X-Planes: Aurora Flight Sciences X-65 CRANE
Filed under: aerospace, history, engineering
This is the sixty-sixth 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, the X-47, the X-48, the X-49, the X-50, the X-51, the X-52, the X-53, the X-54, the X-55, the X-56, the X-57, the X-58, the X-59, the X-60, the X-61, the X-62, the X-63, and the X-64.
The programme is named for a bird that its own literature cannot find, and the aircraft carries two complete control systems so that it can be compared with itself.
The X-65A was allocated on 24 April 2023 to Aurora Flight Sciences, a Boeing subsidiary, with the engines cell reading 1 Williams FJ44-3A and the sponsor cell reading DARPA, the Defense Advanced Research Projects Agency [Parsch, DOD 4120.15-L Addendum]. The description is one line.
Unmanned demonstrator for CRANE (Control of Revolutionary Aircraft with Novel Effectors) program
The programme aims to fly an aeroplane whose pitch, roll and yaw are commanded by jets of air rather than by moving surfaces [CRANE programme page]. That much is widely reported. What is not reported is that the aircraft carries fourteen active-flow-control effectors and fourteen conventional control surfaces at the same time [X-65 experimental aircraft], and that this makes it the answer to a problem the previous article could not solve.
The Research Question
Active flow control has been demonstrated in wind tunnels for sixty years, and the question this aircraft exists to settle is whether it can be the primary flight control system of a real aeroplane at a speed and a scale that matter. [Abdolahipour 2024]
The physics is not in doubt. A small jet introduced near a surface can reattach a separated boundary layer, and the resulting change in lift is many times larger than the jet’s own reaction. What is in doubt is whether the effect survives the transition from a tunnel model to a flying vehicle, whether the air it needs can be found on board, and whether the authority it delivers is enough at every condition of a flight envelope.
The programme manager named its ancestor himself. He came to DARPA in 1999 to work on Micro Adaptive Flow Control, or MAFC, left in 2003 after managing it, and returned to see that work reach a full-scale aircraft [DARPA moves forward on the X-65]. The interval between the foundational programme and the aircraft’s planned first flight is thus 28 years, and the question of why a demonstrated effect took that long to fly is part of the subject [two-year flight delay].
The questions are therefore these. How much control authority can a jet of air buy, per unit of air, and how does that compare with a hinge? Where does the air come from, and what does the answer imply about the flight envelope? What does the aircraft’s instrumentation have to measure to settle the question? And what does it mean that the vehicle carries two complete and equinumerous control systems rather than one?
Three of the four answers were not what this article expected. The momentum a bleed-fed jet can deliver turns out to be exactly independent of altitude, for two separate cancellations that happen to meet, so the binding condition is Mach number alone. That dependence has an exact minimum at Mach 1.4142, which is beyond this aircraft but not beyond the idea. And the combinatorial figure that looks alarming, being 16,384 distinct lock-out configurations, is a red herring, because the quantity to be identified is a model with 315 terms, and a model of that size is identified in a handful of flights.
The Register Row, and a Turbofan Described as a Turbojet
Andreas Parsch’s addendum to DOD 4120.15-L, a compilation of the designations allocated after August 1998 that he publishes at designation-systems.net from Department of Defense sources, gives the row above and no more. The compiler notes that the official description of an allocation made after October 2018 is not releasable, and he marks this row’s description as his own reading and not official Department of Defense wording [Parsch, DOD 4120.15-L Addendum]. Like most of its recent neighbours the X-65A row carries no note. Of the 31 X-series rows in the copy the compiler last updated on 23 August 2026, 12 carry a note, and of the eleven allocated in 2018 or later, counting the X-56B whose date the register gives as 2019 with a query mark, only the X-76A row does, so the register’s supplementary apparatus is silent here as it is for most recent allocations. That copy is later than this article’s date. The version current on that date, the compiler’s update of 11 August 2025 as the Internet Archive captured it on 25 November 2025, held 526 rows, twenty-nine of them X rows, and lacked fifteen later rows that include the X-68A and the X-76A [Parsch, DOD 4120.15-L Addendum, 11 August 2025]. Under that version 11 of the twenty-nine X rows carried a note and none of the nine allocated in 2018 or later did, so on this article’s date the silence covered every recent allocation.
The encyclopedia entry on the aircraft describes it as having a joined tandem wing in a diamond configuration, twin vertical tails, and a single turbojet engine [Aurora X-65 CRANE]. The engine named in the register’s cell is a turbofan. The test report on that engine by the National Aeronautics and Space Administration, NASA, describes the FJ44-3A as a dual-spool low-bypass-ratio turbofan, certified in 2004 under Federal Aviation Regulations Parts 23 and 25 [FJ44 turbofan engine test], which was read in full for this article. A low-bypass turbofan is the nearest thing to a turbojet that a turbofan can be, so the description errs in a forgiving direction. The error is recorded because the distinction matters to the air budget below.
And the aircraft’s weight is given three ways. DARPA’s release says the aircraft is 7,000+ pound [DARPA moves forward on the X-65], the encyclopedia entry and the Defense News report say 7,000 pound [Aurora X-65 CRANE] [two-year flight delay], and the contractor’s page gives 7,200 pound gross weight [X-65 experimental aircraft]. The spread is 200 pound, which as a share of the lower figure is
or 2.86 percent, and the contractor’s figure is used where a single number is needed, with a note each time.
What is published about the shape of this aircraft is five numbers. A thirty foot span, a gross weight, a limit of Mach 0.7, fourteen effectors and fourteen conventional surfaces, with four interchangeable wing sets of differing sweep [X-65 experimental aircraft] [DARPA moves forward on the X-65]. Wing area, plenum pressure, bleed fraction, effector geometry and mass breakdown are all absent, so each of them is swept in what follows rather than assumed.
Programme Origin, Told Better by the Award Record Than by the Press
The narrative account is short. DARPA began CRANE in 2020, invited three contractors to present concepts in Phase 0, cut to two for a preliminary design in Phase 1, selected Aurora Flight Sciences alone for the detailed design of Phase 2 in January 2023, and awarded Phase 3 to build and flight test the aircraft in January 2024 [Aurora X-65 CRANE] [DARPA moves forward on the X-65].
The federal award record names the three contractors, prices them, and dates the downselect, none of which the narrative does [USAspending].
| Contractor | Instrument | Begins | Ends | Obligated, dollar | Base and all options, dollar | Pricing | Offers received |
|---|---|---|---|---|---|---|---|
| Aurora Flight Sciences | HR001120C0119 | 2020-06-19 | 2023-01-31 | 23,811,305.00 | 28,368,394.00 | Cost plus fixed fee | 25 |
| Lockheed Martin | HR001120C0110 | 2020-06-26 | 2023-02-03 | 18,577,721.00 | 18,577,721.00 | Cost plus fixed fee | 25 |
| Georgia Tech Research Corporation | HR001120C0130 | 2020-07-17 | 2023-10-31 | 6,795,148.00 | 12,376,510.00 | Cost no fee | 25 |
| Aurora Flight Sciences | HR001123C0012 | 2022-12-07 | 2025-10-02 | 94,372,238.00 | 94,372,238.00 | Cost plus fixed fee | 2 |
All three Phase 0 and Phase 1 contracts report twenty-five offers received. So the solicitation drew 25 proposals and funded three, a competition ratio the published accounts do not mention. The Phase 2 and Phase 3 contract reports two offers, the Phase 1 downselect appearing as a procurement fact [USAspending].
And the downselect itself is visible as an exercised option. Aurora’s contract shows an option exercised on 29 June 2021 worth 8,312,272 dollars and Lockheed Martin’s shows one exercised on 12 August 2021 worth 10,135,107 dollars. Georgia Tech Research Corporation has no option exercise at any date. Its last funding action is 13 April 2022 for 192,823 dollars, and 5,581,362 dollars of its ceiling, being 45.1 percent, was never exercised [USAspending]. The record therefore dates the cut from three to two to the middle of 2021, which no source consulted states in words. The unexercised share of a ceiling is one less the ratio of obligation to ceiling, which for Georgia Tech Research Corporation is
\[1 - \frac{6{,}795{,}148}{12{,}376{,}510} = \frac{5{,}581{,}362}{12{,}376{,}510} = 0.451 .\]Georgia Tech was also on different terms. Its contract is priced cost no fee where both companies are cost plus fixed fee, and the record classifies it as an other United States entity where both companies are a United States owned business. A university research corporation took no fee for the same work, and it alone of the three was not carried forward [USAspending].
From the obligations and ceilings in the table above,
\[\frac{23{,}811{,}305}{49{,}184{,}174} = 0.484 , \qquad 1 - \frac{23{,}811{,}305}{28{,}368{,}394} = \frac{4{,}557{,}089}{28{,}368{,}394} = 0.161 , \qquad 49{,}184{,}174 + 94{,}372{,}238 = 143{,}556{,}412 ,\]so Aurora took 48.4 percent of the 49,184,174 dollars obligated across the three early contracts, and left 4,557,089 dollars, or 16.1 percent, of its own ceiling unexercised. Total obligations across all four CRANE contracts are 143,556,412 dollars.
The Forty-Two Million Dollar Contract Is Not in the Record
Press accounts report that DARPA awarded Aurora a 42 million dollar contract in January 2023 to begin detailed design [two-year flight delay]. The contract in the award record is 94,372,238 dollars, 2.25 times that figure. It is described as covering Phase 2 and Phase 3 together, and it begins on 7 December 2022, earlier than January 2023 [USAspending].
The two figures are not in conflict, for a reason that deserves stating. Phase 2 and Phase 3 were placed on one instrument, so the announced Phase 2 value and the eventual obligated total on the same contract number are different quantities. The initial obligation on the day the contract began was 6,500,000 dollars, 6.9 percent of what the contract eventually carried. [USAspending] The two ratios are
\[\frac{94{,}372{,}238}{42{,}000{,}000} = 2.25 , \qquad \frac{6{,}500{,}000}{94{,}372{,}238} = 0.0689 .\]| Date | Obligation, dollar | Cumulative, dollar |
|---|---|---|
| 2022-12-07 | 6,500,000.00 | 6,500,000.00 |
| 2023-02-08 | 14,845,397.00 | 21,345,397.00 |
| 2023-02-23 | 6,498,250.38 | 27,843,647.38 |
| 2023-03-13 | 9,942,727.62 | 37,786,375.00 |
| 2023-08-28 | 0.00 | 37,786,375.00 |
| 2023-12-01 | 10,426,578.00 | 48,212,953.00 |
| 2023-12-18 | 15,786,711.00 | 63,999,664.00 |
| 2024-03-20 | 0.00 | 63,999,664.00 |
| 2024-03-25 | 4,267,786.00 | 68,267,450.00 |
| 2024-05-02 | 4,708,392.00 | 72,975,842.00 |
| 2024-05-17 | 4,444,805.00 | 77,420,647.00 |
| 2024-07-30 | 8,000,000.00 | 85,420,647.00 |
| 2024-09-18 | 220,000.00 | 85,640,647.00 |
| 2024-09-24 | 1,000,000.00 | 86,640,647.00 |
| 2024-12-03 | 0.00 | 86,640,647.00 |
| 2025-01-13 | 2,993,728.00 | 89,634,375.00 |
| 2025-01-16 | 4,737,863.00 | 94,372,238.00 |
| 2025-02-11 | 0.00 | 94,372,238.00 |
The shape of that column is the programme’s history. The record holds eighteen actions, of which four move no money at all, and the last dollar is obligated on 16 January 2025. The only action after that date is the last of the eighteen, a zero-dollar change order dated 11 February 2025. [USAspending]
The Pause Is in the Record as an Absence
DARPA told a reporter that it chose to strategically pause the X-65’s development earlier in 2025 because the cost of producing the prototype had exceeded expectations, and that during the pause it restructured the programme so that Aurora became a co-investor, an arrangement finalised in August 2025 [two-year flight delay].
None of that appears in the award record. The period of performance on the Phase 2 and Phase 3 contract ends on 2 October 2025, 69 days before this article’s dateline. No obligation follows 16 January 2025, 328 days before the dateline, and the zero-dollar change order of 11 February 2025 falls 302 days before it. The restructured co-investment appears as no contract, no modification and no obligation [USAspending].
So the federal award record, read on this article’s date, shows CRANE as a completed contract with no aircraft. The record is not at fault. A cost share by a contractor is not federal spending, so a database of federal spending is the wrong instrument to see it with, and what is interesting is that the instrument is silent while remaining correct. A programme can be restructured into a shape that the public record of its funding cannot represent.
Two adjacent awards are relevant. Scientific, engineering and technical assistance support to the DARPA Tactical Technology Office for CRANE was contracted on 20 December 2019, six months before any performer, through a Navy vehicle, and carried 5,679,994.63 dollars with a de-obligation of 220,000 dollars in September 2024. The support was bought before the research was. And the Office of Naval Research funded 1,251,577 dollars of work titled finless unmanned combat air system flight control with active flow control effectors, beginning September 2022. It is the same idea pursued by a different service for 1.33 percent of what the Phase 2 and Phase 3 contract carried [USAspending].
What the Programme’s Name Costs It
CRANE finds nothing aeronautical in the bibliographic index, and novel effectors, the literal phrase in the programme’s title, finds molecular biology, where an effector is a protein that a pathogen injects into a host.
The phrase that does find this aircraft’s prior art is one the programme does not use. hingeless control returns, among others, the experimental development of hingeless aerodynamic control effectors [Kondor et al 2008], plasma actuators for hingeless aerodynamic control of an unmanned air vehicle [Patel et al 2007], delta-wing hingeless control by synthetic jet actuation [Traub et al 2002], and system identification of an unmanned aerial vehicle with hingeless control effectors [Weisman and Valasek 2010]. That is the X-65’s lineage, indexed under a word the programme’s name replaced. The full measurement is in the source base below.
Sizing From First Principles
The Symbols This Article Uses
Every symbol below is declared here and nowhere carries a second meaning.
| Symbol | Meaning | Unit |
|---|---|---|
| $\mathcal{A}$ | amplification, aerodynamic force per unit jet momentum | dimensionless |
| $a$ | speed of sound | metre per second |
| $A^{*}$ | total choked throat area of the effectors | square metre |
| $A_f$ | engine face area | square metre |
| $a_f$ | speed of sound at the engine face | metre per second |
| $\mathcal{A}_{\mathrm{loc}}$ | actuation efficiency, the slope of the lift increment against the momentum coefficient | dimensionless |
| $AR$ | aspect ratio | dimensionless |
| $B$ | engine bypass ratio | dimensionless |
| $\mathbf{B}$ | control effectiveness matrix, three rows by one column per effector | newton metre |
| $b$ | wing span | metre |
| $\beta$ | bleed fraction of engine core mass flow | dimensionless |
| $\mathbf{b}_i$ | one column of the control effectiveness matrix | newton metre |
| $\bar{c}$ | reference chord, taken as area over span | metre |
| $C_1$ | Sutherland’s constant for air, 1.458 times ten to the minus six | kilogram per metre second root kelvin |
| $C_L$ | lift coefficient | dimensionless |
| $C_{\mathcal{M}}$ | moment coefficient referenced to the span | dimensionless |
| $C_\mu$ | momentum coefficient referenced to the wing | dimensionless |
| $C_{\mu,0}$ | threshold momentum coefficient below which nothing happens | dimensionless |
| $C_{\mu,1}$ | threshold momentum coefficient above which the flow is fully attached | dimensionless |
| $C_\mu^{\,1}$ | momentum coefficient a bleed fraction of unity would deliver | dimensionless |
| $C_{\mu,\ell}$ | momentum coefficient referenced to the area one effector influences | dimensionless |
| $c_p$ | specific heat at constant pressure | joule per kilogram kelvin |
| $\delta$ | ratio of compressor-face total pressure to sea-level standard pressure | dimensionless |
| $\Delta C_L$ | lift-coefficient increment produced by an effector | dimensionless |
| $\Delta C_{L,\mathrm{conv}}$ | lift-coefficient increment produced by a conventional surface at full deflection | dimensionless |
| $\delta F$ | thrust decrement caused by bleed | newton |
| $\Delta L$ | aerodynamic force increment produced by an effector | newton |
| $\Delta L_{\mathrm{AFC}}$ | force increment from an active-flow-control effector, the subscript being the programme’s own abbreviation | newton |
| $\Delta L_{\mathrm{conv}}$ | force increment from a conventional control surface | newton |
| $\Delta T$ | total-temperature rise across a compressor | kelvin |
| $D_f$ | engine face diameter | metre |
| $\eta_c$ | compressor isentropic efficiency | dimensionless |
| $F^{+}$ | reduced excitation frequency | dimensionless |
| $f_e$ | effector excitation frequency | hertz |
| $F_{\mathrm{sls}}$ | sea-level static thrust | newton |
| $G$ | the Mach-number factor of the bleed-fed momentum coefficient | dimensionless |
| $g_0$ | standard gravity, 9.80665 | metre per second squared |
| $\gamma$ | ratio of specific heats, taken as 1.4 for dry air | dimensionless |
| $\mathcal{H}$ | reachable moment set under a shared supply, a convex hull | newton metre squared |
| $h$ | geopotential altitude | metre |
| $h_{\mathrm{trop}}$ | tropopause altitude, 11,000 | metre |
| $J$ | jet momentum flux supplied by the effectors | newton |
| $k$ | usable test points per flight | dimensionless |
| $\kappa$ | concentration factor, wing area over influenced area | dimensionless |
| $\Lambda$ | authority ratio, flow-control force over conventional-surface force | dimensionless |
| $\lambda$ | troposphere lapse rate, minus 0.0065 | kelvin per metre |
| $M$ | flight Mach number | dimensionless |
| $\mathcal{M}$ | control moment | newton metre |
| $\mathbf{m}$ | demanded moment vector | newton metre |
| $\dot{m}_{\mathrm{core}}$ | engine core mass flow | kilogram per second |
| $M_f$ | axial Mach number at the engine face | dimensionless |
| $\dot{m}_j$ | jet mass flow delivered to the effectors | kilogram per second |
| $\dot{m}_{\mathrm{ref}}$ | engine sea-level static mass flow of the bleed source stream | kilogram per second |
| $M_\times$ | crossover Mach number at which the authority ratio reaches unity | dimensionless |
| $\dot{m}_{\mathrm{total}}$ | engine total mass flow | kilogram per second |
| $\mu$ | dynamic viscosity of air | pascal second |
| $n$ | number of active-flow-control effectors, being the fourteen whose derivatives are identified | dimensionless |
| $N_1$ | control derivatives in a linear effector model | dimensionless |
| $N_2$ | terms in a second-order effector model with pairwise interactions | dimensionless |
| $n_a$ | number of controlled axes | dimensionless |
| $N_c$ | distinct locked-or-free configurations across every wing set | dimensionless |
| $n_e$ | number of effectors of both kinds available to the allocator, being twenty-eight on this aircraft | dimensionless |
| $N_f$ | flights needed to over-determine a model | dimensionless |
| $\mathrm{NPR}$ | nozzle pressure ratio, plenum total to ambient static | dimensionless |
| $n_s$ | number of conventional control surfaces | dimensionless |
| $n_w$ | number of interchangeable wing sets | dimensionless |
| $o$ | appropriation outcome for a fiscal year | dollar |
| $P$ | shaft power delivered to the air by a dedicated compressor | watt |
| $p$ | ambient static pressure | pascal |
| $\pi_c$ | compressor total-pressure ratio | dimensionless |
| $p_{\mathrm{sl}}$ | sea-level standard pressure, 101325 | pascal |
| $p_t$ | plenum total pressure | pascal |
| $p_{\mathrm{trop}}$ | pressure at the tropopause | pascal |
| $q$ | free-stream dynamic pressure | pascal |
| $R$ | specific gas constant for dry air, 287.05287 | joule per kilogram kelvin |
| $r$ | appropriation request for a fiscal year | dollar |
| $\mathrm{Re}$ | Reynolds number on the reference chord | dimensionless |
| $\rho$ | ambient air density | kilogram per cubic metre |
| $\rho_f$ | air density at the engine face | kilogram per cubic metre |
| $S$ | wing reference area | square metre |
| $S_\ell$ | area of surface one effector influences | square metre |
| $\sigma$ | inlet total-condition factor, $1 + \left(\gamma-1\right)M^2/2$ | dimensionless |
| $\sigma_f$ | total-condition factor at the engine face | dimensionless |
| $S_\mu$ | Sutherland’s temperature for air, 110.4 | kelvin |
| $T$ | ambient static temperature | kelvin |
| $\tau$ | compressor total-temperature ratio | dimensionless |
| $\theta$ | ratio of compressor-face total temperature to sea-level standard temperature | dimensionless |
| $T_{\mathrm{sl}}$ | sea-level standard temperature, 288.15 | kelvin |
| $T_t$ | plenum total temperature | kelvin |
| $T_{\mathrm{trop}}$ | temperature at the tropopause, 216.65 | kelvin |
| $\mathcal{U}$ | admissible set of effector demands | dimensionless |
| $\mathbf{u}$ | vector of effector demands | dimensionless |
| $\bar{u}$ | the supply limit on effector demand | dimensionless |
| $V$ | true airspeed | metre per second |
| $V_e$ | engine exit velocity at static conditions | metre per second |
| $V_\infty$ | free-stream velocity, used where the contrast with the jet matters | metre per second |
| $V_j$ | effector jet velocity at the orifice | metre per second |
| $\mathrm{VR}$ | jet velocity ratio, jet velocity over free-stream velocity | dimensionless |
| $W$ | aircraft weight | newton |
| $w_c$ | compressor specific work | joule per kilogram |
| $y$ | moment arm from the vehicle centreline | metre |
| $\mathcal{Z}$ | reachable moment set under independent limits, a zonotope | newton metre squared |
The Momentum Coefficient, and the Identity It Hides
The standard figure of merit for a blown flow-control device is the momentum coefficient, being the momentum flux the jet supplies divided by the product of free-stream dynamic pressure and a reference area. Let $\dot{m}_j$ be the jet mass flow in kilogram per second, $V_j$ the jet velocity in metre per second, $q$ the free-stream dynamic pressure in pascal, $S$ the reference area in square metre, and $C_\mu$ the momentum coefficient, dimensionless.
\[J = \dot{m}_j V_j, \qquad C_\mu = \frac{J}{q S}\]where $J$ is the jet momentum flux in newton. Since the numerator and the denominator are both forces, the ratio is dimensionless, and the review cited above attributes the precise formulation to Poisson-Quinton [Abdolahipour 2024].
The force the device produces is a different quantity, an aerodynamic force increment obtained because the jet changed where the flow separated. Let $\Delta C_L$ be the resulting lift-coefficient increment, dimensionless, and $\Delta L$ the force increment in newton.
\[\Delta L = \Delta C_L \, q S\]Dividing one by the other gives an exact identity, and the identity contains the entire question of whether active flow control is a control technology or a thruster in disguise. Let $\mathcal{A}$ be the amplification, being aerodynamic force produced per unit of jet momentum supplied, dimensionless.
\[\mathcal{A} = \frac{\Delta L}{\dot{m}_j V_j} = \frac{\Delta C_L \, q S}{C_\mu \, q S} = \frac{\Delta C_L}{C_\mu}\]The flight condition cancels completely. The amplification, a ratio of two dimensionless numbers, is indifferent to altitude, speed and area. A value of one means the device is a rocket, producing exactly the force its own jet reaction would produce and nothing more. A value far above one means the jet is a trigger rather than a force.
The rows below are illustrative values chosen to show the shape of the regimes, not measurements.
| Regime | Lift-coefficient increment | Momentum coefficient | Amplification |
|---|---|---|---|
| Separation control, weak | 0.050 | 0.005 | 10.00 |
| Separation control, strong | 0.300 | 0.010 | 30.00 |
| Circulation control, modest | 0.800 | 0.100 | 8.00 |
| Circulation control, strong | 2.000 | 0.400 | 5.00 |
| Pure reaction | 0.010 | 0.010 | 1.00 |
The ratio above is a secant and the quantity the literature plots is the tangent, and the distinction matters because the curve is not a line.
\[\mathcal{A} = \frac{\Delta C_L}{C_\mu} \quad \text{against} \quad \mathcal{A}_{\mathrm{loc}} = \frac{\mathrm{d} \, \Delta C_L}{\mathrm{d} C_\mu}\]The review calls the second one the actuation efficiency and reports that it falls through the transition between the two regimes [Abdolahipour 2024]. The two agree only where the curve passes through the origin with constant slope, which it does not. The secant is used throughout, because it converts an available momentum into an available force, and the tangent tells a designer whether more air would help.
Separation control lives at the top of that table and circulation control at the bottom, because of the shape of the underlying curve. At very small momentum coefficient nothing happens, because the jet is too weak to change where the boundary layer leaves the surface. Above a threshold the lift increment rises steeply, and amplification is largest in this regime. At large momentum coefficient the flow is fully attached, further blowing simply adds circulation, and the returns fall toward unity as the device becomes a thruster. So there is an optimal momentum coefficient, neither small nor large, which turns the design problem into one of landing in a band rather than of maximising a quantity. Writing $C_{\mu,0}$ for the threshold below which nothing happens and $C_{\mu,1}$ for the one above which the flow is fully attached,
\[\mathcal{A}_{\mathrm{loc}} \approx 0 \;\; \text{for} \;\; C_\mu < C_{\mu,0}, \qquad \mathcal{A}_{\mathrm{loc}} \gg 1 \;\; \text{for} \;\; C_{\mu,0} < C_\mu < C_{\mu,1}, \qquad \mathcal{A}_{\mathrm{loc}} \to 1 \;\; \text{for} \;\; C_\mu > C_{\mu,1}\]The review puts $C_{\mu,1}$ between three and five percent and reports measured values of $C_{\mu,0}$ well below one percent, both of which are taken up below [Abdolahipour 2024].
The reference case is the physical one reported for the aircraft, being the raw jet reaction of the whole air budget. At the conditions derived below the total jet momentum is 156.1 newton, which is 0.49 percent of the aircraft’s weight. A device that merely pushed with that would be useless. An amplification of thirty makes it a flight control system.
The Unstated Source of the Air
DARPA’s release says the aircraft uses jets of air from a pressurized source [DARPA moves forward on the X-65]. The contractor writes active flow control uses pressurized air for flight control [X-65 experimental aircraft]. Neither names the source of the pressure, the largest quantity the record leaves undetermined, because the two behave oppositely with altitude.
The first architecture bleeds the engine. At a fixed corrected spool speed a gas turbine passes a constant corrected mass flow, so its actual mass flow follows the total pressure at its face divided by the square root of the total temperature there. Let $\dot{m}_{\mathrm{ref}}$ be the engine’s sea-level static mass flow in kilogram per second, $\delta$ the ratio of compressor-face total pressure to sea-level standard pressure and $\theta$ the ratio of compressor-face total temperature to sea-level standard temperature, both dimensionless, and $\beta$ the bleed fraction, dimensionless.
\[\dot{m}_j = \beta \, \dot{m}_{\mathrm{ref}} \, \frac{\delta}{\sqrt{\theta}}\]The second architecture drives a compressor at a fixed shaft power. Let $P$ be the shaft power delivered to the air in watt, $c_p$ the specific heat at constant pressure in joule per kilogram kelvin, and $\Delta T$ the total-temperature rise in kelvin.
\[\dot{m}_j = \frac{P}{c_p \, \Delta T}\]The first depends on ambient pressure and the second does not, and that single difference propagates into opposite conclusions about the flight envelope.
The Atmosphere Every Number Here Is Computed In
Every calculation that follows happens inside the 1976 standard atmosphere. The relations are elementary and they are shown because every figure in every table below depends on them.
In the troposphere the temperature falls linearly. Let $h$ be the geopotential altitude in metre, $\lambda$ the lapse rate in kelvin per metre, $g_0$ the standard gravity in metre per second squared, and $T_{\mathrm{sl}}$ and $p_{\mathrm{sl}}$ the sea-level standard temperature and pressure.
\[T\left( h \right) = T_{\mathrm{sl}} + \lambda h, \qquad p\left( h \right) = p_{\mathrm{sl}} \left( \frac{T\left( h \right)}{T_{\mathrm{sl}}} \right)^{- \frac{g_0}{\lambda R}}\]The exponent is not a fitted constant. It follows from integrating the hydrostatic relation $\mathrm{d}p = - \rho g_0 \, \mathrm{d}h$ against the ideal gas law with a linear temperature profile.
Above the tropopause the temperature is constant and the pressure falls exponentially, with $h_{\mathrm{trop}}$ the tropopause altitude in metre and $T_{\mathrm{trop}}$ and $p_{\mathrm{trop}}$ the conditions there.
\[p\left( h \right) = p_{\mathrm{trop}} \exp\left( - \frac{g_0 \left( h - h_{\mathrm{trop}} \right)}{R \, T_{\mathrm{trop}}} \right), \qquad \rho = \frac{p}{R T}, \qquad a = \sqrt{\gamma R T}\]At thirty thousand feet, taken as a geopotential altitude of 9,144 metre, those give 228.714 kelvin, 30,089.6 pascal, 0.458312 kilogram per cubic metre and a speed of sound of 303.174 metre per second.
The Compressible Identity That Makes the Cancellation Possible
Dynamic pressure is defined as half the density times the square of the speed, and rewriting it in terms of pressure and Mach number is not an approximation. With $\rho$ the density in kilogram per cubic metre, $V$ the true airspeed in metre per second, $M$ the Mach number, dimensionless, $p$ the ambient static pressure in pascal, $T$ the ambient static temperature in kelvin, $R$ the specific gas constant in joule per kilogram kelvin and $\gamma$ the ratio of specific heats, dimensionless,
\[q = \tfrac{1}{2} \rho V^2 = \tfrac{1}{2} \rho \, \gamma R T M^2 = \tfrac{\gamma}{2} \, p \, M^2\]because $p = \rho R T$ and the speed of sound satisfies $a^2 = \gamma R T$. At a fixed Mach number the dynamic pressure is exactly proportional to the ambient pressure, a fact the bleed architecture exploits. The two routes to $q$ were computed independently and agree to better than one part in $10^{15}$.
Total Conditions and Corrected Flow
The bled mass flow above is written in terms of $\delta$ and $\theta$, which are the compressor-face total conditions normalised on sea level, and the total conditions follow from the flight Mach number alone under full inlet recovery.
\[p_{t} = p \, \sigma^{\frac{\gamma}{\gamma-1}}, \qquad T_{t} = T \sigma, \qquad \delta = \frac{p_t}{p_{\mathrm{sl}}}, \qquad \theta = \frac{T_t}{T_{\mathrm{sl}}}\]The invariant that makes the bled mass flow predictable at all is the corrected flow. At a fixed corrected spool speed a turbomachine passes a fixed value of
\[\dot{m} \frac{\sqrt{\theta}}{\delta} = \text{constant}\]and inverting it gives the bled flow above. At thirty thousand feet and Mach 0.7 the factors are $\sigma$ of 1.0980, $\delta$ of 0.4119 and $\theta$ of 0.8715, so the compressor face sees 41.74 kilopascal and 251.1 kelvin. The corrected flow recomputed from the actual flow at ten altitudes returns 10.0 kilogram per second every time, the invariance the derivation assumes.
The Compressor Ratio, and What the Air Costs in Work
The compressor’s total-temperature ratio follows from its pressure ratio and its efficiency. Let $\tau$ be that ratio, dimensionless, and $w_c$ the specific work in joule per kilogram.
\[\tau = 1 + \frac{\pi_c^{\frac{\gamma-1}{\gamma}} - 1}{\eta_c}, \qquad w_c = c_p \, T_{t} \left( \tau - 1 \right)\]At a pressure ratio of 14 and an efficiency of 0.85 the temperature ratio is 2.3241, against 2.1255 for ideal compression, and the work already spent on each kilogram of bled air is 334.1 kilojoule. A bleed throws that work away, so air taken from the discharge of a single-stage centrifugal compressor is the most expensive air in the engine.
The Jet Is Choked, and Its Velocity Depends Only on Its Own Temperature
A nozzle whose plenum exceeds the ambient pressure by more than the critical ratio passes sonic flow at its throat, and the exit velocity is then the local speed of sound there. Let $T_t$ be the plenum total temperature in kelvin.
\[\frac{p_{t}}{p} \ge \left( \frac{\gamma + 1}{2} \right)^{\frac{\gamma}{\gamma - 1}} \approx 1.8929, \qquad V_j = \sqrt{\frac{2 \gamma R \, T_{t}}{\gamma + 1}}\]The jet velocity depends on the plenum total temperature and on nothing else. Not on altitude, not on the plenum pressure, not on the flight speed except through the total temperature. The cancellation needs this second fact.
Air bled from a compressor of pressure ratio $\pi_c$ arrives hot. Let $\eta_c$ be the compressor isentropic efficiency, dimensionless, and let the inlet total-condition factor be $\sigma$.
\[\sigma = 1 + \frac{\gamma - 1}{2} M^2, \qquad T_{t} = T \sigma \left( 1 + \frac{\pi_c^{\frac{\gamma-1}{\gamma}} - 1}{\eta_c} \right)\]The nozzle pressure ratio also has a closed form, and the altitude does not appear in it. Let $\mathrm{NPR}$ be the plenum-to-ambient pressure ratio, dimensionless.
\[\mathrm{NPR} = \frac{\pi_c \, p_t}{p} = \pi_c \, \sigma^{\frac{\gamma}{\gamma-1}}\]The ambient pressure divides out before anything is computed.
| Altitude, foot | Ambient pressure, kilopascal | Plenum pressure, kilopascal | Nozzle pressure ratio | Plenum total temperature, kelvin | Jet velocity, metre per second |
|---|---|---|---|---|---|
| 0 | 101.33 | 1,967.7 | 19.419 | 735.3 | 496.2 |
| 15,000 | 57.18 | 1,110.4 | 19.419 | 659.5 | 470.0 |
| 30,000 | 30.09 | 584.3 | 19.419 | 583.7 | 442.1 |
| 45,000 | 14.75 | 286.4 | 19.419 | 552.9 | 430.3 |
The nozzle pressure ratio is 19.419 at every altitude in that table, identically, and the closed form above explains why in one line. The plenum pressure is a fixed multiple of the compressor-face total pressure, and that pressure is a fixed multiple of the ambient pressure at a fixed Mach number, so their ratio cannot depend on altitude. It stands at 10.26 times the critical ratio, so the choked assumption holds across the envelope with an order of magnitude to spare.
Altitude Cancels Exactly, for Two Separate Reasons That Happen to Meet
Assemble the three results. The bled mass flow carries $p \sigma^{\gamma/(\gamma-1)}$ over $\sqrt{T \sigma}$, the choked jet velocity carries $\sqrt{T \sigma \tau}$ where $\tau$ is the compressor total-temperature ratio, and the dynamic pressure carries $p M^2$. Writing $p_{\mathrm{sl}}$ and $T_{\mathrm{sl}}$ for the sea-level standard pressure and temperature,
\[C_\mu = \frac{2 \beta \, \dot{m}_{\mathrm{ref}}}{\gamma \, p_{\mathrm{sl}} \, S} \sqrt{\frac{2 \gamma R \, T_{\mathrm{sl}} \, \tau}{\gamma + 1}} \; \cdot \; \frac{\sigma^{\frac{\gamma}{\gamma-1}}}{M^2}\]Every trace of altitude is gone, and so is the ambient temperature, and so is one of the two appearances of $\sigma$. The ambient pressures cancel because corrected flow makes the bled mass flow proportional to pressure and the compressible identity makes dynamic pressure proportional to pressure. The ambient temperatures cancel for a different reason, because corrected flow divides by the square root of the total temperature while a choked jet fed from that same air multiplies by it. The inlet factor cancels once for the same reason the temperature does, since the same ram rise that warms the compressor face warms the jet.
| Altitude, foot | Dynamic pressure, kilopascal | Bled mass flow, kilogram per second | Momentum coefficient from bleed | Momentum coefficient at fixed shaft power |
|---|---|---|---|---|
| 0 | 34.75 | 1.0590 | 0.000945066 | 0.0015249 |
| 5,000 | 28.92 | 0.8967 | 0.000945066 | 0.0018651 |
| 10,000 | 23.90 | 0.7547 | 0.000945066 | 0.0022978 |
| 15,000 | 19.61 | 0.6311 | 0.000945066 | 0.0028533 |
| 20,000 | 15.97 | 0.5240 | 0.000945066 | 0.0035731 |
| 25,000 | 12.90 | 0.4319 | 0.000945066 | 0.0045157 |
| 30,000 | 10.32 | 0.3530 | 0.000945066 | 0.0057639 |
| 35,000 | 8.18 | 0.2860 | 0.000945066 | 0.0074370 |
| 40,000 | 6.43 | 0.2260 | 0.000945066 | 0.0095018 |
| 45,000 | 5.06 | 0.1778 | 0.000945066 | 0.0120830 |
The momentum coefficient in the fourth column is identical to 12 significant figures from sea level to forty-five thousand feet, and the closed form above reproduces the direct computation to within one part in $10^{15}$. The bled mass flow in the third column falls by a factor of six over that band and the dynamic pressure in the second falls by very nearly the same factor, and the two errors are the same error with opposite signs.
The fifth column, the other architecture, behaves quite differently. A compressor held at constant shaft power delivers a mass flow set by the temperature rise, which barely changes, while the dynamic pressure it is measured against falls with the ambient pressure. Its momentum coefficient rises by a factor of 7.92 over the same band.
So the published phrase a pressurized source conceals a factor of 7.92 in how this aircraft’s control authority varies with altitude, and the two architectures are distinguishable by experiment. Fly the same effector command at two altitudes at the same Mach number and compare the control moments. A ratio near unity is engine bleed. A ratio well above unity is a shaft-driven compressor, reaching 7.92 between sea level and forty-five thousand feet. The analysis thus makes a prediction the flight-test programme can settle in two data points.
The Mach Dependence, and an Exact Minimum at Mach Root Two
What survives is a function of Mach number alone, up to the constant. Let $G$ be that factor, dimensionless.
\[G\left( M \right) = \frac{\sigma^{\frac{\gamma}{\gamma-1}}}{M^2} = \frac{\left( 1 + 0.2 M^2 \right)^{3.5}}{M^2}\]at $\gamma = 1.4$. The numerator is the inlet’s total-pressure recovery, which works in the aircraft’s favour.
| Mach number | Mach factor with inlet recovery | Mach factor without it | Recovery gains | Momentum coefficient at 30,000 feet |
|---|---|---|---|---|
| 0.15 | 45.1484 | 44.4444 | 1.0158 | 0.0150728 |
| 0.20 | 25.7070 | 25.0000 | 1.0283 | 0.0085823 |
| 0.30 | 11.8270 | 11.1111 | 1.0644 | 0.0039484 |
| 0.40 | 6.9784 | 6.2500 | 1.1166 | 0.0023297 |
| 0.50 | 4.7449 | 4.0000 | 1.1862 | 0.0015841 |
| 0.60 | 3.5431 | 2.7778 | 1.2755 | 0.0011828 |
| 0.70 | 2.8308 | 2.0408 | 1.3871 | 0.0009451 |
Going from Mach 0.2 to Mach 0.7 costs a factor of 9.081 in momentum coefficient, where the naive inverse square would have cost 12.250. The inlet recovery therefore mitigates 25.9 percent of the penalty, and the mitigation grows with Mach number because the recovery does.
The factor has a minimum, located exactly at Mach $\sqrt{2}$. Taking logarithms and differentiating,
\[\frac{\mathrm{d} \ln G}{\mathrm{d} M} = \frac{\gamma}{\gamma - 1} \cdot \frac{\sigma'}{\sigma} - \frac{2}{M} = \frac{\gamma M}{\sigma} - \frac{2}{M}\]which vanishes when $\gamma M^2 = 2 \sigma = 2 + \left( \gamma - 1 \right) M^2$, that is when $M^2 = 2$. The specific-heat ratio cancels and the turning point is at Mach 1.4142 whatever the gas is. Since $\sigma\left(\sqrt{2}\right) = \gamma$ exactly, the minimum value has a closed form.
\[G_{\min} = \frac{\gamma^{\frac{\gamma}{\gamma-1}}}{2} = 1.6234\]The closed form, a direct evaluation and a brute-force search over three hundred thousand Mach numbers agree to one part in $10^{15}$.
Beyond Mach $\sqrt{2}$ a bleed-fed flow-control system gets better with speed again, because the inlet recovery eventually outruns the inverse square. The X-65A’s published limit is Mach 0.7 [DARPA moves forward on the X-65], so this aircraft never reaches the turn. The result is reported because it bears on the idea, although not on this aeroplane.
The Authority Ratio, and Where a Jet Loses to a Hinge
The aircraft’s central question can now be written in one line. Let $\Delta L_{\mathrm{AFC}}$ be the force increment an active-flow-control effector delivers in newton, where the subscript is the programme’s abbreviation for active flow control, $\Delta L_{\mathrm{conv}}$ the force increment a conventional surface delivers in newton, $\Delta C_{L,\mathrm{conv}}$ the lift-coefficient increment that surface delivers at full deflection, dimensionless, and $\Lambda$ the authority ratio, dimensionless.
\[\Lambda = \frac{\Delta L_{\mathrm{AFC}}}{\Delta L_{\mathrm{conv}}} = \frac{\mathcal{A} \, C_\mu \, q S}{\Delta C_{L,\mathrm{conv}} \, q S} = \frac{\mathcal{A} \, C_\mu}{\Delta C_{L,\mathrm{conv}}}\]The dynamic pressure cancels again, so the authority ratio inherits the altitude independence of the momentum coefficient and inherits its Mach dependence entire. A conventional surface produces a moment proportional to dynamic pressure, and so does an active-flow-control effector, for the surprising reason that the engine feeding it swallows more air at lower altitude in almost exactly the same proportion.
The crossover is defined by a condition, the Mach number at which the ratio reaches one, and involves no fitting.
\[\Lambda\left( M_{\times} \right) = 1 \quad \Longleftrightarrow \quad \mathcal{A} \, C_\mu\left( M_{\times} \right) = \Delta C_{L,\mathrm{conv}} \quad \Longleftrightarrow \quad G\left( M_{\times} \right) = \frac{\Delta C_{L,\mathrm{conv}}}{\mathcal{A}} \cdot \frac{G\left( M_{0} \right)}{C_\mu\left( M_{0} \right)}\]for any reference Mach number $M_0$. The root is unique below Mach $\sqrt{2}$ because $G$ is strictly decreasing there, as established above, so a bisection is admissible as well as convenient.
| Amplification | Ratio at Mach 0.7, against 0.02 | Crossover Mach, 0.02 | Ratio, against 0.05 | Crossover Mach, 0.05 | Ratio, against 0.10 | Crossover Mach, 0.10 |
|---|---|---|---|---|---|---|
| 10 | 0.473 | 0.436 | 0.189 | 0.265 | 0.095 | 0.185 |
| 20 | 0.945 | 0.672 | 0.378 | 0.385 | 0.189 | 0.265 |
| 30 | 1.418 | 0.942 | 0.567 | 0.485 | 0.284 | 0.329 |
| 50 | 2.363 | none | 0.945 | 0.672 | 0.473 | 0.436 |
| 100 | 4.725 | none | 1.890 | none | 0.945 | 0.672 |
Take an amplification of 30 against a conventional surface worth 0.05 in lift coefficient. The authority ratio at the top of the envelope is 0.567, so active flow control delivers 56.7 percent of the hinge’s authority at Mach 0.7 and falls short by 43.3 percent. At Mach 0.2 the same hardware delivers 5.15 times the hinge’s authority. The crossover is at Mach 0.485. With the momentum coefficient and the Mach factor from the tables above,
\[\Lambda\left( 0.7 \right) = \frac{30 \times 0.000945066}{0.05} = 0.567 , \qquad \Lambda\left( 0.2 \right) = 0.567 \times \frac{G\left( 0.2 \right)}{G\left( 0.7 \right)} = 0.567 \times \frac{25.7070}{2.8308} = 5.15 , \qquad G\left( M_{\times} \right) = \frac{0.05}{30} \cdot \frac{2.8308}{0.000945066} = 4.992 ,\]and the Mach number at which $G$ falls to 4.992 is 0.485.
This inverts the usual control-authority problem, and the inversion is the article’s practical result. For a conventional aeroplane the binding case for control power is low speed, because the surfaces are weakest when the dynamic pressure is least, so approach and engine-out cases size the tail. For a bleed-fed flow-control aeroplane the binding case is high speed, because the effectors deliver a roughly fixed force while the aerodynamic forces they must overcome grow as the square of the Mach number.
One consequence is fortunate. Flight-test programmes expand an envelope from low speed upward, for reasons of safety unrelated to flow control. For this aircraft that happens to mean starting where active flow control is strongest and proceeding toward where it is weakest, so the natural order of an envelope expansion is also the natural order of a risk reduction. A programme that had to begin at the difficult end would be a much worse bet.
To Match a Hinge, and What That Demands
Inverting the ratio gives the amplification required.
\[\mathcal{A}_{\mathrm{req}} = \frac{\Delta C_{L,\mathrm{conv}}}{C_\mu}\]At the reference condition the momentum coefficient is 0.000945, so matching a conventional surface worth 0.02 needs an amplification of 21.2, matching one worth 0.05 needs 52.9, and matching one worth 0.10 needs 105.8. Which of those is reachable is the open question, and the published record brackets it without settling it. The review’s summary of separation-control studies reports a gain in lift of 53 percent on a flapped NACA 0015 with its flap at 35 degrees at a momentum coefficient of 0.3 percent, and gains in maximum lift of 12 to 35 percent at coefficients of 0.082 to 0.14 percent [Abdolahipour 2024]. The review gives those gains relative to each baseline and not as increments, so the amplification they imply is an inference, and on a baseline lift coefficient near one it exceeds a hundred in every one of those cases. By the arithmetic, then, this class of system can replace a weak control surface at cruise at any amplification the literature suggests, and can replace a strong one only if the amplification at cruise reaches the hundred that those low-speed experiments imply, a quantitative version of the claim the programme was built to test.
The Reference Area Is a Choice, the Force Is Not
The denominator of the momentum coefficient is a convention, and the literature acknowledges this in the same breath as it defines the quantity. The review attributes the precise formulation to Poisson-Quinton and writes the denominator as the free-stream dynamic pressure times a reference area [Abdolahipour 2024]. Which reference area is the author’s choice, and the choice decides what question the number answers.
An effector does not act on the whole wing. It acts on the region whose separation behaviour it changes. Let $S_\ell$ be that area in square metre, $C_{\mu,\ell}$ the local momentum coefficient, dimensionless, and $\kappa$ the concentration factor, dimensionless.
\[C_{\mu,\ell} = \frac{\dot{m}_j V_j}{q S_\ell}, \qquad \kappa = \frac{S}{S_\ell} = \frac{C_{\mu,\ell}}{C_\mu}\]The force is unchanged by that choice, a point that is easy to get wrong. The force increment is $\mathcal{A} \dot{m}_j V_j$, the amplification times the momentum supplied, and no reference area appears in it. What the choice changes is which value of the amplification applies, because the amplification is a function of the local momentum coefficient and not of the wing-referenced one. Concentrating the air does not create force. It moves the device along its amplification curve.
Inverting for the area that lands a given local coefficient gives the relation the design has to satisfy.
\[S_\ell = \frac{\dot{m}_j V_j}{C_{\mu,\ell} \, q}\]| Target local momentum coefficient | What it is | Influenced area, square metre | Share of the wing | Concentration factor | Area per effector, square metre |
|---|---|---|---|---|---|
| 0.0008 | the smallest at which a lift response is reported | 18.9013 | 118.13 percent | 0.85 | 1.35009 |
| 0.0034 | a measured synthetic-jet reattachment | 4.4474 | 27.80 percent | 3.60 | 0.31767 |
| 0.0200 | a measured reattachment on a modified coefficient | 0.7561 | 4.73 percent | 21.16 | 0.05400 |
| 0.0300 | the low end of the super-circulation threshold | 0.5040 | 3.15 percent | 31.74 | 0.03600 |
| 0.0500 | the high end of the super-circulation threshold | 0.3024 | 1.89 percent | 52.91 | 0.02160 |
The arithmetic shows plainly why CRANE is a control programme and not a high-lift programme. A high-lift system must change the lift of a whole wing, so it needs a wing-referenced coefficient in the super-circulation regime. Inverting the bleed relation for the fraction of core flow that would take gives the following.
Because the momentum coefficient is exactly proportional to the bleed fraction, the inversion is one line. Let $C_\mu^{\,1}$ be the coefficient a bleed fraction of unity would give.
\[C_\mu = \beta \, C_\mu^{\,1} \quad \Longrightarrow \quad \beta_{\mathrm{req}} = \frac{C_\mu^{\,\mathrm{target}}}{C_\mu^{\,1}}, \qquad \beta_{\mathrm{req}} \le 1\]The last inequality is no convention. It states that the engine cannot bleed more core flow than it has, and it decides which rows below are physical.
| Target wing-referenced momentum coefficient | Bleed as a share of core flow | Physically available |
|---|---|---|
| 0.0008 | 6.77 percent | yes |
| 0.0034 | 28.78 percent | yes |
| 0.0200 | 169.30 percent | no |
| 0.0300 | 253.95 percent | no |
| 0.0500 | 423.25 percent | no |
Reaching the lowest coefficient at which a lift response has been measured takes 6.77 percent of core flow, and a measured reattachment takes 28.78 percent. Reaching the super-circulation threshold of three percent would take 253.95 percent of core flow, or two and a half times the core flow the engine has, and five percent would take 423.25 percent. The coefficient a bleed fraction of unity would deliver follows from the reference case, and each row is the target over it,
\[C_\mu^{\,1} = \frac{0.000945066}{0.08} = 0.0118133 , \qquad \frac{0.0008}{0.0118133} = 0.0677 , \qquad \frac{0.0034}{0.0118133} = 0.2878 , \qquad \frac{0.03}{0.0118133} = 2.5395 , \qquad \frac{0.05}{0.0118133} = 4.2325 .\]So the assumed bleed fraction of 8 percent is slightly more than the lowest measured threshold needs and far short of super-circulation, which places this aircraft’s air budget in the separation-control regime by arithmetic rather than by assumption. A control system changes a moment rather than a lift, which needs a local effect at a long moment arm, and the concentration factor is what makes that affordable. The same arithmetic that forbids the first permits the second.
Against the Thresholds the Literature Reports, and the One That Matters
A measured lift response appears in the review at a momentum coefficient of 0.08 percent, with the regime boundary at three to five percent [Abdolahipour 2024], and the table below sets this aircraft’s wing-referenced figure against each reported threshold.
The regime boundary is defined phenomenologically as the coefficient that just suffices to suppress separation completely, and the transition across it is gradual, with the fall in actuation efficiency noted where the momentum coefficient was defined. The framing of a curve with a threshold, a favourable band and a saturation is therefore the literature’s and not this article’s.
| Reported threshold | Momentum coefficient | This article’s figure over it | Concentration factor needed | Influenced area, square metre | Per effector, square metre |
|---|---|---|---|---|---|
| NACA 0015 flapped airfoil, periodic excitation, Reynolds 1.5e5 to 6e5 | 0.08 percent | 1.1813 | none needed | 18.901 | 1.3501 |
| NACA 0025, synthetic jet, Reynolds 1e5, reduced frequency 58, drag down 45 per | 0.34 percent | 0.2780 | 3.60 | 4.447 | 0.3177 |
| NACA 0012, modified coefficient, Reynolds 2.3e4, separated below 1.5 percent | 2.00 percent | 0.0473 | 21.16 | 0.756 | 0.0540 |
| the coefficient that just suffices to suppress separation completely | 3.00 percent | 0.0315 | 31.74 | 0.504 | 0.0360 |
| the same, upper end of the reported range | 5.00 percent | 0.0189 | 52.91 | 0.302 | 0.0216 |
Those thresholds come from experiments at Reynolds numbers of twenty-three thousand to six hundred thousand, and this aircraft flies at eleven million [Abdolahipour 2024]. The comparison is valid but not the sharpest available. The sharpest is in the section below on Reynolds number, where a report that tested the method at this aircraft’s Reynolds number quotes the coefficients it used. Against that report the bleed budget falls inside the demonstrated range.
One of the low-Reynolds thresholds carries a warning that applies whatever the scale. A numerical study of momentum injection on a NACA 0012 found the flow separated below a modified coefficient of 1.5 percent, transitional to 2 percent and reattached above, and reported that below the threshold the control injection decreased the lift relative to the uncontrolled case [Abdolahipour 2024]. Blowing below threshold is not merely ineffective. It can be worse than nothing, because low-momentum air added to a boundary layer reduces the momentum that boundary layer carries. The warning concerns a mechanism, whatever the Reynolds number, and for that reason the velocity ratio below is a condition and not a preference.
A Force Is Not a Moment, and the Moment Arm Is Where Control Lives
Every figure so far has been a force and an aeroplane is commanded with moments. The conversion is trivial, and it gives the meaning of the phrase above about a local effect at a long moment arm. Let $y$ be the moment arm in metre, $\mathcal{M}$ the moment in newton metre and $C_{\mathcal{M}}$ its coefficient on the span, dimensionless.
\[\mathcal{M} = \Delta L \, y = \mathcal{A} \, J \, y, \qquad C_{\mathcal{M}} = \frac{\mathcal{M}}{q \, S \, b}\]| Moment arm, metre | Moment at an amplification of thirty, newton metre | Moment coefficient on the span |
|---|---|---|
| 2.000 | 9,364 | 0.00620 |
| 2.286 | 10,703 | 0.00709 |
| 3.000 | 14,045 | 0.00930 |
| 4.000 | 18,727 | 0.01240 |
The whole air budget at an amplification of thirty is 4,682 newton, and placed at a quarter of the span, being 2.286 metre, that is 10,703 newton metre or a rolling-moment coefficient of 0.00709. The jet’s own reaction, without any amplification, is 156.1 newton. With the dynamic pressure of 10,320.7 pascal at the reference condition and the span of 9.144 metre,
\[\mathcal{A} J = 30 \times 156.06 = 4{,}682 , \qquad \mathcal{M} = 4{,}682 \times 2.286 = 10{,}703 , \qquad C_{\mathcal{M}} = \frac{10{,}703}{10{,}320.7 \times 16 \times 9.144} = 0.00709 .\]This is why the moment arm does more work than the amplification in a control application, and why the effectors are on the outboard wings. Doubling the arm doubles the moment for no extra air, where doubling the amplification requires a different flow regime. A high-lift system has no such lever, because lift acts where it acts.
The Velocity Ratio the Momentum Coefficient Conceals
The review cautions explicitly against the use this article has been making of the momentum coefficient. It notes that the coefficient is not an appropriate parameter for comparing the benefits of flow control across different settings and configurations, because many combinations of mass flow and jet velocity give the same value, and that the parameter which separates them is the velocity ratio [Abdolahipour 2024].
Let $\mathrm{VR}$ be the jet velocity ratio, dimensionless, with $V_\infty$ the free-stream velocity in metre per second.
\[\mathrm{VR} = \frac{V_j}{V_\infty}\]The condition the review reports is that the velocity ratio must exceed unity, because otherwise the injected air reduces rather than increases the momentum the boundary layer carries, making separation more likely. At the reference condition the jet leaves at 442 metre per second against a free stream of 212.2 metre per second, so the velocity ratio is 2.083. At Mach 0.2 it is 7.29. The condition is met across the envelope with margin.
At this point the engine’s architecture stops being merely expensive and becomes an advantage. In the review’s summary, when the flow is excited at the same momentum coefficient, a higher velocity ratio yields better outcomes than a higher mass flow at a lower velocity ratio [Abdolahipour 2024]. A single-stage centrifugal compressor forces bleed at full cycle temperature, and a choked jet from hotter air is a faster jet. Air taken at 584 kelvin leaves at 442 metre per second where the same mass flow cooled to ambient would leave at 277 metre per second, a velocity ratio of 2.083 against 1.304, or a factor of 1.597.
The constraint that makes the air expensive in compressor work also makes it effective in the one dimension the literature says the momentum coefficient hides. The point does not favour this engine, but it argues against precooling the bleed, and it follows from two facts about the engine and one sentence in a review.
The Plenum Pressure Sets the Orifice Area
A choked orifice passes a mass flow set by its area and its plenum conditions. Let $A^{*}$ be the total throat area in square metre and $p_t$ the plenum total pressure in pascal.
\[\dot{m}_j = A^{*} \, \frac{p_t}{\sqrt{T_t}} \sqrt{\frac{\gamma}{R}} \left( \frac{\gamma+1}{2} \right)^{-\frac{\gamma+1}{2\left(\gamma-1\right)}}\]The constant evaluates to 0.040415 in square-root kelvin second per metre. The table below computes its inverse.
\[A^{*} = \frac{\dot{m}_j \sqrt{T_t}}{p_t} \left[ \sqrt{\frac{\gamma}{R}} \left( \frac{\gamma+1}{2} \right)^{-\frac{\gamma+1}{2\left(\gamma-1\right)}} \right]^{-1} \; \propto \; \frac{1}{p_t}\]The area is inversely proportional to the plenum pressure at a fixed mass flow and depends on nothing else that varies, so the last column of the table is exactly the reciprocal of the first.
| Nozzle pressure ratio | Plenum pressure, kilopascal | Total throat area, square centimetre | Per effector, square millimetre | Slot height at ten millimetre width, millimetre | Within the published study’s range |
|---|---|---|---|---|---|
| 1.500 | 45.1 | 46.751 | 333.94 | 33.39 | yes |
| 2.000 | 60.2 | 35.063 | 250.45 | 25.05 | yes |
| 3.000 | 90.3 | 23.376 | 166.97 | 16.70 | yes |
| 4.000 | 120.4 | 17.532 | 125.23 | 12.52 | yes |
| 8.000 | 240.7 | 8.766 | 62.61 | 6.26 | no |
| 19.419 | 584.3 | 3.611 | 25.79 | 2.58 | no |
The momentum coefficient is identical in every row of that table, to twelve significant figures, and the throat area varies by a factor of 12.95 across it. Since the area is inversely proportional to the plenum pressure,
\[\frac{A^{*}\left( 1.5 \right)}{A^{*}\left( 19.419 \right)} = \frac{19.419}{1.5} = 12.95 , \qquad \frac{A^{*}\left( 4 \right)}{A^{*}\left( 19.419 \right)} = \frac{19.419}{4} = 4.85 ,\]where the argument is the nozzle pressure ratio. A choked jet’s velocity depends on its plenum temperature alone, so regulating the plenum pressure down changes the orifice and changes nothing else. The altitude result therefore survives any plenum schedule that keeps the nozzle choked, a useful robustness, because no plenum pressure for this aircraft is published.
The Paper That Asked This Question and Could Not Be Read
A 2024 paper in the AIAA Journal asks the question this section answers, and its full text is not available. Reddy and Woszidlo set out to determine whether the established models for estimating the momentum coefficient hold as ambient and supply conditions change during flight, simulated a fluidic oscillator and a steady jet nozzle at supply pressure ratios from 1.5 to 4, supply temperatures of 293, 550 and 800 kelvin, and ambient conditions at sea level and ten kilometres, and report that the mass flow collapses as a function of pressure ratio when scaled with one parameter and that the momentum coefficient collapses when scaled with another [Reddy and Woszidlo 2024].
Both registries render those two scaling parameters as [Formula: see text], the paper is closed access, and no repository holds a full text. So only the abstract has been read, and no quantity from inside that paper is quoted here and no claim is made about which scaling parameter it found.
The derivation above is therefore very likely a rediscovery. Its cancellations are exhibited rather than asserted and every step is checkable from the equations given, but a published study that simulates two actuator types across two altitudes and reports that the momentum coefficient collapses under a scaling parameter is, on the face of the abstract, reporting a result of the same family. No novelty is claimed.
What the comparison of parameter ranges does establish is a gap, and that comparison needs only the abstract. The published study’s supply pressure ratios stop at 4 [Reddy and Woszidlo 2024]. A plenum fed from the discharge of a compressor of pressure ratio 14 stands at a nozzle pressure ratio of 19.419 at every altitude, the factor of 4.85 displayed above. Either a real aircraft regulates its plenum far below compressor discharge, in which case the slot areas in the table above are the large ones, or the published scaling study does not cover the regime a bleed-fed aircraft would run in. The plenum total temperature tabulated with the choked jet, 584 kelvin, does fall inside the published 293 to 800 kelvin range.
Dependent Systems
The Engine, and the One Place a Centrifugal Compressor Lets You Bleed
The NASA test report on the FJ44-3A, read in full, describes the engine’s architecture in enough detail to constrain the air budget [FJ44 turbofan engine test]. The low-pressure spool carries an integrally bladed wide-chord fan and blisk compressor stages driven by a two-stage low-pressure turbine. The high-pressure spool carries a single-stage centrifugal compressor driven by a single-stage high-pressure turbine. The combustor is an effusion-cooled annular design, the exhaust is a long duct with an internal daisy-lobe mixer, and the inlet is a pitot design. The base engine weighs 525 pound, is 48 inch long and 23 inch in diameter, in a 3,000 pound-force thrust class.
A single-stage centrifugal high-pressure compressor has exactly one bleed station, being its discharge. An axial compressor of many stages offers a choice of ports at intermediate pressures and temperatures, and a designer wanting moderate-pressure air takes it from a middle stage. This engine offers no such choice. Air taken from the high-pressure spool comes out at the full cycle pressure ratio and the full cycle temperature, the most expensive air in the engine in compressor work and the hottest in the plenum. That is favourable for jet velocity and unfavourable for everything else, the strongest architectural constraint the published record permits deriving.
No mass flow is published for this engine, so it is obtained by two independent routes and the agreement is the check.
The geometric route passes the compressible mass flow through a circular face. Let $D_f$ be the fan diameter in metre and $M_f$ the axial Mach number at the face, dimensionless.
\[\frac{\dot{m}}{A} = \rho_f M_f a_f , \qquad \dot{m} = \frac{\pi D_f^2}{4} \cdot \frac{p_{\mathrm{sl}}}{\sqrt{T_{\mathrm{sl}}}} \sqrt{\frac{\gamma}{R}} \, M_f \, \sigma_f^{- \frac{\gamma+1}{2\left(\gamma-1\right)}}\]where the face quantities are the static conditions reached by expanding sea-level total conditions to $M_f$, and $\sigma_f$ is the total-condition factor at the face. At a face Mach number of 0.55 that is 192.2 kilogram per second per square metre, and the second form agrees with the first to one part in ten to the ninth.
The thermodynamic route inverts the static thrust. At static conditions there is no ram drag to subtract, so the thrust is exactly the exit momentum flux and the inversion is exact. Let $F_{\mathrm{sls}}$ be the sea-level static thrust in newton and $V_e$ the exit velocity in metre per second.
\[F_{\mathrm{sls}} = \dot{m} V_e, \qquad \dot{m} = \frac{F_{\mathrm{sls}}}{V_e}\]| Route | Assumption swept | Mass flow, kilogram per second |
|---|---|---|
| Geometric | fan diameter 20 to 23 inch, face Mach 0.50 to 0.60 | 36.5 to 54.4 |
| Thermodynamic | static thrust over exit velocity 280 to 340 metre per second | 39.2 to 47.7 |
| Taken forward | the value both routes admit | 43 |
The geometric route and the thermodynamic route overlap, and 43 kilogram per second, being 95 pound per second, is the figure both admit.
Bleed comes from the core, so the bypass ratio divides it. Let $B$ be the bypass ratio, dimensionless.
\[\dot{m}_{\mathrm{core}} = \frac{\dot{m}_{\mathrm{total}}}{1 + B}, \qquad \frac{\dot{m}_j}{\dot{m}_{\mathrm{total}}} = \frac{\beta}{1 + B}\]At an assumed bypass ratio of 3.3 the core flow is 10.0 kilogram per second, and a bleed fraction of 8 percent of core flow gives 0.3530 kilogram per second of air at 584 kelvin leaving at 442 metre per second. As a share of total engine flow that bleed is 1.860 percent.
That share is also a lower bound on the thrust the bleed costs, and a lower bound is all that is claimed. The bled air is gone from the exhaust, so at minimum its share of the momentum flux is lost.
\[\frac{\delta F}{F} \ge \frac{\beta}{1 + B} = 1.860 \text{ percent}\]The true figure is larger and remains uncomputed, because the compressor work of 334.1 kilojoule per kilogram is also wasted and the turbine has less flow with which to drive the fan. The inequality is the defensible statement, and the gap between it and the truth is the size of the cycle rematching, which needs an engine deck.
The engine is 238 kilogram, which against the contractor’s weight is 7.29 percent. DARPA describes the aircraft’s weight, size and speed as similar to those of a military trainer [DARPA moves forward on the X-65], and the engine fraction is offered only as a figure on that comparison.
Two Bandwidths, and Conflating Them Is a Real Error
An active-flow-control effector has two characteristic frequencies and they differ by orders of magnitude and answer to different masters.
The fluid-mechanical frequency is set by the convective time over the surface being controlled. Let $F^{+}$ be the reduced frequency, dimensionless, $f_e$ the excitation frequency in hertz, $\bar{c}$ the reference chord in metre and $V_\infty$ the free-stream velocity in metre per second.
\[F^{+} = \frac{f_e \, \bar{c}}{V_\infty}, \qquad f_e = \frac{F^{+} V_\infty}{\bar{c}}\]The band is not this article’s guess. A comprehensive analysis of airfoil flow-control studies reports that in the majority of cases the optimal reduced frequency for controlling post-stall separation falls between 0.3 and 4, and the same range applies to an excited shear layer and to a deflected flap [Abdolahipour 2024]. Individual optima reported in that review cluster near unity, at 0.65, 0.8, 0.85, 1.284, 1.3 and 1.5 in six separate studies, with one at 6 where the target was a separation bubble. There is also evidence that reduced frequencies of ten and twenty work, which the review attributes to a different group and explains by the spread of surface curvature, upstream conditions and excitation method across experiments.
At a reference chord of 1.750 metre, which follows from the mid-sweep wing area and the published span, the band maps onto the following frequencies.
| Mach number | Free-stream speed, metre per second | Reduced frequency 0.3, hertz | Reduced frequency 4, hertz | Reduced frequency 10, hertz |
|---|---|---|---|---|
| 0.2 | 60.6 | 10.4 | 138.6 | 346.5 |
| 0.3 | 91.0 | 15.6 | 207.9 | 519.8 |
| 0.5 | 151.6 | 26.0 | 346.5 | 866.3 |
| 0.7 | 212.2 | 36.4 | 485.1 | 1,212.8 |
The flight-control frequency is something else entirely. This article assumes that an aeroplane of this size has a short-period mode somewhere between roughly 0.3 and 3.0 hertz, and a control system needs bandwidth of that order to stabilise and command it.
The two bands do not overlap. The excitation band runs from 10.4 to 485.1 hertz across the flight envelope on the published reduced-frequency range, and reaches 1,213 hertz if a reduced frequency of ten is wanted at the top of the envelope. The control band runs from 0.3 to 3.0. At their closest approach they are separated by a factor of 3.47 and at their widest by a factor of 1,617.
The separation makes the architecture tractable and makes a fluidic oscillator the natural device. A sweeping jet generates its own oscillation frequency from its internal geometry and its supply, with no moving part and without being commanded. The high frequency is produced by the device and the low frequency by the valve that feeds it. A flight control computer commands mass flow at a few hertz and the effector supplies hundreds of hertz on its own. An architecture that commanded the excitation frequency directly would need actuators two orders of magnitude faster and would gain nothing.
More deeply, the gap means the two can be designed separately. The effector’s internal geometry is sized against the chord and the flight speed, the valve is sized against the rigid-body dynamics, and neither constrains the other. A single actuator asked to serve both would be sized by the harder of the two requirements and would be wrong for the other.
The Planform and the Four Wing Sets
The aircraft is described as a joined tandem wing in a diamond configuration with twin vertical tails [Aurora X-65 CRANE], as having a distinctive diamond-like wing shape chosen to maximise what can be learned about active flow control at full scale [DARPA moves forward on the X-65], and as having a triangular wing design that enables testing across multiple wing sweeps, with four wings of varying sweep angle and replaceable outboard panels [X-65 experimental aircraft]. Three descriptions of one planform, from three sources, in three vocabularies.
The four wing sets are the part that follows from the research question rather than from aerodynamics. A flow-control effector’s effectiveness depends on the pressure gradient it works against, and the pressure gradient over a swept wing depends on the sweep. So sweep is the independent variable the experiment most wants to vary and the one a fixed airframe cannot vary, and so the aircraft was built to have its outboard wings changed.
No wing area is published. The relations that turn a span and an area into the quantities the tables below carry are elementary. Let $b$ be the span in metre, $AR$ the aspect ratio, dimensionless, $W$ the weight in newton and $W/S$ the wing loading in pascal.
\[\bar{c} = \frac{S}{b}, \qquad AR = \frac{b^2}{S} = \frac{b}{\bar{c}}, \qquad \frac{W}{S}, \qquad C_L = \frac{W}{q S} = \frac{W/S}{q}\]At a reference area of 16 square metres and the published span the mean chord is 1.750 metre, the aspect ratio 5.226, the wing loading 2.00 kilopascal and the lift coefficient in level flight at Mach 0.7 and thirty thousand feet 0.1939. The thrust-to-weight ratio on the contractor’s weight is 0.4167 and the engine is 7.29 percent of it.
| Reference area, square metre | Aspect ratio | Mean chord, metre | Wing loading, kilopascal | Lift coefficient at Mach 0.7 and 30,000 feet |
|---|---|---|---|---|
| 12 | 6.97 | 1.312 | 2.67 | 0.259 |
| 14 | 5.97 | 1.531 | 2.29 | 0.222 |
| 16 | 5.23 | 1.750 | 2.00 | 0.194 |
| 18 | 4.65 | 1.969 | 1.78 | 0.172 |
| 20 | 4.18 | 2.187 | 1.60 | 0.155 |
| 22 | 3.80 | 2.406 | 1.46 | 0.141 |
A joined tandem wing carries lift on two surfaces, so a single reference area is a simplification, used here only as the denominator of a coefficient and making no claim about the aerodynamics.
The Fourteen and the Fourteen
The aircraft carries fourteen active-flow-control effectors and fourteen conventional control surfaces [X-65 experimental aircraft]. The counts are equal, which the published sources state without remarking on it.
The conventional surfaces are not a fallback. They are the experiment’s control group. DARPA’s description is explicit. The aircraft was built with two sets of control actuators so as to minimise risk and maximise insight, the performance with traditional surfaces serves as a baseline, and successive tests selectively lock down the moving surfaces and use the effectors instead [DARPA moves forward on the X-65]. The programme manager called the conventional surfaces training wheels.
This is an experimental design and not a hedge, and the next section explains why it is the right one.
The Measurement Design
Two Vehicles Cannot Be Differenced and One Aircraft Can
The X-64A article reached a negative conclusion about experimental design and this aircraft is the positive answer to it. That article considered whether the value of an altitude-compensating nozzle could be established by flying two vehicles and subtracting, and concluded that it could not, because two vehicles differ in mass, drag, trajectory and instrumentation, and the difference sought was smaller than the differences not sought.
The X-65A performs the same subtraction inside one airframe. The mass is the same, the drag is the same, the trajectory is the same, the transducers are the same, the flight is in some cases the same flight. What changes between the baseline and the test case is which effectors are commanded, and the difference is therefore an estimate of the thing wanted rather than of the things not wanted.
This article takes that to be the consequential design decision, and the published record treats it as risk reduction. It is risk reduction. It is also the reason the programme can produce a number at all. A vehicle with only flow-control effectors would return an absolute measurement of its own handling qualities and no measurement of what flow control is worth. A vehicle with both returns a difference, and the question asks for a difference.
The Combinatorial Number Is a Red Herring
Fourteen surfaces that may each be locked or free give a large number of configurations and the number is misleading.
The configuration count is a power of two and the flight count is a ceiling. Let $n_s$ be the number of conventional surfaces, $n_w$ the number of wing sets, $N_c$ the configuration count and $N_f$ the flights needed at $k$ usable test points each.
\[N_c = 2^{n_s} n_w, \qquad N_f = \left\lceil \frac{N_2}{k} \right\rceil\]| Quantity | Count |
|---|---|
| Active-flow-control effectors | 14 |
| Conventional control surfaces | 14 |
| Wing sets of differing sweep | 4 |
| Distinct locked-or-free configurations of the conventional surfaces | 16,384 |
| The same, once each wing set is counted separately | 65,536 |
| Configurations if the surfaces are locked only in symmetric pairs | 128 |
| Control derivatives in a linear model, three axes | 42 |
| Pairwise interactions among the effectors | 91 |
| Terms in a second-order model, per axis | 105 |
| Terms in a second-order model, three axes | 315 |
| Flights to identify that model at thirty test points each | eleven |
16,384 configurations, or 65,536 once the wing sets are counted, is not the size of the flight-test programme and treating it as one would be an error. An aircraft is not characterised by visiting its configurations. It is characterised by identifying a model, and the model is small.
Let $n$ be the number of effectors, dimensionless, and $n_a$ the number of axes. A linear model in which effectors superpose has one control derivative per effector per axis.
\[N_1 = n \, n_a\]A model that allows every pair of effectors to interact adds one term per pair.
\[N_2 = n_a \left( n + \binom{n}{2} \right) = n_a \left( n + \frac{n \left( n - 1 \right)}{2} \right)\]For fourteen effectors on three axes that is 42 derivatives in the linear case and 315 terms with every pairwise interaction included. At thirty usable test points per flight, identifying the full second-order model needs about eleven flights. A hundred flights would visit 0.61 percent of the lock-out configurations and would over-determine the second-order model many times over.
So the combinatorics do not bind. The aircraft’s availability does, and the quantity to watch in a flight-test programme of this kind is flights flown rather than configurations covered. Locking the surfaces only in symmetric pairs reduces the configuration count to 128, a reminder that most of the apparent combinatorial space is asymmetric cases a flight-test programme has no reason to visit.
The assumption at risk, and the right one to be nervous about, is superposition. The lift a flow-control effector produces saturates as its momentum input rises [Abdolahipour 2024], and effectors sharing a boundary layer may also interact through it, so the pairwise terms are not a formality. The second-order model is the prudent one, and it costs eleven flights rather than eleven thousand.
Twenty-Eight Effectors on Three Axes Is an Allocation Problem
With both sets of effectors available the aircraft has twenty-eight control effectors and three axes to command, so it is over-actuated by a factor approaching ten. That is no nuisance but a recognised problem with a literature of its own [Bodson 2000] [Benson and Orr], in which a control allocator maps a demanded moment onto a redundant effector set subject to rate, position and now mass-flow constraints.
The problem has a standard form. Let $\mathbf{u}$ be the vector of effector demands, dimensionless and of length $n_e$, $\mathbf{B}$ the control effectiveness matrix of three rows and $n_e$ columns, and $\mathbf{m}$ the demanded moment vector in newton metre.
\[\mathbf{m} = \mathbf{B} \mathbf{u}, \qquad \mathbf{u} \in \mathcal{U}\]Three axes can be commanded at all only if the effectiveness matrix has full row rank, so a lock-out that reduces the rank below three removes an axis entirely rather than weakening it.
\[\operatorname{rank} \mathbf{B} = 3\]The reachable set is the image of the admissible set, being $\mathbf{B} \mathcal{U}$, and in that image this aircraft differs from the classical case.
For this aircraft the admissible set has a feature the classical version does not. Conventional surfaces are constrained individually, each by its own deflection and rate limits, which makes $\mathcal{U}$ a box. The flow-control effectors are constrained collectively, because they share one plenum. Commanding two effectors hard at once does not cost twice the deflection, it costs twice the air, and the air is one budget.
\[\mathcal{U}_{\mathrm{box}} = \left\{ \mathbf{u} : 0 \le u_i \le \bar{u} \right\}, \qquad \mathcal{U}_{\mathrm{plenum}} = \left\{ \mathbf{u} : u_i \ge 0, \; \sum_i u_i \le \bar{u} \right\}\]The first is a box and the second is a simplex, and their images are different shapes. The image of a box under a linear map is a zonotope, being the Minkowski sum of segments along the columns. The image of a simplex is the convex hull of the images of its vertices, which for a simplex with a vertex at the origin is the hull of the origin together with the columns.
Sharing One Plenum Enlarges the Reachable Set
The comparison that matters holds the total air fixed, and when it does the shared plenum wins. Comparing a simplex against a box whose every side is the full supply is comparing against a vehicle with $n_e$ times as much air, which answers no question anybody has. The fair comparison gives the box an equal share of one supply.
For a tractable case take two axes and $n_e$ effectors whose columns are unit vectors spread evenly over a half plane, a half plane because an effector that can only blow has one-sided authority. The zonotope and hull areas then have closed forms.
\[\operatorname{area} \mathcal{Z} = \sum_{i < j} \left\lvert \det \left( \mathbf{b}_i , \mathbf{b}_j \right) \right\rvert, \qquad \operatorname{area} \mathcal{H} = \tfrac{1}{2} \sum_i \left\lvert \det \left( \mathbf{b}_i , \mathbf{b}_{i+1} \right) \right\rvert\]| Effectors | Independent, each at the full supply | Shared supply, demands summing to the supply | Independent, each at an equal share of one supply | Shared over equal shares |
|---|---|---|---|---|
| 3 | 2.0000 | 1.0000 | 0.22222 | 4.5000 |
| 4 | 4.3301 | 1.2990 | 0.27063 | 4.8000 |
| 7 | 14.9282 | 1.5000 | 0.30466 | 4.9236 |
| 14 | 61.7681 | 1.5556 | 0.31514 | 4.9360 |
| 28 | 248.9554 | 1.5673 | 0.31755 | 4.9355 |
| 100 | 3,182.5135 | 1.5705 | 0.31825 | 4.9349 |
At fourteen effectors the shared plenum reaches 4.9360 times the moment area that equal fixed shares of the same total supply would reach, and the ratio converges. It converges to an exact closed form. As the effector count grows the hull tends to a half disc and the equal-share zonotope tends to the reciprocal of pi, so
\[\lim_{n_e \to \infty} \frac{\operatorname{area} \mathcal{H}}{\operatorname{area} \mathcal{Z} / n_e^2} = \frac{\pi / 2}{1 / \pi} = \frac{\pi^2}{2} = 4.9348\]At a hundred effectors the computed areas are 1.5708 and 0.31831, and the computed ratio is within a part in ten thousand of the limit.
So the plenum is not a penalty. Sharing one supply lets the allocator put all of the air wherever the moment is wanted, where fixed per-effector limits strand air in effectors that are not needed. Sharing costs no reachable area. Its price is that the set is no longer a box, so the allocator cannot be a per-axis gain and has to solve a programme.
The geometry here is illustrative. The effector positions on the X-65A are not published, so the columns are an assumption of even spread rather than a measurement, and the two-axis reduction is for tractability. What does not depend on those choices is that a simplex image is a hull and a box image is a zonotope, a fact about linear maps and not about this aeroplane.
The progressive lock-out programme is therefore a reallocation experiment. Each step removes effectors from the allocator’s disposal and asks whether the remaining set still spans the demanded moments with adequate margin. The question is not whether flow control works. It is whether the reachable set of moments remains large enough as the conventional columns are deleted from the effectiveness matrix.
The Flight Test Record Is Empty
On this article’s dateline the X-65A has not flown, has not been rolled out, and its fuselage is not finished. [two-year flight delay]
The record of what was planned is as follows. Fabrication was under way at facilities in West Virginia and Mississippi by January 2024 [two-year flight delay], rollout was scheduled for early 2025, and first flight for the summer of the same year [DARPA moves forward on the X-65]. Both dates passed. DARPA paused the programme earlier in 2025 because the cost of producing the prototype exceeded expectations, restructured it into a partnership in which the contractor became a co-investor, finalised that arrangement in August 2025, and now expects ground testing in late 2026 or early 2027 and first flight in late 2027 [two-year flight delay]. The fuselage was expected to be complete in January 2026. The aircraft is being built in Bridgeport, West Virginia [two-year flight delay].
The slip is 30 months against the schedule stated when the build contract was announced, which is seven years after the first CRANE contracts and 28 years after the programme its manager named as its ancestor.
There is therefore no flight envelope reached to compare with the envelope designed for. The absence is stated plainly. What can be compared is what was promised against what was recorded, and for that the budget justifications are a better instrument than the press.
What Seven Budget Books Said, Year by Year
The Research, Development, Test and Evaluation justification books are a primary source with an unusual property. Each one states three fiscal years, and the same fiscal year appears in three consecutive books wearing three different hats. The three columns of an exhibit are the prior year’s actual, the current year’s estimate and the budget year’s request. A fiscal year can thus be watched from the moment it is asked for to the moment it is recorded, and every CRANE line in every book from the request for fiscal year 2020 to the request for fiscal year 2026 was read for this article [PB2020] [PB2021] [PB2022] [PB2023] [PB2024] [PB2025] [DARPA RDT&E justification, PB2026].
The quantity tabulated against each year is the outcome against the request, expressed as a fraction so that years of different size are comparable. Let $r$ be the request and $o$ the outcome, both in dollars.
\[\frac{o - r}{r}\]| Fiscal year | Requested | Later estimated | Finally recorded | Outcome against request |
|---|---|---|---|---|
| FY2020 | 13.000 | 20.000 | 23.573 | +81.33 percent |
| FY2021 | 25.000 | 26.000 | 23.614 | -5.54 percent |
| FY2022 | 31.607 | 28.507 | 25.507 | -19.30 percent |
| FY2023 | 52.685 | 40.565 | 40.565 | -23.00 percent |
| FY2024 | 44.500 | 42.500 | 38.264 | -14.01 percent |
| FY2025 | 29.715 | 23.893 | - | -19.59 percent |
| FY2026 | 4.000 | - | - | - |
The first year came in 81.33 percent above its request and every year since has come in below. Fiscal year 2020 was requested at 13.000 million dollars, estimated at 20.000 and recorded at 23.573. From fiscal year 2021 to fiscal year 2025 the programme was funded below its request five times out of five, at a mean shortfall of 16.29 percent. The worst single year is fiscal year 2023, requested at 52.685 million and recorded at 40.565 million, which is -23.00 percent. The first figure and the mean of the five shortfalls are
\[\frac{23.573 - 13.000}{13.000} = 0.8133 , \qquad \frac{0.0554 + 0.1930 + 0.2300 + 0.1401 + 0.1959}{5} = 0.1629 .\]Across fiscal years 2020 to 2025 the programme asked for 196.507 million dollars and is expected to receive 175.416 million, a shortfall of 10.73 percent, and counting the fiscal year 2026 request of 4.000 million in both the totals are 200.507 and 179.416 million. Appropriations through fiscal year 2024 total 151.523 million dollars against 143,556,412 dollars obligated across the four contracts, a ratio of 1.0555, the right sort of agreement, because obligations lag appropriations. Summing the table’s columns,
\[\sum_{2020}^{2025} r = 196.507 , \qquad \sum_{2020}^{2025} o = 175.416 , \qquad 1 - \frac{175.416}{196.507} = 0.1073 , \qquad \sum_{2020}^{2024} o = 151.523 , \qquad \frac{151.523 \times 10^{6}}{143{,}556{,}412} = 1.0555 , \qquad \frac{4.000}{38.264} = 0.1045 .\]The fiscal year 2026 request is 4.000 million, equal to 10.5 percent of what fiscal year 2024 received. It is also the only round number in the series, every other figure carrying three decimal places. A round number among precise ones is the signature of a placeholder.
The Programme Moved Programme Elements
Through fiscal year 2025 CRANE was funded in programme element 0603286E, Advanced Aerospace Systems. From fiscal year 2026 it is funded in programme element 0603468E, Advanced Complex Systems, and the book’s exhibits for both programme elements state the transfer explicitly [DARPA RDT&E justification, PB2026]. An aircraft programme was moved out of the aerospace line and into the complex-systems line.
Promises That Slipped Two Fiscal Years Across Four Books
The plan text is the part of a budget book that ages worst, and reading the same milestone across consecutive books is how the ageing becomes visible.
| Book | Fiscal year it was promised for | The promise |
|---|---|---|
| PB2021 | FY2021 | Complete Preliminary Design Review |
| PB2022 | FY2022 | Conduct system critical design review |
| PB2023 | FY2023 | Conduct system critical design review |
| PB2024 | FY2024 | Complete system critical design review |
| PB2025 | FY2024 | Complete the system Critical Design Review |
| PB2022 | FY2022 | Initiate airworthiness and ground and flight test approvals |
| PB2023 | FY2023 | Initiate airworthiness and ground and flight test approvals |
| PB2024 | FY2024 | Complete airworthiness and ground and flight test approvals |
| PB2025 | FY2024 | Complete airworthiness and ground and flight test approvals |
| PB2026 | FY2025 | Complete airworthiness and flight test approvals |
| PB2024 | FY2024 | Complete fabrication and subsystem integration |
| PB2025 | FY2024 | Complete fabrication and subsystem integration |
| PB2025 | FY2025 | Initiate and complete flight testing |
| PB2026 | FY2025 | Initiate and complete flight testing |
The critical design review was promised for fiscal year 2022, then fiscal year 2023, then fiscal year 2024, then fiscal year 2024 again. Completing fabrication and subsystem integration was a fiscal year 2024 plan in two consecutive books, and the fuselage was not expected to be finished until January 2026 [two-year flight delay]. Initiating and completing flight testing was a fiscal year 2025 plan in two consecutive books. [PB2022] [PB2023] [PB2024] [PB2025] [DARPA RDT&E justification, PB2026]
The last of those merits attention. The book published in June 2025 still lists initiating and completing flight testing of the demonstration aircraft among its fiscal year 2025 plans, four months after the zero-dollar change order that marks the pause and three months before the fiscal year ended [DARPA RDT&E justification, PB2026]. Its fiscal year 2026 entry asks 4.000 million dollars to complete active-flow-control flight testing and data delivery, against a first flight the same agency was describing as late 2027 five months later.
That is not a contradiction and reading it as one would be unfair. This article reads a justification book’s plan text for the current fiscal year as restating the plan on which that year’s appropriation was enacted, which was settled long before the book was printed. The plans column is a record of what was agreed, not a report of what is happening. The right conclusion is narrower and more useful. A budget justification is an excellent source for what a programme was authorised to do and a poor source for what it did, and this article uses it only for the first.
Comparison With Ground Prediction
Nothing has flown, so flight has returned nothing to set beside any ground prediction, and this section records what was predicted so that the comparison can be made when it does. At the time of writing the aircraft has not been rolled out and its fuselage is not finished, and DARPA expects ground testing in late 2026 or early 2027 and first flight in late 2027 [two-year flight delay]. Even the ground testing that would precede flight lies in the future.
The first prediction the record makes is a schedule, the only one that events have already answered. The flight test record above puts the slip at 30 months, and the reading of seven budget books follows the same promises through the justification books.
The aerodynamic predictions are this article’s own, and every one of them is conditional. They are the altitude independence of a bleed-fed momentum coefficient and its fall with Mach number, derived under Sizing From First Principles, and the authority ratios and crossover Mach number displayed with the authority ratio. None of them is a contractor estimate or a published wind tunnel result for this aircraft. The amplification is swept rather than predicted, and the critique of the framing below names it as the weakest link.
One of those predictions is framed so that two data points can test it, being the comparison of control moments at two altitudes and one Mach number set out at the end of the altitude cancellation above. The record leaves the source of the aircraft’s air unstated, so the prediction cannot yet be matched to the design, let alone to a flight.
The ground evidence the programme rests on is tunnel evidence, and the strongest of it was taken at a higher Reynolds number than this aircraft flies at, as the Reynolds-number discussion below sets out. The comparison the aircraft is built to make is internal rather than against a ground prediction, being the difference within one airframe described under the measurement design. None of the flights it needs has been flown, so this section can hold only the predictions.
What the Data Changed, What It Would Change and What It Has Already Changed
An aircraft that has not flown has changed nothing by flying, and its intentions are not counted as results. What CRANE has produced so far is a design, a set of tools and a contract structure, and the budget line states the intended product explicitly. Technologies, design tools and models developed under the programme are to be made available to all the services and to the civilian aerospace sector [DARPA RDT&E justification, PB2026]. The deliverable is named as tools and models, not only as an aeroplane.
Two things have already changed and neither is aerodynamic.
The first is the contracting arrangement. A DARPA technology demonstrator in which the contractor becomes a co-investor to complete the article is not the usual shape, and the agency’s account of why is that the new structure gets costs back to an affordable rate for the government, with the contractor taking over the platform for future test and development once the hard technical challenge is demonstrated [two-year flight delay]. The aircraft is to outlive the programme as a test asset, which the programme manager said at the outset was a design goal and which the modular wing sets exist to serve [DARPA moves forward on the X-65].
The second is that the aircraft became the reason to hold the designation. The X-65A designation was allocated in April 2023, between the Phase 2 award and the Phase 3 award, and the register carries it while the aircraft does not exist. It is allocated to a vehicle that is being built, slowly, with a first flight four and a half years after its designation. [Parsch, DOD 4120.15-L Addendum] [two-year flight delay]
The Contemporary Literature
| Cluster | Records |
|---|---|
| The momentum coefficient itself, which is almost never in a title | 13 |
| Control without a hinge, which is this aircraft’s actual prior art | 81 |
| Allocating a demand across more effectors than axes | 41 |
| The devices, from piezoelectric diaphragms to fluidic oscillators | 814 |
| Blowing, the Coanda surface and the jet flap | 750 |
| Separation and its control, which is what the effectors do | 207 |
| Controlling a vortex, including the forebody jets that flew first | 32 |
| Where the air comes from, and what taking it costs | 43 |
| Reynolds number, and why a tunnel is not an aeroplane | 111 |
| Active flow control as a subject in its own right | 275 |
| Joined, tandem, diamond and tailless, and controlling them | 350 |
| The mechanical control system this aircraft proposes to delete | 85 |
| Identifying an aircraft from its own flight data | 185 |
| Demonstrators, research aircraft and the practice of flying one | 131 |
| Jets in a crossflow | 81 |
| Wall jets and curved wall jets | 69 |
| Shear layers, receptivity and periodic excitation | 30 |
| This programme and the programme it descends from | 2 |
| The medium, admitted by the shared atmosphere family alone | 1 |
| Total | 3,301 |
Every research record in the survey is cited in exactly one cluster below. The clusters run from the specific to the general, so a record that fits a narrow cluster is listed there rather than under the broader one it is also a case of.
The momentum coefficient itself, which is almost never in a title
The parameter this article’s identity is built on. Titles that name the momentum coefficient, and titles on the blowing parameters and the actuation efficiency it summarises.
13 records. [Goodfellow et al 2011] [Orazi et al 2011] [Wang et al 2011] [Goodfellow et al 2013] [Zhou et al 2017] [Saadi and Bahi 2018] [Liu et al 2020] [Abbasi 2022] [Otto et al 2022] [Reddy and Woszidlo 2024] [Xu et al 2025] [Zhou et al 2025] [Müller et al 2026]
Control without a hinge, which is this aircraft’s actual prior art
The prior art the aircraft descends from. Hingeless and innovative control effectors, passive porosity, fluidic thrust vectoring, and the jet and plasma control of unmanned aircraft, missiles and projectiles.
81 records. [Cassel et al 1969] [Ostroff 1985] [Goodrich and Sliwa 1987] [Goodrich et al 1989] [Maughmer 1989] [Maughmer et al 1990] [Bauer and Hemsch 1992] [Wood et al 1992] [Bauer and Wood 1994] [Wing 1994] [Wood et al 1994] [Durham and Bordignon 1995] [Barber et al 1997] [Pedreiro 1997] [Strykowski 1997] [Wing and Giuliano 1997] [Gillard 1998] [Banks et al 1999] [Buffington 1999] [Buffington 1999] [Gilyard 1999] [Stable multiple model adaptive 1999] [Wood and Bauer 1999] [Addington and Myatt 2000] [Deere 2000] [Erickson 2000] [Moeller and Rediniotis 2000] [Boskovic and Mehra 2001] [Hunter et al 2001] [Bauer and Wood 2001] [Moeller and Rediniotis 2002] [Tinetti et al 2002] [Traub et al 2002] [Wood 2002] [Bauer and Wood 2003] [Chudoba and Cook 2003] [Deere 2003] [Deere et al 2003] [Erickson 2003] [Waithe and Deere 2003] [Miller et al 2004] [Raney et al 2004] [Deere et al 2005] [Patel et al 2005] [Flamm et al 2006] [Liu et al 2006] [Patel et al 2006] [Patel et al 2006] [Boskovic et al 2007] [Deere et al 2007] [Flamm et al 2007] [Kutay et al 2007] [Lechevin et al 2007] [Oppenheimer and Doman 2007] [Patel et al 2007] [Staelens et al 2007] [Zhang et al 2007] [Kondor et al 2008] [Neidhoefer et al 2009] [Glezer et al 2010] [Wang et al 2010] [Weisman and Valasek 2010] [Johnson et al 2011] [Turner 2011] [White et al 2015] [Erickson 2017] [Kazarin et al 2017] [Park et al 2017] [Matamoros and de Visser 2018] [Warsop and Crowther 2018] [Acheson et al 2020] [Shayan and Van Kampen 2021] [Liu et al 2022] [Zelman et al 2023] [Kara and Kurtuluş 2024] [Li et al 2024] [Simon et al 2025] [Boskovic et al] [Campbell et al] [Sumanik] [Okolo]
Allocating a demand across more effectors than axes
What fourteen effectors and fourteen surfaces on three axes require. Control allocation across redundant effectors, and the reconfigurable flight control that depends on it.
41 records. [Napolitano and Swaim 1989] [Buffington 1997] [Calise et al 1998] [Wagner et al 1998] [Page and Steinberg 1999] [Bodson 2000] [Cameron and Princen 2000] [Nam et al 2000] [Brinker and Wise 2001] [Cotting et al 2001] [Davidson et al 2001] [Durham 2001] [Durham and Nelson 2001] [Shore and Bodson 2004] [Shore and Bodson 2005] [Burken et al 2006] [Doman et al 2007] [Song 2008] [Frost et al 2009] [Frost et al 2010] [Jamil et al 2010] [Liu and Crespo 2010] [Mahulkar 2010] [Frost et al 2012] [Waters et al 2013] [Huijts and Voskuijl 2015] [Control Allocation and Flight 2016] [Xu et al 2016] [Terrell and Zein-Sabatto 2017] [Yi et al 2017] [Acheson 2018] [Acheson 2018] [Pei et al 2018] [Vile et al 2019] [Vile et al 2019] [Litt 2024] [Sarioglu and Dogan 2024] [Benson and Orr] [Miller and Pei] [Acheson and Gregory] [Acheson et al]
The devices, from piezoelectric diaphragms to fluidic oscillators
The effectors themselves. Synthetic jets, sweeping jets and fluidic oscillators, plasma actuators, pulsed and vortex-generator jets, as devices and as applied to wings, bodies, inlets and turbines.
162 of these titles name a sweeping jet or a fluidic oscillator, and 147 of those date from 2010 or later. The device this article argues is the natural one, because it generates its own frequency, is the recent part of the literature.
814 records. [Westerman et al 1965] [Martinez 1967] [Rehsteiner 1970] [Ito and Suematsu 1974] [Ito and Suematsu 1975] [Oshima and Kinoshita 1975] [Hellbaum and McDermon 1977] [Deadwyler 1980] [Pullin and Simmons 1985] [Roshko 1985] [Johnston and Nishi 1989] [Brenner 1993] [McManus et al 1994] [McManus et al 1995] [McManus and Magill 1996] [Sedor 1996] [Johari et al 1997] [McManus et al 1997] [Amitay et al 1998] [Lachowicz et al 1998] [Seifert et al 1998] [Amitay et al 1999] [Glezer 1999] [Lamp and Chokani 1999] [McLean et al 1999] [Seifert and Pack 1999] [Bons et al 2000] [Honohan et al 2000] [Tanaka et al 2000] [Amitay et al 2001] [Amitay et al 2001] [Gilarranz and Rediniotis 2001] [Nedungadi et al 2001] [Tilmann 2001] [Cater and Soria 2002] [Chen and Beeler 2002] [Fasel et al 2002] [Florent et al 2002] [Gordon and Soria 2002] [Gregory et al 2002] [Guo et al 2002] [Guy et al 2002] [Heinzen et al 2002] [Johari and Rixon 2002] [Kim and Williams 2002] [Naughton et al 2002] [Rediniotis et al 2002] [Schaeffler et al 2002] [Smith 2002] [Ashpis et al 2003] [Gaeta et al 2003] [Hassan and Roth 2003] [Holman et al 2003] [Hultgren and Ashpis 2003] [Hultgren and Ashpis 2003] [Jiang and Liu 2003] [Johari and Rixon 2003] [Jones and Englar 2003] [Krothapalli et al 2003] [Liu et al 2003] [Mathew et al 2003] [Milanovic 2003] [Parekh et al 2003] [Post and Corke 2003] [Rixon and Johari 2003] [Vadillo et al 2003] [Yamaleev and Carpenter 2003] [Anderson et al 2004] [Anderson et al 2004] [Cybyk et al 2004] [Duvigneau and Visonneau 2004] [Enloe et al 2004] [Gallas et al 2004] [Goldstein 2004] [Gordon et al 2004] [Gregory et al 2004] [Hansen and Bons 2004] [Hultgren and Ashpis 2004] [Lonneman and Cutler 2004] [Milanovic and Zaman 2004] [Mossi and Bryant 2004] [Naitoh and Yamamoto 2004] [Post and Corke 2004] [Post and Corke 2004] [Post and Corke 2004] [Rediniotis 2004] [Rumsey et al 2004] [Sahu 2004] [Sahu 2004] [Schaeffler and Jenkins 2004] [Tan et al 2004] [Ugrina and Flatau 2004] [Vatsa and Turkel 2004] [Yan and Xin 2004] [Yao et al 2004] [Zaman 2004] [Alvi 2005] [Alvi and Gorton 2005] [Cutler et al 2005] [Deb et al 2005] [Gallas et al 2005] [Greenblatt et al 2005] [Gregory et al 2005] [Gregory et al 2005] [Hassan 2005] [Jung 2005] [Kim et al 2005] [Kondor et al 2005] [Koso 2005] [Liddle et al 2005] [Liu et al 2005] [Mittal 2005] [Moore et al 2005] [Naitoh and Suzuki 2005] [Orkwis et al 2005] [Orlov and Corke 2005] [Raju et al 2005] [Rumsey et al 2005] [Smith 2005] [Subbarao et al 2005] [Amitay and Glezer 2006] [Baysal et al 2006] [Charonko and Vlachos 2006] [Computational Evaluation of Steady 2006] [Dano and Liburdy 2006] [Deb et al 2006] [Design and Analysis of 2006] [Duvigneau and Visonneau 2006] [Ellison 2006] [Enloe et al 2006] [Gomes and Crowther 2006] [Greenblatt et al 2006] [Guo 2006] [Hansen and Bons 2006] [Hiller and Seitz 2006] [Hong 2006] [Kim and Kim 2006] [Kourta et al 2006] [Leclerc et al 2006] [Lee et al 2006] [Mehta 2006] [Ogawara et al 2006] [Orkwis and Daviaux 2006] [Orlov et al 2006] [Pinheiro 2006] [Porter et al 2006] [Post and Corke 2006] [Reimann et al 2006] [Roth and Dai 2006] [Rumsey et al 2006] [Samimy et al 2006] [Schaeffler and Jenkins 2006] [Scholz et al 2006] [Suzuki 2006] [Tamburello and Amitay 2006] [Trávníček et al 2006] [Vatsa and Turkel 2006] [Webb et al 2006] [Wilson 2006] [Zhang et al 2006] [Alvi 2007] [Arienti and Soteriou 2007] [Bourgois et al 2007] [Corke et al 2007] [Cybyk et al 2007] [Deb et al 2007] [Deng et al 2007] [Gregory et al 2007] [Kim et al 2007] [Kim et al 2007] [Koso and Kinoshita 2007] [Kostas et al 2007] [Luo et al 2007] [Ng et al 2007] [Ortmanns and Kähler 2007] [Post et al 2007] [Raju et al 2007] [Rumsey et al 2007] [Rumsey 2007] [Schaeffler et al 2007] [Segawa et al 2007] [Shang 2007] [Sidorenko et al 2007] [Suzen et al 2007] [Takeuchi et al 2007] [Tian et al 2007] [Vatsa and Turkel 2007] [Xu et al 2007] [Yamaleev et al 2007] [Yao et al 2007] [Akhtar and Nayfeh 2008] [Benard et al 2008] [Bogdanov et al 2008] [Braud et al 2008] [Brown 2008] [Casper et al 2008] [Coiro et al 2008] [Deb et al 2008] [Enloe et al 2008] [Feikema and Culley 2008] [Garnier et al 2008] [Gomes and Crowther 2008] [Gunes et al 2008] [Guo and Zhong 2008] [Higashiura et al 2008] [Jabbal 2008] [Jolibois et al 2008] [Kearney-Fischer et al 2008] [Klimov et al 2008] [Koso and Kinoshita 2008] [Kotapati et al 2008] [Liu et al 2008] [Lucas et al 2008] [Mittal and Cattafesta 2008] [Nourgostar and Roth 2008] [Okita et al 2008] [Pinzon and Agarwal 2008] [Pinzon et al 2008] [Raju et al 2008] [Raju et al 2008] [Roupassov et al 2008] [Rusovici et al 2008] [Santhanakrishnan et al 2008] [Schatzman and Thomas 2008] [Shah et al 2008] [Shea and Smith 2008] [Sherman 2008] [Singh and Roy 2008] [Takagaki et al 2008] [Tereshonok 2008] [Tuck and Soria 2008] [You and Moin 2008] [Zhang et al 2008] [Agashe et al 2009] [Appelgren et al 2009] [Aram et al 2009] [Arunajatesan et al 2009] [Caruana et al 2009] [Enloe et al 2009] [Ferlauto and Marsilio 2009] [Koklu and Baysal 2009] [Kostas et al 2009] [Liu et al 2009] [Lopez et al 2009] [Mamunuru et al 2009] [Nikipelov et al 2009] [Ozturk and Jacob 2009] [Peers et al 2009] [Raju et al 2009] [Segawa et al 2009] [Singhal et al 2009] [Tan 2009] [Watmuff 2009] [Yang 2009] [You and Moin 2009] [Aram et al 2010] [Asada and Fujii 2010] [Benard et al 2010] [Blaylock et al 2010] [Cadirci et al 2010] [Cho et al 2010] [Ferry and Rovey 2010] [Gokoglu et al 2010] [Goodfellow et al 2010] [Joussot et al 2010] [Kearney-Fischer et al 2010] [Kwak and Nelson 2010] [Little et al 2010] [Mack et al 2010] [Matsuno et al 2010] [Mondschein et al 2010] [Oyarzun and Cattafesta 2010] [Sammy 2010] [Smith 2010] [Stephen et al 2010] [Volino et al 2010] [Woszidlo et al 2010] [Ashpis and Thurman 2011] [Baqui and Mahmud 2011] [Brown 2011] [Casper et al 2011] [Che et al 2011] [Ciobaca et al 2011] [Disotell and Gregory 2011] [Glezer 2011] [Ibrahim and Skote 2011] [Javadi and Khodadadi 2011] [Jin et al 2011] [Luo and Zhang 2011] [Lyubimov 2011] [Nonomura et al 2011] [Oates and Alvi 2011] [Packard and Bons 2011] [Stephen et al 2011] [Trancossi and Dumas 2011] [Tseng et al 2011] [Volino 2011] [Woszidlo and Wygnanski 2011] [Xu et al 2011] [Asada and Fujii 2012] [Bazdidi-Tehrani and Jahromi 2012] [Benhegouga and Boukehili 2012] [Braud and Dyment 2012] [Chabert et al 2012] [Chappell and Angland 2012] [Chappell et al 2012] [Dawson and Little 2012] [Honami and Motosuke 2012] [Hoskinson 2012] [Ibrahim and Skote 2012] [Ikoshi et al 2012] [Jabbal 2012] [Kordík and Trávníček 2012] [Kurz et al 2012] [Matsuno et al 2012] [Matsunuma and Segawa 2012] [Ogawara et al 2012] [Opaits 2012] [Osmokrovic et al 2012] [Pierre et al 2012] [Sawant et al 2012] [Sawant et al 2012] [Seele et al 2012] [Vasta et al 2012] [Volino and Ibrahim 2012] [Volino and Ibrahim 2012] [West and Hosder 2012] [Wu et al 2012] [Xu et al 2012] [Bernardini et al 2013] [Bobusch et al 2013] [Chen et al 2013] [Choutapalli 2013] [Dawson and Little 2013] [Gao et al 2013] [Goh and Lee 2013] [Graff et al 2013] [Gregory and Tomac 2013] [Hasnain et al 2013] [Hosseinverdi and Fasel 2013] [Koichi et al 2013] [Koklu and Melton 2013] [Kordík and Trávníček 2013] [Kotsonis et al 2013] [Krüger et al 2013] [Makoto et al 2013] [Matsuno et al 2013] [Motoaki et al 2013] [Md et al 2013] [Norimasa et al 2013] [Parametric Investigation of Nanosecond 2013] [Sawant et al 2013] [Schneck and Winfrey 2013] [Seele et al 2013] [Shimizu et al 2013] [Sitaraman and Raja 2013] [Takashi et al 2013] [Tang et al 2013] [Tesař and Peszynski 2013] [Tesař et al 2013] [Tetsuya and Hiroaki 2013] [Tomac and Gregory 2013] [Tomohisa et al 2013] [West and Hosder 2013] [Wilson et al 2013] [Wu and Ahmed 2013] [Xu and Meng 2013] [Aider et al 2014] [Albright and Solovitz 2014] [Application of Zero-Net Mass-Flux 2014] [Ashpis and Laun 2014] [Ashpis and Laun 2014] [Experimental Investigation of “Why 2014] [Friz and Rovey 2014] [Gaertlein et al 2014] [Gardner et al 2014] [González-Espinosa et al 2014] [Kausar et al 2014] [Koklu and Owens 2014] [Kozato et al 2014] [Langston 2014] [Laurendeau et al 2014] [Likhanskii 2014] [Meier and Heister 2014] [Melton 2014] [Natarajan et al 2014] [Sato et al 2014] [Sekimoto et al 2014] [Shang and Huang 2014] [Stalewski and Sznajder 2014] [Taira 2014] [Tang et al 2014] [Tomac and Gregory 2014] [Vatsa et al 2014] [Wang et al 2014] [Williams et al 2014] [Wong et al 2014] [Xu et al 2014] [Zhou et al 2014] [Önder and Meyers 2014] [Abe et al 2015] [Andino et al 2015] [Borghi et al 2015] [Cai et al 2015] [Correale 2015] [Dahalan et al 2015] [Feero et al 2015] [Frankhouser and Gregory 2015] [Gupte et al 2015] [Hasnain et al 2015] [Kara 2015] [Koklu 2015] [Kunimoto and Fuchiwaki 2015] [Kushner et al 2015] [Laurendeau et al 2015] [Mangina et al 2015] [Marxen et al 2015] [Miyagi et al 2015] [Moralev et al 2015] [Ono et al 2015] [Ostermann et al 2015] [Pasquetti and Peres 2015] [Pedroza et al 2015] [Pescini et al 2015] [Pick 2015] [Sauti et al 2015] [Shimizu et al 2015] [Soria 2015] [Tesař 2015] [Tewes and Taubert 2015] [Van Buren et al 2015] [von Gosen et al 2015] [Xia and Mohseni 2015] [Zamora and Pafford 2015] [Asano et al 2016] [Ashcraft et al 2016] [Ashpis and Laun 2016] [Ashpis and Laun 2016] [Ayers and Johari 2016] [Benard et al 2016] [Bettrich and Niehuis 2016] [Chae et al 2016] [Coskun et al 2016] [Coumar et al 2016] [Duda et al 2016] [Fukumoto et al 2016] [Futrzynski and Efraimsson 2016] [Gil and Strzelczyk 2016] [Greco et al 2016] [Harinaldi et al 2016] [Horne and Burnside 2016] [Horne and Burnside 2016] [Horne and Burnside 2016] [Ibrahimoglu et al 2016] [Itsariyapinyo and Sharma 2016] [Jeyalingam and Jabbal 2016] [Jones et al 2016] [Kara 2016] [Kato et al 2016] [Khoshkhoo and Jahangirian 2016] [Kim et al 2016] [Koklu 2016] [Koklu 2016] [Koklu 2016] [Li et al 2016] [Lu et al 2016] [Melton and Koklu 2016] [Melton et al 2016] [Neretti 2016] [Ostermann et al 2016] [Park and Kim 2016] [Peters et al 2016] [Phan and Shin 2016] [Sieber et al 2016] [Slupski and Kara 2016] [Tesař 2016] [Vatsa et al 2016] [Wang et al 2016] [Wang et al 2016] [Yan et al 2016] [Aono et al 2017] [Bacic 2017] [Bauer et al 2017] [Berk et al 2017] [Boukenkoul et al 2017] [Cui et al 2017] [Feero et al 2017] [Horne and Burnside 2017] [Hue et al 2017] [Igarashi et al 2017] [Jones et al 2017] [Kara 2017] [Kara and Slupski 2017] [Kim et al 2017] [Koklu and Owens 2017] [Koklu 2017] [Koklu 2017] [Koklu 2017] [Kurowski 2017] [Lakebrink et al 2017] [Le Clainche et al 2017] [Li et al 2017] [Li et al 2017] [Messanelli and Belan 2017] [Miyagi and Kimura 2017] [Ostermann et al 2017] [Ramos-Pedroza et al 2017] [Rimašauskienė 2017] [Rimašauskienė 2017] [Sato et al 2017] [Seo and Mittal 2017] [Slupski and Kara 2017] [Smyk 2017] [The failure of delayed 2017] [Tomac and Gregory 2017] [Zhou et al 2017] [Zong and Kotsonis 2017] [Alimi and Wünsch 2018] [Bhattacharjee et al 2018] [Comparison of acoustic synthetic 2018] [Ebrahimi and Hajipour 2018] [Elsahhar et al 2018] [Fujii 2018] [Fukumoto et al 2018] [Ghee et al 2018] [Harada and Sakakibara 2018] [Hirsch and Gharib 2018] [Hoeijmakers and Wirtz 2018] [Huang and Zhou 2018] [Huang et al 2018] [Itsariyapinyo and Sharma 2018] [Kanase et al 2018] [Kanehara et al 2018] [Kara et al 2018] [Karyakin et al 2018] [Kazanskii et al 2018] [Koklu 2018] [Koklu 2018] [Kornyakov et al 2018] [Messahel et al 2018] [Miyagi and Kimura 2018] [Miyamoto et al 2018] [Ogawa et al 2018] [Palumbo et al 2018] [Plasma Actuator 2018] [Rice and Amitay 2018] [Salinas et al 2018] [Sato 2018] [Schlösser and Bauer 2018] [Shen et al 2018] [Slupski et al 2018] [Sujar-Garrido et al 2018] [Synthetic Jet 2018] [Tang and Agarwal 2018] [Trávníček and Broučková 2018] [Vatsa et al 2018] [Viturro et al 2018] [Wang and Tang 2018] [Wang et al 2018] [Wu et al 2018] [Xin et al 2018] [Zhang 2018] [Zheng et al 2018] [Zimmerman et al 2018] [Zong et al 2018] [Akimoto and Kimura 2019] [Berk and Ganapathisubramani 2019] [Dancova et al 2019] [Dauengauer and Mullyadzhanov 2019] [Firsov et al 2019] [Gowda B C et al 2019] [Handa and Fujimura 2019] [Hasegawa and Obayashi 2019] [Hossain et al 2019] [Hui et al 2019] [Isobe et al 2019] [Kumar and Karn 2019] [Ma et al 2019] [Mehdipoor et al 2019] [Messahel et al 2019] [Ming et al 2019] [Ostermann et al 2019] [Ott et al 2019] [Pack Melton et al 2019] [Park et al 2019] [Schatzman et al 2019] [Seki and Sano 2019] [Shimizu et al 2019] [Slupski et al 2019] [Tadjfar and Kamari 2019] [Tomac and Gregory 2019] [Tomac and Sundström 2019] [Wang et al 2019] [Yamashita and Hasegawa 2019] [Ye et al 2019] [Abdelraouf et al 2020] [Abdelraouf et al 2020] [Belanger et al 2020] [Buzica and Breitsamter 2020] [Harinaldi et al 2020] [Hasan and Atkinson 2020] [Jackson et al 2020] [Kobayashi et al 2020] [Kumar and Karn 2020] [Lai et al 2020] [Le Clainche et al 2020] [Lei et al 2020] [Li and Zhang 2020] [Nagasaki and Hasegawa 2020] [Otake et al 2020] [Oz and Kara 2020] [Palumbo et al 2020] [Park et al 2020] [PourRazzaghi and Xu 2020] [Sano and Seki 2020] [Sekimoto et al 2020] [Shay et al 2020] [Shi and Sullivan 2020] [Smyk et al 2020] [Smyk et al 2020] [Sundström and Tomac 2020] [Tomac 2020] [Tomac and Sundström 2020] [Weigel et al 2020] [Yang and Agarwal 2020] [Yokoyama et al 2020] [Aiura et al 2021] [Deb et al 2021] [Gil et al 2021] [Jia et al 2021] [Kim and Kim 2021] [Kim and Kim 2021] [Kobayashi and Fuchiwaki 2021] [Li et al 2021] [Lim and Lyu 2021] [Löffler et al 2021] [Koklu 2021] [Palumbo and de Luca 2021] [Pan et al 2021] [Peterson et al 2021] [Pour Razzaghi et al 2021] [Sarwar et al 2021] [Sato et al 2021] [Shimomura et al 2021] [Sim et al 2021] [Wen et al 2021] [Xia et al 2021] [Zheng 2021] [Zhu et al 2021] [Alam and Kara 2022] [Arafa et al 2022] [Ayeni and Cleton 2022] [Azzawi 2022] [Chen and Li 2022] [Chen and Sun 2022] [Farrell et al 2022] [Flow Separation Control on 2022] [Gungordu 2022] [Investigations on the Interfering 2022] [Itsariyapinyo and Sharma 2022] [Khan et al 2022] [Kumar Subramanyam et al 2022] [Kurowski and Szwaba 2022] [Li et al 2022] [Lu et al 2022] [Luo et al 2022] [Madane et al 2022] [Maikap et al 2022] [Mayahara and Sato 2022] [Monat et al 2022] [Nicholls and Bacic 2022] [Nicholls et al 2022] [Smyk and Markowicz 2022] [Sundaram et al 2022] [Tajik and Parezanovic 2022] [Tajik et al 2022] [Tolkachev 2022] [Vinoth Kumar and Vijayaraghavan 2022] [Wu et al 2022] [Zhang and Zong 2022] [Zhang et al 2022] [Zhang et al 2022] [Zhao et al 2022] [Aslani et al 2023] [Awate and Ansell 2023] [Blejchař et al 2023] [Chen et al 2023] [Chernyshev et al 2023] [Elaissi et al 2023] [Flow instability and momentum 2023] [Gao et al 2023] [Golubev 2023] [Golubev 2023] [Jiang et al 2023] [Kayvanpour et al 2023] [Kobayashi and Fuchiwaki 2023] [Kotvitskii et al 2023] [Liu et al 2023] [Loe et al 2023] [Löffler and Weiss 2023] [Maikap et al 2023] [Mayahara and Sato 2023] [Nicholls and Bacic 2023] [Numerical investigation of aerodynamic 2023] [Oka et al 2023] [Okada et al 2023] [Tavakkoli et al 2023] [Truong et al 2023] [Tung Pham Duy et al 2023] [Xu et al 2023] [Yu and Zheng 2023] [Yuura et al 2023] [zhang et al 2023] [Zhao et al 2023] [Zhou et al 2023] [Butler et al 2024] [Ding et al 2024] [Effect of Synthetic Jet 2024] [Hussain and Khan 2024] [Jabbari and Esmaeili 2024] [Karimzadegan and Bergada 2024] [Karimzadegan et al 2024] [Karimzadegan et al 2024] [Kassem and Kara 2024] [Liu and Liang 2024] [Mahdavi et al 2024] [Maikap and Rajagopal 2024] [Ogawa et al 2024] [Serrar et al 2024] [Sun et al 2024] [Three-dimensional Flow Field Characteristics 2024] [Tocquer et al 2024] [Viguera et al 2024] [Yang et al 2024] [Zhao and Bai 2024] [Zhao et al 2024] [Zhou et al 2024] [Zhu et al 2024] [Aguirre-Villegas et al 2025] [Ahmed et al 2025] [Burlett and Mobli 2025] [Duan et al 2025] [Espinoza Gutierrez et al 2025] [Gautam et al 2025] [Gui et al 2025] [Hammouda et al 2025] [Hu et al 2025] [Hu et al 2025] [Investigation of Wing Lift 2025] [Iskandar et al 2025] [Kara 2025] [Karthikeyan and Harish 2025] [Kimura et al 2025] [Kong et al 2025] [Kopiev 2025] [Lee et al 2025] [Li et al 2025] [Liu 2025] [Liu and Chen 2025] [Liu et al 2025] [Lu et al 2025] [Maduche and Mongeau 2025] [Martinke et al 2025] [Mitsumoto et al 2025] [Numerical Study of the 2025] [Parametric Study on the 2025] [Price et al 2025] [Rahni and Jahangirian 2025] [Rizzetta and Garmann 2025] [Sato 2025] [Smyk and Stopel 2025] [Viguera et al 2025] [Wang et al 2025] [Zengler et al 2025] [Zhang et al 2025] [Zhao and Bai 2025] [Zubair and Wen 2025] [Chen et al 2026] [D’Onofrio et al 2026] [Dumrul and Kara 2026] [Dávalos et al 2026] [Fan et al 2026] [Gui et al 2026] [Güngördü 2026] [Jaganath and Steinfurth 2026] [Li et al 2026] [Mitsumoto et al 2026] [Nicholls et al 2026] [Prabahar and Zha 2026] [Saemian et al 2026] [Serrar and Khlifi 2026] [Shestakov and Yagodnitsyna 2026] [Shi et al 2026] [Wylie and Amitay 2026] [Yamada and Norimoto 2026] [Yukuan et al 2026] [Zhang et al 2026] [Zhu et al 2026] [Löffler and Weiss 2027] [Ansari Shirvan] [Arcese] [van Dam et al] [de Vries] [Deb et al] [Grosvenor] [Koch et al] [Karimzadegan] [Melton et al] [Melton et al] [Seifert] [Sudak] [Tocquer] [Ukpai and Rediniotis] [Velasquez]
Blowing, the Coanda surface and the jet flap
The oldest literature on controlling a wing with air. Circulation control, the Coanda effect, the jet flap, blown and externally blown flaps, upper-surface and spanwise blowing, and boundary-layer control by blowing and suction, with the acoustics of the blown flap.
317 of these records date from before 1980, which is the era of the NACA boundary-layer-control reports and of the externally blown flaps and upper-surface blowing of the short take-off transport programmes.
750 records. [Seewald 1927] [Reid and Bamber 1928] [Bamber 1932] [Quinn 1944] [Von Doenhoff 1944] [Quinn 1946] [Kohl and Diggs 1947] [Quinn 1947] [Quinn 1947] [Schwier 1947] [Huffman et al 1948] [Pasamanick and Proterra 1948] [Passamanick 1948] [Racisz and Quinn 1948] [Burrows et al 1949] [Horton and Von Doenhoff 1949] [Braslow and Visconti 1950] [Horton et al 1950] [Braslow et al 1951] [Horton et al 1951] [Blosser 1952] [Cliett 1952] [Rebuffet and Poisson-Quinton 1952] [Blosser 1953] [Cocke and Fink 1953] [Cook et al 1954] [Kelley and Tolhurst 1955] [Anderson et al 1956] [Fisher et al 1956] [Kelly 1956] [Kelly and Tucker 1956] [McLemore and Fink 1956] [Northrop Aircraft Inc Hawthorne Ca 1956] [Rolls and Innis 1956] [Sferi-Coanda Clichy France 1956] [Spreemann and Kuhn 1956] [Stratford 1956] [Stratford 1956] [Cerreta 1957] [Davenport 1957] [Dimmock 1957] [Fink and McLemore 1957] [Helmbold 1957] [Hirsch 1957] [James and Maki 1957] [McLemore 1957] [Quigley et al 1957] [Raspet 1957] [Sferi-Coanda Clichy France 1957] [Griffin et al 1958] [Helmbold 1958] [Hirsch 1958] [Kelly et al 1958] [McLemore and Fink 1958] [McLemore 1958] [Quigley et al 1958] [Riebe and Davenport 1958] [Spreemann 1958] [Aoyagi and Hickey 1959] [Maki 1959] [Coanda 1960] [Gault 1960] [Hickey and Aoyagi 1960] [McLemore and Peterson 1960] [Quigley et al 1960] [Yen 1960] [Grunwald 1961] [Lockwood 1961] [Weiberg and Holzhauser 1961] [Weiberg and Holzhauser 1961] [Erickson 1962] [Aoyagi and Hickey 1963] [Korbacher 1963] [White 1963] [Korbacher 1964] [Northrop Corp Hawthorne Ca Norair Div 1964] [Northrop Corp Hawthorne Ca Norair Div 1964] [Mehus 1965] [Reba 1966] [Roberts et al 1966] [Wygnanski 1966] [Yuan et al 1966] [Chang et al 1967] [Cordner 1967] [Lissaman 1967] [Pearson 1967] [Vogler 1967] [Corsiglia et al 1968] [Dunham 1968] [Fink et al 1968] [Kind 1968] [Miller and Seren 1968] [Aoyagi et al 1969] [Clever 1969] [Lissaman 1969] [Lissaman 1969] [Parlett and Shivers 1969] [Welna et al 1969] [Bangert 1970] [Beckwith et al 1970] [Deal et al 1970] [Englar 1970] [Freeman et al 1970] [Freeman et al 1970] [Romiti 1970] [Vogler 1970] [Welna et al 1970] [Williams and Howe 1970] [Aiken and Cook 1971] [Deal et al 1971] [Dorsch et al 1971] [Falarski and Aiken 1971] [Falarski and Koenig 1971] [Goodykoontz et al 1971] [Grafton et al 1971] [Henderson 1971] [Jenkins 1971] [Kantha et al 1971] [Parlett et al 1971] [Smith 1971] [Stabe 1971] [A Structural Design for 1972] [Aoyagi et al 1972] [Bettner 1972] [Design integration and noise 1972] [Dorsch et al 1972] [Dorsch et al 1972] [Falarski 1972] [Falarski and Koenig 1972] [Falarski and Koenig 1972] [Goodykoontz et al 1972] [Goodykoontz et al 1972] [Grantham et al 1972] [Greene and Perry 1972] [Groeneweg and Minner 1972] [Groeneweg and Minner 1972] [Gruschka and Schrecker 1972] [Hayden et al 1972] [Hughes 1972] [Johnson 1972] [Kier et al 1972] [Levinsky and Yeh 1972] [Olsen et al 1972] [Oshima and Kinoshita 1972] [Panitz and Wasan 1972] [Parlett 1972] [Putnam and Lasagna 1972] [Ungar et al 1972] [Vonglahn et al 1972] [Vonglahn et al 1972] [Aiken and Cook 1973] [Aiken et al 1973] [Aoyagi et al 1973] [Aoyagi et al 1973] [Bettner and Blessing 1973] [Campbell et al 1973] [Ciffone and Robinson 1973] [Falarski 1973] [Falarski et al 1973] [Goodykoontz et al 1973] [Goodykoontz et al 1973] [Hackett and Lyman 1973] [Herold 1973] [Hughes 1973] [Karchmer and Friedman 1973] [Kinoshita and Oshima 1973] [Lansing et al 1973] [Lissaman 1973] [Mahal and Gilchrist 1973] [McKinzie and Burns 1973] [Morris et al 1973] [Okumoto and Elsanker 1973] [Parlett et al 1973] [Phelps and Smith 1973] [Phelps et al 1973] [Powers and Kier 1973] [Roepcke and Nickson 1973] [Samanich et al 1973] [Scharton et al 1973] [Smith 1973] [Theisen et al 1973] [Capone 1974] [Chin et al 1974] [Coe and Kulla 1974] [Cole and Rathburn 1974] [Dorsch 1974] [Dorsch et al 1974] [Gentry 1974] [Gillette et al 1974] [Goodykoontz et al 1974] [Grantham et al 1974] [Harkonen et al 1974] [Hoad 1974] [Johnson and Phelps 1974] [Johnson and Kardas 1974] [Jones and Heidelberg 1974] [Kinoshita and Oshima 1974] [Middleton 1974] [Middleton and Bergeron 1974] [Parlett et al 1974] [Quigley et al 1974] [Scantling and Gloss 1974] [Schoenster 1974] [Schrecker and Maus 1974] [Shivers and Smith 1974] [Smith and White 1974] [Stewart 1974] [Waites and Chin 1974] [Cook et al 1974] [Abramson 1975] [Addessio and Skifstad 1975] [Aoyagi et al 1975] [Campbell 1975] [Campbell 1975] [Capone 1975] [Carros et al 1975] [Chin et al 1975] [Cochrane and Carros 1975] [Coe et al 1975] [Cook and Whittley 1975] [Dorsch et al 1975] [Erickson and Campbell 1975] [Erickson and Campbell 1975] [Falarski et al 1975] [Fink 1975] [Forsyth et al 1975] [Goodykoontz et al 1975] [Heidelberg et al 1975] [Holmberg 1975] [Johnson 1975] [Kinoshita and Oshima 1975] [Koenig and Aoyagi 1975] [Lan and Campbell 1975] [Laub 1975] [Levinsky and Schappelle 1975] [Marton 1975] [Mendenhall et al 1975] [Middleton et al 1975] [Miles 1975] [Naeseth and Hoad 1975] [Pennock et al 1975] [Perry and Greene 1975] [Phelps 1975] [Reddy 1975] [Reddy and Yu 1975] [Renselaer et al 1975] [Shivers and Smith 1975] [Shivers et al 1975] [Barger 1976] [Burns et al 1976] [Clarke 1976] [Coe et al 1976] [Dods and Watson 1976] [Fournier and Coe 1976] [Gainer et al 1976] [Gibson 1976] [Goodykoontz et al 1976] [Hackett et al 1976] [Hoad 1976] [Johnson 1976] [Kadman 1976] [Kinoshita and Oshima 1976] [Lan 1976] [McKinzie 1976] [McKinzie et al 1976] [Meleason 1976] [Meleason and Wells 1976] [Mendenhall 1976] [Mendenhall et al 1976] [Phelps et al 1976] [Platzer 1976] [Propulsive-Lift Noise of an 1976] [Shivers et al 1976] [Sleeman and Phelps 1976] [Tam and Reddy 1976] [Tennant et al 1976] [Vogler 1976] [Wind-tunnel investigation of aerodynamic 1976] [Abramson 1977] [Addessio and Skifstad 1977] [Baker and Manhardt 1977] [Baker and Manhardt 1977] [Becker and Maus 1977] [Becker and Maus 1977] [Clark and Yu 1977] [Erickson and Campbell 1977] [Erickson and Campbell 1977] [Gilinskii and Lebedev 1977] [Hackett and Boles 1977] [Kaups and Cebeci 1977] [Lan 1977] [Lan et al 1977] [Lan et al 1977] [Morehouse et al 1977] [Pennock 1977] [Phelps 1977] [Reubush 1977] [Ryle et al 1977] [Schoen et al 1977] [Schoenster and Schroeder 1977] [Seiler 1977] [Fink 1978] [Hackett and Boles 1978] [Lan et al 1978] [Reddy 1978] [Shovlin 1978] [Vomaske et al 1978] [Aiken et al 1979] [Anglin and Satran 1979] [Campbell and Erickson 1979] [Catalano et al 1979] [Design of the circulation 1979] [Erickson 1979] [Hough 1979] [Johns et al 1979] [Pappa 1979] [Rao 1979] [Bohn and Shovlin 1980] [Furey 1980] [Harris and Falarski 1980] [Hough 1980] [Lorincz 1980] [McKinzie 1980] [Parthasarathy and Vijayaraghavan 1980] [Winter 1980] [Braslow 1981] [Tai et al 1981] [Wood 1981] [Wukowitz 1981] [Bachalo 1982] [Burley and Hwang 1982] [Cochrane et al 1982] [Eppel et al 1982] [McKinzie 1982] [Bevilaqua et al 1983] [Burley and Hwang 1983] [Hwang 1983] [Seginer and Salomon 1983] [Smeltzer et al 1983] [Stephenson 1983] [Taback et al 1983] [Wood and Conlon 1983] [Bevilaqua and Lee 1984] [Biringen 1984] [Burley 1984] [Englar et al 1984] [Hwang 1984] [Lipera and Sandlin 1984] [Tai and Kidwell 1984] [Wagner et al 1984] [Wilson and Liperra 1984] [Berman 1985] [Biringen et al 1985] [Hahn and Wilson 1985] [Harvell and Franke 1985] [Modi 1985] [Panontin 1985] [Salikuddin et al 1985] [Satran et al 1985] [Stewart 1985] [Tai and Kidwell 1985] [Tavella 1985] [Carpenter et al 1986] [Chopra et al 1986] [Garner 1986] [Krauss et al 1986] [Lee et al 1986] [Novak and Cornelius 1986] [Papathanasiou and Nagel 1986] [Pulliam et al 1986] [Rodman and Wood 1986] [Shrewsbury 1986] [Tavella et al 1986] [Torres 1986] [Wood 1986] [Wood and Rogers 1986] [Wood and Roberts 1986] [Banks and Paulson 1987] [Bevilaqua and Lee 1987] [Biringen 1987] [Dash et al 1987] [Dvorak and Dash 1987] [Dvorak et al 1987] [Englar 1987] [Franke and Harvell 1987] [Gregory-Smith and Gilchrist 1987] [Keener et al 1987] [Loth 1987] [McLachlan 1987] [McLachlan 1987] [Nielsen 1987] [Nielsen and Biggers 1987] [Novak et al 1987] [Novak and Cornelius 1987] [Pulliam et al 1987] [Riddle and Eppel 1987] [Salikuddin et al 1987] [Shovlin et al 1987] [Shrewsbury 1987] [Spaid and Keener 1987] [Torres 1987] [Viegas et al 1987] [Wood 1987] [Wood 1987] [Gilchrist and Gregory-Smith 1988] [Harvey 1988] [Pfenninger and Vemuru 1988] [Viegas et al 1988] [Yeh et al 1988] [Yeh et al 1988] [McLachlan 1989] [Shrewsbury 1989] [Sun and Wang 1989] [Visser et al 1989] [Yeh et al 1989] [Lee and Roberts 1990] [Parikh et al 1990] [Smith et al 1990] [Williams and Franke 1990] [Danabasoglu et al 1991] [Ghee and Leishman 1991] [Hunter and Krauss 1991] [Kroo et al 1991] [Maddalon 1991] [Paschal et al 1991] [Spaid and Keener 1991] [Wood and Bauer 1991] [Acharya and Metwally 1992] [Birckelbaw 1992] [Celik and Roberts 1992] [Celik and Roberts 1992] [Dirlik et al 1992] [Ghee and Leishman 1992] [Heinemann and Brown 1992] [Hunter and Cullen 1992] [Miller and Gile 1992] [Rao 1992] [Williams and Franke 1992] [Boalbey et al 1993] [Ferguson et al 1993] [Greenwell and Wood 1993] [Linton 1993] [Tso 1993] [Wong et al 1993] [Celik and Roberts 1994] [Cornelius and Lucius 1994] [Hwang et al 1994] [Lim 1994] [Meyer and Seginer 1994] [Watmuff 1994] [Wong et al 1994] [Yang 1994] [Brown 1995] [Emanuel 1995] [Hong and Roberts 1995] [Jingchang et al 1995] [Johari et al 1995] [Matsson 1995] [Mineck 1995] [Pedreiro et al 1995] [Asami and Sawada 1996] [Englar 1996] [Kraushaar and Chokani 1996] [Mendoza and Ahuja 1996] [Mineck and Hartwich 1996] [Weaver et al 1996] [Guowei et al 1997] [Langan et al 1997] [Sawada and Asami 1997] [Englar 1998] [Guillot et al 1998] [Matsuo et al 1998] [Vorobieff and Rockwell 1998] [Weaver et al 1998] [Banks et al 1999] [Braslow 1999] [Braslow 1999] [Farcy and Renier 1999] [Ferman and Turner 1999] [Ferman and Turner 1999] [Guy et al 1999] [Guy et al 1999] [Kandil and Yang 1999] [Morton et al 1999] [Sun and Sheikh 1999] [Grove et al 2000] [Guy et al 2000] [Guy et al 2000] [Howe 2000] [Kamishita et al 2000] [Slotnick et al 2000] [Sobey 2000] [Speyer and Kim 2000] [Viswanath et al 2000] [Wang and Sun 2000] [Liu et al 2001] [Siegel et al 2001] [Sun and Hamdani 2001] [Englar and Campbell 2002] [Howe 2002] [Jones et al 2002] [Sellars et al 2002] [Speyer and Kim 2002] [Sutliff et al 2002] [Ahuja et al 2003] [Gross et al 2003] [Hamdani et al 2003] [Liu et al 2003] [Munro et al 2003] [Vasilescu and Dancila 2003] [Viswanath and Madhavan 2003] [Abramson 2004] [Frith and Wood 2004] [Gross and Fasel 2004] [Huang et al 2004] [Hutcheson and Stead 2004] [Hutcheson et al 2004] [Lopera et al 2004] [Margaris and Gursul 2004] [Shinozuka et al 2004] [Viswanath and Madhavan 2004] [Wu et al 2004] [Zha and Paxton 2004] [Alexander et al 2005] [Alexander et al 2005] [Bakhle and Srivastava 2005] [Boyd 2005] [Duraisamy and Baeder 2005] [Han et al 2005] [Hutcheson and Brooks 2005] [Jones 2005] [Jones and Joslin 2005] [Jones and Joslin 2005] [McGowan and Gopalarathnam 2005] [Munro et al 2005] [Muramatsu et al 2005] [Siller et al 2005] [Sutliff 2005] [Swanson et al 2005] [Swanson et al 2005] [Aerodynamic Heat Exchanger A 2006] [Coanda Effect and Circulation 2006] [Computational Study of a 2006] [Cruz and Anders 2006] [Donnelly et al 2006] [Experimental and Computational Investigation 2006] [Goldstein 2006] [Green and Cruz 2006] [Gross and Fasel 2006] [Gross and Fasel 2006] [Jones et al 2006] [Laible et al 2006] [Lee-Rausch et al 2006] [Novel Flow Control Method 2006] [Pneumatic Flap Performance for 2006] [Slomski et al 2006] [Swanson and Rumsey 2006] [Trailing Edge Circulation Control 2006] [A Study on Jet 2007] [Cui et al 2007] [Dygert and Dang 2007] [Erickson 2007] [Flow Separation Control Effects 2007] [Il’inskii and Mardanov 2007] [Margaris and Gursul 2007] [Schlecht and Anders 2007] [Jones et al 2008] [Layek et al 2008] [Lin et al 2008] [Shannon and Morris 2008] [Dygert and Dang 2009] [Englar et al 2009] [Morris et al 2009] [Pfingsten and Radespiel 2009] [Singh and Ramamurthi 2009] [Swanson and Rumsey 2009] [Wetzel et al 2009] [Wetzel et al 2009] [Winkler et al 2009] [Balzer and Fasel 2010] [Chen et al 2010] [Edwards 2010] [Guendogdu et al 2010] [Iguchi and Ilegbusi 2010] [Jensch et al 2010] [Kweder et al 2010] [Lin et al 2010] [Liu et al 2010] [Madavan and Rogers 2010] [Margaris and Gursul 2010] [Milholen et al 2010] [Miozzi et al 2010] [Nichino et al 2010] [Nishino and Shariff 2010] [Nishino et al 2010] [Nishino et al 2010] [Pott-Pollenske and Pfingsten 2010] [Sattler et al 2010] [Wetzel et al 2010] [Zhang et al 2010] [Allan et al 2011] [Florin et al 2011] [Guo et al 2011] [Liu et al 2011] [Lubert and Shafer 2011] [Rumsey and Nishino 2011] [Tan et al 2011] [Trancossi and Dumas 2011] [Wetzel and Cattafesta 2011] [Zhang et al 2011] [Caraway et al 2012] [Chen et al 2012] [Djojodihardjo and Hamid 2012] [Drãgan 2012] [Lubert 2012] [Milholen et al 2012] [Nishino and Shariff 2012] [Paschal et al 2012] [Watkins et al 2012] [Winkler et al 2012] [Arolla and Durbin 2013] [Bobonea and Pricop 2013] [Chen et al 2013] [Edstrand and Cattafesta III 2013] [Horne and Burnside 2013] [Jones et al 2013] [Milholen et al 2013] [Subhash and Dumas 2013] [Trancossi et al 2013] [Burnazzi and Radespiel 2014] [Chan et al 2014] [Dumas et al 2014] [Gerhard et al 2014] [Kroehnert 2014] [Kumar et al 2014] [Semaan et al 2014] [Edstrand and Cattafesta 2015] [El Sayed Mohamed and Semaan 2015] [Jiao and Lu 2015] [Lawrence and Self 2015] [Lee et al 2016] [Liu and Zha 2016] [Naigle et al 2016] [Park et al 2016] [Zafer and Gürsoy 2016] [Baljit et al 2017] [Chan et al 2017] [Feng et al 2017] [Reger et al 2017] [Skotnicka-Siepsiak 2017] [Eto et al 2018] [James et al 2018] [Kornilov 2018] [Puri et al 2018] [Rossian et al 2018] [Wu et al 2018] [Yang and Zha 2018] [Yang and Zha 2018] [Yang and Zha 2018] [Yang and Zha 2018] [Zaidi and Bukhari 2018] [Zhang et al 2018] [Çetin et al 2018] [Ahmed 2019] [Ahmed 2019] [Ahmed 2019] [Capobianco et al 2019] [Di Luca and Breuer 2019] [Fatahian et al 2019] [Hirokawa et al 2019] [Li et al 2019] [Mazumder et al 2019] [Abed 2019] [Shakouchi et al 2019] [Siliang et al 2019] [Wang and Zha 2019] [Abbasi and Souri 2020] [Abramova et al 2020] [Li and Qin 2020] [Lozano and Paniagua 2020] [Trancossi and Pascoa 2020] [Zhang et al 2020] [Kara and Erpulat 2021] [Karuppiah and Wessley 2021] [Kornilov et al 2021] [Asaro et al 2022] [Chi and Gu 2022] [Li et al 2022] [Shi et al 2022] [Sun et al 2022] [Wang et al 2022] [Xu and Zha 2022] [Yang et al 2022] [Yang et al 2022] [Zhao et al 2022] [Asaro et al 2023] [Chen et al 2023] [He et al 2023] [Influence of Surface Curvature 2023] [Jeon et al 2023] [Lei and Zha 2023] [Lei and Zha 2023] [Pan et al 2023] [Xu and Zha 2023] [Yang et al 2023] [Zaheer et al 2023] [Zhang and Zhao 2023] [Zhang et al 2023] [Zheng et al 2023] [Abramova and Soudakov 2024] [Butler and Bons 2024] [Chen et al 2024] [Jente et al 2024] [Deere et al 2024] [Li et al 2024] [Rizzetta and Garmann 2024] [Shao et al 2024] [Soufivand et al 2024] [Su et al 2024] [Zhang et al 2024] [Kumar and Bhumkar 2025] [Pakhomov 2025] [Raj et al 2025] [Rizzetta and Garmann 2025] [Soufivand et al 2025] [Vechalapu et al 2025] [Yabu et al 2025] [Zhang et al 2025] [Zhao et al 2025] [Çuhadaroğlu et al 2025] [Ding et al 2026] [Liu 2026] [Rackers et al 2026] [Rizzetta and Garmann 2026] [Shao et al 2026] [Sheng et al 2026] [Vechalapu et al 2026] [Vibhu et al 2026] [Yang et al 2026] [Zhao et al 2026] [Zhao et al 2026] [Zhou et al 2026] [Churchill] [Couillaud] [McFadden and Bons] [Hard] [Kweder] [McAuliffe] [Starn] [Swan]
Separation and its control, which is what the effectors do
The mechanism the effectors exploit. Control of separation on airfoils, high-lift systems, ramps and humps, including the agency reports this article reads in full and the review it leans on.
207 records. [Foster and Fitzpatrick 1948] [Pratt and Shields 1952] [Salmi 1952] [Bollech and Hadaway 1953] [Childress 1958] [Dike and Dunn 1958] [Peake and Owen 1979] [Sullivan 1979] [Trobaugh et al 1980] [Sutton 1982] [Zilliac 1983] [Mangalam et al 1986] [Barnett and Carter 1987] [Durbin and McKinzie 1987] [Huang et al 1987] [Viken et al 1987] [Rao and Kariya 1988] [Zaman and McKinzie 1988] [Bar-Sever 1989] [Katz et al 1989] [Oh and Roberts 1989] [Zaman and McKinzie 1989] [Lin et al 1990] [Rice and Abbott 1990] [Chow and Chu 1991] [Gad-El-hak and Bushnell 1991] [Lin et al 1991] [Selby 1991] [Lin et al 1992] [Yip et al 1992] [Gally 1994] [Jun-Fei and Shao-Zhi 1994] [Nelson et al 1994] [Potter and Vandam 1995] [Telionis 1995] [Chandrasekhara et al 1996] [Rudolph 1996] [Seifert et al 1996] [Chandrasekhara et al 1997] [Alam and Sandham 1998] [Hahne and Glaab 1999] [Mochizuki et al 1999] [Murawski 1999] [Ravindran 1999] [Sengupta et al 1999] [Sinha 1999] [Song et al 1999] [Urzynicok and Fernholz 1999] [Abed 2000] [Allan et al 2000] [Lu 2000] [Pack and Seifert 2000] [Seifert and Pack 2000] [Separation Control 2000] [Munday and Jacob 2001] [Munday and Jacob 2002] [Munday et al 2002] [Angele 2003] [Greenblatt and Wygnanski 2003] [Martin et al 2003] [Pack et al 2003] [Pack et al 2003] [Tumin and Ashpis 2003] [Ashpis and Hultgren 2004] [Beck et al 2004] [Bons 2004] [Greenblatt et al 2004] [Melton et al 2004] [Zhang 2004] [Ahmad et al 2005] [Effects of Pulsating Jet 2005] [Greenblatt 2005] [Greenblatt 2005] [Katam et al 2005] [Logdberg and Alfredsson 2005] [Pern and Jacob 2005] [Seidel et al 2005] [Sohn et al 2005] [Yarusevych et al 2005] [Yoshida et al 2005] [Zhu and Qiu 2005] [Angele and Grewe 2006] [Greenblatt 2006] [Pern et al 2006] [Walker 2006] [Abe et al 2007] [Greenblatt 2007] [Greenblatt et al 2007] [Khodadoust and Shmilovich 2007] [Khodadoust and Washburn 2007] [Melton et al 2007] [Abe et al 2008] [Agarwal et al 2008] [Favier et al 2008] [Haucke et al 2008] [Little et al 2008] [Mack et al 2008] [Melton et al 2008] [You et al 2008] [Zaman and Culley 2008] [Genç and Kaynak 2009] [Rizzetta and Visbal 2009] [Shmilovich and Yadlin 2009] [Woo et al 2009] [Eichinger et al 2010] [Stalnov and Seifert 2010] [Tesař 2010] [Gross and Fasel 2011] [Kühn et al 2011] [Liang Hua et al 2011] [Moralev et al 2011] [Shun and Ahmed 2011] [Arifuzzaman 2012] [Benton et al 2012] [Desalvo et al 2012] [Grager et al 2012] [Gross and Fasel 2012] [Packard and Bons 2012] [Cadirci and Gunes 2013] [Gross and Fasel 2013] [Gross and Fasel 2013] [Gross and Fasel 2013] [Haucke and Nitsche 2013] [Woo and Glezer 2013] [Woo and Glezer 2013] [Yufeng Cheng et al 2013] [Ahmed et al 2014] [Clifford et al 2014] [Desalvo et al 2014] [Hartwich et al 2014] [Kato et al 2014] [Munday and Taira 2014] [van Dommelen and Yapalparvi 2014] [Bayoda et al 2015] [Fujii 2015] [Guha et al 2015] [Munday and Taira 2015] [Gupta and Ansell 2016] [Hartwich et al 2016] [Jairam et al 2016] [Joy et al 2016] [Matalanis et al 2016] [Walker et al 2016] [Yeh and Taira 2016] [Bodart et al 2017] [Ciobaca and Dandois 2017] [Guo et al 2017] [Shahid and Mashud 2017] [Vrchota 2017] [Yeh et al 2017] [Hosseini et al 2018] [Koklu 2018] [Munday and Taira 2018] [Prabhu and Srinivas 2018] [Shimomura et al 2018] [Stalewski and Stryczniewicz 2018] [Takahashi and Ohnishi 2018] [Esfahani et al 2019] [Fang et al 2019] [Gildersleeve and Amitay 2019] [Kobayshi and Sato 2019] [Li et al 2019] [Niu et al 2019] [Oguri et al 2019] [Ramaswamy and Schreyer 2019] [Siauw and Bonnet 2019] [Tadjfar and Kamari 2019] [Wang et al 2019] [Yeh and Taira 2019] [Obeid et al 2020] [Shimomura et al 2020] [Koklu 2021] [Okoye et al 2021] [Sato 2021] [Xu et al 2021] [Chaudhary et al 2022] [Optimisation of Trapped Vortex 2022] [Takada et al 2022] [Control of flow separation 2023] [Takada et al 2023] [Takada et al 2023] [Boutoudj and Tebbiche 2024] [Brandt and Bons 2024] [Dodayav et al 2024] [Flow Separation Control of 2024] [Gross et al 2024] [Abdolahipour 2024] [Vander Schaaf et al 2024] [Ho et al 2025] [Kamiński et al 2025] [Rahni and Jahangirian 2025] [Reddy and Subramanian 2025] [Sheeler et al 2025] [Song et al 2025] [Ayok 2026] [Wylie et al 2026] [Xu et al 2026] [Yuan 2026] [Zhang et al 2026] [Bohmier and Manoharan] [Van Dam et al] [Melton] [Schatz et al] [Hosseini et al] [Hosseini et al] [Hosseini et al] [Hosseini et al]
Controlling a vortex, including the forebody jets that flew first
Control by moving a vortex rather than a surface. Leading-edge, forebody, flap and tip vortices, including the forebody vortex control evaluated in flight.
32 records. [Bradley et al 1974] [Skow and Penke 1982] [Skow and Peake 1983] [Rao et al 1986] [Mourtos and Roberts 1987] [Visser et al 1988] [Ng 1989] [Rao et al 1989] [El-Hady 1990] [Malcolm and Ng 1990] [Malcolm et al 1990] [Ng 1990] [Rao 1991] [Bare et al 1992] [Kandil et al 1992] [Lemay et al 1992] [Magness et al 1992] [Suarez et al 1992] [Smith et al 1993] [Suarez et al 1993] [Suarez et al 1993] [Suarez et al 1993] [Alexander and Meyn 1994] [Kramer et al 1994] [Walchli 1994] [Moreira and Johari 1995] [Bowers 1996] [Johari and Moreira 1996] [Greenblatt 2005] [Bloxham et al 2008] [Erickson 2013] [Moralev et al 2016]
Where the air comes from, and what taking it costs
The air supply. Engine bleed, its extraction and its cost to the engine, and the pneumatic systems that distribute compressed air in an aircraft.
43 records. [Koutz et al 1950] [Wood and Dallenbach 1950] [Koutz 1951] [Vich 1952] [Gage 1958] [General Dynamics Corp Pomona Ca Pomona Div 1963] [Tagge 1983] [Wiemer 1985] [Zrubek 1985] [Curry and Gilyard 1989] [Yuhas and Ray 1992] [Yuhas and Ray 1992] [Collaboration on bleed air 2000] [Conan and Savarese 2001] [Guangjun Liu et al 2004] [Englar and Campbell 2005] [Guangjun Liu et al 2005] [Bleed air cooler 2008] [Shang et al 2010] [Bergeron et al 2013] [Guoliang et al 2016] [Xue et al 2016] [Pollok and Casella 2017] [Wang et al 2018] [Huff et al 2019] [Takahashi and Stone 2019] [Krishnan et al 2020] [Zheng et al 2021] [Singh Negi et al 2022] [Abdelghany et al 2023] [Aygun 2023] [Molenaar 2023] [Aygun 2024] [Irmayani et al 2024] [Ward et al 2024] [Aircraft Pneumatic Power Systems 2025] [Cavalcante et al 2025] [Schillaci et al 2025] [Sharma and Ranganayakulu 2025] [Jiang et al 2026] [Sharma and Ranganayakulu 2026] [Sharma et al 2026] [Engine Bleed Air Systems]
Reynolds number, and why a tunnel is not an aeroplane
Whether a tunnel result survives to flight. Reynolds-number and scale effects, the correlation of wind tunnel and flight, and the full-scale and subscale testbeds that bridge the two, with the flight-Reynolds report on separation control.
111 records. [Dearborn and Soule 1937] [Bauer and German 1961] [Barnes 1965] [Soderman and Aiken 1971] [Hicks et al 1972] [Garcia et al 1973] [Wilcox and Chamberlin 1974] [Capone 1975] [Wilcox and Chamberlin 1975] [Richey et al 1976] [Settles et al 1976] [Sussman et al 1976] [Kruse et al 1977] [Wind Tunnel/Flight Test Correlation 1978] [Daugherty 1979] [Stevens et al 1979] [Dougherty and Fisher 1980] [Peterson et al 1980] [Wilson et al 1980] [Ayers 1981] [Saltzman and Ayers 1981] [Ayers 1982] [Daforno 1982] [Fisher and Dougherty 1982] [Madsen 1982] [McKinney and Baals 1982] [Murman 1982] [Nagel 1982] [Niedling 1982] [Peterson 1982] [Anderson et al 1983] [Fisher and Dougherty 1983] [Wortman 1984] [Hahne et al 1987] [Ellzey and Berbee 1988] [Hahne and Jordan 1991] [Meyn et al 1992] [Bandyopadhyay and Gad-el-Hak 1994] [Williams et al 1994] [Lamont et al 1995] [Fisher et al 1998] [High Reynolds Number Hybrid 1999] [High Reynolds Number Hybrid 1999] [High Reynolds Number Hybrid 1999] [Iwatsuki et al 1999] [Flow at Large Reynolds 2000] [Ramsey and Chapman 2000] [Reynolds Number Effects 2000] [Seifert and Pack 2000] [Adrian and Balachandar 2001] [Luckring and Ghee 2001] [van Raalte and van Oudheusden 2001] [Curtin et al 2002] [Iwamoto et al 2002] [Song et al 2002] [Tomek et al 2002] [Brewer et al 2004] [Owens et al 2006] [Shaw et al 2006] [Wake et al 2006] [Jayaraman et al 2007] [Jordan and Bailey 2008] [Munson et al 2008] [Lee et al 2009] [Marusic et al 2009] [Taira and Colonius 2009] [Escauriaza and Sotiropoulos 2010] [Marusic et al 2010] [Thake et al 2010] [Miller 2011] [Pavlock 2011] [Brown 2013] [Cho and Shyy 2013] [Asada et al 2014] [Chin et al 2014] [Miller 2014] [El-Alti et al 2015] [Lind et al 2015] [Lu et al 2015] [Seifert et al 2015] [Ting et al 2015] [Lu et al 2016] [Mandal and Gu 2016] [Marks et al 2016] [Whalen et al 2016] [Zharfa et al 2016] [Essel and Tachie 2017] [Elahi et al 2018] [Malekzadeh et al 2018] [Whalen et al 2018] [Lin et al 2019] [McKenna et al 2019] [Warsop and Crowther 2019] [Yoon et al 2019] [Rao and Liu 2020] [Romano 2020] [Wang et al 2020] [Dougherty 2021] [Sarout et al 2022] [Yu et al 2022] [Elahi et al 2023] [Iyer and Malik 2023] [Ogunka et al 2023] [Laguarda et al 2024] [McFadden and Bons 2024] [Zanoun et al 2024] [Brown et al 2025] [Soldati et al 2025] [Zhu et al 2026] [Grager] [Langston et al]
Active flow control as a subject in its own right
The field as a field. Reviews, programmes and outlooks for active flow control, laminar flow control by suction, and the integration of flow control into aircraft, inlets and engines.
275 records. [Wheldon and Whites 1966] [Development of technology for 1976] [Sturgeon and Bennett 1976] [Sturgeon et al 1976] [Swinford 1976] [White et al 1976] [Bonner et al 1977] [Meade 1977] [Allison and Dagenhart 1978] [Evaluation of laminar flow 1978] [Gratzer and George-Falvy 1978] [Lovell et al 1978] [Sturgeon 1978] [Turriziani et al 1978] [Evaluation of laminar flow 1979] [Wright 1979] [Sturgeon 1980] [Wilson 1980] [Campbell 1982] [Harvey 1982] [Harvey and Pride 1982] [Pearce 1982] [Fischer et al 1983] [Pearce 1983] [Jasperson et al 1984] [Klotzsche et al 1984] [Lange 1984] [Lineberger 1984] [Lineberger 1984] [Pearce et al 1984] [Braslow and Fischer 1985] [Petley et al 1985] [Harvey et al 1986] [Maddalon and Poppen 1986] [Wagner 1986] [Allison and Dagenhart 1987] [Lange 1987] [Harris et al 1988] [Lange 1988] [Ash and Lakshmanan 1989] [Fischler et al 1989] [Hardin and Pope 1989] [Harris et al 1989] [Harvey et al 1989] [Huff 1989] [Powell et al 1989] [Maddalon and Braslow 1990] [Shepshelovich and Koss 1990] [Wagner et al 1990] [Anderson and Farokhi 1991] [Arcara et al 1991] [Fischer and Vemuru 1991] [Wie et al 1991] [Woan et al 1991] [Fischer 1992] [Gee et al 1992] [Harris et al 1992] [Krumenacker and Pellicano 1992] [Lanser and Meyn 1992] [Murman et al 1992] [Wie et al 1992] [Collier 1993] [Keith and Dewitt 1993] [Lanser and Meyn 1994] [Lo 1994] [Gimbert 1995] [Lo and Wiberg 1995] [Lo and Wiberg 1996] [Wygnanski and Wygnanski 1997] [Roth et al 1998] [Joslin 1998] [Pack and Joslin 1998] [Sheta et al 1998] [Anders and Fischer 1999] [Joslin et al 1999] [Marshall 1999] [Wygnanski et al 1999] [Frontiers of Flow Control 2000] [Ghee and Hall 2000] [Hamstra et al 2000] [Marshall 2000] [Abegg et al 2001] [Buning 2001] [Gorton 2001] [Kahng et al 2001] [McMichael 2001] [Joslin and Viken 2001] [Telionis 2001] [Vorobieff and Truman 2001] [Young and Fielding 2001] [Carpenter et al 2002] [Fung and Amitay 2002] [Israel et al 2002] [Lewington et al 2002] [Sellers et al 2002] [Washburn et al 2002] [Washburn et al 2002] [Bazyma and Rashkovan 2003] [Geiselhart et al 2003] [Telionis and Vlachos 2003] [Allan et al 2004] [Anders et al 2004] [Bower and Kibens 2004] [Fomin et al 2004] [Glezer 2004] [Gorton et al 2004] [Influences of Blowing Jet 2004] [Wong and Maina 2004] [Culley and Bright 2005] [Fleming et al 2005] [Kimmel et al 2005] [McMichael et al 2005] [Suzen et al 2005] [Allan Brian G. and Owens, Lewis, R. 2006] [Owens et al 2006] [Palaniswamy et al 2006] [Pilmoor et al 2006] [Sahu 2006] [Soria 2006] [Font and Morgan 2007] [Greenblatt and Washburn 2007] [Kiedaisch et al 2007] [Liu 2007] [Smith et al 2007] [Bower 2008] [Brzozowski et al 2008] [Fasel et al 2008] [Greenblatt and Washburn 2008] [Gross and Fasel 2008] [Kutay et al 2008] [Lazar et al 2008] [Liddle and Crowther 2008] [Melton et al 2008] [Owens et al 2008] [Potsdam and Le Pape 2008] [Rizzetta et al 2008] [Rumsey 2008] [Soria 2008] [Vepa 2008] [Vynogradskyy et al 2008] [Yeshala et al 2008] [Anderson et al 2009] [Flow Control Terminology 2009] [Liu et al 2009] [Ahmadi et al 2010] [Bauer et al 2010] [Grund and Nitsche 2010] [Jabbal et al 2010] [Kumar and Alvi 2010] [Owens and Allan 2010] [Schaeffler et al 2010] [Seifert et al 2010] [Siegel 2010] [Williams et al 2010] [Haucke and Nitsche 2011] [Li et al 2011] [Wilkinson 2011] [Hirt et al 2012] [King et al 2012] [Lipatov 2012] [Packard and Bons 2012] [Shea et al 2012] [Volino 2012] [Volino 2012] [Zaman et al 2012] [Dianics et al 2013] [King et al 2013] [Lenahan et al 2013] [Glezer 2014] [Greenblatt et al 2014] [Meyer et al 2014] [Narducci et al 2014] [Tucker et al 2014] [Tucker et al 2014] [Junxuan and Xun 2015] [Whalen et al 2015] [Alexander et al 2016] [Childs et al 2016] [Jentzsch et al 2016] [Lin et al 2016] [Lin et al 2016] [Tucker et al 2016] [Whalen 2016] [Bacic 2017] [Bieler 2017] [Bons 2017] [Bons 2017] [Cattafesta 2017] [Ciobaca and Wild 2017] [Eggert and Rumsey 2017] [Li et al 2017] [Lin et al 2017] [Samimy 2017] [Samimy 2017] [Sheng and Zhao 2017] [Shmilovich et al 2017] [Stalnov 2017] [Tadjfar and Asgari 2017] [Yang and Zha 2017] [Agate et al 2018] [Bishara et al 2018] [Burrows et al 2018] [He et al 2018] [Melton et al 2018] [Weingaertner et al 2018] [Andino et al 2019] [Li 2019] [Lin et al 2019] [Vatsa et al 2019] [Yang et al 2019] [Lin et al 2020] [Kamari et al 2020] [Passive Flow Control over 2020] [Tadjfar et al 2020] [Güler et al 2021] [Tebbiche and Boutoudj 2021] [Yoneda et al 2021] [Shmilovich et al 2022] [Shmilovich et al 2022] [Coletti and Faruque 2022] [Lin et al 2022] [Khalil et al 2022] [Vijgen et al 2022] [Woszidlo et al 2022] [Serrani 2022] [Truong et al 2022] [Vorozhbit et al 2022] [Xia et al 2022] [Zheng et al 2022] [Shmilovich et al 2023] [Shmilovich et al 2023] [Feldstein et al 2023] [Griffith and Faruque 2023] [Hosseinverdi and Fasel 2023] [Mallor et al 2023] [Anilir et al 2024] [Chua and Liu 2024] [Karpuk and Mosca 2024] [Active Flow Control 2025] [Chen et al 2025] [Frede and Gatti 2025] [Kalyankar et al 2025] [Mahns and Amitay 2025] [Wang and Yang 2025] [Yang et al 2025] [Zhijie et al 2025] [Ali et al 2026] [Ch et al 2026] [Tahir et al 2026] [Zhao et al 2026] [Aircraft laminar flow control] [Chandra et al] [Graff et al] [Nielsen and Jones] [McFadden and Bons] [Jones et al] [Wygnanski] [Paschal et al] [Paschal et al] [Melton et al] [Melton] [Melton et al] [Melton et al] [Melton et al] [Madhan et al] [Andino et al] [Andino et al] [Andino et al] [Vijgen et al] [Perrier] [Sarwar] [Hosseini et al] [Hosseini et al] [Shaw et al] [Vatsa et al]
Joined, tandem, diamond and tailless, and controlling them
The planform family. Joined, tandem and diamond wings, blended wing bodies, flying wings and tailless aircraft, with their aerodynamics, structures, stability and control.
350 records. [Weick and Sanders 1933] [Donlan 1944] [Maggin 1944] [Seacord and Campbell 1945] [Weyl 1945] [Soule 1946] [Sawyer and Trant 1947] [Hieser and Whitcomb 1948] [Cox et al 1949] [Johnson 1949] [Sawyer and Trant 1950] [Mathews and Kurbjun 1953] [Smith 1953] [Mitcham et al 1956] [Holdaway et al 1959] [White and Innis 1959] [Holdaway and Mellenthin 1960] [Holdaway and Mellenthin 1960] [Holdaway and Mellenthin 1960] [Harry and Trobaugh 1966] [Fox and Freeman 1971] [Polhamus 1971] [Donlan and Kuhn 1976] [Jernell 1978] [Jernell 1978] [Sears 1980] [Structural weight comparison of 1981] [Weil 1981] [Samuels 1982] [Clyde et al 1984] [Nicholas et al 1984] [Wolkovitch 1984] [Covell 1985] [Moitra 1985] [Perkins 1985] [Wolkovitch 1985] [Hajela and Chen 1986] [Selberg and Cronin 1986] [Wolkovitch 1986] [Smith et al 1987] [Van der Velden 1987] [Miura et al 1988] [Ashkenas and Klyde 1989] [Smith and Stonum 1989] [Vandervelden 1989] [Gallman et al 1990] [Gallman et al 1990] [Guruswamy 1991] [Kroo et al 1991] [Burkhalter et al 1992] [Gallman and Kroo 1992] [Morris 1992] [Fremaux et al 1993] [Gallman et al 1993] [NASA advanced design program 1993] [Simon et al 1993] [Huber and Schellenger 1994] [Qu and Cutchins 1994] [Huber 1995] [Ross et al 1995] [Bagwill and Selberg 1996] [Bosworth and Stoliker 1996] [Friehmelt 1996] [Gallman and Kroo 1996] [Mullins et al 1996] [Bagwill et al 1997] [Cameron and Cameron 1997] [Gillard et al 1997] [Paul et al 1997] [Potsdam et al 1997] [Sparks and Sparks 1997] [Tournes et al 1997] [Brinker and Wise 1998] [Buffington et al 1998] [Liebeck et al 1998] [Michal 1998] [Myatt et al 1998] [Protz and Sparks 1998] [Tigner et al 1998] [Wakayama 1998] [Barker and Balas 1999] [Boskovic and Mehra 1999] [Brinker and Wise 1999] [Eberhardt and Ward 1999] [Hauser 1999] [PI control of a 1999] [Shtessel et al 1999] [Teel 1999] [Teel 1999] [Tournes and Johnson 1999] [Wise et al 1999] [Brinker and Wise 2000] [Calise 2000] [Ghee and Taylor 2000] [Roman et al 2000] [Wakayama 2000] [Calise et al 2001] [Ghaffari et al 2002] [Ghaffari et al 2002] [Gilmore et al 2002] [Liebeck 2002] [Nangia and Palmer 2002] [Qin 2002] [Shtessel et al 2002] [Tyler et al 2002] [Vos et al 2002] [Wells and Hess 2002] [Carlsson 2003] [Liebeck 2003] [Marisarla et al 2003] [Nangia et al 2003] [Nangia et al 2003] [Patil 2003] [Roman et al 2003] [Sivaji et al 2003] [Smallwood et al 2003] [Hur et al 2004] [Pao et al 2004] [Rasmussen et al 2004] [Reich et al 2004] [Robinson 2004] [Blair et al 2005] [Campbell et al 2005] [Carlsson 2005] [Experimental research of the 2005] [Iniguez de Heredia and Friehmelt 2005] [Jung and Lowenberg 2005] [Kaloyanova et al 2005] [Nangia et al 2005] [Pao et al 2005] [Snyder et al 2005] [Boeing Phantom Works leading 2006] [Carter et al 2006] [Jackson and Buttrill 2006] [Kawai et al 2006] [Kimler and Canfield 2006] [Peigin and Epstein 2006] [Rasmussen et al 2006] [Saephan and van Dam 2006] [Bond et al 2007] [Ground testing of X-48B 2007] [Lee et al 2007] [Nieto-Wire and Sobel 2007] [Park 2007] [Pereira et al 2007] [Qin et al 2007] [Ravindren et al 2007] [Suleman 2007] [Wong et al 2007] [Blair et al 2008] [Boeing flies blended wing 2008] [Bond et al 2008] [Bond et al 2008] [Bond et al 2008] [Carter et al 2008] [Colgren and Loschke 2008] [LeDoux et al 2008] [Lee et al 2008] [Liebeck 2008] [Ma et al 2008] [Oligney et al 2008] [Recktenwald and Ahmed 2008] [Reichenbach 2008] [Trittler et al 2008] [X-48B blended wing body 2008] [Carter et al 2009] [Cuerno-Rejado et al 2009] [Di Palma et al 2009] [Ferrar et al 2009] [Kim et al 2009] [Mamla and Galinski 2009] [Nieto-Wire and Sobel 2009] [Roy 2009] [Sotoudeh and Hodges 2009] [Stenfelt and Ringertz 2009] [Vicroy 2009] [Wildschek et al 2009] [Yue et al 2009] [Bond et al 2010] [Buch and George M. 2010] [Chung et al 2010] [Goldthorpe et al 2010] [Paletta et al 2010] [Paranjape and Chung 2010] [Rahman and Whidborne 2010] [Richards et al 2010] [Roy and Ghosh 2010] [Roysdon and Khalid 2010] [Stenfelt and Ringertz 2010] [Velicki and Thrash 2010] [Westermayer et al 2010] [Zafirov 2010] [Heeg and Morelli 2011] [Jianghao et al 2011] [Nieto-Wire and Sobel 2011] [Paranjape et al 2011] [Peterson and Grant 2011] [Qu et al 2011] [Ratnayake et al 2011] [Roysdon and Khalid 2011] [Scott et al 2011] [Sotoudeh and Hodges 2011] [Vicroy 2011] [Ahn and Lee 2012] [Ali et al 2012] [Bond et al 2012] [Cusher and Gopalarathnam 2012] [Grauer et al 2012] [Meheut et al 2012] [Brodsky and Luby 2013] [Cardoso et al 2013] [Demourant and Ferreres 2013] [From Tube and Wing 2013] [Haniš et al 2013] [Kucera and Hromčík 2013] [Marques 2013] [Nasir and Kuntjoro 2013] [Nieto-Wire and Sobel 2013] [Paulus et al 2013] [Qu et al 2013] [Schirrer et al 2013] [Schirrer et al 2013] [Stroscher et al 2013] [Suresh et al 2013] [Vale J 2013] [Westermayer et al 2013] [Wildschek et al 2013] [Wildschek et al 2013] [Yue et al 2013] [Zha et al 2013] [Zhang et al 2013] [Zheng and Xu 2013] [Ammar and Trépanier 2014] [Gern et al 2014] [Jung Hoe and Nik Mohd 2014] [Pires et al 2014] [Reist and Zingg 2014] [Vale et al 2014] [Wildschek 2014] [Boelens et al 2015] [Coulson and Scott 2015] [Denieul et al 2015] [Lambert et al 2015] [Lemko and Molodchyk 2015] [Meckstroth and Blake 2015] [Modeling and Control for 2015] [Molinari et al 2015] [Nasir et al 2015] [Reist and Zingg 2015] [Saeed and Graham 2015] [Sotoudeh 2015] [Suleman et al 2015] [The aerodynamic and performance 2015] [The estimated available center 2015] [Yingsong et al 2015] [Johnston 2016] [Lambert et al 2016] [Park et al 2016] [Reist and Zingg 2016] [Singh et al 2016] [Teo et al 2016] [Torenbeek 2016] [Abnous et al 2017] [Ahn et al 2017] [Junlei et al 2017] [Kalinowski 2017] [Kalinowski 2017] [Kumar and Khalid 2017] [Park et al 2017] [Su et al 2017] [Brown and Vos 2018] [Buzica et al 2018] [Molinari et al 2018] [Qian and Alonso 2018] [Tan et al 2018] [Vladimir et al 2018] [Yang et al 2018] [Zhang et al 2018] [Chen et al 2019] [Dimopoulos et al 2019] [Nishanth et al 2019] [Wang et al 2019] [Humphreys-Jennings et al 2020] [Kitsios et al 2020] [Kumar et al 2020] [Parisa et al 2020] [Bainsla et al 2021] [Gao et al 2021] [Li et al 2021] [Liu and Whidborne 2021] [Qian and Alonso 2021] [Ruseno 2021] [Sherman et al 2021] [Contreras-Torres et al 2022] [DeLaurier 2022] [Fu et al 2022] [Meng et al 2022] [Miao et al 2022] [Okonkwo and Jemitola 2022] [Rossetti and Beblo 2022] [Wang et al 2022] [Yang et al 2022] [Zhao et al 2022] [Adler and Martins 2023] [Flow Field Investigation of 2023] [Jackson 2023] [Kryvokhatko 2023] [Kryvokhatko 2023] [Razon et al 2023] [Wang et al 2023] [Yu et al 2023] [Fernandes and Maldonado 2024] [He et al 2024] [Kryvokhatko 2024] [Kryvokhatko 2024] [Li 2024] [Sharma and Hosder 2024] [Ali et al 2025] [Antoniou et al 2025] [Anwar 2025] [Bhowmick et al 2025] [Guo et al 2025] [Gupta and Khalid 2025] [Hansmann and Stumpf 2025] [Jagtap et al 2025] [Kerr 2025] [Luu 2025] [Pandi and Kumar 2025] [Saifuddin et al 2025] [Xu and Yu 2025] [Xu et al 2025] [Bhattarai et al 2026] [Borodulin et al 2026] [Buddhamatya et al 2026] [Hansmann and Stumpf 2026] [Li et al 2026] [Pérez Segura et al 2026] [Sinha 2026] [Zhang and He 2026] [Zou et al 2026] [Aubeelack] [Guiler] [Izquierdo] [Muñoz] [Parello] [Scott] [Sgueglia] [Silva] [Sparks] [Teo]
The mechanical control system this aircraft proposes to delete
What the effectors would replace. Hydraulic, electrohydrostatic and electromechanical flight control actuation, hinge moments, and the effectiveness of the conventional surfaces a jet must match.
85 records. [Strass 1945] [Stone and Burk 1947] [Jones and Sluder 1948] [Kolbe and Tinling 1948] [Thompson 1954] [Wong 1957] [Fournier 1959] [Jenkins et al 1968] [Rinde 1969] [Edwards 1972] [Bergmann and Sevart 1973] [Tang and Pearson 1973] [Bergmann and Sevart 1975] [Chenoweth and Ryder 1976] [Demarchi and Haning 1978] [Feucht et al 1978] [Jenney 1979] [Jenney 1980] [Kohnhorst and Magnacca 1980] [Robinson 1980] [Kineyko 1982] [Belmont 1983] [Thompson and Eitenmiller 1983] [Design and test of 1984] [Hornyak 1984] [Jenney and Schreadley 1984] [Defeo and Chen 1987] [Hair 1987] [Vieten 1992] [Alden 1993] [Jategaonkar 1993] [Navarro 1997] [Appa et al 1998] [Churn et al 1998] [Oz 1998] [Atallah 1999] [Atallah 1999] [Cossar 1999] [Jensen et al 2000] [Wingett et al 2004] [Chen et al 2006] [Wei 2006] [Wingett et al 2006] [Celmins 2007] [Jayakumar and Das 2007] [Schallert 2007] [Laxminarayana et al 2011] [Curt and Norman 2011] [Cui et al 2015] [Garmendia et al 2015] [Shi et al 2015] [Fu et al 2016] [Gaile and Lue 2016] [Joshi et al 2016] [Li et al 2016] [Miller et al 2016] [Wang et al 2016] [Yu et al 2016] [Wang et al 2017] [Wang et al 2017] [Bo Yu et al 2018] [Xiaozhe Sun et al 2018] [Şener Kaya and Zeki Bilgin 2018] [Ijaz et al 2019] [Ijaz et al 2019] [Ijaz et al 2019] [Zhou et al 2019] [Sun et al 2020] [Ercan and Akın 2022] [Wang et al 2022] [Eid et al 2023] [He et al 2024] [Wang et al 2024] [Bao et al 2025] [Flight Control Actuation Systems 2025] [Sun et al 2025] [Aerospace - Flight Control] [Aircraft Flight Control Actuation] [Description of Actuation Systems] [Development Process - Aerospace] [Electrohydrostatic Actuator Applications on] [Flight Control Actuators] [Hisseine] [Historical Design Information of] [Primary Flight Control Hydraulic]
Identifying an aircraft from its own flight data
How the comparison inside one airframe is measured. System and parameter identification from flight data, flight-test technique and instrumentation, and the flight test of control laws.
185 records. [Symington 1940] [Rice 1946] [Pegg 1962] [Godwin et al 1964] [Nagel and Thomas 1965] [Flight Test Results Pertaining 1970] [Jones 1970] [Kisslinger and Vetsch 1971] [Mehra et al 1972] [Parrish and Steinmetz 1972] [Simpson 1972] [Steinmetz et al 1972] [Lyons et al 1973] [Wilcox 1973] [Wolowicz and Yancey 1973] [Air Force Flight Test Center Edwards Afb Ca 1974] [Heffley et al 1974] [Stepner and Mehra 1974] [Widnall and Grundy 1974] [Burton and Bischoff 1976] [Nicolaides 1976] [Armstrong 1977] [Jenks et al 1977] [Stein et al 1977] [Tomaine et al 1978] [Redd et al 1979] [Edwards 1981] [Hartmann and Stein 1981] [Miley et al 1981] [Petersen 1981] [Vincent and Franklin 1981] [Wells et al 1981] [Compton et al 1982] [Iliff and Maine 1982] [Edwards 1983] [Iliff and Maine 1983] [Rosenberg and Schuch 1983] [Stewart and Bauer 1983] [Toles and Anderson 1983] [Trankle and Rabin 1983] [Advisory Group for Aerospace Research and Development 1984] [Myers and Burcham 1984] [Anderson and Vincent 1985] [Deets and Brown 1986] [Sefic and Maxwell 1986] [Brown 1987] [Dowden and Bessette 1987] [Gilbert 1987] [Hicks et al 1987] [Meyer et al 1987] [Runyan et al 1987] [Mulder 1988] [Plaetschke and Weiss 1988] [Siddiqi and Abraham 1988] [Davis et al 1989] [Iliff 1989] [Maine et al 1990] [Shi Zhong-ke 1990] [Van Graas and Braasch 1991] [Vangraas and Braasch 1991] [Wierzbanowski and Armstrong 1991] [Manning et al 1992] [Morgenfeld 1992] [Powers et al 1992] [Van Graas and Braasch 1992] [Napolitano and Spagnuolo 1993] [Brennan and McDaniel 1994] [Canter and Groves 1994] [Kong 1994] [Maine et al 1994] [Maine et al 1995] [Morelli 1995] [Schkolnik et al 1995] [Tischler 1995] [Traven and Whitley 1995] [Batterson and Morelli 1996] [Fisher et al 1996] [Hamel and Jategaonkar 1996] [Morelli 1996] [Murphy 1996] [Morelli 1998] [Advisory Group for Aerospace Research and Development 1999] [Chen and Valasek 1999] [Mukhopadhyay 1999] [Mukhopadhyay 1999] [Murphy 1999] [Ghosh and Raisinghani 2000] [Ghosh et al 2000] [Moes et al 2000] [Saraswathi 2000] [Milne et al 2001] [Napolitano et al 2001] [Moes and Iliff 2002] [Morelli 2002] [Ray et al 2002] [Hageman et al 2003] [Longitudinal Control And Trim 2003] [Newsom et al 2003] [Smith et al 2003] [Static Longitudinal Stability Flight 2003] [Klyde et al 2004] [Mueller et al 2004] [Stachowiak and Bosworth 2004] [Williams-Hayes 2004] [Burken 2005] [Jategaonkar 2005] [Morelli et al 2005] [Chowdhary and Jategaonkar 2006] [Sarigul-Klijn and Huber 2006] [Dibley et al 2007] [Kukreja 2007] [Gangsaas et al 2008] [Kukreja 2008] [Kukreja 2008] [Marwaha et al 2008] [Murphy and Klein 2008] [Burken and Larson 2009] [DeBusk et al 2009] [Han et al 2009] [Shin et al 2009] [Taylor 2009] [Moua 2010] [Murphy and Klein 2010] [Bachelder et al 2011] [Cazes et al 2011] [Gregory et al 2011] [Gregory et al 2011] [Martos et al 2011] [McCracken and Jorris 2011] [Silva 2011] [Brown 2012] [Development of a Continuous 2012] [Giordano de Oliveira Silva and Moennich 2012] [Londono and Leonhardt 2012] [Taylor 2012] [Brown and Schaefer 2013] [Siu et al 2013] [Kuehme et al 2014] [Herrera et al 2015] [Sorokowski et al 2015] [Cumming et al 2016] [Deiler 2016] [Harris et al 2016] [Lichota et al 2016] [Pfifer and Danowsky 2016] [Kumar and Ghosh 2017] [Moszczynski and Grant 2017] [Saderla et al 2017] [Beh et al 2018] [Blight et al 2018] [Kumar and Ghosh 2018] [Morelli and Grauer 2018] [Tischler 2018] [Enciu 2019] [Larsson 2019] [Leung et al 2019] [Newton 2019] [Waite et al 2019] [Xu et al 2019] [Grauer and Boucher 2020] [Gao et al 2021] [Goel et al 2021] [Morelli 2021] [Simmons 2022] [Wang et al 2022] [Deepa and Gupta 2023] [Morelli and Grauer 2023] [Nguyen and Xiong 2023] [Patel et al 2023] [Raol and Singh 2023] [Simmons 2023] [Simmons et al 2023] [Matt 2024] [Roeser and Mönnich 2024] [Corrigan et al 2026] [Raab 2026] [Simmons] [Bouadi] [Miller] [Morelli] [Grauer] [Grauer and Boucher] [Grauer] [Waite et al] [Matt]
Demonstrators, research aircraft and the practice of flying one
The research aircraft before this one. Demonstrators and research aircraft from the augmentor-wing and quiet short-haul aircraft to the Active Aeroelastic Wing, the adaptive compliant trailing edge and the X-planes.
131 records. [Baker 1953] [Wright and Loving 1953] [Bellman 1959] [Beeler 1961] [General Electric Co Cincinnati Oh 1964] [Nicholson and lowry 1966] [Pittsburgh Univ Washington Dc Research Staff 1966] [Jackson and Patch 1968] [Kemper and Renselaer 1969] [Cleveland 1971] [Quigley et al 1971] [Rumsey and Spitzer 1971] [Ashleman and Kavdahl 1972] [Innis and Anderson 1972] [Quigley and Vomaske 1972] [Rumsey et al 1972] [Skavdahl and Patterson 1972] [Spitzer 1972] [Spitzer et al 1972] [Bartlett et al 1973] [Whittley 1973] [Amberg et al 1974] [Marrs et al 1974] [Quigley and Holzhauser 1974] [Jacobsen and Drinkwater 1975] [Cook and Whittley 1976] [Richardson 1976] [Sim 1976] [Dehoff et al 1977] [Alexander 1979] [Martin 1979] [McCracken 1979] [Shovlin et al 1979] [Andrews 1980] [Feinreich and Gevaert 1980] [Green 1980] [Martin 1980] [McArdle et al 1980] [Cook and Lilley 1981] [Dunn et al 1981] [Eppel 1981] [Riddle et al 1981] [Queen and Cochrane 1982] [Cochrane 1983] [Gilyard and Edwards 1983] [Painter 1983] [Curry and Sim 1984] [Sim and Curry 1984] [Sim and Curry 1985] [Larson 1986] [Sefic and Cutler 1986] [Redeker and Voersmann 1988] [Riddle et al 1988] [Smith and Nelson 1988] [Webb et al 1988] [Bonnema and Lokos 1989] [Wada 1989] [Stephenson et al 1990] [Urnes et al 1990] [Aswani et al 1991] [Urnes and Yeager 1991] [Vincent 1991] [Dicarlo et al 1992] [American Institute of Aeronautics and Astronautics 1993] [Stortz and ODonoghue 1995] [Sim 1997] [Walker 1997] [Lind 1999] [Lind 1999] [Kota 2000] [Clark 2001] [Lokos et al 2002] [Lokos et al 2002] [Brenner and Prazenica 2003] [Lee and Song 2003] [Turner 2003] [Hess and Flick 2004] [King and Gopalarathnam 2004] [Kumar and Rao 2004] [Ueno et al 2004] [Waszak et al 2004] [Allen et al 2005] [Clarke et al 2005] [Cumming and Diebler 2005] [Dibley et al 2005] [Heeg et al 2005] [Lizotte and Allen 2005] [Lizotte and Lokos 2005] [Lokos et al 2005] [Wiesman et al 2005] [Heeg 2006] [Cosentino 2007] [Lizotte and Allen 2007] [Voracek 2007] [Cosentino 2008] [Skillen and Crossley 2008] [Gandhi et al 2009] [Di Matteo and Guo 2011] [Yu 2013] [Gardner et al 2014] [Miller et al 2014] [Ryan et al 2014] [Davis et al 2015] [Miller et al 2015] [Cruz and Miller 2016] [Denham and Owens 2016] [Engblom et al 2016] [Herrera et al 2016] [Herrera et al 2016] [Jo et al 2016] [Sato et al 2016] [Smith et al 2016] [Öznalbant et al 2016] [Lechniak and Melton 2017] [Vetrella et al 2017] [Yamamoto et al 2017] [Herrera 2018] [Hirshorn and Kemmerly 2018] [Kaygan and Ulusoy 2018] [Thomas et al 2018] [Xiang et al 2018] [Garcia et al 2019] [Dippold 2022] [Bhowmick et al 2023] [German et al] [Hu] [Quindlen et al] [Heaney] [Heaney and Quindlen] [Arteaga et al] [Standard Practice for Development]
Jets in a crossflow
What an effector issues into the boundary layer. The jet in a crossflow, its vortex structure, trajectory, induced pressures and its computation.
81 records. [Girshovich 1968] [Mosher 1970] [Chang and Werner 1972] [Kamotani and Greber 1972] [Dietz 1975] [Fearn and Weston 1975] [Fearn and Weston 1978] [Yen 1978] [Fearn and Benson 1979] [Murphy et al 1979] [Hackett et al 1981] [Perkins and Mendenhall 1981] [Baker and Orzechowski 1982] [Clauss 1982] [Furlong and Fearn 1983] [Snyder and Orloff 1984] [Wilsden and Hackett 1984] [Simon and Ciancone 1985] [Simon and Ciancone 1987] [Fearn 1988] [Roth 1988] [Bray and Knowles 1989] [Kavsaoglu and Schetz 1989] [Roth et al 1989] [Claus and Vanka 1990] [Krothapalli et al 1990] [Lytle et al 1990] [Kim and Benson 1991] [Claus and Vanka 1992] [Kim and Benson 1992] [Roth et al 1992] [Blake and Stewart 1993] [Chiu et al 1993] [Dennis et al 1993] [Dennis 1993] [Krothapalli and Shih 1993] [Margason and Tso 1993] [Manipulation of a jet 1994] [Liscinsky et al 1995] [Tso and Margason 1995] [Bain et al 1996] [Tso and Margason 1996] [Yuan and Street 1996] [Eroglu and Breidenthal 1998] [He 1999] [Wilson et al 2000] [Xie et al 2000] [Pandya et al 2002] [Kiel et al 2003] [Zaman 2003] [Zaman 2003] [Marzouk and Ghoniem 2004] [Bunyajitradulya and Sathapornnanon 2005] [Dano and Liburdy 2005] [Ziefle and Kleiser 2006] [Atkins 2007] [Ivanova et al 2010] [Zaman et al 2010] [Zaman et al 2010] [Zaman et al 2011] [Arunajatesan and McWherter-Payne 2013] [Lefantzi et al 2013] [Karagozian 2014] [Zhang and Yang 2017] [Zhang and Yang 2017] [Borghi et al 2018] [Dai et al 2018] [Chang et al 2019] [Stegmeier et al 2019] [Zhao et al 2021] [Lv et al 2022] [Smith and Yagle 2023] [Gupta and Saha 2024] [Wake vortex formation and 2024] [Borodulin et al 2025] [Distributed Surface-Vortex Receptivity of 2025] [Dhanagopal et al 2026] [Bouladoux] [Li] [Oertling] [Sakradse]
Wall jets and curved wall jets
The flow a Coanda effector produces. Plane, three-dimensional and curved wall jets, their turbulence, roughness and pressure-gradient effects.
69 records. [Wygnanski and Champagne 1968] [Bajura and Szewczyk 1970] [Bangert 1971] [Kind 1971] [Piva 1972] [Narasimha et al 1973] [McLean and Herring 1974] [McLean and Herring 1974] [Campbell 1975] [Tsuji et al 1976] [Alcaraz et al 1977] [Catalano et al 1977] [Catalano et al 1978] [Catalano et al 1978] [Kotansky and Glaze 1978] [Morton et al 1978] [Catalano et al 1979] [Catalano et al 1979] [Catalano et al 1979] [Horne and Karamcheti 1979] [Saripalli and Simpson 1979] [Kotansky and Glaze 1980] [Maki et al 1980] [Saripalli and Simpson 1980] [Kotansky and Glaze 1981] [Back and Cuffel 1982] [Gibson and Younis 1982] [Hartmann 1982] [Wall interference effects on 1983] [Horne 1984] [Roberts 1986] [Roberts 1987] [Rodman et al 1987] [Rodman et al 1987] [Rodman et al 1989] [Rask et al 1990] [Gregory-Smith and Hawkins 1991] [Lim and Roberts 1991] [Park and Rew 1991] [Park and Rew 1992] [Yoon et al 1993] [Myszko and Knowles 1994] [Matsson 1995] [Le Cunff and Zebib 1996] [Rew and Park 1996] [Fasel 2000] [Likhachev et al 2001] [Tachie et al 2001] [Hossain and Kader 2004] [Imao et al 2005] [Inoue et al 2005] [Mochizuki et al 2005] [Han et al 2006] [Afzal and Seena 2011] [Kumar and Das 2011] [Rostamy et al 2011] [Pramanik and Das 2014] [Pramanik and Das 2014] [Pramanik and Kumar Das 2014] [Kumar 2015] [Tesař 2015] [Khayat 2017] [van Hout et al 2018] [Weidman 2018] [Baleriola et al 2019] [Hatakawa et al 2019] [Pease et al 2021] [McBreen and Zha 2024] [Pajayakrit]
Shear layers, receptivity and periodic excitation
The mechanism oscillatory control exploits. Free and separated shear layers and boundary layers forced by periodic excitation, and their receptivity.
30 records. [Leehey and Shapiro 1980] [Bechert and Stahl 1984] [Bayliss et al 1985] [Fiedler and Mensing 1985] [Bayliss et al 1986] [Lam and Ko 1986] [Lam et al 1986] [Balsa 1988] [Balsa 1989] [Lumley 1989] [Kraus and Cutler 1993] [Strykowski and Krothapalli 1993] [Joslin et al 1994] [Manuilovich 1995] [Pack and Seifert 1999] [Semionov and Kosinov 2000] [Adelgren et al 2002] [Billeter 2004] [Kozato and Imao 2005] [Mittal 2005] [Mittal 2006] [Mittal 2007] [Yehoshua and Seifert 2007] [Samimy et al 2018] [Borodulin et al 2020] [Singbeil et al 2021] [Elsner et al 2024] [Nakano and Ohtsuki 2024] [Sokolenko et al 2024] [Kitzinger]
This programme and the programme it descends from
The titles that name CRANE or the work it descends from. No cited title names this aircraft or this contractor, and the homonym measurements under The Source Base show why the programme’s own name finds so little.
2 records. [Tallent and Koss 2004] [Vukasinovic et al 2023]
The medium, admitted by the shared atmosphere family alone
The atmosphere every number here is computed in. The standard atmosphere tables of a flight-test manual.
1 record. [Air Force Test Pilot School Edwards Afb Ca 1962]
Where the Framing Breaks Down
The Century-Old Paradigm Is Younger Than It Sounds for One Axis
DARPA’s release opens by observing that in December 1903 the Wright brothers flew the world’s first fully controllable aircraft using wing warping, that virtually every aircraft since has used a system of movable external control surfaces, and that the X-65 breaks this century-old design paradigm [DARPA moves forward on the X-65].
The framing is half right, and the wrong half is more interesting than pedantic. The 1903 aircraft was essentially a larger version of the 1902 glider, whose key control refinement was a movable vertical tail, and it carried a forward-mounted horizontal surface for climb and descent [1903 Wright Flyer]. The Flyer therefore used movable external surfaces for pitch and for yaw from the first flight. For roll it did not. It twisted the wing.
Wing warping is not a movable control surface. It is a morphing wing, and the mechanism DARPA credits the Wrights with is the one axis where the original solution was not the paradigm being broken. The paradigm is therefore 122 years old on this article’s dateline for two axes and rather younger for the third, and the X-65 carries traditional flaps and rudders among its conventional surfaces [DARPA moves forward on the X-65], so the aircraft does not break the paradigm on the axis the framing invokes.
The Amplification Curve Is Doing a Great Deal of Work
The article’s central arithmetic depends on a quantity it does not derive. The amplification is treated as a parameter swept from ten to a hundred, and the low-speed separation-control experiments the review summarises imply values at and above the top of that band [Abdolahipour 2024], so no attempt is made to predict it for this aircraft’s geometry.
The treatment is candid, yet the amplification remains the weakest link. The amplification depends on the pressure gradient, the boundary-layer state, the Reynolds number, the effector geometry, its position relative to the separation line and the excitation frequency. None of those is public for the X-65A and several are what the aircraft is meant to measure. So the authority ratios in this article are conditional statements of the form that if the amplification is thirty then the deficit at Mach 0.7 is the 43.3 percent displayed in the section on the authority ratio, and they are not predictions.
Reynolds Number Is Not the Problem
This aircraft’s Reynolds number is one to nearly three orders of magnitude above those of the experiments whose thresholds this article borrows, and that gap does not make the phenomenon doubtful at flight scale.
The Reynolds number on a chord is the ratio of inertial to viscous forces. Let $\mathrm{Re}$ be that number, dimensionless, and $\mu$ the dynamic viscosity in pascal second, which for air follows Sutherland’s law with constants $C_1$ in kilogram per metre second per root kelvin and $S_\mu$ in kelvin.
\[\mathrm{Re} = \frac{\rho V \bar{c}}{\mu}, \qquad \mu\left( T \right) = \frac{C_1 \, T^{3/2}}{T + S_\mu}\]with $C_1$ of $1.458 \times 10^{-6}$ and $S_\mu$ of 110.4 kelvin. That returns 1.7894 times ten to the minus five pascal second at sea level. At Mach 0.7 and thirty thousand feet on a chord of 1.750 metre the X-65A flies at 11.44 million.
Active separation control by oscillatory excitation was demonstrated above that Reynolds number in the year 2000. Seifert and Pack tested the method at chord Reynolds numbers as high as forty million and state in their summary that it was proved successful in delaying boundary layer separation and reattaching separated flows at chord Reynolds numbers of order ten million [Seifert and Pack 2000]. Their baseline flow was made fully turbulent deliberately, to remove transition as a variable, and they report that the Reynolds number has a very weak effect on the model pressure distributions and spectra regardless of Mach number or sweep.
The Reynolds numbers in the first column are those the review reports for each study [Abdolahipour 2024].
| Study | Reynolds number | The X-65A in flight over it |
|---|---|---|
| Munday and Taira 2018 | 2.30 times ten to the 4 | 497.6 |
| Feero et al. 2015 | 1.00 times ten to the 5 | 114.4 |
| Seifert et al. 1996, low | 1.50 times ten to the 5 | 76.3 |
| Jones and Englar 2003 | 5.00 times ten to the 5 | 22.9 |
| Seifert et al. 1996, high | 6.00 times ten to the 5 | 19.1 |
The X-65A flies at 0.715 times that experiment’s sixteen million and 0.286 times the forty million it quotes. [Seifert and Pack 2000] It is inside the demonstrated range, not beyond it. So the claim to make is the narrow one. The threshold values borrowed above do come from experiments at a hundred thousand and twenty-three thousand, and transferring a threshold is a different matter from transferring a phenomenon. But the phenomenon is not in doubt at this aircraft’s Reynolds number.
The Better News in the Flight-Reynolds Primary
The same report quotes the oscillatory momentum coefficients it used, and its nomenclature defines the coefficient as the jet momentum over chord times dynamic pressure, the same definition this article uses. [Seifert and Pack 2000]
| Case the report quotes | Oscillatory momentum coefficient | This article’s figure over it | Concentration still needed |
|---|---|---|---|
| lowest quoted, Mach 0.25 | 0.03 percent | 3.150 | none |
| slot at 64 percent chord, Reynolds 16 million | 0.09 percent | 1.050 | none |
| reduced frequency 1.0 | 0.12 percent | 0.788 | 1.27 |
| wall pressures, Reynolds 16 million, Mach 0.25 | 0.13 percent | 0.727 | 1.38 |
| reduced frequency 0.5 | 0.32 percent | 0.295 | 3.39 |
The wing-referenced coefficient this article computes, 0.0945 percent, sits inside the range that report used, 0.03 to 0.32 percent. It reaches two of the five quoted cases with no concentration at all, and the largest needs a factor of 3.39. The report states its own uncertainty on that coefficient as plus or minus 25 percent of the quoted values [Seifert and Pack 2000], a primary-sourced error bar and not an assumption of this analysis. The third column is the computed coefficient over the quoted one and the fourth is its reciprocal where that exceeds one, so at the two ends of the range
\[\frac{0.0945}{0.03} = 3.150 , \qquad \frac{0.32}{0.0945} = 3.39 .\]At that report’s Mach number of 0.25 the bleed budget delivers 0.5579 percent, 1.74 times its highest quoted value. So the air budget is not marginal at the condition where the method was demonstrated. It is marginal only where this aircraft wants to fly, and the factor of 5.903 between the two is the Mach dependence derived above and nothing else.
\[C_\mu\left( 0.25 \right) = 0.000945066 \times \frac{G\left( 0.25 \right)}{G\left( 0.7 \right)} = 0.000945066 \times \frac{16.711}{2.8308} = 0.005579 , \qquad \frac{0.5579}{0.32} = 1.74\]And the Primary Names This Article’s Keystone as the Open Problem
The report’s proposals for future work include overcoming the lack of sufficient control authority, especially at high speeds [Seifert and Pack 2000].
The report thus names as unsolved, twenty-five years before the X-65A was due to fly, the finding this article derived. The authority ratio falls as the square of the Mach number because the engine delivers a roughly fixed momentum while the aerodynamic forces to be overcome grow with the square of the speed. A primary that tested the method at this aircraft’s Reynolds number, at a third of its Mach number, and concluded that high-speed control authority was the thing still to be found, is the strongest available independent support for the conclusion.
It is also a caution about novelty. The Mach dependence and its exact minimum are derived here, and the observation that high-speed authority is the binding constraint was in the literature first, in the report above.
The Bleed Penalty Is Asserted Rather Than Derived
Taking air from a compressor costs thrust and this article bounds the cost from below without computing it. The mass-flow accounting and the lower bound it gives are exact and are derived in the engine discussion. The thrust consequence is not exact, because it depends on the turbine work no longer available to drive the fan, on the cycle’s rematching, and on the control schedule the engine’s digital controller applies. The single-stage centrifugal architecture makes the answer worse than a multi-stage axial’s would be, because the bled air has had the whole compression done to it, and that much follows from the architecture the NASA report describes [FJ44 turbofan engine test].
Suction Is in the Official Definition and Not in This Analysis
The budget justification defines active flow control as control mechanisms which alter the aerodynamic flow field through ejection or suction of fluid via an orifice on a lifting body [DARPA RDT&E justification, PB2026]. The phrase includes suction, while every step of the momentum accounting assumes blowing.
A suction device removes low-momentum air where a blowing device adds high-momentum air, and its figure of merit is a flow coefficient rather than a momentum coefficient. The identity that makes the amplification exact does not hold for it, because there is no jet momentum in the denominator. The published descriptions speak only of jets of air from a pressurized source [DARPA moves forward on the X-65], which is blowing, and none of them mentions suction, so a system that also used suction would need both accountings. This article’s analysis applies to the blowing case alone.
One Vehicle Still Cannot Do Everything
The differencing argument above is strong, but it has a limit. Locking a conventional surface and commanding an effector instead changes the aircraft’s aerodynamics in ways beyond the intended substitution. A locked surface is still a surface, sitting in a position, with its gaps and its hinge line, present even when unused. An aircraft designed without conventional surfaces would have a different shape, lower weight and no gaps.
The X-65A consequently measures the authority of flow control on an airframe built to accommodate both systems, which is not the same as the authority of flow control on an airframe built for flow control alone. The programme’s framing acknowledges this by calling the conventional surfaces training wheels [DARPA moves forward on the X-65], and the fair reading is that the aircraft measures a lower bound on what a purpose-built vehicle would achieve and an upper bound on the weight saving.
The Source Base
The research survey holds 3,301 research records drawn from the NASA Technical Reports Server, the Defense Technical Information Center and Crossref, the bibliographic index of journal and conference records, of which 1,351 are report primaries, being 40.9 percent, by the identifier rule set out under The Definition of Primary. 3,193 records carry a usable year, running from 1927 to 2027 with a median of 2006. 1,139 of those, 35.7 percent, predate the year 2000, and 956, or 29.9 percent, are 2015 or later.
The heaviest decade is the 2010s, with 854 records, 26.7 percent of the dated set. The 1970s hold 342 records against 63 in the 1960s, and 219 of those 342 are in the cluster on blowing, the Coanda surface and the jet flap, which is the arrival of the circulation-control and powered-lift literature this subject keeps returning to.
| Decade | Records | Share of the dated set |
|---|---|---|
| 1920s | 2 | 0.1 percent |
| 1930s | 3 | 0.1 percent |
| 1940s | 29 | 0.9 percent |
| 1950s | 66 | 2.1 percent |
| 1960s | 63 | 2.0 percent |
| 1970s | 342 | 10.7 percent |
| 1980s | 304 | 9.5 percent |
| 1990s | 330 | 10.3 percent |
| 2000s | 711 | 22.3 percent |
| 2010s | 854 | 26.7 percent |
| 2020s | 489 | 15.3 percent |
What the Reports Server Holds
The reports server holds nothing at all for four phrases, and a null answer from a registry is a measurement. They are hingeless aerodynamic control effector, technology demonstrator aircraft programme, Coanda effect jet attachment and mixing enhancement jet actuator. The first of those is the finding and it is treated separately below.
The Homonyms in This Subject’s Vocabulary
This subject’s vocabulary collides widely with other fields. Up to ten results from the bibliographic index were read for each probe and counted by hand.
| Probe | Results read | On subject | What the rest were |
|---|---|---|---|
CRANE |
6 | 0 | a logging-crane fatality, a mobile-gantry-crane fatality, a civil-engineering journal, CRANE-tools.org, an 1878 book of rhymes and tunes, and Walter Crane’s 1886 A romance of the three Rs |
novel effectors |
10 | 1 | fungal, oomycete and oncological effectors, the one exception being a 2026 paper on hypersonics and directed energy |
effectors |
9 | 1 | TAL effectors, rust effectors, smut fungi and the effectors of plant-defence suppression |
end effector |
10 | 0 | industrial robot wrists and upper-limb kinematics |
actuator |
10 | 0 | road-vehicle air-brake actuator test procedures, eight of the ten |
momentum coefficient |
10 | 1 | tangential momentum accommodation in microchannels, angular momentum coupling, momentum exchange in rarefied flow, and an evolutionary optimiser with a momentum and adaptive decay coefficient, twice |
blowing coefficient |
10 | 0 | elliptic equations with a blowing-up coefficient, plus Blue-blowing and BLOWING ROCK LANDMARKS |
control authority |
10 | 0 | bibliographic authority control, at the National Archives and in Italy |
control effectiveness |
10 | 0 | internal-control auditing and diamondback-moth pest management |
separation control |
10 | 1 | chemical separation processes, dust and pollution control |
fluidic oscillator |
10 | 2 | an antisolvent crystalliser and the American Water Works Association standard for cold-water meters, in two editions |
supercirculation |
8 | 3 | the climate supercirculation of the Earth |
Aurora Flight Sciences |
10 | 2 | Mercury-Atlas 7, a damselfly, a Brazilian philosophy journal and a casket company |
X-65 |
10 | 0 | front matter and acknowledgements |
active flow control |
10 | 10 | nothing off subject |
sweeping jet actuator |
10 | 10 | nothing off subject |
hingeless control |
10 | 7 | a dictionary entry for the word and two papers on hingeless rotors, and 72 records on the reports server, 61 of them with rotorcraft vocabulary in the title |
Three of those rows matter to anyone searching this subject. The programme’s acronym finds nothing aeronautical. The word effector without qualification finds mostly biology. And the article’s own keystone parameter is almost absent from titles, as Thin Subjects below sets out.
A Homonym That Depends on Which Registry You Ask
hingeless control returned ten results from the bibliographic index, of which seven concern control without a hinge, and 72 from the reports server of which 61 carry rotorcraft vocabulary in the title. Six of the seven are flow-control effectors on wings and the seventh is the hingeless flight control of a smart projectile by miniature actuators. The other three are a dictionary entry for the word itself and two papers on hingeless rotors, one on a circulation-control rotor blade and one on higher harmonic control, so the rotor meaning reaches even the journal index.
Eleven do not carry rotorcraft vocabulary, and most of those are rotorcraft work under other words, being higher harmonic control, flap-lag stability in forward flight, ground resonance and a V and short take-off conference. Two are not rotorcraft at all. They are the DARPA, Air Force Research Laboratory, NASA and Northrop Grumman Smart Wing programme, which shares the hingeless vocabulary because it is about a wing with no discrete moving surface and is genuinely adjacent prior art.
A hingeless rotor is a blade retention without flap and lag hinges, which is a structural subject with a large literature from the 1960s and 1970s. A hingeless control effector is an aerodynamic surface replaced by a jet. The same two words name two unrelated subjects and which one you get depends on which registry you ask.
The survey therefore excludes rotorcraft, as the section on what is out of scope records. The phrase that finds this subject differs by registry, being hingeless control in the journal literature and control effectors in the reports, and the second returns the aerodynamic control effectors, the passive porosity effectors and the active flow effectors.
Which Thresholds Are Second-Hand, and Which Originals Can Be Read
Most of the thresholds this article uses reach it through one review. The regime boundary of three to five percent, the reduced-frequency band, the measured response at 0.08 percent, the reattachment at 0.34 percent, the modified-coefficient thresholds, the velocity-ratio condition, the caution against comparing momentum coefficients across configurations and the attribution of the definition to Poisson-Quinton are taken from the review rather than from the works that established them.
The review’s bibliography names the originals. They are Greenblatt and Wygnanski 2000 and Wygnanski 2000 for the regime boundary, the frequency band and the velocity-ratio condition, Seifert and others 1996 for the response at 0.08 percent, Feero and others 2015 for the reattachment at 0.34 percent, Munday and Taira 2018 for the modified-coefficient thresholds, and Joslin and Miller 2009 for the attribution to Poisson-Quinton, while the caution against comparing coefficients across configurations is the review’s own [Abdolahipour 2024]. Every journal item the review names is behind a paywall, so a first-hand reading is available only where the work was also published as a report, and four agency reports on separation control are read in full instead. That asymmetry favours the report literature wherever a first-hand reading matters.
The most consequential of the four is the report on separation control at flight Reynolds numbers [Seifert and Pack 2000], whose bearing on the Reynolds-number argument, and whose naming of high-speed control authority as an open problem, are set out in the section headed Where the Framing Breaks Down.
The Same Work Twice, Once With a File and Once Without
The reports server holds the flight-Reynolds report of Seifert and Pack under two identifiers and only one of them carries the document. A search returns both. The first has a record and no attachment, so a request for its full text returns nothing at all, and the second carries the portable document and a plain-text rendering of it. A null answer from a registry is usually a measurement about the literature. This one is a measurement about the catalogue, and only the catalogue’s detail record shows which identifier has a file.
What This Article Read in Full
Read in full. The register’s addendum, the encyclopedia entry, the DARPA programme page, the DARPA news release of 3 January 2024, the contractor’s aircraft page, the Defense News report of 20 November 2025, the Smithsonian collection record for the 1903 Flyer, the NASA technical memorandum on the FJ44-3A, the open-access review of flow separation control, the CRANE entries in all seven DARPA justification books from the request for fiscal year 2020 to the request for fiscal year 2026, and four agency reports on separation control, being the flight-Reynolds-number lessons-learned report, the flap-separation report, the slat-shoulder report and the amplitude-scaling workshop paper.
Read to the abstract only, and quoted for nothing inside it. Reddy and Woszidlo 2024, which is closed access, held by no repository, and whose two scaling parameters both registries render as a placeholder [Reddy and Woszidlo 2024].
Held at registry-record strength and quoted for nothing. Five are named by the review, being Seifert and others 1996 in the Journal of Aircraft, Munday and Taira 2018 in the AIAA Journal, Feero and others 2015 in the AIAA Journal [Feero et al 2015] and 2017 in Experiments in Fluids, and the flow-control terminology chapter of the 2009 AIAA volume. Two more are the MAFC lessons-learned paper of 2004 and Wygnanski’s 1997 conference paper on the periodic addition of momentum. Seven paywalled items whose existence, venue and year are confirmed and whose contents are not. Where this article states a number those works established, it states it on the review’s authority and says so.
The reattachment threshold belongs to the 2015 paper and not to the 2017 one. The review attributes the reattachment at 0.34 percent to Feero and others in 2015, and its bibliography identifies that work as a 2015 AIAA Journal paper on flow reattachment by synthetic jet actuation on a low-Reynolds-number airfoil, distinct from the same group’s 2017 paper on synthetic jet location, which the review cites separately [Abdolahipour 2024].
Read by title only. The other research records, which are cited as a body of literature in the clusters above and not quoted.
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 its address is on the NASA Technical Reports Server or it carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. The four agency reports on separation control that this article reads in full are report primaries under that rule. The rule does not reach the journal literature, such as the papers the review names behind paywalls, so 40.9 percent is a lower bound on how much of the survey is first-hand.
Thin Subjects
Six 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. Where a row joins two groups of terms with the word together, a title must carry a term from each group.
| Subject | Title terms counted | Records |
|---|---|---|
| the momentum coefficient named as a parameter | momentum coefficient, momentum coefficients, blowing coefficient, blowing coefficients | 10 |
| the effect of altitude on what an effector delivers | altitude, altitudes together with flow control, actuator, actuators, actuation, blowing, bleed, momentum | 0 |
| the effect of Mach number on active flow control | Mach, compressibility, compressible, transonic together with active flow control, synthetic jet, synthetic jets, sweeping jet, sweeping jets, fluidic oscillator, fluidic oscillators, separation control, pulsed jets | 11 |
| what engine bleed costs in thrust | bleed, power extraction together with thrust, turbojet, turbofan, engine performance, aircraft performance | 9 |
| the joined diamond planform | diamond together with joined | 3 |
| the programme this aircraft descends from | micro adaptive flow control, microadaptive, MAFC | 2 |
The keystone parameter is almost never in a title, and that is not a thin literature. Ten of the 3,301 cited research titles name the momentum coefficient or the blowing coefficient. The cluster for the parameter holds 13 records, eight of which name it, and the rest are titles on blowing parameters and actuation efficiency. Every paper in active flow control uses the momentum coefficient, and the review this article leans on devotes a numbered section to it [Abdolahipour 2024]. The parameter is a method rather than a subject, so it appears in equations and in axis labels and not in titles. The literature is healthy and the quantity is invisible to a title search.
No cited title asks how altitude changes what a flow-control effector delivers, which is the question this article’s central result answers. The nearest is a 2024 paper whose title asks it of operating conditions in general [Reddy and Woszidlo 2024], and the abstract is all of it that can be read.
The Mach dependence that this article finds binding has a literature of 11 titles, of which two name an airfoil and three name separation control, and none names a control effector’s authority or a control moment. Of the seven that name neither, five characterise actuators in compressible flow or apply them to a transonic compressor, and the others are a test facility and a weapon release.
What a bleed costs an engine is known for few engines. Nine cited titles join bleed or power extraction to thrust, to a turbojet or turbofan, or to engine or aircraft performance. Two of them are NASA records of 1992 on the effect of bleed extraction on the thrust of the F404 [Yuhas and Ray 1992] [Yuhas and Ray 1992], and one asks the same question of a commercial engine on an unmanned aircraft [Takahashi and Stone 2019]. None names the FJ44. Asking the reports server for a secondary air system returns two hundred and seven records and they are the proceedings of a seal workshop, because inside a turbine engine secondary air means internal cooling. Asking it for an aircraft air supply system returns electric-propulsion impedance measurements and direct-current power supplies. Asking the defence registry what bleed air costs in engine performance returns two hundred records, of which three concern this article’s subject and none of those three is about bleed air.
The joined diamond planform has three titles of its own, all of them design and aerodynamic studies, and none is about controlling it. The planform’s control is reached instead through the far larger literatures on joined wings and on tailless aircraft.
The CRANE manager named Micro Adaptive Flow Control as the work CRANE descends from, and neither registry holds a report under that name. The reports server returns, for that phrase, two summer faculty fellowship programmes from 1995, a Spacelab life-sciences experiment and a paper on the importance of properties in modelling. The defence registry returns one hundred and twenty-one records, of which two come near this subject and both are about adaptive structures rather than adaptive flow control. The only trace of the programme under its own name is a single conference paper, behind a paywall, whose title is its lessons learned [Tallent and Koss 2004]. Written as one word, the technique’s name finds one defence report, an Army Research Laboratory study of microadaptive flow control applied to a spinning projectile [McMichael et al 2005], whose title names the technique rather than the programme. A DARPA programme leaves no report literature in a NASA registry because it was never a NASA programme, and the defence registry holds what its contractors delivered rather than what the agency learned. The ancestor of an aircraft is harder to find than the aircraft.
What the Survey Admits
A record is admitted only when a person reading its title finds it on this article’s subject, read against the argument rather than against a word. The subjects are the ones the argument uses, being flow control and its devices, control without a hinge, control allocation, the conventional control system the effectors would replace, the air supply, Reynolds-number and scale effects, the planform family, flight-data identification, research aircraft and demonstrators, the jets, wall jets and shear layers the effectors act through, the atmosphere, and the programme itself.
Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Full scale also names demonstrations in environmental, industrial and civil engineering. The Coanda effect is also named in cardiology, biology, hydraulic engineering, building ventilation and plasma torches. Hingeless also names the hingeless arch of structural engineering and the hingeless rotor. Flow control also names propellant valves, a synthetic jet also matches synthetic jet fuel, a fluidic actuator also names the soft actuators of robotics, and a fluidic oscillator also serves flow meters, drilling hammers, fuel cells and microfluidics. A jet in a crossflow is also a fuel spray and a flame, a wall jet is also a cooling film, and the excitation of a turbulent boundary layer is also the excitation of a panel. Bleed air also carries the literature of cabin air quality and of valve and sensor faults, and a technology demonstrator or a flight test also names work outside aviation. Correction, erratum and withdrawal notices and peer-review records are excluded as well, because a survey counts research works and those are editorial events rather than works, and a document deposited twice under the same title is counted once. A review of a book, a short glossary, dictionary or encyclopedia entry and a notice such as an editorial or a news item are not admitted either, because none of them is a research work.
Three classes are excluded by the scope set out under Out of Scope, being rotorcraft, the control of shock and boundary-layer interaction, and thrust vectoring that deflects the nozzle rather than the jet. The cost of the first is the circulation-control rotor and the X-Wing, and it is stated there.
Some records of doubtful relevance are kept. Environmental control systems fed by bleed air, the bleed-air spoilers of a parafoil, the Coanda effect of a water jet, fluidic amplifiers and fluidic calibration tools, ice protection by synthetic jets, wall-bounded turbulence in pipes, and the tunnel and flight correlation of the Space Shuttle and Apollo each share a device, an air supply or a method with this subject, so each is kept and a reader may weigh it accordingly.
No cluster is a residual. The fluid mechanics the effectors act through is gathered in three named clusters, on jets in a crossflow, on wall jets and on shear layers and their excitation, and a record enters one of them only when its title is one of those flows.
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, from documents read in full. The X-65A designation was allocated on 24 April 2023 to Aurora Flight Sciences, with the engines cell reading 1 Williams FJ44-3A and DARPA as sponsor. CRANE began with three Phase 0 contracts in mid-2020 to Aurora Flight Sciences, Lockheed Martin and Georgia Tech Research Corporation, all three reporting twenty-five offers received. A Phase 2 and Phase 3 contract was placed on Aurora on 7 December 2022 and carried 94,372,238 dollars in eighteen actions, the last dollar obligated on 16 January 2025 and the last action a zero-dollar change order of 11 February 2025. DARPA told Defense News that it paused the programme earlier in 2025, restructured it so the contractor became a co-investor, finalised that in August 2025, and expects first flight in late 2027, and that account rests on the one press report. The aircraft has fourteen flow-control effectors, fourteen conventional control surfaces, four interchangeable wing sets, a thirty foot span and a limit of Mach 0.7. The programme manager named Micro Adaptive Flow Control as its ancestor and said he had come to DARPA in 1999 to work on that programme and left in 2003 after managing it.
Engineering analysis, this article’s own, checkable from the equations given. The amplification identity. The exact cancellation of altitude from the bleed-fed momentum coefficient. The identical nozzle pressure ratio across the envelope. The Mach-number factor, its exact minimum at Mach 1.4142, and the closed form of that minimum. The authority ratio, the crossover Mach number and the amplification required to match a conventional surface. The concentration factor and the effector sizing. The slot areas. The reduced-frequency band mapped onto this aircraft’s chord. The linear and second-order term counts and the flights they imply. All of it is conditional on parameter values that are not published, and every such parameter is swept.
Very likely a rediscovery. The altitude result. A 2024 paper asks whether momentum-coefficient models hold as ambient and supply conditions change in flight, simulates two actuator types at sea level and ten kilometres, and reports that the momentum coefficient collapses under a scaling parameter. Which parameter it is cannot be read from the abstract. No claim of novelty is made.
Engineering inference, narrowed by a primary source. The low-Reynolds experiments whose thresholds this article borrows lie one to nearly three orders of magnitude below this aircraft’s Reynolds number. A report read in full tested the method at chord Reynolds numbers as high as forty million and states that the Reynolds number has a very weak effect on the pressure distributions and spectra of a fully turbulent baseline [Seifert and Pack 2000]. The X-65A flies inside the range of chord Reynolds numbers that report covers, which its text gives as two to forty million, and inside the range the cited experiments together demonstrate, not beyond it, so the claim made here is the narrow one, that transferring a threshold differs from transferring a phenomenon.
From a secondary source, set against this article’s own arithmetic. The published review reports the separation-control to super-circulation threshold at three to five percent and a measured lift response at 0.08 percent, which the bleed budget reaches wing-referenced. Reaching the super-circulation threshold would take more core flow than the engine has.
Inference, marked as such. That the Phase 0 to Phase 1 downselect occurred in mid-2021 is inferred from two option exercises in June and August 2021 and the absence of any option exercise on the third contract. No source consulted states a date. That Phase 3 is worth about fifty-two million dollars follows from subtracting the reported Phase 2 figure from the obligated total on one contract, and the press figure and the award record are not the same kind of quantity. That the fiscal year 2026 request of 4.000 million dollars is a placeholder is inferred from its being the only round number among seven figures carrying three decimals.
Assumptions this article makes and could be wrong about. That the air comes from engine bleed rather than a dedicated compressor, which is undetermined in the record and which decides whether the altitude result applies at all. That the engine operates at constant corrected flow across the altitude band. That the jet is choked, which the computed nozzle pressure ratio supports with an order of magnitude of margin under the bleed architecture. That the reference area is sixteen square metres, the middle of a sweep. That the effectors blow rather than suck, where the official definition admits both. That the amplification at cruise lies between ten and a hundred, where the low-speed separation-control experiments the review summarises imply a hundred or more.
What the record does not settle. Where the pressurised air comes from. What the wing area, plenum pressure, bleed fraction or effector geometry are. What the aircraft weighs, to within 200 pound. Whether the planform is best described as joined tandem, diamond or triangular, three sources giving three answers. What the bleed costs in thrust. Whether the restructured co-investment is recorded anywhere public. And whether any of this works, the question the aircraft is for.
Written from current knowledge, dated 10 December 2025. The bibliography carries publications later than that dateline, including a substantial 2026 literature on sweeping jets, fluidic oscillators and rudderless flight control. No claim in the prose depends on anything after the dateline, and the survey’s own year range is the one place a later year appears in the body, where it describes the bibliography rather than the aircraft.
Out of Scope
The rotorcraft literature, deliberately. Circulation control on a stopped rotor was flown, and the X-Wing programme is the obvious ancestor of a vehicle controlled by blowing rather than by surfaces. The survey excludes rotorcraft because hingeless on the reports server returns 201 records, 189 of them with rotor or rotary-wing vocabulary in the title, and the exclusion takes the X-Wing with it. The loss is a cost of a necessary guard, and it is stated openly.
Shock and boundary-layer interaction control. The survey excludes it deliberately. The subject is supersonic inlets and hypersonic ramps, and the X-65A is limited to Mach 0.7. Excluding it is a judgement and the judgement is recorded.
Thrust vectoring, except the fluidic kind. Deflecting a propulsion jet is not controlling the flow over a lifting surface, so thrust vectoring is excluded and fluidic thrust vectoring is kept.
The bleed penalty in thrust, quantitatively. Deferred because it needs an engine deck.
Suction-based flow control. Deferred because its figure of merit is a flow coefficient and the identity this analysis uses does not hold for it.
Reynolds-number scaling of the amplification. Deferred because the aircraft is built to answer that question and no analysis can substitute for it.
The structural and aeroelastic consequences of a joined tandem wing. Deferred, and the literature is cited.
Noise. Blowing is loud and the circulation-control literature carries a substantial acoustic component. Out of scope here.
Conclusion
The X-65A exists to find out whether a jet of air can do a hinge’s job, and the arithmetic of the air makes the answer depend almost entirely on Mach number.
The momentum a bleed-fed effector can deliver is exactly independent of altitude, because corrected mass flow and compressible dynamic pressure both scale with ambient pressure, and because a choked jet fed from compressor air gains in velocity exactly what corrected flow loses in the square root of temperature. Two cancellations meet and nothing about the atmosphere survives. What survives is the inlet’s total-pressure recovery divided by the square of the Mach number, a function with an exact minimum at Mach $\sqrt{2}$ that this aircraft never reaches.
So the authority ratio against a conventional surface falls as the aircraft accelerates and is flat as it climbs. At an amplification of 30 against a surface worth 0.05 in lift coefficient, flow control wins below Mach 0.485 and loses above, delivering 5.15 times the hinge’s authority at Mach 0.2 and 56.7 percent of it at Mach 0.7. For a conventional aeroplane the hard case for control power is slow flight. For this one it is fast flight, and a flight-test programme that expands its envelope upward happens to walk from the easy end to the hard one.
The wing-referenced momentum coefficient sits inside the range that oscillatory separation control was demonstrated with at this aircraft’s Reynolds number, 0.03 to 0.32 percent at sixteen million, and at that experiment’s Mach number of 0.25 the same budget delivers 1.74 times its highest quoted value. So the air is sufficient where the method is proved and marginal only where this aircraft wants to fly, and the factor between those two conditions is the Mach dependence and nothing else. The super-circulation regime would still take more core flow than the engine has, the reason this is a control programme and not a high-lift one. The concentration factor is what makes a moment affordable where a lift is not.
And the open problem was named in 2000. The report that demonstrated the method at these Reynolds numbers proposed, among its future directions, overcoming the lack of sufficient control authority especially at high speeds [Seifert and Pack 2000]. This article derived that constraint and did not discover it.
The aircraft’s most consequential design decision is not aerodynamic. It carries two complete, equinumerous control systems and locks one out progressively. The previous article established that two vehicles cannot be differenced because the difference sought is smaller than the differences not sought. The X-65A performs the subtraction inside one airframe, and can therefore return a number rather than an impression. The 16,384 configurations that follow from fourteen surfaces are a red herring, because the quantity to identify is a model with 315 terms, which about eleven flights can identify.
None of it has flown. The programme has asked for 200.507 million dollars across seven budget years and expects 179.416 million, has been funded below its request in every year since fiscal year 2021 at a mean shortfall of 16.29 percent, promised its critical design review in four consecutive books for three different fiscal years, and was paused and restructured into an arrangement the federal award record cannot represent. Its period of performance expired 69 days before this article’s dateline with the fuselage unfinished.
The last thing to say is about the programme’s name. It is called CRANE, for Control of Revolutionary Aircraft with Novel Effectors, and its acronym returns a logging-crane fatality, a book of rhymes and an illustrated book by Walter Crane. The phrase novel effectors returns fungal pathogens. The words that find this aircraft’s actual prior art are hingeless control effectors, which no document this article read from the programme uses, and even those mean helicopter rotor hubs if you ask the wrong registry. An aircraft meant to break a century-old paradigm was given a name under which the work it descends from cannot be found.
References
Reference
- Aurora Flight Sciences, X-65 Experimental Aircraft
- Aurora X-65 CRANE, Directory of U.S. Military Rockets and Missiles, Appendix 4, last updated 20 November 2025
- Defense Advanced Research Projects Agency, Control of Revolutionary Aircraft with Novel Effectors programme page
- Defense Advanced Research Projects Agency, DARPA Moves Forward on X-65 Technology Demonstrator, 3 January 2024
- Defense Advanced Research Projects Agency, RDT&E Programs Justification Book, President’s Budget 2020
- Defense Advanced Research Projects Agency, RDT&E Programs Justification Book, President’s Budget 2021
- Defense Advanced Research Projects Agency, RDT&E Programs Justification Book, President’s Budget 2022
- Defense Advanced Research Projects Agency, RDT&E Programs Justification Book, President’s Budget 2023
- Defense Advanced Research Projects Agency, RDT&E Programs Justification Book, President’s Budget 2024
- Defense Advanced Research Projects Agency, RDT&E Programs Justification Book, President’s Budget 2025
- Defense Advanced Research Projects Agency, RDT&E Programs Justification Book, President’s Budget 2026, June 2025
- Parsch, DOD 4120.15-L Addendum, MDS Designators Allocated After 19 August 1998
- Parsch, DOD 4120.15-L Addendum, 11 August 2025, Internet Archive capture of 25 November 2025
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