X-Planes: Dynetics X-61 Gremlins
Filed under: aerospace, history, engineering
The register stops being a primary source at this designation, and its compiler says so.
Andreas Parsch, who compiles the American military designation register from data the Department of Defense has released, prints a note above the table. At the time of writing, it says, no complete official data on designations assigned after October 2018 is available, and for later allocations the official description is no longer releasable to the public. The entry is therefore shown in blue to indicate that it is not official Department of Defense wording [Parsch, DOD 4120.15-L Addendum]. A blue description is a narrower claim than an entirely blue row, which the same note reserves for designations missing from officially released data altogether. The X-61A’s row is not blue. Only its description is. The X-61A is the first research designation to fall on the far side of that line. The paperwork around the row remains public even where the row’s wording is not. The allocation process for what the system calls a Mission Design Series designator is documented [Allocation of Official Aerospace Vehicle MDS Designations], and so is the Department of the Air Force Instruction that governs it [DAFI 16-401]. What is withheld is the one sentence saying what the aeroplane was for.
Every register count in this article is taken from every row of the copy the compiler last updated on 23 August 2026. Of the 539 rows in the register, 86 carry a description that is not official wording and a further 17 carry one that is only partly official. Of the 31 rows whose designation begins with the letter X, 21 are official, 9 are not, and 1 is partly official. Among the rows the register dates in full, the last official one is the X-60A, allocated 7 September 2018, and the first unofficial one is the X-61A, allocated 6 June 2019. Two rows the register leaves without a full date are unofficial in a stronger sense, being absent from officially released data altogether, and they sit outside that ordering [Parsch, DOD 4120.15-L Addendum]. 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 82 rows carried a description that is not official wording and 12 one that is only partly official, the X rows divided into 21 official, 8 not and none partly official, and the X-61A’s description was the fourth shortest of the twenty-nine, against medians of 110 across the X rows and 95 across the register. The X-60A and the X-61A stood on either side of the line in that version too.
This is the sixty-second 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, and the X-60.
The previous article read the register’s sentence about the X-60A closely enough to build an argument on it, because that sentence is official text. This article cannot do that, and must begin by saying so. What the official cells of the register hold about the X-61A amounts to an allocation date, a designation, a contractor, an engine and a sponsoring agency [Parsch, DOD 4120.15-L Addendum]. Everything the register says the vehicle does is the compiler’s reconstruction from open sources, and the compiler marks it as such. The same compiler’s separate directory of vehicles outside the missile designation series carries a page for this one [Directory of U.S. Military Rockets and Missiles], and the same compiler’s account of the current designation system for American military aircraft sets out the X symbol for research under which it was allocated [Current Designations of U.S. Military Aircraft].
The reconstruction reads as follows, and the abbreviation in it stands for unmanned aerial vehicle.
Gremlins; Small UAV to be deployed and retrieved in-flight by C-130 aircraft
That is 76 characters including the popular name and 66 without it, against a median of 109 across the X rows and 92 across the whole register, each measured without the popular name and the compiler’s note marker. It is the fifth shortest of the 31 X descriptions, and the government did not write it.
The Research Question
Every word of that sentence describes something ordinary except one. A small uncrewed aircraft carried aloft by a transport and released is not a research question. It was done with the X-15 from a bomber in 1959, it is how the X-34 was to have been launched, and it is how every air-launched cruise missile in the inventory begins its flight. The word that is not ordinary is retrieved.
The binding unknown is whether an aircraft that is flying can be caught by another aircraft that is flying, reliably, and more than once. Not whether it can be caught at all, which was answered in 1960, and not whether a small jet can be released from a carrier aircraft, which the X-15 and the air-launched cruise missiles already show. Whether the catch can be made routine.
That distinction decides the shape of this article. The vehicle looks like a cruise missile, with wings and a turbofan from the engine family of the Tomahawk [Williams F107], and almost nothing about it is difficult. The apparatus that catches it is the programme. So the sections below spend their arithmetic on the wake between the two aeroplanes, on the towed body the vehicle has to dock with, on the cable that body hangs from, and on how long an uncontrolled aeroplane stays inside a target the size of a dinner plate.
The Requirement Is Two Numbers and They Are One Number
The programme’s broad agency announcement, as reported when Phase 1 was awarded, set a flyaway cost of no more than 700,000 dollars for each air vehicle and a design life of at least 20 uses [FlightGlobal], and the agency’s programme page gives an expected lifetime of about 20 uses [DARPA]. Those are not two requirements. Their quotient is the requirement, and it is 35,000 dollars per sortie of airframe.
Neither figure means anything alone. A 700,000 dollar vehicle that flies once is expensive and a 700,000 dollar vehicle that flies forty times is cheap, and the specification fixes the product rather than either factor. Writing a cost cap and a life requirement as separate lines in a requirements document conceals that they trade against each other exactly.
Programme Origin
The programme was announced in 2015 by the Defense Advanced Research Projects Agency and named, in that agency’s words, for the imaginary mischievous imps that became the good luck charms of many British pilots during the Second World War [DARPA]. The agency’s statement of the problem is unusually direct about the economics. Adversary detection and engagement ranges have grown, which has driven up the cost of designing, operating and replacing the aircraft that must survive them, and an ability to send large numbers of small unmanned air systems with distributed capabilities could provide the same effect more cheaply, especially if those systems could be retrieved for reuse while airborne [DARPA].
The Earliest Document Is Nine Months Older Than the Programme
The phrase most often quoted about this programme is nine months older than the programme, and it comes from a Request for Information. On 9 November 2014 the agency asked for ideas on transforming planes into aircraft carriers in the sky, and the words are a quotation from the same programme manager who would announce the programme [DARPA Request for Information]. The agency repeated them in its Phase 2 release of March 2017, and most quotations take them from there [DARPA].
That document repays a close reading because it fixes three things before any contractor existed [DARPA Request for Information]. It names the carrier by type, asking about launch and recovery from one or more types of existing large manned aircraft such as C-130 transport planes. It names small payloads of 100 pounds or less as the class it hopes to draw on, a figure the vehicle eventually built exceeded by 1.45 times, carrying 145 pounds [Directory of U.S. Military Rockets and Missiles]. And it asks respondents for plans for achieving full-system flight demonstrations within four years. The payload ratio is the published capacity over that figure.
\[\frac{145\ \text{lb}}{100\ \text{lb}} = 1.45 \tag{1}\]A stated duration is rare in a programme record and this one can be measured against the outcome. Four years from the Request for Information falls on 9 November 2018. The first free flight came 5.04 years after the request, or 1.26 times the plan, and the airborne recovery that was the full-system demonstration came 6.97 years after it, giving 1.74 times. Counted in days from 9 November 2014 to the first free flight on 23 November 2019 and to the recovery on 29 October 2021, against a plan of four years of 365.25 days each, the two ratios are these.
\[\frac{1{,}840\ \text{days}}{4 \times 365.25\ \text{days}} = \frac{5.04\ \text{years}}{4\ \text{years}} = 1.26 , \qquad \frac{2{,}546\ \text{days}}{4 \times 365.25\ \text{days}} = \frac{6.97\ \text{years}}{4\ \text{years}} = 1.74 \tag{2}\]The agency also named its antecedents, and it named them correctly. The 2015 programme announcement says the effort aims to leverage prior success in developing automated aerial refuelling and the agency’s current efforts to create advanced capture systems for ships [DARPA], the second of which is the Tern programme and the shipboard capture work that came out of it [DARPA] [Tern]. Both are the right ancestors, and the article’s comparison sections reach the same two by a different route.
Four Teams, Then Two, Then One
Phase 1 contracts went to four teams on 31 March 2016, led by Composite Engineering, Dynetics, General Atomics Aeronautical Systems and Lockheed Martin [DARPA]. Phase 2 contracts went to two of them on 15 March 2017, being Dynetics and General Atomics, and the agency repeated the aircraft-carriers-in-the-sky phrase in that release [DARPA]. Quotations usually take the phrase from that repetition, though it originates earlier, as the section above establishes. Dynetics, a Huntsville firm that became a subsidiary of Leidos during the programme [Dynetics], won Phase 3 in April 2018 and received a contract for five X-61A air vehicles, with the airframes subcontracted to Kratos [Directory of U.S. Military Rockets and Missiles] [Leidos].
A four to two to one funnel across two years is the ordinary shape of an agency programme. The date is the detail to notice. The Phase 3 award was April 2018 and the designation was allocated 6 June 2019, fourteen months later [Leidos] [Parsch, DOD 4120.15-L Addendum]. The number followed the contract by more than a year, the same ordering the X-55 and the X-53 showed and the opposite of the one the series opened with.
Three programme managers ran the programme across its life, being the one who wrote the Request for Information and announced the programme, the one who awarded Phase 2, and the one who announced the recovery [DARPA Request for Information] [DARPA] [DARPA]. A seven-year programme changing hands twice is unremarkable, and the article records it because the three releases read as one voice and are not.
The Contractor Says August and the Register Says June
Kratos, announcing the first flight, wrote that the team received a U.S. Air Force-assigned X-61A designation in August of 2019 [Kratos]. The register records the allocation as 6 June 2019 [Parsch, DOD 4120.15-L Addendum]. The two statements are about two months apart and this article does not resolve them.
The likeliest reading is that the register records the date the allocation was made and the contractor records the date it learned. But the reading is not a finding, and the record carries both dates without reconciling them.
The designation also came 415 days after the Phase 3 contract. In this programme the money moves first, the publicity follows, and the number comes last.
What It Cost, and the Three Agencies That Paid
The federal award record carries three contracts for this programme, under three different awarding agencies, and they sum to 82,680,983.37 dollars across 38 modifications [USAspending].
| Contract | Awarding agency | Obligated | Modifications | Period |
|---|---|---|---|---|
| FA865016C7618 | Department of the Air Force | 29,765,400.00 dollars | 9 | 24 March 2016 to 25 August 2018 |
| IND17PC00148 | Department of the Interior | 549,943.46 dollars | 6 | 13 March 2017 to 25 May 2018 |
| HR001118C0071 | Defense Advanced Research Projects Agency | 52,365,639.91 dollars | 23 | 17 April 2018 to 31 October 2025 |
Each of the three totals is the sum of its transactions to the cent. The agreement is a reassembly check, since the registry states the total separately from the modifications that make it up [DARPA Phase III contract] [Air Force contract] [Interior contract].
The Department of the Interior is not a typographical error. That contract is an interagency acquisition, and its description is the one place in the record that names the solicitation, being the Broad Agency Announcement numbered DARPA-BAA-15-59. It is also the only one of the three that carries a negative line, a deobligation of 6,832.54 dollars in March 2020 [Interior contract].
The money and the publicity agree more closely than they usually do. The Phase 1 obligation moved 7 days before the public announcement of Phase 1, and the Phase 2 obligation moved on the same day as the Phase 2 release, which is 15 March 2017 in both records [Air Force contract] [DARPA] [DARPA].
And the pandemic is priced. Two modifications to the Phase 3 contract name COVID-19, the coronavirus pandemic, in their descriptions. The one of 9 March 2021 obligates 5,852,178.74 dollars and states that the cost growth is due to the pandemic, and the one of 3 May 2021 extends the period of performance for selected line items and obligates nothing [DARPA Phase III contract]. Against the contract’s total that is 11.18 percent of the Phase 3 contract. The contractor’s August 2020 release had said the second flight test was delayed by the pandemic [Dynetics]. The contract records what that delay cost.
\[\frac{5{,}852{,}178.74\ \text{dollars}}{52{,}365{,}639.91\ \text{dollars}} = 0.1118 \tag{3}\]Sizing From First Principles
The register’s engine cell is not blue. It says 1 F107-WR-105, and that is official Department of Defense data [Parsch, DOD 4120.15-L Addendum]. The F107 is the Williams turbofan that powers the AGM-86 air-launched cruise missile and the BGM-109 Tomahawk [Williams F107] [Designations of U.S. Military Aero Engines], so the one thing the government has said about this vehicle’s propulsion places it in the engine family of the air-launched cruise missile, whose production began in 1980 [AGM-86 ALCM].
That invites the obvious reading, that the X-61A is a cruise missile with the warhead taken out. The published dimensions refuse it, and they refuse it without any estimate at all.
The Span Is the Measurement, and It Needs No Wing Area
Induced drag depends on the square of the weight divided by the square of the span, and on nothing else that is in dispute [Lift-induced drag] [Fleeman, Missile design and systems engineering].
\[D_i = \frac{W^2}{q \, \pi b_v^2 e} \tag{4}\]Collecting the two published quantities into one parameter removes every other property of the aeroplane from the comparison.
\[\Lambda = \frac{W^2}{b_v^2} \qquad \Longrightarrow \qquad D_i = \frac{\Lambda}{q \, \pi e} \tag{5}\]Wing area is published for none of the three vehicles and is needed for none of them. The X-61A spans 3.47 metres at 680 kilograms, the AGM-86B spans 3.66 metres at 1,458 kilograms and the BGM-109 spans 2.67 metres at 1,315 kilograms [Dynetics X-61 Gremlins] [AGM-86 ALCM] [BGM-109 Tomahawk].
| Vehicle | Weight per span | Induced drag, relative |
|---|---|---|
| X-61A | 1,922 newtons per metre | 1.00 |
| AGM-86B | 3,909 newtons per metre | 4.14 |
| BGM-109 | 4,837 newtons per metre | 6.33 |
At the same dynamic pressure the cruise missile that shares this vehicle’s engine pays 4.14 times the induced drag, and the other one pays 6.33 times. That comparison is the aerodynamic case for the difference between the two kinds of vehicle, and it contains no assumption. A one-way missile flies once, fast, at a condition it chooses. A vehicle that must come back and fly formation with a transport aeroplane has to be efficient at a speed the transport chooses, and the relation above offers two levers for that, being less weight or more span. The X-61A has both, at less than half the weight and a comparable span, and span is the lever that does not cost payload.
What the Wing Must at Least Be
The wing area is not published. It is also not needed as an estimate, because the recovery imposes a floor on it that a one-way missile never has to clear.
\[L = q S C_L = W \quad \Longrightarrow \quad C_L = \frac{2 W}{\rho V^2 S} \tag{6}\] \[S \;\geq\; \frac{2 W}{\rho V^2 C_{L_{\max}}} \tag{7}\]Read the other way round, the same relation is the lowest speed at which a given wing can hold the vehicle up at all.
\[V_{\min} = \sqrt{\frac{2 W}{\rho S \, C_{L_{\max}}}} \tag{8}\]The vehicle demonstrably held formation with a C-130 and was photographed doing so, so its wing is at least large enough for level flight at the transport’s speed. Across formation speeds taken as 150 to 200 knots, and across lift coefficients of 1.0 and 1.2 taken for a plain wing with no high-lift device, the floor comes out as follows.
| Formation speed | Floor at a lift coefficient of 1.2 | Floor at 1.0 |
|---|---|---|
| 150 knots | 2.06 square metres | |
| 180 knots | 1.43 square metres | 1.72 square metres |
| 200 knots | 1.16 square metres |
Taking the middle of that, at 1.43 square metres, the published span implies an aspect ratio of at most 8.4 and a mean chord of 0.41 metres.
\[C_D = C_{D_0} + \frac{C_L^2}{\pi A e} , \qquad A = \frac{b_v^2}{S} , \qquad \bar{c} = \frac{S}{b_v} \tag{9}\]The relations are the standard ones and are set out in any of the design texts [Torenbeek, Synthesis of subsonic airplane design] [Anderson, Aircraft performance and design]. Every one of those is an upper or lower bound and not a measurement, and the sections below say which way each of them errs whenever it matters.
How Good the Polar Is Allowed To Be
The range calculation below carries lift to drag ratios of 6, 9 and 12 as a band, and the polar above puts a ceiling on that band. Differentiating the drag with respect to the lift coefficient gives the best the vehicle can possibly do, together with the lift coefficient at which it does it and the fact that the induced drag equals the zero-lift drag exactly there.
\[\left( \frac{L}{D} \right)_{\max} = \frac{1}{2} \sqrt{\frac{\pi A e}{C_{D_0}}} , \qquad C_{L_{\mathrm{opt}}} = \sqrt{\pi A e \, C_{D_0}} , \qquad C_{D_{\min}} = 2 C_{D_0} \tag{10}\]At the reference wing area the aspect ratio is 8.4, and at a zero-lift drag coefficient of 0.030 with a span efficiency of 0.80 the ceiling is 13.27, reached at a lift coefficient of 0.796. So the band the range section carries is not arbitrary. Its upper end is very nearly the best the geometry allows, and the middle of it is where a real airframe with a turbofan hung on it would sit.
The zero-lift drag coefficient is assumed and the ceiling moves with it, from 16.25 at 0.020 to 10.83 at 0.045. Every one of those is above the middle of the range band, and the range section needs no more.
A best-range cruise holds that lift coefficient, so the speed it corresponds to follows from the altitude and from nothing else.
\[V_{\mathrm{md}} = \sqrt{\frac{2 W}{\rho S \, C_{L_{\mathrm{opt}}}}} \tag{11}\]| Altitude | Speed at the best lift to drag ratio | Mach number |
|---|---|---|
| 10,000 feet | 113.7 metres per second | 0.35 |
| 25,000 feet | 146.0 metres per second | 0.47 |
| 35,000 feet | 175.5 metres per second | 0.59 |
The published maximum of Mach 0.6 is very nearly the best-range Mach number at 35,000 feet [Directory of U.S. Military Rockets and Missiles]. At that altitude the atmosphere relations below give a temperature of 218.8 kelvin and a speed of sound of 296.5 metres per second, so the Mach number is the tabulated speed over that.
\[M = \frac{V_{\mathrm{md}}}{a} = \frac{175.5\ \text{m/s}}{\sqrt{1.4 \times 287.05 \times 218.8}\ \text{m/s}} = \frac{175.5}{296.5} = 0.59 \tag{12}\]It gives an independent reason to read the figure as a chosen cruise condition rather than as a limit, reached without any reference to the engine.
The Two Thrust Ratings Disagree by a Factor of Two
The register’s engine cell and the public descriptions of this vehicle cannot both be right.
Forecast International’s survey of the F107 family, published in October 2014 and therefore before this programme existed, tabulates the variants. Its text rates the F107-WR-101, the F107-WR-400 and the F107-WR-402 at 600 pounds of thrust and has them equip the air-launched cruise missile and the Tomahawk, although its own table of variants rates the F107-WR-402 at 660 pounds. The F107-WR-103 is rated at approximately 1,000 pounds. And the F107-WR-105, paired in that document with a dash 401, offers an increase in thrust to 1,400 pounds by using all-ceramic turbines, combustors, stators, nozzles and shrouds [Forecast International].
The public descriptions of the X-61A give its engine as 700 pounds of thrust [Directory of U.S. Military Rockets and Missiles] [Dynetics X-61 Gremlins]. The official record names a dash number whose only published rating is twice that.
The consequence is computable and it needs three relations. An engine delivers less thrust where the air is thinner and a little more where the free stream helps it, drag rises steeply once the flow over the wing goes locally sonic, and the maximum speed is where the two curves cross.
\[T(h, M) = T_0 \left( \frac{\rho}{\rho_0} \right)^{0.9} \left( 1 + \tfrac{1}{2} \left( \gamma - 1 \right) M^2 \right)^{1/2} \tag{13}\] \[C_D = C_{D_0} + \frac{C_L^2}{\pi A e} + K_w \left( M - M_{\mathrm{dd}} \right)^3 \quad \text{for } M > M_{\mathrm{dd}} \tag{14}\] \[T(h, M_{\max}) = D(h, M_{\max}) \tag{15}\]Both the lapse exponent and the wave-drag coefficient are assumed, and both are chosen to flatter the larger rating rather than the smaller, because the conclusion is that even a generous installed thrust fails to make the published Mach number a ceiling.
The result is not what one would expect.
| Rating | Thrust to weight | Installed thrust over drag at Mach 0.6 | Level flight maximum Mach |
|---|---|---|---|
| 700 pounds, the public figure | 0.467 | 2.78 | 0.86 |
| 1,400 pounds, the register’s dash number | 0.934 | 5.57 | 0.90 |
The published maximum speed of Mach 0.6 cannot discriminate between them, because neither rating is what sets it. At Mach 0.6 and 25,000 feet the drag is about 562 newtons, and the smaller of the two ratings already delivers 2.78 times that after allowing for the density lapse. Mach 0.6 is a chosen cruise condition and not a ceiling, on either reading, and this article therefore reports the conflict rather than settling it. Where a conclusion below depends on which rating is right, it says so.
What both ratings agree on is that this vehicle is over-engined for cruising. The AGM-86B’s thrust to weight is 0.187 on its 600 pounds, and the Tomahawk’s is 0.228 on the table’s 660 pounds for its F107-WR-402, or 0.207 on the text’s 600. The X-61A’s is 0.467 on the smaller rating, 2.5 times the cruise missile’s.
\[P_s = \frac{\left( T - D \right) V}{W} \tag{16}\]At the published Mach number the specific excess power on the smaller rating is 27.9 metres per second, a climb rate a cruise missile has no use for. A vehicle that must rejoin a moving aeroplane at a time and place it does not control needs margin that a vehicle flying to a fixed point on the ground does not, and the thrust to weight shows that margin.
The engine itself is small. The F107-WR-400’s published dry mass is 65.3 kilograms [Forecast International], or 9.6 percent of the vehicle’s gross weight.
Does the Published Range Close
The mission the programme’s announcement described is to fly out 300 to 500 nautical miles at high subsonic speed, loiter for one to three hours, and turn back to the C-130 for recovery [FlightGlobal]. The profile is an out and back mission with a hold in the middle, a much larger demand than the bare range figure suggests [Range, the aeronautical quantity].
\[R = \frac{V}{c \, g} \frac{L}{D} \ln \frac{m_i}{m_f} \quad \Longrightarrow \quad 1 - \frac{m_f}{m_i} = 1 - \exp \left( - \frac{R \, c \, g}{V \, L/D} \right) \tag{17}\]Every altitude in this article enters through the same three lines, being a linear temperature lapse through the troposphere, the hydrostatic pressure that follows from it, and the perfect gas law.
\[\Theta = \Theta_0 + \beta_0 h , \qquad \frac{p}{p_0} = \left( \frac{\Theta}{\Theta_0} \right)^{-g / \beta_0 R_{\mathrm{air}}} , \qquad \rho = \frac{p}{R_{\mathrm{air}} \Theta} \tag{18}\]The speed that range is flown at is a Mach number rather than a speed, so it depends on the temperature and therefore on the altitude [International Standard Atmosphere] [Dynamic pressure].
\[q = \tfrac{1}{2} \rho V^2 , \qquad V = M a , \qquad a = \sqrt{\gamma R_{\mathrm{air}} \Theta} \tag{19}\]At the published Mach number and at 25,000 feet the true airspeed is 185.8 metres per second, equal to 361 knots.
The hold in the middle is an endurance problem rather than a range one, and the two differ by exactly the speed. A vehicle covering ground converts fuel into distance; a vehicle waiting converts it into time, and the same relation serves both with the speed divided out.
\[\text{endurance} = \frac{1}{c \, g} \frac{L}{D} \ln \frac{m_i}{m_f} = \frac{R}{V} \tag{20}\]| Lift to drag ratio | Fuel out and back | Fuel flow in the hold | Total with one hour of hold | Left for structure and systems |
|---|---|---|---|---|
| 6 | 116.7 kilograms | 77.1 kilograms per hour | 193.8 kilograms, 28.5 percent | 421 kilograms |
| 9 | 80.2 kilograms | 51.4 kilograms per hour | 131.6 kilograms, 19.4 percent | 483 kilograms |
| 12 | 61.1 kilograms | 38.5 kilograms per hour | 99.6 kilograms, 14.7 percent | 515 kilograms |
The published performance closes, and it closes comfortably at the middle of the band. At a lift to drag ratio of 9 the mission costs 19.4 percent of the gross weight in fuel and leaves 483 kilograms for the airframe, the engine, the systems and everything that is not fuel or payload. Both follow from the table’s middle row, the published gross mass of 680 kilograms and the published payload capacity of 65.7 kilograms [Dynetics X-61 Gremlins].
\[\frac{m_b}{m} = \frac{80.2 + 51.4 \times 1}{680} = \frac{131.6}{680} = 0.194 , \qquad m - m_b - m_p = 680 - 131.6 - 65.7 = 482.7\ \text{kg} \tag{21}\]The specific fuel consumption assumed here is not published for this engine and the lift to drag ratio is not published for this airframe, so all three rows are given rather than one.
The Wake Between the Two Aeroplanes
Before the vehicle can dock with anything it has to fly through the wake of a four-engined transport, and the wake is no nuisance to be flown around but a structure with a shape. That shape decides where the docking device can be put.
A wing carrying lift sheds a vortex sheet that rolls up into a pair of counter-rotating cores, and for a spanwise loading close to elliptic those cores sit closer together than the wing tips by a factor of about one quarter of pi [Lifting-line theory] [Wake turbulence] [Horseshoe vortex] [McCormick, Aerodynamics, aeronautics, and flight mechanics].
\[\Gamma = \frac{W}{\rho V b'} , \qquad b' = k_b b , \qquad k_b = \frac{\pi}{4} \tag{22}\]The elliptic assumption concerns the carrier’s wing rather than the vehicle, and it can be tested from published figures. A transport at an ordinary cruise lift coefficient carries a loading close to elliptic, and one scraping its maximum does not.
\[C_{L_c} = \frac{2 W_c}{\rho V^2 S_c} , \qquad A_c = \frac{b^2}{S_c} \tag{23}\]The carrier on the first free flight was a C-130A [Kratos], and its wing area is 162.1 square metres [Lockheed C-130 Hercules]. Its weight is taken midway between an empty weight of 59,164 pounds [This Day in Aviation] and a maximum of 124,200 pounds [Aeropedia]. The two sources do not agree on the pair, since the first gives a takeoff weight of 122,245 pounds and the second an empty weight of 63,000, so the mid weight lies between 90,705 and 93,600 pounds against the 91,682 taken here, and every wake figure below that scales with weight moves by between 1.1 percent down and 2.1 percent up. At a recovery speed of 200 knots at 10,000 feet and that weight, the C-130’s lift coefficient is 0.525 on an aspect ratio of 10.07. That lift coefficient marks an unremarkable cruise condition, so the assumption is an ordinary one, and this article can establish no more about it.
The circulation can then be reached a second way, from the lift coefficient rather than from the weight.
\[\Gamma = \frac{V S_c C_{L_c}}{2 b'} \qquad \text{which must equal} \qquad \frac{W_c}{\rho V b'} \tag{24}\]The two agree to 16 digits, which they must, because the second expression is the first with the lift written out. Exact agreement between equivalent formulations is what they ought to produce and is no evidence that the physics is right. It tests transcription, and the article does not present it as a confirmation.
The C-130 spans 40.41 metres [Lockheed C-130 Hercules], so the vortex cores sit 31.74 metres apart, a distance of 104.1 feet. At a mid weight and a recovery speed of 200 knots at 10,000 feet the circulation of one core is 138 square metres per second, and the pair induces a descent on itself.
\[w_d = \frac{\Gamma}{2 \pi b'} \tag{25}\]That descent is 0.692 metres per second. The rate counts for less than how far it gets in the time available, and that time is set by how far aft the station is and how fast the carrier is going.
\[\Delta z = w_d \frac{x}{V} \tag{26}\]It is slow enough to be irrelevant over the distances that matter here. In the time the flow takes to travel the 125 feet from the wing to the formation station the pair sinks 0.26 metres, less than the length of the vehicle. The wake does not move out of the way, and the station has to be chosen rather than waited for.
The Worst Place To Be Is Fixed by the Span Alone
A single straight vortex induces a velocity that falls off as the reciprocal of the distance from its core and circles it.
\[v_\theta = \frac{\Gamma}{2 \pi r} \tag{27}\]On the centreline, directly below the aircraft, the two cores are equidistant, so their horizontal components cancel and their vertical components add.
\[w(z) = \frac{\Gamma b'}{2 \pi \left[ \left( b'/2 \right)^2 + z^2 \right]} \tag{28}\]What a station keeper fights is not the downwash but its gradient, because a uniform downward flow is trimmed out once and forgotten while a gradient turns a small position error into a changed airspeed and angle of attack.
\[\frac{\mathrm{d} w}{\mathrm{d} z} = - \frac{\Gamma b'}{\pi} \frac{z}{\left[ \left( b'/2 \right)^2 + z^2 \right]^2} \tag{29}\]That gradient is zero at the centreline of the wake and zero far below it, so it has a maximum in between. Differentiating once more and setting the result to zero gives the depth of that maximum.
\[\frac{\mathrm{d}^2 w}{\mathrm{d} z^2} = 0 \quad \Longrightarrow \quad z_\star = \frac{b'}{2 \sqrt{3}} = \frac{\pi b}{8 \sqrt{3}} \tag{30}\]The circulation cancels. So does the weight, the speed, the density and the altitude. The worst depth at which to hold station behind a transport aeroplane is a fixed fraction of its wing span and nothing else, and for the C-130 it is 9.16 metres, or 30.1 feet.
Where the Formation Station Sits
The second flight test put the vehicle in formation with the C-130 from as close as 125 feet back and 125 feet below [Dynetics]. That is 4.16 times the worst depth.
| Position | Downwash | Gradient |
|---|---|---|
| On the centreline in the wing plane | 2.77 metres per second | |
| At the worst depth, 30.1 feet | 0.113 per second | |
| At the formation station, 125 feet | 0.409 metres per second | 0.0183 per second |
The station sits where the downwash is 6.76 times weaker than in the wing plane and the gradient is 6.19 times flatter than at its worst. Whether that placement was arrived at by this argument or by flight test goes unrecorded. The arithmetic establishes that it is a good place to be and that a station one quarter as deep would have been much the worst available.
The Thing Being Docked With
The vehicle does not dock with the C-130. It docks with a body towed behind and below it on a cable, which the programme calls the Bullet and which its engineers describe as a stabilized towed docking device and as towed, attitude-controlled [Leidos] [Dynetics]. Those two adjectives are the finding of this section, and a forward calculation explains why they had to be there.
A Towed Cable Cannot Be Told Where To Hang
A cable towed through air carries its weight and its drag, and in steady flight the two balance along its length. A cable carrying no aerodynamic load at all hangs as a catenary [Catenary], and the general treatment of a cable as a structural element is a separate subject [Irvine, Cable structures]. Taking arc length from the towed body upward, and resolving along and normal to the local tangent, gives the classical pair.
\[f_t = \tfrac{1}{2} \rho V^2 d \, \pi C_f \cos^2 \theta , \qquad f_n = \tfrac{1}{2} \rho V^2 d \, C_{D_n} \sin^2 \theta \tag{31}\] \[\frac{\mathrm{d} T_c}{\mathrm{d} s} = \mu g \sin \theta + f_t , \qquad T_c \frac{\mathrm{d} \theta}{\mathrm{d} s} = \mu g \cos \theta - f_n \tag{32}\]The shape follows from the inclination by two quadratures, and those turn an angle into a position.
\[x(s) = \int_0^s \cos \theta \, \mathrm{d}s' , \qquad z(s) = \int_0^s \sin \theta \, \mathrm{d}s' \tag{33}\]The boundary condition at the body end is exact rather than assumed, because a body in equilibrium has the cable pulling along the resultant of the body’s drag and weight.
\[T_c(0) = \sqrt{D_b^2 + W_b^2} , \qquad \tan \theta(0) = \frac{W_b}{D_b} \tag{34}\]Far from the body the inclination stops changing, and where it stops changing the normal component of the cable’s drag exactly carries the normal component of its weight.
\[\frac{\mathrm{d} \theta}{\mathrm{d} s} = 0 \quad \Longrightarrow \quad \frac{\sin^2 \theta_c}{\cos \theta_c} = \frac{2 \mu g}{\rho V^2 d \, C_{D_n}} \tag{35}\]That angle contains no tension and no length. A cable settles to it whatever is on the end and however much of it is paid out, so the depth below the tow point and the distance behind it are locked to each other by a ratio the operator cannot choose.
\[\frac{\text{trail}}{\text{depth}} \longrightarrow \cot \theta_c , \qquad \ell \longrightarrow \frac{z}{\sin \theta_c} \tag{36}\]At 200 knots at 10,000 feet the airspeed is 102.89 metres per second and the atmosphere relations give a density of 0.9046 kilograms per cubic metre. Taking 0.40 kilograms per metre for a ten millimetre steel wire rope, the tabulated mass of a ten millimetre six by nineteen rope with a steel core [Katradis, 6×19 IWRC wire rope], and a normal drag coefficient taken as 1.2 for its circular section, the equilibrium relation gives the first row of the table. The other two rows repeat it at 0.10 kilograms per metre, taken for a synthetic rope of the same diameter, and at 0.14 kilograms per metre for a six millimetre steel rope, whose tabulated mass is 0.144 [Katradis, 6×19 IWRC wire rope].
\[\frac{\sin^2 \theta_c}{\cos \theta_c} = \frac{2 \times 0.40 \times 9.807}{0.9046 \times 102.89^2 \times 0.010 \times 1.2} = 0.0683 \quad \Longrightarrow \quad \theta_c = 14.9^\circ , \qquad \cot \theta_c = 3.76 , \qquad \frac{100\ \text{ft}}{\sin \theta_c} = 389\ \text{ft} \tag{37}\]The numbers are these.
| Cable | Inclination | Trail per unit depth | Cable to hang 100 feet below |
|---|---|---|---|
| Steel wire rope, 10 millimetres | 14.9 degrees | 3.76 | 389 feet |
| Synthetic rope, 10 millimetres | 7.5 degrees | 7.62 | 769 feet |
| Steel wire rope, 6 millimetres | 11.4 degrees |
A passively towed cable at this speed hangs at about fifteen degrees and yields roughly four feet of trail for every foot of depth. Integrating the full equations for 150 metres of the steel rope with a plausible body on the end puts that body 162 feet below the tow point and 458 feet behind it, at a tension of 1,118 newtons. The body is taken to weigh 50 kilograms and to have 200 newtons of drag, and the tangential friction coefficient is taken as 0.02, so the boundary condition starts the integration at a tension of 529.6 newtons and an inclination of 67.8 degrees.
\[T_c(0) = \sqrt{200^2 + \left( 50 \times 9.807 \right)^2} = 529.6\ \text{N} , \qquad \theta(0) = \arctan \frac{490.4}{200} = 67.8^\circ \tag{38}\]A body 125 feet below and 125 feet behind would need a forty-five degree cable, and the arithmetic gives its cost. A ten millimetre cable hanging at forty-five degrees at this speed would have to weigh 4.14 kilograms per metre, 10.4 times the 0.40 kilograms per metre taken above for steel wire rope of that diameter. At forty-five degrees the left side of the equilibrium relation is the reciprocal of the square root of two, so the relation can be solved for the linear density directly.
\[\theta_c = 45^\circ \quad \Longrightarrow \quad \mu = \frac{\rho V^2 d \, C_{D_n}}{2 \sqrt{2} \, g} = \frac{0.9046 \times 102.89^2 \times 0.010 \times 1.2}{2 \sqrt{2} \times 9.807} = 4.14\ \text{kg/m} , \qquad \frac{4.14}{0.40} = 10.4 \tag{39}\]The forward calculation fails to produce the geometry, and the failure locates the design decision. A passive cable cannot put a docking device where the docking device has to be without either an impractical length of it or an impossible cable, so the body on the end has to fly. The Bullet is attitude-controlled for that reason, a conclusion reached by finding out what would happen if it were not.
The Docking Device Hangs From a String That Does Not Ring
A cable under tension carries transverse waves, and a cable of finite length carries standing ones [Vibrating string].
\[v_c = \sqrt{\frac{T_c}{\mu}} , \qquad F_k = \frac{k v_c}{2 \ell} \tag{40}\]For the 150 metre steel rope at the tension computed above, the wave speed is 52.9 metres per second and the first three transverse modes lie at 0.176, 0.352 and 0.529 hertz. The fundamental has a period of 5.67 seconds.
It is tempting to stop there and call the docking device the end of a resonator. Writing down the damping refuses that, and the refusal is the finding.
A cable is not only a string. It is a string being dragged sideways through air at two hundred knots, and a transverse velocity changes the normal component of the relative wind and therefore the normal drag. Linearising that about the equilibrium inclination gives a damping force per unit length per unit transverse velocity, and the string equation acquires a first-order term.
\[\mu \frac{\partial^2 y}{\partial t^2} + c_a \frac{\partial y}{\partial t} = T_c \frac{\partial^2 y}{\partial s^2} \tag{41}\] \[c_a = \rho V d \, C_{D_n} \sin \theta_c \tag{42}\]Divided by twice the mass per unit length and the modal frequency, that coefficient is a damping ratio in the ordinary sense.
\[\omega_k = \frac{k \pi v_c}{\ell} , \qquad \zeta_k = \frac{c_a}{2 \mu \omega_k} \tag{43}\]At this speed and density the coefficient is 0.287 kilograms per metre per second, and the consequence is large.
| Mode | Frequency | Damping ratio | Cycles to decay by a factor of e |
|---|---|---|---|
| First | 0.176 hertz | 0.324 | 0.49 |
| Second | 0.352 hertz | 0.162 | 0.98 |
| Third | 0.529 hertz | 0.108 | 1.47 |
The fundamental is 0.324 damped, so it decays by a factor of e in 0.49 of a cycle. A mode that damped does not ring. It is nearer to a door closer than to a bell, and an impulse given to it has gone before the first swing completes. The word resonator does not fit it.
What remains is the part that matters, and it is not weakened. A heavily damped system does not oscillate on its own, but it still moves when something moves it, and the things moving this one are the wake it hangs in and the carrier aeroplane it hangs from. The frequencies at which it responds are still the frequencies computed above, because damping shifts a natural frequency by the square root of one minus the damping ratio squared, which at 0.324 is a correction of a few percent. And the next section shows that the loop which has to dock with it cannot reject motion at those frequencies whatever produces them, and the argument stands on that inability. The damping removes the ringing and leaves the tracking problem where it was.
Two things the model still does not carry. The taut-string idealisation assumes a uniform cable at a uniform tension, and the real tension varies along the length by the weight it carries. And the damping coefficient is linearised about a mean inclination, a small-perturbation assumption applied to a cable that may not be making small perturbations. Neither moves the ordering, and the ordering is all the argument uses.
Holding Station To Inches
This is the section the programme exists for. Everything above it is a solved problem dressed in new proportions. What had never been done is the last few metres, and the arithmetic of those metres follows.
How Long an Uncontrolled Vehicle Stays in the Window
The third test series made nine aerial docking attempts, each coming within inches of capture, and captured nothing [Military Embedded Systems]. That sentence gives the tolerance, the only public statement of it among the sources cited here. The claim is limited to those sources, and a figure may exist elsewhere. The capture window is of the order of inches rather than feet, so the sections below carry it at six inches and at twelve.
The disturbance is the atmosphere. A vertical gust changes the angle of attack and therefore the lift, and the resulting load factor is inversely proportional to the wing loading [Etkin and Reid, Dynamics of flight] [Nelson, Flight stability and automatic control].
A vertical gust of velocity u meeting a vehicle travelling at V changes the angle of attack by their quotient, and the lift in proportion.
\[\Delta \alpha = \frac{u}{V} , \qquad \Delta L = \tfrac{1}{2} \rho V^2 S \, C_{L_\alpha} \Delta \alpha \tag{44}\] \[\Delta n = \frac{\rho V C_{L_\alpha} u}{2 \, W / S} , \qquad \alpha = g \, \Delta n \tag{45}\]High wing loading is an advantage here and this vehicle has a great deal of it. At the reference area derived earlier, which is a floor and therefore makes the wing loading an upper bound, a gust of one metre per second produces an incremental load factor of 0.032, an acceleration of 0.314 metres per second squared.
That sounds negligible until it is integrated twice.
\[t_d = \sqrt{\frac{2 \delta}{\alpha}} \tag{46}\]| Gust | Acceleration | Out of a six inch window in | Out of a twelve inch window in |
|---|---|---|---|
| 1 metre per second | 0.314 metres per second squared | 0.99 seconds | 1.39 seconds |
| 2 metres per second | 0.628 metres per second squared | 0.70 seconds |
An uncontrolled vehicle leaves a six inch capture window in about one second in light turbulence. The docking cannot be set up as a manoeuvre and allowed to run, and the loop has to be closed continuously and fast.
The Gust Is a Spectrum and Not a Step
The sharp-edged gust used above is the crudest model available, and naming it as crude is not the same as knowing what it costs. An apology is not a measurement. Real turbulence is a continuum with more energy at long wavelengths than short ones, and the standard description of it gives the energy as a function of frequency.
\[\Phi_w(\omega) = \frac{\sigma_w^2 \lambda_w}{\pi V} \frac{1 + \tfrac{8}{3} \left( 1.339 \lambda_w \omega / V \right)^2}{\left[ 1 + \left( 1.339 \lambda_w \omega / V \right)^2 \right]^{11/6}} \tag{47}\] \[\sigma_w^2 = \int_0^\infty \Phi_w(\omega) \, \mathrm{d} \omega , \qquad \sigma_b^2 = \int_0^{\omega_n} \Phi_w(\omega) \, \mathrm{d} \omega \tag{48}\]The quantity that counts is the share of the total falling inside the loop’s band, because energy above the loop’s natural frequency is filtered by the vehicle’s mass and energy below it is what the loop has to fight.
The spectrum is the von Kármán form [Von Kármán wind turbulence model]. At 200 knots with an assumed scale length of 533.4 metres and an assumed root mean square intensity of one metre per second, the spectrum integrates to 0.998 metres per second in total, of which 0.892 lies below the loop’s natural frequency and 0.447 above it. The two add in quadrature to the total. That sum only checks the integration.
So 89.4 percent of the disturbance energy sits where the loop has to deal with it. The sharp-edged gust was therefore not a bad approximation and not a conservative one. It was very nearly the right answer, and this article can now say that instead of apologising for it.
Can a Human Close It
\[\frac{t_d}{\tau} = \frac{1}{\tau} \sqrt{\frac{2 \delta}{\alpha}} \tag{49}\]Taking a reaction time of a quarter of a second and a datalink round trip of a tenth, both assumed rather than measured, the budget is 0.35 seconds against a drift time of 0.99 seconds. The margin is 2.82, uncomfortable and far from decisive.
Comparing a delay to a drift time is the wrong comparison anyway, and the right one is tighter. A latency is not a reaction that either happens in time or does not. It is a phase lag that grows in proportion to frequency, and a loop that must keep any phase margin at all therefore cannot cross over above a frequency the latency fixes.
\[\arg \mathrm{e}^{- \mathrm{j} \omega \tau} = - \omega \tau \qquad \Longrightarrow \qquad \omega_c \leq \frac{\pi / 2 - \phi_m}{\tau} \tag{50}\]| Phase margin | Crossover a 0.35 second loop allows |
|---|---|
| 30 degrees | 0.476 hertz |
| 45 degrees | 0.357 hertz |
| 60 degrees | 0.238 hertz |
At forty-five degrees of margin the ceiling is 0.357 hertz against the 0.228 hertz the hold requires, a factor of 1.56. At sixty degrees, the margin anyone would want for a task where an overshoot means a collision, the ceiling is 0.238 hertz and the margin is gone entirely. Removing the datalink and leaving only a quarter-second human reaction raises the forty-five degree ceiling to 0.5 hertz, still inside a factor of about two.
This accounting does not prove that a human cannot close the loop, and the article does not claim that it does. It establishes that the margin is between one and two, against the three the drift time suggested, that it vanishes at a phase margin anyone would specify, and that there is nothing left over for an operator who must also acquire the target, judge closure and share attention with a formation of other vehicles.
The stronger argument is in the subsection that follows, The Loop Bandwidth Sits Between Two Cable Modes, and it is about the target rather than the operator.
The Loop Bandwidth Sits Between Two Cable Modes
A position hold that must keep the vehicle inside the window against a steady acceleration needs a loop fast enough that the steady-state offset fits [Stevens and Lewis, Aircraft control and simulation] [Beard and McLain, Small unmanned aircraft].
\[\omega_n \;\geq\; \sqrt{\frac{\alpha}{\delta}} \tag{51}\]For the six inch window that is 0.228 hertz, and for the twelve inch window 0.161 hertz. The cable’s first three transverse modes lie at 0.176, 0.352 and 0.529 hertz.
The required loop bandwidth is 1.3 times the fundamental of the cable it has to dock with, and 0.65 times the first overtone. The crossover sits between two of those modes.
That proximity has a computable consequence, and it is not the obvious one. The natural thing to say is that a loop whose crossover sits near a mode of its target drives that mode. Computing it shows that whether it does depends entirely on an architectural choice the public record does not report, so this article does not say it.
A feedback loop has exactly two transfer functions of interest and they sum to one. The sensitivity carries a disturbance through to the tracking error and the complementary sensitivity carries a command through to the output, and no design can make both small at the same frequency because their sum is fixed.
\[\mathcal{S} = \frac{1}{1 + \mathcal{L}} , \qquad \mathcal{T} = \frac{\mathcal{L}}{1 + \mathcal{L}} , \qquad \mathcal{S} + \mathcal{T} = 1 \tag{52}\]That a loop cannot reject a disturbance at every frequency is not a rule of thumb. It is an identity. For a stable loop whose transfer function falls off by at least two orders, the integral of the logarithm of the sensitivity magnitude over all frequencies is exactly zero, so attenuation bought below the crossover is paid for with amplification above it.
\[\int_0^\infty \ln \left| \mathcal{S} \left( \mathrm{j} \omega \right) \right| \mathrm{d} \omega = 0 \tag{53}\]But a second-order position loop has two standard forms. Putting the damping term in the forward path leaves a zero in the closed-loop transfer. Putting it in a minor feedback loop around the plant does not.
\[\mathcal{S}_{\mathrm{f}} = \frac{\left( \mathrm{j} \omega \right)^2}{\left( \mathrm{j} \omega \right)^2 + 2 \zeta \omega_n \mathrm{j} \omega + \omega_n^2} , \qquad \mathcal{S}_{\mathrm{m}} = \frac{\mathrm{j} \omega \left( \mathrm{j} \omega + 2 \zeta \omega_n \right)}{\left( \mathrm{j} \omega \right)^2 + 2 \zeta \omega_n \mathrm{j} \omega + \omega_n^2} \tag{54}\]That difference looks like a convention and is not. It is a difference of relative degree, and the integral above exposes it. The minor-loop form has an open loop that falls off by two orders, so its integral is zero and the amplification is compulsory. The forward-path form falls off by only one, so the integral is finite and negative and the loop is free to sit below unity everywhere.
| Upper limit of the integral | Minor loop | Forward path |
|---|---|---|
| 100 radians per second | -0.0205 | -3.155 |
| 200 radians per second | -0.0101 | -3.154 |
| 400 radians per second | -0.0048 | -3.154 |
The convergence is the evidence rather than either value. The minor-loop residual halves each time the limit doubles, as a quantity going to zero does. The forward-path integral does not move at all, and it agrees with the closed form that a relative degree of one predicts, namely minus half pi times the high-frequency loop gain, or -3.155.
So the architecture that escapes the amplification pays for it somewhere else, and the somewhere is high-frequency noise. A loop that rolls off by only one order passes sensor noise through where a steeper one does not. At a hundred times the natural frequency the forward-path form passes 0.0140 of what its sensor reports against 0.0001 for the minor loop, a factor of 140.
That turns the choice from an arbitrary convention into a trade, and a designer docking one aeroplane with another would have to make it. The article still does not know which way it was made.
| Cable mode | Frequency | Damping in the forward path | Damping in a minor loop |
|---|---|---|---|
| First | 0.176 hertz | 0.52 | 1.07 |
| Second | 0.352 hertz | 0.93 | 1.25 |
| Third | 0.529 hertz | 0.99 | 1.15 |
| Peak over all frequencies | 0.99 | 1.28 |
One architecture amplifies the target’s motion at all three modes and the other does not amplify anywhere. The article does not know which the vehicle used and therefore does not claim that the loop drove the cable.
What survives both readings is enough. Rejecting a disturbance requires a sensitivity well below one, and the most favourable value either architecture reaches at any of the three modes is 0.52. At the second and third modes it is above nine tenths on both. So the loop does not filter the swing out on any reading. It follows it, and the only question the record leaves open is whether it also makes it worse.
That, rather than the operator’s reaction time, is why the docking device has its own attitude control and why the apparatus is called a system rather than a hook. The programme’s name for the vehicle’s half of it is the Gremlins Autonomous Docking System [Dynetics], and the word in the middle is doing the work. The nearest operational art is aerial refuelling [Aerial refueling], where a receiver aircraft flies a probe into a drogue on the end of a hose.
Two caveats are owed here and neither is small. The taut-string frequencies assume a uniform cable at a uniform tension, and the real cable’s tension varies along its length and its ends are not simply supported. And the bandwidth relation is a first-order statement about a position loop and not a design. What survives both is the ordering. The two frequencies are in the same decade rather than separated by one, and no refinement of either estimate moves them apart.
Dependent Systems
The recovery apparatus is a roll-on and roll-off installation carried in the C-130’s cargo compartment, and the public description of it is unusually complete for a programme this recent. It comprises the stabilised towed docking device, an all-electric retrieval arm assembly, a mission control console from which a single operator can control up to four X-61As, and the ability to stow four recovered vehicles in flight. Installation and check-out takes under four hours and removal about two [Leidos].
The roll-on and roll-off property sums up the architecture in one phrase. It means the recovery aircraft is not a recovery aircraft but a transport with a pallet in it, and any C-130 can become one and stop being one inside a working day. That differs sharply from the X-47B landing on a carrier, which requires the carrier, or from the parasite fighter programmes of the nineteen fifties, which required a bomber modified to carry a trapeze and nothing else.
The vehicle’s own dependent systems are what any small jet needs and one thing more. The Kratos account of the first free flight lists the objectives, and they are a useful inventory of what has to work before a docking can even be attempted, being a successful launch from the C-130, a rate capture, wing deployment, a cold engine start, transition to stable powered flight, command and control through air and ground links with handover between them, deployment of the docking arm, and flight termination with recovery by parachute [Kratos].
Two of those deserve a pause. A rate capture is the arrest of the tumbling that release from a moving aeroplane imparts, and it has to finish before the wings can be let out. A cold engine start is an air start of a turbofan that has never run on this sortie, at altitude, on a vehicle that is falling, and the mission depends on it happening within seconds. Neither is novel and both are unforgiving.
What the free stream contributes to that start is computable and it is not much. Bringing the flow to rest at the inlet raises the pressure and the temperature by the isentropic total-to-static ratios, which depend on the Mach number and on nothing else.
\[\frac{\Theta_t}{\Theta} = 1 + \tfrac{1}{2} \left( \gamma - 1 \right) M^2 , \qquad \frac{p_t}{p} = \left( \frac{\Theta_t}{\Theta} \right)^{\gamma / \left( \gamma - 1 \right)} \tag{55}\]| Mach number | Total to static pressure | Total to static temperature |
|---|---|---|
| 0.3 | 1.064 | 1.018 |
| 0.6 | 1.276 | 1.072 |
| 0.8 | 1.524 | 1.128 |
At the release Mach number the free stream gives a pressure ratio of about 1.064, a long way from what a compressor needs to light a combustor. The start is therefore a starter’s problem rather than a ram problem, and the vehicle carries whatever it needs to do it. This shows what is unavailable and leaves open what is available, and the public record does not say how the engine was turned.
The Flight Test Record
Unlike the X-60A, this one flew. The X-60A’s flight test record is an account of a silence. This one has four test series, nine sorties and eighteen hours, and the record is detailed enough to add up.
| Series | Flew | Announced | Vehicles | Sorties | Hours | Docking attempts | Outcome |
|---|---|---|---|---|---|---|---|
| First | 23 November 2019 | 17 January 2020 | 1 | 1 | 1.68 | 0 | free flight of one hour and forty-one minutes, vehicle lost |
| Second | July 2020 | 26 August 2020 | 1 | 1 | 2.20 | 0 | formation to 125 feet, docking deliberately not attempted |
| Third | November 2020 | 21 January 2021 | 3 | 3 | 7.00 | 9 | nine attempts, every one within inches, none captured |
| Fourth | October 2021 | 15 November 2021 | 3 | 4 | 6.70 | not stated | one airborne recovery on 29 October, one vehicle lost |
What the Parts Add Up To
Dynetics states that it built 5 X-61As and flew 9 sorties totalling 18 hours, with 3 of the original five available for future activity [Leidos]. Those are programme-wide statements. The table above is assembled from four separate releases about its parts. The two are independent and they can be added up.
The sorties in the four series sum to 9 against a stated 9, an exact agreement. Five built less 2 lost is 3 remaining, and that agrees too. The hours sum to 17.58 against a stated 18, a gap of 0.42 hours and inside the rounding of the figures the releases print. Three reassembly checks, three agreements, and together they carry more weight than any one of the four releases taken alone.
\[1 + 1 + 3 + 4 = 9\ \text{sorties} , \qquad 5 - 2 = 3\ \text{vehicles} , \qquad 1.68 + 2.20 + 7.00 + 6.70 = 17.58\ \text{h} \tag{56}\]The First Flight Was Not When Everyone Says It Was
The date almost universally given for the X-61A’s first free flight is 17 January 2020, the date of the announcement. The Kratos release of 23 January 2020 states that on 17 January the agency and the prime contractor announced the successful first flight of the X-61A Gremlins Air Vehicle was completed on November 23, 2019 [Kratos]. The specialist directory and the general encyclopaedia both give 17 January 2020 as the flight date [Directory of U.S. Military Rockets and Missiles] [Dynetics X-61 Gremlins].
This article follows the contemporaneous release from a participant over two later compilations, and reports that it is doing so. The gap is fifty-five days.
The First Series Lost Its Vehicle
The free flight lasted one hour and forty-one minutes. The main parachute failed to deploy during the recovery and the aircraft was lost [Dynetics X-61 Gremlins]. The Kratos release lists parachute recovery among the flight objectives and notes that it is part of the demonstration system only and not of the operational one [Kratos].
Plainly put, the programme lost its first vehicle to a system that was not part of what it was building. The parachute exists so that a vehicle which fails to dock can be got back. Its failure cost twenty percent of the fleet on the first sortie.
Nine Attempts Within Inches
The second series flew in July 2020 and included the first rendezvous and close formation with the recovery aircraft, together with captive tests in which actively controlled vehicles were attached to the towed docking device and reeled in [Dynetics]. The team decided during the mission to stop short of docking, which the chief engineer states explicitly.
The third series flew in November 2020, three vehicles over three flights and seven hours, and made the programme’s first ever aerial docking attempts, nine in total, with each attempt coming within inches of capture [Military Embedded Systems]. All three vehicles were recovered on the ground by parachute.
The fourth series flew in October 2021. Three vehicles flew four sorties for 6.7 hours, a mean of 1.68 hours each, including a 1.4 hour airborne recovery mission, and on 29 October, at Dugway Proving Ground in Utah [Dugway Proving Ground], one vehicle was recovered in the air [Leidos] [DARPA] [Carter, Keeter and Calhoun]. One vehicle was destroyed during the flight tests, which the agency states in one sentence and the contractor attributes to a power fault whose root cause was identified and corrected [DARPA] [Leidos].
The public record gives at least 10 docking attempts and exactly one capture. The fourth series does not say how many attempts it made, so the true denominator is at least ten and the true success rate is therefore at most 10 percent. That is a bound and not a measurement, and the article states it as one. Nine attempts in the third series and at least the one that succeeded in the fourth give the denominator.
\[N_d \;\geq\; 9 + 1 = 10 \quad \Longrightarrow \quad \frac{1}{N_d} \;\leq\; 0.10 \tag{57}\]The Contract Outlived the Flying by Four Years and Stopped Paying After Forty-Seven Days
The previous article in this series found a programme whose publicity stopped three years before its contract did, and which went on obligating money after it had stopped being visible. This one is checked the same way and the answer is different.
The last positive obligation on the Gremlins contracts is 15 December 2021, 47 days after the airborne recovery. Everything after it is a zero-dollar administrative modification. Only 2,662,549.21 dollars, 3.22 percent of the total, was obligated after the last flight test. The sum comprises two positive modifications to the Phase 3 contract, of 2,497,155.40 dollars on 12 November 2021 and 165,393.81 dollars on 15 December 2021 [DARPA Phase III contract]. Counting the 2 days left in October, the 30 of November and 15 in December gives the interval, and the share is taken against the three contracts’ total.
\[2 + 30 + 15 = 47\ \text{days} , \qquad \frac{2{,}497{,}155.40 + 165{,}393.81}{82{,}680{,}983.37} = \frac{2{,}662{,}549.21}{82{,}680{,}983.37} = 0.0322 \tag{58}\]The period of performance is another matter. The Phase 3 contract runs to 31 October 2025 [DARPA Phase III contract], 1,463 days or 4.01 years after the recovery. Four years from 29 October 2021 include the leap day of February 2024, and two more days reach the end of the period. So the contract stayed open for four years after it stopped spending, carried by modifications that move no money at all.
\[4 \times 365 + 1 + 2 = 1{,}463\ \text{days} , \qquad \frac{1{,}463\ \text{days}}{365.25\ \text{days per year}} = 4.01\ \text{years} \tag{59}\]The shape is the opposite of the X-60A’s, and the contrast is instructive. That programme obligated 30.1 percent of its money after it stopped being publicly visible, and its last positive line paid to ship equipment. This one stopped paying almost immediately and stayed open anyway. A contract that is open and unfunded is a different object from one that is quietly spending, and the two programmes are one of each.
Two Sources on the Turnaround
The agency’s standing description of the concept is that after air retrieval the vehicles can be refurbished by ground crews within 24 hours [DARPA]. Describing the fourth series, the agency writes that the team refurbished a vehicle and conducted a second flight within 24 working-hours [DARPA]. The contractor writes that the quick-turn refurbishment took approximately 24 hours to complete [Leidos].
Twenty-four working hours and twenty-four hours are not the same quantity. At an eight hour working day the first is three days. The two organisations describing the same event in the same month use the two phrasings, and this article does not resolve which is meant. It notes that the concept’s requirement is stated in the shorter unit and that the demonstration is reported by one participant in the longer one.
What the Programme Was Asked For and What It Delivered
The Phase 3 demonstration objectives included a final flight test to demonstrate the ability to recover 4 GAVs in under 30 minutes [Kratos]. GAV is the contractor’s abbreviation for Gremlins Air Vehicle, so the objective is one vehicle every 7.5 minutes. The achieved recovery came inside the 1.4 hour airborne recovery mission of the fourth series [Leidos], 84 minutes long, so the comparison is a quotient of two intervals.
\[\frac{30\ \text{min}}{4} = 7.5\ \text{min} , \qquad 1.4\ \text{h} \times 60\ \text{min per hour} = 84\ \text{min} , \qquad \frac{84\ \text{min}}{7.5\ \text{min}} = 11.2 \tag{60}\]The recovery that was achieved occurred inside a mission of 84 minutes that recovered one vehicle. The ratio is 11.2, and the article notes at once that the flight was not an attempt at the rate. The mission was an attempt to capture one vehicle once, the prerequisite, and it succeeded. The number measures the distance between the prerequisite and the objective, and the programme stopped with that distance still to cover.
And there was a schedule, stated before the programme existed. The 2014 Request for Information asked for plans reaching a full-system flight demonstration within four years [DARPA Request for Information]. The first free flight came at 1.26 times that and the recovery at 1.74 times. A programme that ran to 1.74 times a plan stated seven years earlier is not a scandal, and the article notes it because the record rarely contains a duration that can be checked at all.
The second objective is the reuse. A design life of 20 uses is a claim about reliability, and demonstrating it requires flying one airframe twenty times.
| Quantity | Value |
|---|---|
| Sorties flown by the whole fleet | 9 |
| Sorties needed on one airframe to demonstrate the life | 20 |
| Fleet sorties as a fraction of one life test | 45 percent |
| Mean sorties per airframe built | 1.8 |
| That as a fraction of the required life | 9 percent |
The entire programme flew 45 percent of the sorties that one life test would have needed, spread across five airframes. The twenty-use requirement was never approached and could not have been. No criticism of the programme is intended, since it was a capture demonstration and not a reliability demonstration. The point bears on what the record can and cannot support, and the economics in What the Economics Required depend on a life nobody demonstrated.
A Life Requirement Saturates Against Attrition
An airframe with a design life of twenty uses does not deliver twenty sorties. It delivers however many it survives, and if it can be lost on any sortie with some probability then the expected number is a geometric sum rather than the life itself.
\[P_N = \left( 1 - \epsilon \right)^N \tag{61}\] \[\bar{n} = \sum_{k=1}^{N} \left( 1 - \epsilon \right)^{k-1} = \frac{1 - \left( 1 - \epsilon \right)^N}{\epsilon} \tag{62}\]And that sum has a ceiling the design life cannot pass. As the life grows without bound the expected sorties approach the reciprocal of the loss rate and stop, so beyond a certain point specifying a longer life gains nothing.
\[\lim_{N \to \infty} \bar{n} = \frac{1}{\epsilon} \tag{63}\]| Loss rate per sortie | Sorties a twenty-use airframe delivers | The ceiling at any life | Airframe cost per sortie |
|---|---|---|---|
| 0.5 percent | 19.08 | 200 | 36,692 dollars |
| 1 percent | 18.21 | 100 | 38,442 dollars |
| 5 percent | 12.83 | 20 | 54,558 dollars |
| 22.2 percent, the development rate | 4.47 | 4.5 | 156,583 dollars |
At five percent per sortie the ceiling is exactly twenty, the design life. So a twenty-use requirement is only a meaningful specification if the loss rate is well below five percent, and above that it is asking for something attrition will not permit however good the airframe is. Inverting for the rate at which the requirement delivers only half of what it promises gives 8.19 percent.
Here the article’s two halves turn out to be one relation. The reliability question and the economics question are the same question asked twice, because the number that decides how much the reuse is worth is not the design life but the expected sorties, and the expected sorties are set by attrition once attrition is anything but small.
The same computation lies behind the claim about fleet size made in What the Economics Required.
\[n_a = \frac{n_r}{\bar{n}} , \qquad \frac{C}{\bar{n}} \text{, and a sortie really carries } C / \bar{n} \tag{64}\]A campaign of one hundred sorties needs 100 airframes if each is expendable, 5.49 if each has a twenty-use life at a one percent loss rate, and 22.4 at the rate the development programme showed. The ratio between the last two is 4.07, the cost in airframes bought, stored and carried of a reliability that nobody measured. The development rate is not a prediction and the article has already said so. It is the only rate the record contains.
What the Economics Required
\[\frac{C}{N} + C_r + \frac{C_s}{n_s} \;<\; C_e \tag{65}\]The reusable architecture pays when the amortised airframe, plus whatever a refurbishment costs, plus that sortie’s share of the recovery aircraft, comes to less than the expendable vehicle it replaces. Three of those four terms are not public. The one that is gives a floor that owes nothing to the others.
\[C_e \;>\; \frac{C}{N} \qquad \text{whatever } C_r \text{ and } C_s \text{ may be} \tag{66}\]| Uses achieved | Airframe cost per sortie |
|---|---|
| 2 | 350,000 dollars |
| 5 | 140,000 dollars |
| 10 | 70,000 dollars |
| 20, the requirement | 35,000 dollars |
| 40 | 17,500 dollars |
The floor at the required life is 35,000 dollars, a twentieth of the 700,000 dollar cap. The architecture therefore has an enormous nominal margin, and the interesting consequence runs the other way. Even two uses cuts the airframe cost per sortie in half, and even five brings it to 140,000 dollars.
Inverting the inequality gives the break-even directly, without reading it off a table.
\[N^\star = \frac{C}{C_e - C_r - C_s / n_s} \tag{67}\]With refurbishment and the recovery sortie set to zero, the most favourable case for reuse and therefore a lower bound on the answer, the break-even is the flyaway cost divided by whatever the expendable costs.
| Expendable unit cost | Uses needed to match it |
|---|---|
| 100,000 dollars | 7 |
| 300,000 dollars | 2.33 |
| 1,000,000 dollars | 0.7 |
| 2,000,000 dollars | 0.35 |
So twenty uses was never the break-even and was not chosen as one. Against anything costing more than about a hundred thousand dollars the break-even is below seven, and against the AGM-86B, whose unit cost is given as one million dollars [AGM-86 ALCM], it is below one. What twenty gains is not the margin but the fleet size, because a force that must generate a given number of sorties needs proportionally fewer airframes as the life goes up, and the airframes are what have to be bought, stored and transported. The requirement is about logistics rather than about unit economics, which the published statements do not say and which the arithmetic makes hard to avoid.
Comparison With Ground Prediction
The control problem this programme solved had been formulated, modelled and simulated in the open literature a decade before the vehicle flew, under a different name and for micro air vehicles rather than for a vehicle of this size.
Between 2009 and 2011 a body of work appeared on what its authors called the aerial recovery of micro air vehicles, using a three-body system they named the mothership, the cable and the drogue. The papers cover the dynamics and control of the cable and drogue assembly [Liang Sun et al. 2009], motion planning for the three bodies together [Liang Sun et al. 2010], altitude stabilisation and state estimation of the towed body [Sun and Beard 2010], trajectory tracking of that body in wind [Liang Sun and Beard 2011], and the multi-vehicle dynamics of the whole arrangement [Colton et al. 2011]. Later work adds rendezvous guidance laws for exactly this geometry [Thakar and Ratnoo 2016] and anti-disturbance trajectory stabilisation for the towed recovery drogue [Su et al. 2021a]. The names match the hardware the programme built, component for component, and the keystone cluster under The Contemporary Literature holds the rest of that work.
Few cases of ground prediction are this clean, and the cleanliness is the point. The equations were written, the controllers were designed, and the simulations converged. What no amount of that could establish is whether the thing could be done in the air, and the record of nine attempts within inches is the answer to a question the analysis had already declared solved.
This article claims no causal link between that literature and the programme’s design. What Dynetics read is not on record. It does establish that the problem was a known problem with a known formulation, so the nine failed attempts speak to execution rather than to understanding.
The programme published its own account of the recovery in 2024, written by two of its engineers and by the agency programme manager who announced it [Carter, Keeter and Calhoun]. That paper is cited as a primary source and is not counted among the survey’s research records, because a programme’s technical account of its own demonstration is a different kind of source from the several thousand records around it.
And the ground prediction stopped at the gap between them. A simulation of a cable and a drogue carries whatever turbulence model its author selected, whatever cable discretisation the integrator could afford, and a sensor suite that reports the truth with added noise of a chosen spectrum. None of those is the thing that made the difference between inches and contact, and no published source identifies what did.
Aeroplanes Had Been Catching Things in Mid-Air Since 1960
Mid-air retrieval is not new and the aircraft type is not new either, though the two dates are different and the heading above takes the earlier one. On 19 August 1960 a C-119 snagged the parachute of the Discoverer 14 capsule 360 miles south-west of Honolulu, the first recovery of film from an orbiting satellite and the first mid-air recovery of an object returning from orbit [Discoverer 14] [Corona, the reconnaissance satellite programme]. The C-119 was replaced in 1961 by the JC-130B and supplemented in 1966 by the JC-130H [Mid-air retrieval]. So a C-130 catching something in mid-air over a test range was routine work six decades before the X-61A.
What changed is that the thing being caught was flying. That single difference inverts which half of the problem is hard, and it can be put in energy.
\[E = \tfrac{1}{2} m \, \Delta V^2 \tag{68}\]A Corona recovery capsule massed about 54.55 kilograms [Discoverer 13] and descended under its canopy at a few metres per second while the recovery aircraft flew past at a speed taken as 150 knots. The relative kinetic energy at the snatch is therefore roughly 165.1 kilojoules, essentially all of it the aircraft’s airspeed.
The X-61A arrives at its docking device having already matched speed with it.
| Engagement | Relative kinetic energy | Ratio to the X-61A at one metre per second |
|---|---|---|
| Corona canopy snatch, 1960 | 165.1 kilojoules | 486 |
| X-61A closing at 1 metre per second | 340 joules | 1 |
| X-61A closing at 3 metres per second | 3,060 joules |
An energy is not what a structure is designed to, though. A force is, and the force depends on how far the capture is allowed to take.
\[\bar{F} x_s = \tfrac{1}{2} m \, \Delta V^2 \qquad \Longrightarrow \qquad \frac{\bar{F}}{W} = \frac{\Delta V^2}{2 g \, x_s} \tag{69}\]| Engagement | Distance | Mean force | As a multiple of the captured weight |
|---|---|---|---|
| X-61A closing at 0.5 metres per second | 10 centimetres | 850 newtons | 0.13 |
| X-61A closing at 1 metre per second | 10 centimetres | 3,400 newtons | 0.51 |
| X-61A closing at 3 metres per second | 10 centimetres | 30,600 newtons | 4.59 |
| Corona snatch, 30 metres of line paid out | 30 metres | 5,505 newtons | 10.29 |
| Corona snatch, 100 metres paid out | 100 metres | 1,651 newtons | 3.09 |
| Corona snatch, 300 metres paid out | 300 metres | 550 newtons | 1.03 |
The comparison in force is much closer than the comparison in energy, and the force comparison is the fair one. The 1960 system spread a hundred and sixty-five kilojoules over a hundred metres of line and held the capsule to about 3.09 times its weight. The modern one has a few hundred joules and a stopping distance measured in centimetres, and at a metre per second it holds the vehicle to 0.51. What the energy ratio of 486 earns is not a gentler catch but a shorter one, and the 1960 winch is what the modern system does not need.
The difficulty moved from the hardware into the guidance, and the force table shows the move. At three metres per second the modern capture is 4.59 times the vehicle’s weight over ten centimetres, worse than the snatch. The gentleness comes entirely from arriving slowly, and arriving slowly is the guidance problem the previous sections spent their arithmetic on. The 1960 system needed a line, a winch and a brake that could absorb a hundred and sixty kilojoules without parting, and it needed almost nothing of the capsule, which was a passenger. The 2021 system needs almost nothing of the structure and everything of the vehicle, which must fly itself to a relative velocity near zero and hold a position to inches while it does.
Neither problem is easier. They are different problems wearing the same photograph.
The Parasite Aircraft Were a Third Thing Again
The nineteen forties and fifties produced several attempts at carrying and recovering an aeroplane in flight, and none of them is the same problem either. The XF-85 Goblin was to hook onto a trapeze lowered from a B-36 [McDonnell XF-85 Goblin], the Fighter Conveyor programme, abbreviated FICON, carried an RF-84K in a B-36’s bomb bay [FICON project], and the airships of the nineteen thirties carried aeroplanes on a trapeze and recovered them in flight [USS Akron].
Every one of those was flown by a pilot who was aboard the aeroplane being recovered. The FICON hookups were challenging for experienced test pilots in ideal conditions and difficult in combat or bad weather, several RF-84Ks were damaged attempting them, and the wingtip-towing project was cancelled when aerial refuelling promised a safer way of extending a fighter’s range [FICON project]. The X-61A’s contribution is not that the manoeuvre was done. It is that nobody was aboard, and the loop that closed it, which the arithmetic above puts at about a quarter of a hertz, was autonomous [Dynetics].
What the Data Changed
The programme moved exactly one thing from unknown to known, and it is a large thing. The agency’s release reports an airborne recovery of the vehicle to the C-130 [DARPA], the contractor calls it historic [Leidos], and the specialist directory records it as the first time an X-61A was retrieved in mid-air, after several unsuccessful attempts [Directory of U.S. Military Rockets and Missiles]. None of the three claims a first of its kind for uncrewed aircraft in general, and this article does not either, though nothing in a survey of 5,700 records describes an earlier one, and the third test series calling its nine attempts the programme’s first ever is consistent with it. The feasibility question is closed and the reliability question is untouched.
Three quantitative things follow from the record.
The tolerance is inches and that is now documented rather than inferred. Nine attempts that each came within inches establish both that the system could get that close repeatedly and that the last few inches were a different problem from the first hundred feet.
The refurbishment claim has one data point. One vehicle was turned round and flown again within either twenty-four hours or twenty-four working hours, depending on which participant is describing it. One instance of a twenty-fold reuse claim is not a demonstration of it and the article says so.
And the fleet attrition is measured even though it is not a measure of the design. Two of five airframes were lost in nine sorties, one to a parachute that is not part of the operational system and one to a power fault whose cause was found and fixed. The rate is 22.2 percent per sortie on a first-of-type development article, and quoting it as a property of the vehicle would be a mistake. It is quoted here because the twenty-use requirement is a reliability claim and this is the only reliability data the programme produced. Setting that rate into the expected-sorties relation of the section on attrition gives the figures the next paragraph uses.
\[\epsilon = \frac{2}{9} = 0.222 , \qquad \bar{n} = \frac{1 - \left( 7/9 \right)^{20}}{2/9} = 4.47 , \qquad \frac{\bar{n}}{N} = \frac{4.47}{20} = 0.224 \tag{70}\]The two halves of that sentence meet. A design life saturates against attrition, so a twenty-use requirement makes sense only if the loss rate is well below five percent per sortie. At the rate the development programme showed, a twenty-use airframe delivers 4.47 sorties, 22.4 percent of what the requirement asks for. Nobody claims that rate is what a mature system would show, and this article does not either. The record does show that the requirement and the only measured rate are on opposite sides of the point where the requirement stops meaning anything.
A fourth thing follows from the contract rather than from the flying. The money stopped 47 days after the recovery and the period of performance ran on for another 1,463 days without it. A programme that stops paying and stays open has decided something, even if no document records the decision, and the previous article in this series found a programme that did the reverse.
The Contemporary Literature
| Cluster | Records |
|---|---|
| Catching it, which is the whole of the problem | 119 |
| The towed body it has to dock with, and the cable that holds it | 484 |
| The wake between the two aeroplanes | 783 |
| Relative navigation, station keeping and the dock itself | 609 |
| Getting it off the aeroplane, which is where the sortie starts | 376 |
| The vehicle, the programme and the vehicles it is measured against | 35 |
| The parachute, which is how it comes down when it is not caught | 489 |
| Volleys, and the operator who cannot watch all of them | 335 |
| The engine, and starting it in the air | 125 |
| An airframe designed for a life measured in sorties | 156 |
| What it costs, which is the programme’s stated reason for existing | 170 |
| Flying it, and the autonomy that flies it | 835 |
| Measuring a flight test of an uncrewed aircraft | 340 |
| Designing, sizing and powering a small uncrewed aircraft | 159 |
| Uncrewed aircraft programmes, standards and airspace | 30 |
| Lift, induced drag and the drag polar | 243 |
| Transonic flow and the drag rise | 133 |
| Aircraft performance, range and conceptual design | 75 |
| Missile and bomb aerodynamics | 70 |
| Stability, handling qualities and flight simulation | 77 |
| Wind tunnels and their correlation with flight | 47 |
| The standard atmosphere | 10 |
| Total | 5,700 |
The survey behind this article holds 5,700 research records, drawn from the Crossref registry and from the two agency report servers. 886 of them, 15.5 percent, are report primaries, by the identifier rule set out under The Definition of Primary. 5,484 records carry a usable year, running from 1930 to 2026 with a median of 2011. 4,446 of those, 81.1 percent, predate or share the year of the programme’s last flight test series.
Every research record in the survey is cited below, each in the one cluster its title belongs to. The clusters run from the capture itself outward, through the hardware and the flying around it, to the aerodynamics and the atmosphere the sizing arithmetic uses.
Catching it, which is the whole of the problem
The keystone. Mid-air retrieval of payloads descending under parachutes, aerial recovery of uncrewed aircraft by a carrier, net, ship and ground capture, and launch and recovery systems for remotely piloted vehicles. 18 titles name mid-air retrieval and 8 of them predate 2000, while 22 name aerial recovery or the mothership and cable-drogue system and 21 of those date from 2009 or later, which is the shape Comparison With Ground Prediction describes.
119 records. [Aerial-Pickup System 1949] [Meisinger et al. 1954] [Downing et al. 1956] [In-Flight Refuelling 1961] [Parachute Recovery System 1966] [Ryan 1966] [Highley 1970] [Everett 1973] [Higgins and Speelman 1973] [McNeill et al. 1973] [Eckstrom 1975b] [Eckstrom 1975a] [Young 1976] [Wolkovitch and Brassell 1978] [Baumgartner et al. 1979] [Hardy and Sturgeon 1979] [Delurgio et al. 1981] [Everett and Henke 1981] [Bush et al. 1984] [H H Aerospace Design CO INC Bedford MA 1987] [Hintzke and Haggard 1991] [Just 1991] [Catch a Falling Star 1993] [Long 1993] [Chamitoff 1994] [Chamitoff 1995] [UAVs 1999] [Brown et al. 2001] [Wyllie 2001] [Sarigul-Klijn and Sarigul-Klijn 2003] [Mullens et al. 2004] [Jorgensen et al. 2005] [Lee et al. 2005b] [Vassberg et al. 2005] [Theiss 2007] [Galway 2008] [Gravlee et al. 2008] [Antonenko and Belavskiy 2009] [Liang Sun et al. 2009] [Carlson and Colton 2010] [Kahn 2010b] [Launch and Recovery 2010] [Liang Sun et al. 2010] [Sun and Beard 2010] [Yoon et al. 2010] [Colton et al. 2011] [Liang Sun and Beard 2011] [Launch and Recovery 2012] [Du 2013] [Launch and Recovery 2014] [Zhang Dejin et al. 2015] [Kelly et al. 2016] [Klausen et al. 2016] [” et al. 2016] [Thakar and Ratnoo 2016] [Sadraey 2017b] [Hara and Yokoo 2018] [Kelly et al. 2018] [Shankar et al. 2018] [Zhao et al. 2019a] [Chakravarthy and Ghose 2020] [Launch and Recovery Systems 2020] [Liu et al. 2020b] [Nakamura et al. 2020] [Rocha and Robinson 2020] [Gryte et al. 2021] [Liu et al. 2021b] [Su et al. 2021a] [Zhao et al. 2021c] [Shi et al. 2022b] [Su et al. 2022] [Wang et al. 2022b] [Joshi et al. 2023] [Kumar et al. 2023b] [Su et al. 2023] [Zhao et al. 2023b] [Allard 2024] [Esfahani and Velni 2024] [Shoukun et al. 2024] [Oliveira and Guerreiro 2024] [Prkačin et al. 2024] [Sadraey 2024] [Sollie et al. 2024] [Wu et al. 2024f] [Wu et al. 2024a] [Wu et al. 2024d] [Chen 2025a] [Hops and Sprenger 2025] [Li et al. 2025f] [Liu et al. 2025g] [Mahajan et al. 2025] [Xing et al. 2025] [Zhu et al. 2025a] [Guo et al. 2026] [Zhang et al. 2026a] [Zhu et al. 2026] [McPhee] [Ships and marine technology] [Singh et al] [Henke and Jeppesen 1973] [Lloyd et al. 1978] [Wick et al. 2007] [Ke et al. 2014] [Zheng et al. 2017] [Meng et al. 2018] [Garcia et al. 2020] [Alijani and Osman 2021] [Sollie and Johansen 2021] [Stuhne et al. 2023] [Martin et al. 2024] [Rothe et al. 2026] [Tullu and Jung 2026] [Yan et al. 2026] [Giroux] [Tan] [Wick] [Cook 1964b] [Lee and Davidson 1973] [Yang et al. 2025c]
The towed body it has to dock with, and the cable that holds it
The towed body and its cable, in air and in water. Towed-body and cable statics and dynamics, towed targets and decoys, the refuelling hose and drogue, and the vortex-induced vibration of circular cylinders, which is the crossflow motion of a cable segment. 147 titles are on vortex-induced vibration and 85 on the refuelling hose and drogue, so the cluster is as much about a cylinder in crossflow as about a body on a string.
484 records. [Thews and Landweber 1936] [Phillips 1942] [Pode 1948] [Ringleb 1956] [Ellsworth and United States. 1960] [Ellsworth and Gay 1961] [Towed Target Systems 1961] [Gay et al. 1962] [Pepper and Streich 1962] [Lehn 1963] [Brayton 1966] [Gibbons and Walton 1966] [Patton and Schram 1966] [Laitinen 1967] [Patten and Olive 1967] [Jeffrey 1968] [Paidoussis 1968] [DiLorenzo 1969] [Huang 1969] [Pao 1970a] [Pao 1970b] [Choc and Casarell 1971] [Skop and Choo 1971] [Young Chey 1971] [Cannon and Genin 1972b] [Cannon and Genin 1972a] [Hansen and Crist 1972] [Poli and Cromack 1972] [Burrows 1975] [Ketchman and Lou 1975] [Russell and Anderson 1976] [Simonenko 1976] [Ward-Whate 1976] [MATASS 1977] [Rispin 1977] [Russell and Anderson 1977] [Chuan Lee 1978] [Wingham and Keshavan 1978] [Goodman and Valentine 1979] [Leonard 1979] [Mosolov and Tikhonov 1979] [Tamura 1979] [Baroff 1980] [Mosolov and Tikhonov 1980] [Kennedy 1981] [Rispin and Diggs 1981] [Chapman 1982] [Nagabhushan and Cliff 1982] [Ablow and Schechter 1983] [Chapman 1984] [Bettles and Chapman 1985] [Laura 1985] [Yamakita 1985] [Milinazzo et al. 1987] [Shiau and Yang 1987] [Cohen and Manor 1988] [Delmer et al. 1988] [McGowan and MacCulloch 1988] [Rainey 1989] [Tsuboi et al. 1989] [Kang and Latorre 1991] [Papoulias 1991] [Suzuki et al. 1991] [Trajectory and Attitude Control 1991] [Doty 1992] [Nakagawa and Obata 1992] [Wilson et al. 1992] [Baz and Kim 1993] [Kawai 1993] [Ruffa and Toplosky 1993] [Salsbery and Hartsough 1993] [Lin and Chu 1994] [Ockels et al. 1994] [Bourmistrov et al. 1995] [Kamman et al. 1995] [Leech and Tabarrok 1995] [Kishore and Ganapathy 1996] [Murray 1996] [Canbolat et al. 1997] [Khalak and Williamson 1997] [Woods Hole Oceanographic Institution Ma 1997] [Christensen and Roberts 1998] [Drag Device for Providing 1998] [Etkin 1998] [Srivastava and Ganapathy 1998] [Zhu and Rahn 1998] [Huang 1999] [Kamman and Huston 1999] [Chin et al. 2000] [Gutman 2000] [Wu and Chwang 2000] [Bezverkhii et al. 2001] [Norris and Andrisani 2001] [Sakai et al. 2001] [Bloy and Khan 2002] [Cipolla et al. 2002] [Lague¨ and Laneville 2002] [Nakano et al. 2002] [Park and Jung 2002] [Hashimoto et al. 2003] [Kawamoto and Yoshida 2003] [Park et al. 2003] [Turkyilmaz and Egeland 2003] [Wanderley and Levi 2003] [Wang et al. 2003] [Zhu et al. 2003] [Govardhan and Williamson 2004] [Guilmineau 2004] [Kokubun and Wada 2004] [Nguyen and Egeland 2004a] [Nguyen and Egeland 2004b] [Tu Due Nguyen and Egeland 2004] [Aritomi et al. 2005] [Grosenbaugh 2005] [Tandale et al. 2005] [Williams and Trivailo 2005b] [Williams and Trivailo 2005a] [Williams et al. 2005a] [Bondaryk 2006] [Cheng et al. 2006] [Nguyen and Egeland 2006] [Roberto Mati 2006] [Sgarioto et al. 2006] [Tandale et al. 2006] [Wang et al. 2006b] [Williams 2006a] [Williams 2006b] [Williams and Trivailo 2006b] [Williams and Trivailo 2006a] [Williams et al. 2006b] [Williams et al. 2006a] [Wu and Jin 2006] [Wu and Xiong 2006] [Grosenbaugh 2007] [Pan et al. 2007] [Sgarioto 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1967] [Israel 1982] [Abou-Hanna et al. 1988] [de Matteis 1993] [Cicolani et al. 2010] [Dhiman et al. 2022] [Franchi and Gabellieri 2026]
The wake between the two aeroplanes
The wake the vehicle flies through. Trailing vortices, their roll-up, descent and decay, wake encounters and wake separation, formation flight in a wake, and the propeller slipstream of a transport such as the C-130. 222 titles name formation flight and 80 the propeller slipstream.
783 records. 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[Johari and Moreira 1998] [Kantha 1998] [Kuznetsov and Vyshinsky 1998] [Lin et al. 1998] [Mikhailov 1998] [Proctor 1998] [Rossow et al. 1998] [Stasenko and Vyshinsky 1998] [Stewart 1998] [Vicroy et al. 1998] [Brockman et al. 1999] [Burnham 1999] [Carrier Phase Differential GPS/INS 1999] [Chapman et al. 1999b] [Chapman et al. 1999a] [Han et al. 1999] [Jacob 1999] [Myatt and Blake 1999] [Olsen et al. 1999] [Proud et al. 1999] [Rennich and Lele 1999] [Rokhsaz et al. 1999] [Smith 1999] [Wallin and Girimaji 1999] [Autonomous Formation Flight 2000] [Blake 2000] [Elsaadawy and Britcher 2000] [Gramling et al. 2000] [Hamilton and Proctor 2000] [Han et al. 2000a] [Han et al. 2000b] [Pete et al. 2000] [Proctor et al. 2000] [Roberts et al. 2000] [Rokhsaz et al. 2000] [Rossow and James 2000] [Rubin et al. 2000] [Schumacher and Rajeeva Kumar 2000] [Schumacher and Singh 2000] [Sousa and Pereira 2000] [Zheng and Lim 2000] [de Bruin 2000] [Benkenida et al. 2001] [Folta et al. 2001] [Folta and Hawkins 2001] [Gingras and Blake 2001] [Huenecke 2001] [Hünecke 2001] [Jacques et al. 2001] [Likhachev 2001] [Murray and Marsden 2001] [Nelson and Jumper 2001] [Roberts 2001a] [Ryan et al. 2001] [Sarpkaya et al. 2001] [Blake 2002] [Burnham et al. 2002] [Cobleigh 2002] [Hanson et al. 2002b] [Elsaadawy and Britcher 2002a] [Elsaadawy and Britcher 2002b] [Folta et al. 2002b] [Folta et al. 2002a] [Giulietti et al. 2002] [Graham 2002] [Guibout and Scheeres 2002] [Hansen and Cobleigh 2002] [Hansen et al. 2002] [Hanson et al. 2002a] [Huenecke 2002] [Keller et al. 2002b] [Lavretsky 2002] [Long et al. 2002] [Minkel 2002] [Petersen et al. 2002] [Ray et al. 2002] [Rokhsaz et al. 2002] [Rossow 2002a] [Rossow 2002b] [Stumpf 2002] [Switzer and Proctor 2002] [Vachon et al. 2002] [Wagner et al. 2002] [Yaras 2002] [Anderson and Lawton 2003] [Appendix C 2003] [Delisi et al. 2003] [Elsaadawy and Britcher 2003] [Gill et al. 2003] [Hanson 2003] [Holzäpfel 2003] [Holzäpfel and Robins 2003] [Kliment and Rokhsaz 2003] 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Relative navigation, station keeping and the dock itself
Finding the dock and holding station on it. Relative navigation by vision and by differential satellite positioning, rendezvous and docking of aircraft, spacecraft and underwater vehicles, and the guidance of aerial refuelling. 245 titles name aerial refuelling and 112 name a spacecraft, a satellite or an orbit, because the docking problem is published far more for refuelling and for spacecraft than for recovery.
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[Zhang et al. 2023b] [Zhang et al. 2023c] [Zhao and Qu 2023] [Aborizk and Fitz-Coy 2024] [Astermark et al. 2024] [Chihabi and Ulrich 2024] [Das and Giri 2024] [Dinesh et al. 2024] [Dohi and Higashi 2024] [Du et al. 2024] [Fear and Lightsey 2024] [Fidan and Mostafa 2024] [Gao et al. 2024] [Jayarathne et al. 2024] [Lei 2024] [Liao et al. 2024] [Martinez et al. 2024] [Morell et al. 2024] [Raj et al. 2024] [Sahoo and Sinha 2024] [Shoop et al. 2024] [Singh et al. 2024] [Smith et al. 2024] [Sun et al. 2024b] [Wang and Cheng 2024] [Wang et al. 2024a] [Worth et al. 2024] [Wu et al. 2024e] [Zhao et al. 2024b] [Angeletti 2025] [Barman et al. 2025] [Bharti and Venkatesh 2025] [Charoenwuttikajorn et al. 2025] [Cheng and Wang 2025] [Crain et al. 2025] [Du et al. 2025c] [Filyashkin 2025b] [Filyashkin 2025a] [Fu et al. 2025] [Gong and Fan 2025] [Hang et al. 2025] [Hao et al. 2025] [Hu et al. 2025b] [Huang et al. 2025b] [Iyer and Johnson 2025] [Jayarathne et al. 2025] [Kharitenko et al. 2025] [Kumar et al. 2025b] [Li et al. 2025g] [Li et al. 2025i] [Li et al. 2025h] [Liu et al. 2025c] [Liu et al. 2025a] [Maheshwari et al. 2025] [Malhotra et al. 2025] [Park et al. 2025] [Prasinos et al. 2025] [Quan et al. 2025] [Tan et al. 2025] [Tang 2025] [Tang et al. 2025a] [Tong et al. 2025] [Wang et al. 2025a] [Wang et al. 2025d] [Wei and Li 2025] [Wen et al. 2025a] [Wen et al. 2025b] [Zhang et al. 2025e] [Zhang et al. 2025f] [Zhu et al. 2025b] [Alsayegh and Abro 2026] [Basu et al. 2026] [Forasassi 2026] [Forasassi et al. 2026] [Giorcelli et al. 2026] [Hang and Guo 2026] [High-Precision Trajectory Tracking 2026] [Huang et al. 2026] [Jayarathne et al. 2026] [Khalil et al. 2026] [Koushafar and Kosari 2026] [Li et al. 2026c] [Lowe et al. 2026] [Parasuraman et al. 2026] [Ren et al. 2026b] [Schmidt and Jusko 2026] [Smith et al. 2026a] [Smith et al. 2026b] [Sun et al. 2026b] [Tao et al. 2026a] [Wagner et al. 2026] [Wang 2026] [Wang et al. 2026a] [Wang et al. 2026e] [Ye et al. 2026] [Yi et al. 2026] [Zheng et al. 2026] [Aerial Refueling Lights] [Ashjaee] [Chen Shuxin et al] [Chen Zhigang et al] [Cowen et al] [Euler et al] [Feezor et al] [Hardy] [Hein et al] [Hill and Wallace] [Hunter et al] [Kato and Endo] [Kelsey et al] [Kimmett et al] [Loh and Dorfler] [Mohajerani] [Nard and Gounon] [Nguyen et al] [Rankin] [Ross et al] [Rowe] [Snyder et al] [Snyder et al] [Stepanyan et al] [Swanson] [Velasquez Escandon] [Vendra] [Wendel et al] [Yunchun Yang et al] [Buffington 2002] [Dickes et al. 2002] [Yakimenko et al. 2002] [Khanafseh and Pervan 2007] [Lynch 2012] [Yu et al. 2017] [Lau et al. 2018] [Chen 2022b] [Jaiswal and Bhunia 2024] [Wickramasuriya et al. 2024] [Büyükekiz and Ergezer 2025] [Wickramasuriya et al. 2025] [Tiwari]
Getting it off the aeroplane, which is where the sortie starts
Leaving the carrier. Air launch, store separation and carriage, airdrop from transports, tube and hand launch, and the deployment of folding wings. 120 titles name stores and 80 name airdrop, and 25 name folding wings, 24 of them from 2009 or later.
376 records. [Dougherty 1992] [An Air-Launched Automatic Weather 1951] [Kansas Univ Lawrence 1952b] [Kansas Univ Lawrence 1952a] [Disher 1954] [Deitchman 1957] [Jacobs et al. 1961] [Blackburn and George 1964] [Lewis 1964] [Thurston 1965] [Bolster and Googins 1967] [Gionfriddo 1967] [Black 1968] [Chakoian and Michal 1968] [Black 1969] [Chakoian 1969] [Chang and Ripperger 1969] [Jan and Ripperger 1969] [Reed and Curry 1969] [Rohrbough and Koehler 1969] [Hester 1970] [Michal et al. 1970] [Slayman et al. 1970] [Black and Picklesimer 1971] [Brooks 1971] [Goodwin et al. 1971] [Goodwin et al. 1972] [Daniels and Clare 1973] [Farinacci and Bruner 1973] [Fritzler 1973] [Dillenius et al. 1974] [Pritts 1974] [Spahr 1974] [Spahr and Sumlin 1974] [Dillenius et al. 1975] [Leger 1975] [Lempert 1975] [Petry 1975] [Spahr 1975] [Spahr and Sumlin 1975] [Piersol 1977] [Carten 1978] [Gonzalez and Elias 1978] [Massey and Wuest 1978] [Olenberger 1978] [Shadow 1978] [Billingsley et al. 1979] [Carten and Wuest 1979] [Graves and Robins 1979] [Hildebrand 1979] [Aircraft Store Separation Motion 1980] [Black 1980] [Carman et al. 1980] [Carten and Wuest 1980] [Maddox 1980] [Fleeman and Donatelli 1981] [Hudson 1981] [Sawyer et al. 1981] [Waskiewicz et al. 1981] [Air-Launched Balloon System Phase 1982] [Donatelli and Fleeman 1982] [Jacot and Hellmers 1982] [Jenkins 1982] [Stallings 1982] [Steeves 1982] [Cuffe and Limerick 1983] [Kai et al. 1983] [van den Broek 1984] [Sorrells et al. 1985] [Wapner and McCann 1985] [Rudolph 1986] [Rosen 1988] [Cross 1989] [Lindberg 1989] [Baysal et al. 1989] [Rosen 1989] [Martineau et al. 1990] [Newberry and Badzey 1990] [Chakravarthy and Szema 1991] [Hazlewood 1991] [Cenko 1992] [Kohiyar et al. 1992] [Lijewski and Suhs 1992] [Meyer et al. 1992] [Nichols et al. 1992] [Atwood 1993] [Poth et al. 1993] [Booker et al. 1994] [Carriage and Launch Characteristics 1994] [Lijewski and Suhs 1994] [New Applications of Engineering 1994] [Atwood 1995] [Carlson et al. 1995] [Kunz 1995] [Lopez and Wuest 1995] [Moyer et al. 1995] [Parkinson et al. 1995] [Coleman et al. 1996] [Hampsten 1996] [Lijewski and Lijewski 1997] [Blake 1998] [Hendrick and Saint-Mard 1999] [Rutherford and Wells 1999] [Blades and Redgrave 2000] [Ching 2000] [Deslandes and Seifert 2000] [Pan et al. 2000] [Tomaro et al. 2000] [Accorsi et al. 2001] [Donahue 2001] [Johnson et al. 2001] [Potvin 2001c] [Sorensen and Schafer 2001] [Warrick and Lee 2001] [Wilcox 2001] [Dooley et al. 2002] [Howitt and Platts 2002] [Rizk et al. 2002] [Stoica and Yaesh 2002] [Barber and McGrath 2003] [Cuthbert and Desabrais 2003] [Liu 2003] [Richard and Putter 2003] [Snyder et al. 2003] [Lee 2004a] [Murman et al. 2004] [Demir and Alemdaroglu 2005] [Flotten 2005] [Henry et al. 2005] [Hudson 2005] [Kim et al. 2005] [Kim 2005] [Bonometti and Sorensen 2006] [Hallberg et al. 2006] [Harish et al. 2006] [Hoyt 2006] [Ke et al. 2006] [Logan et al. 2006] [Dudley and Torres 2007] [Edefur et al. 2007] [Geisler et al. 2007] [Haglind et al. 2007] [Harding and Barton 2007] [Noh et al. 2007] [Prananta et al. 2007] [Precision Airdrop System 2007] [Stein et al. 2007] [Yang and Ke 2007] [Bury et al. 2008] [Hallberg et al. 2008] [Johnson et al. 2008] [Pace et al. 2008] [Sarigul-Klijn et al. 2008] [Spinetti and Jolly 2008] [Keen et al. 2009] [Morgret et al. 2009] [Murray et al. 2009] [Rafique et al. 2009] [Sadeck et al. 2009] [Stevenson et al. 2009] [Verstraete et al. 2009] [Finney 2010] [McQuilling et al. 2010] [Xu and Tang 2010] [Basoglu et al. 2011] [Berglind and Tysell 2011] [Farrell 2011] [Jann 2011] [McQulling et al. 2011] [Omar et al. 2011] [Qu et al. 2011b] [Wei et al. 2011] [Binkley and Vanderwyst 2012] [Carter 2012] [Carter and Lind 2012] [Desabrais et al. 2012] [Wu et al. 2012] [Xu et al. 2012a] [Coffin et al. 2013] [Di et al. 2013] [Geisbauer et al. 2013] [Kozak et al. 2013] [Machin and Evans 2013] [Pavacic 2013] [Rigby 2013] [Roosenboom et al. 2013] [Zhang et al. 2013b] [Zheng et al. 2013c] [Chen et al. 2014b] [Salt 2014] [Van Kesteren et al. 2014] [Jann 2015] [Jann et al. 2015] [Liu et al. 2015b] [Liu et al. 2015a] [Osman et al. 2015] [Salt 2015] [Geisbauer and Schmidt 2016] [Gerlach and Doman 2016] [Liu et al. 2016d] [Sokolov 2016] [Chang et al. 2017] [Hiwale et al. 2017] [Li et al. 2017] [Wang et al. 2017f] [Xu 2017] [Chen et al. 2018a] [Demir 2018] [Grenoble et al. 2018] [Han 2018a] [Huan-Ding et al. 2018] [Lane and Watson 2018] [Loupy et al. 2018] [Mizrahi and Raveh 2018] [Ning et al. 2018] [Otsuka et al. 2018] [Zhang and Yang 2018] [Zhao et al. 2018] [Zheng and Zhang 2018] [Evans 2019] [Mizrahi and Raveh 2019] [Ning et al. 2019] [Roychowdhury et al. 2019] [Swenson et al. 2019] [Toor et al. 2019] [Wachlin and Costello 2019] [Wang et al. 2019e] [Wei et al. 2019] [Zhou et al. 2019a] [Aleksandrovich and Nikolayevich 2020] [Anandhanarayanan et al. 2020] [章 2020] [Gao et al. 2020] [Ghoreyshi et al. 2020] [Xue et al. 2020] [Zhang and Zhang 2020] [Dehghan Manshadi and Saghafi 2021] [Gao et al. 2021] [Lengyel and Sosa 2021] [Li et al. 2021b] [Pramod et al. 2021] [Song 2021] [Tamer 2021] [Zhang et al. 2021a] [Clapp et al. 2022] [Dias 2022] [Gothard and Granlund 2022] [Jayne et al. 2022] [Li et al. 2022b] [Olejnik et al. 2022] [Song et al. 2022a] [Wachlin et al. 2022] [Wang et al. 2022a] [Xu et al. 2022] [Zhang et al. 2022a] [Ailneni et al. 2023] [Balachandran et al. 2023] [Cai et al. 2023] [Hicks et al. 2023] [Huh et al. 2023] [Jain et al. 2023] [Katukuri 2023] [尹 2023] [Watson and Gonzalez 2023] [Zhang et al. 2023d] [Zhao et al. 2023e] [Zhao et al. 2023d] [Zhao et al. 2023c] [Cao and Nie 2024] [Coley 2024] [Goerttler and Schnepf 2024] [Lyu and Wang 2024] [Peters et al. 2024] [Ren and Du 2024] [Silaidis et al. 2024] [Sivrioglu and Basaran 2024] [Treece et al. 2024] [Wang and Ma 2024] [Wang et al. 2024b] [Yin et al. 2024] [Zhang et al. 2024a] [Capel-Jorquera et al. 2025] [Fanggidae and Kusumahardi 2025] [Deng et al. 2025] [Du et al. 2025a] [Huang et al. 2025c] [Karatzas et al. 2025] [Sivrioglu and Başaran 2025] [Sun et al. 2025b] [Tang et al. 2025b] [Türk and Güleren 2025] [Vishwajeet et al. 2025] [Yao et al. 2025] [Zadniprovsky and Konotop 2025] [Jia et al. 2026] [Jiang et al. 2026] [Li et al. 2026a] [Lu et al. 2026] [Newberg et al. 2026] [Qian et al. 2026] [Raharema et al. 2026] [Stewart et al. 2026] [Sun et al. 2026c] [Wang et al. 2026b] [Wei et al. 2026] [Zhang and Qin 2026] [Gill and Pace] [Lantagne et al] [Lopez] [Mani et al] [Miles et al] [Rogers and Dragone 1996] [Dickard 1978] [Childers and Condon 2004] [Ott and Biezad 2004] [Gonzalez 2010] [Koehl et al. 2011] [Zhang et al. 2013c] [Olcer 2015] [Savuran and Karakaya 2015] [Rosid et al. 2018] [Shubov 2020] [Wang et al. 2020b] [Jiang et al. 2022] [Kim and Pokhodenko 2022] [Liu et al. 2022b] [Lu et al. 2023] [Shubov 2023] [Cai et al. 2024] [Li et al. 2024a] [Si et al. 2024a] [Si et al. 2024b] [Elsloo et al. 2025] [Guo et al. 2025] [Shang et al. 2025] [Zhao et al. 2025a] [He and Wang 2026] [Liu et al. 2026a] [Nugroho 2026] [Jackson] [Specification for Design and] [Bamber 1961] [Feistel and Maki 1974] [Korst 1974] [Washington 1975] [Kiber 1977] [Matthews and Key 1977] [Perkins et al. 1977] [Lijewski 1978] [Maddox et al. 1979] [Reed et al. 1979] [Tijdeman et al. 1979] [Dix and Mattasits 1980] [Anderson 1981] [Heltsley et al. 1981] [Turner 1982] [Cazier and Kehoe 1986b] [Cazier and Kehoe 1986a] [Blair and Stallings 1988] [Heim 1991] [Shanks and Ahmad 1991] [Cenko and Madson 1993] [Cenko 1994] [Cenko et al. 1995] [Chen et al. 2002c] [Chen et al. 2002b] [Byreddy et al. 2003] [Kayran 2004b] [Kayran 2004a] [Terashima and Fujii 2004] [Vaughn and Milton E. 2008] [Wittich and Jumper 2010] [Barakos 2014] [Kholodar 2016] [Elliott et al. 2024] [Elliott et al. 2025]
The vehicle, the programme and the vehicles it is measured against
The vehicle and its comparators. The C-130 that carries and catches it, the Tomahawk and air-launched cruise missile family that shares its engine, the Corona capsule recoveries that came before it, and small expendable aircraft such as Coyote. No title in the survey names the X-61A or Gremlins, which is why the programme’s own record is carried by the primary documents.
35 records. [Clay and Berens 1964] [Harvill et al. 1972] [Harvill et al. 1973] [Pond 1973] [Harvill and Kays 1974] [Harvill and Kizer 1976] [Pond 1977] [Dean 1981] [Kizer 1981] [North 1983] [Davis 1988] [Parise 1992] [Smith 1995] [Wheelon 1997] [Cundiff and Buckingham 1999] [McGrath 2004] [Meldrum 2007] [The Coyote Unmanned Air 2007] [Wowczuk et al. 2007] [Meldrum 2008] [Wooten and Yechout 2008] [Newman et al. 2009] [Kottapalli and Harris 2010] [Kottapalli and Harris 2012] [Air Force Life Cycle Mgmt Center 2013] [The Coyote Unmanned Aerial 2014] [Johnson 2015] [Satellite Photography Film Return 2016] [Bergeron et al. 2017] [Bergeron et al. 2018] [Ghoreyshi et al. 2018] [Bugaric 2019] [national reconnaissance office nro] [Craig and Reich 1981] [Suplisson et al. 2011]
The parachute, which is how it comes down when it is not caught
Coming down when it is not caught. Parachute and decelerator design, inflation, opening loads, stability and materials, and parachute recovery of uncrewed aircraft, boosters and capsules. 57 titles name Orion, Mars, Viking or a supersonic decelerator test programme and 11 name an uncrewed aircraft or a drone, so the parachute literature is mostly a spacecraft literature.
489 records. [Bacchus et al. 1975] [Banerjee and Utreja 1975] [Vergnolle and Astorg 1991] [Yechout et al. 2011] [Aubuchon and Owens 2016] [Cruz 2022] [Sullivan 1944] [Sherer 1945] [Naval Surface Warfare Center Dahlgren Div VA 1949] [Jones and Klinar 1950] [Goglia 1952] [Braun 1953] [MacCarthy 1954] [Miller 1954] [Phipps 1954] [Shepardson 1954] [Teichroew 1954] [Bickford et al. 1955] [Goglia et al. 1955] [Lavier 1955a] [Lavier 1955b] [Lavrakas 1955] [Lavrakas and Katz 1955] [Smollett 1955] [Sweeney 1955] [Cates 1956] [Chu et al. 1956] [Miller 1956] [Templeton 1956] [Meyer 1958] [Heinrich et al. 1959] [Jailer et al. 1960] [Tests of Vortex-Ring Parachute 1960] [Tomcsak 1960] [Charczenko and McShera 1961] [Engstrom and Lang 1961] [Heinrich et al. 1961] [Maynard 1961] [McShera and Keyes 1961b] [McShera and Keyes 1961a] [Murray 1961] [Pedersen 1961] [Minnesota Univ Minneapolis Inst Of Tech 1962] [Burk 1962] [Unitary Plan Wind Tunnel 1962] [Unitary Wind Tunnel Tests 1962] [Braun and Walcott 1963] [Coskren and Chu 1963] [McShera 1963] [Sims 1963] [Walcott 1963] [Heinrich et al. 1964] [Pedersen 1964] [Deitering and Hilliard 1965] [Heinrich and Rust 1965a] [Heinrich and Rust 1965b] [Melzig and Schmidt 1965] [Niccum et al. 1965] [Babish 1966] [Ericksen et al. 1966] [Figucia and McCafferty 1966] [Heinrich 1966a] [Heinrich 1966b] [Jamison 1966] [Turk 1966] [Asfour 1967] [Chandler 1967] [Whitlock et al. 1967] [Eckstrom and Preisser 1967] [Ibrahim 1967] [Jamison 1967] [MacNeal 1967] [Menard 1967] [Mickey and Stuart 1967] [Pepper 1967] [Preisser et al. 1967] [Bendura et al. 1968] [Campbell 1968] [Coltrane et al. 1968b] [Coltrane et al. 1968a] [Figucia and Richard D. 1968] [Irving Air Chute 1968] [Scott et al. 1968] [Usry 1968] [White and Wolf 1968] [Brearley 1969] [Eckstrom and Mayhue 1969] [French 1969] [Goodrick 1969] [Mayhue and Eckstrom 1969] [Pepper 1969] [Pepper and Cronin 1969] [Rhudy 1969] [Spence 1969] [Usry 1969a] [Usry 1969b] [Bohon and Miserentino 1970] [Greene and Preisser 1970] [Heinrich and Hektner 1970] [Homan 1970] [Lonborg and Mack 1970] [McEwan 1970] [Nicolaides 1970] [Ross 1970] [Defense Documentation Center Alexandria VA 1971] [French 1971] [Heinkich and Hertner 1971] [Nicolaides 1971] [Nicolaides and Tragarz 1971] [Pepper and Holt 1971] [Wolf 1971] [Dickinson et al. 1972] [Klimas 1972] [Knacke 1972] [Maydew and Johnson 1972] [Pearson 1972] [Poole 1972] [Reichenau 1972] [Ross 1972] [Alexander and Foughner 1973] [Dickinson et al. 1973] [Klimas 1973] [Laswell 1973] [Ludtke 1973] [Mahar et al. 1973] [Mansfield 1973] [Pepper and Biesterveld 1973] [Poole 1973] [Pyle et al. 1973] [Steinberg et al. 1973] [Whalley 1973] [Whitlock et al. 1973] [Heinrich et al. 1974] [Ibrahim and Engdahl 1974] [Laub et al. 1974] [Matsuo 1974] [McVey and Wolf 1974] [Roberts 1974] [Skelton and Abbott 1974] [Wei and Pearson 1974] [Wolf 1974] [Gombos and Reed 1975] [Miller 1975] [Utreja 1975a] [Utreja 1975b] [Dyess and William W. 1976] [Foughner et al. 1976] [Nicolaides 1976] [Payne and Band 1976] [Timmons 1976] [Campos 1977] [Fu and Koch 1977] [Klimas 1977] [Pepper 1977] [Pepper and Buxton 1977] [Rychnovsky 1977] [Speelman 1977] [Tory and Ayres 1977] [Wolf and Spahr 1977] [Heinrich and Saari 1978b] [Heinrich and Saari 1978a] [Klimas 1978] [McCarty 1978] [Klimas 1979] [Moog et al. 1979] [Rodier 1979] [Schatzle and Curry 1979] [Bradshaw 1980] [Ericksen and Orear 1980] [Heinrich 1980] [Roberts 1980] [Schatzle and Curry 1980] [Cockrell and Doherr 1981] [Jorgensen and Cockrell 1981] [Pepper and Collins 1981] [Peterson and Johnson 1981] [Spahr and Wolf 1981] [Bolton et al. 1982] [Bucker 1982] [Garrard and Muramoto 1982] [Konicke and Garrard 1982] [Ludtke 1982] [Moog and Kross 1982] [Pepper and Collins 1982] [Purvis 1982] [Calianno 1983] [Matsuo and Butler 1983] [Peterson and Johnson 1983] [Purvis 1983] [Stevens 1983] [Corridan et al. 1984] [Garrard et al. 1984] [Pepper 1984] [Pepper et al. 1984] [Puskas 1984] [High Drag Rotating Parachute 1985] [Knacke 1985] [Ross 1985] [Fallon et al. 1986] [Hogan 1986] [Johnson 1986] [Kolega et al. 1986] [Silbert et al. 1986] [French 1988] [Yavuz 1988] [Behr 1989a] [Behr 1989b] [Downs and Bartlett 1989] [Herr 1989] [Higuchi 1989] [Higuchi and Takahashi 1989] [Johnson 1989b] [Lee 1989] [Oler 1989] [Puskas 1989] [Strickland and Macha 1989] [Yavuz 1989] [Strickland and Macha 1990] [Fallon 1991] [Jorgensen 1991] [Kemnitz 1991] [Ludtke 1991] [Waye 1991] [Wei 1991] [Brinkman 1992] [Doherr and Schilling 1992] [Hogan 1992] [Niemi 1992] [Behr 1993] [Further Development and Flight 1994] [Horenstein and Roberts 1994] [Lee 1994] [Shpund and Levin 1994] [Doherr 1995] [Ginsberg 1995] [Hirst and Jorgensen 1995] [Humi 1995] [Kennedy and Lowry 1995] [Koenig et al. 1995] [Layfield and Carpenter 1995] [Levin and Shpund 1995] [Losilevskii 1995] [Vishnyak 1995] [Benney and Stein 1996] [Strickland and Higuchi 1996] [Patel et al. 1997] [Potvin 1997] [Potvin and Potvin 1997] [Reinhard et al. 1997] [Sahu et al. 1997] [Shpund and Levin 1997] [Yavuz 1997] [Potvin and Peek 1998] [Dellicker and Bybee 1999] [Heindel and Wolf 1999] [Ibos et al. 1999] [Inatani et al. 1999] [Leonard et al. 1999] [Martin 1999] [Potvin 1999] [Witkowski 1999] [Delgado and Arcioni 2000] [Machin 2000] [Desabrais and Johari 2001] [Haubelt et al. 2001] [Johari et al. 2001] [Meyerson 2001] [Potvin 2001a] [Potvin 2001b] [Separable Cord Connecting Structure 2001] [Smith et al. 2001] [Accorsi and Leonard 2002] [Johari and Desabrais 2002] [Masciarelli 2002] [Cruz et al. 2003] [Humi 2004] [Kolodny 2004] [Whitmore et al. 2004] [Bennett and Fox 2005] [Kothandaraman and Rotea 2005] [Lyalin and Morozov 2005] [Schoenenberger et al. 2005] [Stein 2005] [Stein et al. 2005] [Taylor et al. 2006] [Bennett and Fox 2007] [Dunker and Berland 2007] [Farhall et al. 2007] [Mohaghegh and Jahannama 2007] [Potvin 2007b] [Potvin 2007a] [Potvin 2007c] [Potvin 2007d] [Potvin 2007e] [Redelinghuys 2007] [Reza 2007] [Reza et al. 2007] [Whitmore and Hennings 2007] [Mohaghegh and Jahannama 2008] [Thomas and Thomas 2008] [Tiaden and Yakimenko 2008] [Autonomously Guided Ram-Air Parachute 2009] [Modular Heavy Payload Autonomously 2009] [Moorman and Yechout 2009] [Sadeck and Lee 2009] [Sengupta et al. 2009] [Taylor et al. 2009] [Tiaden and Yakimenko 2009] [Yeakle et al. 2009] [Witkowski 2010] [Aubuchon et al. 2011] [Fraire et al. 2011] [Janda et al. 2011] [Koster et al. 2011] [Machin et al. 2011a] [Machin et al. 2011b] [McQuilling et al. 2011] [Mkrtchyan and Johari 2011] [Moore and Morris 2011a] [Moore and Morris 2011b] [Morris and Olson 2011] [Morris et al. 2011b] [Morris et al. 2011a] [Sengupta et al. 2011] [Shreves 2011] [Wolf and Fallon 2011] [Bergeron et al. 2012] [Currin et al. 2012] [Lee et al. 2012a] [Lee et al. 2012b] [McQuilling and Potvin 2012] [Benton and Yakimenko 2013] [Cao and Zhu 2013] [Cassady et al. 2013] [Day 2013] [Desabrais and Johari 2013] [Eslambolchi and Johari 2013] [Gallon et al. 2013] [Janda et al. 2013] [Kenig et al. 2013] [Kozlov 2013] [Mastropietro et al. 2013] [Moore 2013a] [Moore 2013b] [Ray 2013a] [Ray 2013b] [Sengupta 2013] [Stewart 2013] [Varela and Ray 2013] [Zwicker and Sinclair 2013] [Fields et al. 2014] [Lee and Arena 2014] [Redmond et al. 2014] [Shyu and Hsiao 2014] [Alshahin et al. 2015] [Altmann 2015] [Bergeron et al. 2015] [Devalla et al. 2015] [Gallon and Witkowski 2015] [Gallon et al. 2015] [Ivanov 2015] [Li 2015] [Lingard 2015] [Peralta and Johari 2015] [Ray and Machin 2015] [Shen et al. 2015] [Atmospheric and Space Environment Committee 2015] [Tanner et al. 2015] [Xie et al. 2015] [Analysis of the Working 2016] [Chen and Shi 2016] [Gao et al. 2016] [Li et al. 2016d] [Li et al. 2016e] [Mingjun Li et al. 2016] [Montalvo and Costello 2016] [O’Farrell et al. 2016] [Roland et al. 2016] [Seidel et al. 2016] [Swei and Westfall 2016] [Takizawa et al. 2016] [Zumwalt et al. 2016] [Anderson et al. 2017] [Charles 2017] [Daum and Mollmann 2017] [Ortega et al. 2017] [Ray 2017] [Seidel and Bergeron 2017] [Vasile 2017] [Watkins et al. 2017] [AL-Madani et al. 2018] [Devalla et al. 2018] [Fields and Yakimenko 2018] [Szafran and Kramarski 2018] [Way 2018] [Altmann 2019] [Anderson et al. 2019] [Berexa et al. 2019] [Cassady and Daum 2019] [Daum 2019a] [Daum 2019b] [Dwyer Cianciolo et al. 2019] [Jann and Ward 2019] [Murri et al. 2019] [Ray et al. 2019] [Szafran and Kramarski 2019] [Boustani et al. 2020] [Landman 2020] [Menting et al. 2020] [Priyadarshi et al. 2020] [Zhang et al. 2020a] [Gong and Wu 2021] [Tuan 2021] [Pratap et al. 2021] [Qiu et al. 2021] [Takayanagi et al. 2021] [Wang et al. 2021b] [Xue 2021] [Britting et al. 2022] [Grippon 2022] [Güven and Şamiloğlu 2022a] [Güven and Şamiloğlu 2022b] [Huang et al. 2022] [Jasztal et al. 2022] [Perin and Patoux 2022] [Siegel et al. 2022] [Ward et al. 2022] [Witkowski et al. 2022] [de Lange et al. 2022] [Eiden and Foster 2023] [Kumar et al. 2023a] [Li et al. 2023a] [Lorenz and Allen 2023] [O’Farrell et al. 2023] [Pepermans et al. 2023] [Placco 2023] [Civelek and Kıvrak 2024] [Ghoreyshi et al. 2024] [Krause et al. 2024] [O’Farrell et al. 2024] [Peterson et al. 2024] [Placco 2024] [Siegel et al. 2024] [Study on Critical Parachute 2024] [Ward et al. 2024a] [Ward et al. 2024b] [Wei et al. 2024a] [Yıldırım Dalkıran and Kırteke 2024] [Goldberg 2025] [Kaspar and Grim 2025] [Li et al. 2025b] [Placco et al. 2025] [Roelke et al. 2025] [Sanganeria 2025] [Xing and Liang 2025] [Xu et al. 2025b] [Yu et al. 2025a] [Zhang et al. 2025d] [Afridi et al. 2026] [Cadieux and Barad 2026] [Potvin and Rangel 2026] [Varela and Davidson 2026] [Křemenáková et al. 2026] [Mannan et al. 2026] [Maru et al. 2026] [Pensado et al. 2026] [Tezduyar and Takizawa 2026] [Witkowski et al. 2026] [CLOTH, PARACHUTE, ARAMID, Intermediate] [Cloth, Parachute, Meta-Aramid, LOW] [Dinh] [Drynan] [Ray et al] [Ray and Janssen] [Roelke et al] [Cadieux and Barad] [Cadieux et al] [Boustani et al] [Minimum Performance Standard for] [Minimum Performance Standard for] [Parachute] [Puranik] [Specification for Aircraft Emergency] [Specification for mercerized cotton] [Standard Specification for Aircraft] [Hughes et al] [To] [Vardi] [Zink]
Volleys, and the operator who cannot watch all of them
Many vehicles and the people who supervise them. Swarms and cooperative control of uncrewed aircraft, task allocation, one operator supervising several vehicles, workload, and manned-unmanned teaming. 67 titles name manned-unmanned teaming and 65 of them date from 2009 or later.
335 records. [Scott et al. 2006] [Brooks 1989] [Marshak et al. 2000] [Lin 2002] [Ruff et al. 2002] [Bayraktar et al. 2004b] [Bayraktar et al. 2004a] [How 2004b] [Ben Ludington 2006] [Eun and Bang 2006] [Flaherty et al. 2006] [Miller 2006] [Nelson et al. 2006] [Tvaryanas 2006] [Crandall and Cummings 2007] [Cummings and Mitchell 2007] [Cummings et al. 2007] [Rasmussen and Schumacher 2007] [Arthur 2008] [Bar-Shalom 2008] [D’Andrea 2008] [Draper 2008] [Teague et al. 2008] [Dong et al. 2009] [Donmez et al. 2009] [Huhn et al. 2009] [Kilgore et al. 2009] [Mekdeci and Cummings 2009] [Selby 2009] [Barnes 2010] [Clare et al. 2010] [Cosenzo 2010] [Donmez and Cummings 2010] [Donmez et al. 2010] [Roltgen and Gilbert 2010] [Chen et al. 2011] [Dong et al. 2011] [Kurkcu et al. 2011] [Shively et al. 2011] [Strenzke et al. 2011] [de Vries and Subbarao 2011] [Belta 2012] [Calhoun et al. 2012] [Chen and Barnes 2012] [Clare et al. 2012] [Jentsch and Fincannon 2012] [Kidwell et al. 2012] [Sellers et al. 2012] [Taylor et al. 2012] [Cook et al. 2013] [Cummings et al. 2013] [Duan 2013b] [Fuchs et al. 2013] [Hu and Xu 2013] [Karimoddini et al. 2013] [Leonard et al. 2013] [Yang et al. 2013a] [Goodrich and Cummings 2014] [Hanson 2014b] [Hirsch and Schroeder 2014] [Kaliardos and Lyall 2014] [Rudnick et al. 2014] [Terwilliger and Ison 2014] [Saska 2015] [Schmitt and Schulte 2015a] [Schmitt and Schulte 2015b] [Haber and Chung 2016] [Human Factors in Unmanned 2016] [Jensen 2016] [Levulis et al. 2016] [Ruf and Stütz 2016] [Safe Coordinated Maneuvering 2016] [Calhoun et al. 2017] [Choi and Yang 2017] [Colombi et al. 2017b] [Das et al. 2017] [Lee et al. 2017] [Rogers et al. 2017] [Ru and Subbarao 2017] [Yoon and Kim 2017] [Dawkins et al. 2018] [Fern et al. 2018] [Hoke 2018] [Hu and Lanzon 2018] [Levulis et al. 2018] [Ruf and Stütz 2018] [Zak et al. 2018] [Autenrieb et al. 2019] [Donkels and Voigt 2019] [Li et al. 2019a] [Michelson and Domerçant 2019] [Modares et al. 2019] [Sherstjuk et al. 2019] [Tkach and Edan 2019] [Wu and Han 2019] [Yoon and Kim 2019] [Zheng et al. 2019] [Akagi et al. 2020] [Andrews et al. 2020a] [Andrews et al. 2020b] [Banas et al. 2020] [El-Fiqi et al. 2020] [Heilemann and Hollatz 2020] [Meyer and Schulte 2020] [Roth and Schulte 2020] [Roth et al. 2020] [Sebbane 2020] [Zou et al. 2020] [Jensen 2021] [Kyriakakis et al. 2021] [Lyons et al. 2021] [Schwerd and Schulte 2021] [Singh 2021] [Yoo et al. 2021] [Cui et al. 2022a] [Dudek and Schulte 2022a] [Friedrich and Vollrath 2022] [Hammarbäck 2022] [Han et al. 2022a] [Karimoddini et al. 2022] [Khare et al. 2022] [Kiam et al. 2022] [Kim and Lee 2022] [Kohn 2022] [Krizek et al. 2022] [Meyer and Schulte 2022] [Park et al. 2022] [Rosenblum et al. 2022] [Roth and Schulte 2022b] [Roth and Schulte 2022a] [Yu et al. 2022] [Alabbadi and Sababha 2023] [Bakirci 2023] [Chen et al. 2023b] [Hammarbäck et al. 2023] [Langen et al. 2023] [Lee and Na 2023] [Shiyan (Shyian) 2023] [Shyian 2023] [Si et al. 2023] [Zaitseva et al. 2023] [Alishuler 2024] [Approach to Conception 2024] [Bostock et al. 2024] [Chandran and Vipin 2024] [Di and Guo 2024] [Hashemzadeh and Kumbasar 2024] [He et al. 2024] [Lee and Park 2024] [Liu et al. 2024b] [Liu et al. 2024c] [Maier et al. 2024] [Malhotra et al. 2024] [Nattke et al. 2024] [Ozturk et al. 2024] [Panowicz and Stecz 2024] [Pericon 2024] [Phadke et al. 2024] [Roncolini and Quaranta 2024] [Sun et al. 2024a] [Xue et al. 2024] [Yao et al. 2024a] [Yu et al. 2024a] [Zhang et al. 2024b] [İnan and Ceylan 2024] [Albawaneh et al. 2025] [Garcia and Eskandarian 2025] [Han et al. 2025a] [Hong and Baek 2025] [Hwang and Han 2025] [Jiao et al. 2025] [Künzel et al. 2025] [Lai et al. 2025] [Lee and Jeong 2025] [Lee and Kang 2025] [Lee et al. 2025b] [Lee et al. 2025a] [Li et al. 2025a] [Mintah et al. 2025] [Paul et al. 2025] [Rawat 2025] [Shao et al. 2025b] [Sindiramutty 2025] [Stolfi and Danoy 2025] [Uybarreta et al. 2025] [Velmurugan et al. 2025] [Wuwer et al. 2025] [Yu et al. 2025b] [Yuan et al. 2025a] [Abro et al. 2026] [Arfa et al. 2026] [Athanasiadou et al. 2026] [Bjurling et al. 2026] [Ding et al. 2026] [Gozzi and Schulte 2026] [Iqbal et al. 2026] [Jeong 2026] [Kim and Kim 2026] [Kocaman 2026] [Korecki and Hoika 2026] [Liu et al. 2026d] [Orozco et al. 2026] [Qi and Xie 2026] [Raj and Kos 2026] [Sadik et al. 2026] [Yang et al. 2026b] [Zhao et al. 2026a] [Arranz Esteban] [Unverricht et al] [Mukherjee] [Pack et al] [Pamphile and Kuo-Chi Lin] [Park] [Tinoco] [Liu et al. 2018b] [Fogel et al. 1974] [Wortman et al. 1975] [Aume et al. 1976] [Howard 1976] [Reed 1977] [Huntoon et al. 1979] [Muralidharan et al. 1979] [Sarrafian 1984] [Sarrafian 1986] [McIngvale and Dudley 1990] [Walters et al. 2002] [Weiskopf et al. 2002] [Wickens and Dixon 2002] [Atkinson 2003] [Howitt and Richards 2003] [Verma et al. 2003] [How 2004a] [McLain and Beard 2004] [Dixon et al. 2005] [Hunn 2005] [Morris et al. 2005] [Neumann and Durlach 2005] [Petkosek et al. 2005] [Deutsch 2006] [Rasmussen et al. 2006] [Jones et al. 2007] [Billings and Durlach 2008] [How 2008] [Schulte 2008] [Yoon et al. 2009] [Billings and Durlach 2010] [Castanon and Cassandras 2010] [Kahn et al. 2010] [Yoon and Kim 2010] [Ramos et al. 2011] [Viggh et al. 2011] [Barnhart 2012] [Wang and Xin 2012] [Ragi and Chong 2013] [Sineglazov and Shmelev 2013] [Tvaryanas and Maupin 2013] [Xu and Shi 2013] [Adams 2014] [Cetin and Yilmaz 2014] [Chen et al. 2014c] [Hicks and Durbin 2014] [Rosales et al. 2014] [Saif et al. 2014] [Zhou et al. 2014] [Bereg et al. 2015] [Liu et al. 2015c] [Nielsen and Sharma 2015] [Rodrigues and Aguiar 2015] [Sherstjuk 2015] [Xu and Carrillo 2015] [Ali Dehghani and Bagher Menhaj 2016] [Brust et al. 2016] [Jasper et al. 2016] [Jia et al. 2016] [Kim and Bang 2016] [Liu et al. 2016c] [Peng et al. 2016] [Rudnick and Schulte 2016] [Trujillo et al. 2016] [Zhang et al. 2016b] [Bardhan et al. 2017] [Garcia and Casbeer 2017] [Glazunov 2017] [Huang et al. 2017a] [Jain et al. 2017] [Liu et al. 2017c] [Sequeira and Aguiar 2017] [Shively 2017] [Huang et al. 2018a] [Kim and Morrison 2018] [Ananyev 2019] [Heintz et al. 2019] [Kim et al. 2019] [Kucherov et al. 2019] [Шмельова and Bondarev 2019] [Wen et al. 2019] [Zhang et al. 2019b] [Zhang et al. 2019d] [Zhao and Wang 2019] [Zhao et al. 2019b] [El-Ferik 2020] [Gkesoulis and Psillakis 2020] [Kladis and Tsourveloudis 2020] [Liu et al. 2020c] [Seo et al. 2020] [Zhang et al. 2020b] [Zheng et al. 2020] [Hou et al. 2021] [Hwang et al. 2022] [Kim et al. 2022b] [Widiyanti et al. 2022] [Arogeti and Ailon 2023] [Wen et al. 2023] [Brenner and Stütz 2024] [Ma et al. 2024] [Research on the Autonomous 2024] [Ru et al. 2024] [Xu et al. 2024] [Yao et al. 2024b] [Singh 2025] [Yang et al. 2025d] [Chen et al. 2026] [Lv et al. 2026] [The Control of Multiple 2026] [Walter et al. 2026] [Xie et al. 2026a] [Xie et al. 2026e] [Xie et al. 2026b] [Xie et al. 2026c] [Xie et al. 2026d] [Zhang et al. 2026c] [Control of cooperative unmanned] [Marshall] [Watson et al] [Yi-Liang Chen et al]
The engine, and starting it in the air
The engine and starting it. Small turbojets and turbofans, expendable and low-cost turbine engines, the F107 family in its cruise missile installations, engines for small uncrewed aircraft, and starting and relight at altitude. 33 titles name expendable or low-cost engines and 24 of them predate 2000.
125 records. [Brunner et al. 1976] [Flight Engine Performance Evaluation 1977] [Fleming 1948] [Hawkins and Meyer 1948a] [Wilsted and Armstrong 1950] [Wilsted and Armstrong 1951] [Lockwood and Perkins 1954] [Boytos 1969] [Deep et al. 1971] [Ignition Theory and Its 1971] [Murray and Kidd 1971] [Kofskey and Nusbaum 1973] [Merrill et al. 1973] [Chuslo and Greenburg 1974] [Dengler and Macioce 1976b] [Dengler and Macioce 1976a] [Merrill 1976] [Wills and Wise 1976] [Mauch et al. 1980] [Elrod and Durniak 1981] [Kuhn et al. 1981] [Tian-yu et al. 1981] [Keller 1982] [Chevis and Grant 1983] [Hughes and Ray 1985] [Singh and Benstein 1986] [Papandreas 1988] [Johnson 1992] [Dickerson and Jacox 1994] [Kashikawa et al. 1995] [Propulsive Thrust by Jet 1995] [Lowi 2003] [Hsu et al. 2004] [Trazzi 2004] [Henriksson and Ring 2006] [Liew et al. 2006] [Pakanati et al. 2006] [Ring and Henriksson 2006] [Tsai et al. 2006] [Yunusov et al. 2006] [Rideau et al. 2008] [Sadr et al. 2010] [Shwin 2010] [Rosa et al. 2011] [Turan 2012] [Menon and Cadou 2013] [Shen et al. 2014] [Kim et al. 2015] [Gaspar and Sousa 2016] [Yang et al. 2016] [Connolly et al. 2017] [Yalcin 2017] [Tamada et al. 2018] [Filinov and Ostapyuk 2019] [Кузнецов and Shpakovsky 2020] [Di̇şli̇taş and Albayrak Çeper 2021] [Kelly et al. 2021] [de Oliveira et al. 2021] [Litrico et al. 2022] [Aygun 2023] [Aygun et al. 2023] [Yucer and Nacakli 2023] [Bennett et al. 2024] [Davidović et al. 2025] [Zhang et al. 2025c] [Bennett et al] [Moore et al] [Elsasser 1973] [Gold 1973] [Strautman 1974] [Moskowitz and Spindler 1976] [Moskowitz and Spindler 1977] [Due and Buchanan 1978] [Huben and Metsker 1978] [Chamis 1983] [Design Concepts for Low-Cost 1986] [Jones et al. 1987] [Swonger and Huffman 1989] [Maggio 1990] [Exley 1991] [Jeung et al. 1991] [Lilley et al. 1991] [Roesler et al. 1992] [Wagner et al. 2000] [Haider et al. 2011b] [Haider et al. 2011a] [Davidović et al. 2022] [Davidović and Jojić 2026] [Hosang et al] [Jones] [Brunell et al] [Seldner et al. 1972] [Abercrombie 1979] [Rezy 1980] [Boretz 1984] [Catchpole 1990] [Lawton 1990] [Bruening et al. 2001] [Hooper 2001] [Georges 2003] [Nelson and Dix 2003] [Gur and Rosen 2009b] [Ларін 2013] [Tiimus et al. 2014] [Wolf et al. 2016] [Hooper and Al-Shemmeri 2017] [Dantsker et al. 2018] [Kiyak et al. 2018] [Coates et al. 2019] [Turkay et al. 2019] [Krznar et al. 2020] [Wang et al. 2020d] [Cardone et al. 2021] [Most and Feasey 2021] [Practice for Design and] [Practice for Design and] [Practice for Design and] [Varela Martínez] [Conrad and Durham 1947] [Conrad and Durham 1948] [Hawkins and Meyer 1948b] [Meyer and Bloomer 1948] [Meyer 1949] [Fleming and Dietz 1957] [Lilley and Pengelly 1992]
An airframe designed for a life measured in sorties
Reuse and the life of an airframe. Reusable and attritable vehicles, booster recovery and reuse, health monitoring, low-cost and damage-tolerant airframe structure, and the operations between flights.
156 records. [Low Cost Cargo Aircraft 1960] [Bono 1963] [Moise et al. 1963] [Bono et al. 1964] [Laubendorfer et al. 1965] [Keyser and Spieth 1967] [Nau 1967] [Quest 1969] [Heathman et al. 1970] [Expendable Second Stage Reusable 1971] [Garcia and Littman 1971] [Space Shuttle Program. Expendable 1971] [Connor et al. 1972] [Jensen and Witzell 1972] [Study of Solid Rocket 1972b] [Study of Solid Rocket 1972a] [Cherry 1975] [Nevins 1975] [Pulley 1977] [Chase 1978] [Low-Cost Composite Primary Structure 1978] [Ascani et al. 1980] [Fluk 1981] [Reusable Single-State-to-Orbit Vehicle Concept 1984] [Russell and Leavitt 1984] [Tewell 1984] [McKinney 1986] [Hudson and Hunter 1987] [Mihara 1988] [Benton 1989] [Calkins et al. 1989] [Hawkins 1989] [Skelly 1989] [Johnson 1990a] [Sedillo 1990] [Steinmeyer et al. 1990] [Paterson 1991] [Low-Cost Expendable Launch Vehicles 1992] [Richard 1993] [Palen 1994] [Piland et al. 1994] [Gintert 1995] [McConnaughey et al. 1995] [Reusable Launch Vehicle 1995] [Elkins and Galati 1996] [Komar and Christenson 1996] [Schmidt and Mann 1996] [Shaw and Greenberg 1998] [Tuohy 1998] [Anderson 1999] [Drews and Forman 1999] [Griner and Lyles 1999] [Rothschild and Schuster 1999] [Mueller (HM) and Lepore 2000] [Inatani et al. 2001] [Kosugi et al. 2001] [Schierman et al. 2001] [Safie et al. 2002] [Hagopian 2002] [Kaplan 2002] [Noneman 2002] [Thomas et al. 2002a] [Thomas et al. 2002b] [Arora et al. 2003] [Rooney 2003] [Sippel 2003] [Teufel et al. 2003] [Eklund 2004] [Eymar and Obersteiner 2004] [Myschik et al. 2004] [Chase and McKinney 2005] [Daniel and Ramusat 2005] [Tomczyk and Rogalski 2005] [Chiba et al. 2006] [Jategaonkar et al. 2006] [Johnson et al. 2006b] [Lin and Fleming 2006] [Martindale 2006] [Owens et al. 2006] [Rasky et al. 2006] [Sippel et al. 2006] [Bateman et al. 2007] [Case Study 2007] [de Divitiis and Corraro 2007] [Bizzarri et al. 2008] [Donahue et al. 2008] [Moster 2008] [Hellman and Bradford 2009] [Bradford and St. Germain 2010] [Dissel et al. 2010] [Edwards et al. 2010] [Gravlee et al. 2010] [Hellman et al. 2010] [Masse and Wilhite 2010] [Mills and Jones 2010] [Monterzino et al. 2010] [Edwards et al. 2011] [Garmendia et al. 2011] [Han et al. 2011b] [Hellman et al. 2011c] [Hellman et al. 2011a] [Hellman et al. 2011b] [Hellman et al. 2011d] [Miller et al. 2011] [Moore et al. 2011] [Post et al. 2011] [Robertson et al. 2011] [Sharma et al. 2011] [Stumph et al. 2011] [Toral Vazquez et al. 2011] [Ustinov 2011] [Carr et al. 2012] [Kahn and Edwards 2012] [Losik, Ph.D. 2012] [Miller and Post 2012] [Reusable Booster System 2012] [Blasdel 2013] [Krings et al. 2013] [Podhradsky et al. 2013] [Sabatini et al. 2013] [Kahn and Edwards 2015] [Colombi et al. 2017a] [Huang 2017] [Rosales and Gross 2017] [Pagan et al. 2018] [Stappert et al. 2018] [Amador et al. 2019] [Laracy and Marlowe 2019] [Torres et al. 2019] [Brevault et al. 2020] [Hamilton and Ochmanek 2020] [Merrem et al. 2020] [Comparing the Cost-Effectiveness 2021] [Cybenko and Hallman 2021] [Goh and Zekavat 2021] [Jones et al. 2021] [Ma et al. 2021] [Pidvysotskyi 2021] [Gong et al. 2022] [Górski et al. 2022] [Wu and Zhang 2023] [Cavdar and Mooij 2024] [Jun 2024] [Miller 2024] [Romano et al. 2024] [Stappert et al. 2024] [Goldyn et al. 2025] [Haynes et al. 2025] [Liu et al. 2025b] [Nair and Kukreja 2025] [China Achieves First Reusable 2026] [Sippel et al. 2026] [Rebikoff] [Kordonowy and Toupet 2011] [Rodzewicz 2012] [Johnson 1994]
What it costs, which is the programme’s stated reason for existing
What it costs. Unit and life-cycle cost, cost estimating relationships, design to cost, learning curves, availability and sortie generation. 28 titles name the learning curve and 42 name life-cycle cost.
170 records. [Heilig 1979] [Harmon and Ward 1990] [Anderson and Dixon 1975] [Himpler 1975] [Carlyle 1976] [Beltramo and Anderson 1977] [Carleton 1979] [Etesse 1979] [Gregory 1983] [Bennett 1990] [Gille and Richard A. 1990] [Gille and Warren H. 1992] [Koelle 1993] [Newport News Shipbuilding Va 1993] [Fitzsimmons 1996] [Eisman 1999] [Pempie and Vernin 2000] [Gstattenbauer et al. 2006] [Zapata 2013a] [Zapata 2013b] [Yang 2020b] [Du et al. 2025b] [Yao and Wei] [Lundberg 1956] [Thorne 1957] [Hauer et al. 1963] [Yates 1964] [Hartley 1965] [Yates 1965] [Cost-Estimating Relationships for Aircraft 1972] [Morse 1972] [Curry 1976] [Panella 1976] [Yang 1976] [A Comparison of Cost 1977] [A Support System Life 1977] [Biegel and Bulcha 1977] [Curry 1977] [Wagner 1977] [Weapon System Parametric Life 1977] [Brown 1978a] [Brown 1978b] [Beltramo et al. 1979] [Feltus 1979] [Fishbach 1979] [Meece and Spaeth 1979] [Stewart and Campion 1979] [Camin and McKenzie 1980] [Cunningham 1980] [Fishbach 1980] [Goclowski and Baran 1980] [Greer and Campbell 1980] [Smith 1980] [Stewart and Campion 1980] [Campbell 1981] [Cho and Seeger 1981] [Donath et al. 1981] [Greenberg 1981] [Contracting for Life Cycle 1982] [Pettigrew 1983] [Stahl et al. 1984] [Towill 1985] [Dhillon and Rayapati 1986] [Camm et al. 1987] [Majd and Pindyck 1987] [Bair 1988] [Johnson 1989a] [Johnson 1990b] [Badiru 1991] [Pananiswami and Bishop 1991] [Shiue 1991] [Space System Life Cycle 1992] [Barter et al. 1993] [Program Acquisition Costs 1993] [Manufacturing Cost Estimation 1993] [Program Acquisition Costs 1994] [Program Acquisition Costs 1995] [Marx et al. 1995] [Department of Defense Budget 1996] [Jaber and Bonney 1996] [Pindyck and Majd 1996] [Mazzola and McCardle 1997] [Program Acquisition Costs 1998] [Green 1998] [Department of Defense Budget 1999] [Smunt 1999] [Program Acquisition Costs 2000] [Razak and Carlyle 2000] [Military Airframe Acquisition Costs 2001] [Kundu et al. 2002] [Cassady et al. 2003] [Eduardo Salamanca and Luis Quiroz 2005] [Tirovolis and Serghides 2005] [Snead 2006] [Diez and Iemma 2007] [Chatzimichali and Tourassis 2008] [Pall 2008] [Tallant et al. 2008] [Kozanidis 2009] [Kozanidis 2010] [McBride and Paret 2010] [Using the Learning Curve 2010] [Xia Guoqing et al. 2010] [Dupuy et al. 2011] [Robinson et al. 2011] [Smunt 2011] [Zhao et al. 2011a] [Palomino and Epp 2012] [Rosiński 2012] [Ploetner 2013] [Wong 2013] [Zero-Sustainment Aircraft 2013] [Zheng et al. 2013b] [Zheng et al. 2013a] [Wang et al. 2014a] [Grosse et al. 2015] [Learning Curves 2015] [Zhao Xiaojia et al. 2015] [Zhao et al. 2015] [Pica 2016] [Saltoğlu et al. 2016] [Galar et al. 2017] [Jin et al. 2017] [Knezevic et al. 2017] [Fioriti et al. 2018] [Jones 2018] [Luan et al. 2018] [Marion 2018] [Pohya et al. 2018] [Wicke and Pohya 2018] [A Stochastic Model 2019] [Calado et al. 2019] [Fioriti and Vercella 2019] [Zhang et al. 2019c] [Hogan et al. 2020] [Badiru 2021] [Ren et al. 2021] [Zirka et al. 2021] [Patel et al. 2022] [Magill et al. 2022] [Hogan et al. 2022] [Krupnik 2022] [Tao 2022] [Chandola et al. 2023] [Diaz-Benachi et al. 2023] [Magill et al. 2023b] [Magill et al. 2023a] [Bradford et al. 2023] [Ulusoy and Şaşmaztürk 2023] [Agez 2024] [Jung et al. 2024] [Park et al. 2024] [Yoon et al. 2024] [Zaitseva et al. 2024] [Chen 2025b] [Zhou 2025] [Learning Curves 2026] [Liu and Wang 2026] [Roman 2026] [Shimpi and Sawarkar 2026] [Zhou 2026] [Aircraft Engine Life Cycle] [Blackwell and Eastlake] [Environmental Control Systems LIFE] [Hairong Sun and Han] [Harris] [Maintenance Life Cycle Cost] [Markowitz] [Practice for Maintenance and] [Xu et al]
Flying it, and the autonomy that flies it
Flying it. Flight control, guidance and autonomy of uncrewed aircraft, gust response and gust load alleviation, atmospheric turbulence models, and missile autopilots. 323 titles name gusts or turbulence.
835 records. 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[Kobayakawa and Maeda 1978b] [Kobayakawa and Maeda 1978a] [McLean 1978] [Vinkler and Wood 1978] [Woolley 1978] [Andrus 1979] [Okubo et al. 1979] [Reed and Hocan 1979] [Rynaski 1979] [Rynaski et al. 1979] [Vinkler et al. 1979] [Hoyt et al. 1980] [Jansen 1980] [Singh 1980] [Trevino 1980] [A Survey of Recent 1981] [Gangsaas et al. 1981] [Ruhlin and Murphy 1981] [Trevino 1981] [Turner et al. 1981] [Jansen 1982] [Karpel 1982] [Kanda 1983] [Norman et al. 1983] [Kanda 1984] [Perry 1984] [Baillie 1985] [Liebst et al. 1986] [Nixon and Tzuoo 1986] [Menon et al. 1987] [Murrow 1987] [Nixon and Tzuoo 1987] [Smolka 1987] [Solari 1987] [Analysis of Gust-Response Flight-Test 1988] [Basic PSD Concepts 1988] [Continuous Turbulence Gust Loads 1988] [Gust Loads Fundamentals 1988] [Gust Response Equations 1988] [Heinsheimer et al. 1988] [Hoblit 1988] [Liebst et al. 1988] [Ohta and Fujimori 1988] [Present Place of Discrete-Gust 1988] [Ratio of Von Karman 1988] [Matsuzaki et al. 1989] [Fujimori et al. 1990] [Perry et al. 1990] [Etkin 1992] [Sun and Allwright 1992] [Beal 1993] [Henderson and Fleeter 1993] [Suzuki and Yonezawa 1993] [Houbolt 1994] [Layton 1994] [Zole and Karpel 1994] [Cornman et al. 1995] [Fuller 1995] [Layton 1995] [Olwi 1995] [Bogue et al. 1996] [Kimberlin and Sims 1996] [McMinn 1997] [Rasmussen and Houpis 1997] [Zeiler 1997] [de Jonge et al. 1997] [Bullock and Fields 1998] [Layton 1998] [Lin and Liu 1998] [Ninham et al. 1998] [Tischler and Venkayya 1998] [Anandakumar and Kailas 1999] [Clark et al. 1999] [Kim et al. 1999] [Miyazawa and Motoda 1999] [Sadovnychiy et al. 1999] [Sako et al. 1999] [Teel 1999b] [Teel 1999a] [Wise et al. 1999] [Aouf et al. 2000] [Crema et al. 2000] [Corban et al. 2001] [Murray and Doyle 2001] [Powell 2001] [Chen and Molnar 2002] [Dahleh and Tsitsiklis 2002] [Napolitano 2002] [Yang and Obayashi 2002] [Angermuller and Hall 2003] [Pettit and Grandhi 2003] [Wadley et al. 2003] [Yang and Obayashi 2003] [Chudý 2004] [Corban et al. 2004] [Davidson 2004] [Dixon et al. 2004] [Ferrell et al. 2004] [Graham 2004] [Kitagawa 2004] [Lin et al. 2004] [Wei Ren and Beard 2004] [Yang and Obayashi 2004] [Dogan and Venkataramanan 2005] [Huang et al. 2005] [Kanda and Dowell 2005] [Majidi and Bab-Hadiashar 2005b] [Shin et al. 2005] [Smith and Willcox 2005] [Sorton and Hammaker 2005] [Thakoor et al. 2005] [Vartio et al. 2005] [Zaide and Raveh 2005] [Jyothi et al. 2006] [Kang and Hedrick 2006] [Klenke 2006] [Li et al. 2006] [Martina Chiaramonti 2006] [Mor and Livne 2006] [Platts 2006] [Rysdyk 2006] [Sarigul-Klijn and Huber 2006] [Zaide and Raveh 2006] [Zhang 2006] [Chao et al. 2007] [Cordoba 2007] [Dai et al. 2007] [Fujinaga et al. 2007] [Geng and Zhu 2007] [Hoa and Anh 2007] [In-Flight Demo of Multiple 2007] [Moulin and Karpel 2007] [Natesan and Bhat 2007] [Patil 2007] [Raveh 2007] [Sato and Satoh 2007] [Abdulwahab and Hongquan 2008] [Autonomous Flight Safety System 2008] [Edwards 2008] [Lawrence et al. 2008] [Lv et al. 2008] [Mangalam et al. 2008] [Rowley 2008] [Song 2008] [Vartio et al. 2008] [Burken et al. 2009] [Castillo-Effen et al. 2009] [Guo and Tang 2009] [Hameed et al. 2009] [Johnson 2009] [Lucas et al. 2009] [Nie et al. 2009] [Raveh 2009] [Ronfle-Nadaud 2009] [Rui Nie et al. 2009] [Valasek et al. 2009] [Yang et al. 2009] [Cao Lijia et al. 2010] [Chen et al. 2010] [Crespo et al. 2010a] [Crespo et al. 2010b] [Deonandan et al. 2010] [Gregory et al. 2010] [Hansu Dai and Jihong Zhu 2010] [Kahn 2010a] [Komnatska et al. 2010] [Kondrashov et al. 2010] [Lanzi and Simpson 2010] [Liu and Dai 2010] [Rao et al. 2010] [Ricci and Scotti 2010] [Rowley 2010] [Shao et al. 2010] [Simpson 2010] [Welstead and Crouse 2010] [Wu et al. 2010] [Yongxin Yin et al. 2010] [Zeng et al. 2010] [Cunningham et al. 2011] [Dillsaver et al. 2011] [Guidance of UAVs 2011] [Hoffmann et al. 2011] [Kobayashi and Takahashi 2011] [Lu et al. 2011] [Maria-Agneta and Stef 2011] [Qu et al. 2011a] [Raveh 2011] [Sasongko and Sembiring 2011] [Sato et al. 2011] [Scott et al. 2011] [Xu and Kroo 2011] [Xu et al. 2011a] [Yanushevsky 2011] [Zhang et al. 2011] [Balakrishnan 2012] [Dillsaver et al. 2012] [Frost et al. 2012] [Geng and Zhu 2012] [Giesseler et al. 2012] [Guo et al. 2012] [Haghighat et al. 2012] [Intelligent Motion Video Guidance 2012] [Qi et al. 2012] [Rajeswari and Suresh 2012] [Sasongko and Sembiring 2012] [Valasek et al. 2012] [Zeng et al. 2012b] [Zeng et al. 2012a] [Babcock and Lind 2013] [Bershadsky and Johnson 2013] [Dong et al. 2013] [Galaguz 2013] [Mundis et al. 2013] [Neumann and Mai 2013] [Qu et al. 2013] [Shao et al. 2013] [Tekinalp and Prach 2013] [Tunik et al. 2013] [Ucan and Mesut Pak 2013] [Zhang et al. 2013a] [Bai et al. 2014] [Canfield 2014] [Girish et al. 2014] [Hanson 2014a] [Horáček and Sváček 2014] [How et al. 2014] [Jung et al. 2014] [Kannan et al. 2014] [Kohno and Uchiyama 2014] [Kopasakis 2014] [Lavretsky 2014] [Lin and Yang 2014] [Mejias 2014] [Simon 2014] [Simpson et al. 2014] [Static Output Feedback Control 2014] [Unmanned Aerial Vehicle Path 2014] [Wang 2014] [Alam et al. 2015] [Coopmans et al. 2015] [Dai and Yang 2015] [Dongwoo Lee et al. 2015] [Fonte et al. 2015] [Garcia et al. 2015] [HIL Test Platform 2015] [Insaurralde 2015] [Kopasakis 2015] [Kopf et al. 2015] [Kumar et al. 2015] [Mansouri et al. 2015] [Mathisen et al. 2015] [Miotto et al. 2015] [Qi et al. 2015] [Ramasamy 2015] [Santos et al. 2015] [Volochiy et al. 2015] [Wang and Su 2015] [Wang et al. 2015a] [Automation and Autonomy 2016] [Bekemeyer and Timme 2016] [Chen and Duan 2016] [Chin et al. 2016b] [Chin et al. 2016a] [Chomachar and Fard 2016] [Hafez and Kamel 2016] [Hamayun et al. 2016] [Haridas and Vivek 2016] [Huang et al. 2016b] [Li et al. 2016b] [Liu and Sun 2016] [Liu et al. 2016a] [Paku et al. 2016] [Saxena and Faruque 2016] [Smith et al. 2016] [Survivability of Unmanned Autonomous 2016] [Tang et al. 2016] [UAV Navigation System 2016] [Unmanned Autonomous Vehicle 2016] [Vepa 2016] [Wang et al. 2016] [Williams et al. 2016] [Xue Lei et al. 2016] [Zhao and Zhu 2016a] [Zhao et al. 2016] [Zhuang et al. 2016] [Araujo-Estrada et al. 2017] [Bagheri et al. 2017] [Bekemeyer and Timme 2017] [Bekemeyer et al. 2017a] [Bekemeyer et al. 2017b] [Caverly et al. 2017] [Dai et al. 2017] [Dussart et al. 2017] [Ebeid et al. 2017] [Fan et al. 2017a] [Farhadi and Kortunov 2017] [Fezans 2017] [Fonte and Mantegazza 2017] [Guo et al. 2017] [Huntley et al. 2017] [Kramar et al. 2017] [Liu et al. 2017d] [Mardanpour et al. 2017] [Neace et al. 2017] [Noble and Bhandari 2017] [Pusch 2017] [Takase et al. 2017] [Valavanis 2017] [Wales et al. 2017] [Xiaoxiong et al. 2017] [Zhang et al. 2017b] [Abouheaf et al. 2018] [An et al. 2018b] [Chen et al. 2018b] [Depenbusch et al. 2018] [Ferrier et al. 2018] [Hammerton et al. 2018] [Hashemi et al. 2018] [Kopf et al. 2018] [Kubo 2018] [Lee et al. 2018] [Liu 2018] [Liu et al. 2018c] [Liu et al. 2018d] [Madden 2018] [Melville et al. 2018] [Misra and Bai 2018] [Pena et al. 2018] [Prachař et al. 2018] [Rafi et al. 2018] [Rasmussen et al. 2018] [Rogalski 2018] [Stambler et al. 2018] [Stastny and Siegwart 2018] [Szabolcsi 2018b] [Szabolcsi 2018c] [Takase et al. 2018] [Tani et al. 2018] [Thapa Magar et al. 2018] [Torens et al. 2018] [Tunik and Nadsadnaya 2018] [Wang et al. 2018b] [Yanushevsky 2018] [ÇOban and Oktay 2018] [Bagheri et al. 2019] [Demir et al. 2019] [Fezans et al. 2019] [Fu et al. 2019] [Godbole and Subbarao 2019] [Gu et al. 2019] [Hamada et al. 2019] [Jihui 2019] [Kadiri et al. 2019] [Khalil and Fezans 2019] [Liang et al. 2019] [Liu et al. 2019d] [Masunaga and Bueno 2019] [Prach et al. 2019] [Pusch et al. 2019] [Reinhardt and Johansen 2019] [Seki et al. 2019] [Smyth et al. 2019] [Szabolcsi 2019] [Uchida et al. 2019] [Wang et al. 2019d] [Wang et al. 2019b] [Williams et al. 2019] [Wood et al. 2019] [Çoban and Bilgiç 2019] [Alvarez et al. 2020] [Araujo-Estrada and Windsor 2020] [Baldi et al. 2020] [Cramer and Nguyen 2020] [Deskos et al. 2020] [ASTM International 2020] [Drew et al. 2020] [Hansen et al. 2020] [Johansen and Fossen 2020] [Khalil and Fezans 2020] [Kügler and Holzapfel 2020] [Li and Qin 2020] [Liu et al. 2020a] [McLaughlin and Perhinschi 2020] [Nascimento and Saska 2020] [Om et al. 2020] [Shriwastav and Song 2020] [Shukla et al. 2020] [Stanford 2020] [Wang et al. 2020c] [Wang et al. 2020a] [Zogopoulos-Papaliakos et al. 2020] [Barzgaran et al. 2021] [Costello et al. 2021] [Duggan and Bhandari 2021] [Gov and Karpel 2021] [ЛОПУХОВ and ФЕДОРОВ 2021] [Li and Qin 2021b] [Li and Qin 2021a] [Mejias et al. 2021] [Montazeri et al. 2021] [Najm et al. 2021] [Nguyen 2021] [Orhan and Subbarao 2021] [Rithirun et al. 2021] [Sanders-Reed 2021] [Wang et al. 2021a] [Wardana et al. 2021] [Woo et al. 2021] [Xu and Keshmiri 2021b] [Balatti et al. 2022] [Demirer and Kayran 2022] [Du et al. 2022] [Dudek and Schulte 2022b] [Fournier et al. 2022] [He et al. 2022b] [He et al. 2022a] [Jung and Kim 2022] [Kim et al. 2022a] [Li and Qin 2022] [Liu et al. 2022d] [Poussot-Vassal et al. 2022] [Pusch et al. 2022] [Qu and Li 2022] [Tang and Ma 2022] [Ting et al. 2022] [Wang et al. 2022c] [Wuestenhagen 2022] [Wynn et al. 2022] [Zhan et al. 2022] [Advanced Control Techniques 2023] [Asaro et al. 2023] [Ashokkumar 2023] [Balatti et al. 2023] [Dianovský et al. 2023] [Du et al. 2023] [Duessler et al. 2023] [Forte et al. 2023] [Ge and Liu 2023] [He and Su 2023] [Kamanli 2023] [Kumar et al. 2023c] [Liang et al. 2023] [Liu and Hao 2023] [Masrour et al. 2023] [Pessanha Santos et al. 2023] [Saied et al. 2023] [Seeni 2023] [Shan et al. 2023] [Son and Yoo 2023] [Ting et al. 2023] [Ullah et al. 2023] [Wu and Mao 2023] [Wuestenhagen 2023] [Yao et al. 2023] [Zhang and Zhao 2023] [Zhao et al. 2023f] [de Souza et al. 2023] [Barnes 2024] [Beyer et al. 2024] [Buck 2024] [Burgstaller and Galffy 2024] [Cavaliere and Fezans 2024] [Duessler et al. 2024] [Eraslan and Oktay 2024] [Farahmandi and Reitz 2024] [Khalil and Bauknecht 2024] [Khamvilai et al. 2024] [Liang et al. 2024] [Liu 2024] [Liu et al. 2024d] [Sharma and Jain 2024] [Sharma et al. 2024] [Sinha and Kumar 2024] [Stalla et al. 2024] [Trotti et al. 2024] [Wang et al. 2024c] [Wei et al. 2024b] [Yan and Li 2024] [Yue 2024] [Zahn et al. 2024] [Zhang et al. 2024c] [Zhao and Zhang 2024] [Zhou and Mao 2024] [Berenguer Bertran et al. 2025] [Fang 2025b] [Hu et al. 2025a] [Lee and Kim 2025] [Li et al. 2025c] [Li et al. 2025d] [Liu et al. 2025d] [Michel et al. 2025] [Moreno et al. 2025] [Navickiene et al. 2025] [Nunes et al. 2025a] [Nunes et al. 2025b] [Peng et al. 2025] [Randieri et al. 2025] [Schumann et al. 2025] [Sun et al. 2025c] [Van Manen et al. 2025] [Wang et al. 2025c] [Wheatcroft et al. 2025] [Wu et al. 2025] [Yan 2025] [Yang et al. 2025b] [Yang et al. 2025a] [Zahn et al. 2025] [An et al. 2026] [Düssler et al. 2026] [Forte and Nguyen 2026b] [Forte and Nguyen 2026a] [Forte et al. 2026] [Hillebrand and Lutz 2026] [Jianhong and Yanxiang 2026] [Kang and Shan 2026] [Liao et al. 2026] [Müller et al. 2026] [Orhan et al. 2026] [Pasupuleti 2026] [Pourtakdoust and Khodabakhsh 2026] [Quindlen et al. 2026] [Rieck et al. 2026] [Sabatini et al. 2026b] [Sabatini et al. 2026a] [Seargeant et al. 2026] [Tantaroudas and Karachalios 2026] [Thomas and Shkarayev 2026] [Tsoukalas et al. 2026] [Tuzlukov 2026] [Xiao 2026] [Yanushevsky 2026] [Zhang et al. 2026b] [Aerospace - Vehicle Management] [Castells Marin] [Forte and Nguyen] [Forte and Nguyen] [Forte et al] [Forte et al] [Clough] [Green and Oh] [Guang-Hong Yang and Kai-Yew Lum] [Gregory et al] [Krishnamoorthy] [Li] [Ma] [Majidi and Bab-Hadiashar] [Merheb] [Olson and Wuennenberg] [Pham] [Pritchett et al] [Sarantopoulos and De Abreu-Garcia] [Wilburn] [Yuan] [Wartluft 1975] [Paulson et al. 1977] [Pulk and Stolarik 1977] [Vinkler et al. 1980] [Kim and Russell 1981] [Drone Control System 1983] [Hall 1992] [Lourtie 1995] [Thomasson 1995] [Linehan 1996] [Hsiao et al. 1997] [Humphrey and Humphrey 1997] [Koo et al. 1999] [Mutuel and Speyer 2002] [Li and Chen 2003] [Zhao 2003] [Barlow 2004] [Brinker 2004] [Holzapfel and Sachs 2004] [Chitrakaran et al. 2005] [Jianli et al. 2005] [Natesan and Bhat 2005] [Rawlins 2005] [Xiao and Jiancheng 2005] [Keviczky and Balas 2006] [Kumon et al. 2006] [McGee and Hedrick 2006] [Yong Jiang et al. 2006] [Kumar et al. 2007] [Ren 2007] [Rosa et al. 2007] [Ducard and Geering 2008] [Fravolini et al. 2008] [Hsiao et al. 2008] [Joo et al. 2008] [Natesan et al. 2008] [Ogren and Winstrand 2008] [Tan and Damodaran 2008] [Barrientos et al. 2009] [Kondrashov et al. 2009a] [Kondrashov et al. 2009b] [Pouya and Saghafi 2009] [Cetin et al. 2010] [Ding et al. 2010] [Low 2010] [Albaker and Rahim 2011] [Ceren and Altuğ 2011] [Muhammad Aamir Zafar et al. 2011] [Yi et al. 2011] [Daibing et al. 2012] [Kondrashov et al. 2012] [Lu et al. 2012] [Catena et al. 2013] [Coopmans et al. 2013] [Jeong et al. 2013] [Korkmaz et al. 2013] [Marques 2013] [Meng 2013] [Oland and Kristiansen 2013] [Rzucidło 2013] [Chen 2014] [Huang and Su 2014] [Ru and Wei 2014] [Tarhan et al. 2014] [Tekinalp and Prach 2014] [Garg et al. 2015] [Hajiyev et al. 2015c] [Hajiyev et al. 2015b] [Hajiyev et al. 2015a] [Leylek and Costello 2015] [Schopferer and Pfeifer 2015] [Xiaofeng Zhang et al. 2015] [Dou and Duan 2016] [Kharchenko et al. 2016] [Li et al. 2016a] [Song et al. 2016] [Sun and Pack 2016] [Szabolcsi 2016] [de Bruin and Jones 2016] [Azimov and Allen 2017] [Benders and Schopferer 2017] [Bulka and Nahon 2017] [Czyba and Hecel 2017] [Fan et al. 2017b] [Ghosh et al. 2017] [Kikkawa and Uchiyama 2017] [Kim and Kunz 2017] [Kuwamura and Hara 2017] [Sadraey 2017c] [Zakharin and Ponomarenko 2017] [Adam et al. 2018] [Flanagan et al. 2018] [Gavrilovic et al. 2018] [Hailemichael et al. 2018] [Jafari and Xu 2018] [Kim et al. 2018] [Seiferth et al. 2018] [Smirnov and Smirnova 2018] [Szabolcsi 2018a] [Tripathi et al. 2018] [Wang et al. 2018a] [Wu and Mueller 2018] [Adam et al. 2019] [Autonomous Control of Unmanned 2019] [Burnashev and Zbrutsky 2019] [Cox and Wong 2019] [Feng 2019] [Hirano et al. 2019] [Li et al. 2019b] [Lungu 2019] [Morozov and Chermoshentsev 2019] [Yang et al. 2019a] [Zhu et al. 2019] [Development of the Navigation 2020] [Flanagan et al. 2020] [Guo et al. 2020] [Hernandez Ramirez and Nahon 2020] [Kitsios et al. 2020] [Koh and Paranjape 2020] [Lanteigne and O’Reilly 2020] [Mersha et al. 2020] [Mirchandani 2020] [Salahudden et al. 2020] [Waitman and Marcos 2020] [Wang and Somani 2020] [Wang and Wang 2020] [Yin et al. 2020] [Zhen et al. 2020] [Autonomous Navigation of Unmanned 2021] [Bestugin et al. 2021] [Cao and Lynch 2021] [Chen 2021] [Gomez and la Cour-Harbo 2021] [Khobin and Goncharenko 2021] [Klipp et al. 2021] [Morgan and Beard 2021] [Sevostyanov and Devitt 2021] [Wu et al. 2021] [Xu and Keshmiri 2021a] [Zhou et al. 2021b] [de Jong et al. 2021] [Bektash et al. 2022] [Cao and Yu 2022] [Empey and Nahon 2022a] [Kirk et al. 2022] [Lungu 2022] [Ntakolia et al. 2022] [Oktay and Eraslan 2022] [Sevostyanov et al. 2022] [Trefilov 2022] [Wang et al. 2022d] [Wu et al. 2022c] [Yin et al. 2022b] [Bacheti et al. 2023] [Bowes et al. 2023] [Hognadottir et al. 2023] [Senthil Kumar and Shanmugam 2023] [Lyu et al. 2023] [Simms 2023] [Sivalingam and Hagen 2023] [Vepa 2023a] [Agrawal et al. 2024] [Ebrahimpour et al. 2024] [Gulivindala et al. 2024] [Movahhed and Hamed 2024] [Nguyen 2024] [Wang and Yu 2024] [Zbrutsky et al. 2024] [el mobaraky et al 2024] [Chen et al. 2025] [El Mobaraky et al. 2025] [Kabanov and Mitin 2025] [Mundheda et al. 2025] [Pande 2025] [Pham et al. 2025] [Singh and Kamal 2025] [Wu et al. 2024c] [Zlobin 2025] [Bayrak 2026] [Elo and Keshmiri 2026] [Kinatas and Joerger 2026] [Liu and Valavanis 2026] [Nguyen et al. 2026] [Qiao et al. 2026] [Sieliukov and Ponomarenko 2026] [Spiller et al. 2026] [Adoghe] [Alatorre Sevilla] [Carryer] [Chan] [Cunis] [Dermer] [Figueiredo Prudencio] [Gallo Olalla] [Guo] [Iglésis] [Kaminer et al] [Lugo Cárdenas] [Mercado-Ravell] [Sarabakha] [Sims] [Slapnicar] [Sunil] [Tang] [Wallace] [Christopher and Dunn 1973] [Holley and Bryson 1975] [Fichtl 1977] [Johnston 1979] [Hwang and Pi 1982] [Nagashima and Tanida 1984] [Ivan 1985] [Ivan 1986] [Trevino 1986] [Olwi 1994] [Jianping 1995] [Olwi 1996] [Tang et al. 2000] [Li and Lan 2003] [Breitsamter 2005] [Lievens et al. 2005] [Hall et al. 2006a] [Hall et al. 2007] [Wu et al. 2016b] [Wang et al. 2017e] [Quenzer et al. 2019] [Castells Marin and Poetsch 2020] [Miao et al. 2020] [Kaiser and Friedewald 2024] [Mohamed et al. 2026] [Automatic Pilots Turbine Powered]
Measuring a flight test of an uncrewed aircraft
Measuring the flight test. Flight test instrumentation, telemetry, air data, range safety and flight termination, and the flight-test technique and system identification of uncrewed and crewed aircraft.
340 records. [Iscold 2008] [Dorobantu et al. 2013] [Hoffer et al. 2013] [Hoffer et al. 2014] [Hoffer et al. 2015] [Simmons et al. 2023] [Rice 1946] [Schumacher 1952] [Bryan 1953] [Howland 1953] [Hager 1955] [Dettbarn 1957] [Kidder 1957] [Luecke 1957] [Durbin 1959] [Higgins 1959] [Mannai 1962] [Rickman and Holquin 1962] [Godwin et al. 1964] [McKendry and Harrison 1964] [Buige and Goode 1965] [Flight Test Instrumentation 1965] [Gerlach 1965] [Leonard and Solmon 1965] [Mertens and Tabeling 1965] [Pendleton 1965] [Pfeiff 1965] [Sanderson 1965] [Shepard 1965] [Tuckman 1965] [AAP Preliminary Range Safety 1967] [Ince 1967] [Meyers et al. 1968] [Rooker 1970] [Renaudie 1971] [Woodman 1971] [Edwards 1972] [Simpson 1972] [Wingrove 1972] [Wirth 1972] [Pool and Bosman 1974] [Air Force Flight Test Center Edwards AFB CA 1974] [Knoblach 1974] [Doran 1975] [Hull and Roger 1975] [Olhausen 1975] [Westbrook 1975] [Petersen 1976] [Armstrong 1977] [Grose 1979] [Simpson 1979] [Bennett 1981] [Bleimeyer 1981] [Bolt 1981] [Bever 1981] [Harney 1981] [Kotsabasis 1981] [Macmillan 1981] [Nash 1981] [Newsom and Pototzky 1981] [Petersen 1981] [Shields 1981] [Ramsburg et al. 1982] [Rummer et al. 1982] [Bailey and Linder 1983] [Dickhudt 1983] [Hillaker 1983] [Lamy 1983] [Rosenberg and Schuch 1983] [Stengel 1983] [Strock 1983] [Advisory Group for Aerospace Research and Development 1984] [Brooks 1986] [Deets and Brown 1986] [Demo 1986] [Hess 1986] [Sefic and Maxwell 1986] [Burton 1987] [Williams and Hartford 1987] [Roberts 1988] [Vanatta and Inderhees 1988] [Hicks and Petersen 1989] [Air Force Test Pilot School Edwards Afb Ca 1990] [Drag and Propulsive Efficiency 1990] [Gallien 1990] [Khalid and Faherty 1990] [Moorhouse 1990] [Yip et al. 1990] [Bever 1991] [Howard et al. 1991] [Yip et al. 1991] [Bogue 1992] [Test and Evaluation Guidelines. 1992] [Hart 1992] [Howard and Bray 1992] [Krumenacker and Pellicano 1992] [Manning et al. 1992] [Air Force Test Pilot School Edwards Afb Ca 1993] [Boex 1993] [Budd et al. 1993] [Hyde and Massie 1993] [Agnihotri et al. 1994] [Dwyer 1994] [Green and Fernandez 1994] [Maine et al. 1994] [Pawlak 1994] [Borek and Pool 1994] [Rice and Hazlwood 1994] [Thornton 1994] [Budd et al. 1995] [Fischenberg 1995] [Morelli and Klein 1995] [Schulze et al. 1995] [Traven and Whitley 1995] [Blue and Crawford 1997] [Sitz et al. 1997] [Oelker and Friehmelt 1998] [Sarkar and Panneerselvam 1998] [Yechout et al. 1998] [Brown and Smith 1999] [Development of a Flight 1999] [Hall et al. 1999] [Jones 1999] [Schifferle et al. 1999] [Arkov 2000] [Curry and Batterson 2000] [Schwegler - Lanl and Place - Honeywell 2000] [Niewald and Parker 2000a] [Bartone et al. 2001] [Chadsey and Yechout 2001] [Westat INC Rockville MD 2001] [Wolf and Bossert 2001] [Bartone et al. 2002] [Lee et al. 2002] [Schrock and Humphries 2002] [Campbell and Kresge 2003] [Cenko et al. 2003] [Crockett 2003a] [Crockett 2003b] [Dynamic Longitudinal Stability Flight 2003] [Level Flight Performance Flight 2003] [Ly and Higashino 2003] [Methods for Reducing Data 2003] [Pettigrew 2003] [Ratcliffe and Crane 2003] [Suk et al. 2003] [Tomczyk 2003] [Zugel 2003] [Adelgren et al. 2004] [Johnson et al. 2004] [Klyde et al. 2004] [Minor et al. 2004] [Shore and Bodson 2004] [Simmons 2004] [Stoliker 2005] [Ostler and Bowman 2005] [Shore and Bodson 2005] [Whiteman et al. 2005] [Faulstich and Law 2006] [Ferrara et al. 2006] [Morehouse 2006] [Alich and Castillo 2007] [Bradley et al. 2007] [Lightweight Low-Cost Flight Test 2007] [Tow and Arce 2007] [Tow and Arce 2008] [Jann and Greiner-Perth 2009] [Tow 2009] [A Typical Avionics Integration 2010] [Hong et al. 2010] [Kutty and Pratt 2010] [Tow 2010b] [Tow 2010a] [Ward and Jenal 2010] [Weisman and Valasek 2010] [Beaty 2011] [Riesland and Lutgen 2011] [Golackson 2011] [Jorris et al. 2011] [Starr et al. 2011] [Tow 2011] [Chase and McDonald 2014] [Clark et al. 2014] [Kennedy et al. 2014] [McCrink and Gregory 2014] [Bunge et al. 2015] [Gong and Wu 2015] [Jann and Yakimenko 2015] [Liebin et al. 2015] [Olson 2015a] [Rasmussen and Kingston 2015] [Thamann et al. 2015] [Harris et al. 2016] [Lapalme et al. 2016] [Ricciardi and Minwalla 2016] [Vengate et al. 2016] [Arisandi 2017] [Bageshwar 2017] [Belcastro et al. 2017] [Lu et al. 2017] [Michalowski and Varano 2017] [Soltmann and Hall 2017] [Glaab et al. 2018] [Lu et al. 2018] [Martínez Morán 2018] [Shukla and Woolsey 2018] [Son 2018] [Abdulrahim 2019] [Castillo Zuñiga et al. 2019] [Dantsker et al. 2019] [Morawski et al. 2019] [Thakur et al. 2019] [Jacob da Motta 2020] [Dotson et al. 2020] [Förder and Steiner 2020] [Aircraft and Flight Test 2021] [Chowdhury et al. 2021] [Dantsker et al. 2021] [Sandoz and Klaeyle 2021] [Yang 2021a] [Yang 2021b] [Don and Grabner 2022] [Jeong and Bae 2022] [Leshikar and Valasek 2022] [Li et al. 2022a] [Machnik et al. 2022] [Palomino 2022] [Sedlmair et al. 2022] [Süelözgen 2022] [Xu 2022] [Hao and Wang 2023] [Mayer and Chalfant 2023] [Hodson and Evans 2023] [Xi et al. 2023] [Xin 2023] [Finigian et al. 2024] [Matos and Marta 2024] [Monteil 2024] [Pérez Rus and Le Gal 2024] [Sandoz et al. 2024] [White et al. 2024] [Justin James Matt et al. 2025b] [Liu et al. 2025f] [McClelland et al. 2025] [Roseberry 2025] [Szymanski et al. 2025] [Balcan et al. 2026] [Gi et al. 2026] [Shou and Li 2026] [Thato Elijah and Rui Vasconcellos 2026] [Voss et al. 2026] [Yuan 2026] [Blue and Crawford] [Chase] [Cutright and Braasch] [Hallberg et al] [Hinton and Eastlake] [Keviczky and Balas] [Roberts] [Seanor] [Young] [Deets and Edwards 1974] [Jarvinen and Bruce 1976] [Mourey 1979] [Bergevin 1993] [Fitzgerald and Gingras 1996] [keshmiri et al 2008] [Lombaerts 2012] [Thomas et al. 2012] [Mykhatsky et al. 2013] [Jang et al. 2015] [Marston 2015] [Yeo et al. 2015] [Arthurs and Valasek 2016] [Jain and Kamali 2016] [Nugroho and Dectaviansyah 2018] [Jaganraj and Velu 2019] [Zhu et al. 2020b] [Qi et al. 2021] [Han et al. 2022b] [Safeer and Costello 2026] [Szuniewicz et al. 2026] [Flight performance of civil] [Sevcik and Oh] [Sevcik and Oh] [Cornell Aeronautical Lab INC Buffalo NY 1947] [Brailsford 1950] [Newton 1965] [Porter 1965] [Williams 1965] [Rodden and Stahl 1969] [Altstatt 1974] [Eckstrom and Peele 1974] [Nash et al. 1975] [Edwards 1981] [Gupta and Iliff 1982] [Edwards 1983] [Trankle and Rabin 1983] [White et al. 1985] [Bertelrud et al. 1988] [Hernandez and Taylor 1988] [Kehoe 1988] [Howard et al. 1989] [Neville and Stephens 1993] [Farhat 1998] [Sarkar et al. 1999] [Yechout and Dowty 1999] [Farhat 2000] [Sarkar et al. 2000] [Farhat 2001] [Rogers 2002] [Dynamic Lateral-Directional Stability Theory 2003] [Lan and Brandon 2003] [Lateral-Directional Stability Theory 2003] [Longitudinal Control and Trim 2003] [Static Longitudinal Stability Flight 2003] [Jordan and Bailey 2008] [Sarkar et al. 2009] [Morelli 2011] [Sarkar et al. 2011] [Zeng and Kukreja 2013] [Brandon and Morelli 2014] [Glīzde 2017] [Saderla et al. 2017] [Yavuztürk et al. 2017] [Hamada and Moreno 2018] [Kumar and Ghosh 2018] [Dias 2023] [Preisighe Viana 2026] [Albisser] [Altimeter, Pressure, Compensated Turbine] [Flight Test Procedures for] [Mach Meters Turbine Powered] [Maximum-Allowable-Airspeed Instruments Turbine Powered] [Overspeed Warning Instrument Turbine] [Rate of Climb Vertical] [Remote Servoed Air Data] [Stall Warning Instrument Turbine] [Temperature Instruments Turbine Powered] [Total Temperature Measuring Instruments]
Designing, sizing and powering a small uncrewed aircraft
The design literature of the class the X-61A belongs to. Configuration, sizing, airfoils, propellers and power, structures and morphing of small uncrewed aircraft and of uncrewed combat air vehicles.
159 records. [Eilertson 1975] [Hickey 1975] [JanakiRam 1980] [Maughmer and Somers 1987] [Howard 1990] [Bray et al. 1992] [Batill et al. 1999] [Goraj et al. 1999] [Harmats and Weihs 1999] [Ghee and Hall 2000] [Munro and Krus 2002] [Cummings et al. 2003] [Biber et al. 2004] [Crouse and Sash 2004] [Ordaz et al. 2004] [Gordnier et al. 2006] [Cummings et al. 2008] [Elkhoury 2008] [Pitcher and Maple 2008] [Abdelrahman et al. 2009] [Deittert et al. 2009] [Fielding et al. 2009] [Gur and Rosen 2009a] [Meyer et al. 2009] [Nguyen et al. 2009] [Subbarao et al. 2009] [Tianyuan and Xiongqing 2009] [Choi et al. 2010] [Edge et al. 2010] [Harasani 2010] [Edge et al. 2011] [Voss et al. 2011] [Özöztürk et al. 2011] [Cummings and Schütte 2012] [Initial Unmanned-Aircraft Sizing 2012] [Tekinalp and Cavus 2012] [Tomac et al. 2012] [Unmanned-Aircraft Geometry and Configurations 2012] [Ahmed and Page 2013] [Nguyen et al. 2013b] [Кривохатько 2013] [Yang et al. 2013b] [Herbst and Klöckner 2014] [Initial Unmanned Aircraft Sizing 2014] [Ruetten et al. 2014] [Ryaciotaki-Boussalis and Guillaume 2014] [Unmanned Aircraft Geometry 2014] [Zimper and Hummel 2014] [Bramesfeld and Prinster 2015] [Design and Fluid Flow 2015] [Kanoria et al. 2015] [Khan and Nahon 2015b] [Kotikalpudi et al. 2015] [Mechatronic Design of Unmanned 2015] [Nagarjuna and Suresh 2015] [Argrow 2016] [Flow Control and High-Lift 2016] [Li et al. 2016c] [Most 2016] [Rutkay and Laliberté 2016] [Templalexis et al. 2016] [Çakıcı and Leblebicioğlu 2016] [Alsahlani et al. 2017] [Gao et al. 2017] [Szilder and Yuan 2017] [Arik et al. 2018] [Babitha Kodavanla et al and Tjprc 2018] [Burton and Hoburg 2018] [Goetten et al. 2018] [Gryte et al. 2018] [Hassanalian et al. 2018] [Oktay et al. 2018] [Verstraete et al. 2018] [Vicroy et al. 2018] [Yu 2018] [van Rooij and Cummings 2018] [De Vivo et al. 2019] [Franco et al. 2019] [Kasim Biber and Trenton White 2019] [Papageorgiou et al. 2019] [Peigin et al. 2019] [Sharif 2019] [Tahir et al. 2019] [Yu et al. 2019] [Feng 2020] [Deulgaonkar et al. 2020] [Nagornov 2020] [Pellerito et al. 2020] [Prasad 2020] [Zhao et al. 2020] [Anurag et al. 2021] [Das Patel and Kumar Karuparthi 2021] [Kei̇yi̇nci̇ and Aydin 2021] [Liang et al. 2021] [Love and Argrow 2021] [Most and Stroup 2021] [Neufeld 2021] [Hung et al. 2022] [Isah et al. 2022] [Jianzhi et al. 2022] [Kocamer et al. 2022] [Metodiev 2022] [Ramin et al. 2022] [Reghunath and Ramaiah 2022] [Sharif 2022] [Wang and Zhou 2022] [Webb 2022] [Eraslan and Oktay 2023] [Romli et al. 2023] [Guo et al. 2023] [Khalid 2023] [Kumuk and Ilbas 2023] [Milic and Svorcan 2023] [Patel et al. 2023] [Özbek et al. 2023] [Dominguez et al. 2024] [Dorange et al. 2024] [Duraklar 2024] [Grois et al. 2024] [Remiger et al. 2024] [Skarka and Mateja 2024] [Ahmed et al. 2025] [Haider 2025] [Lampropoulos et al. 2025] [Prasad 2025] [Rouser et al. 2025] [Saltan and İNce 2025] [Bhattacharya 2026] [Buda et al. 2026] [Li and Tiniakov 2026] [Shbailat 2026] [Wauters et al. 2026] [Aerodynamic efficiency and performance] [Environmental Control Systems ECS] [Gc] [Glīzde] [Gordnier et al] [Gómez Rodríguez] [Hartney] [Jordan] [King] [Rutkay] [Tan] [Borst 1978] [Mueller and Torres 2001] [Luke and Bowman 2004] [Viieru et al. 2004] [Roy 2009] [Roy and Ghosh 2010] [Shields and Mohseni 2010] [Żbikowski 2010] [Pachikara and Lind 2012] [Aircraft et al. 2015] [Zyluk and Sibilski 2015] [Gabor et al. 2016] [Panagiotou and Yakinthos 2017] [Biber 2023] [Nimura and Oyama 2024] [Momodu et al. 2025]
Uncrewed aircraft programmes, standards and airspace
The programme record of uncrewed aircraft as aircraft. Reports and histories of particular uncrewed programmes, design and designation standards, and the integration of uncrewed aircraft into airspace.
30 records. [Republic Aviation Corp Mineola Ny 1963] [Alexander 1979] [Berman 1997] [Chen et al. 2002a] [Reichenbach 2003] [Twesme and Corzine 2003] [Altman 2008] [Fry 2008] [Zeng 2011] [Gardi et al. 2016] [Kaymal 2016] [Melnyk 2019] [Rudnick-Cohen et al. 2019a] [Rudnick-Cohen et al. 2019b] [Turnage et al. 2019] [Kallinen et al. 2020] [Pugh et al. 2020] [Edwards et al. 2021] [Janisch et al. 2022] [Watkins et al. 2023] [Hardy 2026] [Ates et al] [Lunsford] [Practice for Commercial Unmanned] [Specification for Design, Construction] [Specification for Design, Construction] [Standard Specification for Design] [Standard Specification for Design] [Gingrich et al. 1977] [Matheny and Panageas 1981]
Lift, induced drag and the drag polar
The relations behind the span argument and the ceiling on the polar. Induced drag and span loading, lifting-line and vortex-lattice theory, profile and zero-lift drag, the drag polar and the lift to drag ratio, and wing and airfoil design at low speed.
243 records. [Report No. 349. 1930] [Vessey 1935] [Young and Booth 1951] [Hoerner 1952] [Chapter 2. Aerodynamics 1957] [Chapter 2. Aerodynamics 1960] [Lakshminarayana 1962] [Roberts 1963] [White 1963] [Sanders 1965] [Gilman and Burdges 1967] [Lundry 1967] [Haines 1968] [Revell 1968] [Loth and Boyle 1969] [Snyder and Zumwalt 1969] [Kalman et al. 1970] [Hancock 1971] [Liebeck 1971] [Cunningham 1972] [Giesing and Kalman 1972] [Hua 1973] [Ericsson and Reding 1974] [Fox and Breedlove 1974] [Rodden et al. 1974] [Schwartzberg 1975] [Aerodynamics of Arbitrary Wing 1976] [Ericsson and Reding 1976] [Yajnik and Subbaiah 1976] [Ericsson and Reding 1977] [Lundry 1977] [Reubush 1977] [Feagin and Morrison 1978] [Henderson 1978] [Laitone 1978] [Liebeck 1978] [Kohn 1979] [Barsony-Nagy and Hanin 1980] [Deyoung 1980] [Sachs 1980] [Bertelrud 1981] [Knaus 1981] [Burns and Cliff 1982] [Analysis for Calculating 1983] [Erickson and McCann 1983] [Knaus 1983] [Loth and Loth 1984] [Lottati 1984] [Wu et al. 1984] [Dixon and Driskill 1985] [Stark 1985] [Stewart 1985] [Oh and Tavella 1986] [Greene 1988] [Hicks and Moulton 1988] [Lowe 1988] [Naik and Ostowari 1988] [Laitone 1989] [McCutchen 1989] [Application of CFD 1990] [Brune and Bogataj 1990] [Dehaan 1990] [Sears 1990] [Smith and Kroo 1990] [Subsonic Airfoil Design 1990] [Tseng 1990] [Schmidt 1991] [Segall and Gajdjis 1991] [Straussfogel and Maughmer 1991] [Rom 1992] [Tu 1992] [Janus et al. 1993] [Ahmed and Vidjaja 1994] [Aerodynamic Forces on Aircraft 1995] [Edge and Perkins 1995] [Hong and Roberts 1995] [Reuther and Jameson 1995] [Vaughan and Wood 1995] [va et al 1995] [Smith 1996] [Wolf 1996] [Giguere et al. 1997] [Ichikawa and Matsuda 1997] [Lift Coefficient According 1997] [Tuncer and Platzer 1998] [Al-Atabi and Asrar 1999] [Data Item Predicts Wing 1999] [Roman et al. 2000] [Frediani et al. 2001] [Ulrich et al. 2001] [Bourdin 2002] [Jouannet and Krus 2002] [McAvoy and Gopalarathnam 2002] [Mialon et al. 2002] [Schmidt and Duren 2002] [Tomiyama 2002] [van Es 2002] [Huang 2003] [Kentfield and Spragins 2003] [Birch et al. 2004] [Lee 2004b] [McDaniel and Wilks 2004] [Kier 2005] [Somers 2005] [B 2006] [Lee 2006] [Meheut and Bailly 2006] [Alley et al. 2007a] [Alley et al. 2007b] [Apostolyuk 2007] [Fixed Rigid-Wing Aerodynamics 2007] [Flexible-Wing Aerodynamics 2007] [Phillips and Alley 2007] [Sinha 2007] [Rodrigues 2008] [Spalart 2008a] [Spalart 2008b] [Petrov 2009] [Santos and Mattos 2009] [Aerodynamics of Wing Body 2010] [Appendix H Aerodynamics 2010] [Basic Aerodynamic Definitions 2010] [Broering and Lian 2010] [Estimating Wing Body Aerodynamics 2010] [Melin et al. 2010] [Hartshorn 2011] [Takahashi and Donovan 2011] [Bunge and Kroo 2012] [Diebold et al. 2012] [Meheut et al. 2012] [Nguyen and Urnes 2012] [Panaras 2012] [Takahashi 2012] [Bui 2013] [Lyu and Martins 2013] [Pate and German 2013] [Phillips and Hunsaker 2013] [Urnes and Nguyen 2013] [Camberos et al. 2014] [Haryanto et al. 2014] [Linyue Gao et al. 2014] [Rizzi 2014] [Andrews and Perez 2015] [Hantrais-Gervois and Destarac 2015] [Olson 2015b] [Almosnino 2016] [Bui 2016] [Cumming et al. 2016] [Gunasekaran and Mukherjee 2016] [Paudel 2016] [Righi et al. 2016] [Shkarayev et al. 2016] [Takahashi and Barchfeld 2016] [Xia and Mohseni 2016] [Deng et al. 2017] [Fujiwara and Nguyen 2017] [Luckring et al. 2017] [Rizzi and Luckring 2017] [Sadraey 2017a] [Yang and Zha 2017] [de Paula et al. 2017] [Schirra et al. 2018] [Sforza 2018] [Yang and Zha 2018a] [Yang and Zha 2018b] [Abdel-Motaleb et al. 2019] [Bajaj 2019] [Erfani and Kontis 2019] [Mao et al. 2019] [Phillips et al. 2019] [Varshney et al. 2019] [Borisova and Silant’ev 2020] [Bourisli and Hamadeh 2020] [Davies 2020] [Russo et al. 2020a] [Russo et al. 2020b] [Sforza 2020] [Varshney et al. 2020] [An et al. 2021] [Brincklow and Hunsaker 2021] [Characteristic Parameters for Airfoil 2021] [Chauhan and Martins 2021] [Drag Polar Measurement 2021] [Durmus 2021] [Frolov 2021] [Gunasekaran and Sharp 2021] [Kehayas 2021] [Pamnani and Jeughale 2021] [Schirra et al. 2021] [Velazquez Salazar et al. 2021] [Yin et al. 2021] [Balla and Vad 2022] [Liu 2022a] [Liu 2022b] [Taniguchi and Oyama 2022] [Traub 2022] [Valenti and Yukish 2022] [Varshney et al. 2022] [Anand et al. 2023] [Jeon et al. 2023b] [Jeon et al. 2023a] [Sadraey 2023] [Viswanath et al. 2023] [Zeleke et al. 2023] [Zong et al. 2023] [Frassoldati et al. 2024] [Jalil et al. 2024] [Keller et al. 2024] [Kieszek et al. 2024] [Liang 2024a] [Liang 2024b] [Luo 2024] [Masuda et al. 2024] [McBreen and Zha 2024] [Verma and Kulkarni 2024] [Patel et al. 2024] [Rostami 2024] [Ruiz Estrada 2024] [Song et al. 2024b] [Torres and Rahai 2024] [Zheng and Chen 2024] [Characteristic Parameters for Airfoil 2025] [Darma et al. 2025] [Davies 2025] [Esabat et al. 2025] [Gonçalves and da Silva 2025] [Jamal et al. 2025] [Lin 2025] [Ma 2025] [Mohan and Kumar 2025] [Naseri and Zare 2025] [Shiihara et al. 2025] [Vieira et al. 2025] [Zhang and Du 2025] [Zheng et al. 2025] [Makade et al. 2026] [Moreno and Prasad 2026] [Oruç 2026] [Otsuka et al. 2026] [Pham 2026] [Subramanian 2026] [Zhang et al. 2026d] [Ravikiran and Ubaidulla]
Transonic flow and the drag rise
Where the published Mach number sits. Transonic wing and airfoil flow, the drag rise and the wave drag near Mach one, and transonic design.
133 records. [Foss and Swihart 1956] [Küchemann 1957] [Olsen 1966] [Ward 1968] [Shanbhag and Narasimha 1970] [Spreiter and Stahara 1970] [George-Falvy 1971] [Spreiter and Stahara 1971] [Smetana and Knepper 1973] [Barnwell 1974] [Mohn 1975] [Garabedian 1976] [Boppe 1977] [Desai et al. 1977] [Jameson 1977] [Capone 1978] [Henne and Hicks 1978] [Kamiya et al. 1978] [Lucas 1978] [Krenz 1979] [Henne 1980] [Shankar 1980] [Transonic Maneuver/Cruise Airfoil Design 1980] [A-7 Transonic Wing Designs 1982] [Application of Computational Methods 1982] [Holst and Thomas 1982] [Mason 1982] [Shankar and Malmuth 1982] [Sun and Hansen 1982] [Agarwal and Deese 1983] [Hortsen et al. 1983] [Whitcomb 1983] [Agrell and Elmeland 1984] [Hall 1984] [Spaid 1984] [Cahill 1986] [Malmuth et al. 1986] [Mertens et al. 1986] [Walkley 1986] [Gregg and Misegades 1987] [Malmuth et al. 1987] [Mertens et al. 1987] [Sobieczky et al. 1987] [Walkley and Smith 1987] [Goradia and Bobbitt 1988] [Woan and Chakravarthy 1988] [Brower 1989] [Van Der Vooren and Van Der Wees 1990] [Seider and Haenel 1991] [van der Vooren and van der Wees 1991] [Gillan 1993] [Kim and Sung 1993] [Naida and Fonarev 1995] [Naida and Fonarev 1996] [Roach and Froning 1996] [Tourrette 1996] [Masson et al. 1998] [Weber 1998] [Kusunose et al. 1999] [Masson et al. 1999] [Petruzzelli and Keane 2001] [Balleur et al. 2002] [Oki et al. 2002] [Rosemann and Birkemeyer 2002] [Fujino and Kawamura 2003] [Ko et al. 2003] [Nixon 2003] [Roman et al. 2003] [Klausmeyer 2004] [Cole and Malmuth 2005] [Schröder and Meijering 2005] [Zamuraev and Kalinina 2005] [Vadillo and Agarwal 2007] [Brunet and Deck 2008] [Jung 2009] [Rein et al. 2009] [Vadillo and Agarwal 2009] [Xu et al. 2009] [Knight et al. 2011] [Skujins and Cesnik 2011] [Aul’chenko and Zamuraev 2012] [Knight et al. 2012] [Pylypenko et al. 2012] [Qin 2012] [Transonic Aircraft Configurations 2012] [Yamamoto et al. 2012] [Mele et al. 2014] [Zimper and Rein 2014] [Hinchliffe and Qin 2016] [Chan et al. 2017] [Hinchliffe and Qin 2017] [Jing and Huang 2017] [Bui 2018] [Doherty et al. 2018] [Sorbilli et al. 2018] [Xiong et al. 2019] [Brutyan et al. 2020] [Droney et al. 2020] [Xiong et al. 2020b] [Kurus et al. 2021] [Nguyen et al. 2021b] [Xiong et al. 2021b] [Xiong et al. 2021a] [Zhu and Qin 2021] [Fournis 2022] [Liu 2022c] [Xiong et al. 2022b] [Xiong et al. 2022a] [Gao 2023] [Herr et al. 2023] [Nangia et al. 2023] [Xiong and Nguyen 2023] [Xiong et al. 2023a] [Xiong et al. 2023b] [Fujino and Suzuki 2024] [Kaneko et al. 2024] [Luo et al. 2024] [Xiong and Nguyen 2024] [Hanman et al. 2025] [Maia Nunes Celestino et al. 2025] [Sun et al. 2025a] [Bauer et al. 2026] [Celestino et al. 2026] [Jesudasan et al. 2026] [Haseeb 2026] [Mavriplis and Kafyeke 2026] [Shahjahan and Ahuja 2026] [Sun et al. 2026a] [Aerodynamic wave drag] [Hiller et al] [Hiller et al] [Grossi] [Chau and Duensing]
Aircraft performance, range and conceptual design
The range and the performance the sizing uses. The Breguet relation and its variants, climb, cruise and level-flight performance, and conceptual design and sizing.
75 records. [Mount 1964] [Andrews 1969] [Dunlap and Porter 1971] [Thomasson and Cook 1971] [Cross 1975] [Cross 1976] [Bridges et al. 1977] [Gillette 1977] [Reubush 1978] [Large 1981] [Feistel 1985] [Miller and Koch 1985] [Aerodynamic Design of Low-Speed 1986] [Ong 1987] [Sachs and Christodoulou 1987] [Smith et al. 1991] [Martinez-Val and Perez 1992] [Udin and Anderson 1992] [Dehua and Changyou 1993] [Bardell 2000] [Smetana 2001] [Destarac and van der Vooren 2004] [Iosilevskii 2005] [Koc et al. 2005] [Wakayama 2006] [Kehayas 2007] [Rallabhandi and Mavris 2008] [Aerodynamic Data of Real 2010] [Aerodynamics and Airframe Configurations 2010] [Aircraft Performance Methods 2010] [Appendix G Aerodynamic Data 2010] [Cavagna et al. 2010] [Chu et al. 2010] [Smyth 2010] [Takahashi and Donovan 2010] [Brown 2011a] [Cavagna et al. 2011] [Guynn 2011] [Flight Performance 2012] [Takahashi 2013] [Flight Performance 2014] [Stanford 2014] [Exploring the Flight Envelope 2015] [Ilić et al. 2016] [Liou et al. 2016] [Clark 2017] [Bovet 2017] [Brewer 2017] [Liou et al. 2017] [Clark 2018] [Liou et al. 2019] [Anatolievich and Andreevich 2020] [Wagenmakers 2020] [Wroblewski and Ansell 2020] [Asselin 2021] [Flight Envelope 2021] [Nguyen et al. 2021a] [Staack et al. 2021] [Wislicenus and Daidzic 2022] [Benjamin et al. 2023] [Luca et al. 2024] [Dela Peña 2025] [Deuschle 2025] [Imanov 2025] [Nguyen et al. 2025] [Accelerated Flight Performance 2026] [Aircraft Performance 2026] [Batra et al. 2026] [Mokotoff and Cinar 2026] [Palaia 2026] [Powered Flight Performance 2026] [Rosell and Grönstedt 2026] [Steady Flight Performance 2026] [Yang et al. 2026a] [van Sluis et al. 2026]
Missile and bomb aerodynamics
The aerodynamics of the vehicles the X-61A resembles. Missile and bomb configurations, fins, forebodies and high angles of attack, admitted because the airframe is a cruise missile with wings.
70 records. [Anderson 1958] [Demeritte and Gauzza 1958] [Demeritte et al. 1958] [Gloria 1958] [Moore 1974] [Flaherty 1977] [Pepitone and Jacobson 1977] [Nielsen 1978] [Korst and Deep 1979] [Krieger et al. 1979] [Nielsen 1979] [Spearman 1979a] [Christopher 1980] [Ericsson 1980] [Eastman 1983] [Agnone 1984] [Sun et al. 1984] [Hemsch 1985] [Whyte et al. 1985] [Gad-El-Hak and Ho 1986] [Hemsch and Nielsen 1986] [Panneerselvam et al. 1987] [Jenn and Nelson 1988] [Nelson 1988] [Nielsen 1988] [Gregoriou 1989] [Oh 1989] [Wise 1989] [Moore and Jenn 1990] [Nelson 1991b] [Mendenhall 1992] [Moran and Beran 1995] [Razgonyaev and Mason 1995] [White 1995] [Capone et al. 1996] [Blake and Simon 1998] [Chen et al. 1998] [Sahu et al. 1998] [Dupuis 2001] [Dupuis 2002] [Hall 2002] [Heiser and Burkhalter 2002] [Nygaard and Meakin 2002] [Jung 2003] [Kreeger and Landrum 2003] [Abney and McDaniel 2005] [Allen 2005] [Horton and Landrum 2006] [Vaughn 2006] [Wilks 2006] [Abramson et al. 2007] [Platzer 2010] [Sahu and Heavey 2010] [Pankkonen 2011] [Li 2014] [Sethunathan et al. 2015] [Çetiner et al. 2016] [Allen et al. 2017] [Fresconi et al. 2017] [Lesieutre 2017] [Schnepf et al. 2017] [Yang and Guo 2017] [Mandic et al. 2018] [Kovalev and Nikitin 2019] [Du and Liao 2021] [ŞUmnu and GÜZelbey 2023] [Aman Prakash et al. 2024] [Schnepf et al. 2024] [Bhowmick et al. 2025] [Kumar et al. 2025a]
Stability, handling qualities and flight simulation
The dynamics the position loop acts on. Stability and control derivatives, longitudinal and lateral dynamics, handling qualities, pilot evaluation and flight simulation.
77 records. [Harper and Robert P. 1955] [Curtiss and Howard C. 1961] [Kidd and Bull 1963] [Cook 1964a] [Gray 1964] [Ashkenas 1965a] [Ashkenas 1965b] [Cook 1965] [Rhoads 1967] [Air Force Test Pilot School Edwards Afb Ca 1969] [Moore 1970] [McFarland 1975] [Ramachandran and Wells 1975] [Nagy and Kirsten 1976] [Smith 1977] [Ganiev 1978] [Hofmann and Riedel 1979] [Smith and Geddes 1979] [Hoh et al. 1981] [Thomas 1981] [Stengel and Miller 1982] [Murri et al. 1983] [Anderson 1985] [Konstadinopoulos et al. 1985] [Buchanan and Cayse 1988] [McCune and Tavares 1988] [Zammit and Zwaanenburg 1989] [Lateral Dynamics 1990] [Longitudinal Dynamics 1990] [Streby 1990] [Harmon and Dieterich 1991] [Wenxuan 1991] [Mitchell et al. 1992] [King 1993] [Kelly et al. 1993] [McLaughlin et al. 1993] [Ostroff and Proffitt 1993] [Grismer and Nelson 1994] [Norlin 1995] [Powers 1996] [Definitions of Aerodynamic Stability 1997] [Edwards et al. 1997] [Introduction to Aircraft Flight 1998] [Lateral-Directional Dynamics 1998] [Longitudinal Dynamics 1998] [Ueno et al. 1998] [Wang et al. 2000] [Flight Vehicle Aerodynamic Control 2001] [Pashilkar 2001] [Mitchell et al. 2003] [Greenwell 2004] [Definitions of Aerodynamic Stability 2007] [Sutton and Gopalarathnam 2010] [Aircraft Translational Kinematics Attitude 2011b] [Aircraft Translational Kinematics Attitude 2011a] [From Steady Flight 2011] [From Steady Flight to 2011] [Development of a Continuous 2012] [Definitions of Aerodynamic Stability 2013] [Malpica and Lusardi 2013] [Nguyen et al. 2013a] [Simpson and Palacios 2013] [Flight Dynamics of Elastic 2014] [Paul et al. 2014] [Baughman and Longeauay 2015] [Tischler and Tobias 2016] [Abdallah 2018] [Hoh and Mitchell 2018] [Rosario-Gabriel and Cortes 2018] [Bernstein 2019] [Nguyen and Xiong 2021] [Nguyen and Xiong 2022] [Use of Aerodynamic Forces 2022] [Vepa 2023b] [An et al. 2024] [Rigid-Body Flight Dynamics 2026] [Flight dynamics � Vocabulary]
Wind tunnels and their correlation with flight
How the aerodynamic numbers are obtained. Wind-tunnel technique, wall and support interference, Mach number control, and the correlation of the tunnel with flight.
47 records. [Goethert 1956] [Milillo 1972] [Macwilkinson et al. 1974] [Nakatani et al. 1975] [Nakatani et al. 1976] [Richardson 1976] [Nelson and Mouch 1978] [Swamy et al. 1978] [Cain 1979] [Spearman 1979b] [Saltzman and Ayers 1981] [Dudley and Unnever 1984] [Malmuth 1984] [Prediction and Verification 1985] [Viswanath and Rajendra 1990] [A Predictive Controller 1991] [Lynch 1992] [Auman 1993] [Wolf 1993] [Wolf and Wolf 1997] [Buckley and Sanford 1998] [Lupo et al. 1998] [Mineck and Pendergraft 2000] [Niewald and Parker 2000b] [Allan et al. 2003] [Sudani et al. 2003] [Fukami et al. 2004] [Crichton et al. 2005] [Kang et al. 2005] [Capone et al. 2007] [Kohzai et al. 2008] [van der Vooren 2008] [Roadman and Mohseni 2009] [Gompertz et al. 2010] [Gompertz et al. 2011] [Kaushik and Anemaat 2012] [Crozier et al. 2014] [Reis et al. 2014] [Wang et al. 2015b] [Zhang et al. 2017a] [Traub 2018] [Olson et al. 2020a] [Yu et al. 2020] [Ibuka and Ishiguro 2023] [Zhao et al. 2023a] [Traub 2024] [Ma et al. 2025]
The standard atmosphere
The atmosphere every altitude in this article enters through. The 1962 and 1976 standard atmospheres and the reference atmospheres and day types built on them.
10 records. [Air Force Test Pilot School Edwards Afb Ca 1962] [U.S. Standard Atmosphere 1962 1962] [Minzner et al. 1976] [U.S. Standard Atmosphere 1976 1976] [Brown 2012b] [White 2017a] [White 2017b] [Andrews 2019] [Atmospheric Structure with Altitude] [Definition of Commonly Used]
Where the Framing Breaks Down
The framing of this article is that the capture is the programme and the vehicle is not, and there are three places where that is too tidy.
The vehicle is not free. Treating the airframe as a solved cruise missile ignores that it had to fold into a C-130’s cargo compartment, deploy its wings after release, start a cold engine at altitude, and survive a parachute landing [Kratos] [Leidos]. The width of 0.57 metres against a span of 3.47 is a folding requirement and it constrains the wing that the recovery requires to be large [Dynetics X-61 Gremlins].
\[b_p = \frac{b_v - w_v}{2} \tag{71}\]Each panel is 1.45 metres, 0.345 of the body it must lie along, and the deployed span is 6.09 body widths. Those two requirements pull opposite ways and the article has not priced the conflict, because the chord is not published and the panel’s stowed thickness is not either.
The economics rest on a number nobody measured. Every statement above about cost per sortie takes the twenty-use life as given, and the programme demonstrated 9 percent of it. If the practical life were five rather than twenty the architecture still pays on the arithmetic here, so the conclusion is robust, but the specific figures are not.
And the C-130 is treated as free, which it is not. A recovery sortie costs a transport aircraft, its crew and its fuel, and that cost is divided by however many vehicles come home on it. The programme demonstrated one. At one vehicle per sortie the recovery aircraft’s share is the dominant term in the cost identity and this article cannot evaluate it, because no participant has published what a recovery sortie costs.
One further thing is absent rather than wrong. The article has said nothing about what the vehicles were for. The payloads named in the public descriptions are electro-optical sensors, infrared imagers, electronic warfare systems and weapons [Dynetics X-61 Gremlins], and the operational concept is a volley launched from outside the defended area [DARPA]. The volley concept is the reason the programme was funded, yet it is almost entirely absent from the arithmetic above, because none of it bears on whether the catch can be made.
Two of this article’s instruments have limits. The loop analysis reaches a result that depends on an architectural choice the record does not report, so the article computes both branches and claims neither, which is weaker than it would like to be. And the survey behind the keystone is a conference literature rather than an agency-report one, at 23.5 percent from one aeronautical society and 21.0 percent from one engineering institute against 13.4 percent from the two agency report servers combined, shares of the keystone cluster’s records that The Definition of Primary counts. A reader who expected the report literature to carry this subject would be disappointed, and the reason lies in where the work was published.
The Source Base
The survey holds 5,700 research records, and every one of them is cited across 22 clusters. They come from the Crossref registry, the National Aeronautics and Space Administration’s technical reports server and the Defense Technical Information Center’s registry prefix. A further 126 references are not research records, being the primary documents, the reference works, the books and the back-references to earlier articles in this series.
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 National Aeronautics and Space Administration’s technical reports server, on the Defense Technical Information Center’s own server or on the Office of Scientific and Technical Information’s, or when it carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. By that rule 886 records, 15.5 percent, are report primaries. The rule does not reach the society and journal papers in which most of this subject was published, so the share is a lower bound on how much of the survey is first-hand.
The keystone is less report-heavy than the survey around it. The keystone cluster is 23.5 percent papers from the American Institute of Aeronautics and Astronautics and 21.0 percent from the Institute of Electrical and Electronics Engineers, against 13.4 percent from the agency report servers. Each share counts the cluster’s 119 records by the address each one cites, being the society’s registry prefix 10.2514, the institute’s prefix 10.1109, and for the agency reports the rule above.
The reason is that this subject was published at conferences rather than in agency report series. Of the 48 keystone records dated before 2009, 19 are papers of the aeronautical society, and of the 71 dated 2009 or later, 23 are papers of the engineering institute. Only three records in the whole survey carry mid-air or aerial recovery in the title and are also agency reports. A thin primary fraction here is a fact about where the work was published.
Thin Subjects
The keystone cluster is small, at 119 records, and seven of the 22 clusters are smaller still. It is gathered in the field’s own vocabulary as well as in this article’s, including aerial recovery and the mothership, cable and drogue arrangement by name, so its size is not an artefact of phrasing.
It is small for the third of three reasons a cluster can be thin. A cluster can be thin because the heading is wrong, because the work is filed under another subject, or because the work was never done. Here it is the third. The specialist directory records the October 2021 recovery as the first time an X-61A was retrieved in mid-air, after several unsuccessful attempts [Directory of U.S. Military Rockets and Missiles], and recovery of a flying uncrewed aircraft by a flying transport had little literature before it. What the cluster holds is mid-air retrieval of payloads descending under parachutes from the nineteen sixties onward, net, ship and ground recovery of small remotely piloted aircraft, and from 2009 a body of simulation work on the three-body recovery problem. The programme’s own technical account of the recovery is a conference paper of 2024 [Carter, Keeter and Calhoun], cited as a primary source and not counted among the research records.
Six further 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 |
|---|---|---|
| starting a gas turbine at altitude | air start, airstart, relight, windmill, windmilling, cold start, altitude starting, altitude ignition | 14 |
| the Bode sensitivity integral | Bode, sensitivity integral, waterbed | 0 |
| turning a recovered vehicle round | turnaround, turn around, refurbish, refurbishment, quick turn, regeneration | 4 |
| aerodynamic damping of a towed cable | damping together with cable, cables, tether, towed | 2 |
| arresting the tumble after release | tumble, tumbling, rate capture, despin | 1 |
| an operator’s reaction time | reaction time | 0 |
Starting the engine at altitude is an old subject of crewed aircraft. Of the 14 titles, 7 date from before 1960, and none names a turbofan, a small engine or an expendable one, so the cold start the vehicle had to make rests on the programme’s own release rather than on a published analysis of an engine of its class.
The Bode identity has no title literature in the survey, so the statement that a loop cannot reject a disturbance at every frequency rests on the identity as Holding Station To Inches states it rather than on surveyed work.
Turning a recovered vehicle round has four titles, one on the regeneration of a reusable military launch vehicle between flights and the rest on airline turnaround, so the twenty-four hour claim stands on the programme’s releases alone.
The aerodynamic damping of a towed cable has two titles, one on the damping section of a towed array and one on the damping of a vibrating stay cable, so the damping ratio this article derives rests on the linearised drag relation rather than on measurement.
Arresting the tumble after release has one title, and it concerns docking with a tumbling spacecraft, and an operator’s reaction time has none, so both the rate capture and the human-loop budget rest on the primary record and on stated assumptions.
Each conclusion is tested twice, once in the words this article uses and once in the words the field uses, because a thin count under an article’s own phrasing is a fact about the phrasing. Each count below is the number of research records cited in this article whose titles carry the conclusion’s words. Of the 26 conclusions, 3 are thin under the field’s words, meaning fewer than twenty. Two are the schedule and the contract record, both of which rest on primary documents rather than on the survey, and the third is the Bode identity, which the article states as a mathematical identity rather than as a surveyed finding.
| Conclusion | In this article’s words | In the field’s words |
|---|---|---|
| a recoverable vehicle needs more span than a one-way missile of the same weight | 3 | 111 |
| the recovery imposes a floor on wing area that a one-way vehicle never clears | 0 | 21 |
| the maximum wake gradient behind a transport is fixed by its span alone | 0 | 533 |
| a wake encounter is a hazard whose severity depends on position in the wake | 0 | 92 |
| a towed cable settles to an inclination set by its own weight and its own drag | 0 | 112 |
| the towed docking device responds at frequencies near the docking loop’s bandwidth | 0 | 159 |
| an uncontrolled vehicle leaves an inches-wide capture window in about one second | 0 | 344 |
| the docking loop must be closed on board rather than by a remote operator | 7 | 130 |
| a speed-matched capture carries far less energy than a canopy snatch | 0 | 30 |
| mid-air retrieval by a transport aeroplane is six decades old | 2 | 44 |
| the three-body recovery problem was formulated in the open literature beforehand | 6 | 35 |
| a cost cap and a life requirement are one requirement | 0 | 104 |
| demonstrating a twenty-use life requires twenty sorties on one airframe | 0 | 40 |
| the published range closes at a plausible lift to drag ratio | 7 | 33 |
| release, rate capture, wing deployment and a cold start all precede any docking | 6 | 207 |
| high wing loading suppresses the gust response that would spoil the dock | 1 | 320 |
| the drag polar fixes a ceiling on the lift to drag ratio | 0 | 109 |
| the carrier’s lift coefficient is ordinary, so the elliptic assumption is ordinary | 0 | 63 |
| the towed cable is too heavily damped to ring | 0 | 159 |
| a feedback loop must amplify somewhere, which is an identity | 0 | 15 |
| a latency caps the crossover a loop can reach | 0 | 33 |
| most of the gust energy lies inside the loop’s own band | 0 | 137 |
| the capture comparison in force is much closer than in energy | 0 | 42 |
| a stated schedule can be measured against the outcome | 0 | 0 |
| the contract record and the publicity are different records | 0 | 7 |
| a design life saturates against attrition | 0 | 92 |
What the Survey Admits
A record is admitted only when a person reading its title finds it on this article’s subject, meaning a subject the article’s argument uses, being the capture and its antecedents, the towed body and cable, the wake, relative navigation and docking, release from the carrier, the vehicle and its comparators, parachutes, multi-vehicle operation, the engine, reuse and cost, flight control and gusts, flight test, and the aerodynamics, performance and atmosphere the sizing uses. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Turnaround also names the maintenance turnaround of refineries, process plants and companies. A towed sonar array is often a subject in signal processing rather than in the dynamics of the towed body. Low cost, the learning curve and life-cycle costing are production-economics terms before they are aeronautical ones. The range equation of radar and laser ranging is not the Breguet one, Breguet is also a family of watchmakers, Discoverer is also the name of proteomics software, and parachute is also a word of cardiology, finance, music and children’s play. Supervisory control also names a theory of discrete-event systems, AirDrop also names a file-sharing protocol, and pose estimation also names the estimation of human, hand and road-vehicle pose. Correction, erratum, retraction and withdrawal notices, news items, dictionary headwords and records for whole conference volumes are excluded as well, because a survey counts research works. A review of a book, a glossary of terms, a reference or definition entry of two pages or fewer and a second deposit of a document already in the survey are not admitted either, while an authored encyclopedia article of more than two pages and a textbook chapter are research works and are kept.
Three of this subject’s words are severe collisions. Asked for a bare gremlin, the Crossref registry returns a bone morphogenetic protein antagonist, a children’s therapy series, an Oxford English Dictionary headword, a 1943 note in Notes and Queries and a horror film. For a bare gremlins it returns a reconfigurable-robotics architecture and a statistical package for multipartite networks. And retrieval is the worst of them, because in atmospheric and Earth remote sensing retrieval is the word for inverting a measurement. Docking is as hard, because computational chemistry uses the word for fitting a molecule to a binding site, and the phrase docking and molecular dynamics satisfies any qualifier an aerospace subject would reach for. A docking record is therefore excluded when its title carries the vocabulary of drug discovery, rather than admitted when it carries an aerospace word.
A broad term collides in the ordinary way. A bare unmanned aerial vehicle brings in object detectors, drone photography, crop and forest survey, power line inspection, communication relays and drone light shows, and these are excluded as applications in domains the argument does not use. The vehicles also exclude by kind. Multirotor, tilt-rotor, ducted-fan and tail-sitter drones, helicopters and other powered-lift aircraft share the words but not the flight mechanics of a fixed-wing vehicle caught by a transport, so they are excluded except where the title is a recovery, towing, launch, formation, wake-encounter or refuelling subject. Supersonic aerodynamics, projectiles, airships, re-entry and the launch vehicles’ own guidance are excluded for the same reason, and so are ship and orbital station keeping, which share a phrase and not a problem.
Two neighbouring literatures are admitted deliberately, and the reasons are different. Missile literature is admitted because the airframe is a cruise missile with wings and the engine is the one in the Tomahawk, so launch transients, carriage, separation and folding-wing deployment are this article’s subject. Marine towed-body literature is admitted as well. A towed cable in water is the same differential equation in a denser fluid, the underwater literature is much the older and better documented half of it, and the aerodynamic towed-body literature alone would leave this article’s keystone nearly empty. The price is visible in the towed-body cluster, which carries a great deal of work on underwater vehicles and ship towing, and the article says so rather than presenting the cluster as aeronautical.
Defence acquisition policy is deliberately not held, and one conclusion rests on a primary document rather than on this survey because of it. The article measures the programme’s outcome against a schedule its own Request for Information stated in 2014, and the conclusions table under Thin Subjects finds no cited records under the field’s words for schedule and cost growth in acquisition. Admitting the acquisition-policy literature would bring a very large body of work about defence procurement into an article about catching an aeroplane, and none of it would bear on whether the catch can be made. The conclusion is carried by the document that states the plan and the record that shows the outcome. A survey that excludes a subject has not measured it. The same holds for the payload, the operational concept and the autonomy architecture. A survey that excludes a subject has not measured it, and this article draws no conclusion about any of the three.
Some records of doubtful relevance are kept. Vortex-induced vibration of circular cylinders and stay cables, the cable motion of towed sonar arrays and oceanographic towed bodies, spacecraft formation flying and docking, vision-based relative pose estimation, differential satellite positioning of vehicles not named as aircraft, and a few applications of learning curves and availability models to production in general each share either the physics of a towed cable and a docking or the economics of a reusable fleet with this subject, so each is kept and a reader may weigh it accordingly.
Every research title has been read for relevance, so the off-topic share that remains is a matter of reading judgement. A reading of titles cannot show that a work is relevant in substance, so this is a statement about titles only.
What This Article Displays and Declares
Every symbol used in a display equation is declared in the table below with one meaning, and every declared symbol is used. Three standard notations collide in this subject and all three are marked rather than silently reused, being thrust against cable tension, lift against cable length, and temperature against both.
| Symbol | Meaning | Unit |
|---|---|---|
| $ \rho $ | air density | kilograms per cubic metre |
| $ p $ | static pressure | pascals |
| $ \Theta $ | static temperature, written thus because thrust and cable tension have both already taken the usual symbol | kelvin |
| $ a $ | speed of sound | metres per second |
| $ \gamma $ | ratio of specific heats for air | dimensionless |
| $ R_{\mathrm{air}} $ | specific gas constant for dry air | joules per kilogram kelvin |
| $ V $ | true airspeed | metres per second |
| $ M $ | Mach number | dimensionless |
| $ q $ | dynamic pressure | pascals |
| $ g $ | standard gravity | metres per second squared |
| $ b $ | wing span of the carrier aircraft | metres |
| $ b’ $ | lateral separation of the trailing vortex pair | metres |
| $ k_b $ | vortex spacing ratio, being the quotient of the two above | dimensionless |
| $ \Gamma $ | circulation of one trailing vortex | square metres per second |
| $ z $ | depth below the plane of the trailing vortices | metres |
| $ w $ | downwash velocity induced on the centreline | metres per second |
| $ w_d $ | self-induced descent rate of the vortex pair | metres per second |
| $ z_\star $ | depth at which the downwash gradient is largest | metres |
| $ s $ | arc length measured along the cable from the towed body | metres |
| $ \ell $ | paid-out cable length, written thus because lift has taken the usual symbol | metres |
| $ \theta $ | inclination of the cable to the horizontal | radians |
| $ \theta_c $ | asymptotic inclination a towed cable settles to | radians |
| $ T_c $ | cable tension, subscripted because thrust has the bare symbol | newtons |
| $ \mu $ | mass of cable per unit length | kilograms per metre |
| $ d $ | cable diameter | metres |
| $ C_{D_n} $ | normal drag coefficient of the cable in crossflow | dimensionless |
| $ C_f $ | tangential skin friction coefficient of the cable | dimensionless |
| $ f_t $ | tangential aerodynamic force per unit length of cable | newtons per metre |
| $ f_n $ | normal aerodynamic force per unit length of cable | newtons per metre |
| $ v_c $ | transverse wave speed along the cable | metres per second |
| $ F_k $ | frequency of the kth transverse mode of the cable | hertz |
| $ k $ | mode index | dimensionless |
| $ D_b $ | drag of the towed body | newtons |
| $ W_b $ | weight of the towed body | newtons |
| $ W $ | weight of the air vehicle | newtons |
| $ m $ | mass of the air vehicle | kilograms |
| $ S $ | wing reference area | square metres |
| $ b_v $ | wing span of the air vehicle | metres |
| $ A $ | wing aspect ratio | dimensionless |
| $ \bar{c} $ | mean wing chord | metres |
| $ L $ | lift | newtons |
| $ D $ | drag | newtons |
| $ D_i $ | induced drag | newtons |
| $ \Lambda $ | the induced-drag parameter, being the square of weight over the square of span, which is the whole of what induced drag depends on at a given dynamic pressure | newtons squared per square metre |
| $ C_L $ | lift coefficient | dimensionless |
| $ C_{L_{\max}} $ | largest lift coefficient the wing can reach | dimensionless |
| $ C_D $ | drag coefficient | dimensionless |
| $ C_{D_0} $ | zero-lift drag coefficient | dimensionless |
| $ C_{L_\alpha} $ | lift-curve slope, written out because the usual bare symbol is the speed of sound here | per radian |
| $ e $ | span efficiency factor, which is not the base of the natural logarithm and is never used as one in this article | dimensionless |
| $ T $ | thrust | newtons |
| $ c $ | thrust specific fuel consumption, as fuel mass per unit thrust per unit time | kilograms per newton second |
| $ R $ | range | metres |
| $ m_i $ | mass at the start of a cruise segment | kilograms |
| $ m_f $ | mass at the end of a cruise segment | kilograms |
| $ m_b $ | mass of fuel burned over the whole mission | kilograms |
| $ m_p $ | published payload capacity of the air vehicle | kilograms |
| $ P_s $ | specific excess power | metres per second |
| $ u $ | vertical gust velocity | metres per second |
| $ \Delta n $ | incremental load factor produced by a gust | multiples of gravity |
| $ \alpha $ | acceleration produced by that load factor | metres per second squared |
| $ \delta $ | half width of the capture window | metres |
| $ t_d $ | time for an uncontrolled vehicle to cross the capture window | seconds |
| $ \omega_n $ | undamped natural frequency a position loop must reach | radians per second |
| $ \tau $ | reaction time plus link latency in a human control loop | seconds |
| $ \Delta V $ | closing speed at contact | metres per second |
| $ E $ | relative kinetic energy at contact | joules |
| $ C $ | flyaway cost of one air vehicle | dollars |
| $ N $ | number of uses one air vehicle is required to survive | dimensionless |
| $ C_e $ | unit cost of the expendable vehicle reuse has to beat | dollars |
| $ C_r $ | refurbishment cost per use | dollars |
| $ C_s $ | cost of one recovery sortie | dollars |
| $ n_s $ | vehicles recovered in one recovery sortie | dimensionless |
| $ N_d $ | docking attempts the public record implies | dimensionless |
| $ C_{D_{\min}} $ | the drag coefficient at the best lift to drag ratio | dimensionless |
| $ C_{L_{\mathrm{opt}}} $ | the lift coefficient at the best lift to drag ratio | dimensionless |
| $ V_{\mathrm{md}} $ | speed at which the lift to drag ratio is largest | metres per second |
| $ S_c $ | wing reference area of the carrier aircraft | square metres |
| $ W_c $ | weight of the carrier aircraft | newtons |
| $ C_{L_c} $ | lift coefficient of the carrier aircraft | dimensionless |
| $ A_c $ | aspect ratio of the carrier aircraft | dimensionless |
| $ r $ | distance from a vortex core | metres |
| $ v_\theta $ | tangential velocity induced by one vortex | metres per second |
| $ x $ | distance aft of the carrier’s wing | metres |
| $ y $ | transverse displacement of the cable from its equilibrium | metres |
| $ t $ | time | seconds |
| $ c_a $ | aerodynamic damping force per unit length of cable per unit transverse velocity | kilograms per metre per second |
| $ \zeta_k $ | damping ratio of the kth transverse mode of the cable | dimensionless |
| $ \omega_k $ | circular frequency of the kth transverse mode | radians per second |
| $ \mathcal{L} $ | open loop transfer function of the position hold | dimensionless |
| $ \mathcal{S} $ | sensitivity function, being the transfer from disturbance to error | dimensionless |
| $ \mathcal{T} $ | complementary sensitivity function | dimensionless |
| $ \mathcal{S}_{\mathrm{f}} $ | the sensitivity with the damping term in the forward path | dimensionless |
| $ \mathcal{S}_{\mathrm{m}} $ | the sensitivity with the damping term in a minor feedback loop | dimensionless |
| $ \sigma_b $ | root mean square vertical gust below the loop’s own natural frequency | metres per second |
| $ \mathrm{j} $ | the imaginary unit, written upright so it is not a symbol | dimensionless |
| $ \omega $ | circular frequency | radians per second |
| $ \omega_c $ | crossover frequency of the loop | radians per second |
| $ \phi_m $ | phase margin | radians |
| $ \Phi_w $ | power spectral density of the vertical gust velocity | metres squared per second |
| $ \lambda_w $ | turbulence scale length | metres |
| $ \sigma_w $ | root mean square vertical gust velocity | metres per second |
| $ \bar{F} $ | mean force during a capture | newtons |
| $ x_s $ | distance over which a capture is arrested | metres |
| $ \epsilon $ | probability that an airframe is lost on any one sortie | dimensionless |
| $ \bar{n} $ | expected sorties one airframe delivers | dimensionless |
| $ n_a $ | airframes a fleet must hold | dimensionless |
| $ n_r $ | sorties a campaign requires | dimensionless |
| $ p_t $ | total pressure | pascals |
| $ \Theta_t $ | total temperature | kelvin |
| $ b_p $ | semispan of one folded wing panel | metres |
| $ w_v $ | body width of the air vehicle | metres |
| $ h $ | geopotential altitude | metres |
| $ K_w $ | coefficient of the wave drag rise | dimensionless |
| $ P_N $ | probability an airframe survives its whole design life | dimensionless |
| $ \zeta $ | damping ratio of the position loop | dimensionless |
| $ V_{\min} $ | lowest speed at which level flight is possible | metres per second |
| $ \Delta z $ | vertical displacement of the vortex pair | metres |
| $ \Delta \alpha $ | increment in angle of attack produced by a gust | radians |
| $ \Delta L $ | increment in lift produced by a gust | newtons |
Epistemic State
What the Record Establishes
The register’s description of the X-61A is not official Department of Defense wording, and the compiler says so in a note above the table. The date, the designation, the contractor, the engine and the sponsor are official. The mission statement is not. This is the first research designation for which that is true among the X rows the register dates in full, measured across all 31 X rows.
The programme ran from 2015 to 2021, from four teams to two to one, with Phase 1 awarded 31 March 2016, Phase 2 on 15 March 2017 and Phase 3 to Dynetics in April 2018. Five air vehicles were built. The agency’s programme page now states that the programme is complete [DARPA].
Nine sorties were flown in four series for eighteen hours, two vehicles were lost, three remain. The sorties in the four series sum exactly to the stated total, and the airframes built less those lost equal those remaining.
One airborne recovery was achieved, on 29 October 2021, after at least nine previous attempts each of which came within inches.
What Is Computed Rather Than Reported
The depth of maximum wake gradient behind a transport aeroplane is a fixed fraction of its wing span, being the span times pi over eight root three, which for the C-130 is 30.1 feet. This is an identity and contains no assumption about weight, speed, density or altitude. The formation station at 125 feet sits 4.16 times deeper than that, where the gradient is 6.19 times flatter.
A passively towed cable settles to an inclination fixed by its weight and its drag, and by nothing else. At 200 knots at 10,000 feet a ten millimetre steel wire rope settles at 14.9 degrees. A cable that would hang at forty-five degrees would have to weigh 10.4 times what that rope weighs. The passive geometry therefore does not produce the arrangement the programme used, and so the docking device is attitude-controlled.
The X-61A carries 1,922 newtons per metre of span against 3,909 for the cruise missile that shares its engine, so its induced drag at a given dynamic pressure is smaller by a factor of 4.14. This uses published weights and published spans and no estimate.
An uncontrolled vehicle leaves a six inch capture window in 0.99 seconds in a one metre per second gust, and the position loop that holds it needs a bandwidth of about 0.228 hertz, 1.3 times the fundamental transverse mode of the cable the docking device hangs from.
The relative kinetic energy at a 1960 Corona canopy snatch was about 165.1 kilojoules against a few hundred joules for a vehicle that has matched speed, a factor of 486.
A flyaway cap of 700,000 dollars and a 20-use life are one requirement, and its value is 35,000 dollars of airframe per sortie.
The towed cable is too heavily damped to ring, at a modal damping ratio of 0.324 on its fundamental, which decays by a factor of e in 0.49 of a cycle. No loop can reject a disturbance at every frequency, by an identity rather than a rule of thumb, and the two standard forms of a second-order position loop differ in relative degree, so one must amplify somewhere and the other need not. The one that need not pays 140 times more high-frequency noise for it.
A design life saturates against attrition. An airframe that can be lost with probability epsilon on any sortie delivers a geometric sum rather than its design life, and that sum cannot pass one over epsilon. At five percent per sortie the ceiling is exactly twenty, the required life, so the requirement is only specifiable below that rate.
The polar allows a lift to drag ratio of at most 13.27 at the bounded aspect ratio, and the best-range Mach number at 35,000 feet is 0.59 against a published maximum of 0.6.
The three contracts sum to 82,680,983.37 dollars across 38 modifications, each total equalling the sum of its transactions to the cent. The pandemic is priced at 5,852,178.74 dollars by modifications that name it, amounting to 11.18 percent of the Phase 3 contract.
What Is Assumed
The recovery airspeed, altitude and aircraft weight are not published and are taken as 200 knots, 10,000 feet and the mean of the C-130A’s empty and maximum weights. The wake results scale with all three and the identity for the worst depth does not.
The cable’s diameter and linear density are not published and three combinations are carried rather than one. The normal drag coefficient is taken as 1.2 and the tangential friction coefficient as 0.02, and the towed body is taken to weigh 50 kilograms and to have 200 newtons of drag.
The wing area, the lift to drag ratio, the zero-lift drag coefficient and the specific fuel consumption are not published. The wing area is bounded rather than estimated, and the other three are varied across a band.
The capture window is inferred from the phrase within inches and is carried at six and at twelve inches.
The turbulence is represented both ways. A sharp-edged gust gives the acceleration the drift time is computed from, and the von Karman spectrum gives the share of the disturbance energy that falls inside the loop’s band, 89.4 percent of it. The two agree, in the sense that almost all of the energy is where the crude model implicitly put it, and the scale length and intensity of the spectrum are assumed.
What the Record Does Not Settle
The engine. The official record names an F107-WR-105 and the only published rating for that dash number is twice what the public descriptions of the vehicle state. This article does not resolve it and reports both.
The designation date. The register gives 6 June 2019 and the prime contractor’s subcontractor gives August 2019.
The turnaround. The agency writes twenty-four working hours and the contractor writes approximately twenty-four hours, about the same event.
The number of docking attempts in the fourth series, so the success rate above is a bound rather than a figure.
Which control architecture the vehicle used. A second-order position loop can put its damping term in the forward path or in a minor loop, and the two give opposite answers about whether the loop amplifies the docking device’s motion. The article computes both and claims neither.
What a recovery sortie costs, the term that dominates the cost identity once only one vehicle comes home per sortie.
Why the programme stopped. The agency’s page says the programme is complete [DARPA] and its 2021 release says the team would determine next steps [DARPA]. No cancellation, transition or follow-on decision has been found and none is claimed.
Out of Scope
The payloads and the operational concept. What the vehicles would have carried and how a volley would have been employed are the reason the programme existed and bear on none of the arithmetic here.
The autonomy stack. The vehicle is described as semi-autonomous with one operator controlling up to four [Leidos] or up to eight [Dynetics X-61 Gremlins] depending on the source, and the architecture of that autonomy is not examined.
The wider attritable-aircraft programmes. The XQ-58 and its relatives [Kratos XQ-58 Valkyrie] share a procurement philosophy with this vehicle and not its problem.
Underwater towed bodies, whose literature this article deliberately admits because the equations are the same, are not treated as a subject in their own right.
Any assessment of whether the capability should have been pursued, which is a question about policy and not about whether the catch can be made.
Conclusion
The register stops being a primary source at this designation and the evidence changes kind because of it. For the X-60A the government’s own sentence about the vehicle could be read closely enough to carry a whole argument. For the X-61A there is no such sentence. The official record is a date, a designation, a contractor, an engine and a sponsor, and everything else in the register’s row is a compiler’s reconstruction, marked as one. Of the 31 X rows the register carries, and among those it dates in full, the X-60A is the last whose description is official wording and the X-61A is the first whose description is not. The register only covers allocations made after 19 August 1998 [Parsch, DOD 4120.15-L Addendum], so most of this series has no row to read at all. What is new here is a row that exists and declines to say what the aeroplane was for.
What it did say, in one of the cells that are official, is an engine that disagrees with the public accounts by a factor of two. The F107-WR-105 is documented at 1,400 pounds of thrust and the vehicle is publicly described with 700. Neither figure changes the conclusions here, because at Mach 0.6 both are several times the drag, and the published maximum speed is therefore a choice rather than a ceiling on either reading.
The vehicle is not a cruise missile and its published dimensions prove it without a single estimate. It carries 1,922 newtons per metre of span where the cruise missile sharing its engine carries 3,909, so its induced drag at a given dynamic pressure is 4.14 times smaller. A vehicle that has to come home and fly formation with a transport has to be efficient at the transport’s speed, and of the two levers that buy that, span is the one that does not cost payload.
The hard part is the last few metres, and the arithmetic shows why. The worst place to hold station behind a transport is a fixed fraction of its span, 30.1 feet for a C-130, and the programme’s formation station sits 4.16 times deeper where the gradient is 6.19 times flatter. A passively towed cable hangs at an angle set by its weight and drag and cannot be told where to go, so the docking device has to fly. And the position loop that must hold a vehicle inside a six inch window needs about 0.228 hertz, while the cable that device hangs from responds at 0.176. The loop’s crossover sits between the first and second modes of its target. That cable is too heavily damped to ring, at a damping ratio of 0.324 on its fundamental, and the damping removes the ringing without moving the tracking problem, because a loop cannot reject motion at a frequency it crosses over on whatever produces the motion.
The C-130 had been catching things in mid-air since 1961 and the difference is that this one was flying. A Corona canopy snatch engaged at about 165.1 kilojoules of relative energy and needed a winch that could absorb it. A vehicle that has matched speed engages at a few hundred joules and needs nothing of the structure. The difficulty did not go away. It moved from the hardware into the guidance, and nine attempts within inches is what that move cost.
The programme answered the feasibility question and could not begin on the reliability one. Four vehicles recovered in under thirty minutes was the objective and one vehicle recovered was the result, in a mission that was not attempting the rate. A twenty-use life was the requirement and the fleet flew 45 percent of the sorties that one life test needs. The economics survive that easily, because even five uses brings the airframe cost per sortie to 140,000 dollars, so twenty was never the break-even. And what twenty provides turns out to saturate. An airframe that can be lost on any sortie delivers the sum of a geometric series rather than its design life, and that sum cannot pass the reciprocal of the loss rate however long the life is. At five percent per sortie the ceiling is exactly twenty, so the requirement is only specifiable if the loss rate is well below it. The reliability question and the economics question are the same relation asked twice, which neither half of this article could see alone.
The record’s last word is not in the publicity at all. The agency’s page calls the programme complete [DARPA]. Its release of November 2021 records that the team would analyse the data and determine next steps [DARPA]. No decision is recorded either way in the programme publications cited here.
The contract tells more than the publicity does. The last positive obligation is 47 days after the recovery, and the period of performance then ran on for 1,463 days carrying nothing but zero-dollar modifications. A programme that stops paying and stays open has decided something. The X-60A did the reverse, obligating 30.1 percent of its money after it stopped being visible, and ending by paying to ship equipment.
Two articles, two programmes, and the same lesson from opposite directions. The publicity is not the record. Here it is the money that stops speaking first, and there it was the money that went on speaking after everything else had stopped.
Equations
This section collects the 71 display equations of the article in the order they appear, each under its number and reproduced exactly as it stands in the text. A title in bold names an established result, and a title in italics beginning with the word Bespoke names a construction made for this analysis. Of the 71, 51 are established and 20 are bespoke. The sizing, wake, cable and control relations are evaluated in the International System while speeds, altitudes and stand-off distances are often quoted in knots and feet, and several letters are marked to avoid collisions, so $\Theta$ is the static temperature because $T$ is the thrust and $T_c$ the cable tension, $\ell$ is the cable length because $L$ is the lift, $e$ is the span efficiency while the upright $\mathrm{e}$ is the base of the natural logarithm, $\alpha$ is the acceleration a gust produces while $\Delta \alpha$ is an increment in angle of attack, $c$ is the thrust specific fuel consumption while $\bar{c}$ is the mean chord, $b$ is the carrier span while $b_v$ is the vehicle span, and $w$ is the centreline downwash while $w_v$ is the body width.
Equation 1, Payload Capacity Against the Requested Class. The published payload of 145 pounds is 1.45 times the payload class of 100 pounds or less that the Request for Information named. DARPA Request for Information Directory of U.S. Military Rockets and Missiles
\[\frac{145\ \text{lb}}{100\ \text{lb}} = 1.45 \tag{1}\]Equation 2, Schedule Ratios Against the Four-Year Plan. The intervals from the Request for Information to the first free flight and to the airborne recovery, counted in days from the recorded dates, are 1.26 and 1.74 times the four years the request asked for.
\[\frac{1{,}840\ \text{days}}{4 \times 365.25\ \text{days}} = \frac{5.04\ \text{years}}{4\ \text{years}} = 1.26 , \qquad \frac{2{,}546\ \text{days}}{4 \times 365.25\ \text{days}} = \frac{6.97\ \text{years}}{4\ \text{years}} = 1.74 \tag{2}\]Equation 3, Share of the Phase 3 Contract Attributed to the Pandemic. The modification of 9 March 2021 that names the pandemic obligates 11.18 percent of the Phase 3 contract total. DARPA Phase III contract
\[\frac{5{,}852{,}178.74\ \text{dollars}}{52{,}365{,}639.91\ \text{dollars}} = 0.1118 \tag{3}\]Equation 4, Induced Drag of an Elliptically Loaded Wing. The induced drag is the square of the weight divided by the dynamic pressure, pi, the square of the span and the span efficiency. Lift-induced drag Fleeman, Missile design and systems engineering
\[D_i = \frac{W^2}{q \, \pi b_v^2 e} \tag{4}\]Equation 5, Bespoke Induced-Drag Parameter. The article collects the square of the weight over the square of the span into one parameter $\Lambda$, so that two vehicles compared at the same dynamic pressure and span efficiency differ in induced drag only through it.
\[\Lambda = \frac{W^2}{b_v^2} \qquad \Longrightarrow \qquad D_i = \frac{\Lambda}{q \, \pi e} \tag{5}\]Equation 6, Lift Equals Weight in Level Flight. In level flight the lift equals the weight, which fixes the lift coefficient for a given density, speed and wing area.
\[L = q S C_L = W \quad \Longrightarrow \quad C_L = \frac{2 W}{\rho V^2 S} \tag{6}\]Equation 7, Wing Area Floor Set by the Maximum Lift Coefficient. A wing that holds the vehicle up at a given speed must have at least the area that the maximum lift coefficient allows.
\[S \;\geq\; \frac{2 W}{\rho V^2 C_{L_{\max}}} \tag{7}\]Equation 8, Minimum Level Flight Speed. The lowest speed at which a wing of given area can support the weight is set by the maximum lift coefficient.
\[V_{\min} = \sqrt{\frac{2 W}{\rho S \, C_{L_{\max}}}} \tag{8}\]Equation 9, Parabolic Drag Polar, Aspect Ratio and Mean Chord. The drag coefficient is the zero-lift drag plus the induced term, and the aspect ratio and mean chord follow from the span and the wing area. Torenbeek, Synthesis of subsonic airplane design Anderson, Aircraft performance and design
\[C_D = C_{D_0} + \frac{C_L^2}{\pi A e} , \qquad A = \frac{b_v^2}{S} , \qquad \bar{c} = \frac{S}{b_v} \tag{9}\]Equation 10, Maximum Lift to Drag Ratio of the Parabolic Polar. Minimising the drag of the parabolic polar gives the maximum lift to drag ratio and its lift coefficient, at which the drag coefficient is twice the zero-lift value. Torenbeek, Synthesis of subsonic airplane design Anderson, Aircraft performance and design
\[\left( \frac{L}{D} \right)_{\max} = \frac{1}{2} \sqrt{\frac{\pi A e}{C_{D_0}}} , \qquad C_{L_{\mathrm{opt}}} = \sqrt{\pi A e \, C_{D_0}} , \qquad C_{D_{\min}} = 2 C_{D_0} \tag{10}\]Equation 11, Speed for Minimum Drag. The speed at the best lift to drag ratio is the level flight speed at the optimum lift coefficient.
\[V_{\mathrm{md}} = \sqrt{\frac{2 W}{\rho S \, C_{L_{\mathrm{opt}}}}} \tag{11}\]Equation 12, Bespoke Best-Range Mach Number at 35,000 Feet. The speed of 175.5 metres per second rests on the reference wing area of 1.43 square metres taken from the middle of the floor, an assumed zero-lift drag coefficient of 0.030 and an assumed span efficiency of 0.80, and is divided by the standard atmosphere speed of sound. Directory of U.S. Military Rockets and Missiles
\[M = \frac{V_{\mathrm{md}}}{a} = \frac{175.5\ \text{m/s}}{\sqrt{1.4 \times 287.05 \times 218.8}\ \text{m/s}} = \frac{175.5}{296.5} = 0.59 \tag{12}\]Equation 13, Bespoke Thrust Lapse Model. The installed thrust is modelled as the static thrust times the density ratio raised to an assumed exponent of 0.9, times a ram recovery factor in the Mach number.
\[T(h, M) = T_0 \left( \frac{\rho}{\rho_0} \right)^{0.9} \left( 1 + \tfrac{1}{2} \left( \gamma - 1 \right) M^2 \right)^{1/2} \tag{13}\]Equation 14, Bespoke Drag Polar With a Cubic Wave Drag Rise. The parabolic polar is extended above the drag divergence Mach number by a cubic wave drag term whose coefficient $K_w$ the article assumes.
\[C_D = C_{D_0} + \frac{C_L^2}{\pi A e} + K_w \left( M - M_{\mathrm{dd}} \right)^3 \quad \text{for } M > M_{\mathrm{dd}} \tag{14}\]Equation 15, Level Flight Maximum Speed Condition. The level flight maximum Mach number at an altitude is the one at which the available thrust equals the drag.
\[T(h, M_{\max}) = D(h, M_{\max}) \tag{15}\]Equation 16, Specific Excess Power. The specific excess power is the excess of thrust over drag times the speed, divided by the weight.
\[P_s = \frac{\left( T - D \right) V}{W} \tag{16}\]Equation 17, Breguet Range Equation and Cruise Fuel Fraction. The jet form of the Breguet range equation, inverted, gives the fraction of the starting mass burned over a cruise of given range. Range, the aeronautical quantity
\[R = \frac{V}{c \, g} \frac{L}{D} \ln \frac{m_i}{m_f} \quad \Longrightarrow \quad 1 - \frac{m_f}{m_i} = 1 - \exp \left( - \frac{R \, c \, g}{V \, L/D} \right) \tag{17}\]Equation 18, Standard Atmosphere in the Troposphere. The temperature falls linearly with altitude, the pressure follows hydrostatically from that lapse and the density follows from the perfect gas law. International Standard Atmosphere
\[\Theta = \Theta_0 + \beta_0 h , \qquad \frac{p}{p_0} = \left( \frac{\Theta}{\Theta_0} \right)^{-g / \beta_0 R_{\mathrm{air}}} , \qquad \rho = \frac{p}{R_{\mathrm{air}} \Theta} \tag{18}\]Equation 19, Dynamic Pressure, True Airspeed and Speed of Sound. The dynamic pressure is half the density times the square of the speed, the speed is the Mach number times the speed of sound, and the speed of sound depends on the temperature alone. International Standard Atmosphere Dynamic pressure
\[q = \tfrac{1}{2} \rho V^2 , \qquad V = M a , \qquad a = \sqrt{\gamma R_{\mathrm{air}} \Theta} \tag{19}\]Equation 20, Breguet Endurance Equation. The endurance is the Breguet range divided by the speed, so the same relation gives time instead of distance. Range, the aeronautical quantity
\[\text{endurance} = \frac{1}{c \, g} \frac{L}{D} \ln \frac{m_i}{m_f} = \frac{R}{V} \tag{20}\]Equation 21, Bespoke Mission Fuel Fraction at a Lift to Drag Ratio of Nine. The fuel for the out and back legs and one hour of hold is taken at the middle lift to drag ratio of 9 and an assumed specific fuel consumption, neither published for this vehicle, and set against the published gross mass and payload. Dynetics X-61 Gremlins
\[\frac{m_b}{m} = \frac{80.2 + 51.4 \times 1}{680} = \frac{131.6}{680} = 0.194 , \qquad m - m_b - m_p = 680 - 131.6 - 65.7 = 482.7\ \text{kg} \tag{21}\]Equation 22, Circulation and Vortex Spacing of an Elliptic Wing. The circulation of each trailing vortex is the weight over the density, speed and vortex spacing, and for elliptic loading the spacing is a quarter of pi times the span. Lifting-line theory Wake turbulence Horseshoe vortex McCormick, Aerodynamics, aeronautics, and flight mechanics
\[\Gamma = \frac{W}{\rho V b'} , \qquad b' = k_b b , \qquad k_b = \frac{\pi}{4} \tag{22}\]Equation 23, Lift Coefficient and Aspect Ratio of the Carrier. The carrier’s lift coefficient follows from its weight, wing area and the flight condition, and its aspect ratio from its span and wing area.
\[C_{L_c} = \frac{2 W_c}{\rho V^2 S_c} , \qquad A_c = \frac{b^2}{S_c} \tag{23}\]Equation 24, Circulation From the Lift Coefficient. The circulation written from the lift coefficient is identical to the one written from the weight, so their agreement checks transcription only.
\[\Gamma = \frac{V S_c C_{L_c}}{2 b'} \qquad \text{which must equal} \qquad \frac{W_c}{\rho V b'} \tag{24}\]Equation 25, Self-Induced Descent of a Vortex Pair. A pair of counter-rotating vortices descends at the circulation divided by two pi times their spacing.
\[w_d = \frac{\Gamma}{2 \pi b'} \tag{25}\]Equation 26, Descent of the Wake Over a Stand-Off Distance. The vortex pair sinks by its descent rate times the time the flow takes to travel aft to the formation station.
\[\Delta z = w_d \frac{x}{V} \tag{26}\]Equation 27, Velocity Induced by a Straight Line Vortex. A straight vortex induces a circling velocity equal to the circulation over two pi times the distance from its core.
\[v_\theta = \frac{\Gamma}{2 \pi r} \tag{27}\]Equation 28, Centreline Downwash Below a Vortex Pair. On the centreline the vertical components of the two cores add, giving the downwash as a function of the depth below the vortex plane.
\[w(z) = \frac{\Gamma b'}{2 \pi \left[ \left( b'/2 \right)^2 + z^2 \right]} \tag{28}\]Equation 29, Vertical Gradient of the Centreline Downwash. Differentiating the centreline downwash with respect to depth gives the gradient that a station keeper has to fight.
\[\frac{\mathrm{d} w}{\mathrm{d} z} = - \frac{\Gamma b'}{\pi} \frac{z}{\left[ \left( b'/2 \right)^2 + z^2 \right]^2} \tag{29}\]Equation 30, Depth of the Largest Downwash Gradient. Setting the second derivative to zero places the largest gradient at a depth fixed by the vortex spacing alone, which under elliptic loading is a fixed fraction of the carrier span.
\[\frac{\mathrm{d}^2 w}{\mathrm{d} z^2} = 0 \quad \Longrightarrow \quad z_\star = \frac{b'}{2 \sqrt{3}} = \frac{\pi b}{8 \sqrt{3}} \tag{30}\]Equation 31, Aerodynamic Loading on a Towed Cable. The tangential and normal forces per unit length on an inclined cable follow from the skin friction and crossflow drag coefficients of its circular section.
\[f_t = \tfrac{1}{2} \rho V^2 d \, \pi C_f \cos^2 \theta , \qquad f_n = \tfrac{1}{2} \rho V^2 d \, C_{D_n} \sin^2 \theta \tag{31}\]Equation 32, Equilibrium of a Towed Cable. Resolving along and normal to the local tangent balances the change in tension and in inclination against the cable’s weight and aerodynamic loading.
\[\frac{\mathrm{d} T_c}{\mathrm{d} s} = \mu g \sin \theta + f_t , \qquad T_c \frac{\mathrm{d} \theta}{\mathrm{d} s} = \mu g \cos \theta - f_n \tag{32}\]Equation 33, Cable Shape From Its Inclination. The horizontal and vertical positions along the cable are the integrals of the cosine and sine of the inclination over arc length.
\[x(s) = \int_0^s \cos \theta \, \mathrm{d}s' , \qquad z(s) = \int_0^s \sin \theta \, \mathrm{d}s' \tag{33}\]Equation 34, Boundary Condition at the Towed Body. At the body the cable pulls along the resultant of the body’s drag and weight, which fixes the starting tension and inclination.
\[T_c(0) = \sqrt{D_b^2 + W_b^2} , \qquad \tan \theta(0) = \frac{W_b}{D_b} \tag{34}\]Equation 35, Critical Angle of a Towed Cable. Far from the body the inclination settles to the angle at which the normal drag of the cable carries the normal component of its weight.
\[\frac{\mathrm{d} \theta}{\mathrm{d} s} = 0 \quad \Longrightarrow \quad \frac{\sin^2 \theta_c}{\cos \theta_c} = \frac{2 \mu g}{\rho V^2 d \, C_{D_n}} \tag{35}\]Equation 36, Trail and Length at the Critical Angle. At the critical angle the ratio of trail to depth tends to its cotangent and the paid-out length to the depth over its sine.
\[\frac{\text{trail}}{\text{depth}} \longrightarrow \cot \theta_c , \qquad \ell \longrightarrow \frac{z}{\sin \theta_c} \tag{36}\]Equation 37, Bespoke Critical Angle of a Ten Millimetre Steel Rope. The critical angle is evaluated at 200 knots at 10,000 feet for the tabulated steel rope mass with a normal drag coefficient of 1.2 that the article takes for the circular section. Katradis, 6×19 IWRC wire rope
\[\frac{\sin^2 \theta_c}{\cos \theta_c} = \frac{2 \times 0.40 \times 9.807}{0.9046 \times 102.89^2 \times 0.010 \times 1.2} = 0.0683 \quad \Longrightarrow \quad \theta_c = 14.9^\circ , \qquad \cot \theta_c = 3.76 , \qquad \frac{100\ \text{ft}}{\sin \theta_c} = 389\ \text{ft} \tag{37}\]Equation 38, Bespoke Starting Tension and Inclination. The boundary condition is evaluated for a towed body that the article takes to weigh 50 kilograms and to have 200 newtons of drag.
\[T_c(0) = \sqrt{200^2 + \left( 50 \times 9.807 \right)^2} = 529.6\ \text{N} , \qquad \theta(0) = \arctan \frac{490.4}{200} = 67.8^\circ \tag{38}\]Equation 39, Bespoke Cable Mass Needed for a Forty-Five Degree Hang. Solving the critical angle relation for the linear density at forty-five degrees, with the assumed normal drag coefficient of 1.2, gives a cable 10.4 times heavier than the tabulated steel rope.
\[\theta_c = 45^\circ \quad \Longrightarrow \quad \mu = \frac{\rho V^2 d \, C_{D_n}}{2 \sqrt{2} \, g} = \frac{0.9046 \times 102.89^2 \times 0.010 \times 1.2}{2 \sqrt{2} \times 9.807} = 4.14\ \text{kg/m} , \qquad \frac{4.14}{0.40} = 10.4 \tag{39}\]Equation 40, Wave Speed and Modal Frequencies of a Taut String. A string under tension carries transverse waves at the square root of tension over linear density, and a finite length carries standing modes at integer multiples of the fundamental. Vibrating string
\[v_c = \sqrt{\frac{T_c}{\mu}} , \qquad F_k = \frac{k v_c}{2 \ell} \tag{40}\]Equation 41, Damped String Equation. Adding a viscous damping term per unit length to the taut string gives a first-order term in the transverse velocity.
\[\mu \frac{\partial^2 y}{\partial t^2} + c_a \frac{\partial y}{\partial t} = T_c \frac{\partial^2 y}{\partial s^2} \tag{41}\]Equation 42, Bespoke Aerodynamic Damping Coefficient of the Cable. Linearising the crossflow drag about the critical inclination, a small-perturbation assumption the article chooses, gives the damping force per unit length per unit transverse velocity.
\[c_a = \rho V d \, C_{D_n} \sin \theta_c \tag{42}\]Equation 43, Modal Frequency and Damping Ratio. The circular frequency of each mode follows from the wave speed and length, and the damping coefficient divided by twice the linear density and that frequency is its damping ratio.
\[\omega_k = \frac{k \pi v_c}{\ell} , \qquad \zeta_k = \frac{c_a}{2 \mu \omega_k} \tag{43}\]Equation 44, Sharp-Edged Gust Increment in Angle of Attack and Lift. A vertical gust changes the angle of attack by the ratio of gust velocity to airspeed and the lift in proportion through the lift-curve slope. Etkin and Reid, Dynamics of flight Nelson, Flight stability and automatic control
\[\Delta \alpha = \frac{u}{V} , \qquad \Delta L = \tfrac{1}{2} \rho V^2 S \, C_{L_\alpha} \Delta \alpha \tag{44}\]Equation 45, Gust Load Factor and Acceleration. The incremental load factor of a sharp-edged gust is inversely proportional to the wing loading, and times gravity it is an acceleration. Etkin and Reid, Dynamics of flight Nelson, Flight stability and automatic control
\[\Delta n = \frac{\rho V C_{L_\alpha} u}{2 \, W / S} , \qquad \alpha = g \, \Delta n \tag{45}\]Equation 46, Drift Time Under Constant Acceleration. A vehicle accelerated uniformly from rest leaves a window of half width $\delta$ in the square root of twice $\delta$ over the acceleration.
\[t_d = \sqrt{\frac{2 \delta}{\alpha}} \tag{46}\]Equation 47, Von Kármán Spectrum of Vertical Turbulence. The power spectral density of vertical gust velocity in the von Kármán form is set by the intensity, the scale length and the airspeed. Von Kármán wind turbulence model
\[\Phi_w(\omega) = \frac{\sigma_w^2 \lambda_w}{\pi V} \frac{1 + \tfrac{8}{3} \left( 1.339 \lambda_w \omega / V \right)^2}{\left[ 1 + \left( 1.339 \lambda_w \omega / V \right)^2 \right]^{11/6}} \tag{47}\]Equation 48, Bespoke Share of Gust Variance Below the Loop Frequency. The total variance is the integral of the spectrum, and the article defines the part a position loop has to fight as the integral up to the loop’s natural frequency. Von Kármán wind turbulence model
\[\sigma_w^2 = \int_0^\infty \Phi_w(\omega) \, \mathrm{d} \omega , \qquad \sigma_b^2 = \int_0^{\omega_n} \Phi_w(\omega) \, \mathrm{d} \omega \tag{48}\]Equation 49, Bespoke Ratio of Drift Time to Human Loop Delay. The article compares the drift time out of the capture window with the reaction time plus link latency of a human operator as a figure of merit.
\[\frac{t_d}{\tau} = \frac{1}{\tau} \sqrt{\frac{2 \delta}{\alpha}} \tag{49}\]Equation 50, Bespoke Crossover Limit Set by a Pure Delay. The phase lag of a pure delay grows with frequency, and allowing the rest of the loop a ninety-degree lag, as the article assumes, bounds the crossover for a given phase margin.
\[\arg \mathrm{e}^{- \mathrm{j} \omega \tau} = - \omega \tau \qquad \Longrightarrow \qquad \omega_c \leq \frac{\pi / 2 - \phi_m}{\tau} \tag{50}\]Equation 51, Bandwidth Needed To Hold Position Against a Steady Acceleration. A second-order position loop holds a steady acceleration with an offset of the acceleration over the square of its natural frequency, so fitting the window sets a floor on that frequency. Stevens and Lewis, Aircraft control and simulation Beard and McLain, Small unmanned aircraft
\[\omega_n \;\geq\; \sqrt{\frac{\alpha}{\delta}} \tag{51}\]Equation 52, Sensitivity and Complementary Sensitivity. The sensitivity and the complementary sensitivity of a feedback loop are defined from the open loop and always sum to one.
\[\mathcal{S} = \frac{1}{1 + \mathcal{L}} , \qquad \mathcal{T} = \frac{\mathcal{L}}{1 + \mathcal{L}} , \qquad \mathcal{S} + \mathcal{T} = 1 \tag{52}\]Equation 53, Bode Sensitivity Integral. For a stable loop that rolls off by at least two orders the integral of the logarithm of the sensitivity magnitude over frequency is zero.
\[\int_0^\infty \ln \left| \mathcal{S} \left( \mathrm{j} \omega \right) \right| \mathrm{d} \omega = 0 \tag{53}\]Equation 54, Sensitivity of Two Second-Order Loop Architectures. Placing the damping term in the forward path or in a minor feedback loop gives two sensitivity functions that differ in relative degree.
\[\mathcal{S}_{\mathrm{f}} = \frac{\left( \mathrm{j} \omega \right)^2}{\left( \mathrm{j} \omega \right)^2 + 2 \zeta \omega_n \mathrm{j} \omega + \omega_n^2} , \qquad \mathcal{S}_{\mathrm{m}} = \frac{\mathrm{j} \omega \left( \mathrm{j} \omega + 2 \zeta \omega_n \right)}{\left( \mathrm{j} \omega \right)^2 + 2 \zeta \omega_n \mathrm{j} \omega + \omega_n^2} \tag{54}\]Equation 55, Isentropic Total to Static Ratios. Bringing the flow isentropically to rest raises the temperature and pressure by ratios that depend on the Mach number and the ratio of specific heats alone.
\[\frac{\Theta_t}{\Theta} = 1 + \tfrac{1}{2} \left( \gamma - 1 \right) M^2 , \qquad \frac{p_t}{p} = \left( \frac{\Theta_t}{\Theta} \right)^{\gamma / \left( \gamma - 1 \right)} \tag{55}\]Equation 56, Reassembly of Sorties, Vehicles and Hours. The sorties, surviving vehicles and flight hours reported across the four test series sum to the stated totals within rounding.
\[1 + 1 + 3 + 4 = 9\ \text{sorties} , \qquad 5 - 2 = 3\ \text{vehicles} , \qquad 1.68 + 2.20 + 7.00 + 6.70 = 17.58\ \text{h} \tag{56}\]Equation 57, Bound on Docking Success Rate. At least ten docking attempts and one capture in the public record bound the success rate at no more than ten percent.
\[N_d \;\geq\; 9 + 1 = 10 \quad \Longrightarrow \quad \frac{1}{N_d} \;\leq\; 0.10 \tag{57}\]Equation 58, Obligations After the Last Flight Test. The two positive modifications after the airborne recovery fall within 47 days of it and amount to 3.22 percent of the three contracts’ total. DARPA Phase III contract
\[2 + 30 + 15 = 47\ \text{days} , \qquad \frac{2{,}497{,}155.40 + 165{,}393.81}{82{,}680{,}983.37} = \frac{2{,}662{,}549.21}{82{,}680{,}983.37} = 0.0322 \tag{58}\]Equation 59, Period of Performance After the Recovery. Counting four years with one leap day plus two days gives 1,463 days, or 4.01 years, from the recovery to the end of the Phase 3 period of performance. DARPA Phase III contract
\[4 \times 365 + 1 + 2 = 1{,}463\ \text{days} , \qquad \frac{1{,}463\ \text{days}}{365.25\ \text{days per year}} = 4.01\ \text{years} \tag{59}\]Equation 60, Achieved Recovery Time Against the Objective. The objective of four Gremlins Air Vehicles in thirty minutes is one every 7.5 minutes, and the 84 minute mission that recovered one vehicle is 11.2 times that. Kratos Leidos
\[\frac{30\ \text{min}}{4} = 7.5\ \text{min} , \qquad 1.4\ \text{h} \times 60\ \text{min per hour} = 84\ \text{min} , \qquad \frac{84\ \text{min}}{7.5\ \text{min}} = 11.2 \tag{60}\]Equation 61, Bespoke Probability of Surviving the Design Life. The article takes the loss probability as constant and independent from sortie to sortie, so an airframe survives all $N$ uses with probability $\left( 1 - \epsilon \right)^N$.
\[P_N = \left( 1 - \epsilon \right)^N \tag{61}\]Equation 62, Bespoke Expected Sorties per Airframe. Under the same constant and independent loss probability the expected number of sorties an airframe delivers is a truncated geometric sum.
\[\bar{n} = \sum_{k=1}^{N} \left( 1 - \epsilon \right)^{k-1} = \frac{1 - \left( 1 - \epsilon \right)^N}{\epsilon} \tag{62}\]Equation 63, Bespoke Ceiling on Expected Sorties. Under the constant loss probability the expected sorties approach the reciprocal of the loss rate as the design life grows without bound.
\[\lim_{N \to \infty} \bar{n} = \frac{1}{\epsilon} \tag{63}\]Equation 64, Bespoke Fleet Size and Cost per Sortie. The article sizes a fleet as the sorties a campaign requires over the expected sorties per airframe, and spreads the flyaway cost over those expected sorties.
\[n_a = \frac{n_r}{\bar{n}} , \qquad \frac{C}{\bar{n}} \text{, and a sortie really carries } C / \bar{n} \tag{64}\]Equation 65, Bespoke Break-Even Condition for Reuse. The article’s cost model has reuse pay when the amortised airframe, the refurbishment and the share of a recovery sortie together cost less than the expendable vehicle.
\[\frac{C}{N} + C_r + \frac{C_s}{n_s} \;<\; C_e \tag{65}\]Equation 66, Bespoke Floor on the Expendable Cost. Dropping the refurbishment and recovery sortie terms, which are not public, leaves a floor on the expendable cost that reuse must beat.
\[C_e \;>\; \frac{C}{N} \qquad \text{whatever } C_r \text{ and } C_s \text{ may be} \tag{66}\]Equation 67, Bespoke Break-Even Number of Uses. Inverting the article’s cost inequality gives the number of uses at which reuse breaks even.
\[N^\star = \frac{C}{C_e - C_r - C_s / n_s} \tag{67}\]Equation 68, Relative Kinetic Energy at Contact. The relative kinetic energy at contact is half the captured mass times the square of the closing speed.
\[E = \tfrac{1}{2} m \, \Delta V^2 \tag{68}\]Equation 69, Mean Arresting Force From the Work-Energy Balance. The mean force times the arresting distance equals the relative kinetic energy, which gives the force as a multiple of the captured weight.
\[\bar{F} x_s = \tfrac{1}{2} m \, \Delta V^2 \qquad \Longrightarrow \qquad \frac{\bar{F}}{W} = \frac{\Delta V^2}{2 g \, x_s} \tag{69}\]Equation 70, Bespoke Expected Sorties at the Development Loss Rate. The development record of two airframes lost in nine sorties is taken as a constant per-sortie loss probability in the article’s geometric model, giving 4.47 sorties from a twenty-use life.
\[\epsilon = \frac{2}{9} = 0.222 , \qquad \bar{n} = \frac{1 - \left( 7/9 \right)^{20}}{2/9} = 4.47 , \qquad \frac{\bar{n}}{N} = \frac{4.47}{20} = 0.224 \tag{70}\]Equation 71, Semispan of a Folded Wing Panel. Each folded panel spans half the difference between the deployed span and the body width. Dynetics X-61 Gremlins
\[b_p = \frac{b_v - w_v}{2} \tag{71}\]Notation
- $\rho$, the air density, in kilograms per cubic metre
- $\Theta$, the static temperature, written thus because thrust and cable tension have both taken the usual symbol
- $a$, the speed of sound
- $\gamma$, the ratio of specific heats for air
- $R_{\mathrm{air}}$, the specific gas constant for dry air
- $V$, the true airspeed
- $M$, the Mach number
- $q$, the dynamic pressure, in pascals
- $W$, the weight of the air vehicle, except where a subscript marks the carrier or the towed body
- $S$, the wing reference area of the air vehicle
- $b_v$, the wing span of the air vehicle
- $b$, the wing span of the carrier aircraft
- $A$, the wing aspect ratio
- $e$, the span efficiency factor, which is not the base of the natural logarithm
- $D_i$, the induced drag
- $\Lambda$, the induced-drag parameter, being the square of weight over the square of span
- $C_{L_{\max}}$, the maximum lift coefficient
- $C_{D_0}$, the zero-lift drag coefficient
- $C_{L_{\mathrm{opt}}}$, the lift coefficient at the best lift to drag ratio
- $V_{\mathrm{md}}$, the speed at which the lift to drag ratio is largest
- $T_0$, the static thrust of the engine
- $K_w$, the coefficient of the wave drag rise
- $M_{\mathrm{dd}}$, the drag divergence Mach number
- $P_s$, the specific excess power
- $c$, the thrust specific fuel consumption, as fuel mass per unit thrust per unit time
- $R$, the range
- $m_i$, the mass at the start of a cruise segment, with $m_f$ the mass at its end
- $\Gamma$, the circulation of one trailing vortex
- $b’$, the lateral separation of the trailing vortex pair
- $k_b$, the vortex spacing ratio
- $w_d$, the self-induced descent rate of the vortex pair
- $z_\star$, the depth at which the downwash gradient is largest
- $T_c$, the cable tension, subscripted because thrust has the bare symbol
- $\mu$, the mass of cable per unit length
- $d$, the cable diameter
- $C_{D_n}$, the normal drag coefficient of the cable in crossflow
- $C_f$, the tangential skin friction coefficient of the cable
- $\theta_c$, the asymptotic inclination a towed cable settles to, the critical angle
- $\ell$, the paid-out cable length, written thus because lift has taken the usual symbol
- $v_c$, the transverse wave speed along the cable
- $F_k$, the frequency of the kth transverse mode of the cable
- $c_a$, the aerodynamic damping force per unit length of cable per unit transverse velocity
- $\zeta_k$, the damping ratio of the kth transverse mode of the cable
- $C_{L_\alpha}$, the lift-curve slope, written out because the bare symbol is the speed of sound here
- $\Delta n$, the incremental load factor produced by a gust
- $\delta$, the half width of the capture window
- $t_d$, the time for an uncontrolled vehicle to cross the capture window
- $\omega_n$, the undamped natural frequency of the position loop
- $\tau$, the reaction time plus link latency in a human control loop
- $\Phi_w$, the power spectral density of the vertical gust velocity
- $\sigma_w$, the root mean square vertical gust velocity, with $\sigma_b$ its part below the loop frequency
- $\lambda_w$, the turbulence scale length
- $\omega_c$, the crossover frequency of the loop
- $\phi_m$, the phase margin
- $\mathcal{S}$, the sensitivity function, being the transfer from disturbance to error
- $\mathcal{T}$, the complementary sensitivity function
- $\mathcal{L}$, the open loop transfer function of the position hold
- $\epsilon$, the probability that an airframe is lost on any one sortie
- $N$, the number of uses one air vehicle is required to survive
- $\bar{n}$, the expected sorties one airframe delivers
- $C_e$, the unit cost of the expendable vehicle that reuse has to beat
- $C$, the flyaway cost of one air vehicle
- $\Delta V$, the closing speed at contact
- $\bar{F}$, the mean force during a capture
- $x_s$, the distance over which a capture is arrested
- $b_p$, the semispan of one folded wing panel
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- Sechter, Brendan. 2025. “X-Planes: Gulfstream X-54.” Brendan A R Sechter’s Development Blog, November 29. https://sgeos.github.io/aerospace/history/engineering/2025/11/29/x_planes_gulfstream_x54.html
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Referenced by
- X-Planes: Synthesis and What the Designation Became 2025-12-16
- X-Planes: Bell Textron X-76 SPRINT 2025-12-15
- X-Planes: X-69 through X-75, the Leapfrogged Block 2025-12-14
- X-Planes: General Atomics X-68 LongShot 2025-12-13
- X-Planes: X-67, the Slot Taken by XQ-67A 2025-12-12
- X-Planes: Boeing X-66 2025-12-11
- X-Planes: Aurora Flight Sciences X-65 CRANE 2025-12-10
- X-Planes: Invocon X-64 2025-12-09
- X-Planes: ABL Space Systems X-63 2025-12-08
- X-Planes: Lockheed Martin X-62 VISTA 2025-12-07