Tuesday, December 27, 2022

Russian Lies

The picture came from a news article published in the AAAS’s journal “Science”,  specifically the 9 December 2022 issue,  designated volume 678 issue 6624,  on page 1036.  The news article was titled “Hero City”,  and was about Kharkiv,  Ukraine,  being a former science center wanting to recover.  I literally photographed the page in the journal magazine. 

The picture shows what appears to be a bombardment missile that was apparently a dud,  embedded in the pavement near the Neutron Source Facility,  at the Kharkiv Institute of Science and Technology.  The missile would appear to be a tube-launched device with fold-out wrap-around fins. There would appear to be six of these fins,  each hinged three places to flip out,  all flipping-out in the same direction. 

The flip-out hinge line is canted with respect to the body axis,  as can be so very clearly seen with the fin more-or-less pointing toward the viewer,  in the center of the visible fin pattern.  All the fins cant the same way,  creating lift forces that sum up,  directed tangential to the missile body surface. 

Thus,  this is a spin-stabilized weapon,  which means in turn that it is otherwise unguided!  That kind of thing is not “targeted” at all,  it is a random area-destruction weapon,  typically launched en masse as an indiscriminate bombardment means.  I spent 20 years in aerospace defense engineering work,  so I really do know what I am talking about here.

“Unguided” makes a lie out of Russian claims they are carefully targeting their strikes in Ukraine! 

They also swore they were not going to invade,  right up to the day before they invaded.  And a bunch of other lies revealed publicly. 

The real takeaway here is that you cannot believe anything the Russians say:  not then,  not now,  and not in the future.  And that includes any possible “peace negotiations”. 

It seems apparent to me that the louder the Russian saber-rattling,  the closer they actually are to losing that war!  So,  why should Ukraine negotiate,  when they are actually winning?  Because of catastrophic damage to their infrastructure?  All that means is that our help is not yet enough. 

But,  the Russians also claimed they will not use nuclear weapons in Ukraine (despite their longstanding doctrine that they would do so in an attempt to avoid defeat on the battlefield). So be prepared for when (not “if”,  “when”) they do “go nuclear”!  The closer they get to defeat,  the more likely it becomes that they will use tactical nuclear weapons on Ukrainian cities!

If Russia loses,  Putin’s regime falls,  and he and all his cronies know it!  A Russia without Putin could be a friend.  Which is the best possible argument for doing everything we can to ensure Ukrainian victory.

References (which I wrote earlier on this topic):

#1. “How To Stop the Ukraine War”,  posted 27 November 2022

#2. “Nuclear War Warning”,  posted 12 September 2022 

Sunday, December 18, 2022

White Trash Christmas 2022

This is the 2022 version of a yard decoration we have put up most of (but not all) the years since about 1998 or thereabouts.  It’s intended to be funny,  and we call it “White Trash Christmas”.  We got the “missile toad” up first,  now this,  and soon the living room Christmas tree.  

For the “missile toad”,  see the article dated 7 December 2021 and titled “Christmas Decoration” on this site. 

The tree is an “iron tree” I designed many years ago.  It would be appropriate outdoors,  no matter the circumstances.  It sets up rather quickly,  and you just wind the light string onto it,  Maypole style. 

The “Santa and his sleigh rig” I made this year out of a lawn tractor wagon as the sleigh,  a plastic Santa with an internal light bulb that I have had for many years,  and a trash bag as the bag of toys. 

The reindeer team is a set of plastic lawn flamingoes rigged with internal lights,  and pipe cleaners glued to their heads as antlers.  There are the classic team of eight,  with “Rudolph” out front,  and “Bambi” bringing up the rear.  All of these are labeled with the appropriate names.

Those who know me,  know that I do have a twisted sense of humor (and so does my wife Ellen).  At any rate,  enjoy!   The view is from the shop yard back toward our house. 

Update 1-2-2023:  As of today,  I took the display down for the season.  Partly in response to possible severe weather,  but mostly because it is past New Year's now.  I plan to put it up again next Christmas season,  in one or another form. 

Thursday, December 15, 2022

Fusion Still Unready To Save Us

Update 12-19-2022 An edited version of this appeared in the Sunday 12-18-2022 Waco "Tribune-Herald" paper as a board-of-contributors column.  


With scientists achieving “breakeven” at the national ignition facility,  their press release has been ballyhooed into notions that fusion is here to save us immediately from energy shortages and climate change.  Wrong!

Excerpted from an NBC News release 12-13-2022:

“While the Livermore team achieved what researchers call a scientific break-even or energy gain, it did not achieve an engineering break-even: The inefficient lasers used in the experiment required about 300 megajoules of energy to fire just 2 megajoules of energy into the experiment. The reaction produced about 3 megajoules of energy.”


“Scientists must now find ways to reduce inefficiencies, burn a larger portion of available fuel during the reaction and harness the energy for use as electricity, said Troy Carter, a professor in UCLA’s department of physics and astronomy and the director of the Plasma Science and Technology Institute.”

And here is an image of the target bay: 

My take on it:

Figured as output/input,  the scientists are comparing fusion energy released (as heat) to the incident laser light energy on the fuel pellet that compressed it:  3 megajoules/2 megajoules = 1.5,  which is greater than 1,  indicating they got more fusion-derived heat energy out,  than they put in as laser light energy (or magnetic confinement energy,  or whatever type of energy the experiment used). 

That definition of the ratio is termed “scientific breakeven”,  and this is the first time that ratio has ever exceeded 1 in anybody’s experiment!  That is quite the significant achievement!  However,  bear in mind that many experimenters have been trying to do that ever since the early 1950’s (some 7 decades ago).

That achievement says getting energy from fusion is actually theoretically possible.  But it ignores the efficiency of producing the input laser (or other) energy,  and it ignores the efficiency of utilizing the output heat to make usable electricity.  The second quoted paragraph above says exactly that,  but without any numbers to “calibrate” the notions.  Allow me to “calibrate” it for you:

Per the quoted data in the first quoted paragraph,  the efficiency of producing those 2 megajoules of laser energy is 2 megajoules/300 megajoules = 0.67%,  which is really,  really low! 

A heat engine is required to produce electricity from the released heat of fusion.  The best of those that we have,  are the steam-powered generators at power plants,  which are limited by the laws of thermodynamics to efficiencies in the range of 25-50%.  I will use that value range for illustration.

What all that really says,  from the viewpoint of any engineer actually tasked to build a powerplant,  is that the output should be the producible electricity,  say 25-50% x 3 megajoules,  or 0.75-1.5 megajoules.  The input is the energy required to actually produce the laser energy in this case,  which is the 300 megajoules quoted. 

Looked at that way,  the ratio is 0.75-1.5 megajoules/300 megajoules,  or about 0.25-0.50%,  and very likely lower than that.  And yet THAT is the ratio that really needs to be greater than 1 for a real-world powerplant design to work!  That would be “engineering breakeven”. 

It took 7 decades to achieve “scientific breakeven”.  It is unrealistic to expect that reaching “engineering breakeven” won’t require a similar number of decades.


What we face:

We face a shortfall of grid capacity as the population increases and as motor fleet electrification proceeds,  plus we face a climate disaster already in progress.  For our energy and climate needs,  it is obviously wiser to count on techniques that we already have operational. Those are fossil fuels,  hydroelectric,  nuclear fission,  solar,  and wind.  Nothing else is operational.

How we can face it:

All the fossil fuels produce greenhouse gas emissions,  and the technologies to reduce or prevent that are simply not operational.  Of the fossil fuels,  the one cleanest of both ordinary pollution and greenhouse gas emissions is natural gas.  But you must pay careful attention to stopping the leaks from,  and the freezing of,  those pipelines and distribution infrastructure.  We know how to do that,  but we have yet to make those into regulatory requirements.  So,  change that lack!

Hydroelectric capacity cannot be expanded much further:  we have already dammed all the dammable rivers in the US.

Solar and wind are already 20+% of the Texas grid capacity,  but because of their intermittent nature and long-distance transmission losses,  they cannot be much more than that percentage,  until “grid-scale” energy storage is operational.  It is not yet operational.

That leaves nuclear fission,  which is free of conventional pollution and free of greenhouse emissions,  but does incur radioactive wastes and risks!  It has to be done “right”,  which prioritizes safety over profit,  which the US Navy has long-demonstrated really works.  It also needs a short-term and a long-term solution for dealing with the nuclear waste stream. 

The short-term nuclear waste solution is using the Yucca Mountain disposal facility already constructed in Nevada,  but so far never used.  Long-term,  we need to re-process spent nuclear fuel,  which might reduce the waste stream amounts,  by a factor approaching 10.

Just cut the red tape (while maintaining and enforcing the safety requirements) and get on with building nuclear plants as rapidly as we can!  We already know how.  No,  it’s not the cheapest source of electricity,  but it alone meets all the steady generation-capacity and emissions requirements.

My recommendations in a nutshell:

Wednesday, December 7, 2022

Invasion at the Border? No, I Don’t Think So!

The problem with the US southern border isn’t the massive numbers of immigrants,  it is our own US government.  Both Congress and the White House are at fault,  over some 7 decades since the end of World War 2.  Congresses and Presidents of both parties are at fault.  This is simply neglect of their sworn duty,  resulting in a variety of criminal outcomes under established law.  Simple as that.  And just that ugly,  too!

When you hear politicians disparaging the threat of terrorists,  criminals,  and evil-doers “invading” across our border,  you are being lied to,  for political gain!  The facts on the ground show that,  statistically speaking,  both guest workers (legal and illegal),  and refugees (whether ultimately admitted or not) are actually more law-abiding than the average US citizen!  It is the smugglers and drug cartels that are the real threat to public safety,  and they are a tiny minority of all those crossing the border!

When you hear politicians advocating for deporting any refugee without a hearing to reduce the purported invasion,  you are being lied to for political gain!  Refugees have the legal right under long-settled US law to a hearing before a federal immigration judge.  They have to be in the US in order to attend their own hearing,  in any practical sense.  Denying them this due process is not just a crime under federal law,  it is also a crime against humanity under international law!  But those same lying politicians failed to tell you that,  didn’t they?

When you hear politicians shouting about sealing or securing the border,  you are being lied to for political gain!  They are really talking about building a border wall,  which inherently cannot solve this problem,  but it does line the pockets of the supporters and cronies who get hired to build it!  Until very recently,  most of this immigration problem,  and the DACA problem,  were created by politicians neglectfully setting the guest worker quotas far too low for decades,  and also by refusing to staff up to address realistic quotas. 

As the figure shows,  the refugee quotas have never been more than about 200-thousand-ish in any given year.  Guest worker quotas are similar, but smaller.  We actually get 10 to 100 times that many guest workers,  which is why there is something like 10 million illegal aliens in this country.  That disparity tells you how out-of-balance our policies are with our laws and the facts on the ground.  And it is our very same lying politicians who have allowed that to happen.  They have been doing that since the end of World War 2.

When you hear politicians lumping all immigrants into the same threat category,  you are being lied to for political gain!  There are guest workers,  who are an integral part of our economy,  legal or not,  and always have been.  To survive they must come:  the jobs are here,  they are there,  and Americans demonstrably do not want to do those jobs.  And then there are refugees,  who are now in recent years the bigger problem,  but one ABSOLUTELY NOT under our control! 

Refugees are driven here by an ever-increasing number of failed states in Central and South America and the Caribbean,  and more recently also around the world.  People escaping those failed states are not at all deterred by our bureaucratic impediments,  they would quite simply rather die than stay where they are.  That’s desperation in the face of death.  Which is the DEFINITION of a refugee!

And then there are the border smugglers,  of both people and of drugs.  Our border patrol people could be far more effective against the drug smugglers,  if they weren’t swamped with illegal guest workers and illegal refugees.  There would be no illegal guest workers and unadmitted refugees if our government did those jobs correctly,  and that would free-up our border patrol agents to go after the drug smugglers.   But your lying politicians failed to tell you that,  as well!

I published an article on this problem back in January of 2019,  here on this site.  It has 3 updates added to it,  but I see no reason to change a single word of what I wrote back then!  That article has more detail about all of these issues,  and more explanation of what I am talking about here.  I recommend that you go to it and read it! 

There is a fast navigation tool on the left side of this page.  You need the date and title of the article you seek.  Click on the year,  then the month,  then the title.  That earlier immigration article was “Border Crisis?  Nope!”,  dated 17 January 2019.

All I can recommend to you now is that you cease re-electing the self-serving politicians who have been lying to you!  Start electing people who might be willing to tell you the real truth!  It doesn’t matter what party they are associated with,  you could not do any worse than what you have right now!

Real truth is not something you hear in an echo chamber on social media,  where you never hear a dissenting view because of the algorithms recommending stuff to maximize ad revenue.  And it is not something you will hear from the various cable TV news services,  desperate to fill time 24/7 and draw in advertising,  to the exclusion of any ethics.  The closest thing you will hear to the truth is from most (but not all) of the old-time traditional media (broadcast TV networks and the newspapers),  and even they are flawed.  But they are the least flawed.

You need to peruse multiple sources.   But they need to be sources that at least try to tell you the truth,  flawed or not.  Or else your efforts to find the truth will be pointlessly in vain.


Once again,  the earlier article that I see no need to change is:  

1-17-19   Border “Crisis”? Nope

Friday, December 2, 2022

The Unchoked Gas Generator As A Throttle For Gas Generator-Fed Ramjets

Update 23 March 2024:  For the readers of this and other similar articles about ramjet propulsion,  be aware that GW’s ramjet book is finally available as a self-published item.  Its title is “A Practical Guide to Ramjet Propulsion”.  Right now,  contact GW at gwj5886@gmail.com to buy your copy. 

He will,  upon receipt of payment by surface mail or Western Union (or similar),  manually email the book to you as pdf files.  This will take place as 9 emails,  each with 3 files attached,  for a total of 27 files (1 for the up-front stuff,  1 each for 22 chapters,  and 1 each for 4 appendices).  The base price is $100,  to which $6.25 of Texas sales tax must be added,  for an invoice total of $106.25. 

This procedure will get replaced with a secure automated web site,  that can take credit cards,  and automatically send the book as files.  However,  that option is not yet available.  Watch this space for the announcement when it is.  

GW is working on a second edition.  No projections yet for when that will become available.


In November 1993,  I gave a paper on the title topic at the JANNAF (Joint Army Navy Nasa Air Force) meeting held at the Naval Postgraduate School in Monterrey,  California.  It was an unclassified paper given at a classified session at that meeting.  It raised quite a stir.

The topic of this paper was threefold: 

(1) documenting the engineering design analysis model for a gas generator-fed ramjet with an unchoked gas generator,  that was capable of evaluating multiple influences,  to include variable throat area,

(2) experimental ground tests that verified the engineering design analysis model,  and

(3) mission predictions evaluating this “unchoked throttle” in a gas generator-fed ramjet propulsion system for an AMRAAM missile,  plus variable drag as candidate means to improve the throttling control. 

This was work I did at what was then Rocketdyne/Hercules in McGregor,  Texas,  ably assisted by Venton A. Kocurek.  Unfortunately,  my friend and colleague Venton is now deceased,  but he was a listed author on the paper that I presented.  That paper is Ref. 1.

I literally photographed the figures in my hard copy of the original presentation,  to produce most of the figures presented herein.  There was no other readily-available way to digitize them.


In most gas generator-fed ramjet designs,  the gas generator is a solid propellant device that is fuel-rich in formulation,  with a choked exit,  meaning the flow is sonic at the minimum area of that exit.  For more details,  see Refs. 2,  3,  and 4

These designs may be fixed flow,  or flow to a fixed delivery history set by the propellant grain design,  or else they can be reliably throttled by varying the choked area of the sonic exit,  per Ref. 5.  As it turned out,  attempting to vary the propellant effective burn rate by means of mechanically-extracted wires proved to be unreliable in test.  That concept was tested at another contractor.  The variable-area valve,  in the form of a pintle valve,  was invented at Rocketdyne/Hercules.  I played a key role in that.

The alternative throttle approach described here is to let the gas generator exit run unchoked,  so that the ramjet engine chamber pressure essentially drives the propellant burn rate inside the gas generator chamber.  If the solid propellant ballistic characteristics and generator exit design are correct,  this can approximate constant fuel/air ratio control quite well,  regardless of the absolute level of the engine airflow.  This has distinct advantages for systems that must fly from low to high altitudes,  and it does this with no moving parts or control systems.  Fuel regulation is limited,  but inherent to the design. 

This technique was demonstrated by the French in flight test (see Ref. 6),  but was not pursued by them,  as they did not have fuel propellants of the required ballistic characteristics (namely burn rate exponents near unity).  We did have appropriate propellants at Rocketdyne/Hercules,  and I pursued this into extensive testing,  on company independent research and development (IR&D) funds,  in full scale engine hardware,  using short-burn gas generators based on convenient lab motor hardware. 

After the JANNAF paper,  we continued testing of various fuel propellants in the unchoked-generator hardware set on IR&D.  We found it to be a safer test method for experimental propellants than the usual choked generator,  because the unchoked generator is essentially a “strand bomb” at only the limited engine pressure.  Many such fuel candidates were tested this way,  including a highly-metallized boron formulation,  and a completely non-metallized “clean fuel” that met NATO min smoke criteria.

The generator effluent stream is the fuel to be burned with air in the ramjet chamber just downstream.  This offers the potential of the far-higher specific impulse of the airbreathing ramjet,  while simultaneously offering the “wooden round” simplicity and reliability of the solid.  Given some sort of fuel rate control to the right fuel/air ratio,  this potential can be achieved across a variety of missions.

Fixed and fixed-delivery designs suffer when flying to high altitudes.  Choked-throttle designs offer some altitude capability at the cost of propellant load displaced by the volume of the throttle.  The unchoked-throttle approach offers high altitude capability without any fuel volume displacement by a throttle valve.  However,  it is not an arbitrary-command throttle technique,  which the choked throttle valve is.

There is a very strong effect of both fuel propellant formulation and ramjet chamber flameholding flowfield geometry,  upon achieved combustion efficiencies,  as described in Ref. 7.  For the IR&D effort,  I used single center port fuel injection into an asymmetric twin inlet geometry.  If choked,  the port was small.  If unchoked,  the port was large.   Results are thus comparable for both choked and unchoked tests,  despite the slightly non-optimal injection geometry.  The heavyweight lab motor as a short-burn gas generator was very convenient,  and I was often able to use the full size flight-like combustors twice,  before refurbishment!  (The IR&D tests included testing experimental insulations,  too.)

Engineering Design Analysis of Unchoked Generators

The simplest design analysis model makes generator fuel flow proportional to ramjet chamber pressure raised to the fuel propellant’s burn rate exponent.  This model includes the assumptions that (1) burning surface is a constant,  that (2) there are no soak temperature effects upon burn rate,  and that (3) changes in ramjet chamber pressure do not affect the speed in the injection port.  Those are generally bad assumptions,  as all of these are first-order effects.

The next simplest model makes the fuel propellant burn rate proportional to ramjet chamber pressure raised to the fuel propellant burn rate exponent,  but allows a variable burning surface.  This still neglects soak temperature and port speed effects.  Both of those are first order effects.

The model presented in the JANNAF paper,  which I devised,  avoids these difficulties.  It only presumes a convergent-only approach to the min port area.  Further,  the ramjet pressure is the actual forward-dome static pressure where the fuel jet enters,  not some other measure of ramjet chamber pressure.  This matches the subsonic jet condition that jet pressure equals surrounding pressure.  See Fig. 1.

It does not presume constant speed through the port,  nor does it presume anything about the fuel propellant burning surface or propellant grain temperature soak-out effects upon burn rate.  It even includes the effects of generator chamber c* velocity,  which reflects gas generator flame temperature and (effective) gas properties.  This model even includes transient c* efficiency effects.

There are 3 things to worry about:  (1) the propellant grain flow rate,  (2) the port flow rate,  and (3) other relevant relationships.  The “other relevant relationships” are how you tie together the propellant grain and subsonic port models.  Each is detailed here,  resulting in a final expression for fuel flow rate as a function of ramjet chamber forward dome pressure.  

Figure 1 – Image of Presentation Chart Showing the Situation to be Modeled

               Propellant grain flow rate

The propellant grain flow rate wf is a function of gas generator expulsion efficiency ηexp,  burning surface S,  propellant density ρ,  and the power law describing burn rate versus chamber pressure r = a PGn.  That relationship is normally expressed as wf = ρ ηexp S a PGn.  The factor “a” in the burning rate law is also a function of the propellant soak-out temperature.

If we let G = ρ ηexp S,  and we let e = (PG/P3)n = (1 + 0.5*(γ – 1)*Mp2)exp where exp = n γ/(γ – 1),  and where Mp is the port Mach number and γ the specific heat ratio of the gas generator effluent stream,  then we have wf = G a e P3n.   Note that “a” scales as fT = exp[σp(T – Tref)] to model grain soak-out temperature T:  a-at-T = a-at-Tref * fT.  Tref is usually taken to be 77 F = 25 C,  and fuel-rich propellant σp usually falls in the 0.2%/F = 0.002/F range,  sometimes a bit higher.  (Fully oxidized σP is usually about half that value.)

               Port flow rate

The port flow rate into the ramjet combustor is wf = ρP VP Ap,  where ρP and VP are the density and velocity at the minimum port area AP,  and the Mach number Mp in that port is subsonic,  which also implies Pjet = P3.  We presume that ideal gas compressible flow considerations apply at specific heat ratio γ,  for the density vs pressure and temperature,  and also for the speed-of-sound.  Speed-of-sound is for the velocity versus Mach number relationship. 

The empirical characteristic velocity c* includes both achieved chamber temperature and effective chamber gas properties,  and there is a time-dependent scaling factor on c* that is denoted by η*,  which can model the start-up effects of low free volume and cold surfaces.  The empirical steady-state c* is best determined from motor tests at various pressures,  and is modeled as another power law c* = K PGm.  For fuel-rich propellants,  m usually falls in the 0.01 to 0.10 range,  larger than for fully-oxidized. Thus,  including the start-up effects,  c* = η* K PGm.

Now,  we let d be a particular Mach number function as d = (1/Mp)*(1 + 0.5*(γ – 1)*Mp2)exp,  where exp = m γ / (γ – 1) – 0.5.  And,  we let B = gc {[(γ + 1)/2]exp}0.5 where exp = (γ + 1)/(γ – 1).  Under these definitions,  the port massflow expression becomes wf = [P3(1-m) Ap B]/[η* K d].   See the third consideration for more definitions.

               Other relevant relationships

The normal power law for propellant burn rate is r = a PGn.  Be aware that when plotting burn rate r versus chamber pressure PG on a log-log plot,  the slope of the line is the exponent n.  There may be different values of n (and therefore “a”) that apply in different regimes of PG.  Be aware that “a” also scales by fT  very nonlinearly with grain soak-out temperature,  as already indicated. 

From theory,  the characteristic c* velocity is a function of achieved chamber temperature TG and gas properties.  The usual equation is c* = {[gc RP TG / γ][0.5*(γ + 1)]exp}0.5,  where exp = (γ + 1)/(γ – 1).  RP is the gas constant Runiv/MW.  This is normally applied to choked nozzles as wf = PG CD At gc / c*.  But with an appropriate port Mach number function (d as described above),  it can be used for unchoked ports. 

For a subsonic jet issuing from the fuel port,  the static pressure in the jet Pjet must equal the surrounding static pressure P3.  Thus Pjet = P3.  The d function then gets you from PG to Pjet which is P3.

We now define flow function f to be the product of flow function e from the grain massflow,  and flow function d from the port massflow.  Thus f = de = (1/Mp)*(1 + 0.5*(γ – 1)*Mp2)exp,  where exp = (n + m) γ / (γ – 1) – 0.5.  We also define factor H to be H = a K,  at any given soak-out temperature.  That is how the grain and port models are tied together.

               Overall Unchoked Flow Rate Relationship

Combining the information from these three sources,  the overall port flow function is

G H f η* = P3(1-n-m) AP B

which determines MP via f from any given value of P3.  G,  H,  AP,  and B are constants for any given mission,  as are n and m.  Finding MP from f is a transcendental (or numerical interpolation) solution.  Once MP is known,  e can be found,  and the grain flow equation yields wf for any value of P3

wf = G a e P3n

The overall propulsion balance of wf versus P3 in an actual engine is iterative,  since the value of P3 depends upon both the value of the captured airflow,  and the delivered fuel flow (as well as the air total temperature).     But for ground test approximation purposes,  the iterative balance need not be calculated,  since test airflow is fixed by intent.  For that,  one plots combustor fuel flow rates versus calculated P3 values at the test total temperature,  parametric upon inputs for air flow rate and mixture ratio.  Then one calculates fuel flow out of the generator as a function of assumed P3 values,  parametric upon burning surface and soak temperature (if applicable).  These are superposed on the same plot.

Any proper ramjet cycle code can be used to compute a map of fuel flow rate wf versus P3 for a given value of air total temperature Tt2,  parametric upon both air flow wa and fuel/air ratio (or equivalence ratio φ),  as shown in Fig. 2.  This creates a sort of carpet-plot map. 

Figure 2 – Image of Presentation Chart Showing Superposed Ramjet Map and Generator Flow Lines

These gas generator relationships as described herein can define fuel flow rate versus the same P3 values as are listed for the ramjet map,  without any iteration to balance P3 in the ramjet engine.  At any given airflow (and air temperature),  where the engine and gas generator wf curves cross,  is where the system will equilibriate.  You just interpolate the P3 and mixture ratio values expected for the test. Mixture ratio is an output,  not an input,  in this scenario.  The figure shows that,  as well.  This presentation approach is something I devised.  It worked rather well.

What is important here is the shape and slope of the generator fuel flow rate curves versus P3.  If the propellant burn rate exponent is exactly unity,  these will be straight lines versus P3.  THAT is exactly-constant fuel/air ratio operation,  which is exactly constant-φ operation,  regardless of the airflow (and air temperature).  A high burn rate exponent very near unity (above or below!) will therefore approximate constant fuel/air ratio control quite closely.  A low fuel propellant exponent will not,  and fuel/air ratio will thus vary as airflow varies.


The first thing I did with this model was to check the sensitivities of the equilibrium point mixture ratio to changes in various design parameters.  I looked at the effects of burn rate,  port area size,  and inlet air total temperature,  and plotted these at two different values of design port Mach number.  The design point was 9.2 lbm/sec air at 800 R,  with an equivalence ratio near 1,  meaning stoichiometric.  Results are given in Fig. 3.  This is a plot of equivalence ratio versus percent change in each parameter.  There is a plot at the low port Mach number,  and another at the higher port Mach number.  

Figure 3 – Image of Presentation Chart Showing Sensitivity of Equivalence Ratio to Various Parameters

The influence of burn rate is very strong indeed,  as evidenced by the very large slopes on the plots associated with it.  Burning surface,  though not plotted,  would have a similar large effect.  The product of burn rate coefficient and burning surface area is in the G factor of the model.

Air total temperature has a much weaker effect,  reflected in its modest slope.  This is true for both the lower and higher port Mach numbers.

The design port area has a small effect (low slope) at the lower port Mach number,  but a much more pronounced effect (steeper slope) at the higher port Mach number.  At first glance that would seem to suggest that a variable port area mechanism might be used to compensate for soak-out changes to burn rate,  and also to compensate for burning surface variations as the propellant web burns.  All that would be required to make this possible,  is designing to a high subsonic port Mach number instead of a very low subsonic port Mach number. 

As seductive as that notion was,  due diligence required that I verify motor stability.  Choked motors are notoriously unstable if burn rate exponent approaches unity too closely.  For the unchoked generator,  we want a burn rate exponent very close to unity,  or even somewhat greater than unity. 

For a conventional choked motor,  the chamber pressure PG drives both grain massflow,  and massflow through the nozzle.  You simply plot the massflow versus pressure curves for the grain and the nozzle onto the same plot.  Where the curves cross is the operating point.  The slope of the nozzle massflow curve needs to be greater than that of the grain massflow curve,  at that operating point,  in order for the motor to be stable. 

In that stable case,  an upward excursion in pressure takes the choked motor to a point where the nozzle massflow is larger than the grain massflow.  That acts to drain the chamber and reduce its pressure back toward equilibrium.  A similar argument prevails for a downward excursion in pressure:  the grain massflow is larger than the nozzle massflow.  That acts to fill the chamber and raise its pressure back toward equilibrium.  THAT is the choked motor stability argument in a nutshell.

For the unchoked port,  both pressures PG and P3 are important,  but the backpressure P3 actually drives the system,  since their ratio is determined by the port Mach number MP.  The most direct analog to the choked motor stability plot is the grain massflow and port massflow versus P3The same slope ratio consideration applies for stability:  the slope of the port massflow curve needs to exceed the grain massflow curve at the design point where the curves cross. 

Because the ratio of the two pressures is controlled by the value of MP,  an alternative format for the stability plot is grain and port massflows plotted versus MP instead.  Because I wanted to investigate whether a low or high value of subsonic MP can be used safely,  that format was selected here. 

The propellant used for this investigation was LPH-258,  an early version of a choked-generator throttling fuel,  of which some mixes showed a lower exponent in the very low pressure range,  a higher exponent in an intermediate range,  and a lower exponent in the high range of pressures.  This particular mix tested as having an exponent greater than unity in that intermediate range. 

Plots of grain and port massflow versus MP were made for the low range of pressures and the intermediate range,  where it was anticipated that unchoked test articles might be operated.  The breakpoint between those pressure ranges was at PG = 65 psia for this mix of propellant.  Those plots are given in Fig. 4

On the left hand plot,  where exponent is less than unity,  the slope of the nozzle massflow is larger than the slope of the grain massflow at the indicated operating point where the curves cross,  where port Mach number is roughly MP = 0.7.    This indicates stable operation with this propellant is feasible at higher subsonic MP,  when operating in the low range of P3 and PG

On the right hand plot,  where the exponent is greater than unity,  there are actually two curve crossings,  indicating two candidate operating points,  one near MP = 0.7,  the other nearer MP = 0.95.  The nozzle curve slope is greater than the grain massflow curve at the lower MP,  but the reverse is true at the upper MP!  That upper point is unstable,  and is so close to choking,  that the generator could easily and spontaneously choke and explode!  The stable lower point is just not that far away from the upper unstable point.  A sufficient disturbance (like a sudden P3 drop for any reason) could drive the motor to the instable condition,  whereupon it might explode. 

Figure 4 – Image of the Presentation Chart Showing Unchoked Stability Plots For 2 Regimes of Exponent

The lessons here were rather clear.  First,  you want lower values of subsonic MP,  most especially when the exponent is near or exceeds unity.  Second,  to maximize the stability margin at that lower stable operating point,  you need to design for very low values of MP indeed,  closer to 0.1 than 0.5.  Third,  that low MP design choice makes modulating AP unattractive for compensating burn rate,  soak-out,  or burning surface variations,  precisely because the sensitivity to that variable is going to be so low.

Short-Burn Full-Scale Ground Tests

The test hardware is shown in Fig. 5,  along with some data on the first four successful live-burn tests conducted in it.  The gas generator was a standard 6-inch heavyweight lab motor with one or two cartridge-loaded internal burning propellant grains.  The inlet and combustor rig was full-scale,  flight-like hardware borrowed from the contract VFDR (variable-flow ducted rocket,  being a choked,  valve-controlled gas generator-fed ramjet) program,  and insulated on IR&D. 

The lab motor is coupled to the combustor with a custom adapter forward dome that was fabricated on IR&D.  It was detail-designed by my friend and colleague Jerry Lammert.  The big injector tube in the figure was only used once,  on the very first test,  which resulted in a “no-burn” (airbreathing ignition failure) in the ramjet.  After that,  the big injector tube was deleted from the test rig. 

The direct-connect test facility at Rocketdyne/Hercules by this date had 20 lbm/sec airflow capability at up to 1660 R total temperature.  It used two 10 lbm/sec lines that used pebble bed heaters,  one capable of 1210 R,  the other capable of 1660 R.  These tests were run at open-air nozzle conditions,  although the facility had high altitude capability by means of a supersonic diffuser plus a steam ejector.  

Figure 5 – Image of the Presentation Chart Showing Test Hardware and Initial Tests to be Run

Venton Kocurek was still a fairly recent hire at that time,  and I “broke him in” on ramjet work planning for these tests and reducing the data afterward.  Plus,  we did some of the “dirty-fingernails” test article assembly and post-test disassembly work together.

The very first test run in this configuration was a no-burn run with a propellant designated LPH-563A.  However,  even though no ramjet combustion was obtained,  we did demonstrate that the fuel flow followed the airflow variations in this unchoked generator mode.  That data is given in Fig. 6

The left panel shows plots versus time for the pressure at the air metering venturi,  and the combustor P3 response.  The right panel shows the traces versus time for combustor P3 and generator PG.  It is quite clear that the fuel tracked the air,  in a fair approximation to constant fuel/air ratio.  

The no-burn on that very first test was attributed to the fuel injector.  The proof:  after its deletion,  we never had any trouble again,  lighting the ramjet combustor,  with any of the fuels tested.  

Figure 6 – Image of the Presentation Chart Showing Unchoked Fuel Control in a No-Burn Test

Subsequent to the 4 live-fire tests presented at the JANNAF meeting,  a series of experimental fuels was tested in this same hardware set,  as full-scale,  short-burn tests.  Some of those were unchoked with graphite nozzle inserts of very large diameter and internal-burning grains,  others were choked with graphite insert nozzles of very small diameter and end-burning grains.  All were simple single-port dome injection on centerline,  which while not “tuned up” for max performance,  performed well enough to see the correct trends among the experimental propellants.   

Flight Predictions

I had Venton Kocurek modify an Air Force-supplied trajectory program called ZTRAJ to correctly model the unchoked generator option.  He was more of an expert at computer programs than I was,  and he was aware of my full-blown unchoked analysis,  which made him the perfect choice.  This was a large effort that took some time,  but Venton did an outstanding job. 

We did not use the full-blown,  full-capability unchoked generator analytical model for this.  Instead,  we used the intermediate model described above,  that essentially just makes fuel flow a power function of P3,  using n as the exponent.  But,  we added correction factors for modeling variations in burning surface,  and for modeling the effects of soak-out temperature upon burn rate.  The actual changes to the code were more complex than just that notion,  as is illustrated in Fig. 7.  

Figure 7 – Image of the Presentation Chart Showing the Modifications to the ZTRAJ Code

We already had the ZTRAJ computer model for the throttled ducted rocket ramjet,  here designated TDR.  We had the data for the fixed-flow ducted rocket ramjet,  designated FFDR,  and so we easily set up a computer model of it.  I sized an unchoked generator propulsion scheme for these same basic missile models,  termed “backpressure rate control” or BRC.  My as-sized BRC is shown in Fig. 8.  The as-sized TDR and FFDR are shown in Fig. 9.  A comparison of sizepoint data among the 3 designs is given in Fig. 10.  All three were sized using the same low-percentage boron fuel,  thus entirely removing fuel characteristics as a variable,  from the fuel management and performance comparison.

These vehicles size quite differently,  because of their quite-different propulsion characteristics.  The FFDR sizes at cold takeover,  cold-soaked,  where it runs the leanest.  It has to meet Air Force-specified thrust margins,  at a min takeover speed supplied by the integral (nozzleless) booster.  It has to meet an inlet pressure margin specification at sizing.  At warmer conditions,  it has more-than-minimum thrust margin,  and runs richer in mixture.  This enrichment reduces its takeover thrust margin again,  when soaked out hot,  because it runs over-rich,  which in turn reduces performance once again.

The TDR sizes at the hot takeover conditions,  soaked out hot.  It has to meet min thrust margin requirements soaked out hot,  and also an inlet pressure margin.  It exceeds thrust requirements at colder conditions,  because its mixture ratio is under full control with the throttle valve system. 

The BRC was sized at its shock-on-lip Mach number,  hot soaked on a hot day,  at max tolerable mixture.  Thrust margin was maximized at this condition.  For all 3 propulsion systems,  inlet size was constant,  only the ramjet throat area A5 was revised to match-up the engine balance in the sizing. 

Figure 8 – Image of the Presentation Chart Showing the As-Sized BRC Missile

Figure 9 – Image of the Presentation Chart Showing the As-Sized TDR and FFDR Missiles

Figure 10 – Image of the Presentation Chart Showing Sizepoint Data Variations for All 3 Missiles

There are 4 plots in Figure 10.  Upper left is thrust margin versus soak-out temperature at min takeover speed.    Lower left is equivalence ratio vs soak temperature.  Equivalence ratio is a measure of mixture strength:  1 is stoichiometric,  greater than 1 is fuel-rich,  less than 1 is lean.   Upper right is inlet pressure margin data versus soak temperature.  These need to stay positive,  and they do.  Lower right is a normalized specific impulse versus soakout.  These data were normalized to stay unclassified,  and probably need to remain so for ITAR (international traffic in arms regulation) reasons. The BRC generally falls intermediate in min takeover performance values between the TDR and the FFDR.

The missions chosen for evaluation were co-altitude head-on engagements,  with the launch aircraft and the target both flying at Mach 0.9.  Standard day conditions were presumed.  Upon seeing the launch,  the target turns 180 degrees and accelerates rapidly at thrust/weight = 1 to Mach 1.5 as an attempt to get away,  converting the engagement to a tail chase.  This was evaluated at 20,000 feet with the target making his turn at 9 gees,  and at 40,000 feet with the target making his turn at 4 gees in the thinner air. 

Missile engagement limitations were intercept Mach 2.26 at 33 gees at 20,000 feet,  and intercept Mach 2.60 at 18 gees at 40,000 feet in the thinner air.  To be a hit,  miss distance had to be no more than 10 feet. See Fig. 11.

These computer simulations were run with our modified ZTRAJ code,  by Venton Kocurek under my guidance.  The code already had fuel control options to model the FFDR and the TDR.  By adding the BRC to it,  we could do this comparative study.

What results are of interest are F-pole versus launch range,  and intercept Mach versus launch range,  plotted for several different launch ranges (each launch range its own computer run).  End of mission could be propulsion limited (out-of-propellant and coasting down) or time-limited (battery life for the guidance).   Launch range is self explanatory,  being the horizontal separation distance between the two aircraft when the missile is launched.  F-pole is the slant range between launch aircraft and target at the time the missile intercepts the target. It is related to something called an “F-pole turn” by the combat pilots.

The TDR,  BRC,  and FFDR missiles (as I sized them) were evaluated on these missions.  The Air Force asked us to include some dive brake “drag flippers” on the BRC,  to determine if drag modulation might be a better way to help manage the fuel supply in the BRC.  These brakes would “trigger” at a set speed,  to keep the vehicle flying slower,  thus hopefully conserving fuel.  The Air Force suggested that we use a 3500 feet per second trigger speed.  Initial runs were made using that suggested trigger speed.

Figure 11 – Image of the Presentation Chart Showing the Two Missions Used For Evaluation

Results for the two altitudes in terms of F-pole versus launch range are given in Fig. 12.  Results for intercept Mach versus launch range are given in Fig. 13.  These results were normalized to avoid classification,  and probably should remain normalized because of ITAR. 

At the low altitude,  there was little difference in the F-pole performance versus launch range among all the configurations.  The TDR did the best,  the BRC intermediate,  and the FFDR the least.  Drag flippers on the BRC made very little difference,  as the missile just barely reached the trigger speed. 

The story at the high altitude was similar,  except that there was a significant shortfall of F-pole performance of the FFDR relative to the TDR.  The BRC was intermediate,  but very nearly as good as the TDR.  Here,  the drag flipper trigger speed was never reached by the BRC missiles at all,  so there is no difference traceable to it.

Figure 12 – Image of the Presentation Chart Showing F-Pole Results

For the intercept Mach versus launch range results,  the story is still quite similar.  The spread between TDR and FFDR is almost zero at the lower altitude,  but considerable at the high altitude. 

At the low altitude,  the BRC does a little worse than the FFDR,  but only just a little.  The drag flippers made very little difference,  with the drag flipper BRC very slightly worse than the plain BRC. 

At the high altitude,  the BRC configurations both did almost as well as the TDR,  and much better than the FFDR.  The drag flippers made no difference,  not being triggered at all on this mission.  

Figure 13 – Image of the Presentation Chart Showing Intercept Mach Results

At this point,  we re-ran only the BRC,  with and without the drag flippers,  on only the 40,000 foot mission.  The only change was lowering the drag flipper trigger speed to 3100 ft/sec,  so that they would trigger over a more significant portion of the mission. 

The results of this revision are given in Fig. 14.  This shows only intercept Mach versus launch range,  and that for only the two BRC configurations.

There is a significant difference between the plain BRC and the BRC with the drag flippers.  The plain BRC simply does far better.  It has higher intercept speeds at longer launch ranges.

Apparently,  the fuel that might have been saved by slowing down,  instead gets eaten-up overcoming the extra drag,  and then some.  Therefore,  drag modulation is just not very attractive as a means to improve the fuel regulation in the BRC propulsion scheme. 

We already know the BRC design responds weakly to port area modulation,  because stability margins demand very low port Mach numbers at very large port diameters. 

It would appear that designs featuring as low a propellant burn rate sensitivity σP as possible,  and as neutral a surface-web trace as possible,  is the best route for further development of BRC propulsion.

These results were communicated to the Air Force before the JANNAF presentation was made.  

Figure 14 – Image of the Presentation Chart Showing Intercept Mach at Higher Altitude and Lower Trigger Speed

Final Remarks

Further tests of experimental fuel propellants were made in this short-burn test hardware,  but not in time for the JANNAF presentation.  These tests are well-described in Refs. 4 and 7,  including some color photography from those tests,  plus there was a propellant “shoot-off” on the contract VFDR program.  The two low-percentage boron fuels reported in the JANNAF presentation were part of that “shoot-off”,  along with a high-metal boron-titanium propellant,  and a non-metallized “clean fuel” that met NATO min smoke criteria,  despite being oxidized with ammonium perchlorate.   I developed both of those very rapidly on IR&D,  using these short-burn test methods and hardware.  The contract “shootoff” verified that all four of those IR&D fuels were every bit as good as the two contract fuel propellants. 

The problem of achieving low propellant burn rate temperature sensitivity had been addressed earlier on IR&D,  and on the contract VFDR programs,  with something called the “strand augmented end burner” (SAEB).  Those gas generators on the contract programs were end burners,  fitted with a throttle valve.  The SAEB version used LPH-563A fuel rich matrix propellant,  with a fully-oxidized strand propellant using the same binder system.  The plain end burner used LPH-453 propellant,  which had been developed from the much earlier LPH-258 formulation that I tested unchoked on IR&D.

By fitting such grains with fully-oxidized propellant strands that had burn rates always higher than the majority fuel-rich matrix propellant,  we divorced the burn rate ballistics from the fuel effluent characteristics that we needed.   The strands had half or less the temperature sensitivity of the matrix fuel propellant.  That allowed more of the valve area turndown to address fuel rate turndown for high altitude,  instead of compensating for temperature sensitivity.  See Fig. 15 for an image of the SAEB.

Figure 15 – The End-Burning Dual-Propellant SAEB Design

Designs like the FFDR could feature either end-burning or internal-burning grain designs,  using high intrinsic burn rates in the end-burners,  and low intrinsic burn rates in the internal-burners,  just all at high chamber pressures.  The end burners have slightly-higher cross-sectional loadings.  There is no propellant displacement by a throttle valve or its interstage in the FFDR.

The BRC featured internal-burning grain designs using high intrinsic burn rates,  just at very low chamber pressures where the actual burn rate is low.  To solve the propellant burn rate temperature sensitivity issue,  we needed a similar two-propellant solution for the internal-burning designs. 

On IR&D,  I had my friend and colleague W. Ted Brooks develop a model for such a device.  He named it the “circumferentially-augmented radial burner” (CARB).  Ted Brooks (now deceased) was my mentor in internal ballistics when I was a young engineer,  and he wrote the NASA monograph on internal ballistics (Ref. 8).  

I believe the CARB would have worked very well,  but we never got to test it.  See Fig. 16 for an image of the CARB design. 

Figure 16 – The Internal-Burning Dual-Propellant CARB Grain Design

All of these gas generator designs use case-bonded grain technology,  but must survive cold soak to -65 F without cracking the propellant or peeling its bond away from the case.  End-burning designs are the worst offenders in this respect,  but some high cross sectional-loading internal burners also suffer.  Solid elastomer internal case insulation is just not compliant enough to do that job.  At Rocketdyne/Hercules,  we invented something called the stress-relieving liner that was compliant enough to serve this function successfully.  See Fig. 17.  

Figure 17 – The Stress-Relieving Liner Design That Supports End-Burners and Other Designs

As an aside,  the integral booster shown above for the 3 configurations analyzed above was a “nozzleless booster”.  This used a two-propellant overcast to minimize the losses otherwise inherent in a nozzleless booster rocket,  which ejects no booster nozzle assembly or debris.  That design and those propellants were developed on IR&D and went to the contract VFDR program for validation,  and they became the baseline.  That concept is illustrated in Fig. 18

Figure 18 – The Dual-Cast Nozzleless Booster Concept

Right after the subject JANNAF presentation described here,  the plant closure announcement was made.  The following November (1994),  I was laid off in the first wave of layoffs,  being most closely associated with new product IR&D work,  not ongoing contract work.  That ended my career in aerospace defense work,  there being a massive industry contraction underway,  after the fall of the Soviet Union. 

The plant finally closed for good within another year (by late 1995).  The sad tale of what happened to the incredible gas generator-fed ramjet (and nozzleless booster) technologies that we had,  is covered by refs. 4,  5,  and 7.  All of that was lost!  If the US military wants a ramjet missile of AMRAAM class today,  then they have to buy the “Meteor” from the Europeans.  It’s a TDR type of gas generator-fed ramjet,  very similar to what we had.  Their valve geometry is a bit different,  but it is the same basic notion. 


Most (but not all) of these references are articles posted elsewhere on this site.  The others can be located by an internet search,  excepting possibly this particular JANNAF presentation (ref. 1),  which is why I wrote this article.  There is a catalogue of some related articles that may be relevant,  in Ref. 9

To quickly find any of the articles on this site,  you need the date and title to use in the navigation tool,  left side of this page.  Click first on the year,  then the month,  then on the title if need be (if multiple articles were posted in that month).  Clicking on any figure in an article lets you see all the figures enlarged.  Top right is an X-out feature that takes you right back to the article.

#1. Gary W. Johnson and Venton A. Kocurek,  “Evaluation of Unchoked Generator Ducted Rocket Ramjets”,  paper given at the 1993 JANNAF meeting held at the Naval Postgraduate School,  Monterrey,  CA,  given November 17, 1993.

#2. Gary W. Johnson,  “Primer On Ramjets”,  article posted on http://exrocketman.blogspot.com,  10 December 2016.

#3. Gary W. Johnson,  “Ramjet Cycle Analyses”,  article posted on http://exrocketman.blogspot.com,  21 December 2012.

#4. Gary W. Johnson,  “The Ramjet I Worked On The Most”,  article posted on http://exrocketman.blogspot.com,  2 August 2021.

#5.  Gary W. Johnson,  “Use of the Choked Pintle Valve for a Solid Propellant Gas Generator Throttle”,  article posted on http://exrocketman.blogspot.com,  1 October 2021.

#6. Propulsion and Energetics Panel Working Group 22,  “Experimental and Analytical Methods for the Determination of Connected-Pipe Ramjet and Ducted Rocket Internal Performance”,  AGARD Advisory Report 323,  July 1994.

#7.  Gary W. Johnson,  “Ramjet Flameholding”,  article posted on http://exrocketman.blogspot.com,  3 March 2020.

#8.  W. Ted Brooks,  “Solid Propellant Grain Design and Internal Ballistics”,  NASA SP-8076,  March 1972.

#9.  G. W. Johnson,  “Lists of Some Articles By Topic Area”,  article posted on http://exrocketman.blogspot.com,  21 October 2021.  

Thursday, December 1, 2022

How Ramjets Work

Update 23 March 2024:  For the readers of this and other similar articles about ramjet propulsion,  be aware that GW’s ramjet book is finally available as a self-published item.  Its title is “A Practical Guide to Ramjet Propulsion”.  Right now,  contact GW at gwj5886@gmail.com to buy your copy. 

He will,  upon receipt of payment by surface mail or Western Union (or similar),  manually email the book to you as pdf files.  This will take place as 9 emails,  each with 3 files attached,  for a total of 27 files (1 for the up-front stuff,  1 each for 22 chapters,  and 1 each for 4 appendices).  The base price is $100,  to which $6.25 of Texas sales tax must be added,  for an invoice total of $106.25. 

This procedure will get replaced with a secure automated web site,  that can take credit cards,  and automatically send the book as files.  However,  that option is not yet available.  Watch this space for the announcement when it is.  

GW is working on a second edition.  No projections yet for when that will become available.


A ramjet scoops up air,  decelerates it,  and increases its pressure by the pitot ram effect.  It then burns fuel with that air,  at the elevated pressure,  which accelerates its speed some.  Expanding that stream back to ambient pressure in the nozzle requires that elevated combustion pressure,  and produces a really fast exhausted stream.  That nozzle thrust less the ram drag of the ingested air is the “net jet thrust”.  That net jet thrust must exceed the airframe drag plus all the propulsion-related drags.  

Ramjets prefer critical-to-supercritical inlets to maximize captured airflow,  in order to maximize thrust.  For a ramjet,  subcritical spilled air is not only added drag,  it is also lost thrust.  Gas turbines,  on the other hand,  actually need a subcritical inlet in order to match the captured airflow to the throughflow demanded by the gas turbine at any given rotor speed and altitude.  I've got all that well described in detail in the "Fundamentals of Inlets" article dated 9 November 2020.  

The RJ-43 ramjets that pushed the old Bomarc missile used V-gutter stabilization.  The old Talos missile had a ramjet with an inverted can-type combustor,  sort of like the usual can-type combustors in gas turbines,  but reversed,  with radial flow outward instead of inward. 

Figure 1 – Basic Notions

For more details about any of this stuff,  plus related information,  please go look at some of my ramjet articles on "exrocketman".  There's a sort of catalogue article with many of the articles listed with titles and dates,  by topic area.  That one is "Lists of Some Articles By Topic Area",  dated 21 October 2021.  There is a navigation tool on the left side of the page.  Click on the year,  then the month,  then the title if need be.  That's how to get to the one you want,  the fastest.  Just jot down the titles and dates you want from the catalogue article,  then go right to them.  

Flameholding is a stable recirculation of partly-combusted hot gas behind some wake-producing feature,  where it mixes with fresh air and fuel,  reaching a mixed temperature high enough to cause fuel-air ignition.  That recirculating wake zone is required because the flow speed is far higher than the flame propagation speed.  This process has to happen continuously.  I have an article on "exrocketman" titled "Ramjet Flameholding" and dated 3 March 2020.  It's got a whole lot more detail.  

Too high a speed in the inlet diffuser air can literally blow out the recirculation flame like blowing out a match.  Too high a flow speed in the combustor can also blow it out.  Too low a diffuser air temperature,  too low a diffuser and combustor pressure (as at high altitude),  and too small a wake-creating feature,  reduces flame stability and can preclude ever getting any ignition at all.  If the flameholder goes out,  so does the whole engine!  These things are very configuration-specific,  and they vary from fuel to fuel,  too.  There are no general rules. 

It's bad enough in subsonic flow in a ramjet.  These flameholding things get really "iffy" in the supersonic flow inside a scramjet.  And yes,  flameholding indeed applies to scramjet,  until and unless the supersonic air static temperature greatly exceeds the fuel autoignition temperature. 

The same subsonic flameholding physics applies to gas turbine engine afterburners,  too.  Turbine combustor cans are a little different,  as up in the forward end,  mixture is rich and flow speed is less than flame propagation speed.  That's the flameholder.  About midway down,  mixture is leaning down near stoichiometric and flow speed is greater than flame speed.  The forward end is what pilots that mid-can burn.  The aft end of the can is not burning,  the hot gas is just being diluted down with excess air to a tolerable turbine inlet temperature.  The perforated can liner is air-cooled on its outside,  with air introduced into the interior through the pattern of holes.  Fuel injection is generally through the forward dome,  and the spark ignition to start it off,  is located fairly close by that forward dome.  

Figure 2 – About Flameholding

If you fly too fast,  the gas turbine combustor can liner melts,  because the captured and compressed air is so hot that it is no longer "cooling air".  Same goes for the compressor and turbine blading.  Most gas turbine engines are limited to about Mach 2.5 speeds.  There have been a few that reached Mach 3,  but those are extraordinary designs.  There was one that could reach Mach 3.5 in the Mig-25,  but it had a very short lifetime ~ 500 hours,  and you didn't overhaul it,  you replaced it entirely. 

That same overheated-air problem is why a ramjet (or a gas turbine afterburner) cannot use a simple V-gutter flame stabilizer above about Mach 3.5-ish.  Those are bathed in very hot flame on the downstream side,  and cooled by the inlet air on the upstream side.  Too fast,  and the inlet air is too hot to qualify as “cooling air” anymore.  I ran the numbers for a simple ramjet V-gutter flameholder at 40,000 feet altitude on a standard day,  with a 1-inch leg length for the stabilizing angle-type element.  Those numbers verify what I said about a top speed for any ramjet that uses V-gutter (or can-type) stabilization.  An insulated sudden dump flameholder is simply required to fly Mach 4+.

Figure 3 – Overheat Limits on V-Gutter

Update 12-6-2022 

I forgot to discuss the heat protection scheme for the combustor and nozzle of a ramjet (again similar to a gas turbine afterburner,  if you look at air-cooled technologies). Because of the high-speed "it's not cooling air anymore" problem,  the air cooling technologies common in afterburners and early ramjets cannot be used for flight speeds in the stratosphere above about Mach 3 to 3.5.  The captured air is simply too hot to serve that cooling function.  At lower altitudes,  that speed limit is even lower.

For flight at Mach 3.5+,  you simply have to use ablative technologies!  The fiber-reinforced rubber compounds that serve well in solid rockets are inadequate for that function in ramjets.  The exposure times,  and the mass fluxes that drive heating by scrubbing action,  are far too severe in the ramjet.  The strength and durability of the insulation needs to be roughly factor-10 better than the rubber-based rocket insulations.

Of the rubber compounds,  silicone rubber (specifically PDMS,  poly dimethyl silicone),  has the higher charring temperature.  It is still silicone at 600-700 F,  and is charring to carbon at around 1000 F.  It forms a carbon char layer,  but that layer sheds too easily,  and fractures too easily.  However,  if you add short carbon fiber to the formulation,  the char layer is a little stronger,  and adheres to the virgin rubber very much better.  

Adding silica powder to the formulation produces a sticky viscous silica melt that further strengthens the char layer against fracture,  and by a very significant amount.  Adding silicon carbide powder to the formulation strengthens both the virgin rubber and the char layer by the solid aggregate effect,  similar to the stones in concrete.  That silicon carbide aggregate does not melt at ramjet flame temperatures,  although it probably would in solid rockets.   

The result of all these additions is a char layer that resists fracture from applied air forces,  and that resists being sheared off the virgin material beneath.  That char layer has a little bit higher thermal conductivity than the virgin material,  but it still has an insulating effect.  If you also mechanically retain it,  you can continue to use it as insulation,  even when the virgin material is gone. 

There are two materials available,  that are formulated like this.  One is Dow Corning's DC 93-104 material.  The other is "Type 0" from Shin Etsu Silicones.  Being intended as military products,  neither is advertised to the public,  although you can buy them.  I have tested them both in full scale engine hardware as combustor insulators.  They perform quite similarly to each other.  Impregnating carbon cloth with PDMS polymer does not perform as well,  because it lacks the strengthening effects of the silica and silicon carbide powders.   I have tested that,  too. 

The shearing effect of the mass flux scrubbing is higher in the ramjet nozzle (same massflow,  smaller flow cross section area),  but not as high as in the solid rocket.  It is not necessary to use graphite throat inserts in the ramjet nozzle,  the way it is required in solid rocket nozzles.  The approach to the nozzle throat and the supersonic expansion cone,  may be silica phenolic ablative,  in both the ramjet and the rocket.  Those choices are well-tested,  and they work.  The ramjet nozzle can be a monolithic chunk of silica phenolic.  Correct fiber orientation is important to getting best performance out of it.   

This ablative construction was adequate for a long stratospheric cruise burn at Mach 4 in the ASALM design in ground testing and in flight test,  and it survived all the way up to Mach 6 on a short transient,  in one ASALM-PTV flight test.  This is just how you have to build them,  if you want to fly faster than about Mach 3 to 3.5.