Shape the flow.
Account for the energy.

Could electrodes collect the 515.7 kJ/kg?

Simple version: Imagine a fast ball slowing down. Its motion energy changes form; a nearby wire does not automatically catch that energy as electricity. In this ideal inlet model, the air's motion energy becomes a change in the air's pressure-and-temperature energy. No electrical energy is produced.

What the number means

At the model's default Mach 5 inlet and Mach 2 outlet, 515.7 kJ per kilogram is the calculated decrease in flow kinetic energy. The model gives an equal increase in static enthalpy and keeps total enthalpy constant. It is an energy-accounting result for the stated perfect-gas assumptions, not a measured store of electricity or a prediction for an actual vehicle.

What an MHD generator would add

A magnetohydrodynamic (MHD) generator is a separate process: a sufficiently electrically conductive gas moving through a magnetic field can produce electrical output. Extracting energy brakes the gas. The conductivity, magnetic-field system, pressure loss, cooling and electrical conversion all affect the complete energy balance. Ordinary passive electrodes in air do not convert the inlet's pressure or temperature rise directly into electricity.

What has been demonstrated

A short-duration ground test ran a scramjet combustor with an MHD generator installed downstream in hot exhaust at simulated Mach-8 conditions. The public reports give figures with different levels of detail and access; keep each number attached to its own source.

The retained 32-page AFRL preprint copy provides useful boundary detail: for Test 3, 6.52 kW was dissipated at the load bank, 14.38 kW is a post-test active-channel estimate excluding end losses, and 14.80 kW is the calculated matched-load maximum. The paper abstract describes 14.8 kW as a peak electric output, but its Table VI and notes classify the 14.80-kW value as analysis rather than the measured load-bank point. General Atomics separately reports a preliminary 15-kW peak over the active section; closeness in scale does not prove identical processing or measurement boundary. AFRL's 2-10-kW summary range is compatible in scale with load-bank readings across the listed tests, but does not identify a matching output definition. Its separate summary phrase that output was “limited only” by rig mass flow is summary wording for that demonstration, not a general scaling law: the detailed report discusses combustion efficiency, plasma and ionization conditions, possible seeding variation, and electrical losses; it also states that NaK seed flow was not directly measured (Table VI, printed p. 27 / PDF p. 29; discussion, printed p. 29 / PDF p. 31). These caveats do not establish a vehicle-level power or thrust benefit. AFRL summary · official report record. The 2008 journal analysis of HVEPS Run 3 discusses measured load current and voltage and voltage differences along the channel; it does not close vehicle-bus power or provide a complete uncertainty budget. Retained third-party indexed preprint copy; selected Table VI rows checked against the official NTIS/NTRL PDF | Ishikawa et al. (2008), pp. 1444-47. These are short-duration ground-test generator results, not flight performance or an inlet-to-generator-to-accelerator demonstration.

Two plotted traces from one labelled HVEPS run

Simple version: The paper draws two lines for electricity sent to a resistor. It explains how the fast DAQ power trace was made. It says the Fluke backup meter recorded terminal voltage, but does not explain how that second line was converted to power. So that line cannot be an independent power check. The report links “Run 3” to Test No. 3 (UTRC 213.3); the plotted readings are not the original data file.

What energy would these plotted lines imply?

Simple version: Power tells us how fast energy moves. Add the little slices under a power-versus-time line and we estimate energy. Across the 3.9 seconds sampled (19.1 to the 23.0-second plot edge), the DAQ curve suggests about 11.6 kJ dissipated in the resistor. The Fluke-labeled curve would imply about 10.3 kJ only if its plotted values are power; the report does not document that calculation. This window is not shown to match the test's nominal three-second power interval.

Graph-read trapezoid estimates for the Figure 18 Run 3 load dump

Source trace	Conditional energy estimate over 19.1–23.0 s	Amplitude-only sensitivity	Exact base-12 form of graph-read rational
Filtered 1 kHz DAQ, 21 plotted samples	about 11.6 kJ (unrounded calculation: 11.6205 kJ)	10.8405–12.4005 kJ	B.7542830A44BAA214165225B5…₁₂
Source-labeled 50 Hz Fluke curve, 21 graph-read samples	about 10.3 kJ (unrounded calculation: 10.271 kJ)	9.491–11.051 kJ	A.3303557B7485461889B98428…₁₂

Method: composite trapezoidal integration of the graph-read samples; 1 kW·s = 1 kJ. The first 0.1 s after the plot's 19 s boundary is unsampled and excluded; the final point sits at the 23 s plot edge. The sensitivity column shifts every ordinate together by ±0.2 kW across the 3.9 s sampled span. It is only an amplitude sensitivity check: not a confidence interval, not a complete uncertainty bound, and not instrument uncertainty. The source labels both curves as external load-dump power, but does not document the Fluke curve’s power calculation or current pairing. Do not treat it as an independent power measurement, or add or average the curves. This is energy dissipated in a ground-test resistor, not energy recovered for a vehicle bus. Table VI separately reports 6.52 kW for Test No. 3; its 57.82 A and 1.95 ohm give 6.519 kW by I-squared-R, consistent with that rounded table value. Figure 18's graph ends at 6 kW, so it cannot verify 6.52 kW exactly. The paper says its post-test analysis averaged 100 filtered 1 kHz samples from a subjectively chosen maximum-power region, while this integral covers 3.9 plotted seconds. The paper does not publish exact sample indices or tie Figure 18's 19-23 s axis to Table IV's nominal three-second power-generation hold. These are related views of the same test, but not a reconciled power history or a measured three-second energy total. The report crosswalks Run 3 to Test No. 3 (UTRC 213.3) through Table V and Figure 27; the plot still supplies no raw DAQ file or calibration package. Figure 18 spans 0–6 kW, so its graph-read trace cannot verify Table VI's 6.52 kW exactly. Table VI's 57.82 A and 1.95 ohm are internally consistent with 6.519 kW by I-squared-R. The report says 100 filtered 1 kHz samples from a subjectively selected maximum-power region were averaged for post-test analysis, but does not publish their indices. Its Figure 18 19–23 s axis is not linked to Table IV's nominal three-second hold; this 3.9-second integral is not an exact reconciliation or measured three-second energy total. Base-12 digits are exact conversions of the decimal graph-read rationals (DAQ 23241/2000 kJ; Fluke 10271/1000 kJ); they encode the same approximate readings and add no physical precision. Integrated values and sensitivity method · CSV · Full digitization and integration methods · JSON.

What the original report labels: Figure 16 contains raw terminal voltage and current traces explicitly identified as Test No. 1. Figure 18 contains load-dump power labelled Run 3, not a raw voltage/current pair; Table V maps Test No. 3 to UTRC 213.3 and Figure 27 explicitly labels the Run 3 model/data set as Test No. 3. Do not use Figure 18 to claim a reconstructed Test 3 trace or a complete power balance. A separate indexed extract attributed to AFRL-PR-WP-TP-2007-232 mixed in a voltage/current Figure 2 caption, but that report number belongs to Thibodeaux's distinct space-charge study (ADA473277, AIAA 2007-4518); the official HVEPS report is AFRL-PR-WP-TP-2007-233 (ADA471429), whose Figure 2 is a combustor-rig schematic. Official NTIS/NTRL record for the separate 2007-232 report · Thibodeaux AIAA 2007-4518 metadata · HVEPS test-results paper, AIAA 2007-3880. Some secondary citations show 3881; DOI registration supports 3880.

What experiments measured — and what the cycle still needs

Simple version: A generator can take some electricity from hot, moving gas. But the whole engine only helps if its returned benefit is worth the extra power, heat, pressure loss and equipment needed to make it work.

What the official HVEPS report says: its best reported test separates three different quantities. Test 3 has 6.52 kW reported load-bank dissipation (reduced from recorded electrical channels; consistent with the listed 57.82 A and 1.95 Ω via I²R ≈ 6.52 kW); a post-test analysis estimated 14.38 kW across the active channel after excluding end-region losses; and Table VI gives 14.80 kW at a matched load, its maximum for the 89.0% mean-combustion case. At 81.5% and 96.5% combustion efficiency, its low/high analyses give 15.98 and 15.19 kW, respectively. All three matched-load figures are post-test calculations, not measured load-bank outputs; 14.80 kW should not be described as the directly measured load-bank output. The abstract calls 14.8 kW an electric-output peak, but Table VI and its notes place 14.80 kW in the calculated matched-load column. The 15-kW participant summary is close to the active-channel estimate, but exact run and meter equivalence is not stated. AFRL's broad 2–10-kW range is compatible in scale with measured load-bank outputs across the listed runs; the public summary does not confirm that this is precisely the same quantity.

HVEPS Test 3: do not treat these outputs as equivalent

Value	Quantity	Evidence type
6.52 kW	Power dissipated at the external load bank	Reported load-bank dissipation, reduced from electrical channels; Table VI lists 57.82 A and 1.95 Ω (I²R ≈ 6.52 kW)
14.38 kW	Output across the active generator portion, excluding end-region losses	Post-test derived quantity reported in Table VI
14.80 kW	Maximum output at a matched load	Post-test load-line model estimate, not the measured load-bank point

How the reported values changed across the analysed tests

The report gives six reduced test points, not a single general-purpose power number. For each point, the load-bank column is the power dissipated at the actual selected resistance; the active-channel column excludes end-region losses; and the matched-load column is a post-test calculation. The bars keep those categories separate.

Table VI values transcribed from the AFRL report; Test 3 is shown at mean combustion efficiency

Test	Peak field (T)	Combustion efficiency	Load-bank dissipation (kW), reported measured point	Active-channel power (kW), end losses excluded	Matched-load maximum (kW), post-test analysis
1	1.48	91.0%	3.81	6.55	8.24
2	1.48	85.0%	3.20	4.00	7.76
3	1.48	89.0% mean case	6.52	14.38	14.80
5	1.80	81.5%	5.55	7.25	8.09
6	1.80	77.0%	5.83	8.46	8.48
7	1.80	82.0%	2.10	2.98	6.94

The paper reports seven powered tests, but Test 4 is missing from the reduced results because its scramjet pressure distribution was anomalous. It also reports three combustion-efficiency cases for Test 3; this display uses the mean case and leaves the low/high matched-load calculations in the caption. These are rig-level generator results under brief ground-test conditions. None is power returned to a propulsion accelerator or net aircraft power.

The paper also says unregulated end regions reversed the Hall field and caused losses; the authors estimated roughly 25–60% end-region loss. This is a real engineering lesson about where power is measured and how a generator is loaded, not evidence of an aircraft-level net gain. The test lasted only seconds under ground-facility conditions; the electrical load was a resistive bank, and no accelerator loop, installed-system mass or vehicle thrust benefit was tested. Retained third-party indexed preprint copy; selected Table VI rows checked against the official NTIS/NTRL PDF · AIAA conference-paper record · General Atomics participant summary.

What the HVEPS report measured—and which inputs it leaves open

Simple version: HVEPS measured electricity from one generator on a ground rig. To know whether a whole aircraft could gain energy, researchers would also need matching air, fuel and seed flows, all the power used to run the equipment, heat and pressure losses, and thrust. The report does not give all of these together for the same moment. Its flow numbers have different statuses: Table II contains calculated target points; Table III lists the MHD-test set conditions and, separately, a March 2006 unseeded baseline. Neither table gives species flow synchronized to Test 3’s selected power samples. Lineberry et al. (2007), Tables II–III (printed pp. 9 and 11; inspected in the retained preprint).

A closer look at one measured electrical trace

Simple version: The generator switches on, produces electricity briefly, then winds down. The first graph keeps the fast wiggles in the recorded voltage and current; the second smooths the same run so the broad changes are easier to follow.

The report identifies these as HVEPS MHD Test 1, Figures 16 and 17. Figure 16 shows terminal voltage and net load current recorded at 1 kHz from about 27 to 35 seconds. The authors place seed injection near 27.68 s and the main generation interval at about 3 s, ending near 30.7 s. They attribute the current spike near 32.2 s to purging the NaK feed while the slower ethylene shutoff briefly left combustion and seeding overlapping. They describe slower signal variation as combustion unsteadiness and faster fluctuations as electrical arcing in the channel.

What this does not establish: These are Test 1 images, not Test 3 samples behind the 6.52 kW load-bank result. A ten-point filter suppresses fast variation and changes the displayed waveform. The retained report copy supplies plotted traces, not machine-readable samples with a full calibration and uncertainty record; these images alone do not support a precise time-integrated energy estimate. No synchronized complete-loop input/output or vehicle-thrust benefit was demonstrated.

HVEPS Test 3: what the retained report measures and leaves open

Quantity	What the report gives	What remains open
Load-bank electricity	Reported load-bank dissipation: 6.52 kW; Table VI lists 57.82 A at 1.95 Ω. I²R gives 6.519 kW, consistent with rounding. Figures 16–18 show recorded electrical traces, including a plotted 1 kHz Test 1 voltage/current trace.	No machine-readable synchronized Test 3 samples, calibration certificates, or complete electrical uncertainty budget were found in the retained report/source search. The plotted Test 1 trace is not a Test 3 data file.
Generator-channel power	14.38 kW post-test active-channel estimate; 14.80 kW calculated maximum at matched load.	These are not the measured load-bank operating point.
NaK seed flow	The setup and intended feed are described.	The authors say NaK flow was not directly measured; its actual run-by-run rate is unknown.
Air and reactant flow	Tables II–III contain target, demonstration-series set-condition and separate baseline flow records, summarized in the figure above and transcribed in the downloadable ledger.	No species-flow record is synchronized to the selected Test 3 electrical samples. Do not use the target or baseline flows to calculate kJ/kg from those kW values.
Uncertainty	Table VI gives ±7.5% accuracy for combustion-efficiency calorimetry.	That is not an uncertainty estimate for electrical output; meter and propagated uncertainties remain open.
Support power and heat	The report describes the magnet, seed system, heat-sink channel, and purge/cooling sequence.	A synchronized total of magnet, conditioning, controls, seed, cooling, and rejected-heat terms on one boundary.
Accelerator and vehicle force	No accelerator or thrust value is reported for this HVEPS test.	A matched generator-to-accelerator run, nozzle force, installation losses, and vehicle comparison.

This ledger is limited to the inspected report; “not reported here” does not prove that no additional records exist. The test establishes a short-duration ground generator result, not a closed energy loop or aircraft benefit. Retained third-party indexed preprint copy; selected Table VI rows checked against the official NTIS/NTRL PDF · AIAA paper record · Source-to-claim ledger · JSON · Open questions · CSV · Rebuild the CSV · Python.

A three-dimensional model checked against HVEPS Run 3

Simple version: Researchers measured how much current came out of the generator. A computer model then tried to reproduce that pattern. It matched the middle of the generator well, but the model and measurements differed near the two ends.

Ishikawa and colleagues’ 2008 open journal paper analyzes the experimental HVEPS Run 3 conditions and results described in Lineberry et al. (2007). It is a numerical re-analysis of that ground test, not a new experiment or a source of synchronized raw telemetry. The paper compares the calculated load current with the measured current across the channel.

Accessible table of the approximate graph readings

Approximate Figure 6 reads, not source raw data

Insulator number	3D model current · graph read	Measured current · graph read
3	≈42 A	≈58 A
5	≈60 A	≈58 A
7	≈73 A	≈58 A
8	≈76 A	≈58 A
9	≈77 A	≈58 A
10	≈72 A	≈58 A
12	≈65 A	≈58 A
14	≈61 A	≈58 A
16	≈59 A	≈58 A
18	≈58 A	≈58 A
20	≈59 A	≈58 A
22	≈58 A	≈58 A
24	≈59 A	≈58 A
26	≈61 A	≈58 A
28	≈66 A	≈58 A
30	≈72 A	≈58 A
31	≈71 A	≈58 A
32	≈68 A	≈58 A
34	≈61 A	≈58 A

How the model was set up: The paper describes a fully coupled three-dimensional fluid and electrical calculation: time-dependent compressible flow equations, steady Maxwell equations under the MHD approximation, and thermochemical-equilibrium properties. For Run 3 it used inlet pressure 0.284 atm, inlet temperature 2,480 K, Mach 2.02, a 1,000 K wall and peak magnetic field 1.48 T. Its computed pressure-based MHD interaction parameter was 0.0034, so the authors expected only a small change to the flow field.

A fitted input, not an independent validation: The ideal thermochemical calculation predicted too much current. The researchers multiplied ideal scalar conductivity by δ = σ/σ_ideal = 0.813 to bring modeled current closer to measurements in the active channel. That means 81.3% of the ideal value was retained—a reduction of about 18.7%, not a loss of 81.3%. The authors said the cause was unclear and suggested incomplete combustion and non-uniform mixing, seed distribution or temperature as possible contributors. Because δ was adjusted against the same measurements, the resulting agreement is a calibration-like comparison, not independent validation.

Losses and limits: The calculation produced about 100 V total electrode voltage drop, roughly 30% of its modeled induced voltage in the active region. These values depend partly on its arcing model and imposed 1,000 K wall temperature. The grid had 128 × 41 × 21 cells; the paper says about 0.2 mm cells would be needed to resolve a near-wall arc scale around 1 mm, so its grid was coarse for that feature. It identifies eddy-like currents in the end PTO regions but says more detailed electrodynamics are needed to quantify their power-loss effect. The article does not close auxiliary loads, whole-vehicle energy, net thrust or an aircraft benefit.

Reference-number note: Ishikawa et al. cite their Run 3 experimental source as AIAA-2007-3881 (their Reference 3), while the DOI record and other project records identify the HVEPS test-results paper as AIAA 2007-3880. This numbering mismatch is unresolved; we preserve what each source says rather than silently correcting it. The underlying report record is AFRL/NTIS-NTRL ADA471429.

Ishikawa et al. (2008), full paper, Figures 4–11 and conclusions, pp. 1444–47 · AIAA 2007-3880 DOI record (numbering discrepancy above). Local retained PDF SHA-256: E903DFB069B9A8C600646A1DD45DA59D911327BB8F863A88DEB01C0CBDA4E7B7.

A second HVEPS generator test campaign at UTSI

Simple version: Researchers ran hot combustion gas through a small magnetic generator, recorded electrical, pressure and thermal data at several channel locations, and compared the results with a computer model. This shows what one generator component did and how its model compared with the measurements.

Keep the experiments separate: the 2008 UTSI annual report describes eight combustion-driven tests in the UTSI Propulsion Laboratory, using a separate combustor, a Hall MHD channel and a superconducting magnet. The AIAA paper identifies the demonstration firings as August 2007. This is not the December 2006 UTRC scramjet-driven air/seed test described in the adjacent HVEPS evidence: the facilities, flow arrangements and reported measurements differ, even though both sit within the wider HVEPS program.

What it establishes: component-level MHD generation and measured-versus-modelled electrical and thermal distributions in this UTSI setup. The report calls the plotted power a distribution of internal power developed along the channel; it is not a whole-engine surplus. Do not merge it with the separate UTRC Test 3 load-bank value of 6.52 kW, and do not infer an accelerator benefit, vehicle thrust, or closed system efficiency. Neither HVEPS campaign supplies a synchronized whole-vehicle energy-and-force balance.

A separate NASA hot-gas experiment in 1980 measured gross electrical output from a cesium-seeded hydrogen–oxygen combustion stream. The nominal conditions were 10 atm combustion pressure, 0.5 kg/s mass flow, 7 MW thermal input and a peak magnetic field of 5 T. Two Hall-duct configurations reached reported maximum outputs of 87.5 kW and 153 kW at the generator load. Dividing those outputs by the stated thermal input gives 1.25% and 2.19%, respectively. This transparent output-to-input comparison is not net plant efficiency: the report does not close the magnet, cooling, seed, pump and other facility loads, and electricity was not returned to a propulsion accelerator. The 58 cm duct ran in pulsed tests; data runs lasted five seconds, and its exhaust was water-quenched at atmospheric pressure. NASA-TM-81424 record · Download the 19-page NASA report (PDF).

What this short test established — and the limits NASA listed

Simple version: The team made and measured electricity from hot gas for a few seconds. That proved the generator component could work in this test rig. It did not show that a whole engine would gain useful power after magnets, cooling, pumps and other equipment were counted.

Evidence boundaries from NASA-TM-81424; printed page numbers follow the report

Question	What the report says	What remains unshown
What was tested?	A cesium-seeded hydrogen–oxygen combustor fed a Mach-2 Hall generator in a cryomagnet; nominal conditions included 10 atm, 0.5 kg/s, 7 MW thermal input, 5 T peak field and a 58 cm duct (printed pp. 2–4).	This is a laboratory combustion-gas generator. No flight engine or propulsion accelerator was powered by its output.
How long and where did the exhaust go?	The reported data runs lasted 5 seconds; high-field operation was pulsed. The duct exhaust was water-quenched, with the flow discharged at atmospheric pressure (printed pp. 2–4, 8).	The proposed H₂/O₂ topping-plant case needed very low sub-atmospheric exhaust pressure. NASA says generator performance there was not established.
What constrained output?	For the 4:1 area-ratio duct, a shock appeared at about 7 atm and below even with no power extraction; stronger field moved the shock upstream and changed the output trend. In separate open-circuit tests, breakdown occurred above about 50 V per insulator after roughly 2.5 seconds of seed injection; damage was found on anode-side insulators (printed pp. 6–7).	These limits are specific to the reported ducts and conditions. They warn that stronger magnetic field does not guarantee proportionally more usable power.
Was large-scale cycle performance demonstrated?	The report says an attractive proposed topping plant required roughly 40% enthalpy extraction and that very large facilities and vacuum testing would be needed (printed pp. 6–8).	The report explicitly leaves this extraction level and low-pressure performance as open questions. Its 87.5 and 153 kW values are generator outputs, not proof of net plant efficiency.

Source: J. Marlin Smith, Experiments on H₂-O₂ MHD Power Generation, NASA-TM-81424 (1980), printed pp. 2–8. NASA report record · NASA-hosted PDF.

Optional base-12 arithmetic cross-check

The plotted ratios use the report’s numbers: 87.5 kW ÷ 7,000 kW = 0.0125 in decimal, which is 0.01(9724) in base 12 (digits 9724 repeat). The operands are 73.6₁₂ kW and 4074₁₂ kW. For the second duct, 153 ÷ 7,000 = C9₁₂ ÷ 4074₁₂ = 0.021857… in decimal, reported as 2.19% after rounding. Base 12 changes the notation; it does not change the measurements, uncertainty or efficiency boundary.

Conditions, evidence categories, source hash and arithmetic · JSON

Before the test: how oxygen enrichment could change the hot gas

Simple version: Hot gas does not always let electricity move through it. Before the test, the team used calculations to see how adding oxygen might change whether this hot gas could carry electricity. This helped choose test conditions; it was not a result from the generator test.

The published Figure 11 plots design-level estimates for conductivity and diagonal MHD power density. Its curves are model calculations, not experimental measurements. This original redraw uses approximate readings from the published raster plot; no pointwise numerical file is provided. Dots mark estimated source points, and connecting lines are visual guides only.

Keep the two power-density quantities separate. Table II lists 8.06 S/m and 7.81 MW·m⁻³·T⁻² for its 85% target at 35% oxygen enrichment; 7.81 is a Faraday parameter. Figure 11 instead plots diagonal power density normalized by magnetic-field squared, about 0.19 near the 34.5%, 85% design point. These definitions differ, so the values are not a contradiction or direct comparison. The report says RASCAL and LyTec thermochemical codes produced the design calculations; their solver inputs and pointwise output are not available here. A separate, unseeded March 2006 baseline measured 84% mean combustion efficiency, but that does not make these curves measurements.

This calculation helped researchers choose conditions for a hot-flow generator test. If future tests show that useful electricity can be recovered after all losses are counted, this research could help engineers study energy use in very fast aircraft. Figure 11 itself does not show electrical output, net energy recovery, a generator-to-accelerator loop or flight performance. Official NTIS/NTRL ADA471429 report · Wide graph · Phone graph · Approximate readings · CSV · Methods and limits · JSON · Rebuild · Python

What newer scramjet studies add

Simple version: A computer study can give us a useful map, but it is still a map. One 2024 study modelled electricity generation inside one scramjet MHD channel. Its abstract reports that the generator efficiency stays near 22%, while the channel takes less than 0.35% of the hot flow’s enthalpy in the listed cases. That means the model predicts converting a small slice of the flow’s energy, even if the generator converts part of that slice to electricity. The abstract does not define exactly what each percentage is divided by, so neither number tells us the useful net energy for a whole aircraft. Do not read either curve as whole-engine or net efficiency.

Abstract-reported model values; the full model has not been independently reproduced here

Magnetic field (T)	Generation efficiency reported (%)	Enthalpy-extraction rate reported (%)	Evidence type
1	22.5	0.026	Simulation, as reported in abstract
2	22.3	0.10	Simulation, as reported in abstract
3	22.0	0.21	Simulation, as reported in abstract
4	21.5	0.34	Simulation, as reported in abstract

A separate 2025 study adds a mathematical MHD generator after the scramjet combustor. Its baseline engine model was compared with one Mach-7 test point, with reported isolator errors of 2% in Mach number, 4.65% in static temperature, and 17.28% in static pressure. The added MHD channel was compared with a CFD simulation for one channel condition, not with an experiment of an operating MHD generator. For a 2.5 T magnetic field and load factor 0.4, the paper predicts a 3.58% specific-impulse penalty at 0.5% enthalpy extraction and 6.43% at 0.9%. These are model outputs for post-combustor energy extraction; they are not measured thrust losses and do not test an electricity-return loop. I reviewed selected publisher-indexed PDF text; the publisher blocked direct PDF retrieval, so a full visual page-by-page check remains open. Liu, Wu & Meng (2025), Journal of Propulsion Technology · Official article record · Publisher PDF.

A 2026 screening study separates two magnetic-plasma propulsion ideas

Simple version: A powerful magnet can guide forces on an electrically conducting gas, but the magnet does not supply the energy. In an aircraft concept, energy would come from the moving air and the system would have to overcome electrical, heat and pressure losses. In a space rocket, the spacecraft instead carries propellant and electrical power. These are different engines with different energy accounts.

Lieu’s paper, available online on 6 September 2026 as an in-press journal pre-proof, presents a reduced-order model for both cases. Its abstract describes the aircraft case as a hypersonic MHD thrust augmentor in which ionized shock-layer or boundary-layer gas helps make a larger captured air stream conductive. For one representative Mach 7, 30 km, 0.5 m² scenario, the model estimates a 5 kN thrust increment would require about 11 MW of ideal power removed from the flow and plausibly tens of megawatts of electrical power after losses. These are author-reported screening estimates, not measured performance.

The paper’s space case is separate: it accelerates onboard propellant with a plasma device. The paper therefore does not show that the atmospheric 516 kJ/kg ideal inlet energy can be converted into usable electricity, that a complete aircraft energy loop closes, or that an MHD system has flown. We checked the publisher metadata, abstract and indexed highlights; the full text was not independently reviewed here. Lieu (2026), Aerospace Science and Technology, article 113752, DOI 10.1016/j.ast.2026.113752 · Publisher record and abstract.

A real design question: what does it cost to keep the gas conducting?

Simple version: To make a gas generate electricity, it must carry electric current. One proposed way to help was to keep the gas ionized with an outside power source. A NASA model from 2001 found that, in one example, this ionizer needed much more power than the generator made.

In that modeled case, the ionizer demand was about 827 MW, while the MHD generator produced about 151 MW—roughly 5.48 times as much input as gross generator output. Their simple arithmetic difference is 676 MW (827 MW minus 151 MW): the listed ionizer demand is that much greater than the listed gross generation. This subtraction compares only those two rounded model values; it is not net aircraft power or a complete vehicle power balance. The authors assumed a 100%-efficient ionizer, an optimistic idealization, and reported a modeled case rather than a hardware test. The same table reports the ionizer demand as about 85% of the modeled hydrogen fuel-energy rate, using complete combustion at room temperature. This ratio compares the two listed electrical powers only; it is not a complete vehicle power balance. It does not prove that every MHD design fails. It shows why any proposed design must count ionization and other support loads alongside the electricity it generates. NASA record · Conference paper PDF (Table 1, printed pp. 5–6; conclusions, p. 7).

Two HVEPS papers, two kinds of evidence

Simple version: One paper reports a ground test; another describes a computer study. A computer study can help explain a test, but it is not another test. We have not found enough open model files to check whether the computer study reproduces the experiment.

Related HVEPS publications: source and evidence status

Publication	Evidence type	What is available here	What it does not establish
Lineberry et al. (2007), AIAA 2007-3880 / AFRL preprint ADA471429	Hot-gas ground test of a generator component	The retained report copy gives reduced Table VI values. Its PDF hash and locators are in the downloadable input ledger.	An official copy was retrieved through the NTIS/NTRL ADA471429 record (32 pages; SHA-256 CCBC90C0BC0626328B058023D153D2F268767F85DAFD8BFD2A0DBFFACCFA1521). Its hash differs from the retained third-party file. Side-by-side comparison of Table VI (printed p. 27 / PDF p. 29) confirms the displayed rows, including Test 3 low, mean and high load-line cases. The retained color file remains the basis for existing source-image crops. The official DTIC search reported offline on 2026-10-02; the NTRL route supplied this report copy. Synchronized Test 3 flow/electrical files and a complete electrical calibration package are still absent from this report. Official NTIS/NTRL record and PDF download (ADA471429).
Gotoh et al. (2007), AIAA 2007-4015	Computational analysis associated with HVEPS	Crossref confirms the paper’s bibliographic record; DOI metadata and source status are linked below.	Full paper, model inputs and machine-readable results were not located in this bounded review. It has not been independently reproduced and cannot be presented as a measurement or as a resolution of the test-data gaps.

Crossref registers the HVEPS test-results paper as AIAA 2007-3880. Some later bibliographies show “2007-3881”; this is treated as a likely miscitation, not a proven universal correction. Bibliographic details, copy hash and access limits: HVEPS publication and provenance record · JSON · Run-level input ledger · JSON. The official DTIC site reported its public reports search offline on the date above; this does not show that no official copy exists.

These recent studies sharpen the question for future research: what does an MHD stage contribute after its extraction, field, ionization, cooling, pressure-loss and mass costs are all counted against the same engine baseline? Their published models do not settle that full comparison.

NASA’s MAPX work describes a different, externally powered accelerator facility: a 1.5-MWe arc heater drives a 2-MWe MHD accelerator inside a 2 T magnet. Those are facility component ratings, not measured net power returned by an aircraft. The NASA report states that a meaningful fuel-fraction improvement would require electrical augmentation power to exceed the unaugmented source’s thermal power, and calls the onboard power-density challenge daunting. Its 2008 status report was still preparing full-up assembly and testing; the ratings do not establish that the propulsion loop achieved that condition. NASA MAPX status record · Full NASA/TP, introduction and conclusions.

One later turbojet-cycle report leaves a reproducibility question. Eq. (2) (printed p. 5 / PDF p. 9) defines extracted power using mass flow, Cp and generator-inlet total temperature. Using an explicitly chosen heat-capacity range of 1.0-1.2 kJ/(kg K), the Mach 4.75 and 5.25 values in the report's prose imply about 5.9-8.3 MW, while a 76-point digitization of Figure 5 (printed p. 8 / PDF p. 12) reads about 69.9 and 87.7 MW. The 1.0-1.2 range is our sensitivity assumption; NASA does not give its numeric Cp or pointwise NPSS inputs in the inspected report record. A reverse calculation offers another clue: pairing the report's approximate prose endpoints at Mach 4.75, 5.25, 6.00 and 6.75 with the plotted curve gives implied effective Cp values near 12 kJ/(kg K). That cluster is compatible with a shared scale factor or convention, but approximate endpoint pairings can produce a similar pattern. It does not establish NASA's Cp, exact matched run points, or the cause. The same author's 2013, 239-page Kent State dissertation revisits the NPSS cycle in Chapter 5 (printed pp. 80–102; PDF pp. 102–124). It repeats the 45–90 MW extracted-power range and the Mach 4.75–5.25 prose values in §5.4.2 (printed p. 92 / PDF p. 114), and Figure 5.5 gives the corresponding model plot. Table 5.1 (printed p. 82 / PDF p. 104) lists generic NPSS file types and names, not the study's runnable deck or pointwise output. I found no numerical Cp value in the thesis passages describing the equation, so this follow-up does not resolve the mismatch or provide an independent reproduction. No value is corrected and no source error is alleged. NASA/TM-2011-217136 record · NASA report PDF: Eq. (2), Figure 5 and Mach-point text · Official OhioLINK/Kent State dissertation record · Full dissertation PDF.

What this tells us: the four implied values average 12.316 kJ/(kg K), but this does not prove a single heat capacity or convention was used. These are approximate statements from the same report, and the last two are analyst-paired trend endpoints, not matched operating-point records. NASA's PDF describes Cp as constant-pressure specific heat but supplies no numeric value, units, property schedule, or NPSS input deck. The apparent scale difference is therefore unresolved. Review the full digitization method and limitations.

What remains uncertain

Whole-cycle results depend on the configuration and assumptions. The 2000 NASA report includes a full-cycle performance curve; its result is reproduced below as an approximate reading of the published graph because the report provides no numerical point table. Separately, a peer-reviewed 2004 Journal of Propulsion and Power article by Riggins reports that thermally balanced MHD-bypass simulations underperformed the conventional scramjet across the studied Mach 8–12.2 range. Its institutional record currently exposes citation and abstract, not the full paper or numerical curves. This more detailed result and the 2000 simplified cycle have different assumptions and boundaries; do not combine them as one benchmark. Neither establishes flight performance or net vehicle benefit. Riggins (2004), DOI 10.2514/1.4980 · Missouri S&T record and abstract.

Equation reference note: In the final 2000 report, the Figure 2 discussion points to Eqs. 25 and 28 for the generator and accelerator pressure ratios, but those equation numbers identify diffuser relations in the final equation sequence. By their contents, the component relations are Eqs. 36 and 53. The earlier 1999 NASA preprint used a different numbering: its Eqs. 26 and 30 give the generator and accelerator pressure-ratio relations, and its Figure 2 discussion points to those same numbers. This suggests the final report may retain stale cross-references after renumbering; the reason is not documented. We use the equations by content. This comparison does not verify the digitized curve, our reconstruction, or flight performance. 1999 NASA preprint record · Preprint PDF (Eqs. 26, 30 on PDF p. 8; Figure 2 discussion on p. 11).

Inspect a separate equation-based reconstruction (preliminary)

This independent calculation applies the report's simplified cycle equations. It is not author code, test data, or a vehicle-performance prediction. The calculation uses explicit perfect-air constants and added pressure closures; its ideal ambient-matched nozzle is expanded to ambient pressure separately at every Mach number, so it is not a fixed-nozzle design. Unit pressure ratios are assumed for the pre-ionizer and cooling expansion. The Figure 2 reference case fixes the burner exit at 3000 K while also applying positive energy in the accelerator. The cycle equation therefore necessarily puts accelerator-exit temperature above the report's separate 3000 K accelerator limit for every successful positive-extraction sample. This is a conditional model result, not evidence of tested operation. The dual-cap curve lowers burner temperature to satisfy both constraints; it is a new sensitivity case, not NASA's plotted result.

Explore one calculated cycle point

Simple version: A generator takes some energy from the hot moving air; after a small pre-ionizer share, an accelerator returns some energy to the exhaust. This paper model lets you inspect the temperature and thrust bookkeeping. It is a calculation, not a working aircraft.

Flight Mach number

1.00–12.00

Generator extraction ratio0 — no extraction0.250.50Temperature ruleFigure 2 burner cap; report accelerator capEnforce both caps (new sensitivity)

Mach values are precomputed at 0.05 intervals from 1 to 12; extraction values are the three cases shown in the report.

Loading the calculated cases…

Energy removed in MHD generator

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Pre-ionizer share

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Energy added by accelerator

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Stagnation temperature into burner

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Stagnation temperature out of burner

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Stagnation temperature out of accelerator

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Calculated nozzle exit Mach

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Specific thrust

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Generator / accelerator total-pressure ratios

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Specific thrust is normalized per inlet-air mass flow, not total engine force. The model’s pressure-thrust term is zero only because it assumes nozzle exit pressure equals ambient pressure.

Changing a control updates the model explanation and readouts.

The downloadable overlay retains 95 earlier approximate graph readings as an audit history. Its residual statistics describe differences from those project readings; they cannot establish disagreement with NASA's numerical results, and their original graph-reading allowances are not validated total uncertainty.

Why the comparison changed. At flight Mach 6 and generator extraction ratio 0.25, this conditional equation reconstruction gives 0.697 kN·s/kg. The earlier claim of a clear mismatch used an old graph reading of 0.58 ± 0.05 and is withdrawn. A direct raster observation is 0.713 kN·s/kg at its actual calibrated Mach 5.996; evaluating the same model at that Mach gives 0.698, a signed model-minus-reading difference of −0.0155 kN·s/kg. This is a comparison with a manually read image, not NASA-tabulated output. The visible ink band is not total uncertainty, so the comparison establishes neither validated agreement nor a NASA model error. It does not show that NASA’s figure or report is wrong. At exact Mach 6 the reconstructed accelerator-exit stagnation temperature is about 3,418 K. The report states a 3,000 K burner limit for Figure 2 and separately describes the same general temperature limit for the accelerator (NASA PDF pp. 10 and 26); enforcing both requires the distinct dual-cap sensitivity case, not silent reinterpretation of the plotted curve. The energy split itself closes within the model: about 458.84 kJ/kg-air extracted, of which 22.94 is assigned to pre-ionization and 435.90 to the accelerator. These are conditional calculated values, not measurements.

One unresolved reference in the original report: the Figure 2 discussion says the generator and accelerator pressure ratios use Eqs. 25 and 28, but those equation numbers describe diffuser relations; the MHD component pressure-ratio equations are numbered 36 and 53. This reconstruction uses Eqs. 36 and 53 by component definition. The report does not clarify this cross-reference inconsistency. A typo is plausible but unconfirmed; this does not establish that Figure 2 is wrong.

What if the nozzle exit pressure is not ambient?

NASA's thrust equation includes both momentum and pressure thrust. The current reconstruction sets exit pressure equal to ambient, which makes the pressure term zero. The report lists a nozzle total-pressure ratio of 0.98, but does not publish the nozzle expansion efficiency or a fixed exit geometry for this plotted case. The graph below therefore sweeps an explicitly chosen exit-pressure ratio, from 0.7 to 1.4 times ambient. It derives the exit area separately at each point from mass continuity, so it is a boundary sensitivity—not a fixed-nozzle prediction and not a fit to NASA's curve. In this conditional calculation, momentum and pressure contributions partly offset one another; the total stays between about 0.694 and 0.697 kN·s/kg-air across this illustrative sweep. The selected range is not specified by NASA, so this does not bound what a real fixed nozzle would do. The reference case also reaches about 3,418 K after the accelerator, above the report's separate 3,000 K limit.

Comparison plot · SVGCalculated cycle samples · CSVAssumptions and equations · JSONReproduce calculation · PythonRequired raster comparison input · CSV

The NASA 2002 conference record and the related 2004 peer-reviewed Riggins journal article are separate bibliographic records in the same line of analysis. Both report less favorable modeled performance for their studied bypass configuration; the 2004 abstract attributes this to MHD irreversibility and cooling requirements as well as pressure loss from the inverse cycle. The university record does not provide the article's full text or numerical curves, so no Riggins points are reconstructed here. A 2005 peer-reviewed comment and author reply also exist, but their texts have not been checked in this review and are not used to settle the technical debate. These records must not be merged with NASA's simpler 2000 Figure 2. Separate 2011 turbojet-cycle studies concern a different engine class, and a separate electrode-patch flow-control concept addresses another configuration. None establishes a net hypersonic vehicle benefit.