The Lockheed X-27 never existed. No airframe was completed and no engine was ever run in one [American X-Vehicles, NASA SP-2003-4531], and no pilot ever sat in anything but a mock-up, which one account describes as wood with a metal skin [The Super Starfighter, The Aviationist]. The designation was issued, the aeroplane was not built, and the gap between those two facts is the subject of this article. This is the twenty-eighth 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, and the X-26.

The aeroplane that was not built was the CL-1200 Lancer, a private venture of the Lockheed Advanced Development Projects office under Clarence Johnson, and it was a re-winged, re-engined F-104 Starfighter offered for export. Lockheed paid for it [Lockheed CL-1200 Lancer]. The United States Air Force did not, and the designation it issued was a promise of support that never arrived [American X-Vehicles, NASA SP-2003-4531].

This article is unusual in the series because its subject produced no data at all. There is no flight record, no published wind-tunnel report, and no test literature under the vehicle’s own name, although the type’s aerodynamic studies and wind-tunnel testing are recorded as Skunk Works work [Lockheed CL-1200 Lancer]. A search of the National Aeronautics and Space Administration’s Technical Reports Server for the Lancer returns no records. What survives is a set of numbers from a sales brochure and a parent aircraft that flew in military service for half a century [Lockheed F-104 Starfighter], and that turns out to be enough for analysis, because a derivative can be checked against the thing it was derived from.

The Research Question

The X-27 had two research questions, and they were not the same question.

The stated one is on the record. The X-27 was to be a high-performance research aircraft derived from the CL-1200, built to test advanced-technology engines and equipment, and it was to fly at Mach 2.6 [Lockheed CL-1200 Lancer]. That is a specific and answerable engineering question, and this article treats it as the keystone.

The operative one is visible in what the aeroplane was for. The CL-1200 was a sales article. It had lost the competition it was designed for, its manufacturer had spent its own money on it, and an X-designation would have brought government funds to build a flying demonstrator that no customer had yet agreed to buy [Lockheed CL-1200 Lancer] [American X-Vehicles, NASA SP-2003-4531]. The designation was being asked to do commercial work.

The article treats the first as the technical keystone and the second as the historical one, and it does not pretend that either subsumes the other.

The Binding Unknown

Take the stated question at face value and it names one thing that had never been done in this airframe.

The F-104’s propulsion installation was designed around a turbojet at Mach 2, the speed for which the fixed inlet cones of later F-104s were optimised [Lockheed F-104 Starfighter]. The X-27 proposed a turbofan at Mach 2.6 [Lockheed CL-1200 Lancer]. Those two changes are not independent and neither is small.

  • A turbofan is not a turbojet with better fuel consumption. It swallows more air, it is physically larger, and its fan is far less tolerant of non-uniform flow at its face than a turbojet’s first compressor stage.
  • Mach 2.6 is not Mach 2.0 with more thrust. The total-pressure recovery an inlet can achieve falls steeply with Mach number, and the temperature the skin reaches rises steeply.

So the binding unknown is a single compound question. Can a turbofan be fed at Mach 2.6 through an inlet descended from a Mach 2.0 turbojet installation, in an airframe built of aluminium alloy?

Three sections below answer the three parts of that, and two of the answers are negative.

Why the Keystone Is Not Manoeuvrability

The obvious keystone would be manoeuvrability, because the sales case was about it and the competition turned on it. It is treated at length here, and the answer is more favourable to Lockheed than the outcome suggests.

But manoeuvrability is not what the X-designation was assigned for. The designation was assigned to a proposed Mach 2.6 demonstrator of engines and equipment [Lockheed CL-1200 Lancer], and an article that silently replaces a programme’s stated purpose with a more interesting one is writing about a different programme. Both are treated, and they are kept apart.

Programme Origin

The Lancer was not commissioned. It was offered, twice, into competitions it did not win, and the designation is first recorded after the first of those defeats [Lockheed CL-1200 Lancer]. The order of events makes the programme legible, so this section takes them in order.

The Starfighter’s Wing

The F-104 Starfighter first flew in 1954 and was designed to one requirement above all others, namely to climb fast and go fast in a straight line. It has a wing of 196.1 square feet and a span of 21.94 feet, the reference geometry the National Aeronautics and Space Administration’s handling-qualities compilation gives for the F-104A [Aircraft Handling Qualities Data, NASA CR-2144], and a thickness-to-chord ratio of 3.36 percent, with a leading edge sharp enough that ground crews fitted protective covers over it [Lockheed F-104 Starfighter]. The aircraft was a superb interceptor and a poor fighter, and the cause lies in the geometry. No failing of manufacture is needed to explain it.

The aspect ratio follows from the span and the area.

\[A = \frac{b^2}{S} = \frac{(21.94\ \mathrm{ft})^2}{196.1\ \mathrm{ft}^2} = 2.455 \tag{1}\]

That is a very low number for a wing meant to turn. The wing loading is the other half of the problem.

\[\frac{W}{S} = \frac{27{,}300\ \mathrm{lb}}{196.1\ \mathrm{ft}^2} = 139.2\ \mathrm{lb/ft}^2 \tag{2}\]

Here $W$ is the F-104G’s design gross weight of 27,300 pounds as the National Aeronautics and Space Administration’s survey of aircraft performance tabulates it, and the survey gives the same 139.2 [Quest for Performance, NASA SP-468].

An aircraft that must generate lift equal to several times its weight in a turn, from a small wing of low aspect ratio, pays for that lift in drag, and the drag ends the turn.

The International Fighter Aircraft Competition

By the late 1960s the United States was supplying fighters to allied air forces under military assistance arrangements. The International Fighter Aircraft competition was run to provide an effective low-cost fighter for allied air forces [Northrop F-5].

The entrants were what the industry already had, adapted.

Northrop won in November 1970. The decision removed the Lancer’s primary market at a stroke, because the aircraft had been designed for the customers the competition was about to direct elsewhere, and no existing F-104 operator subsequently expressed interest. [Lockheed CL-1200 Lancer]

Two Accounts of the Designation

The sources diverge on what happened next, and the article leaves the disagreement unresolved because the record leaves it so.

One reading is that the Air Force wanted the aircraft flown. Under this reading the service planned to buy at least one example under the designation X-27 as a technology demonstrator, and the programme died for want of appropriated money [Lockheed CL-1200 Lancer].

The other reading is that the designation was sought rather than offered. Under this reading Lockheed pursued an X-designation as a route to federal funding for a demonstrator that would carry a sales campaign, and the military services were opposed because they did not want competition for the funding needed to complete the F-14 and F-15 programmes [American X-Vehicles, NASA SP-2003-4531].

These are not compatible accounts of who wanted what, and both appear in otherwise careful secondary sources. What is not in dispute is the outcome. Congressional and Air Force support was close to absent, no money was appropriated, and nothing was built beyond a mock-up. [Lockheed CL-1200 Lancer] [American X-Vehicles, NASA SP-2003-4531]

The Second Attempt

Lockheed offered the CL-1200-2 into the Lightweight Fighter competition of 1972, and lost again. General Dynamics and Northrop received the prototype contracts that became the YF-16 and the YF-17.

The Lightweight Fighter programme is the sharpest possible commentary on the Lancer, because it funded the thing Lockheed had asked for, namely flying prototypes of lightweight fighters built to demonstrate a concept rather than to fill an order. It funded somebody else’s [Lightweight Fighter program].

A Navy derivative, the CL-1400 and CL-1400N, was studied, combining the forward fuselage, intake and wing of the CL-1200-2 with the rear fuselage of the X-27 [Lockheed CL-1200 Lancer]. The record traces it no further.

The Vehicle

Three designations name closely related aeroplanes and the record sometimes conflates them. The CL-1200-1 was the turbojet aircraft entered in 1970, the X-27 was the proposed demonstrator derived from the Lancer, and the CL-1200-2 was the turbofan development of the X-27 offered in 1972 [Lockheed CL-1200 Lancer]. Nothing in this section was ever built, and the figures are the manufacturer’s throughout.

What Changed From the F-104

The Lancer was a major modification of the Starfighter [American X-Vehicles, NASA SP-2003-4531]. It reused the Starfighter’s basic fuselage structure, outer wing panels virtually identical to the Starfighter’s, and its landing gear, hydraulic and electrical systems [Lockheed CL-1200 Lancer].

Quantity F-104G CL-1200-2 and X-27 Change
Wing area 196.1 ft² 300.0 ft² +53.0 percent
Span 21.94 ft 29.17 ft +33.0 percent
Aspect ratio 2.455 2.836 +15.5 percent
Length 54.75 ft 57.25 ft +30.0 in
Empty weight 13,996 lb 17,885 lb +27.8 percent
Loaded weight as published 27,300 lb, design gross 24,385 lb, normal loaded not like for like
Maximum takeoff 29,083 lb 35,000 lb +20.3 percent
Engine J79-GE-11A turbojet TF30-P-100 turbofan a change of class
Thrust with afterburner 15,600 lbf 25,000 lbf +60.3 percent
Wing loading at the published loaded weight 139.2 lb/ft² 81.3 lb/ft² −41.6 percent
Thrust to weight at the published loaded weight 0.571 1.025 +79.4 percent

The F-104G weights are the National Aeronautics and Space Administration’s [Quest for Performance, NASA SP-468]. The CL-1200-2 weights are Lockheed’s estimates, which [Lockheed CL-1200 Lancer] attributes to [Air Enthusiast, Volume One] and which also lists 17,250 pounds empty and 32,500 pounds gross, the figures [X-27 specifications] gives for the X-27. The analysis below uses the CL-1200-2 figures throughout. The two loaded weights are defined differently. The F-104G figure is a design gross weight and the CL-1200-2 figure a normal loaded weight, so the wing-loading and thrust-to-weight changes in the last two rows overstate the change at equal loading and are best read as upper bounds.

Four changes matter and the rest follow from them.

The wing grew by half and moved. It went from a mid-set position to a shoulder position and moved aft, while retaining the F-104’s 10 degrees of anhedral and its aerofoil section [Lockheed CL-1200 Lancer].

The tail came down. The F-104’s T-tail, with the horizontal surface on top of the fin, was replaced by a conventional horizontal tail on the rear fuselage [Lockheed CL-1200 Lancer].

The engine changed class. The J79 turbojet became the TF30 turbofan, and the difference in physical envelope is not incidental [Lockheed CL-1200 Lancer].

Engine Length Diameter Dry weight Airflow
J79-GE-17 208.69 in 39.06 in 3,835 lb 170 lb/s
TF30-P-100 241.70 in 48.90 in 3,985 lb 260 lb/s
Difference +33.01 in +9.84 in +150 lb +52.9 percent

The lengths, diameters, dry weights and airflows are the published ratings of the two engines [General Electric J79] [Pratt and Whitney TF30]. The last row gives the differences, and its airflow entry is a ratio less one.

\[\Delta L = 241.70 - 208.69 = 33.01\ \mathrm{in}, \qquad \Delta D = 48.90 - 39.06 = 9.84\ \mathrm{in}, \qquad \frac{\dot m_{\mathrm{TF30}}}{\dot m_{\mathrm{J79}}} - 1 = \frac{260}{170} - 1 = 0.529 \tag{3}\]

The fuselage was stretched 30 inches, which the record attributes to a 46 percent increase in internal fuel [Lockheed CL-1200 Lancer]. The engine that had to go inside it is 33.01 inches longer than the J79-GE-17. The comparison table uses the J79-GE-17 because those are the J79 dimensions the article holds, while the F-104G column above names the J79-GE-11A, so the differences are measured against a sister variant of the engine the F-104G carried and not against that engine itself. The stretch falls short of the engine length difference by

\[\Delta L - \Delta L_{\mathrm{fus}} = 33.01 - 30 = 3.01\ \mathrm{in} \tag{4}\]

where $\Delta L_{\mathrm{fus}}$ is the fuselage stretch, which is close enough that either consideration could have set it. The article declines to claim which one did, because the record states only the fuel figure.

The Intakes

The F-104 uses fixed half-cone side inlets [Lockheed F-104 Starfighter]. The CL-1200 replaced them with translating shock cones having four inches of axial movement. The X-27, according to the record, was to have had intakes of rectangular form instead [Lockheed CL-1200 Lancer].

Why the shape changed is not recorded. Section Sizing From First Principles computes one. A single cone cannot do the job at Mach 2.6.

The Mock-Up

One full-scale mock-up was completed in a Lockheed hangar. Reports indicate that up to three fuselages were worked before termination [Lockheed CL-1200 Lancer].

A mock-up is not evidence about performance and this article does not treat it as any. It is evidence about intent and about how far the money went, and it is used here for those two purposes alone.

Sizing From First Principles

Everything in this section is computed from published geometry and published engine ratings. None of it is a measurement, because there is nothing to measure. What it produces is an independent prediction to set beside the manufacturer’s prediction, and the ground-prediction section makes clear that the comparison is between two predictions rather than between a prediction and a fact.

The Flight Condition

The International Standard Atmosphere gives the conditions at the altitude every performance claim is quoted at. The compressible-flow relations used from here to the end of the inlet section are standard and are set out in Shapiro and Anderson, which are the sources for every identity below that carries no other citation. Below 11 kilometres the temperature falls linearly with height at the standard lapse rate.

\[T(h) = T_0 - \lambda h, \qquad T_0 = 288.15\ \mathrm{K}, \qquad \lambda = 0.0065\ \mathrm{K/m} \tag{5}\]

Above the tropopause it is constant, and the pressure falls exponentially.

\[p(h) = p_{11} \exp\left(-\frac{g_0 (h - h_{11})}{R T}\right) \tag{6}\]

The density follows from the equation of state.

\[\rho = \frac{p}{R T} = \frac{23{,}842.3}{287.05 \times 218.81} = 0.3796\ \mathrm{kg/m^3} \tag{7}\]

At 35,000 feet, which is 10,668 metres and above the tropopause, this gives a temperature of 218.81 kelvin, a density of 0.3796 kilograms per cubic metre, and a speed of sound of

\[a = \sqrt{\gamma R T} = \sqrt{1.4 \times 287.05\ \times 218.81} = 296.54\ \mathrm{m/s} = 663.3\ \mathrm{mph} \tag{8}\]

The article is written in Mach number, the ratio of airspeed to the speed of sound.

\[M = \frac{V}{a} \tag{9}\] \[M = \frac{1{,}700\ \mathrm{mph} \times 0.44704}{296.54\ \mathrm{m/s}} = \frac{760.0}{296.54} = 2.563 \tag{10}\]

The claimed maximum speed of 1,700 miles per hour at 35,000 feet is therefore Mach 2.563, consistent with the Mach 2.57 quoted in the reference article’s specification table and with the Mach 2.5 quoted in its performance summary as a rounding. The X-27’s stated test objective of Mach 2.6 sits just above it [Lockheed CL-1200 Lancer].

Two further quantities are used throughout and are defined here so that later sections can call on them, following Anderson. The dynamic pressure is what converts a coefficient into a force, and the specific heat at constant pressure follows from the gas constant and the ratio of specific heats.

\[q = \tfrac{1}{2}\rho V^2 \tag{11}\] \[c_p = \frac{\gamma R}{\gamma - 1} = \frac{1.4 \times 287.05}{0.4} = 1004.7\ \mathrm{J/(kg\,K)} \tag{12}\]

At 15,000 feet and Mach 0.9, the condition every manoeuvre result below is evaluated at, the dynamic pressure is

\[q = \tfrac{1}{2} \times 0.7708 \times 290.0^2 = 32{,}415\ \mathrm{Pa} = 677.1\ \mathrm{lb/ft^2} \tag{13}\]

The heating this flight condition produces is the subject of the cluster on aerodynamic heating, recovery temperature and thermal protection below, and the period’s measurements of it in flight include these.

The Temperature the Skin Reaches

Air brought to rest against a surface gives up its kinetic energy as heat. The total temperature follows from energy conservation in a compressible flow.

\[\frac{T_t}{T} = 1 + \frac{\gamma - 1}{2} M^2 \tag{14}\]

A real surface does not recover all of it, because the boundary layer conducts some heat away along the surface as it converts the rest. The recovery factor accounts for that, and for a turbulent boundary layer it is the cube root of the Prandtl number.

\[T_r = T\left(1 + r\,\frac{\gamma - 1}{2} M^2\right), \qquad r = \Pr^{1/3} \approx 0.896 \tag{15}\]

Evaluating at 35,000 feet gives the table on which the structural argument depends.

Mach Speed Total temperature Recovery temperature Yield retained by 2024-T81, half-hour exposure
1.00 663 mph −10.6 °C −15.1 °C 100 percent
2.00 1,327 mph 120.7 °C 102.5 °C 89 percent
2.20 1,459 mph 157.5 °C 135.5 °C 85 percent
2.50 1,658 mph 219.2 °C 190.8 °C 74 percent
2.56 1,698 mph 232.5 °C 202.7 °C 71 percent
2.60 1,725 mph 241.5 °C 210.8 °C 68 percent

The standard treatments of compressible flow used throughout this section are Shapiro and Anderson, and the aerodynamic design context is Kuchemann.

The last column is read from the Department of Defense handbook curve of tensile yield strength at temperature for 2024-T81 aluminium alloy, as a percentage of the room-temperature value, on the curve for one-half hour at temperature [Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5J]. That figure, Figure 3.2.3.4.1(b), is plotted in degrees Fahrenheit, so each recovery temperature is converted before it is read.

\[T_{\mathrm{F}} = 1.8\,T_{\mathrm{C}} + 32, \qquad 1.8 \times 210.8 + 32 = 411.4\ ^{\circ}\mathrm{F} \tag{16}\]

The readings are given to the nearest percentage point, which is about the precision the printed curve allows. At Mach 1.0 the recovery temperature lies below the curve’s range, and the room-temperature value applies. Half an hour is the shortest exposure the handbook plots, and longer exposure lowers the curve. At the Mach 2.6 recovery temperature the handbook’s five exposure curves read as follows [Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5J].

Exposure at 411 °F 1/2 hour 10 hours 100 hours 1,000 hours 10,000 hours
Yield retained 68 percent 67 percent 57 percent 44 percent 28 percent

The half-hour column is therefore the most favourable reading the handbook supports, and an airframe that accumulated many hours at that temperature over a service life would sit on one of the lower curves.

The shape of that column is the finding. At Mach 2.0, where the F-104 lived, the structure keeps 89 percent of its strength. At Mach 2.6 it keeps 68 percent, and a wing sized for a given load factor at full strength is a wing that no longer reaches it.

Work on elevated-temperature alloy behaviour and creep is large and spans the period. Two clusters below contain it, one on aluminium alloys and their strength when hot and one on titanium, other alloys and composites at elevated temperature. The measurements of aluminium alloys at temperature closest to the handbook curve above follow.

Does a Dash Evade the Temperature?

The obvious defence is that Mach 2.6 was a dash number rather than a cruise number, and that a structure does not reach its steady-state temperature in a short excursion. The defence is testable.

Treat a panel of skin as a lumped thermal mass heated by convection from the boundary layer. The balance is first order and its time constant is

\[\tau = \frac{\rho_s c_s t}{h} \tag{17}\]

where $\rho_s$ is the density of the skin, $c_s$ its specific heat, $t$ its thickness, and $h$ the convective coefficient. The coefficient is not assumed. It comes from the turbulent flat-plate Stanton number evaluated at the Eckert reference temperature, which accounts for the property variation across a high-speed boundary layer.

\[T^* = T_e\left(0.5\left(1 + \frac{T_w}{T_e}\right) + 0.16\,r\,\frac{\gamma-1}{2}M_e^2\right) \tag{18}\] \[\mathrm{St} = 0.0296\,\mathrm{Re}_x^{-1/5}\,\Pr^{-2/3}, \qquad h = \mathrm{St}\,\rho^* u_e c_p \tag{19}\]

The Reynolds number in that correlation is a defined quantity, and the viscosity inside it comes from Sutherland’s law, both as given in Anderson.

\[\mathrm{Re}_x = \frac{\rho^* u_e x}{\mu^*}, \qquad \mu(T) = \frac{1.458 \times 10^{-6}\,T^{3/2}}{T + 110.4} \tag{20}\] \[\mathrm{Re}_x = \frac{0.2109 \times 771.0 \times 5.0}{2.2598 \times 10^{-5}} = 3.598 \times 10^{7} \tag{21}\]

For a two-millimetre aluminium skin five metres back from the nose at Mach 2.6 and 35,000 feet, the Reynolds number is $3.60 \times 10^7$, the coefficient is 185.5 watts per square metre kelvin, and

\[\tau = \frac{2780 \times 875 \times 0.002}{185.5} = 26.2\ \mathrm{s} \tag{22}\]

The transient from a cold start then follows directly.

\[T_{\mathrm{skin}}(t) = T_\infty + \left(T_r - T_\infty\right)\left(1 - e^{-t/\tau}\right) \tag{23}\]
Time at Mach 2.6 Skin temperature Fraction of the way Yield retained
30 s 148.4 °C 68.1 percent 83 percent
60 s 190.9 °C 89.9 percent 74 percent
120 s 208.8 °C 99.0 percent 69 percent
180 s 210.6 °C 99.9 percent 68 percent

Thermal Stress in a Restrained Skin

Losing yield strength is not the only thing high temperature does. A skin that wants to expand and is restrained by cooler structure behind it develops stress without any aerodynamic load at all.

Thermal stress, thermal buckling of heated panels, and the thermoelastic analysis of restrained structure are a large period literature, driven by the aircraft that were trying to fly faster than aluminium comfortably allows.

\[\sigma_{\mathrm{th}} = E\,\alpha\,\Delta T \tag{24}\]

Taking aluminium alloy at a Young’s modulus of 72 gigapascals and a coefficient of thermal expansion of 23 parts per million per kelvin, and the full excursion from a cold start to the recovery temperature at Mach 2.6,

\[\sigma_{\mathrm{th}} = 72 \times 10^{9} \times 23 \times 10^{-6} \times 190.8 = 316\ \mathrm{MPa} \tag{25}\]

The retained yield at that temperature is about 272 megapascals. The handbook’s room-temperature A-basis yield strength for 2024-T81 sheet from 0.010 to 0.249 inch thick is 58 ksi in the long-transverse direction [Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5J], and with the 68 percent from the table above

\[\sigma_{\mathrm{yield}}(T_r) = 0.68 \times 58\ \mathrm{ksi} \times 6.895\ \frac{\mathrm{MPa}}{\mathrm{ksi}} = 0.68 \times 400\ \mathrm{MPa} = 272\ \mathrm{MPa}, \qquad \frac{316}{272} = 1.16 \tag{26}\]

The fully restrained thermal stress exceeds it, at 116 percent.

That number is an upper bound and not a prediction, because no real airframe is fully restrained. All of the structure heats, so the stress depends on the difference in temperature between skin and substructure, and a better use of the formula is to invert it and ask how much difference the material can afford.

\[\Delta T_{1/2} = \frac{0.5\,\sigma_{\mathrm{yield}}(T)}{E\,\alpha} = \frac{0.5 \times 272 \times 10^{6}}{72 \times 10^{9} \times 23 \times 10^{-6}} = 82\ \mathrm{K} \tag{27}\]

Eighty-two kelvin of differential consumes half the remaining strength. That allowance is small for a structure with a thin hot skin over cooler spars and frames, so the Mach 2.6 objective posed a thermal-stress problem on top of the strength problem. The record is silent on it.

The defence does not survive. The skin is nine-tenths of the way to its equilibrium temperature after one minute. A dash long enough to be useful is long enough to heat the structure, and the time constant is short because aluminium skin is thin and conductive, the same properties that recommended it for everything else.

This is not a novel observation about the era. The F-104 could have flown faster had its aluminium skin been able to withstand the heating [Lockheed F-104 Starfighter], the X-15 was of Inconel X heat-sink construction [American X-Vehicles, NASA SP-2003-4531], and the SR-71 was built of titanium [Lockheed SR-71 Blackbird]. The point here is narrower. The X-27 proposed to reach a speed in that regime while inheriting an aluminium airframe, and no source explains how. The only provision against heating that the record names is the strengthened windshield of the F-104S [Lockheed CL-1200 Lancer].

The Inlet

An engine at supersonic speed is fed by a device whose job is to slow the air to a speed the compressor can accept while losing as little total pressure as possible. Total pressure is the currency, because thrust follows from the pressure the engine has to work with, and every shock wave the air crosses spends some of it irreversibly.

The measure is the total-pressure recovery, the ratio of total pressure at the engine face to total pressure in the free stream.

\[\eta = \frac{p_{t2}}{p_{t\infty}} \tag{28}\]

The standard reference for this subject is Seddon and Goldsmith, and the propulsion-integration side is covered by Oates and by Mattingly.

The literature on supersonic inlet design, shock systems, recovery and capture is one of the largest bodies of work in applied gas dynamics. Its records fill the cluster on supersonic inlets, shock systems and pressure recovery below, the largest in this survey, and this section draws on the following period studies and reviews.

The Standard the Design Had to Meet

A military specification defines a reference recovery against which an inlet is judged [Inlet Performance, NASA Glenn Research Center]. It is an engineering standard rather than a law of nature, and so the right yardstick for a claim in a brochure.

\[\eta_{\mathrm{ref}} = 1 - 0.075\,(M - 1)^{1.35}, \qquad M > 1 \tag{29}\]
Mach Reference recovery
1.5 0.9706
2.0 0.9250
2.2 0.9041
2.6 0.8585
3.0 0.8088

The Pitot Inlet as a Baseline

A pitot inlet is a hole facing forward. The air crosses one normal shock and that shock does all of the compression. The total-pressure ratio across a normal shock is a closed form.

\[\frac{p_{t2}}{p_{t1}} = \left[\frac{(\gamma+1)M^2}{2 + (\gamma-1)M^2}\right]^{\frac{\gamma}{\gamma-1}} \left[\frac{\gamma+1}{2\gamma M^2 - (\gamma-1)}\right]^{\frac{1}{\gamma-1}} \tag{30}\] \[\eta_{\mathrm{pitot}}(2.0) = 0.7209, \qquad \eta_{\mathrm{pitot}}(2.6) = 0.4601 \tag{31}\]

At Mach 2.6 a pitot inlet throws away more than half the total pressure. That sets the scale of what the cone gains.

Computing a Single Cone

A conical spike ahead of the cowl generates a conical shock. The air crosses that oblique shock first, losing much less total pressure than it would across a normal shock at the same free-stream Mach number, and then crosses a weaker normal shock at the throat.

The flow behind a conical shock is not uniform. That distinguishes it from the two-dimensional wedge case, and it is why the cone needs an integration where the wedge has a formula.

The conical-flow literature is distinct from the inlet literature that uses it. Its reports published the tabulations that made the integration usable before computers.

The governing relation is the Taylor-Maccoll equation, written here for the velocity components normalised by the maximum adiabatic velocity.

\[\frac{dV_r'}{d\theta} = V_\theta' \tag{32}\] \[\frac{dV_\theta'}{d\theta} = \frac{V_r' V_\theta'^2 - a'^2\left(2V_r' + V_\theta' \cot\theta\right)}{a'^2 - V_\theta'^2}, \qquad a'^2 = \frac{\gamma-1}{2}\left(1 - V_r'^2 - V_\theta'^2\right) \tag{33}\]

Every oblique shock relation reduces to a normal one through the component of Mach number along the wave, the bookkeeping that lets a single set of formulae serve both cases.

\[M_{n1} = M_1 \sin\beta \tag{34}\] \[M_{2}^{2} = \frac{1 + \frac{\gamma-1}{2}M_{n1}^{2}}{\gamma M_{n1}^{2} - \frac{\gamma-1}{2}} \bigg/ \sin^{2}(\beta - \theta_d) \tag{35}\]

The wave angle cannot fall below the Mach angle, the angle of the weakest disturbance the flow will carry, and that bound limits every search below. The oblique-shock and Mach-angle relations are standard, in Shapiro and Anderson, and the inlet application of them is Seddon and Goldsmith.

\[\mu = \arcsin\frac{1}{M}, \qquad \mu(2.0) = 30.00^\circ, \qquad \mu(2.6) = 22.62^\circ \tag{36}\]

The integration starts immediately behind the shock, where the oblique shock relations give the deflection from the wave angle $\beta$,

\[\tan\theta_d = 2\cot\beta\,\frac{M_1^2 \sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2} \tag{37}\]

and proceeds inward until the flow becomes tangent to a surface. That surface is the cone. The problem is solved in the inverse direction, because Taylor-Maccoll integrates from a known shock angle to whatever cone that shock implies, so a wanted cone angle is reached by search.

Running that integration and following it with a normal shock at the throat gives the recovery of a single-cone inlet.

Cone half-angle Mach 2.0 shock Mach 2.0 recovery Mach 2.6 shock Mach 2.6 recovery
15° 33.91° 0.8515 27.69° 0.6243
20° 37.80° 0.8980 31.86° 0.6881
25° 42.53° 0.9245 36.64° 0.7315
27.5° 45.20° 0.9269 39.23° 0.7421
30° 48.08° 0.9210 41.94° 0.7442
32.5° 51.23° 0.9061 44.78° 0.7373
35° 54.75° 0.8822 47.77° 0.7215
37.5° detached none 50.95° 0.6968

This table contains the article’s central technical result.

At Mach 2.0 the best single cone reaches 0.9269 against a reference of 0.9250. It clears the standard, by two-tenths of a point. The F-104’s arrangement was adequate for the speed it was built for. That result is unsurprising, and it serves as the control showing the method is not biased against the design.

At Mach 2.6 the best single cone reaches 0.7442 against a reference of 0.8585. It falls short by 11.44 points.

And that shortfall is a floor. The calculation above is inviscid. It charges nothing for boundary-layer bleed, duct friction, the diffuser, or operation away from the design point. A real inlet does worse than this. The reference standard, by contrast, is what a competent real inlet was expected to achieve including all of those losses, since the specification carries an inlet efficiency factor for them [Inlet Performance, NASA Glenn Research Center]. An idealised calculation that still cannot reach a practical standard shows that the shortfall is no artefact of pessimistic assumptions.

Two Ramps in a Rectangular Intake

A rectangular intake can carry two or more plane compression ramps where a round one carries a single cone. Each additional oblique shock takes a share of the compression, and spreading the compression across more and weaker shocks costs less total pressure than concentrating it, a result due to Oswatitsch.

Computing the two-ramp arrangement requires the same oblique-shock relation applied twice, followed by a normal shock.

\[\eta_{\mathrm{2-ramp}} = \frac{p_{t2}}{p_{t1}}\bigg|_{\delta_1} \cdot \frac{p_{t3}}{p_{t2}}\bigg|_{\delta_2} \cdot \frac{p_{t4}}{p_{t3}}\bigg|_{\mathrm{normal}} \tag{38}\]

Oswatitsch’s result also says how to divide the compression. For a given number of oblique shocks the recovery is greatest when they are of equal strength, meaning equal normal Mach components.

\[M_1 \sin\beta_1 = M_2 \sin\beta_2 = \cdots = M_n \sin\beta_n \tag{39}\]

The theorem can be checked directly, and a fair check holds both searches to the same constraint. An equal pair searched without the turning constraint, set against an unequal pair searched with it, appears to win only by exceeding a limit the other obeys. Under the same twenty-five degree cap the two agree closely.

Mach Best equal pair Recovery Best free pair Recovery Free advantage
2.0 10.8° + 10.8° 0.9569 10.4° + 11.1° 0.9570 0.010 points
2.6 12.5° + 12.5° 0.8251 11.4° + 13.6° 0.8261 0.104 points

The free optimum beats the equal-strength arrangement by a tenth of a point at most, which confirms the theorem.

The search must be constrained or it returns nonsense. An unconstrained optimisation returns four degrees followed by twenty at Mach 2.0, for a recovery of 0.9974, and that is arithmetic rather than a design. A total deflection of thirty-six degrees has to be turned back at the cowl and would separate the duct. Capping total turning at twenty-five degrees, taken here as about what external compression can physically deliver, gives usable answers.

Mach Best two-ramp Recovery Mach before the normal shock Gain over the best single cone
2.0 10° + 11° 0.9567 1.243 +2.98 points
2.6 11° + 14° 0.8260 1.603 +8.18 points

The two-ramp arrangement recovers 8.18 of the 11.44 points the single cone gives away at Mach 2.6, and only 2.98 points at Mach 2.0 where nothing needed recovering.

The record states that the X-27 was to have rectangular intakes and does not say why. This is why. The article presents this as an inference from the physics, offered as an explanation that fits, with no documented rationale behind it. The explanation has a sharp signature, since the change gains almost nothing at the speed the CL-1200 was sold at and a great deal at the speed the X-27 was to be tested at, the pattern one would expect if the change was made for the test programme.

Inlet-engine compatibility, distortion, and the compressor’s response to it form the other half of this subject, and the clusters on inlet distortion and inlet-engine compatibility and on compressor stall, surge and casing treatment below collect that work. The period’s compatibility procedures and surveys appear here.

Why the Engine Choice Makes the Inlet Harder

The TF30 is the wrong engine to put behind a marginal inlet, and this is documented rather than inferred. The engine was prone to compressor stall at high angle of attack when the throttle was moved sharply, and in the F-14, whose widely separated nacelles turned a stall into asymmetric thrust, it was dangerous enough to threaten departure. The F-111 suffered less because its mission involved gentler handling [Pratt and Whitney TF30].

A fan is more sensitive to inlet distortion than a turbojet’s compressor, because the fan’s outer span operates at high relative Mach number and low solidity, and a circumferential total-pressure defect passing through it appears as a rotating incidence excursion. The Lancer’s inlets sit on the sides of a fuselage, ahead of a wing, at whatever angle of attack the aeroplane is flying.

Research on compressor stall and surge, its inception, and its suppression is one of the most sustained programmes in turbomachinery.

This article does not claim the Lancer would have suffered the F-14’s problems. It had a single engine, so asymmetry was not available to it, and its inlets are differently placed [Lockheed CL-1200 Lancer]. What it does claim is narrower and better supported. The combination the X-27 proposed put a distortion-sensitive engine behind an inlet that the calculation above shows was working near its limit, at a Mach number beyond anything the installation’s ancestor had flown, and the record contains no evidence that the combination was ever tested in any facility.

The Spike Travel, Inverted

The cone must move. As Mach number rises the conical shock lies closer to the axis, so holding the shock on the cowl lip requires the apex to move forward.

With the apex a distance $L$ ahead of the lip and the lip at radius $r$, the shock-on-lip condition is purely geometric.

\[\tan\beta = \frac{r}{L} \qquad \Longrightarrow \qquad L = \frac{r}{\tan\beta} \tag{40}\]

The travel needed between two Mach numbers follows immediately.

\[\Delta L = r\left(\cot\beta_{\mathrm{hi}} - \cot\beta_{\mathrm{lo}}\right) \tag{41}\]

The shock-on-lip condition and the capture-area bookkeeping that follows it come from Seddon and Goldsmith.

The record gives the travel and not the radius. Four inches of movement is documented, but the diameter of the Lancer’s inlets is not. So the relation is inverted. Inversion is the sound move when a parameter is unknown, and it turns a quoted number into a checkable one.

\[r = \frac{\Delta L}{\cot\beta_{\mathrm{hi}} - \cot\beta_{\mathrm{lo}}} \tag{42}\]

Taking the shock held on the lip from Mach 2.0 to Mach 2.6, and the two side inlets as half-cones so that their combined capture area is $\pi r^2$,

Cone half-angle Shock at M 2.0 Shock at M 2.6 Implied lip radius Implied total capture area
20° 37.80° 31.86° 12.51 in 3.417 ft²
25° 42.53° 36.64° 15.73 in 5.401 ft²
27.5° 45.20° 39.23° 17.26 in 6.500 ft²
30° 48.08° 41.94° 18.58 in 7.535 ft²

This calculation comes from the work on capture area, spike and cone geometry, mass-flow ratio and the spillage that follows from operating away from the design point. That work also belongs to the cluster on supersonic inlets, shock systems and pressure recovery below, and the translating-spike and additive-drag reports nearest to the calculation are listed here.

Testing the Inversion

An inversion that cannot be tested is a rearrangement. This one can be tested, because the engine’s airflow is documented independently.

The capture area needed to admit a given physical mass flow at full capture is

\[A_c = \frac{\dot m}{\rho_\infty V_\infty} \tag{43}\]

The TF30-P-100 is documented at 260 pounds per second, or 117.93 kilograms per second [Pratt and Whitney TF30]. At Mach 2.0 and 35,000 feet the free-stream mass flux is $\rho_\infty V_\infty = 225.0$ kilograms per square metre per second, so

\[A_c = \frac{117.93}{225.0} = 0.524\ \mathrm{m}^2 = 5.639\ \mathrm{ft}^2 \tag{44}\]
Assumed cone half-angle Implied capture from the travel Required by the engine Error
20° 3.417 ft² 5.639 ft² −39.4 percent
25° 5.401 ft² 5.639 ft² −4.2 percent
27.5° 6.500 ft² 5.639 ft² +15.3 percent
30° 7.535 ft² 5.639 ft² +33.6 percent

The error column is the implied capture area $A_{\mathrm{travel}}$ measured against the required one, which at twenty-five degrees is

\[\varepsilon = \frac{A_{\mathrm{travel}} - A_c}{A_c} = \frac{5.401 - 5.639}{5.639} = -0.042 \tag{45}\]

A twenty-five degree cone reconciles the two published figures to within 4.2 percent, and twenty-five degrees is an ordinary half-angle for a supersonic inlet of the period.

This is the strongest result in the article, and the reason deserves care. Two numbers were published by different people for different purposes, namely a spike travel of four inches quoted as an airframe feature, and an airflow of 260 pounds per second quoted as an engine rating. Neither was derived from the other. Shock-on-lip geometry and a mass-flow balance connect them through a cone angle that nobody published, and asking for a cone angle that satisfies both returns a conventional one.

Reproducing two independent quoted figures from one model carries far more weight than reproducing either alone. No other result here comes as close to a measurement.

What it does not establish should be equally clear. It does not confirm the aircraft would have worked. It confirms only that the published airframe and engine figures are mutually consistent, evidence that the design was worked out rather than sketched.

A Note on Corrected Flow

Converting the engine’s maximum corrected airflow to physical airflow at Mach 2.6 gives 356 kilograms per second, three times the sea-level rating. The corrected flow relation is

\[\dot m_{\mathrm{corr}} = \frac{\dot m \sqrt{\theta}}{\delta}, \qquad \theta = \frac{T_{t2}}{288.15}, \qquad \delta = \frac{p_{t2}}{101325} \tag{46}\]

The arithmetic is right and the premise is wrong. Corrected airflow and the engine matching it governs are treated in Oates and Mattingly. A compressor does not hold its maximum corrected flow while its inlet total temperature rises by two hundred kelvin, because the corrected speed falls and the operating point walks down the map. The engine’s flow schedule at high Mach is not in the public record, so the comparison above is made at Mach 2.0 using physical flow, where the engine is near its rating and the assumption is defensible. The point is stated because a number that is not credible counts as a finding.

The Metric the Competition Used

By 1970 the argument about fighters had moved. Top speed and rate of climb had been the currency of the 1950s, and the F-104 was designed to win on them [Lockheed F-104 Starfighter]. What replaced them was energy manoeuvrability, the framework associated with John Boyd and Thomas Christie, which asks not how fast an aircraft can go but how much energy it can gain or hold while turning.

The framework’s primitive is energy height, the altitude an aircraft would reach if it traded all its speed for height without loss, and it is written out below. The treatment followed here is Whitford, with the equations of motion behind it in Stevens and Lewis.

This heading is among the thinnest in the article and the thinness is a finding. Of the research records the article cites, one carries energy height, energy state or minimum time to climb in its title. The subject is not small. It is indexed elsewhere, inside trajectory optimisation and inside the optimum-climb literature, and its foundational documents are Air Force internal reports that no journal indexed [Energy-maneuverability theory].

\[h_e = h + \frac{V^2}{2g} \tag{47}\]

At 15,000 feet and Mach 0.9 that is

\[h_e = 4{,}572 + \frac{290.0^2}{2 \times 9.80665} = 4{,}572 + 4{,}289 = 8{,}861\ \mathrm{m} = 29{,}072\ \mathrm{ft} \tag{48}\]

The central quantity is specific excess power, the rate of change of that height and not an independent definition.

\[P_s = \frac{dh_e}{dt} = V\,\frac{T - D}{W} \tag{49}\]

The thrust-to-weight ratio is the other term the comparison turns on, and the table in What Changed From the F-104 gives it without writing it out.

\[\frac{T}{W} = \frac{25{,}000\ \mathrm{lbf}}{24{,}385\ \mathrm{lb}} = 1.025 \tag{50}\]

A re-winged F-104 improves on the old metrics. The question is what it does to this one.

The framework and its consequences for fighter design are set out in Whitford, and Boyd’s part in it is treated at length in Coram.

Energy manoeuvrability, sustained turning performance and the comparison of combat aircraft performance have a smaller literature than the other subjects treated here, and the list below is not padded.

That thinness has the cause given above. Boyd’s work in particular is not indexed where the rest of this article’s sources live [Energy-maneuverability theory].

Building a Drag Polar Without a Measurement

Every manoeuvre result below runs through the drag polar.

\[C_D = C_{D_0} + K C_L^2 \tag{51}\]

Neither coefficient is available for this aircraft, so both are constructed, and the construction is stated in full.

The Parasite Term, Held Deliberately Constant

$C_{D_0}$ is estimated by the equivalent-skin-friction method of Raymer, in which a coefficient standing for friction, form, interference and roughness together is applied to the wetted area. The drag data underlying such coefficients is Hoerner, and the sizing method is also given by Nicolai.

\[C_{D_0} = C_{fe}\,\frac{S_{\mathrm{wet}}}{S_{\mathrm{ref}}} = 0.0035 \times 4.5 = 0.0158 \tag{52}\]

The same value is used for all four aircraft compared below. It is a deliberate control and makes no claim to accuracy. Holding parasite drag equal turns the comparison into one about wing loading and thrust-to-weight, which is the question being asked. Where the answer depends on the value, the sensitivity is reported instead of a number.

The Induced Term and the Aerofoil

The F-104’s inheritance shows in $K$. The elliptical result assumes the leading edge develops its full suction peak.

\[K_{\mathrm{full}} = \frac{1}{\pi A e} \tag{53}\]

A thin wing with a sharp leading edge cannot develop it. The flow separates at the edge rather than turning around it, and the limiting case is that the resultant force tilts back with the surface, so that

\[K_{\mathrm{none}} = \frac{1}{C_{L_\alpha}} \tag{54}\]

At these aspect ratios the lift-curve slope is nowhere near $2\pi$, and using the high-aspect-ratio value would understate the very penalty this section exists to measure. The form used is that of Raymer and Nicolai. The Helmbold-Diederich form applies.

\[C_{L_\alpha} = \frac{2\pi A}{2 + \sqrt{4 + \dfrac{A^2\beta^2}{\eta^2}\left(1 + \dfrac{\tan^2\Lambda_{c/2}}{\beta^2}\right)}}, \qquad \beta = \sqrt{|1 - M^2|} \tag{55}\]

The real wing sits between the two limits, so the article blends them and reports the full range and picks no single value, because a conclusion that survives every leading-edge suction fraction is stronger than a point estimate.

\[K = s\,K_{\mathrm{full}} + (1 - s)\,K_{\mathrm{none}}, \qquad 0 \le s \le 1 \tag{56}\]
Aircraft Aspect ratio $C_{L_\alpha}$ at M 0.9 $K$ at $s=0$ $K$ at $s=0.5$ $K$ at $s=1$
F-104G 2.455 3.592 0.2784 0.2113 0.1441
CL-1200-2 2.836 4.064 0.2460 0.1854 0.1247
F-5E 3.824 5.158 0.1939 0.1432 0.0925
F-15A 3.014 4.275 0.2339 0.1756 0.1173

Every line of that table draws on the literature of low-aspect-ratio and thin-wing aerodynamics, leading-edge behaviour, wave drag and the area rule, which the clusters on wings, aspect ratio and vortex flows and on drag polars, wave drag and supersonic aerodynamics below divide between them. From the period, these papers treat low aspect ratio wings, drag due to lift, leading-edge suction and the area rule.

Sustained Turning

An aircraft holds a turn when thrust equals drag at the load factor concerned. Setting $T = D$ and substituting the lift coefficient required at load factor $n$,

\[C_L = \frac{n W}{q S} \tag{57}\]

then solving for the load factor gives

\[n_{\mathrm{sus}} = \sqrt{\frac{q S}{K W}\left(\frac{T}{W} - \frac{q S C_{D_0}}{W}\right)} \tag{58}\]

and the turn rate follows from the load factor and the speed, as does the radius, the other axis of the diagram this framework is usually drawn on.

\[\dot\psi = \frac{g\sqrt{n^2 - 1}}{V} \tag{59}\] \[R = \frac{V^2}{g\sqrt{n^2 - 1}} \tag{60}\]

The load factor is also what the bank angle costs, in level flight.

\[n = \frac{1}{\cos\phi} \tag{61}\]

At the sustained load factor computed below the Lancer is banked at

\[\phi = \arccos\frac{1}{6.34} = 80.9^\circ, \qquad R = \frac{290.0^2}{9.80665\sqrt{6.34^2 - 1}} = 1{,}371\ \mathrm{m} = 4{,}496\ \mathrm{ft} \tag{62}\]

Evaluating at 15,000 feet and Mach 0.9, a representative combat condition, gives the comparison on which the sales case rested.

Suction Aircraft Sustained $n$ Turn rate $P_s$ at 1 g
0.0 F-104G 2.94 5.36 °/s 416 ft/s
0.0 CL-1200-2 5.50 10.48 °/s 823 ft/s
0.0 F-5E 4.58 8.67 °/s 461 ft/s
0.0 F-15A 6.06 11.58 °/s 860 ft/s
0.5 F-104G 3.38 6.25 °/s 430 ft/s
0.5 CL-1200-2 6.34 12.13 °/s 830 ft/s
0.5 F-5E 5.33 10.15 °/s 467 ft/s
0.5 F-15A 6.99 13.41 °/s 866 ft/s
1.0 F-104G 4.09 7.68 °/s 443 ft/s
1.0 CL-1200-2 7.73 limit binds 836 ft/s
1.0 F-5E 6.64 12.71 °/s 473 ft/s
1.0 F-15A 8.56 limit binds 872 ft/s

The weights behind the table are sourced, but they are not equally loaded. The F-104G, F-5E and F-15A are evaluated at the design gross weights and afterburning thrusts that the National Aeronautics and Space Administration’s survey tabulates [Quest for Performance, NASA SP-468]. The survey gives the F-15C and not the F-15A, so the F-15A rows use the F-15C’s 44,500 pounds and two F100-PW-100 engines of 23,904 pounds of thrust, the nearest variant it tabulates. The CL-1200-2 is evaluated at its normal loaded weight of 24,385 pounds. As fractions of each aircraft’s maximum weight these are

\[\frac{27{,}300}{29{,}083} = 0.939, \qquad \frac{15{,}745}{20{,}486} = 0.769, \qquad \frac{44{,}500}{68{,}000} = 0.654, \qquad \frac{24{,}385}{35{,}000} = 0.697 \tag{63}\]

for the F-104G, F-5E, F-15A and CL-1200-2 respectively. The F-104G is carried much nearer its maximum than the others, so its rows understate it by an amount the sources do not allow to be fixed. They bound the F-104G from below and are not a like-for-like measure of what the redesign gained.

The period and contemporary work on turning performance, load factor and combat aircraft comparison stands behind this table.

The result is favourable to Lockheed and it is robust. At every leading-edge suction fraction the Lancer out-turns the F-5E that beat it, comfortably, and it sits close behind the F-15A.

The specific excess power comparison is the striking one. At 830 feet per second against the F-15A’s 866, the Lancer is within 4.2 percent of an aeroplane its own service had judged too expensive to equip the whole Air Force with. [Lightweight Fighter program] The shortfall is taken relative to the F-15A at a leading-edge suction fraction of 0.5,

\[1 - \frac{P_{s,\mathrm{CL\text{-}1200\text{-}2}}}{P_{s,\mathrm{F\text{-}15A}}} = 1 - \frac{830}{866} = 0.042 \tag{64}\]

The ranking does not depend on the parasite drag assumption.

$C_{D_0}$ F-104G CL-1200-2 F-5E F-15A
0.0150 3.39 6.36 5.36 7.02
0.0175 3.35 6.29 5.26 6.93
0.0200 3.30 6.21 5.15 6.84
0.0250 3.22 6.06 4.93 6.66

A model with a free parameter that reproduces an expectation has demonstrated very little. What this one has demonstrated is narrower and firmer, because the ordering is invariant across the plausible range of both free parameters. The claim concerns the ordering alone, and the absolute numbers should not be quoted as predictions of what the aircraft would have achieved.

And it makes the political story quantitative. The claim that some in the Air Force saw the Lancer as a threat to the F-15 is usually reported as an attitude. By the arithmetic, the attitude was not unreasonable. An aeroplane within 4.2 percent of the F-15’s specific excess power, offered as a low-price export fighter [Lockheed CL-1200 Lancer], is an awkward thing to have flying while the case for the expensive one is before Congress. The article states this as a consistency between the physics and the reported attitude, not as evidence of anyone’s motive.

Corner Speed and the Binding Limit

The corner speed is the lowest speed at which the structural limit load factor can be reached aerodynamically.

\[V^* = \sqrt{\frac{2\,n_{\mathrm{limit}}\,W}{\rho\,S\,C_{L_{\max}}}} \tag{65}\]
$C_{L_{\max}}$ Stall speed at sea level Corner speed at 15,000 ft Mach
1.0 154.9 kt 528.9 kt 0.844
1.2 141.4 kt 482.8 kt 0.771
1.4 131.0 kt 447.0 kt 0.713

The corner speed is built on the stall speed, the same relation at a load factor of one, and both are standard sizing relations in Raymer and Nicolai.

\[V_{\mathrm{stall}} = \sqrt{\frac{2W}{\rho\,S\,C_{L_{\max}}}} , \qquad V^{*} = \sqrt{n_{\mathrm{limit}}}\;V_{\mathrm{stall}} \tag{66}\]

The maximum lift coefficient is the weakest input in this article. A thin sharp-edged wing of aspect ratio 2.8 does not achieve much of one, and the record supplies no figure. The table is therefore given across a range and no single value is asserted.

Work on high lift, boundary-layer-control blowing, and approach-speed reduction bears directly on this, and the F-104 blew bleed air over its trailing-edge flaps to lower its landing speed by more than 30 knots [Lockheed F-104 Starfighter]. The cluster on boundary-layer control, high lift and short take-off below holds that work, and its blown-flap studies of swept-wing aircraft from the F-104’s period are listed here.

Dependent Systems

Every system below is dimensioned against the keystone rather than described for its own sake. The order is by dependency, since the engine change drives the fuselage, the fuselage drives the intakes, and the wing follows from the manoeuvre requirement that the engine change made reachable.

Propulsion

Treated at length above. The summary is that the engine change is the largest single change in the aircraft, and it drives most of the others. Against the J79-GE-17 it is 33.01 inches longer, 9.84 inches wider, and it swallows 52.9 percent more air, differences computed in the section headed What Changed From the F-104. The fuselage stretch, the redesigned centre and rear fuselage, the enlarged intakes and the translating cones all follow from it.

For the engine, see the cluster on turbofans, turbojets and installed thrust below. Of its work on turbojets and turbofans for supersonic fighters, the reports nearest this aircraft’s case are these.

Ram Drag

An engine at high Mach spends a large part of its gross thrust cancelling the momentum of the air it swallowed. Net thrust is the difference between what leaves and what arrived.

The literature under this heading is thin, and the cause is instructive. Of the research records the article cites, three carry ram drag, momentum drag or installed performance in their titles, all of them in the contemporary survey and none in the list under this heading. The subject is not thin. The heading is. Thrust and drag bookkeeping is settled inside the papers on inlet additive drag and spillage already cited above, because deciding what counts as inlet drag and what counts as lost thrust is the same accounting question.

\[F_{\mathrm{net}} = \dot m\left(V_e - V_0\right) \tag{67}\]

The second term is the ram drag, and at Mach 2.6 the free stream arrives at 771 metres per second.

\[D_{\mathrm{ram}} = \dot m V_0 = 117.93 \times 771.0 = 90{,}926\ \mathrm{N} = 20{,}441\ \mathrm{lbf} \tag{68}\]

The engine’s rated 25,000 pounds of net thrust therefore requires 45,441 pounds gross, so 45.0 percent of the gross thrust is spent on the momentum of the air.

The thrust equation and the propulsive efficiency that follows from it are standard, in Oates and Mattingly.

The relation is more useful inverted than asserted, because holding the sea-level rating across the Mach range is not defensible. Asking instead what exhaust velocity the rating would require at that condition gives a checkable number.

\[V_e = \frac{F_{\mathrm{net}} + \dot m V_0}{\dot m} = \frac{111{,}206 + 90{,}926}{117.93} = 1{,}714\ \mathrm{m/s} \tag{69}\] \[V_{e,\,\mathrm{static}} = \frac{F_{\mathrm{net}}}{\dot m} = \frac{111{,}206}{117.93} = 943\ \mathrm{m/s} \tag{70}\]

Seventeen hundred metres per second is within reach of an afterburning nozzle, so the requirement is not absurd. What it is not is free. A higher exhaust velocity needs a higher total pressure at the engine face, and the inlet section showed the single cone failing to deliver that total pressure at this Mach number. The two halves of the keystone are the same problem seen from either end.

The propulsive efficiency at that condition follows.

\[\eta_p = \frac{2V_0}{V_0 + V_e} = \frac{2 \times 771.0}{771.0 + 1714} = 0.621 \tag{71}\]

Aerodynamics

The wing grew 53.0 percent in area and 33.0 percent in span while retaining the F-104’s 10 degrees of anhedral and, on outer panels virtually identical to the F-104’s, its aerofoil section [Lockheed CL-1200 Lancer]. Aspect ratio rose only 15.5 percent, from 2.455 to 2.836, because the area grew nearly as fast as the span squared.

The lift the wing produces is the coefficient carried on the dynamic pressure and the area. Every load factor below is measured against that identity, and the drag data behind the coefficients used with it is Hoerner, with the configuration context in Kuchemann.

\[L = q\,S\,C_L \tag{72}\]

That is the limit of what the redesign could do without a new wing. The induced-drag penalty of a low aspect ratio is not much relieved by going from 2.455 to 2.836, and the table above shows the Lancer’s $K$ remaining above the F-5E’s at every suction fraction. What made the Lancer competitive was not the wing. It was the thrust.

Moving the wing to the shoulder position has consequences the sources pass over and this article does not resolve. A high wing changes the interference field at the wing-body junction, alters the downwash at the tail, and modifies the rolling moment due to sideslip, which is presumably why 10 degrees of anhedral was retained on a configuration whose wing position already supplies an effective dihedral increment.

Stability and Control

The equations of motion and the stability derivatives behind this discussion follow Stevens and Lewis.

Moving the tail off the fin is the most defensible change in the aircraft. A T-tail on a low-aspect-ratio wing risks the horizontal surface entering the wing wake at high angle of attack, whereupon pitch control is lost while the aircraft is already pitching up. The F-104 had a well-documented and unforgiving departure behaviour [Lockheed F-104 Starfighter].

The tail’s contribution to longitudinal stability is carried by the tail volume coefficient, which collects the geometry into one number, and by the rate at which the wing’s downwash turns the flow the tail sees.

Downwash surveys behind wings, neutral-point determination and the static longitudinal stability of wing and tail combinations are among the oldest quantitative subjects in the field, and the measurements behind the relations below are mostly period work. The clusters on wings, aspect ratio and vortex flows and on stability, control and flying qualities below hold them, and the period downwash and neutral-point reports among them are these.

\[V_H = \frac{S_t\,l_t}{S\,\bar{c}} \tag{73}\] \[C_{m_\alpha,\,\mathrm{tail}} = -a_t\,V_H\,\eta_t\left(1 - \frac{d\varepsilon}{d\alpha}\right) \tag{74}\] \[\mathrm{SM} = -\frac{C_{m_\alpha}}{C_{L_\alpha}} = \frac{x_{np} - x_{cg}}{\bar{c}} \tag{75}\]

The tail geometry of the CL-1200 is not in the public record, so these are written to show what the change acted on. They yield no number, and no static margin is asserted.

One thing they do let us test is an expectation that turns out to be wrong. The far-field downwash gradient goes inversely with aspect ratio, which invites the conclusion that a low-aspect-ratio wing washes its tail harder and therefore suffers more.

\[\frac{d\varepsilon}{d\alpha} \approx \frac{2\,C_{L_\alpha}}{\pi A} \tag{76}\]
Aircraft Aspect ratio $C_{L_\alpha}$ Far-field $d\varepsilon/d\alpha$
F-104G 2.455 3.592 0.931
CL-1200-2 2.836 4.064 0.912
F-15A 3.014 4.275 0.903
F-5E 3.824 5.158 0.859

The expectation does not survive being written down. The lift-curve slope falls with aspect ratio at very nearly the same rate as the divisor, so the ratio is almost flat, and the F-104 differs from the F-5E by eight percent, far short of the large factor the framing implied. The negative is reported rather than dropped, and it means the tail-position argument has to rest on the wake geometry at high angle of attack, as it does, and cannot rest on a downwash gradient that does not discriminate. The far-field form also overestimates what a tail at a finite distance sees, so the absolute values should not be read as tail conditions.

The argument draws its wake geometry and pitch-up evidence from the cluster on stability, control and flying qualities below, including these reports.

Structure and Materials

The airframe is aluminium alloy, apart from titanium frames, longerons and skin around the jet exhaust [Lockheed CL-1200 Lancer], and the analysis above establishes that this is the constraint the Mach 2.6 objective runs into. At Mach 2.0 the structure gives up about a tenth of its yield strength and at Mach 2.6 about a third, and the transition happens across a narrow band because the recovery temperature goes as the square of the Mach number while the strength curve falls steeply through the same range.

Armament and Stores

Nine stations, one on the fuselage centreline, three under each wing and one at each wingtip. The gun is the 20 millimetre M61 with 725 rounds, with a 30 millimetre DEFA cannon of the French Direction des Études et Fabrications d’Armement offered as an alternative for customers already equipped for it. Up to 12,000 pounds of ordnance on short-range missions, a maximum of four AIM-7 or typically six and up to ten AIM-9 air intercept missiles [Lockheed CL-1200 Lancer].

The wingtip stations are inherited thinking. The Lancer kept wingtip fuel tanks of the same type and capacity as the F-104’s [Lockheed CL-1200 Lancer]. On a wing half again as large the tip station is a choice rather than a necessity, and a tip store on a short span carries a large rolling-inertia penalty into the rapid rolling manoeuvres the aircraft was being sold on.

Instrumentation

Nothing is known about what an X-27 would have carried, because no X-27 was instrumented. A research aircraft built to test propulsion at Mach 2.6 would have needed inlet rakes, engine-face pressure instrumentation dense enough to compute a distortion descriptor, and skin thermocouples. The article notes what such a programme would have required and asserts nothing about what was planned.

The Flight Test Record

There is none.

Its emptiness is the most important fact about the subject. No X-27 was built. No CL-1200 was built. Nothing flew. [American X-Vehicles, NASA SP-2003-4531] [Lockheed CL-1200 Lancer]

What exists is the following, and the article is careful to distinguish the well-attested from the reported.

An article about an aeroplane that never flew is not thereby an article without evidence. The evidence is the design record and the parent aircraft, and the preceding sections have used both. What must not happen is the quiet substitution of a prediction for a measurement, and the next section exists to prevent it.

Comparison With Ground Prediction

In every other article in this series, this section compares what was predicted on the ground with what was measured in the air. Here there is no air.

So the comparison is between the manufacturer’s prediction and an independent prediction, and that is a much weaker thing, because two predictions that agree may share an assumption rather than share a truth. The section is written to make the weakness explicit.

Claim Independent estimate Verdict
1,700 mph at 35,000 ft Mach 2.563 by definition Internally consistent
Initial climb 60,000 ft/min Best sea-level $P_s$ 49,332 ft/min Claim exceeds the estimate by 21.6 percent
Takeoff run 1,450 ft 1,078 ft at $C_{L_{\max}}$ 1.2 Claim is conservative
Combat radius 367 nmi 0.192 of still-air range Consistent with practice
Fuel increase 46 percent Needs the F-104G’s internal fuel, which no cited source states Not checked
Spike travel 4 in Implies 5.401 ft² against 5.639 ft² needed Agrees to 4.2 percent

The claims in the first column are the manufacturer’s published estimates [Lockheed CL-1200 Lancer].

The Climb Claim Exceeds the Ceiling

Specific excess power is a hard ceiling on steady rate of climb, and one line of algebra, given by Whitford, shows why. Differentiating energy height and holding speed constant leaves the climb rate equal to $P_s$, and any acceleration takes from the same budget.

\[\frac{dh_e}{dt} = \frac{dh}{dt} + \frac{V}{g}\frac{dV}{dt} = P_s \qquad \Longrightarrow \qquad \left.\frac{dh}{dt}\right|_{\max} = P_s \tag{77}\]

The claimed 60,000 feet per minute is 305 metres per second, and the best $P_s$ the published thrust and weight produce at sea level is 250.6 metres per second at Mach 1.095.

Sea-level Mach $P_s$
0.3 17,468 ft/min
0.6 35,803 ft/min
0.9 47,035 ft/min
1.095 49,332 ft/min
1.2 48,585 ft/min

The claim exceeds the computed ceiling by 21.6 percent. For claimed climb rate $\dot h_{\mathrm{claim}}$ and the largest $P_s$ in the scan,

\[\frac{\dot h_{\mathrm{claim}}}{P_{s,\max}} - 1 = \frac{60{,}000}{49{,}332} - 1 = 0.216 \tag{78}\]

The maximum lies between the round Mach numbers, so it has to be found by a fine scan. A coarse grid that stops at Mach 1.2 takes the peak as 48,585 feet per minute and overstates the shortfall,

\[\frac{60{,}000}{48{,}585} - 1 = 0.235 \tag{79}\]

or 23.5 percent. The fine scan puts the maximum at Mach 1.095.

Two explanations fit and the article cannot choose between them. The figure may be a zoom rather than a steady climb, in which case it is a transient trade of speed for height and is not a rate of climb in the sense the ceiling applies to. Alternatively the thrust or weight assumptions here are conservative. The figure is not supported by the aircraft’s own published thrust and weight under a steady interpretation, and that this is the only headline claim in the brochure of which that is true.

The Unchecked Fuel Claim

The record states a 46 percent increase in internal fuel from a 30-inch stretch [Lockheed CL-1200 Lancer]. The weight breakdown gives the Lancer’s clean disposable load as the difference between its normal loaded and empty weights.

\[W_{\mathrm{fuel,\ clean}} = W_{\mathrm{loaded}} - W_{\mathrm{empty}} = 24{,}385 - 17{,}885 = 6{,}500\ \mathrm{lb} \tag{80}\]

Testing the 46 percent against that figure needs the F-104G’s internal fuel capacity, and none of the sources cited here states it. The claim is therefore left as the manufacturer’s, neither confirmed nor contradicted. The difference above is also an upper bound on the clean fuel load rather than the fuel load itself, because a normal loaded weight ordinarily includes the pilot, ammunition and oil as well as fuel.

The Takeoff Claim Is Conservative

The ground roll is not taken from a rule of thumb. The acceleration is integrated from rest to lift-off against thrust, drag, and the rolling friction on whatever weight the wing is not yet carrying, following the method in Raymer.

Takeoff and landing ground-run prediction is a small and practical literature, and the period work supplies the friction coefficients and the lift-off margins used here.

\[s = \int_0^{V_{\mathrm{LOF}}} \frac{V\,dV}{a(V)}, \qquad a(V) = \frac{T - D - \mu\left(W - L\right)}{W/g} \tag{81}\] \[V_{\mathrm{LOF}} = 1.1\,V_{\mathrm{stall}} \tag{82}\]
$C_{L_{\max}}$ at takeoff $V_{\mathrm{LOF}}$ Computed roll Claim
1.0 170.4 kt 1,296 ft 1,450 ft
1.2 155.6 kt 1,078 ft 1,450 ft
1.4 144.1 kt 922 ft 1,450 ft

The claim is longer than the computation at every assumption, which is the direction that does not oversell. The integration takes full afterburner and makes no allowance for installation losses, so it is optimistic by construction, and the gap between the two is the room that optimism occupies.

The Radius Claim Holds

The Breguet range equation carries no gravitational constant when the specific fuel consumption is quoted per hour, because such a figure is already a weight of fuel per unit thrust per unit time.

\[R = \frac{V}{c_t}\,\frac{L}{D}\,\ln\frac{W_0}{W_1} \tag{83}\]

The Breguet relation and the mission bookkeeping around it are as given in Raymer and Nicolai. The end weight is the start weight less the usable fraction of the fuel, and the logarithm acts on their ratio. The start weight is the maximum takeoff weight, and the fuel is the remainder of that weight after the empty weight and the 4,000 pound bombload the radius is quoted with [Lockheed CL-1200 Lancer].

\[W_{\mathrm{fuel}} = W_0 - W_{\mathrm{empty}} - W_{\mathrm{stores}} = 35{,}000 - 17{,}885 - 4{,}000 = 13{,}115\ \mathrm{lb} \tag{84}\] \[W_1 = W_0 - f\,W_{\mathrm{fuel}} = 35{,}000 - 0.85 \times 13{,}115 = 23{,}852\ \mathrm{lb} \tag{85}\] \[\frac{W_0}{W_1} = \frac{35{,}000}{23{,}852} = 1.4674 \tag{86}\]

The mission factor is then a defined ratio, and quoting it keeps a Breguet integral from being mistaken for a mission.

\[k_m = \frac{R_{\mathrm{combat}}}{R_{\mathrm{still\,air}}} = \frac{367}{1{,}914} = 0.192 \tag{87}\]
$L/D$ $c_t$ Still-air range The 367 nmi claim as a fraction
6.0 0.85 /h 1,436 nmi 0.256
7.0 0.85 /h 1,675 nmi 0.219
8.0 0.85 /h 1,914 nmi 0.192
9.0 0.85 /h 2,154 nmi 0.170

A combat radius is not half a range. It pays for climb, descent, a combat allowance at maximum power, reserves, and an outbound leg flown with stores hung on it. This article takes the ratio to run about 0.15 to 0.25 in practice, as an assumed band rather than a sourced one. The claim lands inside that band for a lift-to-drag ratio of 7 or more and just above it at 6, and is therefore credible, though with less room than a lighter empty weight would give.

This is a negative result for the suspicion that the radius claim is inflated, and it is reported as such.

What the Data Changed

Nothing, because there was no data.

That sentence is the finding rather than an admission. Every other article in this series can point to a measurement that entered the literature. This one cannot, because the programme was cancelled at the point where it would have begun producing evidence.

What the programme changed is a different question, and the effect is small but not zero.

  • It did not influence the F-15. No source cited here connects the Lancer to any F-15 design decision.
  • It did not influence the Lightweight Fighter programme technically, though it demonstrates that the argument for funding lightweight-fighter prototypes was in the air before that programme existed.
  • It produced no literature. This is the second consecutive article in the series to report that, and the third in which the subject generated no development literature because nothing was developed.

The programme’s context is the literature on procurement, competitive prototyping, export fighters and acquisition policy, which the cluster on defence acquisition, prototyping and the arms trade below contains, while the lightweight fighter programme’s own record sits in the cluster on the F-104, the J79 and later named fighters. The two clusters include these.

A Designation Without an Aircraft

The X-27 is the third consecutive designation in this series that did not go to a research aeroplane, and the pattern is now firm enough to name.

  • X-25, a civil autogyro design ordered in modified form to investigate a rescue concept.
  • X-26, a commercially available sailplane bought for training, two of which were modified for quiet observation.
  • X-27, a manufacturer’s private-venture export fighter that was never built [American X-Vehicles, NASA SP-2003-4531].

The first two were aircraft that existed and were bought for properties they already had. The third did not exist at all. In all three, the X-designation was doing something other than marking a research aeroplane built to answer a research question.

In the X-27’s case the designation was doing procurement work. An X-designation carried the implication of federal interest, and the Lancer needed federal interest and never obtained it. The designation was issued and the money was not, which makes the X-27 an unusually clean example of the designation and the programme coming apart.

This article does not claim the designation system was abused. The number was allocated for a proposed research aircraft with a stated research purpose, as the system intends. The observation is narrower. By 1971 an X-designation could be allocated to an aeroplane whose primary purpose was commercial, and the allocation could precede any commitment to build it. [Lockheed CL-1200 Lancer] The fact concerns what the system had come to permit, and the closing article of this series assembles it with the rest of that evidence.

The Contemporary Literature

Cluster Records
Supersonic inlets, shock systems and pressure recovery 518
Inlet distortion and inlet-engine compatibility 264
Drag polars, wave drag and supersonic aerodynamics 195
Compressor stall, surge and casing treatment 192
Wings, aspect ratio and vortex flows 166
Turbofans, turbojets and installed thrust 153
Air combat, agility and aircraft performance 114
Aerodynamic heating, recovery temperature and thermal protection 109
Aluminium alloys and their strength when hot 92
Titanium, other alloys and composites at elevated temperature 84
Conceptual design, optimisation and the derivative aircraft 83
Stability, control and flying qualities 68
The F-104, the J79 and later named fighters 59
Fighter aircraft design, requirements and history 43
Defence acquisition, prototyping and the arms trade 41
Thermal stress, thermal buckling and thermoelasticity 34
Boundary-layer control, high lift and short take-off 28
Other aeronautical literature 1
Total 2,244

The argument sits inside the bodies of work above. This section surveys what has happened since, on the standing expectation that an article of this kind should double as a review of the current literature. The reading is not neutral. Each body of work is placed by what it says about the X-27’s binding question.

In short, every one of the X-27’s technical problems is still an active subject, and the problem that has moved least would have killed it.

Supersonic inlets are now computed but are still hard

The Taylor-Maccoll integration above is what the era had. Contemporary inlet design is a computational-fluid-dynamics and optimisation problem, and the subjects that dominate it are shock-wave and boundary-layer interaction, starting and unstart, variable geometry, and the design of inward-turning and waverider-derived compression surfaces.

What has not changed is the total-pressure budget. The shock losses computed above are exact inviscid gas dynamics and no amount of computation makes them smaller. The modern literature recovers losses at the margins, in bleed management and in diffuser design, and confirms the size of the central problem without dissolving it.

Among the records of the cluster on supersonic inlets, shock systems and pressure recovery below, these treat bleed, buzz, unstart, diffusers and inward-turning inlets.

Distortion is better understood and no less dangerous

The X-27’s exposure was a distortion-sensitive fan behind a marginal inlet. That combination is now a named design discipline with its own descriptors and standards, and the surrounding work covers distortion descriptors, fan stability under circumferential and radial defects, and the closely related problem of boundary-layer-ingesting propulsion, which deliberately accepts distortion in exchange for propulsive efficiency.

The comparison is instructive. A modern boundary-layer-ingesting fan accepts distortion the TF30 could not survive, and it does so because the fan is designed for it from the outset. The X-27 proposed the opposite, an engine designed for clean flow placed behind an inlet asked to work beyond its ancestry.

The cluster on inlet distortion and inlet-engine compatibility below covers that discipline. Its standards, its distortion generators, the TF30’s measured response and the boundary-layer-ingesting fan are represented by these.

Compressor stall is a control problem now

Stall and surge were phenomena to be avoided by margin in 1971. They are now phenomena to be detected and actively suppressed, with stall-precursor detection, casing treatment, and active control all mature subjects.

Had the X-27 flown, this is the technology that would have rescued it, and it did not exist.

On active control, casing treatment and the detection of stall inception, the cluster on compressor stall, surge and casing treatment below includes the following.

Hot structures moved to materials the X-27 did not have

The aluminium limit computed above comes from the alloy. The contemporary answer is not a better aluminium but a different material, and the literature covers titanium alloys, thermal barrier coatings, metallic thermal protection and elevated-temperature creep in aerospace alloys.

That literature falls in the clusters on titanium, other alloys and composites at elevated temperature and on aerodynamic heating, recovery temperature and thermal protection below. It includes the following papers.

Conceptual design became a numerical discipline

The sizing exercise above is a 1970s method executed by hand. Contemporary conceptual design is multidisciplinary optimisation, and the part of it most relevant here is the literature on derivative design, meaning how much of an existing aircraft can be kept when the requirement changes.

The Lancer is a derivative-design problem and the modern literature has a name for its failure mode. Reusing a fuselage, an aerofoil and a systems architecture constrains the solution far more than the retained parts are worth, and quantifying that trade has become a research subject in its own right.

Its multidisciplinary and derivative-design work, part of the cluster on conceptual design, optimisation and the derivative aircraft below, includes these.

Agility metrics settled the argument the competition was having

Energy manoeuvrability was contested in 1970 and is standard now [John Boyd]. The contemporary literature on agility metrics, specific excess power and trajectory optimisation is the direct descendant of the diagrams Boyd was drawing, and it still states aircraft performance in the framework on which the Lancer performs well.

Which sharpens the historical point. On the metric that won the argument, the Lancer was a good aeroplane. It lost anyway, and no source cited here says that it lost on performance.

In the cluster on air combat, agility and aircraft performance below, these papers address agility metrics, specific excess power models and agility requirements.

Acquisition scholarship has a category for what happened

The Lancer’s fate is a case in a well-developed literature on competitive prototyping, defence acquisition and arms transfer. A private venture seeking government funds to build a demonstrator for an export market it had already lost is a recognisable pattern, and a reader wanting the general case should turn to the modern work on prototype policy and on foreign military sales.

That work forms the cluster on defence acquisition, prototyping and the arms trade below. On prototype policy, military assistance and foreign military sales it includes these.

Ram drag stayed in the literature and supersonic cruise has reframed it

The subsections above do not reach the keystone’s other half. The engine section computed that 45 percent of gross thrust at Mach 2.6 is spent on the momentum of the air the engine swallowed, and that the exhaust velocity the rating implies needs total pressure the inlet was struggling to deliver. That is a propulsion-integration problem, and its literature never went quiet. Of the 30 titles in the survey that name spillage, additive drag or forces, ram drag, inlet drag, installed thrust or performance, installation effects or losses, or thrust and drag bookkeeping, every decade from the 1960s to the 2020s holds between 2 and 7.

It is live again in new terms. Supersonic civil transport, variable-cycle engines and boundary-layer-ingesting propulsion have all put thrust-and-drag bookkeeping back at the centre of the design problem, and the question of where the airframe ends and the engine begins is being argued in the same terms the X-27 would have had to settle.

The clusters on turbofans, turbojets and installed thrust and on drag polars, wave drag and supersonic aerodynamics below divide this literature between them. On thrust and drag bookkeeping, the supersonic transport and variable-cycle work and the boundary-layer-ingesting case, it includes these.

Thermal stress is now a coupled problem

The article computes a thermal stress with a modulus, an expansion coefficient and a temperature difference, and gets a number comparable to the mechanical allowable. That calculation is a century old and remains the right first move. What has changed is that the coupling is no longer neglected.

Contemporary work treats the aerodynamic heating, the temperature field, the resulting stress and the change in stiffness as one problem rather than four, under the name aerothermoelasticity, because at high Mach the structure’s deformation changes the flow that is heating it. For the X-27 this would have mattered less than for a hypersonic vehicle, but the eighty-two kelvin figure computed above is the kind of number a coupled analysis exists to refine.

The coupled and aerothermoelastic work in the cluster on thermal stress, thermal buckling and thermoelasticity below includes these.

The Lancer is now a recognised design problem with a literature of its own

A derivative aircraft is not a cheap aircraft, and the modern literature puts numbers on it. Reusing a fuselage cross-section, an aerofoil and a systems architecture buys development cost and schedule at the price of a constrained design space, and researchers now try to measure that price.

Of the contemporary threads, only this one takes the article’s subject as its object of study. The Lancer retained the F-104’s aerofoil section and its 3.36 percent thickness ratio, which is why its aspect ratio could only reach 2.836 and why its drag-due-to-lift stayed above the F-5E’s at every assumption tested. The modern framing would call that inherited constraint the dominant term in the trade, and would try to price it before committing rather than after losing a competition.

The derivative-design studies belong to the cluster on conceptual design, optimisation and the derivative aircraft below, among them these.

The X-27’s real problem has a modern answer

Nobody could tell whether the Lancer would work without building it. The programme’s difficulty came down to that. The mock-up settled nothing, the brochure figures were the manufacturer’s own, and neither competition was decided on any measurement of the aeroplane.

Evaluating an aircraft that does not exist is now a research programme. Surrogate modelling, uncertainty quantification in conceptual design and model-based systems engineering all exist to answer, before metal is cut, the question the X-27 could only have answered by flying.

This is the closest thing to a resolution the article’s central difficulty has, and it arrived fifty years late. It is also the reason this article could be written at all. The analysis above is a primitive version of the same idea, taking published geometry and published ratings and asking what they imply, and its one clear success, the reconciliation of the spike travel with the engine’s airflow, is the kind of consistency check a modern framework automates.

Surrogate, uncertainty and systems-engineering work is also part of the cluster on conceptual design, optimisation and the derivative aircraft below. Examples follow.

Supersonic inlets, shock systems and pressure recovery

The keystone’s first half. Spike, cone, ramp and mixed-compression inlets, the shock systems that compress the flow, bleed, buzz, starting and unstart, diffusers and the total-pressure recovery the inlet sections above compute.

54 of these titles name a spike, a centerbody, a cone or a ramp, and 10 of those date from before 1960, so the two inlet geometries the article compares have a literature running from the period that designed them to the present. The optimum shock system the inlet sections compute is set out in Oswatitsch 1947.

518 records. 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[Barry 1966] [Barry 1971] [Barry 1968] [Batterton et al. 1974] [Baydar et al. 2018] [Baydar et al. 2016] [Baydar et al. 2017] [Beheim and Gertsma 1956] [Beke and Allen 1953] [Benson 1994] [Benson and Anderson 1983] [Benton et al. 2021] [Berto et al. 2020] [Biesiadny and Wendt 2004] [Bisek 2014] [Bisek 2015] [Bisek et al. 2012] [Bogar et al. 1983] [Bowditch 1973] [Bowditch and Musial 1957] [Braun and Podleski 2019] [Bravo-Mosquera et al. 2019] [Broadley et al. 2023] [Brophy and Hawk 1990] [Burns et al. 2015] [Burris 1966] [Burrows et al. 2025] [Bush 1985] [Cai and Huang 2022] [Cai et al. 2022a] [Cai et al. 2022b] [Campbell and Syberg 1984] [Campbell et al. 1985] [Carlin et al. 2003] [Carrier et al. 2001] [Castner et al. 2018] [Chang and Hsu 1960] [Chapman et al. 2005] [Idris et al. 2020] [Cheikh and Chen 2017] [Chen and Tan 2019] [Chen et al. 2017] [Chen et al. 2018] [Chen et al. 2019] [Chen et al. 2020b] [Chen et al. 2021c] [Chen et al. 2023] [Chen et al. 2025b] [Chen et al. 2025c] 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and Nucci 1946] [Ferri and Nucci 1951] [Fink and Anderson 1983] [Fleeter et al. 1974] [Gahlot and Singh 2020] [Forsythe et al. 1998] [Fradenburgh and Wyatt 1953] [Fraiser 1960] [Frey 2014] [Frohnapfel et al. 2018b] [Fujii et al. 2021] [Fujimoto and Niwa 1993] [Gaglio et al. 2023] [Gahlot and Singh 2019] [Gartling 1970] [Ge et al. 2021] [Gilinsky et al. 2000] [Gillen and Loth 2011] [Gillen and Loth 2015] [Goonko and Mazhul 2011] [Gorton 1953] [Gorton 1954] [Gounko and Mazhul 2012] [Grenson and Beneddine 2018] [Guan and Yarng 1984] [Guan and Yarng 1987] [Guimarães et al. 2018a] [Haas and Karanian 1981] [Halwas and Aggarwal 2019a] [Halwas and Aggarwal 2019b] [Hamed 1995] [Hancock 1985] [Harloff and Smith 1995] [Hartsell 1960] [Hasel et al. 1953] [Hawkins et al 1976] [He et al. 2026] [Heath et al. 2016] [Henderson 1965] [Hodder 1981] [Hodder et al. 1981] [Hoffman 2000] [Howard et al. 1951] [Howerton and Slater] [Howlett and Hunter 1986] [Hu 2024] [Hu et al. 2024] [Huang et al. 2016] [Huang et al. 2026] [Hube 1968] [Hunt and Hunt 2021] [Iek et al. 1993] [Influence of Back Pressure 2017] [Inger 1986] [Connors et al. 1957b] [Jiao et al. 2017] [Jin et al. 2022] [Jin et al. 2023a] [Jin et al. 2023b] [Johnson and Lawing 1977] [Johnson and Wu 1975] [Johnson III and Wu 1974] [Johnson and Montoya 1973] [Jules and Barnhart 1998] [Jung et al. 2015] [James et al. 2021] [James and Kim 2022] [Kamman and Hall 1975] [Kang et al. 2024b] [Kang et al. 2024a] [Kapoor et al. 1992] [Kapoor et al. 1994] [Kawamura et al. 1987] [Kazula and Höschler 2020] [Kazula and Höschler 2021] [Kazula et al. 2019] [Kennon 1989] [Keppler 1966] [Khan and Hasan 2021] [Khobragade and Kumar 2022] [Khobragade et al. 2021] [Khobragade et al. 2024] [Kim and Kwon 2015] [Kim and Lee 2022] [Kim and Park 2026] [Kim et al. 2011] [Kong and Park 2018] [Kong et al. 2022] [Kong et al. 2026] [Kopasakis et al. 2012b] [Kopasakis et al. 2012a] [Kotov et al. 2018] [Kozakiewicz et al. 2025] [Krause 1981] [Krivec et al. 1984] 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and Yuceil 2021] [Taghi-Abad et al. 2026] [Tang et al. 2025b] [Tang et al. 2025c] [Taylor 1968] [Thomas et al. 1999] [Thomas and Stueber 2013] [Tindell 1980] [Tindell 1981] [Tomczak 2026] [Tongguang et al. 2015] [Toro et al. 1999] [Trefny et al. 2014] [Trefny and Wasserbauer 1986] [Tudosie 2017a] [Tudosie 2017b] [Tudosie 2018] [Tudosie and Prisacariu 2022] [Tudosie and PĂUnescu 2017] [Tudosie et al. 2019] [Türkkahraman et al. 2024] [Utomo and Bura 2019] [Vaca-Rios and Cerón-Muñoz 2025] [Veeresh Kumar et al. 2021] [Vinogradov et al. 2017b] [Vinogradov et al. 2017a] [Walker et al. 2005] [Wan and Guo 2007] [Wang and Zhao 2026] [Wang et al. 2013a] [Wang et al. 2015] [Wang et al. 2022b] [Wang et al. 2023g] [Wang et al. 2023c] [Wang et al. 2023b] [Wang et al. 2023f] [Wang et al. 2023i] [Wang et al. 2025h] [Wang et al. 2025g] [Wang et al. 2025c] [Wang et al. 2025a] [Wang et al. 2025b] [Wang et al. 2025e] [Wang et al. 2025f] [Wang et al. 2026d] [Wang et al. 2026e] [Wang et al. 2026a] [Wasserbauer and Willoh 1968] [Wasserbauer et al. 1996] [Wasserbauer and Gerstenmaier 1978] [Watanabe et al. 2019a] [Watanabe et al. 2019b] [Wegener 1977] [Whalen and Wilcox 1956] [Wilcox 1957] [Williams and Hunt 1980] [Williams and Stevens 2006] [Willis 1981] [Woollett et al. 1974] [Wu et al. 2022] [Xie et al. 2025a] [Yaghmaee and Roberts 1986] [Yamaguchi 1964] [Yamamoto et al. 2020] [Yang and Lei 2011] [Yang et al. 2026b] [Yao et al. 2017] [Yeom et al. 2015] [Yonke et al. 1995] [You et al. 2016] [Yu et al. 2021b] [Yuan et al. 2021a] [Yuan et al. 2021b] [Yuan et al. 2023] [Zhang 2020a] [Zhang et al. 2015b] [Zhang et al. 2018] [Zhang et al 2020] [Zhang et al. 2026a] [Zhang et al. 2026d] [Zhao et al. 2022c] [Zhigalkin and Lyubimov 2024] [Zhu et al. 2020]

Inlet distortion and inlet-engine compatibility

The turbofan’s exposure. Total-pressure, swirl and temperature distortion at the engine face, its descriptors and generators, inlet and engine compatibility, and boundary-layer-ingesting propulsion, which accepts distortion by design.

264 records. [Abbasi et al. 2018] [Ahuja and Mavris 2022] [Alendar et al. 2022] [Alford et al. 1962] [Wang et al. 2023a] [Anderson and Levy 1991] [Assessment of the Inlet/Engine] [Li et al. 2023a] [Atassi et al. 2019] [Bakhle et al. 2014] [Bakhle et al. 2018] [Baretter et al. 2021] [Battiston et al. 2025] [Benichou et al. 2021] [Bhunia et al. 2026] [Bilwakesh et al. 1971] [Bilwakesh et al. 1972] [Bond and Key 2025] [Bond and Key 2026] [Bond et al. 2025] [Bowditch and Coltrin 1983] [Braithwaite and Soeder 1980] [Braithwaite 1973] [Braithwaite and Soeder 1979] [Brilliant and Bauer 1977] [Burstadt and Calogeras 1974] [Burstadt and Wenzel 1976] [Burstadt et al. 1971] [Callahan and Stenning 1971] [Calogeras and Burstadt 1974] [Calogeras and Coltrin 1969] [Calogeras et al. 1974] [Campbell and Ellis 1971] [Campion 1954] [Carnevale et al. 2016] [Chen et al. 1987] [Chennuru et al. 2025] [Ciepluch 1948] [Concept Designed and Developed 1995] [Costakis 1974] [Costakis 1975] [Crea et al. 2025] [Da et al. 2020] [Davoudzadeh et al. 1987] [Debogdan et al 1975] [Debogdan et al. 1977] [Deng et al. 2026] [Di-Marco et al. 2023] [Diamantidou et al. 2022] [Dicus 1975] [Dunham 1962] [Greitzer 1972] [Herrick 2011] [Herrick 2014] [Lei et al. 2026] [Reich and Wimbauer 1975] [Dong et al. 2015] [Dong et al 2018] [Du et al. 2023] [Duvall and Arnaiz 1977] [Sun et al. 2024a] [Ellis and Brownstein 1974] [Evans et al. 1974] [Ezrokhi and Khoreva 2018] [Fan et al. 2024] [Fan et al. 2025] [Fan et al. 2026a] [Fan et al. 2026c] [Fan et al. 2026b] [Fang and Wang 2023] [Fang et al. 2023a] [Feng et al. 2022] [Ferrar et al. 2016] [Frohnapfel et al. 2017] [Frohnapfel et al. 2018a] [Frohnapfel et al. 2021] [Fuqun et al. 1985] [GAS Turbine Engine Inlet] [Gelder 1957] [Geng et al. 2025] [Goldberg and Boxer 1959] [Gray and Martins 2018] [Gray et al. 2020] [Gray et al 2017] [Jones et al. 2020] [Gu et al. 2023] [Guidelines for Characterization of] [Guimaraes et al. 2015] [Guimarães et al 2018] [Guo et al. 2021a] [Hall et al 2017] [Hall et al. 2022b] [Hall et al. 2022a] [Hawthorne et al. 1978] [Hayden and Untaroiu 2021] [Hayden et al. 2023] [Hill and Defoe 2020] [Hou et al. 2017] [Hubble and Smith 1979] [Inlet Total-Pressure-Distortion Considerations for] [Jacocks and Kneile 1975] [Karl et al. 2025] [King et al. 1976] [Klann et al. 1984] [Korn 1974a] [Korn 1974b] [Kramer and Hall 2026] [Kumar and Pradeep 2022] [Kwiatkowski et al. 2022] [Lee et al. 2019b] [Lee et al. 2018] [Lee and Liou 2018] [Lee et al. 2019a] [Leinhos et al. 2000] [Lengyel-Kampmann et al. 2024] [Lesser and Niehuis 2014] [Li et al. 2020a] [Li et al. 2020b] [Li et al. 2021b] [Li et al. 2022a] [Li et al. 2023d] [Li et al. 2024f] [Li et al. 2024k] [Li et al. 2024b] [Li et al. 2024j] [Li et al. 2024e] [Li et al. 2025c] [Liang and Zhang 1989] [Liu and Vo 2024] [Liu et al. 2022a] [Liu et al. 2022c] [Liu et al. 2023a] [Liu et al. 2023b] [Liu et al. 2025d] [Liu et al. 2026b] [Lomax and Heaslet 1956] [Lowe 2020] [Lu et al. 2019] [Lu et al. 2025b] [Lu et al. 2025a] [Lu-ning et al. 2021] [Lucas et al. 2014] [Luo Ju 2009] [Ma et al. 2018] [Ma et al. 2025d] [Ma et al. 2025c] [MacManus et al. 2017] [Maekawa et al. 1978] [Maghsoudi et al. 2020] [Magrini and Benini 2026] [Mao and Zhang 2025] [Masaki et al. 2021] [Mazzawy and Banks 1976] [Mazzawy and Banks 1977] [Mehalic 1988] [Melick et al. 1975] [Melick et al. 1978] [Melick 1973] [Menegozzo and Benini 2020] [Min et al. 2018] [Ming et al. 2023] [Moirou et al. 2023] [Moore 1973] [Moore and Lueke 1974] [Musa et al. 2024] [Muth et al. 2009] [Mårtensson 2021] [Mårtensson and Billson 2024] [Mårtensson et al. 2022] [Naruse et al. 2022] [Naseri et al. 2016] [Nelson et al. 2014] [Overall 1976] [Page et al. 2018] [Pan et al. 2022] [Pan et al. 2024a] [Pan et al. 2024b] [Panton 1972] [Park et al. 2026] [Petkovic et al. 2025] [Pečinka et al. 2017] [Piovesan et al. 2025] [Plourde and Stenning 1968] [Prasad 2025] [Processing and Validating CFD] [Provenza et al 2018] [Qiang et al. 2024] [Qiu et al. 2023a] [Qiu et al. 2023b] [Qiu et al. 2024] [Rao et al. 2022] [Reedy and Gorrell 2025] [Saleem Yusoof et al. 2016] [Sanders 1980] [Sedlock 1985] [Seidel et al. 1980] [Shang et al. 2021] [Sitaram et al. 2023] [Soeder and Bobula 1979b] [Soeder and Bobula 1979a] [Soeder and Bobula 1982] [Soeder and Mehalic 1984] [Steenken et al. 1999] [Stenning 1980a] [Sun et al. 2022] [Sun et al. 2024b] [Sun et al. 2024d] [Sun et al. 2025a] [Sun et al. 2025c] [Sussman 1968] [Pan et al. 2024c] [Tan and Suder 2003] [Tanguy et al. 2018] [Tanida 1972] [Tao et al. 2022] [Tesch and Steenken 1978] [Jahani et al. 2022] [Valencia et al. 2017] [Valencia et al. 2020] [Van Deusen and Mardoc 1972] [Dippold 2022] [VanSchalkwyk et al 2001] [Verma et al. 2020] [Wallner et al. 1955] [Wallner et al. 1954] [Wang et al. 2013b] [Wang et al. 2017a] [Wang et al. 2020a] [Wang et al. 2023e] [Wang et al. 2024b] [Wang et al. 2024c] [Wang et al. 2024a] [Wang et al. 2025d] [Williams and Yost 1973] [Won 1990] [Wu et al. 2024b] [Wu et al. 2024a] [Wu et al. 2026] [Xie et al. 2023] [Xu and Hu 2022] [Xu et al. 2021] [Xu et al. 2022] [Xu et al. 2023] [Xu et al. 2025] [Yamamoto and Ng 1997] [Yan et al. 2025] [Yang et al. 2021d] [Yang et al. 2022b] [Yeh 1959] [Yu et al. 2026b] [Yuan et al. 2026] [Zachos et al. 2016] [Zhang and Hou 2015] [Zhang and Vahdati 2018] [Zhang and Vahdati 2019] [Zhang et al. 2020b] [Zhang et al. 2021b] [Zhang et al. 2024a] [Zhang et al. 2024d] [Zhao et al. 2017] [Zhao et al. 2022b] [Zhao et al. 2023] [Zhipeng et al. 2015] [Zhou et al. 2019]

Drag polars, wave drag and supersonic aerodynamics

The drag side of the sizing. Drag polars and their estimation, wave drag and the area rule, conical flow, and supersonic and transonic aerodynamics of bodies and configurations.

195 records. [2015] [Abraham et al. 2024] [Aerodynamic Drag in Cruising 2020] [Afridi et al. 2024] [Aircraft Drag 2010] [Antaran et al. 1992] [Army War Coll Carlisle Barracks Pa 1952] [Back and Cuffel 1966] [Ban et al. 2018] [Bennet-Clark 1972] [Bera 1975] [Bera† 1980] [Bleviss and Struble 1954] [Briggs 1960] [Brown 1961] [Brown 1946] [Browne et al 1948] [Bull and Bridges 1983] [Burkhalter 1982] [Bushnell 1990] [Butler 1982] [Cassetti 1978] [Chen and Li 2020] [Chester 1953] [Chin 1977] [Chin 1978] [Clarke and Wallace 1964] [Craidon 1986] [Cui et al. 2024] [Dai and Zhang 2023] [Davis 1971] [de Paula et al. 2017] [Dehua and Changyou 1993] [Desai et al. 1977] [Design and Numerical Analysis 2024] [Dickey 1959] [Durmus 2021] [Durston and Stonum 1987] [Evvard 1947] [Felix et al. 2026] [Ferrari 1958] [Flow Structure and Parameter 2023] [Gillespie 1960] [Gilman and Burdges 1967] [Golubkin 1980b] [Goodman 1949] [Gorbovskoi et al. 2019] [Goto et al. 2021] [Goulos et al 2021] [Graham et al. 1954] [Gringorten and Tattelman 1970] [Groth 1961] [Guderley 1987] [Guderley 1988] [Gudmundsson 2014] [Gur et al. 2010] [Götten et al. 2021] [Hall and Heitmeyer 1951] [Hancock 1959a] [Hancock 1959] [Hantrais-Gervois and Destarac 2015] [Hartley et al. 1965] [Hawkins and Penland 1997] [Hernandez et al. 1994] [Hillier 1970] [Hoerner 1936] [Holdaway et al. 1959] [Hrubecky 1963] [Hsu and Anderson 1961] [Hui 1975] [Hunt and Gowadia 1981] [Hunziker 1960] [Isugiyama 1976] [Jack 1951] [Jones 1972] [Jones 1976] [Jones 1956] [Jones 1953] [Kawamura and Karashima 1957] [Kayser and Danberg 1974] [Kohn 1979] [Kraiko and Tilliaeva 1973] [Laitone 1978] [Lee and Franz 1976] [Leslie and Perry 1954] [Levy 1959] [Levy and Yoshikawa 1959] [Li and Geiselhart 2021] [Li and Geiselhart 2026] [Lock 1957] [Lomax 1957] [Lovell 2001] [Maikapar 1959] [Maikapar 1966] [Maise 1970] [Malmuth 1966] [Malmuth et al. 1987] [Malone and Peavey 1999] [Margolis 1947] [Margolis et al. 1958] [Martin and Brazzel 1970] [Mathur 1998] [Matranga and Armstrong 1959] [Mazurov 2015] [Mazurov 2019] [McMillin and Wood 1986] [Menees and Boyd 1959] [Miles 1953] [Miller et al. 1983] [Mizobata et al. 2024] [Moeckel and Evans 1951] [Moga 1980] [Narayan 1975] [Nelson and Welsh 1960] [Nielsen 1985] [Nielsen et al. 1953] [Orman et al. 1951] [Oruç 2026] [Osborne and Kelly 1953] [Ostieri and Tognaccini 2018] [Ostowari and Naik 1986] [Oswatitsch 1952] [Oswatitsch 1958] [Oswatitsch 1980] [Panov and Shvets 1967] [Panov et al 1966] [Payne 1980] [Petersen 1957] [Petruzzelli and Keane 2001] [Pfaff 1965] [Pfaff 1968] [Polhamus 1968] [Portnoy 1963] [Ramaswamy and Viswanathan 1975] [Reist et al. 2022] [Reukauf and Burcham 1976] [Osborne and Kelly 1960] [Rowe 1958] [Rylov 1974] [Sachs 1977] [Sachs 1980] [Sahoo and Peetala 2010] [Sahu 1986] [Sandahl 1948] [Shevell 1978] [Sibulkin 1951] [Singh and Dwivedi 2022] [Smart et al. 1994] [Smith 1954] [Solomon 1955] [Stancil 1979] [Stanišić 1961] [Steer 2003] [Stewart 1956] [Stewartson 1950] [Stocker 1951] [Stone 1945] [Sugiyama 1977] [Sun and Smith 2019] [SUPERSONIC FLIGHT 2014] [Takovitskii 2020] [Takovitsky 2018] [Thein 2018] [Thomas 1942] [Ting et al. 2018] [Transonic and Supersonic Flight 1992] [Vaisakh et al. 2019] [van Es 2002] [Vasil’ev 1970] [Vieira et al. 2025] [Vira and Fan 1982] [von Doenhoff and Horton 1942] [Walkley 1986] [Wallskog 1954b] [Wallskog 1954a] [Ward 1949] [Ward 1968] [Wasserman 1952] [Wetzel 1955] [Whitcomb 1953] [Whitcomb and Sevier 1960] [Winograd and Miles 1956] [Wood and Miller 1985a] [Li and Geiselhart 2020] [Xu 2023] [Yajnik and Subbaiah 1976] [Yamanaka and Kamimura 1975] [Yamazaki et al. 2019] [Yoshida 2009] [Zaman et al. 2025] [Zhang 2020b] [Zhang 2024] [Zhang et al 2015] [Zuo 2021] [Zuo 2023]

Compressor stall, surge and casing treatment

What a distorted inlet does to a compressor. Rotating stall and surge, their inception, warning and active control, and casing treatment, in aero-engine and in industrial machines alike.

192 records. [Ahmad et al. 2021] [Akhlaghi and Azizi 2023] [Akhlaghi et al. 2022] [Alone et al. 2016] [Amann et al 1975] [Analysis of Anti-Surge Control 2021] [Anantachaisilp and Lin 2020] [Anti-Surge Control of Centrifugal 2021] [Anti-Surge Reason and Control 2021] [Application of Centrifugal Compressor 2021] [Application of PLC 2021] [Application Practice of Anti-Surge 2021] [Aribi and Boushaki 2023] [Axial Transonic Compressor Stall 2022] [Azizi and Brouwer 2017] [Bammert and Mobarak 1976a] [Bammert and Mobarak 1976b] [Batayev et al. 2022] [Boussios et al 1992] [Breugelmans 1975] [Burwell and Patterson 1985] [Cabrera Cruz et al. 2020] [Cao et al. 2022] [Cevik et al. 2016] [Chen et al. 2026b] [Chi et al. 2022] [Cossar et al 1980] [Cumpsty and Greitzer 1982] [Daniele and Teren 1975] [Daniele and Teren 1975] [Day et al 1978] [Day et al. 1978a] [Dean and Young 1977] [Dehner et al. 2021] [Ding et al. 2024] [Discussion on Anti-Surge Control 2021] [Discussion on Control Points 2021] [Discussion on the Anti-Surge 2021] [Discussion on the Application 2021] [Dodds and Vahdati 2015b] [Dodds and Vahdati 2015a] [Dong et al. 2025] [Dong et al. 2026] [Du et al. 2025] [Dvirnyk et al. 2019] [Zhang et al. 2023] [Emmons et al 1955] [Emmons et al. 1955a] [Faltin and Beneda 2023] [Fang et al. 2023b] [Fu et al. 2021a] [Fu et al. 2021b] [Furukawa et al. 2015] [Galindo et al. 2022] [Gao et al. 2015] [Gao et al. 2017] [Gray 1969] [Greitzer 1976] [Greitzer 1976] [Greitzer 1976a] [Greitzer 1980] [Grimshaw et al. 2025] [Guan et al. 2019] [Guo 2023] [Guo et al. 2022a] [Guo et al. 2022b] [Guo et al. 2025] [Güllü and Aran 2023] [Günaydın and Doğu 2025] [Hah 2018] [Hah 2022] [Hamaguchi et al. 2020] [Hansen et al 1981] [Harman 1978] [Hawthorne et al. 1955] [Hickman and Morris 2017] [Hosseindokht et al. 2026] [Huang et al. 2019] [Huppert 1955] [Huppert and Benser 1953] [Imani et al. 2017] [Imani et al. 2018] [Ji et al. 2022] [Jia et al. 2024] [Ka 2018] [Kawase and Rona 2019b] [Kawase and Rona 2019a] [Khaleghi 2015] [Kim et al. 2022] [Kim et al. 2026] [Kiss and Spakovszky 2018] [Kolnsberg 1979] [Kosuge et al 1982] [Koyyalamudi and Nagpurwala 2016] [Laderman 2021] [Li et al. 2015a] [Li et al. 2019b] [Li et al. 2021c] [Li et al. 2022b] [Li et al. 2022c] [Li et al. 2023c] [Li et al. 2024c] [Lin et al. 2022] [Liu et al. 2016b] [Liu et al. 2024b] [Liu et al. 2025c] [Lou et al. 2022] [Ludwig 1979] [Mao and Liu 2016] [Mao et al. 2017] [Margalida et al. 2020] [Marshall 1973] [Marty et al. 2022] [Mays 1971] [McQueen 1976] [Chi et al. 2021] [Mechanism Study 2023] [Mikhailov et al. 2017] [Miura et al. 2021] [Molana et al. 2020] [Moru et al. 2022] [Neverlien et al. 2020] [Ohyama 1978] [Pakle and Jiang 2018] [Paraguassu 2015] [Patil 2018] [Peacock 1978] [Prince 1976] [Qiao et al. 2026] [Quan et al 2024] [Rains 1955] [Righi et al. 2018] [Sakata and Ohta 2017] [Schaffrath et al. 2025] [Semlitsch and Mihăescu 2016] [Shahin et al. 2016] [Shahriyari et al. 2024] [Sheng et al. 2020] [Sheng et al. 2023] [Shiriaev et al. 2026] [Song et al. 2019b] [Sonoda et al. 2009] [Sovran 1959] [Starken and Lichtfuss 1970] [Stenning 1980] [Strub and Suter 1965] [Sun et al. 2015a] [Sun et al. 2021c] [Sun et al. 2021b] [Sun et al. 2021a] [Sun et al. 2024f] [Sun et al. 2024c] [Sun et al. 2025b] [Sun et al. 2026] [Taghavi-Zenouz and Behbahani 2017] [Tanaka and Murata 1975] [Tanaka and Murata 1975] [Tanaka and Murata 1975] [Thapa et al. 2025] [The Reason and Strategy 2021] [Tondl 1979] [Uddin and Gravdahl 2016] [Shahriyari and Khaleghi 2024] [Valensi 1958] [Venturelli and Benini 2016] [Vu et al. 2025] [Wang et al. 2020b] [Wang et al. 2021c] [Wang et al. 2022a] [Wang et al. 2024e] [Wang et al. 2026b] [Wasserbauer et al 1985] [Wu et al. 2025] [Xie and Marrani 2021] [Xinqian and Anxiong 2015] [Xue et al. 2024] [Yang et al. 2022c] [Yaylak et al. 2026] [Yi and Sun 2024] [Zhang and Malekgoudarzi 2020] [Zhang and Wang 2022] [Zhang and Wu 2026] [Zhang et al. 2016] [Zhang et al 2021] [Zhang et al. 2022] [Zhang et al. 2024c] [Zhang et al. 2024b] [Zhang et al. 2025a] [Zhang et al. 2026e] [Zhao et al. 2019] [Zhao et al. 2025b] [Zhu and Yang 2020]

Wings, aspect ratio and vortex flows

The planform the Lancer inherited and changed. Aspect ratio, downwash, tip and leading-edge vortices, delta and low aspect ratio wings, and the lifting-surface theory behind the induced term of the drag polar.

166 records. [2024] [Abdolahipour et al. 2022a] [Abdolahipour et al. 2022b] [Abdul-Kaiyoom et al. 2025] [Aleisa et al. 2023] [Anderson 1947] [Aoyagi and Hickey 1959] [Axelson and Crown 1948] [Banks and Paulson 1987] [Bauer and McMillin 1988] [Benaouali and Kachel 2019] [Bertram and Ulmann 1953] [Bilanin and Donaldson 1975] [Bird et al. 1952] [Biriukov 1959] [Bowers 1981] [Brown 1959] [Buchholz 1992] [Buchholz and Tso 1993] [Butter and Hancock 1971] [Buzica and Breitsamter 2020] [Campbell 1976] [Carreyette 1950] [Chen et al. 2025a] [Clark and Richie 1977] [Coe and Kulla 1974] [Coe 1976] [Cole 1980] [Corcione et al. 2023] [Crane 1948] [Crane and Beckhardt 1948] [Davis 1952] [Davis 1973b] [Davis 1973d] [Davis 1973a] [Deitchman 1954] [Demir et al. 2023] [Deyoung 1950] [Doggett and Soistmann 1989] [Dong et al. 2020] [Dong et al. 2022] [Dowell and Ventres 1970] [Epstein 1954] [Figge 1973] [Fisher and Williams 1958] [Foster and Fitzpatrick 1948] [François et al. 2021] [Fuller 1967] [Ghaffari 2005] [Ghee et al. 1999] [Golubkin 1980a] [Griffin et al. 1958] [Hanazaki and Yamazaki 2024] [Hancock 1960] [Harold and Haefeli 1950] [Hayes and Sleeman 1959] [He and Zhang 2025] [Helmbold 1958] [Hobbs et al. 1996] [Hoffler et al. 1986] [Hopkins 1975] [Hunn 1954] [Hwang et al. 1980] [Hövelmann and Breitsamter 2015] [Hövelmann et al. 2016] [Ichikawa et al. 2021] [Jaquet 1951] [Jenkins and Kuhl 1977] [Jones et al. 1947] [Jones and Unangst 1963] [Kelley and Tolhurst 1955] [Kelly et al 1958] [Kholyavko 1971] [Kida and Miyai 1978] [Kinard et al. 1995] [Kishi et al. 2022] [Klein 1999] [Kopzon 1958] [Lai and Kamaruddin 2018] [Lamar 1986] [Lamar 1987] [Lampropoulos and Sarris 2025] [Lapin et al. 1952] [Larrabee 1975] [Lawrence 1953] [Lee and Kim 2024] [Lee and Ko 2018] [Lemay et al. 1988] [Leslie 1952] [Lichtenstein 1952] [Lin et al. 2026] [Lockwood 1966] [Lourenco et al. 1996] [Maki 1959] [Malicki et al. 2023] [Mamonova et al. 2019] [McCormick 1959] [McLemore 1958] [McLemore and Peterson 1960] [Miller 1983] [Miller 1986] [Mitsuyasu 1956] [Morton 1956] [Muchmore 1988] [Murphy and Klein 2006] [Nagler 2022] [Ness 1971] [Newsome and Thomas 1986] [Nicholas et al. 1984] [Northrop Aircraft INC Hawthorne CA 1952] [Northrop Aircraft INC Hawthorne CA 1953] [O’Kelly 1954] [Ogawa and Takeda 2015] [Raj et al. 2003] [Paziresh et al. 2017] [Penland et al. 1975] [Penland et al. 1978] [Peterson and Menees 1959] [Pfnür and Breitsamter 2019] [Polhamus 1966] [Queijo and Wolhart 1951] [Queijo et al. 1954] [Quigley et al 1960] [Ramakrishna et al. 2019] [Rebuffet and Poisson-Quinton 1952] [Report No. 609 Experimental 1937] [Report No. 648 Design 1939] [Reykers and Fonck 2019] [Ribner 1960] [Roberts 1965] [Rockwell 2001] [Roy Salam and Bil 2016] [Rudolph 1997] [Said et al. 2018] [Sakata and Davis 1977] [Sakata et al. 1975] [Schuldenfrei et al. 1947] [Schulderfrei et al. 1951] [Shen and Wen 2018] [Shindo and Joppa 1980] [Silverstein and White 1937] [Skoog 1951] [Skow et al. 1982] [Sogukpinar 2018] [Spencer 1961] [Spooner and Martina 1948] [Spreiter and Sacks 1951] [Sugiyama 1971b] [Sugiyama 1971a] [Surwase and Kumar 2025] [Sutton 1959] [Torenbeek 1971] [Van Dommelen 1995] [Verma and Kulkarni 2024] [Verma and Manisankar 2025] [Vidal 1962] [Wabick et al. 2023] [Walker and Berggren 1948] [Wentz 1987] [Wood and Miller 1985b] [Wood et al. 1983] [Woodward 1956] [Wright et al. 1978] [Yan et al. 2016] [Yang et al. 2026a] [Zimmerman 1935]

Turbofans, turbojets and installed thrust

The engine the designation was requested to test. Turbofan and turbojet cycles, afterburning and variable-cycle engines, nozzles, engine test and control, and the installed thrust that the ram drag argument turns on.

153 records. [Aydın et al. 2025] [Feng et al. 2026] [Gu et al. 2026] [Jain 2025] [Mubarak and Tide 2018] [Abdulhamitbilal et al. 2021] [Anatomy of a Turbofan 1970] [Armstrong et al. 1980] [Ashry et al. 2019] [Ashwood 1973] [Auman 1993] [Babu 2021b] [Babu 2021a] [Baerst and Hughes 1978] [Bagby and Andersen 1966] [Baidya et al. 2018] [Balli and Caliskan 2021] [Banks et al. 1981] [Bayati and Williston 1977] [Beale and Miller 1975] [Benson 1997] [Berezovsky 2018] [Bezborodova and Filinov 2021] [Birch et al. 1978] [Boytos 1969] [Branstetter et al 1971] [Breaks 1973] [Briones and Rankin 2024] [Bristol Siddeley Viper Mark 1963] [Brodsky 1970] [Brodzik 2024] [Burns and Kirchgessner 1987] [Capello et al. 2019] [Capone and Reubush 1983] [Castner et al. 2017] [Castor 1983] [Chaney 1999] [Chapman 1979] [Chen et al. 2021a] [Child and Henderson 1978] [Coalson 1968] [Coalson and Csavina 1976] [Cowles 1981] [Crown 1950] [da Fonseca Filho et al. 2019] [Dai et al. 2023a] [Davidson 1964] [Development Testing 1970] [Di̇şli̇taş and Albayrak Çeper 2021] [Drewes 1987] [Due 1987] [Dugan 1972] [Dugas 1968] [Egan and Shadowen 1979] [El-Sayed 2026] [Evans and Chamblee 1966] [Fett 1971] [Franciscus 1987] [Gabriel et al 1953] [Guo et al. 2024] [GÜRbÜZ and Acarer 2022] [Hartmann 1968] [Heltsley and Crosswy 1983] [Herrick 1986] [Hurley 1951] [Hutchinson et al. 2021] [Jakubowski 2019] [Jiali and Jihong 2015] [Kalkan 2024] [Karol and Hatch 1969] [Kast 1980] [Katz 1971] [Kbab et al. 2023] [Kim et al. 2015] [Klein and Abeykoon 2015] [Koutz and Hensley 1952] [Krebs 1976] [Krenkel and Salzman 1968] [Kuprowicz 1999] [L’Ecuyer et al. 1971] [Lambert and Mizukami 1999] [Pratt and Whitney Aircraft (United States) et al. 1960] [Lewis 1976] [Li et al 2019] [Li et al. 2024i] [Liew et al. 2005] [Liu and Sirignano 2000] [Lucas 1978] [Ma et al. 2025b] [MacInnis 1994] [Magrini and Benini 2023] [Mauch et al. 1980] [McAulay and Abdelwahab 1972] [McGuigan 1970] [Menon et al. 2023] [Mikhail 1979] [Mixed Flow Turbofan Engine 2018] [Mock 1951] [Morris et al. 1976] [Nageswara Rao and Kushari 2020] [Neitzel and Hemsworth 1966] [Niknamian 2019] [Okelah 1985] [Panzeri et al. 2018] [Parisen et al. 1948] [Parker 1991] [Patel and Chudoba 2026] [Piccirillo et al. 2024] [Pismennyi] [Prasad and Rivera 1996] [Presz et al. 1971] [Purser and Spear 1947] [Rajagopalan and Siddiqi 1985] [Rakipoğlu and Avcı 2026] [Ramjet Supersonic “Flight Tests” 1958] [Resta et al. 2021] [Robins et al. 1985] [Rosell] [Rosen 2001] [Roth et al. 2005] [Rudnitski] [Sanders and Palasics 1948] [Schweiger 1987] [Semlitsch and Mihăescu 2021] [Shariatzadeh et al. 2015] [Shoshany‐Tavory et al 2023] [Shufan et al. 2018] [Stephenson 1953] [Suchocki et al. 2015] [Sun et al. 2015b] [Takahashi 2017] [Tate and Gillard 1975] [Taylor 1991] [The Fiat G80 Turbojet 1952] [The Hawker P1127 Vectored 1990] [The Rolls-Royce RB.211 Three 1968] [The Rolls-Royce Spey Junior 1967] [Thrust Vectoring 2020] [Trefny and Benson 1995] [Tudosie 2024] [Watson 1953] [Werner and Wolter 2010] [White and Wills 1972] [Wilde and Pickerell 1968] [Yahiaoui 2024] [Yalcin 2017] [Yang and Yu 2026] [Yao et al 2022] [Yonke et al. 1985] [Zahir et al. 2023] [Zebbiche and Youbi 2023] [Zhang et al. 2025b] [Zhang et al. 2026c]

Air combat, agility and aircraft performance

The case the Lancer was sold on. Energy manoeuvrability and specific excess power, turn performance, climb and minimum-time paths, and agility metrics and requirements.

11 titles in the survey name energy manoeuvrability or specific excess power, from 1972 to 2026. The measure the competition argued over is still the one in which aircraft performance is presented.

114 records. [Aircraft Performance 2010] [Aircraft Steady Level Turning 2011] [Aircraft Steady Turning Flight 2011] [Aircraft Basic Forces 1995] [Alexander et al. 1992] [Ali et al 2017] [Anderson 1989] [Anderson et al. 1973] [Anderson and Bray 1951] [Anderson and Bray 1955] [Andrews 1969] [Atesoglu and Özgören 2006] [Atesoglu and Özgören 2007] [Beaufrere 1988] [Beck and Cord 1995] [Blake et al. 1990] [Blank and Shinar 1982] [Caddy and Arnold 1988] [Chung 2007] [Capone 1979] [Chou] [Coordinated Turning Flights 1995] [Cord 1989] [Corner 1940] [Crowe 1936] [Degree Turning Performance] [Erickson and Campbell 1977a] [Erickson and Campbell 1977b] [Foss 1981] [Foss 1984] [Gedeon and Takahashi 2014] [Gloss 1974] [Guang et al. 2014] [Guang et al. 2015] [Herbst and Krogull 1973] [Hill and Bowles 1976] [Hitzel and Osterhuber 2018] [Hoffman and Stalford 1991] [Hom et al. 1983] [Iliff 1977] [Irwanto 2017] [Jeans and Tribble 1979] [Johnson 1972] [Karabacak and Turan 2020] [Karniadakis 2004] [Kelley 1975a] [Kelley 1975b] [Khalid 2025] [Kigotho et al 2022] [Kish et al. 2019] [Kostin and Zhuravskiy 2023] [Krupa 2019] [Kutschera and Render 1999] [Kutschera and Render 2003] [Langan and Samuels 1995] [Large 1981] [Levin 1997] [Lin 1982a] [Lin 1982b] [Loh and Lusty 1974] [Maitra 2010] [Mancini and Vos 2019] [Manolescu 1994] [Mason 1983] [Mason et al. 1983] [Merritt et al. 1985] [Miele 1954] [Miele 1955] [Nelms and Bailey 1974] [Ngan and Biezad 1996] [Olwi 1995] [Oruc and Baklacioglu 2022] [Oruc and Baklacioglu 2023] [Papageorgiou et al. 2018] [Paranjape and Ananthkrishnan 2023] [Parlier 1986] [Pennington and Meintel 1980] [Rafiq and Qureshi 2022] [Ransom 1983] [Ray and Taylor 1965] [Raymer 1991] [Reinbold et al 2026] [Rodgers 1966] [Sadraey 2017] [Satyanarayana et al. 1975] [Schneider 1990] [Schrage 1990] [Schuster 1995] [Sederstrom et al. 1973] [Seginer and Salomon 1983] [Silton et al. 2014] [Sivaramakrishnan 1981] [Spearman and Sawyer 1977] [Srivastav and Ponnani 2011] [Takahashi 2012] [Tamboli 1956] [Tamrat 1988] [Theodorsen 1959] [Tritschler et al. 2025] [Turn Performance and Maneuver 2021] [Turning Flight 1997] [Turning Flights of Turbojet 1995] [Turning Performance 1992] [Voß and Klimmek 2023] [Wang et al 2017] [Wang et al 2020] [Wang et al. 2021b] [Wang et al. 2026c] [Whittley 1952] [Wilson et al 1993] [Wood and Livingston 1971] [Yajnik 1977] [Yan et al. 2024] [Yongxi Lyu et al. 2016]

Aerodynamic heating, recovery temperature and thermal protection

The structural half of the keystone, as heat. Aerodynamic and kinetic heating, the recovery temperature and the adiabatic wall, transient skin temperature, and cooling and thermal protection.

20 titles name the recovery temperature, the recovery factor or the adiabatic wall temperature. The relation that puts the skin at 210.8 degrees Celsius is measured and settled, and a literature of measurements is the shape a settled subject takes.

109 records. [Afanas’ev et al. 2019] [Air Force Research Lab Edwards AFB CA 2000] [Back et al. 1967] [Barone et al. 2022] [Baryshev et al. 1972] [Bergstedt et al. 1959] [Biswas et al. 2026] [Brinich 1961] [Cess 1964] [Chen and He 2025] [Chen et al. 2021d] [Chen et al. 2024] [Chou and Smith 1974] [Dai et al. 2023b] [Ding et al. 2020] [Duan et al. 2026b] [Abbasi and Esmailzadeh Vali 2024] [Feng et al. 2020] [Fischer and Norris 1949] [Flanagan 1992] [Гадеев et al. 2017] [Gliszczyński et al. 2021] [Gridnev 1991] [Gupta and Ramkumar 2015] [Gözükara and Ceylan 2024] [Hao et al. 2024] [Herwig 2000] [Hodge et al. 1985] [Hodge et al. 1986] [Honeycutt 1970] [Hongpeng and Weiqiang 2016] [Horton 1954] [Hu et al. 2023] [Ivanov 2022] [Johnson and Adcock 1981] [Karimi and Oboodi 2018] [Kaye and Yeh 1955] [Kinsler 1958] [Kurganov 2006] [Leadon and Scott 1956] [Leontiev et al. 2017b] [Leontiev et al. 2017a] [Leontiev et al. 2022] [Li et al. 2024g] [Li et al. 2026] [Lin et al. 2021] [Liu and Cao 2017] [Luce 1949] [Maples 1979] [Mugalev et al. 1985] [Nagamatsu et al. 1960] [Negaard 1979] [Ohwada et al. 2019] [Pasiuk 1963] [Peck et al. 2020] [Peng-ju et al. 2015] [Persh 1955] [Pfyl and Presley 1961] [Popovich et al. 2014] [Popovich et al. 2021] [Powell and Glickstein 1988] [Qu et al. 2019] [Rand 1963] [Reggiori 1972] [Ren et al. 2021] [Rubio and Ballard 1967] [Rumsey and Lee 1961] [Schoeler 1987] [Shimada and Ohwada 2020] [Shiryaev and Serebryansky 2022] [Shiryaev et al. 2023] [Si et al. 2019] [Smith 1967] [Smith 2021] [Snodgrass 1955] [Sreekumar et al. 2025] [Stephens 1959] [Straight and Harrington 1973] [Sturek et al. 1983b] [Sturek et al. 1983a] [Sun and Zhu 2019] [Sun et al. 2020] [Taguchi et al. 2017] [Tang et al. 2024] [Tang et al. 2025a] [Tewfik and Giedt 1960] [Vitols et al. 2026] [Walker 1955] [Wang et al. 2023h] [Wang et al. 2024d] [Wang et al. 2024f] [Winkler 1954] [Xie et al. 2016] [Xie et al. 2025c] [Xin-guo et al. 2015] [Yadav and Guven 2015] [Yang and Liu 2017] [Yang et al. 2021b] [Yih et al. 1952] [Yu et al. 2021a] [Yu et al. 2025a] [Yu et al. 2025b] [Zhao et al. 2025a] [Zhu and Zhao 2016] [Zhu et al. 2018a] [Zhu et al. 2018b] [Zhu et al. 2022] [Zhuang and Lu 2015] [Zien and Ragsdale 1979]

Aluminium alloys and their strength when hot

The material the X-27 would have been built of. Aluminium alloys at elevated temperature, and their creep, fatigue, fracture and design data.

92 records. [Allen and Mahorter 1964] [Awerbuch 1980] [Ayres 1977] [Bouzekova-Penkova and Miteva 2022] [Brodrick 1976] [Brown 1970] [Cao and Zhang 2023] [Carlson and Schwope 1952] [Cervay 1972] [Cervay 1975] [Chang et al. 1953] [Chen et al. 2013] [Cho and Findley 1983] [Composite Material Comprising Reinforced 1978] [Dahlberg 1963] [Development of an Improved 1975] [Duncheva et al. 2020] [Edahl and Domack 2004] [Erich 1980] [Fine 1959] [Fine and Weertman 1983] [Galkin and Sergeev 1976] [Giuliano 2016] [Go and Wilshire 1992] [Golovin 1982] [Hall et al. 1997] [Hamilton et al. 1997] [Hansen 1972] [Hawk and Wilsdorf 1988] [Heath-Smith 1965] [Holl 1975] [Inglis and Larke 1958] [Iseki and Nicholas 1979] [Jain and Liang 2020] [Ji et al. 2021] [Johnson et al. 1960] [Kothari 1973] [Lee and Chen 2005] [Jones 1973] [Kothari 1971] [Kramer and Potter 1966] [Kumar et al. 2022] [Kun et al. 2018] [Lai and Findley 1980] [Lawley and Koczak 1984] [Lawley and Koczak 1985] [Lee and Sanders 2002] [Lee 1998] [Lee 2003] [Lee and Chen 2002] [Lee and Munafo 2002] [Li et al. 2024h] [Liu et al. 2016a] [Lypchanskyi et al. 2024] [Mahorter and Robert G. 1961] [Mathauser and Deveikis 1955] [Mathauser and Deveikis 1957] [Minnicino et al. 2009] [Montano 1967] [Mozley 1943] [Neshpor et al. 1991] [Ohashi and Ohno 1982] [Papirno 1966] [Papirno and Gerard 1962] [Parris et al. 1957] [Paton et al. 1982] [Radon 1969] [Reynolds 1993] [Shechtman 1981] [Shen 2017] [Shirinzadeh Dastgiri et al. 2023] [Sih and Chou 1989] [Srivatsan 1999] [Srivatsan and Anand 1998] [Stickley and Brownhill 1964] [Su and Young 2017] [Su et al. 2023] [Sullivan 1978] [Taig 1961] [Tanaka and Nojima 1971] [Tirpak 1985] [Tomczyk and Seweryn 2017] [Tomczyk and Seweryn 2021] [Torić et al. 2018] [Vorob’ev and Bich 1977] [Wang and Trapp 1958] [Weiss and Gegal 2014] [Yamauchi et al. 1988] [Zaidi 1988] [Zhang et al. 2009] [Zhang et al. 2026b] [Zubair et al. 2022]

Titanium, other alloys and composites at elevated temperature

The materials the X-27 did not use. Titanium alloys and their processing, nickel and other superalloys, creep and fatigue at temperature, and composite and ceramic structure.

84 records. [Arkoosh and Fiore 1972] [Balashov and Petukhov 1969] [Bhandari et al 2025] [Bloxsom 1958] [Carew et al. 1956] [Chen et al. 2020a] [Chen et al. 2021b] [Chen et al. 2022] [Davis 1973c] [Davis et al. 1972] [Dobeš et al. 2019] [Ebied et al. 2018] [Experimental Study 2020] [Fang et al. 2022] [Feng et al. 2025] [Gehring and Engle 1963] [Glenn and Koch 1973] [Glorioso 1960] [Guo et al. 2021b] [Han and Seo 2016] [Hashin and Humphreys 1980] [Heimerl and Hardrath 1965] [Imig 1973] [Initial Damage Mechanism 2019] [Islam et al. 2015] [Jeans et al. 1983] [Jeffs and Lancaster 2015] [Johnson et al. 1959] [Kaczorowski et al. 2015] [Khademi et al. 2019] [Kolom 1969] [Kovács et al. 2023] [Krashchenko and Statsenko 1981] [Krivenyuk et al. 1971] [Li and Sun 2022] [Li et al. 2021a] [Li et al. 2024a] [Li et al. 2024d] [Li et al. 2025a] [Lin et al. 2020] [Lunde 1977] [Maksimovich et al. 1977] [Malashenko and Vashchilo 1975] [Malvi and Roy 2021] [Mills 1978] [Ochonogor et al 2017] [Palienko et al. 1976] [Perepezko 2001] [Reymer et al. 2018] [Rhomberg 1972] [Richards and Thompson 1991] [Sajadifar et al. 2023] [Sanchez-Carmona and Cuerno-Rejado 2018] [Sandstrom and White 1961] [Saxena 1998] [Semenov 1981] [Shi-feng et al. 2018] [Shkaraputa 1976] [Sinaiskii et al. 1972] [Sosnin and Torshenov 1970] [Stamatelos and Labeas 2025] [Szusta 2018] [Tadini et al. 2017] [Tao et al 2024] [Tian et al. 2021] [Toffol and Ricci 2023] [Tuninetti et al. 2024] [Uemura et al. 2020] [Uludag and Turan 2015] [Valoppi et al. 2017] [Vorob’ev and Galiakhmetov 2023] [Wang et al. 2018] [Wang et al. 2021a] [Wei et al. 2022] [Wen et al. 2022] [White 1997] [Xiaokang et al. 2018] [Xu et al. 2020] [Yang et al. 2021a] [Yang et al. 2021c] [Yang et al. 2022a] [Yu et al. 2026a] [Zheldubovskii and Ishchenko 1982] [Zhong et al. 2024]

Conceptual design, optimisation and the derivative aircraft

How an unbuilt aircraft is now evaluated. Conceptual and preliminary design, multidisciplinary optimisation, surrogate models and uncertainty, and derivative design.

83 records. [Abu Salem et al. 2023] [Al-Shamma et al. 2017] [Albuquerque et al. 2018] [Allison et al 2015] [Arnson et al. 2026] [Babaei et al. 2018] [Bianchi et al 2020] [Horvath and Wells 2018] [Bryson and Rumpfkeil 2019] [Chell et al. 2021] [Cheng et al. 2016] [Coen and Foss 1985] [Cummings et al. 2018] [Di Bianchi et al. 2018] [Du 2026] [Duan et al. 2026a] [Dudley 1986] [Golombek et al. 2026] [Hackman and Richardson 1964] [He and Shi 2025] [Hon et al. 2022] [Hosseini et al. 2024] [Jelev et al. 2019] [Ji et al. 2024] [Khatri and Sinha 2023] [Kretov 2021] [Kumar 1999] [Leng et al 2024] [Li and Geiselhart 2022] [Li et al. 2009] [Liu and Jiang 2022] [Lukyanov et al. 2024] [Michal 1998] [Tint 2018] [Mokotoff et al. 2026] [Moorhouse and Jenkins 1975] [Moëns 2022] [Munjulury et al. 2015] [Nam and Mavris 2018] [Ng and Willcox 2016] [Pan et al. 2017] [Park et al. 2015] [Park et al 2016] [Park et al 2016] [Park et al 2018] [Powers et al. 1983b] [Prigent et al. 2015] [Qin 2026] [Ramachandran and Wells 1974] [Ramachandran and Wells 1975] [Raymer 1998] [Riccobene and Ricci 2015] [Roelofs et al. 2021] [Roskam and Dusto 1969] [Roskam et al. 1968] [Safavi et al. 2015] [Saporito et al. 2023] [Saraswathi 2000] [Saves et al. 2024] [Schwartz 1988] [Setayandeh and Babaei 2020] [Sgueglia et al. 2020] [Shi 2025] [Siedlak et al. 2017] [Stephan et al. 2024] [Subramanian and DeLaurentis 2016] [Sóbester 2021] [Tao and Sun 2019] [Tao et al. 2020] [Tfaily et al. 2024] [Tfaily et al. 2026] [Tian and Li 2020] [Tich et al. 1987] [Todorov et al. 2023] [Triplett 1980] [Tyan et al. 2017] [Veresnikov 2025] [Veresnikov et al. 2026] [Wang et al. 2023j] [Wilson et al. 2023] [Xu and Yu 2025] [York et al. 2018] [Ünal et al. 2023]

Stability, control and flying qualities

The control problem of a high tail and a short wing. Longitudinal and lateral stability, tail and canard effects, departure, spin and deep stall, and flying qualities.

68 records. [Air Force Test Pilot School Edwards Afb Ca 1989] [Air Force Test Pilot School Edwards Afb Ca 1990a] [Air Force Test Pilot School Edwards Afb Ca 1990b] [Anderson 1985] [Anglin 1978] [Ansari et al. 2022] [Archbold 1945] [Baron 1953] [Bielat 1959] [Bihrle and Barnhart 1982] [Bihrle and Billy 1980] [Bollech and Kelly 1954] [Bryant 1933] [Bykerk et al. 2020] [Casteel and Weyl 1970] [Chambers and Bowman 1971] [Cook 1965] [Cornell Aeronautical Lab INC Buffalo NY 1947] [Crowe 1937] [Cunis et al. 2020] [Deitchman 1953] [Dias 2023] [Ding 2023] [Donlan 1976] [Driver 1958] [Eberle and Fowler 1971] [Eulrich and Mesiah 1974] [Farhat et al. 2000] [Gates 1940] [Gilbert et al. 1976] [Gilruth and White 1941] [Goud and Dwivedi 2022] [Hamed 1993] [Harper and Robert P. 1955] [Hess 1986] [Hewes 1950] [Hwang and Pi 1979] [Irsyad Lukman and Agoes Moelyadi 2018] [Jenney 1935] [Kleckner 1945] [Kleckner 1946] [Langham 1978] [Lovell and Wilson 1947] [Malcolm and Ng 1991] [Malikov and Miltsov 2019] [Milenković-Babić et al. 2017] [Millidere et al. 2022] [Min et al. 2024] [Mungall 1948] [Neal and Smith 1970b] [Neal and Smith 1970a] [Neumark 1950] [Nguyen et al. 1976] [Powers 1966] [Ramamurti 2011] [Reid 1937] [Roache 1965] [Rodgers 1965] [Sachs 1975] [Schwanz 1972] [Sleeman and Byrnes 1953] [Sleeman 1957] [Squires 2002] [Swortzel and Barfield 1976] [Washington et al. 1968] [Watanabe et al. 2023] [Weissman 1973] [Wisniewski 1951]

The F-104, the J79 and later named fighters

The aircraft by name. The F-104 and its J79, the competitors and successors the Lancer was measured against, and the later fighter and demonstrator programmes named in their titles.

No title in the survey names the X-27, the CL-1200 or the Lancer. The aircraft this article is about survives in the literature only through its parent, and thirteen titles name the F-104 or its J79, of which five name the engine.

59 records. [Background 1998] [Barham 1994] [Biesiadny et al. 1978] [Birkler 2001] [Bogdan 2015] [Brantley and Stabrylla 1979] [Brignac et al. 1976] [Capone and Berrier 1980] [Dietz and Bailey 1973] [Enzinger 1988] [Esser and Ruff-Stahl 2021] [F-104 Resource Tape 1992] [Farr 1976] [Friend and Sefic 1972] [Friend and Sakamoto 1978] [Gill and Sain 1981] [Gleason and Martone 1980] [Haering and Burcham 1984] [Hebbar et al. 1991] [Hicks and Huckabine 1989] [Hild and Crocker 2006a] [Hild and Crocker 2006b] [Hild and Crocker 2008] [Hoerter et al. 1991] [Hughes and Johnson 1972] [Hughes and Mackall 1984] [Iliff et al. 1970] [Jackson 1980] [Johns 1998] [Kim 2024] [Kohn 1964] [Kong et al. 2017] [Kurtenbach 1978] [Lane and Behenna 1991] [Latham 2020] [Loren et al. 1992] [Marshall and Schweikhard 1973] [Marshall 1971] [McKeehen and Cord 1997] [Morgenfeld 1992] [Myers and Walsh 1988] [Navy Participation 1998] [Neville et al. 1992] [Nicholson 1985] [Piccirillo and Aronstein 1997] [Poorman 1980] [Ray et al. 1988] [Scherz and Williams 1978] [Siano 2014] [Smith and Burgess 1960] [Smith et al. 1976] [Smith et al. 1984] [Song et al. 2019a] [Studer 2012] [von Hlatky and Rice 2018] [Weeks 1986] [Whoric 1973] [Whoric 1977] [Woelk 1989]

Fighter aircraft design, requirements and history

Fighters as a class. Fighter design method, requirements, configuration studies and the history of fighter development, where no narrower cluster above claims the title.

43 records. [A Canadian Light Fighter 1940] [A New Fighter Aircraft 2003] [Almuradi 2021] [Bennett 1990] [Branger 1972] [Bunton and Denegri 2000] [Bureau of Aeronautics (navy) Washingtondc 1949] [Caap and Elemeland 1986] [Cordeaux 1991] [Crites et al. 1992] [Design Sheets for New 2003] [Dollyhigh and Foss 1985] [Eberhardt 2005] [Fighter and Attack Aircraft 2008] [Fundamentals of Fighter Design 2001] [Griffin 2012] [Heiss et al. 1992] [Herbst 1980] [Jayakrishnan and Pant 2005] [Jenista and Bodden 1989] [Kitowski 1986] [Kuchar and Wolf 1993] [Kwon and Sankar 1991] [Kwon and Sankar 1992] [Lewis 2002] [Liddell 1950] [Madelung 1977] [Planeaux and Barth 1988] [Powers et al. 1983a] [Russell 2014] [Spearman 1983] [Spearman 1984] [Spearman et al. 1977] [Squires 2004] [St. Aubyn 2015] [Stanley 1980] [The Cutting Edge 1998] [The Potez Multi-Seater Fighter 1935] [Wages 1971] [Ward 1989] [Weirich and Rueger 1999] [Whitford 1991] [Whitford 1995]

Defence acquisition, prototyping and the arms trade

The literature for what happened to the programme. Military aircraft procurement and competition, prototyping policy, cost, and arms export and military assistance.

41 records. [A Comparison of Cost 1977] [Anicetti 2023] [Arthur W. 2022] [Beesly 1966] [Beesly 1966a] [Behavior Patterns of Three 2022] [Bennett 2003] [Boger and Nussbaum 1990] [Boger et al 1989] [Carey 1982] [Carlyle 1976] [Cate 2003] [Choi 2026] [Coble et al 2014] [Department Of Defense Washington Dc 1997] [Diphda and Wiswayana 2026] [Duddy et al. 2020] [Esau 2024] [Fast 2014] [Fellers and Patierno 1970] [Franck et al. 2012] [Gregory and Wilcox 1970] [Grytsyshen et al. 2025] [Harle 1979] [Hellemeier 2019] [Higham and Holley 1966] [Kaplan 1980] [Likhachev 2024] [Linden 2022] [Lorell 1989] [Military Presence and Arms 2025] [Phillips 1999] [Rosenthal 1975] [Rosenthal and Brandeau 1983] [Sowter 1973] [Taufik Budi Cahyana et al. 2023] [Thankachan 2025] [Um 2016] [Wardana et al. 2022] [Watkins 2019] [Yusof and Rahim 2017]

Thermal stress, thermal buckling and thermoelasticity

The heating as load. Thermal stress in skins and structures, thermal buckling, and the thermoelastic and aerothermoelastic coupling the article’s eighty-two kelvin figure belongs to.

34 records. [2016] [Ayers 1962] [Calligeros and Dugundji 1961] [Chai et al 2017] [Chai et al. 2020] [Chen and Xia 2022] [Cong et al. 2024] [Dixon et al. 1961] [Ganilova et al. 2021] [Ganilova et al 2022] [Gellatly and Gallagher 1964] [Gellatly et al 1965] [Gutiérrez Álvarez and Bisagni 2021] [Jenkins 1979] [Kang et al 2024] [Li et al 2015] [Loveless and Boswell 1954] [Ma 2021] [Mahlmeister et al 1955] [Mansfield 1967] [Matsumoto and Sekiya 1975] [Parkes 1953] [Parkes 1954] [Parkes 1956] [Parkes 1956] [Rivello 1965] [Sebata and Ushijima 2021] [Sebata and Ushijima 2022] [Shao et al. 2016] [Tani 1978] [Uthgenannt 1971] [Wang et al. 2023d] [Xie et al 2025] [Xue et al. 2020]

Boundary-layer control, high lift and short take-off

The low-speed end of the envelope. Blowing and suction, high-lift devices, and take-off and landing, on which the article’s take-off claim rests.

28 records. [Aerodynamic and Landing Measurements 1960] [Anglin and Satran 1980] [Baker 1966] [Cliett 1952] [Cordner 1967] [Desyatnik 2015] [Edwards 2010] [Goranson 1942] [Hawks 1982] [Horton et al. 1951] [Inger and Zee 1978] [Kuchinka 1966] [Kuz’mich et al. 1975] [Linnell 1963] [Muehter 1974] [Papadales and Basil S. 1979] [Probst and Melber-Wilkending 2021] [Radespiel et al. 2016] [Raspet 1957] [Roberts et al. 1966] [Rumsey et al. 2019] [Selegan 1983] [Sleeman 1961] [Smith et al 1979] [Spreemann 1958] [Thomas 1965] [Toll 1942] [Williams and Butler 1963]

Other aeronautical literature

The residual, reported and not hidden. On-subject work that belongs to no cluster above, being a wind tunnel and flight correlation of the XB-70. It is too small to name.

1 records. [Peterson 1982]

Where the Framing Breaks Down

The keystone framing is weaker here than anywhere else in this series and the reasons should be stated plainly.

There was no keystone, because there was no programme. A research aircraft’s keystone is the question its hardware was dimensioned against. The X-27’s hardware was never dimensioned against anything, because it was never built. The keystone treated here is a stated test objective in a proposal, a much softer thing.

The Mach 2.6 objective may not have been serious. A proposal written to attract funding names attractive numbers. The article has computed what Mach 2.6 would have required and found two obstacles, but it cannot establish that anyone at Lockheed intended to sustain that speed rather than to touch it briefly in a demonstration.

The manoeuvre comparison flatters the Lancer in one respect. It uses the manufacturer’s weights and the engine’s rated thrust. Manufacturer’s weights for an aircraft that was never built carry no allowance for the growth a built airframe may show, and installed thrust is below rated thrust by an inlet-and-nozzle allowance this article has not applied. Both errors push the same direction.

The comparison aircraft are not contemporaneous with each other. The F-15A entered service in 1976 [McDonnell Douglas F-15 Eagle], the F-5E in 1973 [Northrop F-5], and the CL-1200-2 never. Comparing them at a single flight condition is a comparison of designs and not of what any of them would have done against each other.

And the political reading is the softest thing in the article. That the arithmetic is consistent with the reported Air Force attitude is a consistency and not a cause. People are perfectly capable of opposing a programme for reasons unrelated to its specific excess power.

The Source Base

This article has a poorer source base than any other in the series and the reader should know it.

There is no primary literature about the subject. The National Aeronautics and Space Administration’s Technical Reports Server returns nothing for the CL-1200 or the Lancer. No wind-tunnel report exists in the open literature. No test report exists because no test occurred.

The vehicle facts come from secondary aviation history, principally Lockheed’s own estimates as published in Air Enthusiast in 1971 and quoted by the Lancer reference article, Buttler on American secret projects, Johnson for the Skunk Works memoir, and Jenkins for the surrounding experimental-aircraft context, and those sources disagree with one another on the matter of who wanted the X-designation, which the article reports rather than resolves.

The physics comes from primary literature about everything except the vehicle. Supersonic inlet design, conical flow, compressor stall, elevated-temperature alloy behaviour and fighter performance analysis are all richly documented in period reports and journals, and the article is built on those. That is the method this subject requires. The evidence is gathered on the physics rather than on the vehicle.

The engine and airframe numbers are the load-bearing figures and they come from reference sources rather than from documents. The 260 pounds per second, the four inches of spike travel and the weight breakdown are each stated in secondary literature without a cited primary source. The inlet agreement computed above is a check on their mutual consistency and is offered as partial corroboration of figures that are otherwise uncorroborated.

The research survey holds 2,244 research records drawn from Crossref, the NASA Technical Reports Server and the Defense Technical Information Center, of which 612 are report primaries, being 27.3 percent, by the identifier rule set out under The Definition of Primary. The median publication year is 2003. Of the 2,233 dated records, 805 were published in 1982 or earlier, the period in which the aircraft was proposed and its parent was in service, being 36.1 percent, and 1,000 were published in 2015 or later, being 44.8 percent.

Every figure in this article is given as a count and a fraction together, because a fraction moves with its denominator. A period count can stand still while its fraction falls, simply because the contemporary base around it is larger, and neither movement is a fact about coverage.

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when its address is on the NASA Technical Reports Server or it carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. The NACA and NASA reports on inlets, heating and the F-104 are report primaries under that rule. The rule does not reach the journal papers of the same period, such as the conical flow and supersonic diffuser papers of the 1950s, so 27.3 percent is a lower bound on how much of the survey is first-hand. No document of the X-27 programme itself is in the survey under any rule, for the reason given above.

Thin Subjects

Eight subjects that this article’s derivations depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms, with a hyphen read as a space. Where a row joins two groups of terms with the word together, a title must carry a term from each group.

Subject Title terms counted Records
the X-27 or the CL-1200 Lancer by name X-27, CL-1200, Lancer 0
the F-104 and its J79 engine F-104, Starfighter, J79 13
the optimum multi-shock system of Oswatitsch Oswatitsch, optimum shock, shock diffuser, shock diffusers 2
the corrected airflow of an engine corrected airflow, corrected air flow, corrected flow, corrected mass flow 0
corner speed and sustained turn rate corner speed, corner velocity, sustained turn, sustained turning 1
ram drag ram drag 1
2024 aluminium alloy when hot 2024 together with elevated temperature, elevated temperatures, high temperature, creep, heating, 500 F, hot 8
the international and export fighter competitions international fighter, export fighter, F-5E, Tiger II 1

The aircraft has no literature of its own. The survey agrees with the reports server, and every vehicle figure in this article rests on the secondary sources named above.

The parent is thin too. Of the 13 titles, 5 name the J79 and 3 concern experiments flown in the F-104 or equipment fitted to it, so the derivative argument rests on the parent’s published dimensions rather than on a body of F-104 analysis.

The optimum shock system is a classic with almost no successors by name. One of the two titles is Oswatitsch’s own report on the efficiency of shock diffusers and the other extends a different rule of his to unsteady flow, so the single-cone and two-ramp recoveries computed above rest on the original source.

The reconciliation of spike travel with airflow has no published counterpart. No title in the survey names a corrected airflow, so the 4.2 percent agreement above is the article’s own and cannot be compared with a published analysis.

The two quantities the turning argument turns on are almost never a title’s subject. The single title compares corner speed with the speed for best turn, and the rest of the turning literature is framed in terms of turn performance, energy manoeuvrability and agility.

Ram drag is almost never a title’s subject. The one title naming it concerns a laser-propelled lightcraft, and the subject otherwise appears under installed thrust and thrust and drag bookkeeping, which is where the subsection on it above places it.

The alloy’s hot strength is documented, but not for the temper the article uses. None of the 8 titles names a T8 temper, so the handbook figure for 2024-T81 after half an hour at temperature is the only source for the strength the structural argument uses.

The competition the Lancer lost has no technical literature. The one title naming the F-5E uses it as a research platform, so the comparison with the winner rests on the article’s own drag polars.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject. The records come from the National Aeronautics and Space Administration’s Technical Reports Server, the Defense Technical Information Center and the journal literature. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Agility also names agility in the organisational, sporting and software senses. Distortion also names distortion in the optical, statistical, electrical and perceptual senses. Procurement and acquisition also name the procurement of medical officers, drugs and military manpower and the acquisition of language skills and data, and the procurement budget books are excluded with them. Elevated temperature, thermoelasticity, aspect ratio, inlet and prototype also reach into medicine and biology, polymer physics, civil engineering and geology, batteries, piston engines and industrial compressors, ground power plants and plasma physics. An inlet is also the inflow boundary of a simulation or of a combustor, a pump is not a compressor, and the supersonic nozzle of a condensing separator or a steam turbine shares the inlet’s gas dynamics and none of its subject. Fighter also names fire fighters, freedom fighters and the pilots themselves as a subject of psychology and manpower, and Starfighter also names a film, a video game and cultivars of lettuce and lily. Drag also names a performance art, a clause in company law and the drag-reducing additives of pipelines, and Tiger names everything from the animal to a reentry test unit. A record is also excluded when its title carries this subject’s vocabulary but studies something the argument never uses. Air-combat tactics and manoeuvre decision algorithms take the aircraft’s performance as given and are excluded, while agility metrics and energy manoeuvrability are kept. Noise and acoustics, reentry and space vehicles, flight-control law design, engine accessories, test cells, combustors and engine health, ejector nozzles and thrust reversers, aircraft subsystems including fuel and equipment thermal systems, human factors, and acquisition administration that concerns neither competition, prototyping, cost nor export are excluded. So are design and handling studies of airliners and other transports, rotorcraft, vertical and short take-off aircraft, small unmanned aircraft, flying wings, missiles and projectiles when the title names no method or phenomenon this article uses, and materials work on welding, corrosion, forming, heat treatment and surface processing, steels, the alloys of power and nuclear plant, and the mechanics of graded and nanotube composites. Correction, erratum and withdrawal notices, journal issues, conference volumes, figure records, encyclopedia and dictionary entries, unsigned items, and trade and science news items are excluded as well, because a survey counts research works and not the notices and items attached to them. A signed comment on a paper, a discussion of a paper, the author’s closure or reply to it, and a signed letter on a research subject are research works, because each argues about a result, and they are admitted when their subject is the article’s. The residual cluster admits under the same rule and holds the on-subject records that no named cluster claims.

Some records of doubtful relevance are kept. The surge control of industrial centrifugal compressors is kept because surge is the same instability in any compression system, and studies that use the F-104 as a platform for other experiments are kept because they are part of the parent aircraft’s record. Titanium, nickel and refractory alloys at temperature are kept although many of their titles concern engines rather than airframes, because the review of hot structures above turns on the materials the X-27 did not have. Design-optimisation methods demonstrated on another vehicle are kept because the article argues that such methods are the modern answer to its central difficulty, and a reader may weigh all of these 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.

Epistemic State

Historical fact, well attested.

  • The CL-1200 Lancer was a Lockheed private venture derived from the F-104.
  • It was entered in the International Fighter Aircraft competition and Northrop’s design won in November 1970.
  • The designation X-27 was allocated in connection with a proposed demonstrator.
  • No aircraft was built. One full-scale mock-up was completed.
  • The CL-1200-2 was offered into the 1972 Lightweight Fighter competition, which selected the YF-16 and YF-17.
  • The X-27 was to have had rectangular intakes where the CL-1200 had translating cones.

Historical fact, reported but not independently corroborated here.

  • That up to three fuselages were worked before termination.
  • That the mock-up was of wood with a metal skin, which rests on a single account in aviation journalism.
  • That elements within the Air Force viewed the design as a complication for the F-15.
  • The published performance estimates, weights and dimensions, all of which trace to manufacturer’s figures reproduced in secondary sources.

Contested in the sources, and left contested.

  • Whether the Air Force sought the X-27 or Lockheed sought the designation. Both accounts appear in otherwise careful secondary sources and the article does not adjudicate.

Engineering analysis, computed here and reproducible from the stated inputs.

  • The recovery temperature at Mach 2.6 and the resulting strength retention.
  • The skin thermal time constant and the transient that follows from it.
  • The single-cone and two-ramp inlet recoveries, by integration of Taylor-Maccoll.
  • The implied cowl radius from the quoted spike travel and its agreement with the engine’s airflow.
  • The drag polar, sustained load factors, turn rates and specific excess power.
  • The Breguet range and the implied mission factor.

Inference, labelled as such.

  • The X-27’s rectangular intakes were adopted because one cone cannot meet the standard at Mach 2.6. The physics supports it and no document states it.
  • The fuselage stretch was driven partly by the engine’s greater length. The stretch is within three inches of the difference and the record attributes it to fuel.
  • That the reported Air Force concern about the F-15 was quantitatively reasonable. The arithmetic is consistent with it, which is not the same as establishing it.

Not established, and stated so.

  • Whether the aircraft would have reached Mach 2.6 at all.
  • Whether the TF30 would have proved acceptable behind that inlet.
  • What maximum lift coefficient the wing achieved, which is the weakest input above.
  • Whether any of the manufacturer’s estimates would have survived contact with a real airframe.

Out of Scope

  • The F-104’s accident record in European service, which is a substantial subject of its own and bears on the Lancer only through the handling inheritance.
  • The full history of the Lightweight Fighter programme and the YF-16 and YF-17, which belong with the articles on those designations.
  • The detailed design of the F-15, referenced here only as the aircraft the Lancer was said to threaten.
  • The politics of foreign military sales in the period, treated here only far enough to explain what the International Fighter Aircraft competition was for.
  • The CL-1400 and CL-1400N naval studies, for which the public record is thinner still.
  • Boyd’s biography and the wider reception of energy manoeuvrability, which the references cover.

Conclusion

The X-27 was a designation attached to an aeroplane that did not exist, issued for a research purpose, in support of a commercial one.

The technical question it named was real. A turbofan at Mach 2.6 behind an inlet descended from a Mach 2.0 turbojet installation, in an aluminium airframe, is a difficult proposition, and this article has computed two reasons why.

The inlet cannot meet the standard with one cone. The best single-cone arrangement falls 11.44 points short of the reference recovery at Mach 2.6, and that figure is a floor because the calculation charges nothing for viscosity. Two ramps recover 8.18 of those points, which would explain why the X-27’s intakes were to be rectangular.

The structure cannot hold its strength at that speed. The recovery temperature at Mach 2.6 is 210.8 degrees Celsius, where the handbook gives 2024-T81 aluminium alloy about 68 percent of its yield strength after half an hour, and the skin reaches nine-tenths of that in one minute, so a dash does not evade it.

Against that, the aeroplane was a better fighter than the one that beat it. On sustained turn rate and on specific excess power the Lancer clears the F-5E comfortably at every assumption tested, and sits within 4.2 percent of the F-15A’s specific excess power. The sales case was not fraudulent. It was not what the customers were buying, and no source cited here says that performance decided either competition.

And one thing in the record checks out with a precision this subject has no right to. Four inches of spike travel, quoted as an airframe feature, and 260 pounds per second of airflow, quoted as an engine rating, are reconciled by a twenty-five degree cone to within 4.2 percent. Nobody published that cone angle. Two numbers published for unrelated reasons agree through geometry connecting them, and that is the closest an aeroplane which never existed can come to leaving a measurement behind.

The next article treats the X-28, the Osprey I that the Navy evaluated as Project Air Skimmer, and returns to the pattern the X-27 broke, namely an aircraft that existed and flew.

Equations

This section collects the 87 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 87, 68 are established and 19 are bespoke. Lines mix International System units with the United States customary units of the record, with each conversion stated where it is made, the atmosphere is the International Standard Atmosphere, and the parasite drag of 0.0158, the leading-edge suction fraction, the maximum lift coefficient, the skin and material properties, the usable fuel fraction of 0.85 and the lift-to-drag ratio of the radius check are values the article assumes or scans across rather than measurements.

Equation 1, Aspect Ratio of the F-104G Wing. The documented span of 21.94 feet and wing area of 196.1 square feet give an aspect ratio of about 2.46. aspect ratio

\[A = \frac{b^2}{S} = \frac{(21.94\ \mathrm{ft})^2}{196.1\ \mathrm{ft}^2} = 2.455 \tag{1}\]

Equation 2, Wing Loading of the F-104G. The design gross weight of 27,300 pounds over the wing area gives a wing loading of 139.2 pounds per square foot, as the survey of aircraft performance also tabulates. Quest for Performance, NASA SP-468

\[\frac{W}{S} = \frac{27{,}300\ \mathrm{lb}}{196.1\ \mathrm{ft}^2} = 139.2\ \mathrm{lb/ft}^2 \tag{2}\]

Equation 3, Engine Length, Diameter and Airflow Differences. The published ratings give the TF30 33.01 inches more length and 9.84 inches more diameter than the J79, and about 53 percent more airflow. J79 TF30

\[\Delta L = 241.70 - 208.69 = 33.01\ \mathrm{in}, \qquad \Delta D = 48.90 - 39.06 = 9.84\ \mathrm{in}, \qquad \frac{\dot m_{\mathrm{TF30}}}{\dot m_{\mathrm{J79}}} - 1 = \frac{260}{170} - 1 = 0.529 \tag{3}\]

Equation 4, Engine Length Difference Less the Fuselage Stretch. The documented 30 inch stretch falls 3.01 inches short of the engine length difference. CL-1200 Lancer

\[\Delta L - \Delta L_{\mathrm{fus}} = 33.01 - 30 = 3.01\ \mathrm{in} \tag{4}\]

Equation 5, Temperature in the Standard Troposphere. Below 11 kilometres the standard temperature falls linearly from 288.15 kelvin at the standard lapse rate of 0.0065 kelvin per metre. Anderson Shapiro International Standard Atmosphere

\[T(h) = T_0 - \lambda h, \qquad T_0 = 288.15\ \mathrm{K}, \qquad \lambda = 0.0065\ \mathrm{K/m} \tag{5}\]

Equation 6, Pressure in the Standard Lower Stratosphere. Above the tropopause the standard temperature is constant and the pressure falls exponentially with height from its value at 11 kilometres.

\[p(h) = p_{11} \exp\left(-\frac{g_0 (h - h_{11})}{R T}\right) \tag{6}\]

Equation 7, Density at 35,000 Feet from the Equation of State. The ideal gas law at the standard pressure and temperature of 35,000 feet gives a density of about 0.380 kilograms per cubic metre.

\[\rho = \frac{p}{R T} = \frac{23{,}842.3}{287.05 \times 218.81} = 0.3796\ \mathrm{kg/m^3} \tag{7}\]

Equation 8, Speed of Sound at 35,000 Feet. The speed of sound at the standard temperature of 218.81 kelvin is about 296.5 metres per second.

\[a = \sqrt{\gamma R T} = \sqrt{1.4 \times 287.05\ \times 218.81} = 296.54\ \mathrm{m/s} = 663.3\ \mathrm{mph} \tag{8}\]

Equation 9, Mach Number. The Mach number is the ratio of airspeed to the speed of sound.

\[M = \frac{V}{a} \tag{9}\]

Equation 10, Mach Number of the Claimed Maximum Speed. The claimed 1,700 miles per hour at 35,000 feet is Mach 2.563, consistent with the quoted Mach 2.57. CL-1200 Lancer

\[M = \frac{1{,}700\ \mathrm{mph} \times 0.44704}{296.54\ \mathrm{m/s}} = \frac{760.0}{296.54} = 2.563 \tag{10}\]

Equation 11, Dynamic Pressure. The dynamic pressure is half the density times the square of the speed. Anderson

\[q = \tfrac{1}{2}\rho V^2 \tag{11}\]

Equation 12, Specific Heat at Constant Pressure. The specific heat at constant pressure of a perfect gas follows from the gas constant and the ratio of specific heats.

\[c_p = \frac{\gamma R}{\gamma - 1} = \frac{1.4 \times 287.05}{0.4} = 1004.7\ \mathrm{J/(kg\,K)} \tag{12}\]

Equation 13, Bespoke Dynamic Pressure at the Manoeuvre Condition. At 15,000 feet and Mach 0.9, the condition the article chooses for every manoeuvre result, the standard atmosphere gives a dynamic pressure of about 677 pounds per square foot.

\[q = \tfrac{1}{2} \times 0.7708 \times 290.0^2 = 32{,}415\ \mathrm{Pa} = 677.1\ \mathrm{lb/ft^2} \tag{13}\]

Equation 14, Total Temperature. Energy conservation in a compressible flow gives the total temperature as the static temperature times one plus half of $\gamma - 1$ times the square of the Mach number. total temperature

\[\frac{T_t}{T} = 1 + \frac{\gamma - 1}{2} M^2 \tag{14}\]

Equation 15, Recovery Temperature with a Turbulent Recovery Factor. A surface recovers only a fraction $r$ of the kinetic temperature rise, and for a turbulent boundary layer that fraction is the cube root of the Prandtl number. recovery factor Prandtl number

\[T_r = T\left(1 + r\,\frac{\gamma - 1}{2} M^2\right), \qquad r = \Pr^{1/3} \approx 0.896 \tag{15}\]

Equation 16, Celsius to Fahrenheit Conversion of the Recovery Temperature. The recovery temperature of 210.8 degrees Celsius is about 411 degrees Fahrenheit, the scale of the handbook figure. Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5J

\[T_{\mathrm{F}} = 1.8\,T_{\mathrm{C}} + 32, \qquad 1.8 \times 210.8 + 32 = 411.4\ ^{\circ}\mathrm{F} \tag{16}\]

Equation 17, Thermal Time Constant of a Lumped Skin Panel. A skin panel heated by convection behaves as a first-order lumped thermal mass whose time constant is its areal heat capacity over the convective coefficient.

\[\tau = \frac{\rho_s c_s t}{h} \tag{17}\]

Equation 18, Eckert Reference Temperature. The Eckert reference temperature at which boundary layer properties are evaluated accounts for property variation across a high-speed boundary layer. Eckert reference temperature

\[T^* = T_e\left(0.5\left(1 + \frac{T_w}{T_e}\right) + 0.16\,r\,\frac{\gamma-1}{2}M_e^2\right) \tag{18}\]

Equation 19, Turbulent Flat-Plate Stanton Number and Heat Transfer Coefficient. The turbulent flat-plate Stanton number correlation gives the convective coefficient from properties at the reference temperature. Stanton number Eckert reference temperature

\[\mathrm{St} = 0.0296\,\mathrm{Re}_x^{-1/5}\,\Pr^{-2/3}, \qquad h = \mathrm{St}\,\rho^* u_e c_p \tag{19}\]

Equation 20, Local Reynolds Number and Sutherland’s Law. The local Reynolds number is built from reference density, edge velocity and distance over the reference viscosity, which Sutherland’s law gives as a function of temperature. Anderson

\[\mathrm{Re}_x = \frac{\rho^* u_e x}{\mu^*}, \qquad \mu(T) = \frac{1.458 \times 10^{-6}\,T^{3/2}}{T + 110.4} \tag{20}\]

Equation 21, Bespoke Reynolds Number Five Metres Back from the Nose. At Mach 2.6 and 35,000 feet a station the article takes as five metres back from the nose has a Reynolds number of about $3.6 \times 10^7$.

\[\mathrm{Re}_x = \frac{0.2109 \times 771.0 \times 5.0}{2.2598 \times 10^{-5}} = 3.598 \times 10^{7} \tag{21}\]

Equation 22, Bespoke Thermal Time Constant of the Skin. A two-millimetre aluminium skin, a thickness the article assumes with representative density and specific heat, has a time constant of about 26 seconds.

\[\tau = \frac{2780 \times 875 \times 0.002}{185.5} = 26.2\ \mathrm{s} \tag{22}\]

Equation 23, First-Order Skin Temperature Transient. From a cold start the skin temperature approaches the recovery temperature exponentially with the thermal time constant.

\[T_{\mathrm{skin}}(t) = T_\infty + \left(T_r - T_\infty\right)\left(1 - e^{-t/\tau}\right) \tag{23}\]

Equation 24, Fully Restrained Thermal Stress. A fully restrained material heated through a temperature change carries a stress equal to Young’s modulus times the expansion coefficient times that change.

\[\sigma_{\mathrm{th}} = E\,\alpha\,\Delta T \tag{24}\]

Equation 25, Bespoke Fully Restrained Thermal Stress at Mach 2.6. With a modulus of 72 gigapascals and an expansion coefficient of 23 parts per million per kelvin taken as representative of aluminium alloy, the full excursion to the recovery temperature gives about 316 megapascals.

\[\sigma_{\mathrm{th}} = 72 \times 10^{9} \times 23 \times 10^{-6} \times 190.8 = 316\ \mathrm{MPa} \tag{25}\]

Equation 26, Bespoke Retained Yield Strength and Stress Ratio. The handbook room-temperature yield of 58 kilopounds per square inch times the 68 percent retained at temperature is about 272 megapascals, which the representative fully restrained stress exceeds by sixteen percent. Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5J

\[\sigma_{\mathrm{yield}}(T_r) = 0.68 \times 58\ \mathrm{ksi} \times 6.895\ \frac{\mathrm{MPa}}{\mathrm{ksi}} = 0.68 \times 400\ \mathrm{MPa} = 272\ \mathrm{MPa}, \qquad \frac{316}{272} = 1.16 \tag{26}\]

Equation 27, Bespoke Temperature Differential Consuming Half the Strength. Inverting the thermal stress relation with the representative modulus and expansion coefficient shows that 82 kelvin of differential consumes half the retained yield.

\[\Delta T_{1/2} = \frac{0.5\,\sigma_{\mathrm{yield}}(T)}{E\,\alpha} = \frac{0.5 \times 272 \times 10^{6}}{72 \times 10^{9} \times 23 \times 10^{-6}} = 82\ \mathrm{K} \tag{27}\]

Equation 28, Total-Pressure Recovery. Total-pressure recovery is the ratio of total pressure at the engine face to free-stream total pressure. total-pressure recovery Seddon and Goldsmith

\[\eta = \frac{p_{t2}}{p_{t\infty}} \tag{28}\]

Equation 29, Military Specification Reference Recovery. The military specification reference recovery falls below one as a power of the supersonic excess of the Mach number. Inlet Performance, NASA Glenn Research Center

\[\eta_{\mathrm{ref}} = 1 - 0.075\,(M - 1)^{1.35}, \qquad M > 1 \tag{29}\]

Equation 30, Normal Shock Total-Pressure Ratio. The total-pressure ratio across a normal shock has a closed form in the upstream Mach number and the ratio of specific heats. normal shock pitot inlet

\[\frac{p_{t2}}{p_{t1}} = \left[\frac{(\gamma+1)M^2}{2 + (\gamma-1)M^2}\right]^{\frac{\gamma}{\gamma-1}} \left[\frac{\gamma+1}{2\gamma M^2 - (\gamma-1)}\right]^{\frac{1}{\gamma-1}} \tag{30}\]

Equation 31, Pitot Inlet Recovery at Mach 2.0 and 2.6. A pitot inlet recovers about 0.72 of the total pressure at Mach 2.0 and 0.46 at Mach 2.6.

\[\eta_{\mathrm{pitot}}(2.0) = 0.7209, \qquad \eta_{\mathrm{pitot}}(2.6) = 0.4601 \tag{31}\]

Equation 32, Taylor-Maccoll Radial Velocity Equation. In the Taylor-Maccoll formulation the derivative of the normalised radial velocity with respect to the polar angle equals the normalised polar velocity. Taylor-Maccoll equation

\[\frac{dV_r'}{d\theta} = V_\theta' \tag{32}\]

Equation 33, Taylor-Maccoll Polar Velocity Equation. The second Taylor-Maccoll equation gives the derivative of the normalised polar velocity, with the local speed of sound from the adiabatic energy equation. Taylor-Maccoll equation

\[\frac{dV_\theta'}{d\theta} = \frac{V_r' V_\theta'^2 - a'^2\left(2V_r' + V_\theta' \cot\theta\right)}{a'^2 - V_\theta'^2}, \qquad a'^2 = \frac{\gamma-1}{2}\left(1 - V_r'^2 - V_\theta'^2\right) \tag{33}\]

Equation 34, Normal Mach Component of an Oblique Shock. An oblique shock acts on the component of the upstream Mach number normal to the wave.

\[M_{n1} = M_1 \sin\beta \tag{34}\]

Equation 35, Downstream Mach Number of an Oblique Shock. The downstream Mach number follows from the normal shock relation applied to the normal component and the turned flow direction. Shapiro Anderson Seddon and Goldsmith

\[M_{2}^{2} = \frac{1 + \frac{\gamma-1}{2}M_{n1}^{2}}{\gamma M_{n1}^{2} - \frac{\gamma-1}{2}} \bigg/ \sin^{2}(\beta - \theta_d) \tag{35}\]

Equation 36, Mach Angle. The wave angle cannot fall below the Mach angle, whose sine is the reciprocal of the Mach number, 30.00 degrees at Mach 2.0 and 22.62 at Mach 2.6. Shapiro Anderson Seddon and Goldsmith

\[\mu = \arcsin\frac{1}{M}, \qquad \mu(2.0) = 30.00^\circ, \qquad \mu(2.6) = 22.62^\circ \tag{36}\]

Equation 37, Theta-Beta-Mach Relation. The oblique shock relation gives the flow deflection angle from the wave angle and the upstream Mach number. oblique shock

\[\tan\theta_d = 2\cot\beta\,\frac{M_1^2 \sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2} \tag{37}\]

Equation 38, Recovery of a Two-Ramp Inlet. The recovery of a two-ramp inlet is the product of the total-pressure ratios across its two oblique shocks and the terminal normal shock.

\[\eta_{\mathrm{2-ramp}} = \frac{p_{t2}}{p_{t1}}\bigg|_{\delta_1} \cdot \frac{p_{t3}}{p_{t2}}\bigg|_{\delta_2} \cdot \frac{p_{t4}}{p_{t3}}\bigg|_{\mathrm{normal}} \tag{38}\]

Equation 39, Oswatitsch Equal-Strength Condition. For a given number of oblique shocks the recovery is greatest when the shocks have equal normal Mach components. Oswatitsch

\[M_1 \sin\beta_1 = M_2 \sin\beta_2 = \cdots = M_n \sin\beta_n \tag{39}\]

Equation 40, Shock-on-Lip Condition. The shock from a cone apex a distance $L$ ahead of a lip at radius $r$ meets the lip when the tangent of the wave angle is their ratio.

\[\tan\beta = \frac{r}{L} \qquad \Longrightarrow \qquad L = \frac{r}{\tan\beta} \tag{40}\]

Equation 41, Cone Travel Between Two Mach Numbers. Holding the shock on the lip at two Mach numbers requires a travel equal to the lip radius times the difference of the cotangents of the two wave angles. Seddon and Goldsmith

\[\Delta L = r\left(\cot\beta_{\mathrm{hi}} - \cot\beta_{\mathrm{lo}}\right) \tag{41}\]

Equation 42, Bespoke Lip Radius Implied by the Documented Travel. Inverting the travel relation on the documented four inches, with the shock taken to be held on the lip from Mach 2.0 to Mach 2.6, gives the lip radius.

\[r = \frac{\Delta L}{\cot\beta_{\mathrm{hi}} - \cot\beta_{\mathrm{lo}}} \tag{42}\]

Equation 43, Capture Area for a Given Mass Flow. The capture area needed to admit a mass flow at full capture is that flow over the free-stream mass flux.

\[A_c = \frac{\dot m}{\rho_\infty V_\infty} \tag{43}\]

Equation 44, Capture Area Required by the TF30 at Mach 2.0. The documented 117.93 kilograms per second over the standard free-stream mass flux at Mach 2.0 and 35,000 feet needs about 5.64 square feet of capture. TF30

\[A_c = \frac{117.93}{225.0} = 0.524\ \mathrm{m}^2 = 5.639\ \mathrm{ft}^2 \tag{44}\]

Equation 45, Bespoke Capture Area Error at a 25 Degree Cone. At a cone half-angle the article assumes as 25 degrees, the capture area implied by the travel falls 4.2 percent short of the engine’s requirement.

\[\varepsilon = \frac{A_{\mathrm{travel}} - A_c}{A_c} = \frac{5.401 - 5.639}{5.639} = -0.042 \tag{45}\]

Equation 46, Corrected Airflow. Corrected airflow is the physical airflow times the square root of the total temperature ratio over the total pressure ratio to sea-level standard values. corrected flow

\[\dot m_{\mathrm{corr}} = \frac{\dot m \sqrt{\theta}}{\delta}, \qquad \theta = \frac{T_{t2}}{288.15}, \qquad \delta = \frac{p_{t2}}{101325} \tag{46}\]

Equation 47, Energy Height. The energy height is the altitude plus the kinetic energy per unit weight.

\[h_e = h + \frac{V^2}{2g} \tag{47}\]

Equation 48, Bespoke Energy Height at the Manoeuvre Condition. At 15,000 feet and Mach 0.9, a condition the article takes as representative of combat, the energy height is about 8,860 metres.

\[h_e = 4{,}572 + \frac{290.0^2}{2 \times 9.80665} = 4{,}572 + 4{,}289 = 8{,}861\ \mathrm{m} = 29{,}072\ \mathrm{ft} \tag{48}\]

Equation 49, Specific Excess Power. The specific excess power is the rate of change of energy height, the speed times excess thrust over weight. specific excess power

\[P_s = \frac{dh_e}{dt} = V\,\frac{T - D}{W} \tag{49}\]

Equation 50, Thrust-to-Weight Ratio of the CL-1200-2. The rated 25,000 pounds of thrust over the normal loaded weight of 24,385 pounds is a thrust-to-weight ratio of about 1.03.

\[\frac{T}{W} = \frac{25{,}000\ \mathrm{lbf}}{24{,}385\ \mathrm{lb}} = 1.025 \tag{50}\]

Equation 51, Parabolic Drag Polar. The drag coefficient is a parasite term plus an induced factor times the square of the lift coefficient.

\[C_D = C_{D_0} + K C_L^2 \tag{51}\]

Equation 52, Bespoke Parasite Drag Coefficient Used for All Four Aircraft. An equivalent skin-friction coefficient of 0.0035 on a wetted-to-reference area ratio of 4.5 gives 0.0158, a value the article holds equal across the four aircraft as a deliberate control. Raymer

\[C_{D_0} = C_{fe}\,\frac{S_{\mathrm{wet}}}{S_{\mathrm{ref}}} = 0.0035 \times 4.5 = 0.0158 \tag{52}\]

Equation 53, Induced Drag Factor with Full Leading-Edge Suction. With full leading-edge suction the induced drag factor is the elliptical result of one over pi times aspect ratio times efficiency.

\[K_{\mathrm{full}} = \frac{1}{\pi A e} \tag{53}\]

Equation 54, Induced Drag Factor with No Leading-Edge Suction. With no leading-edge suction the resultant force tilts back with the surface and the induced drag factor is the reciprocal of the lift-curve slope. Raymer Nicolai

\[K_{\mathrm{none}} = \frac{1}{C_{L_\alpha}} \tag{54}\]

Equation 55, Helmbold-Diederich Lift-Curve Slope. The Helmbold-Diederich form gives the lift-curve slope of a low-aspect-ratio swept wing with a compressibility correction. Helmbold-Diederich Raymer Nicolai

\[C_{L_\alpha} = \frac{2\pi A}{2 + \sqrt{4 + \dfrac{A^2\beta^2}{\eta^2}\left(1 + \dfrac{\tan^2\Lambda_{c/2}}{\beta^2}\right)}}, \qquad \beta = \sqrt{|1 - M^2|} \tag{55}\]

Equation 56, Leading-Edge Suction Blend of the Induced Drag Factor. The induced drag factor is a blend of the full-suction and zero-suction limits weighted by the leading-edge suction fraction $s$. Raymer

\[K = s\,K_{\mathrm{full}} + (1 - s)\,K_{\mathrm{none}}, \qquad 0 \le s \le 1 \tag{56}\]

Equation 57, Lift Coefficient at Load Factor. The lift coefficient required at load factor $n$ is $n$ times the weight over dynamic pressure times wing area.

\[C_L = \frac{n W}{q S} \tag{57}\]

Equation 58, Sustained Load Factor. Setting thrust equal to drag at the required lift coefficient gives the sustained load factor in terms of thrust-to-weight, the polar and the dynamic pressure.

\[n_{\mathrm{sus}} = \sqrt{\frac{q S}{K W}\left(\frac{T}{W} - \frac{q S C_{D_0}}{W}\right)} \tag{58}\]

Equation 59, Turn Rate. The turn rate in a level turn is gravity times the square root of the squared load factor less one, over the speed.

\[\dot\psi = \frac{g\sqrt{n^2 - 1}}{V} \tag{59}\]

Equation 60, Turn Radius. The radius of a level turn is the speed squared over gravity times the square root of the squared load factor less one.

\[R = \frac{V^2}{g\sqrt{n^2 - 1}} \tag{60}\]

Equation 61, Load Factor and Bank Angle in a Level Turn. In a level turn the load factor is the reciprocal of the cosine of the bank angle.

\[n = \frac{1}{\cos\phi} \tag{61}\]

Equation 62, Bespoke Bank Angle and Turn Radius of the Lancer. At the sustained load factor of 6.34 that the article’s constructed polar gives at the manoeuvre condition, the bank is about 81 degrees and the radius about 1,370 metres.

\[\phi = \arccos\frac{1}{6.34} = 80.9^\circ, \qquad R = \frac{290.0^2}{9.80665\sqrt{6.34^2 - 1}} = 1{,}371\ \mathrm{m} = 4{,}496\ \mathrm{ft} \tag{62}\]

Equation 63, Evaluation Weights as Fractions of Maximum Weight. The tabulated evaluation weights are 0.94, 0.77, 0.65 and 0.70 of the maximum weights of the F-104G, F-5E, F-15A and CL-1200-2. Quest for Performance, NASA SP-468

\[\frac{27{,}300}{29{,}083} = 0.939, \qquad \frac{15{,}745}{20{,}486} = 0.769, \qquad \frac{44{,}500}{68{,}000} = 0.654, \qquad \frac{24{,}385}{35{,}000} = 0.697 \tag{63}\]

Equation 64, Bespoke Specific Excess Power Shortfall Relative to the F-15A. At a leading-edge suction fraction of 0.5 and the common parasite drag control the Lancer’s specific excess power is 4.2 percent below the F-15A’s. Lightweight Fighter

\[1 - \frac{P_{s,\mathrm{CL\text{-}1200\text{-}2}}}{P_{s,\mathrm{F\text{-}15A}}} = 1 - \frac{830}{866} = 0.042 \tag{64}\]

Equation 65, Corner Speed. The corner speed is the lowest speed at which the structural limit load factor can be reached at the maximum lift coefficient.

\[V^* = \sqrt{\frac{2\,n_{\mathrm{limit}}\,W}{\rho\,S\,C_{L_{\max}}}} \tag{65}\]

Equation 66, Stall Speed and Corner Speed. The stall speed is the corner speed relation at a load factor of one, so the corner speed is the square root of the limit load factor times the stall speed. Raymer Nicolai

\[V_{\mathrm{stall}} = \sqrt{\frac{2W}{\rho\,S\,C_{L_{\max}}}} , \qquad V^{*} = \sqrt{n_{\mathrm{limit}}}\;V_{\mathrm{stall}} \tag{66}\]

Equation 67, Net Thrust of a Jet Engine. The net thrust is the mass flow times the difference of exhaust and flight velocities, the second term being the ram drag.

\[F_{\mathrm{net}} = \dot m\left(V_e - V_0\right) \tag{67}\]

Equation 68, Ram Drag at Mach 2.6. The documented TF30 airflow at the standard free-stream speed for Mach 2.6 at 35,000 feet carries a ram drag of about 20,400 pounds.

\[D_{\mathrm{ram}} = \dot m V_0 = 117.93 \times 771.0 = 90{,}926\ \mathrm{N} = 20{,}441\ \mathrm{lbf} \tag{68}\]

Equation 69, Bespoke Exhaust Velocity to Hold the Rated Thrust at Mach 2.6. If the sea-level net thrust rating were held at Mach 2.6, a supposition the article tests rather than asserts, the exhaust velocity would have to be about 1,710 metres per second.

\[V_e = \frac{F_{\mathrm{net}} + \dot m V_0}{\dot m} = \frac{111{,}206 + 90{,}926}{117.93} = 1{,}714\ \mathrm{m/s} \tag{69}\]

Equation 70, Static Exhaust Velocity at the Rated Thrust. The rated net thrust over the documented airflow at rest implies an exhaust velocity of about 943 metres per second.

\[V_{e,\,\mathrm{static}} = \frac{F_{\mathrm{net}}}{\dot m} = \frac{111{,}206}{117.93} = 943\ \mathrm{m/s} \tag{70}\]

Equation 71, Bespoke Propulsive Efficiency at Mach 2.6. The Froude propulsive efficiency at the hypothetical exhaust velocity that holds the rated thrust at Mach 2.6 is about 0.62.

\[\eta_p = \frac{2V_0}{V_0 + V_e} = \frac{2 \times 771.0}{771.0 + 1714} = 0.621 \tag{71}\]

Equation 72, Lift. Lift is the lift coefficient carried on the dynamic pressure and the wing area. Hoerner Kuchemann

\[L = q\,S\,C_L \tag{72}\]

Equation 73, Horizontal Tail Volume Coefficient. The horizontal tail volume coefficient is the tail area times the tail arm over the wing area times the mean aerodynamic chord.

\[V_H = \frac{S_t\,l_t}{S\,\bar{c}} \tag{73}\]

Equation 74, Tail Contribution to Pitch Stiffness. The tail contributes to pitch stiffness in proportion to its lift-curve slope, its volume coefficient, its efficiency and one minus the downwash gradient.

\[C_{m_\alpha,\,\mathrm{tail}} = -a_t\,V_H\,\eta_t\left(1 - \frac{d\varepsilon}{d\alpha}\right) \tag{74}\]

Equation 75, Static Margin. The static margin is the negative ratio of pitch stiffness to lift-curve slope, equal to the distance from centre of gravity to neutral point over the mean aerodynamic chord.

\[\mathrm{SM} = -\frac{C_{m_\alpha}}{C_{L_\alpha}} = \frac{x_{np} - x_{cg}}{\bar{c}} \tag{75}\]

Equation 76, Far-Field Downwash Gradient. The far-field downwash gradient is approximately twice the lift-curve slope over pi times the aspect ratio.

\[\frac{d\varepsilon}{d\alpha} \approx \frac{2\,C_{L_\alpha}}{\pi A} \tag{76}\]

Equation 77, Specific Excess Power as a Ceiling on Climb Rate. Differentiating the energy height and holding speed constant leaves the climb rate equal to the specific excess power, which is therefore its ceiling. Whitford

\[\frac{dh_e}{dt} = \frac{dh}{dt} + \frac{V}{g}\frac{dV}{dt} = P_s \qquad \Longrightarrow \qquad \left.\frac{dh}{dt}\right|_{\max} = P_s \tag{77}\]

Equation 78, Bespoke Excess of the Climb Claim over the Computed Ceiling. The claimed 60,000 feet per minute exceeds by 21.6 percent the largest specific excess power that the article’s constructed polar and the published thrust and weight produce.

\[\frac{\dot h_{\mathrm{claim}}}{P_{s,\max}} - 1 = \frac{60{,}000}{49{,}332} - 1 = 0.216 \tag{78}\]

Equation 79, Bespoke Excess over a Coarse Mach Scan. A coarse scan that stops at Mach 1.2 takes the peak of the constructed specific excess power as 48,585 feet per minute and overstates the excess at 23.5 percent.

\[\frac{60{,}000}{48{,}585} - 1 = 0.235 \tag{79}\]

Equation 80, Clean Disposable Load of the Lancer. The normal loaded weight less the empty weight gives a clean disposable load of 6,500 pounds. CL-1200 Lancer

\[W_{\mathrm{fuel,\ clean}} = W_{\mathrm{loaded}} - W_{\mathrm{empty}} = 24{,}385 - 17{,}885 = 6{,}500\ \mathrm{lb} \tag{80}\]

Equation 81, Takeoff Ground Roll Integral. The ground roll is the integral of speed over acceleration up to lift-off speed, with the acceleration set by thrust less drag and rolling friction.

\[s = \int_0^{V_{\mathrm{LOF}}} \frac{V\,dV}{a(V)}, \qquad a(V) = \frac{T - D - \mu\left(W - L\right)}{W/g} \tag{81}\]

Equation 82, Lift-Off Speed. The lift-off speed is taken by the usual sizing convention as 1.1 times the stall speed.

\[V_{\mathrm{LOF}} = 1.1\,V_{\mathrm{stall}} \tag{82}\]

Equation 83, Breguet Range Equation. The Breguet range is speed over specific fuel consumption times the lift-to-drag ratio times the logarithm of the start to end weight ratio. Breguet range equation Raymer Nicolai

\[R = \frac{V}{c_t}\,\frac{L}{D}\,\ln\frac{W_0}{W_1} \tag{83}\]

Equation 84, Fuel Weight on the Radius Mission. The maximum takeoff weight less the empty weight and the 4,000 pound bombload leaves 13,115 pounds of fuel. CL-1200 Lancer

\[W_{\mathrm{fuel}} = W_0 - W_{\mathrm{empty}} - W_{\mathrm{stores}} = 35{,}000 - 17{,}885 - 4{,}000 = 13{,}115\ \mathrm{lb} \tag{84}\]

Equation 85, Bespoke End Weight of the Radius Mission. Burning a usable fuel fraction the article takes as 0.85 leaves an end weight of about 23,850 pounds.

\[W_1 = W_0 - f\,W_{\mathrm{fuel}} = 35{,}000 - 0.85 \times 13{,}115 = 23{,}852\ \mathrm{lb} \tag{85}\]

Equation 86, Bespoke Breguet Weight Ratio. The start weight over the end weight that the assumed usable fuel fraction gives is about 1.47.

\[\frac{W_0}{W_1} = \frac{35{,}000}{23{,}852} = 1.4674 \tag{86}\]

Equation 87, Bespoke Mission Factor. The article defines the mission factor as the claimed combat radius over the still-air Breguet range, about 0.19 at an assumed lift-to-drag ratio of 8 and specific fuel consumption of 0.85 per hour.

\[k_m = \frac{R_{\mathrm{combat}}}{R_{\mathrm{still\,air}}} = \frac{367}{1{,}914} = 0.192 \tag{87}\]

Notation

  • $A$, the wing aspect ratio
  • $b$, the wing span
  • $S$, the wing reference area
  • $W$, the weight, with $W_0$ and $W_1$ the start and end weights in the Breguet relation
  • $\lambda$, the temperature lapse rate in the standard atmosphere
  • $R T$, the specific gas constant $R$ times the temperature $T$
  • $\rho$, the air density
  • $a$, the speed of sound
  • $\gamma$, the ratio of specific heats, taken as 1.4 for air
  • $M$, the Mach number
  • $q$, the dynamic pressure
  • $c_p$, the specific heat at constant pressure
  • $T_t$, the total temperature
  • $T_r$, the recovery temperature
  • $\Pr$, the Prandtl number
  • $\tau$, the thermal time constant of the skin
  • $T^*$, the Eckert reference temperature
  • $\mathrm{St}$, the Stanton number
  • $\mathrm{Re}_x$, the local Reynolds number
  • $\sigma_{\mathrm{th}}$, the fully restrained thermal stress
  • $E\,\alpha$, the product of Young’s modulus and the coefficient of thermal expansion
  • $\eta$, the total-pressure recovery
  • $p_{t2}$, the total pressure at the engine face or behind a shock
  • $\beta$, the shock wave angle in the inlet relations and $\sqrt{ 1 - M^2 }$ in the lift-curve slope relation
  • $\theta_d$, the flow deflection angle across an oblique shock
  • $\mu$, the Mach angle in Equation 36, the viscosity in Equation 20 and the rolling friction coefficient in Equation 81
  • $A_c$, the inlet capture area
  • $\dot m$, the engine mass flow
  • $h_e$, the energy height
  • $P_s$, the specific excess power
  • $C_{D_0}$, the parasite drag coefficient
  • $K$, the induced drag factor
  • $C_{L_\alpha}$, the lift-curve slope
  • $n$, the load factor
  • $V^*$, the corner speed
  • $C_{L_{\max}}$, the maximum lift coefficient
  • $V_e$, the exhaust velocity, with $V_0$ the flight velocity
  • $\eta_p$, the propulsive efficiency
  • $V_H$, the horizontal tail volume coefficient
  • $\bar{c}$, the mean aerodynamic chord
  • $\mathrm{SM}$, the static margin as a fraction of the mean aerodynamic chord
  • $x_{np}$, the longitudinal position of the neutral point, with $x_{cg}$ that of the centre of gravity
  • $\frac{d\varepsilon}{d\alpha}$, the downwash gradient at the tail
  • $c_t$, the thrust specific fuel consumption
  • $k_m$, the mission factor

References

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