem et al. 2022] [van der Maas 1959] [van Es 2002] [Varner 1986] [Varshney et al. 2020] [Vatsa et al. 1989] [Velasquez] [Velden 1997c] [Venkataraman and Seiler 2016] [Venkataraman and Seiler 2019] [Venkataramanan and Dogan 2004] [Verhaagen 1997] [Verhaegen 1987] [Vermeersch et al. 2015] [Verstynen 1974] [Vicini and Quagliarella 1998] [Visonneau et al. 2015] [Vlachos and Telioinis 2003] [Vocke and Nunez 2016] [Vrabel 1988] [Vrdoljak 2003] [Wadia et al. 1998] [Waggoner 1980] [Wagner 1985] [Wahidi and Troolin 2019] [Waite et al. 2020] [Wakimoto et al. 2021] [Waldmann et al. 2016] [Walker and Berggren 1948] [Wallace 1952] [Wang 1980a] [Wang 2026] [Wang et al. 2007] [Wells et al. 1981] [Wells et al. 1982] [Wentz and Nyenhuis 1984] [Werner 2018] [Werner et al. 2022] [Wey et al. 2012] [Weyburne 2009] [Weyburne 2012a] [Weyburne 2012b] [Whalen and Bragg 2005] [Whitby 1991] [White 1963] [White 1993] [White 2004] [Whittaker and Doolan 2025] [Whittley and Garland 1961] [Wiberg et al. 2014] [Widmayer and Tomassoni 1971] [Willard and Kranzler 1996] [Williams 1965] [Williams 2003] [Willis 1964] [Wilson 1981] [Winchenbach 1997] [Wind Tunnel 2022] [Wind Tunnel Interference 1983] [Wind Tunnel Test Techniques 2024] [Windsor 1970] [Wing Design 2012] [Wing Design Considerations 2021] [Woodward 1968] [Woolard 1974] [Woolf 2012b] [Wooten and Yechout 2008] [Wright 1962] [Wu 1978] [Wu 1986] [Wyborny and Requardt 1974] [Xie et al. 2016] [Xiong et al. 2021] [Xiong et al. 2023] [Xu et al. 2019b] [Xu et al. 2019d] [Yamaguchi et al. 1993] [Yamamoto et al. 2012] [Yanagihara et al. 1999] [Yang and Wu 2016] [Yang et al. 2014] [Yasuaki and Egami 1999] [Ye et al. 2021] [Yen 1978] [Yih et al. 1952] [Yokozeki et al. 2014] [Zannetti and Onofri 1984] [Zartarian 1956] [Zartarian and Hsu 1955] [Zeising and Gerhardt 1993] [Zeng and Kukreja 2013] [Zerihan and Zhang 2000] [Zhang] [Zhang et al. 2000] [Zhang et al. 2011] [Zhang et al. 2023] [Zhang et al. 2024c] [Zhang et al. 2026c] [Zhao 1988] [Zhao 2021] [Zhao 2026a] [Zhao 2026b] [Zhao and Yang 2014] [Zhao et al. 2014] [Zheng and Ramaprian 1993] [Zhou et al. 2022] [Zhou et al. 2025a] [Zhu et al. 2023] [Zhu et al. 2026] [Zierten and Rettie 1977] [Zsoldos and Devenport 1992] [Ćurčić et al. 2016] [Čečrdle et al. 2022]

Blended and hybrid wing body configurations

The configuration itself, and the second largest cluster. Planform definition, centrebody structure, the non-circular pressure vessel, spanload and the trade against the tube and wing. The literature writes the configuration’s name both ways, and of the 636 titles in this cluster 115 hyphenate blended-wing-body or hybrid-wing-body while 253 write it as separate words, so a search of this literature must read a hyphen as a space.

636 records. [Abdullahi et al. 2026] [Abnous et al. 2017b] [Abnous et al. 2017a] [Adamo 2023] [Adegbindin et al. 2016] [Adhikari and Wei 2026] [Adler and Martins 2023] [Олег Львович Лемко and Євген О. Кушніренко 2014] [Ahn et al. 2017] [Ahuja et al. 2025] [Ahuja et al. 2026] [Aleisa et al. 2023] [Ali et al. 2011] [Ali et al. 2012] [Ali et al. 2024] [Ali et al. 2025b] [Ali et al. 2025c] [Ali et al. 2025a] [Alipour et al. 2022] [Almosnino 2016] [Ammar and Trépanier 2014] [Ammar et al. 2017] [Ang and Ng 2026] [Antoniou et al. 2025] [Arntz and Atinault 2015] [Asaro and Vos 2025] [Asaro et al. 2025] [Atmaca et al. 2026] [Aubeelack] [Aubeelack et al. 2023] [Bahl et al. 2020] [Bahr et al. 2014] [Bai et al. 2022] [Bainsla et al. 2021] [Begin 1983] [Berger et al. 2011] [Bertsch et al. 2025] [Bhattarai et al. 2026] [Bishara et al. 2018] [Boeing Flies Blended Wing 2008] [Boeing Phantom Works Leading 2006] [Bolsunovsky et al. 2001] [Bourdin et al. 2007] [Brodsky and Luby 2013] [Brown and Vos 2018] [Buch and George M. 2010] [Buddhamatya et al. 2026] [Burley et al. 2014] [Burnside et al. 2016] [Cai et al. 2013] [Cai et al. 2014] [Cai et al. 2021] [Cameron and Cameron 1997] [Cameron and Princen 2000] [Campos and Marques 2021] [Carlsson 2003] [Carlsson and Kuttenkeuler 2003] [Carter et al. 2009] [Chan 2019] [Chan et al. 2024] [Chao et al. 2017] [Chaplin 1990] [Chen et al. 2019] [Chen et al. 2024a] [Chen et al. 2026b] [Chhabra et al. 2015] [Chung et al. 2024] [Chung et al. 2025] [Clark and Gerhold 1999] [Colas et al. 2018] [Md. Akhtar khan 2016] [Contreras-Torres et al. 2022] [Cook and de Castro 2004] [Cook and Hauser 2018] [Cui et al. 2023] [Cui et al. 2025] [Czech et al. 2012] [Dakka and Johnson 2019] [Danowsky et al. 2017] [Davis et al. 2025] [Dehpanah and Nejat 2015] [Dela Peña 2024] [DeLaurier 2022] [Demourant and Ferreres 2013] [Denieul et al. 2015] [Denieul et al. 2018] [Deslich et al. 2021] [Dickey et al. 2016] [DiMaggio et al. 2022] [Dimopoulos et al. 2019] [Ding et al. 2024] [Dinovitzer et al. 2019] [Diyana Nasri Huang et al. 2018] [Tjahjana et al. 2021] [Donaldson et al. 2011] [Dong et al. 2024a] [Dong et al. 2024c] [Dong et al. 2025] [Doty et al. 2014] [Wells and Olson 2011] [Du Cray et al. 2025] [Durmus 2021] [Durmuş 2025] [Ebrahimi Fakhari et al. 2024] [Ehlers et al. 2011] [Einicke et al. 2025] [Eleghasim et al. 2026] [Experimental Investigation of Synthetic 2023] [Romli et al. 2023] [Felder et al. 2009] [Felder et al. 2012] [Felder et al. 2025] [Feng et al. 2026] [Fernandes and Maldonado 2024] [Fernandes et al. 2025] [Fernando 2018] [Ferrar et al. 2009] [Ferrell et al. 2013] [Firdaus Mohamad et al. 2010] [Flanagan et al. 2020] [Flansburg 2017] [Flow Control and High-Lift 2016] [Arora et al. 2023] [Fremaux et al. 1993] [From Tube and Wing 2013] [Fu et al. 2022] [Fu et al. 2024b] [Fukuda and Takimoto 2014] [Galea et al. 2003] [Gan et al. 2014] [Gang et al. 2019] [Gangoli Rao et al. 2014] [Gao and Smith 2020] [Garcia et al. 2016] [Garmendia et al. 2015] [Garmendia et al. 2016] [Gatlin et al. 2012] [Gatto et al. 2010] [Gauvrit-Ledogar et al. 2018] [Gebbie et al. 2005] [Gebbie et al. 2007] [Geiselhart et al. 2003] [Gern 2013] [Gern 2015] [Gilmore et al. 2002] [Gingerich et al. 2026] [Goldberg et al. 2015] [Goldberg et al. 2017] [Goldthorpe et al. 2010] [Granzeier 2002] [Gray and Zingg 2024] [Gray et al. 2021] [Gregory et al. 2007] [Ground Testing of X-48B 2007] [Gu et al. 2022] [Gu et al. 2023a] [Guan 2013] [Guo and Thomas 2015a] [Guo and Thomas 2015b] [Guo and Thomas 2016] [Guo et al. 2013] [Guo et al. 2014] [Guo et al. 2015] [Guo et al. 2016] [Gupta and Khalid 2025b] [Gupta and Khalid 2025a] [Gupta et al. 2016] [Guruswamy 1991] [Hakim and Choukri 2024] [Hakim et al. 2025] [Hall et al. 1999] [Handa and Srinivas 2022] [Haniš et al. 2013] [Hansen et al. 2007] [Hansmann and Stumpf 2025] [Hansmann and Stumpf 2026] [Hassairi and Abid 2021] [Hawley 1999] [He et al. 2018] [Heath et al. 2013] [Hill et al. 2004] [Hong and Ma 2016] [Hooker 2014] [Howe 2001] [Huang and Wei 2025] [Huang and Zhang 2020] [Huang et al. 2015] [Huber 1995] [Huber 2022] [Huber et al. 2012] [Humphrey et al. 2026] [Humphreys-Jennings et al. 2019] [Humphreys-Jennings et al. 2020] [Hutcheson et al. 2014] [Hutcheson et al. 2016] [Iniguez de Heredia and Friehmelt 2005] [Ishrak et al. 2024] [Islam et al. 2024a] [Ito et al. 2016] [Izadpanahi and Mardanpour 2018] [Izquierdo] [Jackson 2023] [Jackson and Buttrill 2006] [Jagtap et al. 2024] [Jagtap et al. 2025] [Joseph et al] [Jegley et al. 2021] [Jia et al. 2021] [Jiang et al. 2019] [Jiang et al. 2025] [Jianghao et al. 2011] [Jiguang Li et al. 2016] [Johnston 2016] [Joseph et al. 2025] [June et al. 2018] [Jung and Lowenberg 2005] [Jung Hoe and Nik Mohd 2014] [Kale and Pendharkar 2021] [Kania et al. 2025] [Karimi Kelayeh and Djavareshkian 2024] [Karpuk et al. 2020] [Karpuk et al. 2023] [Kashitani et al. 2015] [Katsurayama and Imamura 2015] [Kawai 2011] [Keidel et al. 2019] [Keidel et al. 2020] [Keller 2024] [Kerr 2025] [Khadiv et al. 2025] [khan et al 2019] [Khandelia 2024] [Kim and Liou 2013] [Kim and Oh 2025] [Kim et al. 2025] [Kim and Liou 2012] [Kim et al. 2016] [Kimmel and Bradley 2004] [Kirner et al. 2016] [Kitsios et al. 2020] [Kleemann et al. 2020] [Ko et al. 2003] [Koster et al. 2011] [Kotikalpudi et al. 2018] [Kroo 1990] [Kucera and Hromčík 2013] [Kumar and Khalid 2017] [Kumar et al. 2020a] [Kumar et al. 2020b] [Kumar et al. 2021] [Kumaran et al. 2021] [Kummer et al. 2012] [Kuntawala et al. 2011] [Kuntjoro et al. 2015] [La Rocca et al. 2002] [Laban et al. 2002] [Lampropoulos et al. 2025] [Larkin and Coates 2017] [Latif et al. 2017] [Lee et al. 2008] [Lee et al. 2018] [Legriffon et al. 2023] [Leifsson et al. 2013] [Lesalli and Cahyono 2020] [Li 2015] [Li 2024] [Li and Cai 2026] [Li and Guo 2013] [Li and Qin 2020] [Li et al. 2017b] [Li et al. 2018b] [Li et al. 2023c] [Li et al. 2023a] [Li et al. 2026a] [Lian and Wu 2018] [Liang et al. 2016] [Liebeck 2003] [Liebeck 2008] [Liebeck et al. 1998] [Liebeck 2004] [Liebeck et al. 1996] [Liersch and Bishop 2018] [Lin et al. 2008] [Liou and Lee 2010] [Liou et al. 2016] [Liou et al. 2017] [Liou et al. 2019] [Liu and Whidborne 2021] [Liu and Zhang 2022] [Liu et al. 2012] [Liu et al. 2019a] [Liu et al. 2025a] [Liu et al. 2026a] [Loechert et al. 2018] [Lord et al. 2016] [Loughban 2020] [Love and Kapania 2020] [Lovejoy 2006] [Lu et al. 2012] [Lucky Bose et al. 2024] [Luu 2025] [Moe and Pyone 2019] [Lyu and Martins 2013] [Lyu and Martins 2014] [Lyu et al. 2024] [Ahmad et 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Stall, departure and the uncommanded roll-off

The subject of the article’s central finding. Maximum lift, separation onset, wing drop, departure boundaries and recovery. This is the cluster the scaling argument bears on, since separation onset is the phenomenon a Froude-scaled model reproduces least faithfully and the one this aeroplane was built to find.

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Reynolds number, scale effect and the transfer to full scale

The half of similitude that a free-flight model gives up. Scale effect on maximum lift, tunnel-to-flight correlation and extrapolation to full scale. Nine of these records match this survey’s subject terms only when a hyphen in the title is read as a space, among them a paper on correcting wind-tunnel pressure coefficients for Reynolds number effect.

523 records. [Abraham 1970] [Adrian and Balachandar 2001] [Agrawal et al. 2024] [Ahlefeldt 2017] [Ahmad and Li 2022] [Airil] [Alexander and Griffin 1974] [Alexander et al. 1973] [Algozino et al. 2015] [Alhosseinihamedani et al. 2019] [Amin and Das 2013] [Anyoji et al. 2010] [Aono et al. 2018] [Ariff et al. 2015] [Arko and McQuilling 2012] [Asada and Kawai 2018] [Atef and Baz 2023] [Athkuri and Nived 2026] [Author 1980] [Ayers 1982] [Ayok 2026] [Baker and Squire 1982] [Balla and Vad 2022] [Balzer and Fasel 2010] [Bandyopadhyay and Gad-el-Hak 1994] [Barnaud et al. 2019] [Batther and Lee 2022] [Becht and Knight 1995] [Beckwith 1974] [Bennington and Simpson 2004] [Benton and Visbal 2017] [Benton and Visbal 2018a] [Benton and Visbal 2019] [Bertelrud 1998] [Bertelrud et al] [Beyers 1983] [Bigdeli and Monfared 2020] [Bodavula et al. 2019] [Bohl and Hrynuk 2024] [Boschetti et al. 2004] [Boughou et al. 2023] [Bounecer and Bahi 2018] [Boutilier and Yarusevych 2012] [Brasseur 1994] [Braud et al. 2024] [Brehm et al. 2008] [Brendel and Mueller 1987a] [Brendel and Mueller 1987b] [Brion et al. 2006] [Broeren et al. 2017] [Brunner et al. 2021] [Bucci et al. 1997] [Coupier and Salez 2023] [Burt and Uselton 1974] [Bushnell 1998] [Bushnell and Greene 1991] [Busquet] [Carreno Ruiz and D’Ambrosio 2023] [Carter et al. 2008] [Cebeci 1995] [Cebeci and McLlvaine 1989] [Cecchini et al. 2026] [Chacin and Cantwell 2000] [Chamberlin and Blaha 1973] [Chandra et al. 2024] [Chandrasekhara et al. 1996] [Chen et al. 2020] [Chien 1980] [Chien 1982] [Choudhuri and Knight 1995] [Choudhuri and Knight 1996] [Ciobaca and Dandois 2017] [Rohit et al. 2020] [Conigliaro 1983] [Corlett et al. 1980] [Cuvier et al. 2014] [Darbandi et al. 2006] [Davis 1968] [De Crombrugghe] [Della Rocca et al. 2008] [Demoret et al. 2020] [Deriat and Guiraud 1987] [Desabrais and Johari 1999] [Determination of the Reynolds 2012] [Djenidi and Antonia 1993] [Doerffer and Dallmann 1989] [Dong et al. 2019b] [Donovan and Selig 1989] [Donovan et al. 2022] [Dougherty 1975] [Dougherty and Fisher 1980] [Drag Scale 2020] [Dróżdż and Elsner 2016] [Dróżdż et al. 2021] [Duan et al. 2020] [Dufau et al. 2023] [Dwyer 1983] [Dyke 1971] [Effect of Sting Plunging 1978] [Zhou et al. 2024] [Ekaterinaris et al. 1994] [Eldridge-Allegra et al. 2023] [Elfeky et al. 2024] [Ellsworth and Mueller 1989] [Elsaadawy and Britcher 2000] [Elsaadawy and Britcher 2004] [Elsayed et al. 2022] [Emmerson and Verstraete 2020] [Esabat et al. 2025] [Evangelista et al. 1987] [Evangelista et al. 1989] [Fan et al. 1993] [Fan et al. 2019] [Fehrs and Helm 2025] [Fiore et al. 2025] [Fleming and Simpson 1994] [Fleming et al. 1995] [Foch and Toot 1989] [Fujita et al. 1988] [Fukushima et al. 2015] [Fukushima et al. 2020] [Furlong and Fitzpatrick 1950] [Furlong and Fitzpatrick 1947] [Gao 2022] [Gao et al. 2025b] [Gargano et al. 2011] [Gatto 2009] [Ghate et al. 2026] [Ghia and Ghia 1997] [Gibson 2002] [Gloss and Sewall 1983] [Goodyer and Kilgore 1972] [Goodyer and Kilgore 1973] [Gopal et al. 2026] [Gopalakrishnan and Tafti 2009] [Gopalarothnam and McGowan 2008] [Gowree et al. 2023] [Grager et al. 2011] [Grager et al. 2012] [Gross and Fasel 2011] [Gross and Fasel 2013] [Große and Schröder 2009] [Guerreiro and Sousa 2012] [Gupta and Ansell 2018] [Gupta et al. 2025] [GÜLer et al. 2021] [Hall and Kern 1996] [Hall and Mohseni 2007] [Hammer and Shumway 2026] [Hanus et al. 1991] [Hardy 1972] [Haucke and Nitsche 2013] [Hauser et al. 2011] [Hayes et al. 1999] [Hendrickson and Agarwal 2020] [Hess and James 1975] [High Reynolds Number Flows 1992] [Hillewaert et al. 2014] [Holdo 1993] [Holze et al. 2002] [Honarmand et al. 2019] [Hou et al. 2026a] [Howard and Kindelspire 1990] [Hoxey et al. 1997] [Hsiao 1988] [Hu and Yang 2008] [Huang et al. 2020b] [Hutchings and Hall 2021a] [Hutchings and Hall 2020] [Hutchings and Hall 2021b] [Imamura and Tamaki 2020] [Inger 1989] [Islam et al. 2009] [Islam et al. 2024b] [Ito 2009] [Ito et al. 2018] [Itsariyapinyo and Sharma 2016] [Jackson et al. 1982] [Nissen and Gadeberg 1944] [Jansen and Mueller 1983] [Jardin and Colonius 2018] [Jeon et al. 2024] [Jeyapandian and Mukherjee 2014] [Jones et al. 2017] [Jones et al. 2018] [Ju et al. 2026] [Junnai Zhai and Rebstock] [Kang 2025] [Kang et al. 2015a] [Kasibhotla and Tafti 2015] [Kawai and Asada 2013] [Kawasoe et al. 2015] [Kay et al. 2020] [Keadle and McQuilling 2013] [Kemp and Adcock 1982] [Kerho 2007] [Khan et al. 2017] [Khedr et al. 2021] [Khodadoust and Shmilovich 2007] [Khodadoust and Washburn 2007] [Kilgore 1982] [Kilgore and Dress 1984] [Kilgore et al. 1974] [Kim and Chang 2009] [Kim and Chang 2010] [Kim et al. 2009a] [Kim et al. 2015] [Komurasaki and Kuwahara 2006] [Korst et al. 1994] [Kosgei 2017] [Kosugi and Hashimoto 2004] [Krishnan and Roy 2022] [Kruse et al. 1977] [Kumawat et al. 2025] [Kwon and Park 2005] [Kyeremeh et al. 2023] [Ladson 1988] [Ladson and Hill 1987] [Landman et al. 2022] [Langston et al. 2025a] [Langston et al. 2025b] [Larose and D’Auteuil 2008] [Law 1973] [Lazaro et al. 2007] [Lazaro et al. 2008] [Lee et al. 2003] [Lee et al. 2006] [Lehmkuhl et al. 2020] [Lei et al. 2013] [Lemley and Mullans 1973] [Leuckert et al. 2008] [Leung and Redonnet 2022] [Levin and Shyy 2001] [Lewandowski 1989] [Li and Zhang 2025] [Li et al. 2024e] [Lian and Shyy 2006] [Lian and Shyy 2007] [Liang et al. 2022] [Liebeck 1989] [Liebeck 1992] [Lin and Pauley 1996] [Lin et al. 2014] [Lin and Dominik 1997] [Lindhorst et al. 2015] [Liu 1992] [Liu and Xiao 2020] [Liu et al. 2006b] [Lockwood Taylor 1956] [Loftin and Bursnall 1950] [Loiseau and Szechenyi 1974] [Long et al. 2022] [Lopes Marchiori et al. 2025] [Lopez Lopez et al. 2026] [Lorber and Carta 1987] [Loth and Matthys 1995] [Loving 1966] [Lu et al. 2011] [Luckring and Ghee 2001] [Luh and Mack 1984] [Lutz 2015] [Lávička and Matas 2012] [Ma et al. 2010a] [Madsen 1982] [Mahns and Amitay 2025] [Makino and Nagai 2014] [Makizono et al. 2015] [Malik et al. 2013] [Mangalam and Pfenninger 1984] [Manning and Rouser 2023] [Manning et al. 2025] [Manohar and Ramkissoon 2016] [Mao and Hamdani 2001] [Marchman and Abtahi 1985] [Marchman and Chang 1988] [Marks et al. 2024] [Marongiu and Tognaccini 2010] [Marouf et al. 2020] [Mateer and Bertelrud 1983] [Mathioulakis and Georgantopoulou 2025] [Matsumoto 1994] [Maughmer et al. 2021] [McGhee et al. 1988] [McKinney and Baals 1982] [Kim 2006] [Meckelnborg and Hölling 2026] [Mehrotra and Robinson 1982] [Michelsen and Mueller 1987] [Michna and Rogowski 2022] [Miley 1982] [Milholen et al. 2012] [Miotto et al. 2021] [Mitsudharmadi and Cui 2010] [Mitsuo and Aoki 2018] [Miyaji and Nagasawa 2017] [Miyakawa et al. 1985] [Mohamed et al. 2017] [Mohamed et al. 2021b] [Mokhtar 2005] [Mokry 1974] [Montelpare and Ricci 2004] [Morgado et al. 2016] [Mori et al. 2015] [Morris and Rusak 2013] [Morris et al. 2023] [Morris and Rusak 2022] [Morse and Liburdy 2007] [Mueller 1984] [Mueller and Torres 2001] [Muhlstein et al. 1974] [Mydlarski and Warhaft 1996] [Nagai 2013] [Nagamatsu 1980] [Nagel 1982] [Nagib 2004] [Nangia et al. 2023] [Neuhaus et al. 2020] [Neuwerth et al. 1998] [Neuwerth et al. 1999] [Numata et al. 2013] [Oh and Choi 2018] [Ol 2007] [Ol and Gharib 2001] [Ol et al. 2005] [Ol et al. 2009] [Oo et al. 2020] [Owens and Wahls 2001] [Pacciani et al. 2010] [Pacciani et al. 2012] [Packard and Bons 2011] [Packard and Bons 2012] [Padureanu et al. 2024] [Panton 2002] [Park et al. 2019] [Durhasan 2020] [Paula] [Payne et al. 2000] [Peng et al. 2016] [Penland and Romeo 1971] [Perraud et al. 2010] [Peterson 1982] [Pfenninger and Vemuru 1989] [Pirozzoli and Bernardini 2013] [Pohl et al. 2019] [Pohlen and Mueller 1983] [Pott-Pollenske et al. 2013] [Potter and Whitfield 1957] [Prapamonthon et al. 2019] [Prediction and Verification 1985] [Purtell et al. 1981] [Quest and Wright 2002] [Quest et al. 2002] [Quinn 1945] [Racisz 1947] [Rahal and Dutta 2024] [Raman et al. 2000] [Ray 2000] [Rayar 2020] [Re 2005] [Reckzeh and Hansen 2006] [Reding et al. 1979] [Rege et al. 2015] [Reisenthel 1995] [Reisenthel and Childs 1994] [Report No. 581. Measurements 1937] [Reubush 1975b] [Reubush 1975a] [Rezende Dessimoni Carvalho and Brito 2019] [Rist 1996] [Ritter et al. 2016] [Rival et al. 2010] [Rizzetta and Visbal 2010] [Roberts] [Robinson et al. 1974] [Rocha Ribeiro and Wolf 2025] [Rodriguez et al. 2020] [Roepke 1972] [Rona and Soueid 2010] [Rothmayer and Bhaskaran 1994] [Rudnik and Germain 2009] [Rusak and Morris 2005] [Rusak and Morris 2011] [Hariyadi et al. 2022] [Samardžić et al. 2013] [Sana and Tanaka 2026] [Sankar and Tassa 1980] [Sansica and Hashimoto 2023] [Sato and Takahama 2024] [Saunders 1996] [Saunders 2008] [Scale Effects on Turbulent 1981] [Schaefer 1986] [Schobeiri et al. 2005] [Schrader et al. 1988] [Schreck et al. 1994] [Sedaaghi and Ebrahimi 2025a] [Sedaaghi and Ebrahimi 2025b] [Sekimoto et al. 2018] [Selig and Guglielmo 1997] [Settles et al. 1976] [Shahrbabaki et al. 2014] [Shepshelovich et al. 1989] [Sherer et al. 2009] [Shi et al. 2026] [Shields and Mohseni 2011] [Shrestha and Candler 2018] [Shum and Marsden 1994] [Silva et al. 2009] [Boughou et al. 2022] [Smits 1995] [Solis et al. 2024] [Song and Eaton 2004] [Song et al. 2017] [Spratley et al. 1977] [Spreiter and Steffen 1946b] [Spreiter and Steffen 1946a] [Squires 2004] [Sriram et al. 2025] [Srivastava and Sarkar 2015] [Stallings 1979] [Stewart 1990] [Stock 2002] [Stollery and Murthy 1977] [Stuessy et al. 1997] [Stutz et al. 2022] [Sudhakar and Karthikeyan 2021] [Sudharsan and Sharma 2024] [Tadjfar and Asgari 2017] [Taira and Colonius 2009] [Tang 2006] [Tang 2008] [Thake et al. 2010] [Thomas 1991] [Tilvaldyev et al. 2025] [Timmer 2008] [Tobing 2019] [Toot 1989] [Toppings and Yarusevych 2021] [Toppings and Yarusevych 2025b] [Toppings and Yarusevych 2025a] [Traub 2024a] [Traub and Akerson 2010] [Traub et al. 1998] [Tsuji and Nakamura 1999] [Ulbrich 2004] [Ullah et al. 2020] [Unt et al. 2025] [Uselton 1978] [Uselton and Haberman 1982] [Uselton and Uselton 1975] [Vadsola et al. 2021] [Valarezo 1992] [Vaquero et al. 2022] [Vaziri et al. 2018] [Viala and Aupoix 1995] [Vicroy 2011] [Vorburger et al. 1985] [Vrchota et al. 2017] [Wahidi and Bridges 2010] [Wake et al. 2006] [Walcott 1963] [Walker and Bons 2018] [Walker et al. 1988] [Wang and Khalid 2025] [Wang and Lai 2024] [Wang et al. 2013a] [Wang et al. 2013b] [Wang et al. 2014] [Wang et al. 2015b] [Wang et al. 2015a] [Wang et al. 2018c] [Wang et al. 2018d] [Wang et al. 2022c] [Wayman 1994] [Wayman and Randle 1995] [Wei et al. 2019] [Wei et al. 2023] [White and Gibson 2004] [Wilcox 1973] [Wild 2002] [Wild 2012] [Wild 2013] [Willemsen et al. 1985] [Williams et al. 1999] [Wilson and Chou 1985] [Wing Tunnel Model 1998] [Winski et al. 2025a] [Wo and Covert 1989] [Wu and Moin 2009] [Wu and Xia 2026] [Xia et al. 2022] [Xu et al. 2018] [Yang and Hu 2008] [Yang and Li 2008] [Yang et al. 2007] [Yang et al. 2023] [Yao and Yeo 2018] [Yao et al. 2010] [Yao et al. 2021] [Yarusevych et al. 2004] [Yarusevych et al. 2005b] [Yarusevych et al. 2005a] [Yarusevych et al. 2006] [Yeh et al. 1993] [Yen and Huang 2011] [You et al. 2013] [Younghans et al. 1982] [Yu et al. 2024a] [Yuan et al. 2004] [Yuan et al. 2007] [Zhang and Hodson 2007] [Zhang and Hodson 2009] [Zhang and Schlüter 2012] [Zhang et al. 2002] [Zhang et al. 2007a] [Zhang et al. 2017b] [Zhang et al. 2026a] [Zhao et al. 2022c] [Zhou et al. 2021] [Ziadé et al. 2018] [Zilstra and Johnson 2024] [Zilstra and Johnson 2026] [Ümütlü et al. 2022]

Flight control law design and envelope protection

The system that made an unstable aeroplane flyable. Control law architecture, gain scheduling, limiters and handling qualities. The X-48C needed new limiters because its handling qualities differed from the B model, which is the clearest published statement that the noise modification cost something.

500 records. [Abel and Newsom 1981] [Abrams and Weinstein 1974] [Advanced Aircraft Control 2026] [Aerospace - Flight Control] [Aerospace - Flight Control] [Aerospace - Vehicle Management] [Aerospace Active Inceptor Systems] [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 1988e] [Air Force Test Pilot School Edwards Afb Ca 1988c] [Air Force Test Pilot School Edwards Afb Ca 1988d] [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 1992b] [Aircraft Control 2016] [Aircraft Flight Control 2014] [Aircraft Flight Control Actuation] [Aircraft Flight Control Systems] [Aircraft Longitudinal Handling Qualities 2011] [Al Tahtawi and Yusuf 2019] [Al-Shehabi and Newman 2002] [Alag and Duke 1985] [Alag and Kaufman 1974] [Alatorre et al. 2023] [Alazard 2001] [Altunkaya et al. 2024] [Amato et al. 2022] [Anderson 1970] [Anderson 1960] [Application of dynamic flight] [Arent and Falatko 1992] [Ashkenas 1965a] [Autenrieb 2025] [Automatic Flight Control System 2000] [Avanzini and Minisci 2010] [Bachelder and Aponso 2020a] [Bachelder and Aponso 2020b] [Bachelder and Klyde 2003] [Bachelder et al. 2023] [Back-Up Flight Control System 1983] [Bailey 1984] [Ballouz and Chang] [Battipede et al. 2004b] [Bazill and Jenney 1970] [Beamer] [Beaufrere 1988] [Beh et al. 2018] [Belkharraz and Sobel 2000] [Bennani and Looye 1998] [Berdjag et al. 2010] [Berra et al. 2017] [Bertolino et al. 2024] [Bicego] [Bihrle 1970] [Bilendo and Shouzhao 2018] [Birckelbaw and Corliss 1992a] [Black and Moorhouse 1979] [Blight et al. 2018] [Blue et al. 2002] [Bodson 2001] [Boeing Vertol Co Philadelphia Pa 1983] [Boothe et al. 1974] [Bottasso and Montinari 2013] [Bouadi] [Boudreau 1976] [Boudreau 1977] [Bowes and Miller 1976] [Bradshaw et al. 1985] [Breneman and Lower 1992] [Breul 1963] [Broderick] [Brown 1970] [Brown 2009] [Burcham and Burken 1994] [Burken et al. 2009] [Burken et al. 2010] [Cable Assemblies Aircraft, Proof] [Carlin and Blair 1983] [Carter and Cooper 1968] [Carter and Stephenson 1999] [Cartocci et al. 2024] [Chalk et al. 1969] [Chance Vought Corp Dallas Tx 1979] [Chapter 12. Control 1994] [Chapter 13. Control 1994] [Chen and Xin 2017] [Chen et al. 2016b] [Chen et al. 2024b] [Chen et al. 2026a] [Cheng et al. 2007] [Chin et al. 1987] [Chowdhary and Johnson 2008] [Chowdhary and Johnson 2009] [Chowdhury and Keshmiri 2022] [Clark 1964] [Cleveland 1971] [Clews 1973] [Clifford 1968] [Comer and Chakraborty 2024] [Comer et al. 2026b] [Conceptual and Preliminary Design 2017] [Configuration Development and Flying 2021] [Connelly 1982] [Cooke 2010] [Cord 1989] [Corliss et al. 1983] [Corraro et al. 2011] [Corwin et al. 1989] [Cotting and Burken 2001] [Cotton 1974] [Crombie and Moorhouse 1980] [Crother et al. 1973] [Cruz and Kienitz 2007] [Cully and Boller 1973] [Curry et al. 1965] [Marilena 2012] [Davis et al. 1977] [Deckert 1981] [Deets and Szalai 1972] [Demarchi and Haning 1978] [Dendy and Tribken 1968] [Desai et al. 1976] [Description of Actuation Systems] [Design Guidelines for Aircraft] [Design Objectives for Flying] [Design Objectives For Handling] [Development of a robust 1994] [Di Rito and Schettini 2016] [DiFranco 1971] [Dobos-Bubno and Hartsook 1977] [Dukes 1970] [Efremov et al. 1998] [Ellis 1972] [Elsamra et al. 2020] [Enciu et al. 2025] [Enns 2003] [Estimation and Sensitivity 2026] [Falkena et al. 2010] [Fan and Hall 2014] [Feedback Flight Control 2026] [Ferreres and Puyou 2006] [Field et al. 2002] [Fleck 1983] [Flight Control 2015] [Flight Control Actuation Systems 2025] [Flight Control Actuators] [Flight Control Design 2015] [Kim 2008] [Flight Control System Design 2011] [Flight Envelope Awareness/Protection] [Flying Qualities 2003] [Fosdick 1970] [Franchi 2019] [Frost et al. 2000] [Frost et al. 2002] [Fujimori 2011] [Fujimori et al. 1999] [Fujiwara et al. 2003] [Fujizawa] [Funk 1975] [Gainer 1963] [Gang An et al. 2018] [Gao et al. 2021b] [Gao et al. 2021d] [Gao et al. 2021f] [Gao et al. 2021a] [Gao et al. 2021e] [Gao et al. 2021c] [Gao et al. 2021g] [Garrec and Kubica 2005] [Gaylor 1984] [Gee et al. 1976] [General Electric Co Schenectady Ny 1952] [Generally on automatic flight] [Gerken 1979] [Goetzendorf-Grabowski and Antoniewski 2016] [Goldstein 1982] [Graham 1986] [Grantham and Nguyen 1977] [Gray 2008] [Gray 1964] [Gregory et al. 2011] [Ground and Flight Testing 2000] [Grudzinski and Tarabishy 2000] [Guerrero and Corliss 1991] [Guo and Liu 2012] [Ha 1990] [Hall 1969] [Handling Qualities 2000] [Harper and Sardanowsky 1969] [Hart 1956] [Hart 1968] [Hartman 2019] [Hartmann et al. 1979] [Hastedt et al. 2022] [Herrmann and Ben-Asher 2016] [Hess 1990] [Hess 2004] [Hess 2005a] [Hess 2005b] [Hess 2006] [Hess 2010] [Hess 2012] [Hess 2013] [Hess and Peng 2018] [Hill 1987] [Himich and Kineyko 1981] [Hoh 1982] [Hoh and Mitchell 1983] [Hoh and Mitchell 2018] [Hoh et al. 1981] [Hoh et al. 2011] [Horn et al. 1998] [Horowitz et al. 1980] [Horsnell 1967] [Hoyt et al. 1980] [Huang et al. 2017] [Huang et al. 2020a] [Huff 1949] [Hyde and Glover 1993] [Industrial Considerations for Flight 2000] [Integrated Flight Instruments and] [Integrated Rudder and Brake] [Introduction 2017] [Ioannou and Rooney 1989] [Jackson and Coyle 1983] [Jackson and Patch 1968] [Jeanneau] [Jeanneau] [Jebakumar et al. 2019] [Jeffrie and Rolston 1972] [Jenney 1979] [Jenney 1980] [Jenney et al. 1982] [Jia-Hui et al. 2025] [Jin and Wang 2015] [Johnson 1965] [Johnson and Redus 1968] [Johnston et al. 1974] [Joos and Pfife 2012] [Juhasz et al. 2015] [Kaden et al. 2013] [Kai 2024] [Kaneshige et al. 1999] [Kang et al. 2013] [Kangyu et al. 2025] [Karlsson] [Karpenko and Sepehri 2006] [Katayanagi 2001] [Katt and Raymont 1977] [Ke et al. 2015] [Kempel 1971] [Kempel 1982] [Key 1971] [Khrabrov and Sidoryuk 2010] [Khrabrov and Sidoryuk 2013] [Khuat et al. 2025] [Kineyko 1982] [Klyde et al. 2007] [Kocurek et al. 1997] [Kohnhorst and Magnacca 1980] [Kolesnikov 2005] [Konar et al. 1974] [Kotfilia and Painter 1969] [Krachmalnick et al. 1967] [Krings and Thielecke 2012] [Krishnakumar et al. 2012] [Kubica and Livet 1994] [Lai et al. 2017] [Langton 2006] [Larson 1986] [Lee and Dudginski] [Lee and Vining 2018] [Li and Chang] [Li et al. 2009] [Li et al. 2017a] [Li et al. 2018a] [Li et al. 2020] [Li et al. 2025c] [Lin et al. 1998] [Linear Quadratic Flight Control 2026] [Liu and Xu 2026] [Liu et al. 2009b] [Liu et al. 2022] [Liu et al. 2025b] [Liu et al. 2026b] [Lombaerts and Looye 2011] [Lombaerts et al. 2010] [Lombaerts et al. 2016] [Lu 2024] [Lusardi 2023] [Ma et al. 2024] [Malaek et al. 2006] [Manning and Gleason 1992] [Mant 1972] [Martin 1963a] [Martin 1963b] [Masaoka and Hashimoto 2024] [Masarati et al. 2014] [Mattei and Scordamaglia 2008] [Matthews 1998] [McCuish and Caldwell 2018] [McKenzie 1973] [McMaster and Schenk 1973] [Mei et al. 2024] [Meola et al. 2013] [Methodology for Investigation of] [Mikami and Uchiyama 2015] [Miller 1968] [Mineck 1976] [Model-Based Approaches for Fast 2013] [Moncayo et al. 2010] [Montgomery 1971] [Mooij 1985] [Moore et al. 2024] [Moreira et al. 2022] [Motyka and Reynolds 1971] [Musso et al. 2024] [Nagata et al. 1973] [Nagy and Kirsten 1976] [Napolitano et al. 2001] [Nardi 1970] [Nettleton 1965] [Nguyen 2011] [Nguyen and Cord 1999] [Nield 1981] [Nikiforuk et al. 1990] [Nonlinear Model Following Control 1989] [Northrop Aircraft INC Hawthorne CA 1952a] [Nuthi and Subbarao 2014] [Oelker and Brieger 2006] [Ogren et al. 1974] [Ohara 1964] [Oosterom and Babuska 2001] [Optimization and Flight-Test Evaluation 2017] [Optimization and Piloted Simulation 2017] [Ostheimer and Giguere 1963] [Paine 1950] [Papa and Stoliker 1988] [Patel et al. 2014] [Patterson 1968] [Patterson 1984] [Peng et al. 2022a] [Perhinschi et al. 2005] [Petersen 1979] [Phillips] [Placement in Flight Control 2026] [Portapas and Cooke 2020] [Powers and Kier 1973] [Prasad and Unnikrishnan 2006] [Primary Flight Control Hydraulic] [Prosvirin and Kharchenko 2016] [Qian et al. 2022] [Quantitative Design Requirements 2017] [Queinnec et al. 2006] [Rabenberg and Palarz 1983] [Rafi et al. 2012] [Rang et al. 1979] [Ratliff and Pagilla 2008] [Redeker 1987] [Research and Design 2022] [Reynolds et al] [Rickard 1978] [Rinde 1969] [Rising 1982] [Ro et al. 1992] [Robbins et al. 2023] [Robinson] [Robinson 1968] [Robinson 1969] [Robinson et al. 1989] [Rooney et al. 1982] [Rosa et al. 1974] [Roscoe et al. 1975] [Roskam and Henry 1973] [Ross et al. 1973] [Rotorcraft Handling Qualities Design 2011] [Rustenburg 1972] [Ryu and Andrisani 2000] [Sadati et al. 2011] [Sadovnitchii et al. 1997] [Saetti and Rogers 2020] [Sagoo] [Sanders et al. 2018] [Sanfilippo 1970] [Savelev and Neretin 2022] [Schmidt 1986] [Schmidt 1995] [Schreadley 1977] [Shafer et al. 1989] [Shankar et al. 2004] [Shen and Chen 2025] [Shen et al. 2022] [Shi et al. 2018a] [Shin and Kim 2014] [Shives 1974] [Shmul et al. 2018] [Shweyk and Weltz 2005] [Shweyk et al. 2012] [Siddiqi and Abraham 1988] [Simsek and Tekinalp 2015] [Simulation Requirements for Flight 2017] [Singh et al. 2017] [Sissingh 2015] [Slater 1974] [Smith 1967] [Smith 1977] [Smith 1991] [Smith 2023] [Smith et al. 1971] [Smith et al. 1973b] [Solies 1995] [Sonneveldt et al. 2011] [Sparks et al] [Steeb et al. 1979] [Steer 2003] [Steer 2004] [Stengel 1973] [Stephan 2025c] [Stich 2012] [Stolarik 2007] [Stougie et al. 2024] [Strand and Ennis 2012] [Su 2014] [Subba Reddiar Pappu et al. 2015] [Sun et al. 2017] [Sun et al. 2020] [Swarnkar and Kothari 2016] [Tang et al. 2009] [Taranto and Abdulrahim 2023] [Tekles et al. 2014] [Terminology for Flight Control] [Terminology for Redundant Flight] [Test Techniques for Flight 2021] [Tonon and Belluati 2018] [Urnes and Yeager 1991] [Validation and Verification Process] [Van Baelen et al. 2018] [Van Gool and Weingarten 1981] [Vehicle Management Systems] [Vepa 2023b] [Vinkler and Wood 1978] [Vinkler et al. 1979] [Voigt et al. 2019] [Vomaske et al. 1978] [Vukobratović and Stojić 1986] [Waite et al. 2021] [Waitman et al. 2019] [Walker and Postlthewaite] [Waltz et al. 1983] [Wang and Lei 2017] [Wang and Wu 2025] [Wang et al. 2017a] [Wang et al. 2021b] [Wang et al. 2021a] [Wang et al. 2024d] [Wang et al. 2025c] [Waszak et al. 2002] [Weidemann and Leondes 1979] [Weiser 2025] [Well 2006] [Wells 2002] [Whitbeck and Hofmann 1978] [Whitbeck et al. 1982] [Wichgers] [Wilson and Peters 2009] [Wilson et al. 2014] [Wise et al. 1999b] [Woolley 1978] [Wu 2014] [Wu et al. 2022] [Xargay et al. 2010] [Xiaoxiong et al. 2011] [Xin et al. 2012] [Yang] [Yang and Morales 2021] [Ye et al. 2007] [Yin et al. 2020] [Yin et al. 2023] [Yomchinda et al. 2009] [Younkin 1968] [Yu and Jiang 2012] [Yu et al. 2020] [Yu et al. 2021] [Yue et al. 2017] [Yue et al. 2025] [Yuksek and Inalhan 2022] [Zaludin 2012] [Zamani Fekri and Mobed] [Zhang et al. 2018a] [Zhang et al. 2020a] [Zhang et al. 2026b] [Zhishuai and Lingling 2022] [Zhong et al. 2021] [Zouaoui and Rami 2004] [Zuhri 2025]

Aircraft noise, shielding and the quiet configuration

The X-48C’s reason for existing. Airframe and engine noise, shielding by the planform, community metrics and the certification quantity. A configuration that puts its engines above a broad body has a noise argument no tube and wing can make, and the C model was built to fly it rather than compute it.

462 records. [A Potential Flow Model 1976] [A Preliminary Investigation 1976] [A Review of Core 1975] [Moshkov et al. 2018a] [Acoustic Characteristics 1976] [Acoustic Investigation 1975] [Nagamatsu et al. 1976] [Nagamatsu 1976] [Agarwal 2004] [Agarwal and Dowling 2005] [Agarwal and Dowling 2007] [Ahtye and Kojima 1976] [Aircraft Noise 2022a] [Aircraft Noise 2022b] [Aircraft Noise 2012a] [Aircraft Noise 2012b] [Aircraft Noise Prediction 1989] [Aircraft Noise 2012c] [Aircraft Noise Sources 1989] [Airframe Noise Radiation 1993] [Akatsuka 2024] [Akatsuka et al. 2022] [Akatsuka et al. 2025] [Ali et al. 2016] [An Experimental Investigation 1976] [An Experimental Study 1976a] [An Experimental Study 1976b] [Angelino et al. 2019] [Appelbaum et al. 2018] [Arntzen M. 2012] [Asada and Kawai 2026] [Asmatulu et al. 2009] [Aujogue] [Balint and Balint 2015] [Ballard 1967] [Barbosa and Dezan 2013b] [Barbosa and Dezan 2013a] [Barton and Mixson 1980] [Bashforth 1981] [Bauer 1979] [Bauer and Munson 1977] [Bauer et al. 2009] [Bauer et al. 2012] [Baumann and Waggoner 2018] [Belyaev et al. 2015] [Benek 1977] [Benito 1986] [Berge et al. 1993] [Berman 1980] [Berton 2016] [Berton 2023] [Berton and Majjigi 2025] [Bertsch et al. 2010] [Bhat and Gall 1975] [Birch 2023] [Bishop and Pearsons 1965] [Blacodon 2005] [Blacodon 2007] [Blandeau et al. 2018] [Blech et al. 2024] [Block 1979] [Block 1981] [Bloomer 1979] [Brehm et al. 2015] [Broadbent 1976] [Brooks and Humphreys 1999] [Brown 2015] [Brown and Ahuja 1984] [Butzel 1981] [Butzel 1982] [Bychkov and Faranosov 2020] [Calder and Gupta 1977] [Cantos et al. 2024] [Casalino and Barbarino 2011] [Casalino et al. 2006] [Casper et al. 2004] [Castner and Lake 2012] [Certified Aircraft Noise Data 2012] [Chapkis and Marsh 1977] [Chiba et al. 2007] [Christophe et al. 2023] [Clark et al. 2021] [Clauss et al. 1979] [Conticelli et al. 1975] [Core Engine Noise 1975] [Core Engine Noise Due 1976] [Coward and Griffiths 2024] [Cross and Watts 1983] [Cumming et al. 2013] [Cutting Engine Noise 2007] [Czech et al. 2022] [Dash et al. 2003] [Davies and Moreau 2025] [Davy and Remy 1998] [Delfs 2024] [Denisov et al. 2016] [Diagnostic Calculations of Airframe-Radiated 1976] [Diamond et al. 2024] [Dieumegard] [Dimino 2024] [Dittmar 1986] [Dobrzynski 1980] [Dobrzynski 2010b] [Dobrzynski 2010a] [Dobrzynski and Heller 1977] [Dobrzynski et al. 2000] [Dobrzynski et al. 2002] [Doelling 1961] [Doelling and Bolt 1961b] [Doelling and Bolt 1961a] [Doherty and Butzel 1979b] [Dougherty 1977] [Duct Acoustics 1976] [Effect of Forward Speed 1976] [Eisenhut and Strohmayer 2026] [Electroacoustics. 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2024] [Carpenter et al] [Forward Velocity Effects 1976] [Franken and Kerwin 1958] [Franzoni and Bliss 2000] [Fratello and Shearin 1975] [Fukushima et al. 2014] [Gaeta et al. 2009] [Gao and Qiang 2018] [Gasaway 1969] [Gasaway 1970] [Gerhold and Kim 1983] [Gibs et al. 1976] [Giladi and Menachi 2024] [Girvin 2009] [Glover and O’Boy 2021] [Goddard 1991] [Goldschagg 2013] [Goodykoontz and Gutierrez 1977] [Gordon 1961] [Gorji-Bandpy and Azimi 2012] [Goyal et al. 2025] [Graham et al. 2014] [Greatrex and Brown 1959] [Greska et al. 2004] [Grewal et al. 2001] [Groeneweg 2024] [Groom et al. 2025] [Grosche et al. 1997] [Grosveld 1983] [Ground-Plane Microphone Configuration for] [Guo and Thomas 2026] [Guo et al. 2002] [Guo et al. 2019] [Hall 2024] [Hassan et al. 2014] [Hayama et al. 2013] [Hayden et al. 1975] [Helffer et al. 2014] [Heller and Dobrzynski 1977] [Hersh et al. 1976] [Hirt 1991] [Ho et al. 2011] [Holbeche and Hazell 1981] [Homans et al. 1978] [Hou et al. 2026c] [House Noise-Reduction 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Tailless stability and control, and directional authority

What a configuration without a tail gives up. Directional stability, vertical surface sizing, yaw authority and the Dutch roll. A tailless aeroplane makes its yaw moments out of drag rather than out of a rudder on a long arm, which is the mechanism behind the weakness this article’s arithmetic then compounds for the X-48C.

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Transport aircraft design, sizing and fuel efficiency

What the configuration was for. Sizing, weight estimation, cruise efficiency and the fuel burn comparison that motivates the whole line of work.

314 records. [Abraham and Costello 2009] [Aircraft Case Studies 2026] [Aircraft Characteristics 2022] [Aircraft Classification Statistics 2010] [Aircraft Components and Subsystems 2011] [Aircraft Conceptual Design 2012] [Aircraft Design 2024] [Aircraft Design Optimization 2013] [Aircraft Moments of Inertia 1996] [Aircraft Sizing Engine Matching 2010] [Aircraft Weight and Center 2010] [Aircraft Weight Distribution 2012] [Aircraft/Engine System Constraint Analysis 2018] [Aircraft/Engine System Mission Analysis 2018] [Ajaj et al. 2013] [Ali and Al-Shamma 2026] [Altman 2015] [Altman 2019] [Anipko et al. 2020] [Ardema 2003] [Ascani 1974] [Aschenbeck 1964] [Autry and Victorazzo 2019] [Babčan and Janovec 2021] [Bagdatli et al. 2019] [Baier et al. 2014] [Barlow 1929] [Barton] [Bateman 1986] [Bendarkar et al. 2013] [Berci and Torrigiani 2020] [Berry 2000] [Bil 1989] [Bindolino et al. 2010] [Blasi and Core 2007] [Brewer 2017] [Brown 1989] [Bryson 1971] [Burger 1983] [Butler et al. 1998] [Butler et al. 1999] 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[Eisler] [Electric Aircraft 2024] [Elham and Ghasemi 2023] [Estimating the Takeoff Wing 2010] [Fazeli et al. 2016] [Felix et al. 2026] [Fielding and Vaziry-Z 1995] [Finger et al. 2018] [Finger et al. 2020] [Finger et al. 2022] [Fioriti 2014] [Frulla 2021] [Führer et al. 2016] [Gabriele 1991] [Gagnon and Zingg 2015] [Gallian 1980] [Galloway 1989] [Gates 1949] [Generic Aircraft Design Flowchart 2017] [Ghenaiet 2007] [Ghiringhelli et al. 2015] [Giles 1995] [Gilyard et al. 1999] [Golombek et al. 2025] [Golombek et al. 2026] [Govindarajan and Sridharan 2020] [Goyal 2026] [Gudmundsson 2014a] [Gudmundsson 2014b] [Gudmundsson 2014c] [Gudmundsson 2022] [Hajela and Bach 1989] [Hajela and Chen 1988] [Hammond 1986] [Hannon et al. 2008] [Harish et al. 2018] [Hayase 1974a] [Hayase 1974b] [Heidary and Kosari 2024] [Henne 1989] [Hill and Waters 1974] [Hiyama 1974] [Hollingsworth Peter and Patel Dipesh 2012] [Hon et al. 2022] [Horvath and Wells 2018] [Howe 2000c] [Howe 2000b] [Howe 2000a] [Hu et al. 2026] [Huang and Cheng 2022] [Huang et al. 1996] [Hughes Tool Co Culver City Ca 1963] [Hutchin 2019] [Ibrahim 2004] [Ibrahim and Bil 2013] [Incorporating Agility Flight Test 1994] [Ingram et al. 2015] [Initial Sizing 2024] [Initial Tail Sizing 2013] [Isikveren 2003] [Jackson 2010] [Janardhan and Grandhi 2003] [Jansen and Perez 2014] [Jansen et al. 2016] [Johnson 1972] [Johnson 1985] [Joseph et al. 2022] [Matt et al] [Kamal and Ramirez-Serrano 2019] [Kaminer et al. 1996] [Kaminer et al. 1997] [Kao et al. 2018] [Karabacak and Turan 2020] [Karagoz et al. 2019] [Karunanidhi et al. 2022] [Komarov et al. 2012] [Kowalski et al. 2021] [Krengel et al. 2019] [Kretov 2020] [Kroo 1983] [Kulfan and Vachal 1978] [Landtmeters and Slingerland 2005] [Lange 1984] [Lanham 1979] [Lawson 1969] [Layton and Kee 1983] [Lefebvre and Zha 2016] [Lehmann 1980] [Lin and Afjeh 2003] [Liseitsev 2025] [Liu and Elham 2019] [Liu and Wu 2003] [Logan 1989] [Lorenz 2001] [Lutz et al. 2025] [Luz and Alexander 2004] [Ma et al. 2022] [Maciolek and Wallischeck 1977] [Major Changes 1993] [Mane et al. 2007] [Marinus and Maison 2016] [Martindale et al. 1974] [Martins 2016] [Mason 2013] [McDonald 2007] [McMasters and Kroo 1998] [Meier and Olson 1988] [Melis et al. 2019] [Michaut et al. 1989] [Mirosavljevic et al. 2009] [Mishra and Chakraborty 2024] [Mistree 1987] [Mokotoff and Cinar 2026] [Mokotoff et al. 2025] [Moorhouse and Jenkins 1975] [Myklebust and Gelhausen 1993] [Nam and Mavris 2018] [Nam et al. 2005] [Neufeld 2021] [Newman and Stanzione 1991] [Nigam et al. 2015] [OBrien and Takahashi 2024] [Oole 1993] [Chiozzotto 2017] [Palaia et al. 2025] [Pant and Fielding 1999] [Park 2025] [Park and Park 2025a] [Park et al. 2025] [Parker 1986] [Peck and Hudson 1956] [Perez and Jansen 2014] [Pierson and Ong] [Ploetner 2013] [Pogosyan 2025] [Poll and Schumann 2020] [Pornet and Isikveren 2015] [Preliminary Fuselage Sizing 2010] [Preliminary Sizing 2010] [Rajpal and Pant 2011] [Ramamoorthy and Sinha 1980] [Raymer 1992] [Raymer 1998] [Raymer 2012b] [Raymer 2012a] [Raymer 2018] [Raymer 2024] [Raymer and Crossley 2002] [Roberts and Decker 2013] [Rodriguez and Liscouët-Hanke 2025] [Rogan et al. 1986] [Rosenstein 1989] [Rosin et al. 2004] [Roskam 1985] [Roskam 1986] [Roth and Crossley 1998] [Ryan-Simmons and Agarwal 2025] [Sabeti and Winter 2024] [Sabeti et al. 2024] [Sadraey 2026] [Saeedipour and Neil Stevenson 1998] [Sagdeo 1990] [Sanchez-Carmona and Cuerno-Rejado 2018] [Sanghi 2003] [Sanghi et al. 1998] [Schmidt and Vos 2014] [Scholz 2021] [Schwartz 1988] [Segall 2008] [Sensmeier and Samareh 2005] [Seywald 1994] [Shirakawa] [Shushnar] [Silva] [Simos and Jenkinson 1986] [Sirigireddy and Ahner 2026] [Sizing from a Conceptual 2024] [Sizing the Engine 2002] [Sizing the Engine 2018] [Sizing Trade Studies 2024] [Skillen and Crossley 2005] [Skillen and Crossley 2008] [Slingerland 2005] [Smaili et al. 2018] [Snyder 1990] [Solvey 1951] [Sridharan and Govindarajan 2021] [Staack] [Stamm and Woods 2024] [Stanford 2021] [Straub 1973] [Stringer et al] [Stroub 1989] [Svoboda 1999] [Takahashi and Lemonds 2015a] [Takahashi and Lemonds 2015b] [Tamboli 1956] [Taylor and Hunsaker 2023] [Taylor and Rogers 2014] [Toffol and Ricci 2023] [Tong and Naylor 2008] [Torenbeek 2013] [Torenbeek 2020] [Trade Studies and Sizing 2010] [Trial of a New 2008] [Ugwueze et al. 2023] [Vallone] [VanLandingham and Hall 2023] [Velden 1997a] [Vlasov 2022] [Vos 2019a] [Vos 2019c] [Wampler et al. 1988] [Wang et al. 2024e] [Werner-Westphal et al. 2008] [Whitford 1992] [Whitford 1994] [Wildermuth et al. 1974b] [Wildermuth et al. 1974a] [Winter et al. 2021] [Worked Manned Aircraft Detail 2017] [Wortmann et al. 2015] [Wrenn and Dovi 1987] [Wrenn and Dovi 1988] [Xie et al. 2021] [Yang 2025] [Yang et al. 2021] [Young 2010a] [Yuhara et al. 2016] [Zafi and Chakraborty 2023] [Zaimis et al. 2024] [Ünal et al. 2023]

Parameter identification and flight test technique

How the aeroplane was made to give up its derivatives. Multisine excitation, doublets, in-flight stability margin estimation and envelope expansion. A subscale vehicle makes this cheaper and more dangerous at once, because a cheap airframe can be risked and a fast one is harder to catch.

309 records. [Abate and Klomfass 2005] [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 1962c] [Air Force Test Pilot School Edwards Afb Ca 1962a] [Air Force Test Pilot School Edwards Afb Ca 1979] [Air Force Test Pilot School Edwards Afb Ca 1992a] [Aksteter et al. 1994] [Alford and Knarr 1999] [Anderson and Vincent 1985] [Armstrong 1977] [Asselin 2021] [Bach and Wingrove 1983] [Bajaj 2019] [Balcan et al. 2026] [Banerjee et al. 2026] [Bare-Airframe Identification from Data 2006] [Bare-Airframe Identification from Data 2012] [Barron 1967] [Bombois et al. 2021] [Bombois et al. 2025] [Boukhebouz et al. 2021] [Branson and Fry 1994] [Brennan and McDaniel 1994] [Brieger et al. 2008] [Brimelow 1970] [Bromberg and Hansen 1965] [Brown and Bradley 1981] [Bucharles et al. 1990] [Burnett 2002] [Burton and Bischoff 1976] [Butts and Lawless 1990] [Carico 1998] [Carico et al. 2005] [Chapter 2. Exploring 2005] [Cheney 1988] [Clarke and Roskam 1982] [Cockrell and Doherr 1981] [Colin et al. 2019] [Cooke 1980] [Coombe 1970] [Coopmans et al. 2015] [Crama and Schoukens] [Crama and Schoukens 2001c] [Crama and Schoukens 2001b] [Crama and Schoukens 2002] [Crama and Schoukens 2005] [Cruz et al. 1969] [Csurcsia 2022] [Cunningham and Hubbard 2018] [de Franca Arruda 1993] [De Jesus Mota and Botez 2009] [de Mendonça et al. 2013] [Deepa and Gupta 2023] [Development of a Continuous 2012] [Dong et al. 2024d] [Dorobantu et al. 2013] [Drag and Propulsive Efficiency 1990] [Duke and Lux 1983] [Dunlap and Porter 1971] [Enciu 2019] [Energy Approach to Performance 2003] [Eulrich and Rynaski 1980] [Evans et al. 1994] [Everett and Oster 1994] [Exploring the Flight Envelope 2015] [Fechter and Mills 1988] [Figwer 2009] [Figwer 2013] [Figwer 2017] [Fletcher 1994] [Fletcher 2008] [Newman and Greeley 2017] [Flight Test Maneuvers 2008] [Flight Test Manual 1959] [Flight Test Planning 2021] [Stoliker 2005] 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and Fu 1993] [Kallel and Kanoun 2022] [Kamal et al. 2015] [Kammer 2025] [Kang et al. 2021] [Karkar and Gökmenoğlu 2024] [Karpenko and Sepehri 2009] [Kay and Panagos 2004] [Kelly 1988] [Khoshlahjeh et al. 2011] [Kimberlin 2003] [Klein 1978] [Klein 1989] [Klein and Morelli 1992] [Klyde et al. 2004] [Kuehme et al. 2014] [Kukreja 2008] [Kumar and Rao 2004] [Kumar et al. 2008] [Kuppuswamy and Kiran 1981] [Larsson and Enqvist 2016] [Larsson et al. 2020] [Lataire and Pintelon 2009] [Lebacqz 1974] [Lee 1985] [Lee et al. 2007] [Leon et al. 2009] [Level Flight Performance Flight 2003] [Level Flight Performance Jet 2003] [Li 2026] [Lichota 2023] [Lichota et al. 2019b] [Lichota et al. 2019a] [Lichter et al. 2009] [Limitations and Flight Envelope 2017] [Liu et al. 2018a] [Londono and Leonhardt 2012] [Long 1968] [Longitudinal Control and Trim 2003] [Louali et al. 2011] [Luo et al. 2018] [Lykins and Keshmiri 2010] [Mallozzi et al. 2014] [Manaï et al. 2005] [Mancini et al. 2014] [Mancini et al. 2016] 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2026] [Zhou et al. 2025b] [Zhou et al. 2026b]

Propulsion, airframe integration and installed performance

Engines on top of a body rather than under a wing. Integration, inlet behaviour, boundary layer ingestion and installed thrust. Thrust is also the quantity this article shows the model does not scale, which the propulsion literature frames.

288 records. [A Vectored-Engine-over-Wing Propulsive-Lift Concept 1976] [Aarnes and White 1975a] [Aarnes and White 1975b] [Abdel-Fattah and Link 1992] [Adamson et al. 1978] [Advanced Ducted Propulsor In-Flight] [Afjeh and Reed 2003] [Ahuja et al. 2017] [Aircraft Engine Controls 2012] [Aircraft Engine Controls 2017] [Aircraft Engine Efficiency 2018] [Aian et al. 2014] [Albrecht et al. 2023] [Amick et al. 1955] [Anderson 1990] [Army Service Forces Washington Dc 1940] [Arthur et al. 2023] [Bacon and Roskman 1995] [Bagby 1963] [Bagy] [Banazadeh et al. 2007] [Bangert et al. 1983] [Barnhart 1989] [Batill and Hoffman 1984] [Batill et al. 1983] [Beitler 1984] [Simmons et al] [Benyamen and Keshmiri 2022] [Berens and Bissinger 1998] [Bidwell and Mohler, y R 1995] [Binkley et al. 2015] [Blaesser and Frederick 2020] [Borger 1981] [Bos 1999] [Bowers 1980] [Braman et al. 1983] [Breer 1978] [Brichet et al. 2015] [Bright and Simon 1992] [Bucknell 1987] [Burova et al. 2025] [Campbell 1973] [Cavcar and Cavcar 2003] 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1980] [Ford 1993] [Forliti and Diaz-Guardamino 2008] [Freeman and Klunk 2018] [Fuel Cell Demonstrator Aeroplane 2007] [Furusawa and Kitamura 2020] [Gallagher 1968] [Garg 1993] [Garg and Mattern 1991] [Garg and Ouzts 1991] [Garg et al. 1990] [Garnica and Takahashi 2017] [Gary and McDonald 2014] [Gilkey et al. 1995] [Glasgow 1974] [Glover and O’Boy 2023] [Golladay and Gendler 1947] [Gu et al. 2017] [Gubanov 2019] [Guidelines for the Integration] [Guidelines for the Integration] [Hahn 2012] [Haloulakos 1982] [Hamilton and Welge 1992] [Han et al. 2026b] [Han et al. 2026a] [Hartmann et al. 2021] [Havey and Kline 1989] [Hawkswell et al. 2022] [Helicopter Engine/Airframe Interface Document] [Henderson 1987] [Henderson 1990] [Hernanz et al. 2015] [Hiller Aircraft Corp Palo Alto Ca 1965a] [Hiller Aircraft Corp Palo Alto Ca 1965b] [Hines 1978] [Hirschel et al. 2025] [Hirschkron et al. 1979] [Hokenson 1986] [Hoogreef and Soikkeli 2022] [Imrak et al. 2021] [In-Flight Thrust Determination] [In-Flight Thrust Determination for] [Integrated Flight/propulsion Control 1985] [Investigations of Propulsion Integration 1992] [Ishii et al. 2013] [Jagtap 2025] [Jet Thrust Measurement 2003] [Jones et al. 2021] [Kaeli et al. 2019] [Kawai 1973] [Keller 2025] [Khailany et al. 2025] [Khasheinejad and Montazeri-Gh 2025] [Kim and Choi 2024] [Kitowski 1992] [Klepper et al. 2017] [Kowalski 2014] [Kuhn et al. 2026] [Kunkle and McGlone 1979] [Lambregts 1983] [Lange and Rudnik 2019] [Langston 2018] [Latham and Sorensen 1972] [Leitner 1986] [Lemmin 1986] [Lewerenz 1987] [Li and Geiselhart 2024] [Li et al. 2000a] [Li et al. 2023b] [Lichen et al. 2025] [Licheva and Liscouet-Hanke 2023] [Liston and Small 1992] [Lucas 1978] [Luers and Fiscus 1984] [Ma et al. 2020] [Mace and Nyberg 1992] [Mattingly 1989] [May and Richey 1979] [McCarroll and Jackel 1961] [McCarthy 1987] [McGuigan 1970] [MCMillan and Preston 1966] [Mengle 2011] [Merceruio et al. 2011] [Miao et al. 2020] [Mihaescu et al. 2012] [Minimization of Jet 1976] [Mishler and Wilkinson 1992] [Moens and Gardarein 2001] [Mongia et al. 1979] [Moorhouse and Citurs 2018] [Mount 1964] [Mueller et al. 2024] [Murphy and MacManus 2011] [Mutz et al. 1964] [Nallasamy and Groeneweg 1990] [Neves et al. 2026] [Newell and Herrick 1979] [Nichols and Heikkinen 2010] [Nichols et al. 2011] [Nichols et al. 2015] [Novik and Otto 1947] [Nutu 2025] [Oganyan and Loginov 2025] [Palumbo et al. 2022] [Pan et al. 2024] [Park and Park 2025b] [Patel and Chudoba 2026] [Patterson et al. 2015] [Pelton 1976] [Picard and Whitley 2002] [Porter 1984] [Postlethwaite 1998] [Postlethwaite and Bates 1998] [Powers and Robinson 1992] [Prasad and Rivera 1996] [Propeller/Propfan In-Flight Thrust Determination] [Propulsion 2024] [Propulsion System Thrust Sizing 2010] [Propulsive-Lift Noise 1976] [Rajendran et al. 2022] [Reid 1988] [Rein and Gardner 2015] [Reinert and Adams 2003] [Review of Inlet/Airframe Integration 1986] [Solutions et al. 2020] [Richey et al. 1968] [Richey et al. 1976] [Richey et al. 1977] [Richey et al. 1983] [Robinson and High 1974] [Rodriguez 2007] [Rossow et al. 1994] [Saghafi and Banazadeh 2009] [Salay and Elliott 1996] [Sallee 1973] [Schierman and Lowell 1992] [Schwartz 1975] [Scoppe 1973] [Shmelоv et al. 2019] [Shovlin 1978] [Silva and Guimarães 2020] [Smeltzer et al. 1974] [Smith 1966] [Smith 2014] [Smith et al. 2004] [Staley 1975] [Stankowski et al. 2016] [Stephan 2025d] [Stuermer 2023] [Stuermer 2024] [Su et al. 2025] [Sullivan 2002] [Surber and Sedlock 1978] [Sutliff 1973] [Tabei et al. 1992] [Taylor 1971] [Tennant] [The Effects of Forward 1976] [Three-Dimensional Viscous Design Methodology 1986] [Thrust Vector Control 2026] [Time-Dependent In-Flight Thrust Determination] [Transducer 1987] [Tsai 1979] [Tsentis et al. 2023] [Tsujikawa and Nagaoka 1990] [Tudosie 2018] [Uncertainty of In-Flight Thrust] [Vance 1973] [Veldhuis and Rentema 1995] [Venkatraman 2009] [Vinz and Raichle 2024] [Von Glahn et al. 1974c] [Vos 2019b] [Vyatkov et al. 2025] [Wahler and Elham 2025] [Wang and Mesbahi 2021] [Wang et al. 2011] [Wang et al. 2023a] [Wannenburg 1963] [Warsch et al. 2026] [Weber and Karemaa 1972] [Weisshaar and Allen 1991] [Werle 2022] [White et al. 1983] [Whitten and Woodrey 1977] [Whittley 1964] [Wilson and Benson 1978] [Wilson and Wright 1977] [Wind Tunnel/Flight Test Correlation 1978] [Wolf 1974] [Wu] [Wu and Chow 1984] [Wu and Mora-Camino 2012] [Yao et al. 2022] [Yezzi and Donguy 1986] [Yu et al. 2016] [Yuu et al. 1989] [Zaman 1996] [Zha et al. 1998] [Zhang et al. 2020b] [Zhang et al. 2024a] [Zheng et al. 2019]

High-lift devices, slats and separation control

The leading edge, which the X-48B tested in two configurations. Slats, flaps and separation control. The programme flew slats extended and slats retracted, which brackets exactly the behaviour the Reynolds mismatch makes least certain.

213 records. [Abramson 1975] [Abramson 1977] [Agrawal et al. 2025] [Alam et al. 2022] [Alauzet et al. 2026] [Ando et al. 2017] [Arena et al. 2021] [Bending of an Aircraft-Wing 2019] [Bidwell 2005] [Blank 1995] [Boer and Van Hengst 1993] [Brandt and Bons 2024] [Brandt et al. 2023] [Butler and Bons 2025] [Cao et al. 1998] [Carr 1984] [Cerreta 1957] [Chen et al. 2003a] [Chen et al. 2003b] [Chen et al. 2004] [Chen et al. 2011] [Chen et al. 2018] [Chow et al. 2002] [Ciobaca and Wild 2014] [Clark and Goc 2026] [Cliett 1952] [Corjon et al. 1999] [Couillaud] [Winski et al] [Cox et al. 2009] [Dargel and Thiede 2002] [Le et al. 2025] [Design of the Circulation 1979] [Development of High-Lift Wing 1990] [Dierke et al. 2010] [Dike and Dunn 1958] [Dobrzynski et al. 1998] [Edge and Perkins 1995] [El Sayed M. et al. 2018] [Eliasson 2007] [Eliasson 2008] [Englar 1970] [Feng and Wang 2020] [Fleury et al. 2015] [Franke 2015] [Gadzhimagomedov et al. 2022] [Genc et al. 2008] [Geng et al. 2023] [Ghee and Taylor 2000] [Ghee and Taylor 2004] [Greenwell and Wood 1993] [Greenwell and Wood 1994] [Gross and Fasel 2012] [Gu et al. 2023b] [Gueraiche and Popov 2018] [Guerreiro and Hubbard 2008] [Hahn et al. 2012] [Hahn et al. 2013] [Hariyadi et al. 2024] [Hartmann and Leicht 2015] [Hebert and Joseph 1970] [Hebert et al. 1970] [Hendrickson and Agarwal 2021] [Henning et al. 2012] [Horn et al. 2007] [Horne and Burnside 2013] [Hosseini et al. 2019] [Huehne et al. 2013] [Ichikawa et al. 2021] [Imamura et al. 2007] [Jenkins et al. 2004a] [Jenkins et al. 2004b] [Jente et al. 2018] [Jiang and Zhang 2017] [Kaepernick et al. 2005] [Kashitani et al. 2022] [Keller 2013] [Keller 2019] [Keller and Rudnik 2015] [Keyes 1968] [Khorrami et al. 2004] [Klein et al. 2016] [Kolb et al. 2007] [Kuo and Sarigul-Klijn 2009] [Kuzmina 2026] [Lacy and Sclafani 2016] [Landa et al. 2016] [Lei 2008] [Lei and Kwak 2005] [Lessard 2000] [Li et al. 2021a] [Li et al. 2024b] [Liebeck 1971] [Lin and Wang 2025] [Lindblad and de Cock 1999] [Liu et al. 2009a] [Liu et al. 2018d] [Lockard and Choudhari 2009] [Lu et al. 2018] [Manor et al. 1993] [Mayer et al. 2019] [McFadden and Bons 2025] [McGinley et al. 1998] [Melber-Wilkending et al. 2004] [Mele et al. 2016] [Mello et al. 2004] [Mendoza et al. 2002] [Meyn et al. 1993] [Micha´lek et al 2010] [Mishra and Baeder 2016] [Modi and Triplett 2003] [Moitra et al. 2011] [Monat et al. 2024] [Moore and Hymer 2001] [Mouton and Davy 2024] [Mouton et al. 2023] [Mouton et al. 2024] [Murali] [Murayama et al. 2024] [Nakayama et al. 2008] [Neves and Mariani 2024] [Northrop Aircraft INC Hawthorne CA 1952b] [Northrop Aircraft INC Hawthorne CA 1956] [O’Pray and Lissaman 1972] [Oh and Tavella 1986] [Olson and Stridsberg 1979] [Pack Melton 2014] [Pack Melton et al. 2023] [Pan et al. 2026a] [Pascioni and Cattafesta 2016] [Peng et al. 2022b] [Perera 2023] [Pham and Marshall 2011] [Pino Romainville] [Prabhakar 2013] [Pugliese and Englar 1979] [Pulliam and Sclafani 2014] [Qiu et al. 2018] [Raj Mohamed et al. 2022] [Rakowitz et al. 2008] [Rang and Heinze 2017] [Reader 1976] [Reader 1980] [Ren et al. 2024] [Richard et al. 2014] [Richard et al. 2017] [Rinoie et al. 2006] [Rizzetta and Visbal 2016b] [Rizzetta and Visbal 2016a] [Roberts 1965] [Roberts et al. 1966] [Rogers et al. 2000] [Rudnik 2013] [Sang 2009] [Sawada and Inoue 1993] [Schramm et al. 2016] [Sears 1983] [Shah 1991] [Siewert and Stewart 1965] [SlEWERT and Stewart 1967] [Songlin and Xianfu 1996] [Spens and Bons 2022] [Spens et al. 2023] [Stanewsky and Rosemann 2001] [Stumpf 2002] [Syverud et al. 1993] [Takeda et al. 2003] [Takeda et al. 2004] [Tal and Nguyen 2015] [Taylor and Gammon 2019] [Tewes and Taubert 2015] [Tinoco et al. 1986] [Turner 2024] [Turner et al] [Trobaugh et al. 1980] [Turner et al. 2017] [Twiss et al. 2019] [Ura et al. 2006] [Ura et al. 2008] [va et al 1995] [Vasile et al. 2010] [Victor et al. 2016a] [Victor et al. 2016b] [Volino 2010] [Vrchota 2017] [Walker et al. 2016] [Walker et al. 2018] [Wang 2022] [Wang 2024b] [Wang et al. 2021d] [Wang et al. 2024c] [Wild 2015] [Wilkins et al. 2014b] [Wilkins et al. 2014a] [Humphreys et al. 2023] [Humphreys et al] [Williams and Howe 1970] [Winski et al. 2025b] [Wood and Rogers 1986] [Yadala Venkata et al. 2018] [Zhang et al] [Zhang et al] [Yavuz and Rockwell 2006] [Ye 2025] [Yilmaz and Yillikci 2005] [Yokokawa et al. 2006] [Yokokawa et al. 2008] [Yoon et al. 2011] [Zauner et al. 2025] [Zeiger et al. 2002] [Zhang 2010] [Zhang et al. 2018b] [Zhao et al. 2015]

Remotely piloted operation and the ground station

How the aeroplane was actually flown. Ground stations, displays, link behaviour and the pilot who is not aboard. This matters more here than in most of the series, because Froude scaling compresses the aeroplane’s time while leaving the pilot’s reaction time exactly where it was.

207 records. [Abdul Sathar Eqbal et al. 2018] [Abeyratne 2016] [Abeyratne 2019] [Adelgren et al. 2004] [Ale Isaac Khoueini] [Alexander 1979] [Army Scientific Advisory Panel Washington Dc 1977] [Aume et al. 1976] [Ausserer and Harmon 2012] [Badole et al. 2022] [Baigang 2024] [Barnwell et al. 2003] [Battipede et al. 2005] [Baumann and Gal-Or 1992] [Baumgartner et al. 1979] [Becker et al. 2011] [Benoit et al. 2014] [Borst 1978] [Bruce et al. 1998] [Burton and Hoburg 2018] [Cetinsoy 2015] [Chamitoff 1994] [Chamitoff 1995] [Chang and Laliberté 2023] [Chase and McDonald 2014] [Choi et al. 2010] [Clark 1983] [Cordero et al. 2014] [Corraro et al. 2003] [Cunningham et al. 2011] [D’yakonov et al. 2018] [Dantsker et al. 2018] [Dantsker et al. 2020] [Dantsker et al. 2023] [Bertoli et al. 2016] [De Giorgi et al. 2017] [Deets and Brown 1986] [Demir et al. 2019] [Determination of External Power 2019] [Синеглазов and Дьяков 2011] [Edwards 1972] [Edwards 1981] [Eilertson 1975a] [Eilertson 1975b] [Ergocmen and Yavrucuk 2020] [Evolution of Human Systems 2016] [Fas-Millán and Pastor Llorens 2019] [Fitzgerald and Gingras 1996] [Flight performance of civil] [Fogel et al. 1974] [Ford 1977] [Foster et al. 2020] [Foy and Lawrence 2005] [French 1988] [Friedrich et al. 2022] [Fulkerson et al. 1980] [Fullmer et al] [Garcia-Hernandez et al. 2017] [García-Hernández et al. 2018] [Glizde and Urbaha 2019] [Glizde and Urbaha 2020] [Glīzde] [González Mendoza 2026b] [González Mendoza 2026a] [Gregory et al. 1977] [Gunes et al. 2019] [Guo and Xu 2000] [Guzel and Atesoglu 2014] [Gómez Rodríguez] [Gómez-Rodríguez and Cuerno-Rejado 2025] [Gómez-Rodríguez et al. 2018] [Haaland and Sworder 1987] [Hall] [Hall 2014] [Hall 1992] [Harmats and Weihs 1999] [Hasan et al. 2022] [Hicks and Durbin 2014] [Hinton and Eastlake] [Hobbs 2017] [Hobbs 2023] [Hoffelner et al. 2023] [Holleman 1976] [Howard and Bray 1992] [Howard et al. 1991] [Howse 2011] [Human Systems Integration 2016] [Huntoon et al. 1979] [Hyde and Massie 1993] [Initial Unmanned Aircraft Sizing 2014] [Initial Unmanned-Aircraft Sizing 2012] [Jameson 2009] [JanakiRam 1980] [Janakiram and Scruggs 1981] [JanakiRam and Scruggs 1982] [Jardin and Mueller 2007] [Jardin and Mueller 2009] [Jenn 1998] [Jie and Jung 2011] [Johnson et al. 2011] [Jorris et al. 2011] [Jun et al. 2021] [Jung et al. 2012] [Jung et al. 2019] [Iain and Jones 2011] [Kearns 2018] [Kellett 1996] [Kellett et al. 1996] [Khan and Nahon 2015] [Krohn 1988] [Krznar et al. 2018] [Kubo and Suzuki 2008] [Kügler and Holzapfel 2020] [Lam et al. 2020] [Larsen 1975] [Layton 1974] [Lee and Kim 2024] [Leite et al. 2009] [Li et al. 2025d] [Li et al. 2025g] [Linehan 1996] [Lu 2017] [Manjarrez et al. 2023] [Marshall] [Maughmer and Somers 1987] [McMinn and Jackson 2002] [McReynolds] [Mehta 2013] [Menhaj and Rajaei Salmasi 2000] [Merhav and Grunwald 1978] [Minor et al. 2004] [Morris 1983] [Motter et al. 2006] [Murray and Wild 2026] [Nachmani 2007] [Nelms et al. 1976] [Nicholson et al. 1988] [Nix et al. 2009] [Olson 2015] [Orchard 2023] [Pan et al. 2026b] [Park 2019] [Paulson et al. 1977] [Prudente and Cavalieri 2007] [Pugh et al. 2020] [Pulk and Stolarik 1977] [Quraishi 1989] [Sadraey 2017] [Sarrafian 1984] [Sarrafian 1986] [Sato and Muraoka 2013] [Seaberg et al. 1972] [Seanor] [Sekimoto et al. 2020] [Selig 2010] [Shmelova et al. 2017] [Simon and Rajesh 2022] [Sineglazov and Shmelev 2013] [Singh et al] [Singhal et al. 2019] [Slapnicar] [Sridharan et al. 2024] [Stiltner et al. 2010] [Stone] [Stone et al. 2006] [Słowik et al. 2017] [Teng and Grant 2023] [Thato Elijah and Rui Vasconcellos 2026] [The Path Forward 2016] [Torres et al. 2011] [Training Issues for Remotely 2016] [Turnage et al. 2019] [Tvaryanas 2006] [Tvaryanas and Maupin 2013] [Udroiu and Blaj 2016] [Urnes 2012] [Vandersteen 1987] [Varela Martínez] [Vengate et al. 2016] [Vinkler et al. 1980] [Wallace et al. 2011] [Wang and Wang 2016] [Wang et al. 2004a] [Wang et al. 2022a] [Wanngoen et al. 2020] [Wells 1995] [Welp et al. 1975] [White 2005] [Wickens and Dixon 2002] [Wolfe] [Wortman et al. 1975] [Xiaoxiao and Zhu 2025] [Xing and Yu 2012] [Xinghua 2018] [Xu et al. 2019c] [Yan et al. 2024] [Yan et al. 2025a] [Yang 2021] [Yip et al. 1990] [Yip et al. 1991] [Yuan 2026] [Yuma Test Center Yuma Proving Ground AZ 2008] [Zafirov 2010] [Zhang and Yu 2012] [Zhou and Huang 2022] [Ziemba et al. 1989] [Zogopoulos-Papaliakos et al. 2020]

Control allocation and redundant control effectors

Twenty surfaces and one pilot. Allocation, blending, daisy chaining and the overactuated problem. The X-48B carries twenty individually actuated trailing-edge surfaces, so allocation is not a refinement here but the means by which the aeroplane is controlled at all.

193 records. [Abrishami and Gong 2020] [Addington and Myatt 2000b] [Ahmad et al. 2008] [Ahmadi et al. 2012] [Akram et al. 2020] [Alwi and Edwards 2007] [Alwi and Edwards 2009] [Andersen et al. 1996] [Antonakis and Biannic 2024] [Atay et al. 2021] [Baggi et al. 2020] [Battipede et al. 2004a] [Belsterling 1976] [Benosman et al. 2007] [Bian et al. 2018] [Bian et al. 2019] [Binwen Lu et al. 2016] [Bodson 2000] [Boskovic and Mehra] [Boskovic et al] [Boskovic et al. 1998] [Buffington 1997] [Buffington 1999a] [Buffington 1999b] [Buffington et al. 1999] [Buğday and Saetti 2023] [Burken et al. 2001] [Casavola and Garone 2008] [Casavola and Garone 2010] [Cassaro et al. 2018] [Chudoba and Cook 2003] [ChunSheng Liu et al. 2012] [Cong et al. 2023b] [Control Allocation and Flight 2016] [Cordeiro et al. 2024] [Cristofaro and Faleschini 2024] [Cristofaro and Galeani 2014] [Cristofaro and Johansen 2016] [Cristofaro et al. 2015] [Cristofaro et al. 2017] [Cui et al. 2016] [de Vries and Van Kampen 2019] [Demenkov 2011] [Doman and Oppenheimer 2002] [Doman and Sparks 2002] [Dong et al. 2016] [Dong et al. 2024b] [Duan and Okwudire 2019] [Durham et al. 2016] [Frame-Wise Control Allocation 2016] [Franze et al. 2013] [Frost et al. 2010] [Frost et al. 2012] [Galeani and Sassano 2018] [Garmendia and Mavris 2016] [Gillard 1998] [Goodrich and Sliwa 1987] [Govoni and Cristofaro 2023] [Guan et al. 2025] [Guo et al. 2026] [Hallberg and Kaminer 1999] [Han et al. 2025] [Hansen et al. 2022] [Harkegard] [Harris et al. 2022] [Henderson and Lavretsky 1999] [Himawan and Branjangan 2017] [Hou et al. 2026b] [Hu et al. 2012] [Huang 2016] [Huang and Duan 2019] [Ijaz et al. 2019b] [Ijaz et al. 2019a] [Innocenti and Tonon 1988] [Jenkins 1973] [Jianjun Ma et al. 2008a] [Jianjun Ma et al. 2008b] [Jing and Ma 2025] [Jingping et al. 2011] [Jo et al. 2016] [Kang et al. 2015b] [Kang et al. 2023d] [Kara-Mohamed 2023] [Kefayat and Kamali 2024] [Kendall et al. 2015] [Kendall et al. 2017] [Khan et al. 2012] [Lang and de Ruiter 2021] [Li and Li 2014] [Li et al. 2011] [Li et al. 2012] [Li et al. 2017c] [Li et al. 2018c] [Li et al. 2024c] [Li et al. 2025a] [Li et al. 2025f] [Liang et al. 2021] [Lin et al. 2019] [Lingyu et al. 2006] [Liu et al. 2018b] [Liu et al. 2018c] [Liu et al. 2020a] [Liu et al. 2025c] [Lou et al. 2024] [Lu et al. 2019] [Lu et al. 2026] [Ma et al. 2010b] [Ma et al. 2012] [Matamoros and de Visser 2018] [Acheson and Gregory] [Acheson et al] [Acheson et al] [Ming-Chao and Ju 2016] [Naskar et al. 2015] [Naskar et al. 2016] [Nelson and Durham 2002] [Nguyen et al. 2018b] [Ozdemir and Horn 2009] [Park et al. 2017b] [Pascucci et al. 2017] [Pfeifle and Fichter 2021] [Pfeifle and Fichter 2023] [Prochazka et al. 2018] [Qin et al. 2023b] [Qin et al. 2023a] [Rajput et al. 2018] [Raney et al. 2000] [Re 2014] [Renken 1985] [Sadien et al. 2019] [Sadien et al. 2020] [Saetti 2025] [Saetti and Horn 2018] [Sanghi et al. 2022] [Scalera and Durham 1999] [Scordamaglia et al. 2025] [Shayan and Van Kampen 2021] [Shearwood et al. 2020a] [Shearwood et al. 2020b] [Shearwood et al. 2021a] [Shi et al. 2012] [Silva et al. 2026] [Singh] [Singh et al. 1999] [Sinha and Patra 2026] [Song et al. 2014a] [Stam and de Visser 2025] [Stephan 2025a] [Tabassum and Bai 2022] [Tang et al. 2025] [Tariq and Nahon 2020] [Nakamura-Zimmerer and Miller] [The Geometry of Control 2016] [Tohidi et al. 2018] [Tohidy and Sedigh 2013] [Tol et al. 2014] [Venkataraman and Doman 2001] [Vermillion et al. 2007] [Vile et al. 2020] [Virnig and Bodden 1994] [Wahler et al. 2023] [Wakayama 2008] [Wang et al. 2008] [Wang et al. 2018e] [Wang et al. 2019d] [Wang et al. 2021e] [Wang et al. 2024a] [Wang et al. 2025a] [Wilde et al. 2008] [Williams et al. 2025] [Xu et al. 2020] [Yang and Gao 2020] [Yang and Shen 2007] [Yang et al. 2009] [Yang et al. 2010] [Ye et al. 2009] [Yiming et al. 2019] [Yin et al. 2019] [Zaccarian 2007] [Zaki et al. 2017] [Zelman et al. 2023] [Zhan and Wang 2017] [Zhang 2017] [Zhang and Wang 2018] [Zhang et al. 2007b] [Zhang et al. 2008] [Zhang et al. 2025b] [Zhang et al. 2026d] [Zhao et al. 2026b] [Zhen and Cui 2023] [Zhong et al. 2009] [Zhu et al. 2015] [Zou et al. 2012]

Dynamic scaling, similitude and what a subscale model can answer

The keystone, and a smaller literature than the question deserves. Froude scaling, relative density, the mass and inertia relations and the free-flight model as an instrument. It is companion to the Reynolds cluster rather than separate from it, the first holding what is matched and the second what is surrendered.

189 records. [Aarons et al. 2011] [Ahlefeldt and Quest 2014] [Akaryildiz et al. 2024] [Allen et al. 2015] [Ananda et al. 2017] [Baggi et al. 2022] [Balawi et al. 2015] [Baldwin 2007] [Banazadeh and Hajipouzadeh 2019] [Bennett 1947] [Beyers et al. 1997] [Bilanin 1987] [Bogos 2020] [Boisseau 1955] [Bovais et al. 1992] [Bowles et al. 2016] [Brandt et al. 2019] [Brower 2024] [Buckley and Morfey 1983] [Buckley and Morfey 1984] [Burnside and Horne 2012] [Carraway 1988] [Chambers et al. 2019] [Chambers 2010] [Chedrik et al. 2004] [Comer et al. 2024] [Comer et al. 2026a] [Constantin et al. 2022] [Courtin et al. 2020] [Cox et al. 2012] [Croom et al. 1988] [Croom et al. 2000] [Cumming and Kramer 1966] [Cunningham et al. 2008] [Dantsker 2024a] [Dantsker 2024b] [Dantsker and Mancuso 2019] [Dantsker and Selig 2015] [Davey and Ochoa-Cabrero 2023] [Stephens and Envia 2012] [Dean 2024] [Deitchman 1957] [Dick 2015] [Dickson et al. 2010] [Dimensional Analysis and Dynamic 2015] [Dimensional Analysis and Dynamic 2009] [Doherty] [Draper and Hewes 1948] [Droandi et al. 2014] [Du et al. 2024] [Du et al. 2025b] [Du et al. 2025a] [Eger et al. 2013] [Elena 2026] [Elzinga et al. 2014] [Eney 1981] [Fan et al. 2024] [Free-Flight Models 1953] [Freidmann 2001] [Fremaux 1995] [Friedmann 1998] [Friedmann 2000] [Frostig and Simitses 2001] [Gonzales et al. 2021] [Grana and Shanks 1952] [Guo et al. 2017] [Hammer et al. 2026] [Han et al. 2015] [He et al. 2021] [Hermes and Olivier 2013] [Hueschen 2011] [Hutter and Jöhnk 2004] [Harasani 2015] [Ivler et al. 2019] [Iwakawa et al. 2015] [Janna 2020] [Jarosław et al. 2026] [Jayaraman et al. 2022] [Johnson 1949] [Jordan and Bailey 2008] [Chambers 1988] [Jouannet et al. 2008] [Jouannet et al. 2012] [Keller et al. 2026] [Kepler 1980] [Kittirungsi et al. 2007] [Kobayakawa and Maeda 1978] [Kong et al. 2023] [Korzun and Cassel 2020] [Kunwar and Chakraborty 2025] [Kunwar et al. 2026] [Lam and Stollenwerk 1966] [Laumann 1966] [Lavan and Drummond 1987] [Lu et al. 2015] [Lu et al. 2016] [Luo et al. 2014] [Luo et al. 2016] [Mahdavi Talaromi and Abdollahzadeh 2026] [Mandal and Gu 2016] [Mas Colomer] [Mas Colomer et al. 2017] [Massa and Cervenka 1995] [McClure and Sirbaugh 1991] [Mitcheltree 2003] [Monaco et al. 2006] [Murch et al. 2009] [Nadell et al. 2022b] [Nadell et al. 2022a] [Nadell et al. 2023] [Nakamura and Oishi 2000] [Nepomuceno et al. 2022] [Niemi and Bevillard 2015] [Obermark 2004] [Olejnik et al. 2019] [Ouellette et al. 2012] [Ouellette et al. 2014] [Pan et al. 2025a] [Pieper et al. 2018] [Potvin 2001] [Preisser 1979] [Preisser 1980] [Price and Earl A. 1981] [Price and Glidewell 1981] [Principles of Dynamic Similarity 2022] [Pulsonetti] [Pusztai et al. 2024] [Ragheb et al. 2013] [Raymer 2001b] [Raymer 2001a] [Repperger 1995] [Richardson et al. 2014] [Robinson and Price 1975] [Rosen 1989] [Ross 1979] [Ruan and Aagren 2025] [Ruiz Garcia et al. 2022] [Sadovnychiy et al. 1998] [Saify et al. 2025] [Scaling and Similitude 1638 2017] [Scherberg and Rhode 1927] [Schmitz et al. 2024] [Sellers 2000] [Shalaby 2018] [Shawler 1981] [Shepheard 1965] [Shi et al. 2018b] [Shi et al. 2023a] [Similitude Relationships and Scaling 1992] [Similitude Dimensional Analysis 2007] [Simitses et al. 2000] [Simmons and Ackerman 2026] [Simmons et al. 2025] [Simon et al. 2023] [Simon et al. 2024] [Singleton and Yeager 2000] [Sobron 2018] [Song et al. 2013] [Starkey et al. 2012] [Straub et al. 1984] [Suleman 2007] [Tai et al. 2026] [Tian 1980] [Tian et al. 2007] [Tierney et al. 2019] [Tierney et al. 2021] [Risch and Heersema] [Tosti 1961] [Turner 1965] [Uppoor et al. 2026] [Viswanathan 2005] [Waltham 1997] [Wang et al. 2019a] [Wang et al. 2020d] [Wang et al. 2020c] [Wang et al. 2020a] [Wang et al. 2021c] [Wang et al. 2025g] [Wang et al. 2026c] [Ward et al. 2026] [Warsop and Crowther 2019] [Williams 2021] [Williams et al. 1994] [Wu 2006] [Yarlett et al. 2000] [YiFan et al. 2024] [Yue et al. 2022] [Zhou 2023] [Zhu 2014]

Structures, materials and the airframe

The centrebody problem in general form. Loads, panels, composites and the non-circular pressure vessel that is the configuration’s hardest structural question.

174 records. [Abou Khalil] [Abumeri and Chamis 1996] [An et al. 2018] [Anwar 2025] [Arney et al. 1964] [Barsh 1944] [Barthelemy et al. 1994] [Bauch and Lair 1970] [Baumgartner et al. 1958] [Bazin and Fields 2015] [Belkharraz and Sobel 2001] [Bilger et al. 1981] [Boudreault 1983] [Bramsiepe et al. 2018] [Brewer 1953] [Brodersen 2002] [Browne 1990] [Burris and Bender 1969] [Butler 1972] [Carlin and Bevan 1986] [Castrichini et al. 2018] [Cea and Palacios 2021] [Cella and Biancolini 2012] [Chen 2010] [Cheng 1982] [Chopra and Datta 2003] [Clay 2004] [Clay and Berens 1964] [Coleman 1952] [Coleman 1954] [Coleman 1957] [Coleman 1958] [Connelly et al. 2024] [Cornell Aeronautical Lab INC Buffalo NY 1953] [Craddock 1973] [Daines 1966] [Danowsky and Schulze 2016] [Darden 1984] [Delgado Regis et al. 2004] [Deneff 1973] [Dickinson 1953] [Doherty and Butzel 1979a] [Douglas Aircraft Co Long Beach Ca 1962] [Dvorak et al. 1947] [Ekquist 1965] [Ekvall and Young 1976] [England 1975] [Esposito et al. 2026] [Failure of Aircraft Wing 2019] [Fanthorpe C. et al. 2012] [Forte et al. 2023] [Fu et al. 2024a] [Gallagher and Wei 2008] [Gerdes 2011] [Giessler and Nash 1971] [Glenn and Koch 1973] [Gottlieb 1987] [Green and Fernandez 1994] [Griffiths and Visser 2000] [Grover 1966] [Gurdal 2002] [Hanff and Huang 1991] [He 2015] [Heckl et al. 1962] [Hepler et al. 1973] [Heyong and Ye 2011] [Horton and Mayers 1965] [Horvath and Wrenn 2021] [Hwang et al. 2003] [Itoh and Kobayashi 2000] [Johnson 1994] [Joo et al. 2012] [Joo et al. 2014] [Kain et al. 1978] [Kaprilevskaya and Kozlov 2018] [Kautz 1972] [Kawazoe and Kato 2005] [Kenway and Martins 2014] [Kier 2005] [Konstantinovskaya et al. 2024] [Kumar 2025] [Lee 1980a] [Li et al. 2024a] [Lindsey 1977] [Liu and Sun 2025] [Lo et al. 1995] [Maekawa et al. 2007] [Magee and Taylor 1971] [Mahen 2026] [Mahulkar 2010] [Mangalam et al. 2010] [Marchinski 1974] [Marsden and Price 2001] [Martin 1964] [Martinez et al. 1987] [Masud and Khan 2015] [Matsuzaki et al. 1987] [McDonnell Aircraft Corp St Louis Mo 1950] [Miller and Pollock 1955] [Milos 1998] [Milos and Squire 1996] [Tang 1970] [Mishler et al. 1959] [Montel and Thielecke 2015] [Moon 1996] [Moosavian et al. 2014] [Morote and Liaño 2012] [Mosby 1965] [Moshier 2006] [Nangia and Palmer 2007a] [Newell 1939] [Norton 1990a] [Norton 1990b] [Norwood 1992] [Pak and Lung 2011] [Pan and Cheng 1995] [Panel Discussion 1976a] [Parikh et al. 1994] [Park 2007] [Pechaud and Kim 2001] [Pretorius] [Rakowitz et al. 2003] [Rand 1963] [Rhoads 1952] [Ricci et al. 2016] [Roberts and Brown 1988] [Robinson 2004] [Robinson and Robinson 1950] [Rockwell 1994] [Rom 1992c] [Rosende 1979] [Ross 1984] [Rotor Noise 1976c] [Smrithika 2025b] [Sachs et al. 1956] [Sachse 1998] [Schneider 1976] [Scott et al. 2014] [Shih and Ding 1996b] [Shlien 1991] [Siegel 1972] [Simon et al. 2017] [Smith 1968] [Smith et al. 1973a] [Smrithika 2025a] [Spearman 2007] [Supersonic Transport Wing Minimum 1992] [Taha and Bauomy 2021] [Torenbeek 1972] [Tsushima et al. 2022] [Ulbrich 2002] [Van Gaasbeek 1980] [Vaughan 1948] [Vaughan 2015] [Wada and Tamayama 2019] [Wei and Nie 2005] [Weiss et al. 2013] [Weisshaar 1978] [What’s under the skin?] [What’s Under the Skin?] [What’s under the Skin? 1999] [Whetstone and Robinson 1946] [Wilhem 1970] [Wing Loads 1996] [Xu and Song 2014] [Yamashiro and Livine 2009] [Yeager et al. 1997] [Yen and Hsu 2007] [Yeo and Romander 2012] [Yihao et al. 2024] [Zhang 2025] [Zhu and Li 2023] [Zientarski et al. 2015] [Çelik and Yavuz 2016]

Rotorcraft, V/STOL and powered lift

Aircraft that lift on rotors, fans and deflected thrust. Helicopter and tiltrotor flight dynamics, vertical and short takeoff handling, powered-lift control and their flight test. They are kept because their stability, control law and flight test literature is the literature this article draws on, applied to another kind of aircraft.

86 records. [Alscher et al. 1966] [Barrett 1952] [Bedford and Lowenberg 2006] [Bell Aerospace Co Buffalo Ny 1956] [Birckelbaw and Corliss 1992b] [Bird 1970] [Bowes 1978] [Briardy et al. 1970] [Brogan et al. 1961] [Brown 1950] [Burks 1981] [Byrnes et al. 1974] [Celi 2015] [Cohan and Hirsh 1966] [Creasey et al. 1966] [Curtiss et al. 1967] [Deel et al. 1972] [Desvigne and Embacher 2025] [Deveaux 1965] [Doblhoff 1956] [Dominick and Watts 1967] [Dooley and Yeary 1979] [Duvivier and McCallum 1960] [Egerton and Fitzpatrick 1967] [Falcone et al. 1974] [Finnestead and Connor 1969] [Finnestead et al. 1970] [Gaonkar and Peters 1986] [Gaonkar et al. 1981] [Goldberger 1966] [Gorton and Hoad 2002] [Gupta et al. 1984] [Hargraves 1961] [Hayama et al. 2021] [Head 1966] [Higher-Order Modeling of Coupled 2006] [Higher-Order Modeling of Coupled 2012] [Hirsh 1965] [Hoffstedt et al. 1973] [Hughes and Wernicke 1974] [Jenkins and Marks 1975] [Judas and Deligiannidis 2013] [Liu et al. 2023] [Lockheed-Georgia Co Marietta 1969] [Lopez et al. 2021] [Louisse and Marshall 1974] [McPherson 1977] [Melton and Hall 1968] [Meyers et al. 1968] [Miesner et al. 2020] [Modelling Helicopter Flight Dynamics 2007] [Modelling Helicopter Flight Dynamics 2018] [Moschetta 2010] [Nagata et al. 1968] [Nguyen and Webb 2025] [Nicholson and lowry 1966] [Oliveira] [Painter and Erickson 1984] [Parlier 1983] [Pieper 1965] [Pittsburgh Univ Washington DC Research Staff 1966] [Piziali 1964] [Piziali and Duwaldt 1962] [Putman 1961] [Putman 1969] [Rais-Rohani and Baker 1994] [Rau and Greenwood 2022] [Rhodes 1969] [Roberts et al. 1967] [Schrage and McKeithan 1989] [Schwartz and Wray 1969] [Shastry et al. 2018] [Simon and Savage 1975] [Snyder 1950] [Sullivan 1993] [Taamallah 2015] [Tangler 1979] [The Boeing Canard Rotor/wing 2004] [Turk and Watts 1964] [Vagianos and Rooney 1964] [Van Wyckhouse 1966] [Wang et al. 2019c] [Whitfield and Blackburn 1965] [Wyrick 1965] [Yamato et al. 1988] [Yu and Sirohi 2026]

Aeroelasticity, flutter and flight vibration

The airframe as an elastic body in the airstream. Flutter prediction and suppression, aeroelastic tailoring, buffet and flight vibration surveys. The X-48B was dynamically scaled as a rigid body [Taylor 2009], so this is the half of dynamic similitude the aeroplane did not attempt.

82 records. [Aeroelasticity Problems in Compressible 2010] [Alyanak and Pendleton 2017] [Asher et al. 1957] [Balachandran 2014] [Bennett and Abel 1981] [Bennett and Abel 1982] [Bolds 1961] [Bolds 1962] [Brenner 2001] [Brown et al. 1980] [Byreddy et al. 2003] [Cazier and Kehoe 1986] [Cea and Palacios 2023] [Chuban 2005] [Clarke et al. 2005] [Davis and Hoffler 2009] [Deangelis 1981] [Dowell 1996] [Dugundji and Ghareeb 1965] [Engelbrecht] [Extended Models of Large 2012] [Farhat 1999] [Farhat 2001] [Ferede 2022] [Flight Dynamics of Elastic 2014] [Fujino et al. 2003] [Gonzalez et al. 2023] [Grauer and Boucher 2017] [Graves et al. 2003] [Heidersbach et al. 2024] [Herrmann and Nemat-Nasser 1966] [Hu et al. 2009] [Jones 1970] [Jones and Nisbet 1976] [Kawakami et al. 2008] [Kayran 2007] [Kehoe 1988] [Kehoe and Freudinger 1994] [Keye and Rudnik 2009] [Kim et al. 2009b] [Lee et al. 1991] [Lesoinne 2007] [Lind 2003a] [Lind 2003b] [Mukhopadhyay 1995] [Nash et al. 1975] [Neuert and Dinkler 2020] [Newsom and Pototzky 1981] [Nguyen et al. 2018a] [Oz 1998] [Pachikara and Lind 2012] [Pancini dos Santos and Marques 2024] [Raveh 2011] [Richter and Patil 2010] [Rimer et al. 1983] [Rimer et al. 1984a] [Rimer et al. 1984b] [Sarıgül and Erbay 2026] [Sevy and Earls 1970] [Spivey et al. 2020] [Sudha et al. 2018] [Tang and Dowell 2000] [Tang and Dowell 2001] [Tantaroudas et al. 2015] [Tao et al. 2023] [Thomas 1961b] [Thomas 1961a] [Ting et al. 2017] [Tran and Lind 2010] [Triplett 1980] [Vepa 2023c] [Vijayakumar et al. 2014] [Wang et al. 2018a] [Weisshaar 1979] [Winther et al. 2000] [Wu 1975] [Yang and Wan 1978] [Yates and Bennett 1972] [Yates et al. 1983] [Yoo et al. 2002] [Zettel et al. 2023] [Zimmerman and Weissenburger 1964]

Flight test instrumentation, air data and test data processing

How a flight test measures what it measures. Air data probes and angle-of-attack vanes, data acquisition and recording, and the processing and management of test data. The X-48B carried two air data booms measuring total and static pressure, static temperature, angle of attack and sideslip [Risch et al. 2009], and every derivative identified in flight rests on them.

69 records. [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 1993] [Aircraft and Flight Test 2021] [Angle of Attack Indicator 1960] [Nogales 2020] [Bach and Parks 1987] [Bach 1980] [Bever 1992] [Bleimeyer 1981] [Bogue 1992] [Bowen et al. 1985] [Brooks 1986] [Che et al. 2021] [Chen et al. 2021a] [Day and Guthrie 1958] [Dean 1942] [Design and Installation of] [Dodgson 1973] [Douglas Aircraft CO INC Santa Monica CA 1963] [Emerson et al. 1955] [Flight TEST Procedures for] [Freuler and Hoffmann 1977] [Garman and Andrisani 2003] [Gibson 1981] [Gracey 1980] [Gregory and McCrink 2016] [Hensley 1994] [Hermann et al. 1984] [Ivanković et al. 2023] [Jain et al. 2019] [Jann and Greiner-Perth 2009] [Karam 1975] [Kaye 1983] [Kish et al. 2017] [Knighton 1992] [Kohn and Pangilinan 1986] [Large et al. 1981] [Leckman and Bennett 1978] [Liu 2023a] [Luo and Katz 2017] [Martin 1978] [Martos and Rogers 2018] [McElreath 1972] [Methods for Reducing Data 2003] [Miniaturised Inertia! Measurement Unit 2005] [Monteil 2024] [Moul and Taylor 1981] [Moum 2010] [Naval Air Test Center Patuxent River MD 1963] [Oosterom and Babuska 2006] [Pawlak 1994] [Pommier-Budinger et al. 2016] [Previati et al. 2012] [Redeker and Voersmann 1988] [Rimmer 1952] [Rogers 2019] [Sanderson 1965] [Schafer 1962] [Stouder 1981] [Strader et al. 2016] [Vaughn and Lindsay 1988] [Ward and Berge 2012] [Ward and Binford 1986] [Whitmore 1988] [Wilkin Perry 1943] [Yokota et al. 2021] [Zhai et al. 2024]

Flight test programmes, organisations and their history

The institutions and campaigns of flight test. Programme overviews of named aircraft, test centres, ranges and test management, and the history of research flight. The X-48B’s own flight test campaign is among them, together with the Environmentally Responsible Aviation project from which the X-48C’s noise objective came [The Environmentally Responsible Aviation project, a technology development project].

61 records. [Adolph 1981] [Air Force Flight Test Center Edwards AFB CA 1970] [Air Force Flight Test Center Edwards AFB CA 2002] [Air Force Test Pilot School Edwards Afb Ca 1990d] [Air Proving Ground Center Eglin AFB FL 1954] [Air Proving Ground Center Eglin AFB FL 1955] [Army Aviation Board Fort Rucker Al 1964] [Broughton 1978] [Carico 1995] [Cook 1981] [Cosenito 2010] [Cusimano and Johnson 1994] [Dawson 2015] [Dwyer 1994] [Enzinger 1988] [Eppley 1963] [Experience Gained during Development 2010] [Gentry 1968] [Hart 1992] [History of Supersonic Transport 2020] [Hoadley 1988] [Immenschuh 1988] [Jann et al. 1999] [Lux-Baumann and Burkes 2005] [Jordan 1974] [Kempel and Painter 1994] [Kennedy 1986] [Lang 1981] [Manning et al. 1992] [Mascitti and McLean 1976] [McTigue and Ryan 1968] [Mertaugh 1998] [Meyersburg 1968] [Miller 1973] [Morgenfeld 1992] [Morger 1988] [Nakadate 2005] [Nicholson 1985] [O’Connor 1982] [Redelinghuys et al. 2015] [Rhea and Moore 1988] [Rice 1946] [Rice and Hazlwood 1994] [Roberts 1988a] [Roberts 1988b] [Robertson and Hartfield 1992] [Shields 1981] [Silberg and Haas 2011] [Svendsen 1994] [The Environmentally Responsible Aviation project, a technology development project] [Thornton 1994] [Thornton and Lamy 1992] [Townsend and Phillips 1955] [Townsend and Phillips 1956] [Veletas 2026] [Wagner 1973] [Wang 2024a] [Williams 1981] [Wissler 1981] [Woodman 1971] [Wright 1987]

The atmosphere and the flight condition

The medium, named rather than assumed. Standard atmosphere properties, density altitude and the speed of sound. The kinematic viscosity ratio and the relative density readings in this article are taken from the standard atmosphere, so the literature that defines it belongs in the survey.

60 records. [A 2006] [A Standard Atmosphere 2022] [Air Force Test Pilot School Edwards Afb Ca 1962b] [Altmann 2011] [Analysis of Gust-Response Flight-Test 1988] [Appendix a Standard Atmosphere 2021] [Appendix a. the Standard 2011] [Appendix B 2003] [Appendix E Standard Atmosphere 1979] [Appendix E Standard Atmosphere 2004] [Approximations for the thermodynamic and transport properties of high-temperature air] [Ashburn et al. 1970] [B-34. U. S. Standard 1963] [Buck et al. 2004] [Buck et al. 2005] [Definition of the Standard 1954] [Dennis P. Dykstra 1980] [Herbert] [ICAO Standard Atmosphere 2021] [International Standard Atmosphere 2010] [Kang et al. 2023a] [Kang et al. 2023b] [Kaushik 2018] [King-Hele 1964] [Kurzke and Halliwell 2018] [Lehman and Kaplan 1965] [Minzner et al. 1976] [Other Publications 1987] [Pelton and Hannah 1976] [Peters 1977] [Pressures and Temperatures 2000] [Properties of the U.S. 2014] [Properties of the U.S. 2024] [Report No. 538 Altitude-Pressure 1935] [Space environment natural and] [Standard Atmosphere 1997] [Standard Atmosphere 2005] [Standard Atmosphere 2014] [Standard Atmosphere 2023] [Standard Atmosphere 2024] [National Bureau of Standards 1927a] [National Bureau of Standards 1927b] [Standard Atmosphere Data 1992] [Standard Atmospheric Profilesa aSource 2002] [Sutherland 1893] [Minzner 1976] [The Flight Environment 2021] [The International Standard Atmosphere 2017] [The International Standard Atmosphere 2026] [The NBS-NACA tables of thermal properties of gases] [The Standard Atmosphere 1920] [The Standard Atmosphere 1964] [The Standard Atmosphere 1976] [Turns and Kraige] [U. S. Standard Atmosphere 1963] [U.S. Standard Atmosphere 1976 1976] [1976 US Standard Atmosphere 2014] [Vaughan 2003] [Yaroshevsky 2010] [Zuppardo 1993]

Flight mechanics and aircraft performance

The equations the scaling relations are written in. Equations of motion, steady, gliding and turning flight, range, endurance and performance methods, mostly as chapters of reference texts. The Froude ratios in this article are dimensional consequences of these equations, which is why their reference statements belong in the survey.

57 records. [Aircraft Cruise in Steady 2011b] [Aircraft Cruise in Steady 2011] [Aircraft Equations of Motion 2003] [Aircraft Equations of Motion 2014] [Aircraft Equations of Motion 2022] [Aircraft Maneuvers and Flight 2011] [Aircraft et al. 2011b] [Aircraft Mechanics 2026] [Aircraft Model 2025] [Aircraft Models 2012] [Aircraft Operating Envelope 2010] [Aircraft Performance 2003] [Aircraft Performance 2014] [Aircraft Performance 2026] [Aircraft Range and Endurance 2011] [Aircraft et al. 2011a] [Aircraft Steady Gliding Longitudinal 2011b] [Aircraft Steady Gliding Longitudinal 2011a] [Aircraft Steady Level Turning 2011b] [Aircraft Steady Level Turning 2011a] [Aircraft Steady Longitudinal Flight 2011b] [Aircraft Steady Longitudinal Flight 2011a] [Aircraft Steady Turning Flight 2011b] [Aircraft Steady Turning Flight 2011a] [Appendix 2011] [Ashley 1967] [Baghiyan 2020] [Barnard 2004] [Buell 1970] [Complete model of aircraft] [Computational Flight Dynamics 2016] [Cook 2000] [Flight dynamics � Vocabulary] [Flight Envelope 2021] [Flight Envelopes 2012] [Flight Vehicle Performance 2001] [From Steady Flight 2011] [From Steady Flight to 2011] [Hightower 1985] [Lynch 2001] [Krishnamurthy and Luckner 2017] [Linear Flight-Dynamics Analysis 2023] [Miller and Koch 1985] [Nominal aircraft dynamics] [Northrop Aircraft INC Hawthorne CA 1953] [Piloted Aircraft Performance 2004] [Rigid-Body Flight Dynamics 2026] [Schwanz 1972] [Sinha and Ananthkrishnan 2017d] [Sinha and Ananthkrishnan 2017a] [Sinha and Ananthkrishnan 2017b] [Stephan 2025b] [Streby 1990] [Takeoff and Landing Theory 2003] [Thelander 1965] [Wenxuan 1991] [Young 2010b]

Unconventional wings, joined, oblique, swept forward, morphing and flexible

Configurations that, like the blended wing body, depart from the tube and wing. Joined, oblique, forward-swept, variable-sweep and morphing wings, wing-in-ground-effect craft and flexible-wing and parafoil gliders. They are this literature’s other experiments in configuration, kept apart from the blended wing body cluster because none of them is one.

44 records. [Ahad and Graham 2007] [Beatty et al. 1977] [Bird 1973] [Blair et al. 2008] [Bonnema and Smith 1988] [Clyde et al. 1984] [Design of Unique Aircraft 2024] [Dizdarevic and Dizdarevic 2022] [Folding Wing Flight Test 2018] [Further Development and Flight 1994] [Goddard and Eastgate 2010] [High-Altitude Long-Endurance HALE Sensor 2026] [Islam et al. 2025] [Kentfield and Spragins 2004] [Kress 1983] [Krone 1980b] [Krone 1980a] [Lange and Moore 1979] [Lazos 2005] [Leonard 2001] [McMurtry et al. 1981] [Nangia and Palmer 2007b] [Nicolaides 1976] [Oblique Wing Aircraft 2020] [Painter 1983] [Powers et al. 1992] [Rasmussen et al. 2006] [Ro et al. 2010] [Ryan Aeronautical Co San Diego Ca 1962] [Ryan Aeronautical Co San Diego Ca 1963] [Sakamoto and Cota 1965] [Smith and Srokowski 1983] [Smith et al. 1987] [Spacht 1980] [Spinning Aircraft and Nonspinning] [Trancossi et al. 2016] [Traub 2024b] [Vale et al. 2014] [Variable Sweep Wing Design 1980] [Vishwanathan] [Ward et al. 2011] [Willan 2011] [Xiong et al. 2019] [Yamazaki and Kusunose 2014]

Flight simulation and simulators

The ground instrument that stands in for flight. Simulation models and their exchange, simulator fidelity and motion requirements, and in-flight simulation. Every X-48B mission was rehearsed in the simulation mode of its ground control station before it was flown [Risch et al. 2009], and the programme reports the aeroplane as closely matching simulation in up-and-away flight and landing [Vicroy 2011].

43 records. [Abbott et al. 1982] [Aircraft Simulation Model 2022] [Almanza et al. 1994] [Branson 1994] [Brunner 1996] [Carlson et al. 1980] [Chen et al. 2008] [Crosbie and Eyth 1981] [Evans and Schilling 1983] [Flight Simulation 2016] [Harding and Bass 1990] [Hayden 1970] [Hofmann and Riedel 1979] [Jackson and Hildreth 2002] [Jackson and Hildreth 2006] [Kurtzberg 1963] [Math Model Assembly 2023] [McIntyre 1963] [Moormann] [Morlang and Strassburger 2025] [Pan et al. 2014] [Rawson 1963] [American Institute of Aeronautics and Astronautics 2021] [Rediess and Melton 1994] [Research and Analysis 2022] [Richards and Dismukes 1982] [Riedel 1979] [Sato 2006] [Simulation in Support 1988] [Spitzer et al. 1972] [Staley 1976] [Modeling and Simulation CoS 2011] [Swanson et al. 1992] [Taghizad et al. 2021] [Taylor et al. 2025] [Tischler and Tobias 2016] [Wang and Song 2025] [Warner 1995] [Weingarten 2004] [Woltkamp et al. 1988] [Zapico et al. 2008] [Zhixin 2022b] [Zhixin 2022a]

Where the Framing Breaks Down

The reference vehicle’s weight is derived, and the one quoted figure is a round number in a magazine. The figure of 854,875 pounds comes from inverting the cube of the scale ratio on the model’s own weight. The 500-ton figure names no source and no weight definition, so it corroborates the derivation and enters no calculation [Jacobs 2007, Thinking outside the tube, Wired]. The comparison against Liebeck also depends on the scaling law, and the ratio of 1.649 under the cube becomes 1.414 under the square of span. If the model was not weight-scaled with the precision assumed, the number moves and the comparison against Liebeck moves with it.

The relative density factor is now quantified, and it changes the answer. Taking the model’s condition at the field elevation of Rogers Dry Lake raises the implied full-scale weight from 854,875 pounds to 914,885, and taking it at the ceiling raises it to 1,157,634. No source consulted states the altitude at which the weight scaling was set, so 854,875 pounds is reported as a lower bound and every comparison drawn from it inherits that status.

The BWB-17 does not fit the same arithmetic. At 6 percent scale and 120 pounds [Liebeck 2004],

\[b_{\text{ref}} = \frac{17}{0.06} = 283\ \text{ft}, \qquad W_{\text{full}} = \frac{120}{0.06^{3}} = 555{,}556\ \text{lb} \tag{37}\]

The implied span agrees with the 280 feet of Liebeck’s second-generation design to within 1.2 percent, and the implied weight falls at 0.675 of that design’s 823,000 pounds, so either the BWB-17 answered to an earlier and lighter reference design or it was not weight-scaled to the vehicle described in the same paper. The record does not say which, and this article does not guess.

The wing area enters one section and rests on one programme document. The figure of 100.5 square feet is the correlation update’s, given in a presentation slide without the reference definition behind it [Vicroy 2011]. It enters only through the reference chord $c = S/b$ used to put the Reynolds numbers on an absolute footing, and the ratio of 40.35 does not depend on it at all, because the chord cancels between model and full scale. A reader who distrusts the area should discard the two absolute Reynolds figures and keep everything else, and the argument is built on the ratio for that reason.

The X-48C’s moment-arm loss is a sensitivity and not a measurement. No source consulted publishes the sweep of the outer trailing edge, the spanwise station of the C model’s twin tails, or the vertical surface areas of either aeroplane. The inboard station of 2.5 feet and the tail arm of order ten feet are assumptions, chosen to be plausible rather than derived, and the tabulated shifts move with them. What does not move is the sign, since the geometry admits no reading in which moving a surface inboard on an aft-swept planform lengthens its arm. The engine-count half of the same argument is exact, resting only on published thrusts and weights.

The claim that departure onset does not transfer from the flight vehicle is argued from the scaling relations and has not been measured. No source consulted states a full-scale departure angle of attack, so there is nothing to compare the model’s limiting angle against. A quantified Reynolds correction is not attempted, because it depends on the configuration’s separation behaviour, which is the unknown in question.

The claim is about the flight vehicle and must not be read as a claim about the programme. The programme ran higher-Reynolds tunnel tests as well and reports its free-flight method as correlating well with the observed flight limits [Vicroy 2011]. This article does not claim that the departure boundary was left to the model, because it was not.

The correlation update is a conference presentation rather than a technical report, so its findings arrive as summary lines without the data behind them [Vicroy 2011]. The stall angles of 24 and 14 degrees, the phrase about departure limiter assaults and the pitching-moment finding are quoted from slides, and a reader wanting the supporting curves will not find them there.

The X-48B’s own weight and thrust are stated two ways as well. The flight-test papers give a maximum weight of 525 pounds and 54 pounds of installed thrust an engine, while the fact sheet gives a gross weight of 523 pounds and three 50-pound engines of about 150 pounds combined, and the correlation update gives 523 pounds and a static thrust of 162 pounds [Risch et al. 2009] [Regan 2008] [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090] [Vicroy 2011]. At 523 pounds the implied full-scale weight is 851,618 pounds rather than 854,875, and at 50 pounds an engine the model’s thrust to weight is 0.2857 and its excess over the full-scale design 1.272 rather than 1.374. Each changes the size of a result, and neither reverses its sign.

The X-48C’s engine thrust is stated differently by two sources, 89 pounds in the fact sheet and 75 in the 2011 presentation [X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090] [Vicroy 2011]. Every engine-out figure for the C model moves with that choice, from 2.378 down to 2.004 against the full-scale trijet. The conclusion keeps its direction while its size shifts.

The full-scale thrust comparison uses Liebeck’s second-generation design and not the reference vehicle. The 0.2245 thrust-to-weight figure belongs to an 823,000-pound, 800-passenger commercial design [Liebeck 2004]. If the military reference vehicle is thrustier, the model’s 1.374 excess shrinks, and the engine-out conservatism shrinks with it.

The Source Base

The survey rests on 6,622 research records assembled from Crossref, the NASA Technical Reports Server and the Defense Technical Information Center, of which 977 are primaries, being 14.8 percent, and 974 of those are report primaries by the identifier rule set out under The Definition of Primary. Thirteen primaries are cited by identifier, three of them journal and conference papers that the identifier rule does not reach.

The programme’s own documents carry the argument. The ground-to-flight correlation update answers the article’s keystone question directly and reports the stall angles [Vicroy 2011]. The flight-test progress paper of the NASA and Boeing test team reports the first 39 flights and the uncommanded roll-offs [Risch et al. 2009], the in-flight stability analysis reports the multisine excitation behind the envelope expansion [Regan 2008], and the post-stall command tracking paper reports the high angle of attack tests [Goldthorpe et al. 2010].

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when it is a NASA Technical Reports Server url or carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. The same report is therefore reachable through Crossref and through the Defense Technical Information Center under two different labels, and a rule keyed on where a record was found rather than on what it is would count such a report as secondary.

The definition excludes the conference papers of the American Institute of Aeronautics and Astronautics, abbreviated AIAA, that are among the most important sources here. Three of the article’s central documents are AIAA papers written by the people who flew the aeroplane, and no metric keyed on publisher will call them primary. 14.8 percent is a lower bound on how much of this survey is first-hand, and the thirteen identifier-cited primaries are the ones that actually carry the argument.

Thin Subjects

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, with a hyphen read as a space.

Subject	Title terms counted	Records
the viscosity of air and its variation with temperature	kinematic viscosity, dynamic viscosity, sutherland, viscosity temperature, transport properties of air	1
the relative density factor and model mass scaling	relative density, mass scaling, inertia scaling, moment of inertia, ballasting, mass properties	4
engine-out on a two-engine against a three-engine layout	engine out, engine inoperative, asymmetric thrust, asymmetric power, critical engine, minimum control speed, engine failure, propulsion failure, thrust asymmetry, one engine, lateral trim, control power requirement	29
thrust to weight as a scaling invariant	thrust to weight, thrust loading, power loading, installed thrust, thrust required, excess thrust, climb performance, takeoff performance, thrust sizing	3

The viscosity of air is the clearest case, and its one record is Sutherland’s own paper. The word viscosity also names the viscosity of lubricating oils, canola oil, molten metals, protein solutions and supercooled sucrose, and the Saybolt conversion tables of the American Society for Testing and Materials, none of which is this subject. The viscosity of air as a function of temperature is not an under-served subject. It was settled by Sutherland in 1893 and has lived in tables ever since [Sutherland 1893] [U.S. Standard Atmosphere 1976 1976] [The NBS-NACA tables of thermal properties of gases].

This is the fourth kind of thin, which is a subject whose vocabulary does not discriminate, compounded by the third, which is a subject so settled it stopped generating papers. A bibliographic search is the wrong instrument for a tabulated physical constant, and the right one is the table itself, cited by its identifier.

Engine-out on a two-engine against a three-engine layout is a real but small literature about a configuration choice most transports do not face. That thrust to weight is invariant under Froude scaling is almost never published, because it follows from a force scaling as the cube and is dimensional analysis rather than a finding, so the article’s claim stands on the arithmetic.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject, which is the scaling, aerodynamics, flight dynamics, control, testing, noise, propulsion, design and structure of the aeroplane and of the free-flight model that stands for it, read against the argument rather than against a word. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Similitude and Froude scaling also belong to hydraulics, soil mechanics, glaciology, fire research and civil engineering. Remotely piloted aircraft are also a tool of agriculture, ecology, geology, medicine and journalism, and remotely operated machines also work on the ground and under water. Stability margin also describes electrical power grids, ground robots and nuclear reactors. Sizing also applies to clothing, transistors, numerical methods and military forces, and atmosphere also names weather, climate and atmospheric optics. Multisine excitation also measures batteries, living tissue and radio amplifiers, and the wind tunnel also tests cars, trains, bridges and buildings. Thrust also names a property of bearings, and rudder also names the rudder of a ship.

Spaceflight and weaponry share this subject’s aerodynamics and its test facilities but not its vehicle, so their records are excluded. Orbital mechanics and spacecraft control, launch and re-entry vehicles, hypersonic vehicles and the hypersonic and impulsive facilities that test them, missiles, projectiles, bombs and stores are excluded, except where a title’s subject is a method this article uses, such as free-flight testing, tunnel scale effects, control allocation or parameter identification, stated in its own terms. Aircraft subjects the argument does not use are excluded as well, among them airline and airport operations, air traffic and airspace integration, navigation, maintenance, tyres and ground handling, electrical and fuel systems, seats and crew equipment, accident statistics, teaching and military operations, and so are drones used as tools of another trade, with their path planning, swarming and machine vision. A record whose title and first author repeat another’s is one work deposited twice, a conference paper and its journal version or one report under two identifiers, and only the earliest deposit is counted. Correction, erratum, corrigendum and withdrawal notices, and the indexes and bibliographies printed in the back matter of books, are excluded too, because a survey counts research works and those are editorial events or parts of works.

Reviews of books, reference and definition entries and notices are not admitted, and a document deposited twice is admitted once. An authored encyclopedia article of more than two pages and a chapter of a textbook are research works and are kept. A publisher’s record of a whole conference volume, which lists a meeting’s papers and carries none of its own, and an abstract-journal listing are not admitted either.

Some records of doubtful relevance are kept. Multisine signal design and control allocation stated for any plant, structural similitude for scaled plates, shells and beams, the identification of missile, re-entry and parachute aerodynamics from flight data, free-flight testing in hypersonic facilities, the aerodynamics of wings at hypersonic speed, and the flight of birds and insects where the title is wing aerodynamics or a dynamically scaled model each share a method or a phenomenon with this subject, so each is kept and a reader may weigh it accordingly. No residual cluster remains, and every record sits in a cluster named for what its titles are.

Every research title has been read for relevance, so the off-topic share that remains is a matter of reading judgement. A reading of titles cannot show that a work is relevant in substance, so this is a statement about titles only.

Epistemic State

Historical Fact

The dates, the flight counts, the two configurations, the builder, the engine fits, the modification list for the X-48C and the block structure of the flight test programme are taken from NASA and Boeing publications and from the two AIAA papers. The uncommanded wing roll-off, the behaviour of lateral stick during it, the six and two occurrences in the two slat configurations and the successful pitch-over recoveries are reported in the flight-test progress paper. The stall angles of 24 and 14 degrees, the controllability three degrees beyond maximum lift, the six-block structure of phase one to flight 80, the description of the departure limiter assaults as highly successful, the plot of ground tests on axes of vehicle scale against chord Reynolds number, the finding that support interference on pitching moment was much larger than anticipated, the statement that the free-flight method correlated well with observed flight limits, and the list of comparisons never made are reported in the ground-to-flight correlation update. The departure boundary was not left to the flight vehicle alone. The programme ran a suite of ground tests spanning more than two decades of Reynolds number, up to about 70 million in the National Transonic Facility, as the correlation update records.

Verified by Independent Derivation

The scale factor of 0.085000 from the published span and reference span. The Froude ratio table. The time compression of 3.430 and the Reynolds penalty of 40.35. The comparison against the X-36 at 1.815 and 5.979. The ladder of three candidate vehicles and the factor of 2.247 in Reynolds number attributable to the X-48A cancellation. The implied full-scale weight of 854,875 pounds and its ratios against Liebeck’s design brought to the same span, 1.649 under the cube of span and 1.414 under its square, with 1.765 and 1.513 on the field-elevation reading and 2.234 and 1.915 at the ceiling. The scaled weights of 518,274 and 604,653 pounds. The fractions of 0.855, 0.915 and 1.158 that the three implied weights form of 1,000,000 pounds. The thrust-to-weight figures of 0.3086 and 0.2245 and their ratio of 1.374. The asymmetric thrust fractions of 0.10286, 0.17800 and 0.07485 and the ratios of 1.374, 2.378 and 1.731 that follow. The absolute Reynolds numbers of $6.24 \times 10^6$ and $2.52 \times 10^8$ at the stated reference chord. The kinematic viscosity ratio of 1.281 between 10,000 feet and sea level on the standard atmosphere, and the effective penalty of 51.7 that follows. The implied full-scale weights of 914,885 and 1,157,634 pounds at the two non-unity readings of the relative density factor. The full-scale equivalent speed of 404.7 knots. The BWB-17’s implied reference span of 283 feet and weight of 555,556 pounds, within 1.2 percent of the 280-foot span and at 0.675 of the 823,000-pound weight of Liebeck’s second-generation design.

Analysis

The division of the flight results into Froude-governed conclusions that transfer and Reynolds-governed conclusions that do not. The identification of the disagreement between Liebeck’s stated stall progression and the observed roll-off as the disagreement the scale factor predicts. The reading of the engine-out test as conservative because the model is over-thrusted. The geometric argument that moving a vertical surface inboard on a swept planform shortens its moment arm, and the tabulated sensitivity of that shift to an assumed sweep angle. The reading of the X-48C as doubly penalised on its weakest axis, by engine count exactly and by moment arm approximately. The placing of the article’s criticism on how the flight result is repeated rather than on how it was obtained.

Inference

That the reference vehicle is heavy for its span, inferred from the implied weight being 1.414 to 1.649 times a passenger design brought to the same span. That it is the heavy-lift military aeroplane for refuelling and cargo that Boeing described, consistent with that excess, with the Air Force’s stated interest and with the magazine’s figure of 500 tons, though the scale relations do not show how much of the excess the military role explains. That bracketing the leading edge with two slat configurations hedges the Reynolds uncertainty, a reading of the test matrix and not a stated rationale.

What the Record Does Not Settle

The reference vehicle’s actual weight, which no technical source consulted states and one magazine gives as a round 500 tons. The reference definition behind the correlation update’s wing area. The positions of the vertical surfaces on either aeroplane, and the sweep of the outer trailing edge. The full-scale departure angle of attack. Whether the BWB-17’s weight answers to the design published alongside it. Whether the X-48C’s noise objective was met, an acoustic result this article does not have. Which of the two published thrust ratings the X-48C actually flew with, 75 pounds an engine or 89, on which every engine-out figure for that aeroplane depends. What the aeroplane does past the departure boundary, which the programme itself lists as having no flight comparison at all.

Out of Scope

The acoustic measurements and the shielding result of the X-48C, which need a noise dataset this article does not have. The structural design of the non-circular pressure vessel, the configuration’s hardest problem but outside flight dynamics. The economics of the blended wing body against the tube and wing. The later Boeing and NASA transonic truss-braced and blended configurations that followed the X-48. The military airlift requirement that motivated Air Force interest.

Conclusion

The X-48 is the aeroplane in this series whose most consequential property is its size. It flew 122 times, it was controllable throughout the low-speed envelope, it departed in uncommanded wing roll-offs at a limiting angle of attack, and it recovered every time [X-48 Research, All Good Things Must Come to an End, NASA] [Risch et al. 2009]. All four of those statements are true of a 20.4-foot aeroplane, and only three of them are evidence about a 240-foot one.

The departure boundary does not carry from the flight vehicle, and a reader wants it most. A free-flight model buys dynamic fidelity by surrendering Reynolds number, and at 8.5 percent the surrender is a factor of 40.35. That factor governs separation onset, and the most quoted single result of the flight programme is a separation phenomenon.

From the flight vehicle is the necessary qualification, and the campaign record supplies it. It flew both leading-edge configurations, which bracket the behaviour the scale factor makes least certain, and it plotted its ground tests on axes of scale against Reynolds number, up to about 70 million in the National Transonic Facility, short of the full-scale region the plot marks [Vicroy 2011]. The Reynolds-governed half was approached in the tunnels rather than assumed away. The campaign used both kinds of instrument, one that flies and one that reaches Reynolds number.

The disagreement this article began with survives that. The design paper says the outer wing keeps flying into the stall and the ailerons stay effective [Liebeck 2004]. The flight report says the aeroplane rolls off uncommanded and that roll input makes it worse [Risch et al. 2009]. No amount of flying the model resolves that, and the programme’s list of what it could not compare includes post-departure behaviour [Vicroy 2011].

What the X-48 proved is that a control system can hold a large tailless transport at low speed and recover it from its own edge, three and a half times faster than the aeroplane will have to. In 2000 that was the open question and it is no longer.

The most useful thing in the record is not a result but a lesson about instruments. Asked where its ground-to-flight comparisons were poor, the programme does not name the stall or the scale factor. It names first the support that held the model in the tunnel [Vicroy 2011]. A campaign that spent nearly six years and 122 flights worrying about Reynolds number was caught out by the supports that held its tunnel models, and the lesson is worth more to the next programme than any number in this article.

Equations

This section collects the 37 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 37, 26 are established and 11 are bespoke. Lengths, speeds, weights and thrusts are in feet, knots, pounds and pounds force, every ratio $r$ is model over full scale with $n$ the length ratio, and $\sigma$ is the relative density factor in its definition but stands for the ratio of full-scale to model air density in the weight ratio, so that it is one when both fly in the same air.

Equation 1, Scale Factor from the Published Spans. The published span of 20.4 feet over the published reference span of 240 feet gives a length ratio of 0.085000, which agrees with the published 8.5 percent scale. X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090 Risch et al. 2009 Boeing flies X-48C blended wing body research aircraft

\[n = \frac{20.4\ \text{ft}}{240\ \text{ft}} = 0.085000 \tag{1}\]

Equation 2, Froude and Reynolds Numbers. The Froude number is the ratio of inertial to gravitational force and the Reynolds number the ratio of inertial to viscous force.

\[Fr = \frac{V^{2}}{Lg}, \qquad Re = \frac{VL}{\nu} \tag{2}\]

Equation 3, Speed Ratio under Froude Matching. Equal Froude numbers for model and aeroplane fix the speed ratio at the square root of the length ratio.

\[\frac{V_m^{2}}{L_m g} = \frac{V_f^{2}}{L_f g} \implies r_V = \frac{V_m}{V_f} = \sqrt{\frac{L_m}{L_f}} = \sqrt{n} \tag{3}\]

Equation 4, Relative Density Factor. The relative density factor compares the mass of a body with the mass of air that a cube of its characteristic length contains.

\[\sigma = \frac{m}{\rho l^{3}} \tag{4}\]

Equation 5, Weight Ratio with an Atmospheric Term. Matching the relative density factor makes the weight ratio the cube of the length ratio divided by a density term that is one when model and aeroplane fly in the same air.

\[r_W = \frac{n^{3}}{\sigma} \tag{5}\]

Equation 6, Froude Scaling of Speed, Time and Angular Rate. For a dynamically scaled model in the same air, speed and time scale as the square root of the length ratio and angular rate as its reciprocal.

\[r_V = \sqrt{n}, \qquad r_t = \sqrt{n}, \qquad r_\omega = \frac{1}{\sqrt{n}} \tag{6}\]

Equation 7, Froude Scaling of Weight, Inertia and Reynolds Number. For the same model, weight scales as the cube of the length ratio, moment of inertia as its fifth power and Reynolds number as its power of three halves.

\[r_W = n^3, \qquad r_I = n^5, \qquad r_{Re} = n^{3/2} \tag{7}\]

Equation 8, Reynolds Ratio as a Consequence of Froude Matching. With kinematic viscosity unchanged, the Reynolds ratio is the product of the speed ratio fixed by Froude matching and the length ratio.

\[r_{Re} = r_V \, r_L = n^{1/2} \cdot n = n^{3/2} \tag{8}\]

Equation 9, Dynamic Pressure and Wing Loading Ratios. In the same air both the dynamic pressure and the wing loading scale linearly with the length ratio. Etkin and Reid, Dynamics of flight McCormick, Aerodynamics, aeronautics and flight mechanics

\[r_q = \frac{\rho V_m^{2}}{\rho V_f^{2}} = r_V^{2} = n, \qquad r_{W/S} = \frac{n^{3}}{n^{2}} = n \tag{9}\]

Equation 10, Time Compression of the X-48B. Any interval in the model is the full-scale interval times the square root of the length ratio, or 0.2915 of it.

\[t_m = t_f \sqrt{n} = 0.2915 \, t_f \tag{10}\]

Equation 11, Bespoke Model Duration of a Three-Second Motion. A full-scale motion of three seconds, an illustrative duration the article chooses, takes 0.875 seconds in the model.

\[t_m = 3 \times 0.2915 = 0.875\ \text{s} \tag{11}\]

Equation 12, Angular Rate Ratio of the X-48B. Angular rates in the model are faster than at full scale by the reciprocal of the square root of the length ratio, a factor of 3.430. Chambers 2010

\[r_\omega = \frac{1}{\sqrt{n}} = 3.430 \tag{12}\]

Equation 13, Time and Reynolds Ratios of the X-48B Against the X-36. The Froude scaling laws evaluated at the published scales of 8.5 and 28 percent give the X-48B dynamics 1.815 times faster and a Reynolds shortfall 5.979 times larger than those of the X-36. X-36 Tailless Fighter Agility Research Aircraft, NASA

\[\frac{r_t^{-1}(0.085)}{r_t^{-1}(0.28)} = 1.815, \qquad \frac{r_{Re}^{-1}(0.085)}{r_{Re}^{-1}(0.28)} = 5.979 \tag{13}\]

Equation 14, Reynolds Number on the Mean Geometric Chord. The Reynolds number is formed on a reference chord taken as the published wing area divided by the published span, which gives 4.926 feet. X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090 Vicroy 2011

\[Re = \frac{V c}{\nu}, \qquad c = \frac{S}{b} = \frac{100.5}{20.4} = 4.926\ \text{ft} \tag{14}\]

Equation 15, Model Reynolds Number at Maximum Speed at Sea Level. The published maximum speed of 118 knots on the mean geometric chord with the sea-level kinematic viscosity of the standard atmosphere gives a model Reynolds number of $6.24 \times 10^{6}$. X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090 Vicroy 2011

\[Re_{\text{model}} = \frac{199.2 \times 4.926}{1.5723 \times 10^{-4}} = 6.24 \times 10^{6} \tag{15}\]

Equation 16, Full-Scale Reynolds Number at the Corresponding Condition. Scaling the model speed and chord to full size by the Froude relations and keeping the sea-level viscosity gives a full-scale Reynolds number of $2.52 \times 10^{8}$.

\[Re_{\text{full}} = \frac{683.1 \times 58.0}{1.5723 \times 10^{-4}} = 2.52 \times 10^{8} \tag{16}\]

Equation 17, Full-Scale Speed Implied by the Model Maximum. Inverting the Froude speed ratio on the published model maximum of 118 knots gives a full-scale speed of 404.7 knots. X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090

\[V_f = \frac{118}{\sqrt{0.085}} = 404.7\ \text{kt} \tag{17}\]

Equation 18, Kinematic Viscosity Ratio at the Model Ceiling. Kinematic viscosity is dynamic viscosity over density, and the standard atmosphere makes it 1.281 times larger at the published ceiling of 10,000 feet than at sea level. X-48 Hybrid/Blended Wing Body, NASA Dryden Fact Sheet FS-090

\[\nu(h) = \frac{\mu(h)}{\rho(h)}, \qquad \frac{\nu(10{,}000)}{\nu(0)} = \frac{2.0135 \times 10^{-4}}{1.5723 \times 10^{-4}} = 1.281 \tag{18}\]

Equation 19, Bespoke Effective Reynolds Penalty at the Ceiling. The article defines an effective penalty as the Froude Reynolds penalty multiplied by the viscosity ratio for a model flown at its ceiling against an aeroplane approaching at sea level.

\[P_{\text{effective}} = n^{-3/2} \times \frac{\nu(10{,}000)}{\nu(0)} = 40.35 \times 1.281 = 51.7 \tag{19}\]

Equation 20, Bespoke Reynolds Penalty and Time Compression as Functions of Span. The article writes its Reynolds penalty and time compression as functions of model span alone, with the reference span held fixed at 240 feet.

\[P(b) = \left(\frac{b_{\text{ref}}}{b}\right)^{3/2}, \qquad \tau(b) = \left(\frac{b_{\text{ref}}}{b}\right)^{1/2} \tag{20}\]

Equation 21, Bespoke Cost of Substituting the X-48B for the X-48A. The ratio of the two span-based penalties, with the reference span held at 240 feet for both vehicles, prices the substitution of the 20.4-foot model for the 35-foot one.

\[\frac{P(20.4)}{P(35)} = \left(\frac{35}{20.4}\right)^{3/2} = 2.247, \qquad \frac{\tau(20.4)}{\tau(35)} = \left(\frac{35}{20.4}\right)^{1/2} = 1.310 \tag{21}\]

Equation 22, Bespoke Full-Scale Weight Implied by the Model Weight. Inverting the cube law on the published maximum model weight of 525 pounds assumes that the model was weight-scaled in the same air as the aeroplane, a relative density term of one. Risch et al. 2009 Regan 2008

\[W_{\text{full}} = \frac{525\ \text{lb}}{n^3} = 8.549 \times 10^{5}\ \text{lb} \tag{22}\]

Equation 23, Implied Full-Scale Weight with the Density Ratio Restored. Restoring the density term, the implied full-scale weight is the model weight over the cube of the length ratio times the ratio of full-scale to model air density.

\[W_{\text{full}} = \frac{W_m}{n^{3}} \cdot \frac{\rho_f}{\rho_m} \tag{23}\]

Equation 24, Bespoke Liebeck Design Scaled by the Cube of Span. Scaling Liebeck’s 823,000 pound design from 280 to 240 feet assumes geometric similarity, so that weight follows the cube of span. Liebeck 2004

\[W(240) = 823{,}000 \times \left(\frac{240}{280}\right)^{3} = 518{,}274\ \text{lb} \tag{24}\]

Equation 25, Bespoke Implied Weight Over the Cube-Scaled Design. The ratio sets the weight implied by the model under a relative density term of one against the Liebeck design scaled by the cube of span. Liebeck 2004

\[\frac{W_{\text{full}}}{W(240)} = \frac{854{,}875}{518{,}274} = 1.649 \tag{25}\]

Equation 26, Bespoke Liebeck Design Scaled by the Square of Span. Scaling the same design to a 240-foot span under the alternative assumption of constant wing loading makes weight follow the square of span. Liebeck 2004

\[W_{2}(240) = 823{,}000 \times \left(\frac{240}{280}\right)^{2} = 604{,}653\ \text{lb} \tag{26}\]

Equation 27, Thrust to Weight Ratio of the X-48B. Three engines of 54 pounds installed thrust against the published maximum weight of 525 pounds give a thrust to weight ratio of 0.3086. Risch et al. 2009 Regan 2008

\[\left(\frac{T}{W}\right)_{\text{model}} = \frac{3 \times 54\ \text{lbf}}{525\ \text{lb}} = 0.3086 \tag{27}\]

Equation 28, Thrust to Weight Ratio of the Liebeck Design. Three engines of 61,600 pounds thrust against the published gross weight of 823,000 pounds give a thrust to weight ratio of 0.2245. Liebeck 2004

\[\left(\frac{T}{W}\right)_{\text{full}} = \frac{3 \times 61{,}600\ \text{lbf}}{823{,}000\ \text{lb}} = 0.2245 \tag{28}\]

Equation 29, Bespoke Thrust to Weight of the Model Over the Full Scale. Taking Liebeck’s design as the full-scale aeroplane that the model represents, the model carries 1.374 times its thrust to weight ratio.

\[\frac{(T/W)_{\text{model}}}{(T/W)_{\text{full}}} = \frac{0.3086}{0.2245} = 1.374 \tag{29}\]

Equation 30, Asymmetric Thrust Fraction with One Engine Failed. With one of $N_e$ equal engines failed, the asymmetric thrust as a fraction of weight is the thrust to weight ratio divided by the engine count.

\[\frac{\Delta T}{W} = \frac{T}{W} \cdot \frac{1}{N_e} \tag{30}\]

Equation 31, Asymmetric Thrust Fractions of the X-48B and X-48C. The asymmetric thrust fraction is 0.10286 for the three-engine X-48B and 0.17800 for the two-engine X-48C at the fact sheet’s 89 pounds an engine.

\[\left(\frac{\Delta T}{W}\right)_{B} = \frac{0.3086}{3} = 0.10286, \qquad \left(\frac{\Delta T}{W}\right)_{C} = \frac{0.3560}{2} = 0.17800 \tag{31}\]

Equation 32, Asymmetric Thrust Fraction of the Liebeck Trijet. The same fraction for the three-engine Liebeck design is 0.07485.

\[\left(\frac{\Delta T}{W}\right)_{\text{full}} = \frac{0.2245}{3} = 0.07485 \tag{32}\]

Equation 33, Bespoke Engine-Out Asymmetry Ratios. The ratios set each model’s asymmetric thrust fraction against that of Liebeck’s design, taken as the full-scale aeroplane, and the X-48C against the X-48B.

\[\frac{0.10286}{0.07485} = 1.374, \qquad \frac{0.17800}{0.07485} = 2.378, \qquad \frac{0.17800}{0.10286} = 1.731 \tag{33}\]

Equation 34, Vertical Tail Volume Coefficient. The directional tail volume coefficient is the vertical surface area times its moment arm divided by the wing area and span.

\[V_v = \frac{S_v \, l_v}{S \, b} \tag{34}\]

Equation 35, Moment Arm Shift on a Swept Trailing Edge. Moving a surface inboard along a trailing edge swept at angle $\Lambda$ moves it forward by the spanwise shift times the tangent of the sweep.

\[\Delta l_v = \Delta y \, \tan \Lambda \tag{35}\]

Equation 36, Measured Stall Angles with Slats Extended and Retracted. The correlation update reports stall at 24 degrees with slats extended and 14 degrees with slats retracted, a difference of ten degrees. Vicroy 2011

\[\alpha_{\text{stall}}^{\text{slats out}} = 24^\circ, \qquad \alpha_{\text{stall}}^{\text{slats in}} = 14^\circ, \qquad \Delta\alpha = 10^\circ \tag{36}\]

Equation 37, Bespoke Reference Span and Weight Implied by the BWB-17. The published 6 percent scale and 17-foot span give a reference span of 283 feet, and inverting the cube law on the published 120 pounds assumes the model was weight-scaled in the same air. Liebeck 2004

\[b_{\text{ref}} = \frac{17}{0.06} = 283\ \text{ft}, \qquad W_{\text{full}} = \frac{120}{0.06^{3}} = 555{,}556\ \text{lb} \tag{37}\]

Notation

• $n$, the length ratio of model to full scale
• $Fr$, the Froude number
• $Re$, the Reynolds number
• $\nu$, the kinematic viscosity, with $\nu_0$ its sea-level value
• $L_m$, the model length, with $L_f$ the full-scale length
• $V_m$, the model speed, with $V_f$ the full-scale speed
• $r_V$, the speed ratio, with $r_t$, $r_\omega$, $r_W$, $r_I$, $r_{Re}$, $r_q$ and $r_{W/S}$ the ratios of time, angular rate, weight, moment of inertia, Reynolds number, dynamic pressure and wing loading
• $\sigma$, the relative density factor in its definition, and in the weight ratio the ratio of full-scale to model air density
• $\rho$, the air density, with $\rho_f$ and $\rho_m$ its values at the full-scale and model conditions
• $m$, the mass
• $l$, the characteristic length
• $c$, the reference chord, taken as wing area over span
• $S$, the wing reference area, with $S_v$ the area of a vertical surface
• $b$, the wing span, with $b_{\text{ref}}$ the full-scale reference span
• $\mu$, the dynamic viscosity
• $P_{\text{effective}}$, the effective Reynolds penalty at the model ceiling
• $P(b)$, the Reynolds penalty as a function of model span, with $\tau(b)$ the time compression
• $W_{\text{full}}$, the implied full-scale weight, with $W_m$ the model weight
• $\frac{T}{W}$, the thrust to weight ratio
• $N_e$, the number of engines
• $\Delta T$, the asymmetric thrust with one engine failed
• $V_v$, the vertical tail volume coefficient
• $l_v$, the distance from the centre of gravity to the aerodynamic centre of the vertical surface
• $\Delta y$, the inboard shift of the surface along the span
• $\Lambda$, the sweep angle of the outer trailing edge
• $\alpha_{\text{stall}}$, the stall angle of attack

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