Tuesday, February 4, 2020

One of Several Ramjets That I Worked On

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. 

Update 27 January 2026 It turns out I need to collect 6.75% sales tax,  not 6.25%.  That makes it price $100.00 + tax $6.75 = bill $106.75.  

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.

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One of the many things I got to work on,  when I was a defense industry engineer,  was the foreign technology exploitation of the Russian surface-to-air missile (SAM),  known to NATO as the SA-6 “Gainful”.  In Russia,  this was known as the 2K12 “Kub” (“Cube”) system,  with the missile itself a product of Vympel (no longer in existence).  It was the Vympel model 3M9 / 9M9 surface to air missile.

The SA-6 "Gainful" anti-aircraft SAM first appeared in public in the 1967 May Day parade in Red Square,  after the supporting technologies for it disappeared from the Russian unclassified literature in 1962.  It reached Russia’s client states in time for the 1973 “6-Day War” between Israel and Egypt.  That event led to my involvement,  as described below.  It had heavy,  voluminous vacuum-tube type electronics,  that also just happen to be nuclear-hard,  on the battlefield. 

SA-6 had been replaced by a rocket SAM with solid-state electronics in Russia by the 1980’s,  but it remains in the possession of some former client states.  It was in the hands of Serbian militias in the Balkans during the 1990’s Balkan wars,  where it downed the only F-117A stealth fighter ever lost to enemy fire.   It is now considered quite obsolete,  and is on public display as cutaway items (see Figure 1 and Figure 2),  yet those few still out there remain quite the potent SAM threat,  even today.

 Figure 1 – Cutaway Mockup of SA-6 “Gainful” on Public Display


In the first figure,  the forward cutaway areas show the seeker/radar electronics.  The yellow area forward of the big mounting ring (not a part of the missile) is the location of the blast-fragmentation warhead.  Aft of the ring one can see the four supersonic spike-type side mounted inlets and the forward control fins.  The yellow area aft of the fins is the forward portion of the solid rocket booster that is packaged inside the ramjet combustor.  The fixed tail fins are aft of the aft mounting ring. 


 Figure 2 – Another View of the Cutaway Mockup of the SA-6 “Gainful”


In the second figure,  the yellow zone aft of the aft mounting ring is the aft end of the solid rocket booster propellant in the aft end of the ramjet combustor.  The fuel-rich solid propellant gas generator is located aft of the forward fins,  between the inlets,  and is not very apparent in either figure shown here. 

These public display mockups are not entirely correct.  There was no room about the ramjet nozzle in which to package the actuators for moving surfaces on the aft fins.  Control was actually achieved by moving the forward fins,  against fixed aft fins.  And,  the booster nozzle was nested inside the rather large ramjet nozzle,  and ejected at boost-sustain transition (as were the inlet port covers).

At the time of its first appearance in the 1967 May Day parade in Moscow’s Red Square,  the CIA misidentified SA-6 as a solid rocket system with "exaggerated fairings".  This SAM was really a ramjet missile with 4 side-mounted supersonic inlets.  How CIA analysts managed to make that mistake still mystifies me to this very day.

Unlike other ramjets of that time (Talos and Bomarc for the US,  SA-4 “Ganef” for the Russians,  all SAM’s),  SA-6 “Gainful” was NOT a liquid-fueled ramjet,  it did not feature a single nose inlet,  and it did not have a staged-off or “carry-along” rocket booster.  It was the first flying example of something now termed an “integral booster” or “integral rocket-ramjet” (IRR).

The SA-6 ramjet sustainer was unlike anything seen before,  except in the odd patent.  At the time,  it was termed a “ducted rocket”,  although that terminology is vague and subject to multiple incorrect interpretations.  It is more properly termed a “fuel-rich solid-propellant gas generator-fed ramjet”,  or just “gas generator-fed ramjet” with the “fuel-rich solid propellant” part of that terminology simply understood.   

Some History

By the 1973 “6-Day War”,  this Russian system had been given to client states,  notably Egypt.  Because it had about 3 times the "legs" of a solid rocket system of that size,  and 1950/1960-vintage heavy and voluminous vacuum-tube electronics,  it knocked down Israeli Phantoms like ninepins,  and cost them about 30% of their air force,  in only those 6 days. 

That was a technological "Pearl Harbor" that really upset the entire West.  These events do happen!  (And that one has not been the only one during my lifetime.)  Once it was understood that SA-6 really was a ramjet,  that spawned a lot of ramjet work in the US defense industry that persisted until about the year 2000.  Which is exactly why I was the “ramjet guy” at Rocketdyne-McGregor,  with my training in propulsion and high-speed aerodynamics.

The Israelis captured damaged SA-6 hardware on the battlefield,  took it apart,  made drawings,  and tried to understand what it really was.  They didn't fully understand what had proved to be a ramjet,  but that was NOT liquid-fueled!  So they went to the CIA with it.

The CIA went to DOD,  and this foreign technology exploitation project became a joint Army-Navy program under the name "Group Work".  Different pieces went to different contractors,  among them the ramjet fuel supply and combustor to the plant where I worked in Texas.  That plant was then known as Rocketdyne-McGregor,  later Hercules-McGregor,  and was finally closed under the name ATK.  Our contract was run out of Army MICOM in Huntsville,  Alabama.

Being the only front-line working Rocketdyne-McGregor "ramjet guy",  of course I worked on the “Group Work” project to exploit the SA-6 technology.  This was 1978.  I had the Israeli drawings (they were labeled in Hebrew,  by the way,  but I can read millimeters) plus examples of the inlet and gas generator injector dome hardware,  and real chunks of Russian fuel propellant to work with. 

My team colleagues were Rocketdyne-McGregor propellant chemists L. Gale Herring and Jim Muesse,  and an Israeli chemist from Technion: Moshe Gill.  Our project engineer was Sam McClendon,  and our program manager was Bill Miller.  For “chemist”,  think propellant formulation chemist.

I was the only working/line mechanical engineer among the 3 chemists.  Between the four of us,  we actually figured out how this gas generator-fed ramjet with a pressed-propellant fuel grain really worked,  and how it was built.  The end-burning fuel propellant charge was a compressed stack of individual discs.  We duplicated materials,  processes,  conducted static generator firings,  and did airbreathing ground tests of the ramjet in subscale. 

It was my suggestion to “stage” the compression of the pressed fuel propellant grain that broke-open the path to success.  The secret was not to use full compression forming the individual discs,  so that the stack could then consolidate properly under full compression.  Poor consolidation of the stack led to motor explosions.  The chemists found out how to tailor the burn rates within each disk,  so that burn rate properties could be varied down the stack.   I was the one who did the gas generator interior ballistics and ramjet combustor performance analysis for the tests.

We did so well that we got a second contract (1979) to use other contractors' results along with our own,  to characterize the actual engagement envelope of the SA-6 missile weapon system.  We used our ramjet results with other groups’ results for the booster,  the vehicle aerodynamics and weight statement,  the supersonic inlet aerodynamics,  and a ramjet cycle analysis from Ken Watson at WPAFB that reflected significant injected axial momentum for the fuel. 

I was the working engineer for that second effort,  too,  as well as its project engineer.  I did the trajectory predictions and target engagement analyses that characterized the SA-6 SAM system correctly.  (The Mach 1.5 takeover speed in “Jane’s” is incorrect;  it is actually just about Mach 1.8 takeover,  for an inlet design with an inlet shock-on-lip speed of Mach 1.9.) 

This intensive effort was just another part of what I did for ramjet work in general at Rocketdyne / Hercules in McGregor,  Texas.  (Plus I also did a lot of solid rocket work.)  At the time,  the highest classification of “Group Work” information associated with its propulsion was “confidential”.  It had a 12-year interval to downgrade to “unclassified” (by about 1990 or 1991).  Between that,  and the cutaways on public display,  it may be presumed that everything about this propulsion system is now both unclassified,  and entirely in the public domain.  Which means it is OK for me to publish this.

Bill Miller and Sam McClendon are still with us as of this writing,  although long retired and quite elderly.  Gale Herring and Jim Muesse passed away long ago.  I will be 70 this coming summer,  if I live that long.  If chemist Moshe Gill is still alive in Israel,  then he and I are the only two still alive in the West who know how to make that fuel propellant.  It’s actually very good stuff.  And I also know how to make a castable equivalent.  At the very least,  this high-magnesium stuff makes an excellent ramjet combustor igniter.   And I used it as such for many years.

I am thus the only one left alive in the West who knows how that SA-6 ramjet combustor works in detail,  and why flameholding (as distinct from mixing) was NOT an issue with the magnesium-rich fuel effluent from its gas generator unit.  I also know how every piece of that engine and fuel supply was constructed,  and why they were done the way they were done.  Evaluating all of those things was what our “Group Work” contracts were all about.

Technical Items

Figure 3 shows a diagram of the inboard profile of an SA-6 missile.  


Figure 3 – 3M9M Gainful Cutaway (via Vestnik-PVO)

The items numbered in the figure are listed below.  The items in red text are things I have added to the original source,  based on what I personally know from “Group Work”.

1 1SB4M CW monopulse semi-active homing
    seeker with Doppler closure rate capability
2 3E27 CW radio two channel proximity fuse
    (30 m nominal radius)
3 3N12 57 kg blast-fragmentation warhead
4 1SB6M autopilot
5 ramjet intake ducts
6 9D16K sustainer gas generator charge (67 kg
    LK-6TM reducing propellant) 65% Mg 20%
    Na-nitrate
7 frangible seals round phenolic caps with O-ring,
    held not-shouldered by shear wires, shouldered
     home by boost pressure
8 boost stage solid propellant charge 172 kg VIK-2
    propellant
9 exhaust nozzle ramjet nozzle very large, booster
    nozzle nested inside on O-ring in ramjet throat,
    boattail part of booster nozzle, eject ass’y also
    includes aft support for cartridge-loaded booster
    grain
10 cruciform tail fins

11 cruciform wing

Ramjet Inlets

The ramjet intake ducts were something determined by another contractor to be what is called a “shock-follower inlet” during “Group Work”.  This is a mixed-compression inlet whose minimum (throat) area is oversized-enough to “start” (swallow the shock system) without resort to starting bleed cutbacks in the cowl sidewall,  or inlet throat bleed slots.  Basically,  the inlet throat must swallow all the potential subcritical airflow,  in order to “start” easily.  (This easy starting is inherent in all of the all-external compression inlet designs.)

For those who do not know,  a mixed-compression inlet has both external compression and internal compression features.  External compression is that accomplished by the shock wave system upon the exposed spike or ramp features ahead of the cowl lip.  Internal compression is that accomplished by the contraction of flow channel area (and the associated shock wave pattern) aft of the cowl lip.  

There are all-external compression supersonic inlets with the min (throat) area right at the capture station,  and there are mixed-compression supersonic inlets with the throat downstream of the capture station,  from a practical technological standpoint.

That “shock follower” design approach substantially reduces supercritical pressure recovery performance,  which is objectionable for the excessive pressure losses at very high flight speeds.  However,  max speed in an SA-6 is only about Mach 2.8,  thus eliminating that objection!  Given that situation,  this approach is then a good compromise design for easy construction,  easy starting,  and low cowl lip drag,  simultaneously! 

The supersonic inlets were made from standard-size round aluminum tubing available in Russia,  fitted with a protruding spike centerbody positioned upon 3 fins,  in turn connected to the duct wall.  The axial spike position was set by a tooling jig,  and the centerbody fins then spot-welded to the outer tube.  The lip of the cowl capture station was beveled to a sharp edge around the external circumference. 

These ducts were positioned on the airframe such that best capture performance was obtained,  with all-subsonic transfer of the air aftward to the combustor forward dome.  There,  flow was turned 30 degrees inward,  off axial,  for the symmetric 4-port entry into the forward end of the combustor,  through the periphery of its forward dome.

This 30-degree turn was accomplished by hot-bending the sand-filled inlet tubing over a mandrel,  after the dome bolt-up fittings had been spin-welded to them.  This process left small compression wrinkles on the inner surfaces of the turns.  But,  because the ducts are round,  the pressure losses caused by these imperfections were undetectable,  in terms of post-turn pitot pressure (relative to pre-turn pitot pressure).  That is precisely because round ducts have no corners to hold vortices and separations.

Transition Gear:  Inlet Port Covers

Ramjet combustor pressures are very similar to inlet pitot pressures:  a few,  to a few dozen,  psia.  Booster pressures are a few hundred to a thousand-or-so psia.  That requires inlet obturation during boost,  lest hot booster gas jet out of the inlets in reverse!  The SA-6 design did this function with totally passively-ejected inlet port covers.  No pyrotechnics or controls were needed at all.

These port covers were hemispherical caps with cylindrical skirts, convex to the booster chamber,  and sealed with an O-ring into the inlet tubes.  They were held in place with small radial shear wires in the skirts,  not quite shouldered-home into the inlet tubes.  Boost pressure would shoulder them fully home,  breaking the shear wires.  Then upon booster pressure tailoff at burnout (a very rapid bleed-down of pressure to slightly below local atmospheric),  the low-supersonic inlet pitot pressures at takeover Mach (about 1.8) would pop these port covers out of their inlet tubes.  All four port covers would easily fit through the ramjet throat simultaneously. 

Solid Propellant IRR Booster

The solid propellant booster for the SA-6 was a double-base propellant in a hollow cylindrical form,  cartridge-loaded,  and burning on both the outer and inner surfaces.  It was mechanically supported at its forward end by the gas generator cover,  and at its aft end by the ejectable booster nozzle structure. 

This is a fairly-neutral thrust-time profile created by this booster grain design approach,  as evaluated by another contractor.  At web burnout,  the fast chamber pressure drop activated a switch,  that in turn simultaneously activated the gas generator igniter and the booster nozzle ejection pyrotechnics.  Both of these were two-item-redundant initiator systems. 

The gas generator igniter was a ring-shaped device located in the gas generator chamber immediately-adjacent to the grain ignition surface.  It was not quite the same as the “BKNO3” igniters often used for rocket motors in the West.  It was required to generate sustained hot gas flow washing the grain ignition surface,  for a significant period of time.  Beyond that,  I no longer remember exactly what it was. 

The ejectable booster nozzle was a small-throat/large exit diameter device nested within the ramjet nozzle upon an O-ring seal.  It was held in place by 3 “fingers” between the nozzle assembly and 3 slots cut into the ramjet nozzle exit cone.  These “fingers” were held in place by a confining clamp about the booster nozzle,  but within the external aerodynamic shell of that booster nozzle assembly. 

There were two pyrotechnic charges on that clamp,  either of which could open it.  Once opened,  the “fingers” and the booster nozzle were pushed aft out of the ramjet nozzle,  by the decaying booster pressure.  From that point,  everything was entirely passive.

Ramjet Combustor

The SA-6 ramjet nozzle throat area itself was about 90-95% of the insulated combustor flow area.  That proportion is utterly infeasible with fuels that require flameholding with air (such as the liquid hydrocarbons),  but is entirely feasible with fuels that are hypergolic-ignition with air.  This proportion allows very much larger inlet airflow for more thrust,  but inherently means that the ramjet nozzle supersonic expansion is limited indeed.  Being hypergolic,  no combustor igniter is needed to start the burn.

The so-called “hydrocarbon” gas generator fuels,  and the liquid hydrocarbon fuels,  require flameholding and a combustor igniter to start the burn.  They are anything but “hypergolic” ignition!  They require throat/combustor area ratios in the 60-65% range for reasons of flame stability and practical inlet duct size. 

The SA-6 combustor is about 12.5 inches diameter,  and about 6 diameters long.  It is fed by 4 inlet airstreams,  and some 12 entering fuel stream ports,  as indicated in Figure 4.  The more the entering air and fuel streams are divided,  the quicker mixing can occur.  The gentle air entry angle of 30 degrees reduces mixing turbulence intensity,  but this is compensated by the long combustor proportion. 

High mixing rates and thus high combustion efficiencies are thus achieved by the long combustor with multi-subdivided fuel and air streams.  Yet geometries like this are incompatible with flameholding,  for non-hypergolic fuels.  That is not a problem for the SA-6,  with its gas generator effluent dominated by hypergolic magnesium vapors.  But one cannot just substitute a conventional flameholding fuel into this combustor:  it will not flamehold,  which means it will not burn!

The ramjet combustor is a steel tube lined with a thin layer of something resembling silica phenolic ablative.  Ordinarily,  this thin layer would be inadequate as a combustor insulator,  because the magnesium-air flame is as hot as any other fuel burning with air,  and because of the condensed particles of magnesium oxide product.  That cloud of hot particles drives very high internal radiative heating of the wall.  Because the external airflow does not exceed flight speed Mach 2.8,  external aero-heating is not the driving issue.  Mach 2.8 flight is just not that bad.  Internal heating is the real driving issue for design. 

However,  the same condensed magnesium oxide product coats the ablative liner very quickly with a layer of solid white magnesium oxide “slag”.  Because the stoichiometric air/fuel ratio is about 3,  there is a lot of this slag coating very quickly deposited. 

As we found in the subscale ramjet tests,  this is a very effective protectant for the steel ramjet case that is the missile aft airframe.  We were able to test and retest on the same subscale insulation sleeves many times,  for a much longer accumulated burn than would ever be seen in flight. 


 Figure 4 – Inlet and Fuel Entry Geometries for SA-6


The two adjacent fuel entry ports for each inlet entering stream provide some impetus for re-turning the air back to axial direction,  reducing the total pressure loss,  despite the lack of physical walls.  This relies upon collision of the airstream with the associated pair of fuel streams.  It is in this way that “synergistic” behavior is obtained:  more downstream total pressure recovery than one might otherwise expect.  The 4 ports dedicated to dome center injection really do also increase this effect. 

All of these physics are far outside of what applies to more conventional fuel-air flameholding.  This SA-6 combustor and its fuel and air entry design is ONLY applicable to truly hypergolic fuels!

There is a fiber-reinforced phenolic cover over the 12-port dome that is the gas generator outlet.  It keeps the fuel grain from being hot-gas ignited,  during the booster burn.  That cover is also the forward mechanical support for the IRR booster propellant grain.  It is held in place with an aluminum screw,  and sealed by an O-ring. 

After the booster burns out,  when the gas generator ignites,  the pressure rise in the gas generator breaks the aluminum screw at about 200 psia.  The gas generator dome cover then departs downstream right after the inlet port covers.  It all fits through the ramjet nozzle throat,  even simultaneously.

Fuel-Rich Solid Propellant Fuel Supply

This is a pressed propellant system rich in magnesium,  resembling (but not at all the same as) a magnesium flare composition.  Average propellant composition values are 65% magnesium by mass,  20% sodium nitrate by mass,  and 5% each (by mass) carbon black,  naphthalene,  and mineral oil.  The naphthalene is the hard white solid often described as a moth repellant in the West. 

These ingredients are “dry-mulled” together as powders,  then compacted in a press.  The naphthalene and the mineral oil make this compactibility happen.  The carbon black and the mineral oil are the mold lubricants.  This has nothing to do with any conventional cast propellant processing in the West,  and a whole lot more to do with magnesium flare processing,  except that Teflon is not involved,  and two separate press operations are required,  unlike with flares. 

What we found at Rocketdyne-McGregor was that burn rate was controlled more by the magnesium particle size,  not so much the sodium nitrate oxidizer particle size.  This is understandable,  since magnesium dominates the composition,  and by far.  It proved easiest experimentally to tailor propellant burn rates with magnesium particle size than anything else.  The SA-6 gas generator proved to have higher burn rate initially, and lower burn rate later,  for a net slightly-regressive burn profile. 

As it turned out,  the choice of sodium nitrate as the fuel propellant oxidizer was in part driven by the radar return of the missile exhaust plume in ramjet operation.  This made tracking where the missile really was (versus where it needed to be) rather easy.  The sodium ions stood out like radar beacons in the exhaust plume. 

The fuel propellant grain was mostly a stack of otherwise-identical fuel propellant discs,  each with its own burn rate.  These were a sort of flat disc shape modified with circular “whorls”.  The running joke at Rocketdyne-McGregor was that the fuel propellant grain was a stack of “camel turds”.  See Figure 5

During the first contract,  these discs were initially pressed to full compaction at 17,000 psi,  then stacked into a fuel grain,  and re-pressed at the same 17,000 psi to “consolidate” the stack.  That process proved to be completely ineffective!  Flame would flash into the disc interface areas,  over-pressuring the test lab motors to the explosion point,  within milliseconds of ignition.  Bonding agents did not alleviate this.

The solution to this dilemma proved to be a notion based on a child’s mud pie:  barely “hang” the discs together at a reduced compaction pressure (about 5000 psi),  then stack these up in desired burn rate order,  and finally compact the stack (at 17,000 psi) to full density.  5000 psi got density variations through the stack matching the samples of Russian propellant.  Compacting instead to 7000 psi eliminated all the observed variations seen in the Russian samples.  But the main lesson was that the stack would not consolidate unless there was about 30% compaction potential still left in the discs.

Either way,  the final compaction of the stack to 17,000 psi eliminated the flashing of flame onto the interfaces between discs.  There is a “mold bloom” on stack diameter that occurs between the two compactions.  It necessitates either two slightly-different tooling diameters,  or else filing-off the grain stack OD to fit the case diameter for the second compaction operation.  


 Figure 5 – The Individual Fuel Grain Discs Make Up a Gas Generator


The SA-6 gas generator case was another standard-size tube of an annealed titanium alloy.  There was no liner or insulator;  instead,  the grain stack was wrapped in what amounted to Kraft paper,  then inserted into the case.  With tooling installed,  this stack was compacted to 17,000 psi inside that case,  squeezing it out against the Kraft paper and stretching the case slightly.  This crushing action on the paper against the case completely inhibited burning down the sides of the grain stack.  The two-stage pressing operation eliminated burning on the interfaces between discs. 

All the discs were dimensionally identical except two:  (1) the forwardmost disc had a flat face matching the flat forward closure plate of the gas generator,  and (2) the aftmost disc had a configured ignition surface featuring a center peak. In the SA-6,  burn rates were higher at the ignition end,  and lower in each disc to the lowest rate at the forwardmost disc.  Burning surface is also slightly regressive.

Burn rates were about 20-30% regressive ignition-to-burnout.   This crudely compensated for nozzle throat area reduction due to magnesium oxide slagging,  for a crudely-neutral pressure trace with time,  at about 300 psi (20 bar). The flow rate trace with time was slightly regressive,  like the burn surface.

The forward case closure was installed such that two screw holes in it were open.  Something resembling Elmer’s Glue-All was injected by one screw hole to fill the void gap between grain and closure,  until it extruded out the second screw hole.  Screws were inserted into these holes,  and the glue allowed to set.

The gas generator igniter ring was installed adjacent to the ignition surface of the fuel grain,  followed by the aft generator closure,  which had the 12-hole injection dome into the combustor.  This injection dome was sealed by installation of the closure cap,  that doubled as the forward booster grain support. 

Subscale testing revealed that the fuel injection ports really did “optimize” as sonic-only ports.  Ramjet direct connect tests confirmed a ramjet performance decrement,  if the port exit Mach number was supersonic.  Each of these ports was a graphite insert in the basic steel structure.

From a ballistics standpoint,  there are three processes operating during the SA-6 gas generator burn.  One is the regressive distribution of burn rates down the stack of discs.  Another is the slag buildup in the fuel ports with time.  The third is the slight regressive variation in effective burning surface of an essentially end-burning grain,  starting from a surface that is not flat.

These result in a grossly-neutral pressure-time history,  and a slightly-regressive effluent massflow-versus-time history.  This is a fixed delivery history,  there is no control of fuel flow rate.  Such is a good compromise for the effects of increased scooped airflow versus flight speed,  over-balanced by decreased air density with altitude,  as the SAM climbs out on its way to its target.    

The SA-6 is a SAM intended to hit aircraft targets from under-5000 to about-60,000 feet altitudes.  Its fixed fuel delivery trace is a sort of middle-of-the-road compromise to cover those extremes.  It will be near-perfect fuel/air ratio as the SAM accelerates toward a middle-altitude target,  too rich against very high altitude targets,  and too lean against targets near the surface.  But,  because the fuel effluent is hypergolic with air,   there are no risks of lean or rich blowouts!

The gross characteristics of the gas generator effluent as a fuel are stoichiometric air/fuel ratio about 3.0 (by mass),  and lower heating value about 8300 BTU/lbm.  This effluent is heavily-dominated by magnesium vapor,  which is hypergolic with air,  even at room temperatures. 

Ramjet Ground Tests

In the early years when “Group Work” was done,  the McGregor plant had a small direct-connect ramjet test facility.  Its airflow capacity was up to 5 lbm/sec at up to 750 F total temperature,  for a usable time of about 1 minute or so.  This was a very simple blowdown-type facility using bottled air and a two-stage regulator control feeding a calibrated choked venturi meter upstream of the air heater.  The heater was a simple pebble-bed heater,  electrically heated to the desired temperature before the test. 

The main advantage here with the pebble bed heater is that the air supplied to the test article is really air,  not “vitiated air” from a combustion heater with oxygen replenished.  That requires very sophisticated controls,  the pebble bed does not.  With reactive metal fuels,  especially magnesium,  the excess water vapor and carbon dioxide in vitiated air are a reactive oxidizer,  not an inert. 

If you test metallic fuels in a vitiated air system,  you will get bad answers in the form of over-optimistic performance numbers.  Our facility was almost unique around the country at that time,  in using real air,  so as to get realistic performance with metallic fuels,  as well as the hydrocarbon fuels.

The test hardware we used was essentially based on 6-inch commercial pipe hardware (tubes and flanges).  Motor explosion safety was by use of neckdown bolts on items containing propellant.  This hardware was specifically designed not to throw shrapnel in the event of a motor explosion event. 

The thrust stand in those days was not calibratable for accurate tare forces,  so we relied on performance computed from static pressure measurements,  knowing the total/static ratio at the combustor exit from its nozzle contraction ratio,  and that its nozzle throat was choked.  The stand was a small table atop 3 flexures underneath it,  and restrained by a thrust transducer.  We took thrust data,  but did not rely on it for performance,  during those early days.  That changed later (see below).

This facility had both photography and altitude simulation capability.  This was before cheap video,  so the photography was real film sequence cameras and real movie film cameras.  It usually took about half a week to a week,  after the test,  to get the photographic results.

The altitude simulation used a second-throat supersonic diffuser sealed to the nozzle housing with a rolling-diaphragm seal,  and belling-out to a steam ejector that pumped the decelerated stream back up to barometric. Open-air nozzle testing was preferred,  if at all possible in terms of nozzle choke.

Instrumentation in those early times was two moving-paper oscillograph recorders,  with a total of about 24 channels.  We used some 8 thermocouples and some 16 pressure and force channels,  to record the conditions throughout the air system,  test article,  and altitude rig (if any).  These traces were reduced manually with scales and pencils,  and hand-drawn plots.  This took about 40 man-hours per test to accomplish.  (That also changed several years later to digital data acquisition and computer-processing,  but still using my same test item cycle analysis,  which included transient air system effects).

In the 3 years leading up to our “Group Work” testing,  I had developed the procedures,  test order document format,  and (most importantly) the test item cycle analysis for pressure (and thrust) based performance.  At this stage of our testing development,  I witnessed every test from outside the blockhouse,  and about 75 feet away from the stand,  which was definitely a 5-sense experience! 

Over the course of some 8 years testing (of which the “Group Work” tests were a only small part),  I witnessed about 120 such tests.  We had a very good experimental test record:  only 4 of these 120 exploded.  Quite exciting.  You cannot help but turn and run;  the fight-or-flight impulse just takes over.

The test hardware we used for the “Group Work” tests was an air-entry section that had 4 inlets equally spaced,  entering at 30 degrees.  The inlet/combustor area proportion was comparable to SA-6 at about 40% area ratio.  This was 6-inch pipe size steel hardware,  insulated with silica phenolic sleeves to a 4.6 inch combustor ID.  We used enough sections downstream to get about 6-7:1 L/D ratio for the chamber,  and tested with a graphite nozzle insert that was sonic-only for test data reduction simplification.

We had other inlet entry sections that entered at 45 degrees,  and which could be two inlets either 90 or 180 degrees apart,  at inlet/combustor area ratios near 50%.  These (and the 4-inlet rig) could have the lab motor gas generators “stepped back” so that the fuel injection plane was at,  or ahead,  of the air entry station.  4 and 6 inch lab motors could be used.  We did not use these other inlet entry sections for “Group Work”.  Instead,  we fired a variety of magnesium and hydrocarbon fuel propellants in all of them for other projects,  both contract and IR&D.

The gas generators we used for “Group Work” were standard heavyweight 4-inch diameter laboratory motors,  spaced with adapters such that the injection orifice plane was right at the inlet dump plane,  to be as close to the SA-6 geometry as we could possibly get.  In testing,  it did not matter whether we had one injection port or four,  so we usually just tested with one.  These gas generators used graphite discs with drilled holes to make the sonic ports.

It was well after the “Group Work” testing that we began expanding our test facility.  Eventually,  it had two independent air lines,  each 10 lbm/sec flow rate,  with the 750 F pebble bed heater on one,  and a 1200 F pebble bed heater on the other.  The test stand air entry got revised for larger flight-like hardware,  and well-calibrated for tare forces,  so that both pressure and thrust-based performance were obtained.  This used the same altitude ejector,  but with a new,  larger second-throat supersonic diffuser.  I played a major role in all of this expansion.  It was all scrapped when the plant got closed.

A sketch of our test facility arrangement,  as it was in those early years,  is given in Figure 6.


 Figure 6 – McGregor Ramjet Facility As It Was For “Group Work”


Engine / Inlet Proportions

From the very beginning,  we did our ramjet nomenclature and performance definitions in accord with the standards set forth in CPIA 276.  The relevant station numbering and combustion efficiency definitions are shown in Figure 7

The SA-6 has four side-mounted inlets,  similar to the side-mounted entry shown in the figure.  These are equally-spaced 90 degrees apart around the circumference of the vehicle.  These inlets are round,  unlike the 2-D inlets illustrated in the figure.  The swept out capture area AC is the sum of four circles,  each the inside diameter of the inlet tubing.   This is sort of like the round nose inlet in the figure,  but it is just that there are four of them.

For the SA-6,  station 2 is after the 30-degree bend,  but before the sudden dump into the chamber.  The round tubing from which these inlets are made is the same inside diameter at station 2 as it is at station C.  Thus A2 = AC

The SA-6 combustor is a constant diameter tube,  so that A3 = A4.  Dimensions are such that A2/A4 ~ 0.40,  and so also AC/A4 ~ 0.40.  A5/A4 is just about 0.90 to 0.95,  and A6/A4 ~ 1.0.  I can no longer find my old set of drawings to pin these ratios down to their exact values. 


 Figure 7 – Nomenclature and Reporting Definitions Per CPIA 276


Missile Engagement Characteristics

Our second contract was also run out of MICOM in Alabama.  The Army gave us the results from the other contractors for the vehicle weight statement,  vehicle aerodynamics,  inlet aerodynamics,  and booster performance.  They confirmed to us that this SAM flew as semi-active radar homing using proportional navigation with modest gravity bias. 

USAF supplied us a ramjet-capable trajectory code called ABTRAJ,  from Ken Watson at WPAFB in Ohio.  I did the rest.  My targets were thing like F-4’s and F-15’s. 

Against a mid-level maneuvering target,  SA-6 is still powered at intercept,  and doing about Mach 2.8.  At mid altitudes,  it is capable of maneuvering at about 44 gees turn acceleration.  This occurs about 30 km out from the launch site.  A rocket that size would be coasting,  able to pull fewer gees,  and only about 10-15 km out. That explains neatly the losses seen by the Israelis in the 6-Day War.

At the very highest altitudes,  SAM speed is nearer only Mach 2,  and the thin air reduces gee capability for the SAM,  and for its targets.  Near the deck,  speed is about Mach 2.5,  and in the thick air,  the SAM has full maneuver gees,  as do its targets.  High and low altitude ranges to intercept are somewhat shorter,  nearer 15-20 km.

This SAM is late-1950’s vacuum tube technology.  Its radar is lower frequency that those used today.  It flies command-guided from the launch site until its on-board seeker can find and lock onto the target.  At that point it goes autonomous,  ignoring commands from the launch site.  That usually happens around 2-3 seconds from impact,  which is around a nautical mile (or maybe 2 km) from the target.

The rocket-powered SAM with solid-state electronics that replaced SA-6 is the SA-11.  It covers about the same engagement zone with only a solid rocket,  because its payload is both smaller and lighter.  One can fire SA-6 missiles using SA-11 guidance and control equipment at the launch site,  but one cannot fire SA-11 missiles using SA-6 guidance and control equipment at the launch site.   

There is one “sort-of” unexpected advantage to the older lower-frequency on-board radar seeker of the SA-6.  As it turns out,  stealth characteristics of aircraft are very frequency-dependent.  These designs are for more modern,  higher-frequency radars.  It turns out that stealth aircraft are just not very stealthy at the older,  lower SA-6 frequencies.  This neatly explains the shootdown of an F-117A in the Balkans by an SA-6 missile.

Signature Issues

I have already indicated that sodium ions in the ramjet exhaust plume make it a huge radar target.  This starts with the transition to ramjet propulsion,  about 3-4 seconds after launch.  That allows the ground operator to easily track the missile,  so that he may effectively command-guide it close enough to the target that its on-board radar seeker can go autonomous. 

The infrared situation is different.  The hot slag particles in the exhaust plume are still close to chamber temperature,  up close to the missile,  but these are spread thinly in space.  This is about 1 to 1.5 micron radiation in terms of color temperature,  but the total signature emitted is not very large at all,  because of how thinly those particles are spread.  It’s as if the effective emitting area is far smaller than the perceived plume area.

As for aeroheated hot skin temperatures,  these are at most the external air stream recovery temperature,  very little different from the total temperature.  Even at 2.8 Mach at sea level,  this total temperature is only about 870 F,  and colder still at slower speeds and higher altitudes.  There just isn’t very much signature emitted from surfaces that cold,  even at 100% emissivity.

Visually,  this is a “smoky” system,  although its smokiness is far less than a rocket of equal thrust.  Such rockets leave an opaquely-dense white smoke trail.  This ramjet leaves a very translucent thin white trail.  That is the air dilution effect at work. 

There is some video footage from the 6-Day War showing what is reported to be an SA-6 traveling against a clear blue sky on a bright day.  The plume is white in color,  but very thin to the eye,  indeed.  On a gray,  misty,  overcast day,  it would be almost invisible to the naked eye. 

Final Comments About All the Other Ramjet Work I Did

When I first hired on at Rocketdyne-McGregor straight out of graduate engineering school,  it was originally to be an understudy structural engineer.  That was December 1975.  But my training in propulsion and especially aerodynamics came to the attention of local managers within a couple of months,  as they struggled to deal with a solid propellant gas generator-fed ramjet application known as “ducted rocket”.  Nobody else knew what the inlets were for,  or how they worked.

This change for me included helping with the construction and checkout,  already underway,  of a ramjet direct-connect test facility.  Initially that facility had a clean-air airflow capability up to 5 lbm/sec,  at up to 750 F total temperature,  using a pebble bed heater.  It had about a 1 minute blowdown capacity,  and it used a second-throat supersonic diffuser and steam ejector for its altitude simulation option.

Plus,  these efforts included a cooperative IR&D project between McGregor and the Marquardt Company in Los Angeles,  to develop fuel rich solid propellant gas generators,  and test them with air.  These efforts are how I got started in ramjet work,  and how I first got to know some experts at Marquardt,  and at WPAFB. 

These were notably Joe Bendot and Bob Ozawa at Marquardt,  and E. Tom Curran at WPAFB.  Ozawa was the V-gutter flameholder expert,  and Curran the coaxial dump flameholder expert.  I eventually became the side dump flameholder expert.

These efforts (plus a continuing McGregor IR&D effort in airbreathing propulsion) initially focused on various cast and pressed high-magnesium fuel propellants.  We tested at McGregor in a 4-inlets-at-30-degrees configuration,  and Marquardt tested in a two-inlets-at-45-degrees-and-90-degrees-apart configuration.  Ours was driven by tales we had heard about the SA-6.  This preceded “Group Work”.

We added hydrocarbon fuels during these efforts,  and immediately ran into failed combustor ignition troubles with them,  while Marquardt did not.  The sizes were not that different,  but the inlet entry geometries were! 

Later on,  we tested in the same two-inlets-at-45-degrees-and-90-degrees-apart configuration,  and most (but not all) of our combustor ignition troubles went away.  But the troubles returned,  with our attempted testing in a two-inlets-at-45-degrees-and-180-degrees-apart configuration.  Symmetry versus asymmetry was the common thread here.  About this time,  Hercules bought the McGregor plant from Rocketdyne.

Ultimately,  I found that there were two problems:  (1) symmetrical inlet entry geometries incompatible with the physical characteristics of the hydrocarbon fuel propellant effluents,  and (2) providing an adequate combustor ignition stimulus.  Neither was an issue with 50%-or-higher magnesium,  which was just hypergolic with air at any air temperature.

These compatible-geometry results are at strong variance with the many flameholding geometries that work with liquid fuels,  but then,  so are the solid gas generator fuel effluent physical properties.  The main difference was the solid soot content that reacted something like 10 to 100 times slower than the carbon monoxide gas content.  

The soot has to be “centrifuged-out” of the flameholding recirculation,  which requires asymmetry-of-entry to organize the recirculation into a single strong vortex.  This effect is worse at smaller diameters than larger.  Simple,  but subtle!  And not widely believed by others in the business at the time. 

The combustor ignition stimulus had to be much better than just waiting for gas generator igniter debris to reach the combustor.  Tiny rocket motors loaded with castable high-magnesium fuel-rich propellant,  firing directly into the flameholding recirculation zone,  proved to be utterly reliable.  It means you need to know exactly where that zone is,  and just how it works.  We had these answers by about 1978.  They served us well for many years.  I cannot say the same for our competitors.

These IR&D efforts were aimed at a series of “6.2 technology development” programs from USAF at WPAFB.  These were targeted at a proposed ramjet propulsion upgrade for the AIM-120 AMRAAM missile.  A couple of these were named DRED and DR-PTV.  The “DR” was “ducted rocket”. 

If memory serves,  these programs ran through about 1979 or 1980.  They did establish that the ramjet AMRAAM engine would have reduced-smoke hydrocarbon fuel,  burned in an asymmetrical  two-inlets-at-45-degrees-90-degrees-apart inlet entry configuration.  The “Group Work” effort was underway alongside all this.  The differences between magnesium and hydrocarbon could not be more stark. 

The baseline design for that AMRAAM engine at that time was a fixed flowrate delivery history that we often called “FFDR” for “fixed-flow ducted rocket”.  The USAF began to insist on eliminating the rocket-ramjet transition ejecta,  that being the ejectable booster nozzle and inlet port covers.  Because the trajectory studies showed serious rich and lean blowout risks trying to cover a wide range of target altitude,  USAF also wanted a means of controlling the fuel flow.

McGregor developed on IR&D a gas generator throttle valve (a variable-area choked throat device),  and the high-exponent fuel propellants to make it work effectively.  Atlantic Research developed a wire-pulling gadget that coned the burn surface in response to the wire extraction rate.  This varied burn surface area and effective burn rate against fixed throat area. 

Atlantic Research never solved an erratic flashing of fire down the side of the moving wire,  which caused motor explosions.  We solved all of our problems (including motor explosions on a linear control,  by developing a reliable nonlinear control),  and so we won the VFDR (“variable flow ducted rocket”) contract from USAF. This was about 1981 or 1982 or so,  if memory serves.

We even adapted the coning notion to cast propellant strands,  instead of wires,  which divorced the strand ballistic properties from the fuel properties of the matrix propellant.  This plus our throttle valve and nonlinear control became the VFDR baseline gas generator design.  It was named SAEB,  for “strand-augmented end burner”.

About this same time,  McGregor teamed with Marquardt and Martin-as-prime for a liquid ramjet program called ASALM-PTV.  Marquardt was to supply the ramjet and inlet port cover,  we at McGregor were to supply the integral booster,  complete with ejectable booster nozzle. 

My part in ASALM started with support to the thermal-structural design on the ejectable nozzle,  and support to the ballistics design analysis of the booster propellant grain design.  That was my introduction to the keyhole-slot grain design,  that I now like so much for application to ramjet boosters. 

It went on to a contract we had,  to investigate feasibility of a variable geometry ramjet nozzle.   This led to live fire tests of a design that worked after a 900-second burn.  This was a “lollipop” in the ramjet throat.  It was not chosen to fly on ASALM.  However,  ASALM was my first encounter with the coaxial center-dump flameholder geometry.

I did get to visit the very large (100 lbm/sec) direct-connect test facility operated by Martin at its Orlando facility.  That is where I first encountered the dense kerosene-like synthetic liquid fuel RJ-5/Shelldyne-H. Ultimately,  ASALM flew 7 times in flight tests at Eglin AFB in 1980.  6.5 of those tests were fully successful.  The very first one suffered a throttle runaway,  and accidentally set a speed record at about Mach 6.

This was about the same time as we at McGregor were enlarging and updating our own facility on IR&D.  We went to two air lines,  at up to 10 lbm/sec each.  Eventually,  we added a 1200 F pebble bed heater to the second line.  We added tank farm capacity to keep the 1-minute blowdown,  and a larger diffuser for larger test articles.  Eventually we went to a big air tank trailer for our “tank farm”.

Starting on IR&D,  and transitioning to a USAF contract,  we developed a dual propellant overcast grain design for a “nozzle-less booster” for the ramjet upgrade to AMRAAM.  This eventually became the standard booster design for the ramjet AMRAAM,  because it eliminated all the booster nozzle ejecta.  Port cover ejecta were eliminated simply by retention,  for burn-up in place.  The port covers folded inward,  together between the entering inlets.

Key to the success of our nozzle-less booster design was overcast of a lower-rate propellant over a higher-rate propellant.  The nozzle-less performance decrement was held to only 15-20% in this way. We tested this in the full scale ramjet AMRAAM hardware multiple times.  It was very reliable.

For the interval from December 1983 to March 1987,  I left the McGregor plant to work at what was then known as Tracor Aerospace Austin,  in the airborne countermeasures and deception business.  Among the many things I did there,  one relates to the ramjet work being discussed here.  This was a small ram-fed airbreathing combustor that was a hot gas generator for an infrared decoy. 

For this combustor I used the ASALM coaxial dump technology,  but I had to stop-down the nozzle substantially,  to slow the flow speeds enough to have flame stability in such a small size.  This combustor was 1.5 inches ID and 3 inches long.  In it I successfully burned hydrogen,  propane,  gasoline,  jet fuel,  and alcohol. I got started writing my own ramjet cycles codes for this effort,  as well as very practical experiences burning liquid fuels in ram combustors.  And I invented a low-density ceramic insulator that was reusable for hours of burn on this project (see Figure 8)


Figure 8 – Small Decoy Combustor Ceramic Insulator


While at Tracor,  I stayed in contact with friends at McGregor,  helping them with teething troubles in the new upgraded test facility,  as they prepared to bid the second VFDR program.   The USAF sponsors insisted that Hercules-McGregor do a joint venture with Atlantic Research,  before they would award it. They wanted Atlantic Research’s boron fuel because it looked so good (theoretically on paper).

I initially returned to McGregor in program management.  But,  I was soon reassigned to project engineering,  made the principal investigator for airbreathing propulsion IR&D,  and informally managed the entire plant IR&D program for the chief engineer.  For airbreathing IR&D,  I went to work on boron and clean fuels,  and on an unchoked-throat gas generator that could provide constant fuel-air ratio “control” with no moving parts or controls at all.

The unchoked-throat effort led to a very safe and convenient way to test experimental fuels rapidly in the direct-connect facility.  This really accelerated the fuels development effort at McGregor.  We did not win the actual contract to test this technology for USAF,  so we just continued on IR&D,  which led to a paper on it at the Naval Postgraduate School.  We were able to test successfully in full-scale AMRAAM hardware,  for a tenth what USAF paid their contractor,  who never got their subscale engine to burn at all.  Our paper was right after theirs at the meeting.  It made quite a stir at that meeting.

While all this was going on,  I got involved in some aspects of a USN program called AAAM.  This was a nose-inlet ramjet with liquid fuel and a coaxial center dump flameholder.  McGregor was to supply the ramjet case and integral booster. 

This was a very speculative investigation program,  in that high flight speed aeroheating was too much for aluminum,  and weight allowances would not allow steel.  We flow-formed the case from a beta-phase ductile titanium that was not in Mil Hndbk 5.  This held much promise until we found that the alloy would age at room temperature into uselessness.  USN killed the project when that happened.

For VFDR,  I was able to bring two different boron fuels and a non-metallized smokeless fuel from IR&D to the VFDR testing program by about 1992.  The contract already had two McGregor low-aluminum fuels,  one having the SAEB technology.  Atlantic Research brought their boron fuel.   In the refereed tests witnessed by USAF,  all of these performed about the same,  except for Atlantic Research’s boron,  which seriously underperformed.  Clearly,  theoretical paper evaluations can be quite misleading.

Nasty corporate politics induced Hercules to close the McGregor plant while VFDR was still underway.  The other Hercules tactical location refused to learn how to cast the thick propellants we used,  and did not want the airbreathing programs.  So everything we had done at McGregor for the ramjet AMRAAM over 2 decades went to our joint venture partner Atlantic Research.  (Hercules sold it to ATK,  who actually closed it,  about a year after the first wave of layoffs that took me.)

Atlantic Research (of course) made their underperforming boron fuel the baseline VFDR fuel,  and (not surprisingly to me) in ground tests it failed to ignite at simulated middle and high altitudes.  That “killed” the ramjet AMRAAM application as far as USAF was concerned,  so the technology never flew in that missile.  Something very much like it is flying today in the “Meteor” missile produced by the Europeans.   

The gas generator and throttle technology did make it into the USN gunnery target drone “Coyote”,  which is powered by a gas generator-fed ramjet using the underperforming Atlantic Research boron fuel.  It leaves a black smoky trail of what looks like unburned fuel (also unsurprising to me). 

Being a new technology development guy,  I was laid off in the first wave,  when the plant closure announcement was made in 1994.  I never worked in the defense industry again,  since a million and a half other aerospace engineers were also unemployed that same year.  The McGregor test facility (like so much other plant equipment) was broken-up and scrapped.  No other facility anywhere in the country ever learned our methods of casting thick propellant mixes.  What a waste!

All I have been able to do since is advise or assist a few small groups about ramjet propulsion technology,  or run studies for myself.  I have written a set of cycle codes to do sizing and point performance work for these ventures.  These include both high-speed and low-speed ramjet designs. 

And I have written a very practical “how-to” book on ramjet propulsion.  AIAA did not want to publish it,  so I will have to devise a way to self-publish it.  Watch this space for updates about that.

As for my friends the other experts:  Bob Ozawa passed away a long time ago.  E. Tom Curran is in assisted-living with his wife.  I don’t know if Joe Bendot (the ejector ramjet guy) is still alive,  but if he is,  he would be about age 90.  As near as I can tell,  there are none like us anymore.

Related Posts About “Ramjet”

These are the postings on this site related to ramjet propulsion. The list is in reverse order,  newest first.

Date                                    title
2-4-2020                            One of Several Ramjets That I Worked On (this article)
1-2-2020                            On High Speed Aerodynamics and Heat Transfer
1-9-2019                            Subsonic Inlet Duct Investigation
1-6-2019                            A Look at Nosetips (or Leading Edges)
1-2-2019                            Thermal Protection Trends for High Speed Atmospheric Flight
11-12-2018                       How Propulsion Nozzles Work
7-4-2017                            Heat Protection Is the Key to Hypersonic Flight
6-12-2017                          Shock Impingement Heating Is Very Dangerous
12-10-2016                       Primer on Ramjets
11-26-2015                       Bounding Analysis:  Single Stage To Orbit Spaceplane, Vertical Launch
11-17-2015                       Why Air Is Hot When You Fly Very Fast
8-16-2014                          The Realities of Air Launch to Low Earth Orbit
11-17-2013                       Payload Comparisons
11-6-2013                          HTO/HL Launch With Ramjet Assist
8-20-2013                          Applying Ramjet to Launch Accelerators
3-18-2013                          Low Density Ceramic Non-Ablative Ceramic Heat Shields
12-21-2012                       Ramjet Cycle Analyses
8-16-2012                          Third X-51A Scramjet Test Not Successful
8-22-2010                          Two Ramjet Aircraft Booster Studies
7-23-2010                          More Strap-On Pod Ramjet Engine Data
7-11-2010                          More Ramjet Performance Numbers for the Strap-On Pod
2-28-2010                          Preliminary Acceleration Margins for Baseline Pod
2-20-2010                          Ramjet Strap-On Pod Point Performance Mapping
2-20-2010                          Ramjet Strap-On Pod Concept
2-20-2010                          Inlet Data for Ramjet Strap-On Pod

(edit 2-8-20) Posts About Pulsejet

Pulse jet is NOT ramjet,  but I do know something about that,  too.  There are a few posts on this site by me about pulse jet which draw readership.  These are listed here for pulse jet enthusiasts. 

5-20-12  Recommended Broad Design Guidelines for Valveless Pulse Jet Combustors

4-30-12  Big Student Pulse Jet an Even Larger Hit at TSTC

3-6-12   Student Pulse Jet a Hit at EAA Meeting

11-12-11 Student Pulse Jet Project

Saturday, January 18, 2020

Funny Op-Ed Page Cartoon

This op-ed page cartoon appeared in the Saturday Waco "Tribune-Herald" this date.  It was embedded in an opinion piece about which people will argue.  But this cartoon itself is actually funny in a black humor sort of way,  and is actually rather truthful about what has been going on.

Here it is without further comment.  Enjoy!



Here is an even funnier one that appeared in the Waco "Trib" Wednesday 3 March 2020.  It speaks for itself,  given the current impending pandemic:



Update 4-25-2020 here is another one I myself drew:

Update 5-14-2020:  Here is another one my wife found on Facebook and sent me. 



Thursday, January 2, 2020

On High Speed Aerodynamics and Heat Transfer

These topics are complicated,  interconnected,  and difficult to master well enough to enable doing the work.  Yet they can be intuitively understood easier than most people suspect.  This is really just an “understanding” article,  not a “how-to” article.

For atmospheric flight from high subsonic to high supersonic,  and even low hypersonic,  the standard compressible flow analyses apply,  which are based upon the ideal gas assumption.  Primarily,  that means all the kinetic energy of motion goes into internal energy,  which raises temperature.  None goes into ionization.  And,  the usual equation of state PV = nRT can be used.

This energy deposition effect shows up quite directly as the “stagnation” or “total” temperature trend with Mach number,  for any given static (thermodynamic) temperature,  and for any given gas specific heat ratio Ï’.  That equation is quite simple:

 Ttot = Tstatic (1 + c1 M2)  where c1 = 0.5*(Ï’ – 1) 

That same ideal-gas fluid mechanics model underlies much of the heat transfer correlations that apply to various geometries and situations.  At low speeds,  even fairly high subsonic,  there is not enough viscous dissipation due to velocity shear in the boundary layer,  to raise its cross-layer temperature profile.  Thus,  under those conditions,  the static gas temperature is usually taken as the driving temperature for heat transfer to the adjacent surface. 

Once supersonic,  that boundary layer temperature profile shows a temperature peak termed “recovery temperature”,  which is only a little less than the total temperature.  Because that hotter layer of gas is so closely adjacent to the surface (being down in the boundary layer),  it effectively drives the heat transfer to that surface.  In that case,  the driving temperature is the recovery temperature.

The equation for calculating recovery temperature is also fairly simple,  but requires knowledge of the gas Prandtl number PR and whether or not the flow is laminar or turbulent:

 Trec = r*(Ttot-Tstatic) + Tstatic  where r = PRn  and n = 0.5 laminar,  0.333 turbulent

In the supersonic speed ranges where those correlations actually apply,  there are heat transfer models for stagnation zones that use total temperature,  and there are heat transfer models for lateral surfaces that use recovery temperature.  Those lateral surface models can be the simpler static temperature models,  but only if the speed is slow enough that no viscous dissipation occurs (essentially subsonic).

The “division” between “supersonic flow” and “hypersonic flow” has to do with how rapidly the overall shock wave geometry changes with increasing speed.  That rate of change is quite rapid at low supersonic speeds,  but decreases to near-zero at hypersonic speeds.  The changeover point depends upon the bluntness of the flying object.  Very blunt objects such as space capsules traveling heat-shield-forward are hypersonic at about Mach 3,  while “pointy” objects like aircraft at near-zero angle-of-attack,  or missiles,  are hypersonic at about Mach 5.

The limit to this type of compressible flow analysis occurs at hypersonic speeds when the gas begins to ionize,  throwing the underlying ideal gas-based compressible fluid mechanics model into error.  That in turn throws the heat transfer correlations into error.  Once the error becomes significant,  one needs to be using non-ideal gas assumptions,  where the equation of state PV = nRT no longer applies.  And,  one needs to be using heat transfer correlations actually developed for that regime.

There is a rule-of-thumb for the effective gas temperature that drives heat transfer,  in such hypersonic flight that ionization is significant.  That rule-of-thumb is only approximate,  but quite simple:

Temperature in deg K is numerically equal to velocity in meters/second

What Figure 1 shows is the trends of ideal-gas compressible flow-based total temperature,  and the entry rule-of-thumb temperature,  versus flight Mach number from 0 to 10,  for air at 15 C.


 Figure 1 – Calculated Driving Temperature Trends Mach 0 to 10

In the figure,  the blunt and “pointy” speeds for hypersonic flight are noted.  The two temperature estimates cross at Mach 5,  and are still close at Mach 6,  but not so much at Mach 7.  Your vehicle aerodynamic coefficients (such as drag and lift coefficients) become more-or-less constant at the hypersonic transition points indicated. 

Once you are supersonic,  the heat transfer correlations that use total or recovery temperature apply.  These and the compressible fluid mechanics techniques are the models to use,  up to about Mach 5 for sure,  maybe to Mach 6,  but probably not Mach 7.  The errors of not allowing for ionization are getting too large for any sort of design analysis that you could trust,  past about Mach 6.

This not only applies to aerodynamics and heat transfer,  but also to any sort of propulsion cycle analysis that uses ideal-gas compressible fluid mechanics!    Or to anything else that uses those same compressible fluid mechanics modeling techniques.

Figure 2 shows just how rapidly the modeling error increases as speeds increase to those in the entry range.  This is the same sort of plot of the same variables as in Figure 1,  just extended out to Mach 30.  Typical of a re-entering warhead would be Mach 15. 

At Mach 15,  the entry rule-of-thumb is that heat transfer driving temperature for the heat shield stagnation point will be near 5000 K,  and actual non-ideal gas models would get something in that same ballpark.  But classical ideal-gas compressible flow models would estimate that temperature to be about 13,000 K.  The error disparity is immense!  The difference is due to kinetic energy going into ionization instead of raising thermodynamic temperature.  It’s no longer the same gas.  

 Figure 2 – Calculated Driving Temperature Trends Mach 0 to 30

Recommendations:

If you are very “pointy” in shape,  the supersonic/hypersonic transition is about Mach 5;  if blunt,  it is just about Mach 3. 

“Pointy” objects at very high angles of attack (~20-30 degrees or more) are going to behave more like blunt objects,  because the “pointy” nose simply does not face directly into the oncoming slipstream.

You may use ideal-gas based compressible fluid mechanics up to about Mach 5,  to maybe Mach 6,  without significant error.  For flight in air,  that corresponds to roughly 2500 K total temperatures,  just about where air dissociation into ionized plasma becomes significant.

Beyond about Mach 6,  you need to be using a non-ideal gas based fluid mechanics model,  or else just real experimental data. None of the compressible-fluids-based heat transfer correlations apply.  

Once there is supersonic flow,  your heat transfer models for lateral surfaces should include viscous dissipation effects:  they should be formulated in terms of recovery temperature as the driving temperature.  It is the hot sublayer in the boundary layer whose temperature drives heat transfer.

Compressibility itself is modeled differently for heat transfer:  typically as a reference temperature for gas properties termed T* that is distinct from the average film temperature.  One needs to be doing that,  even at high subsonic speeds. 

Beyond about Mach 6,  your stagnation point heat transfer model should switch to an entry-range correlation;  below that,  you can use one based on classical compressible flow total temperatures.

If you are flying fast enough that ideal-gas compressible fluid mechanics is not applicable,  it is very likely that any propulsion cycle analysis (other than a simple rocket) is also inapplicable,  as these are almost universally based on ideal-gas compressible fluid flow.

Heat Protection Applications:

For entry hypersonics,  the situations depicted in Figure 3 apply for a blunt capsule traveling above Mach 3,  at zero or low angle-of-attack (AOA).  There is a stagnation point near the center of the heat shield.  That is the location of highest applied pressure,  and highest heat transfer coefficient “h”. 

Because of the bluntness,  subsonic flow behind the bow shock prevails over the heat shield,  with the sonic line near its periphery,  as illustrated.  Most such shapes have a “tumble-home” angle exceeding 20 degrees,  so that the flow separation point is also at the periphery of the heat shield.  

 Figure 3 – Typical Flow Field Characteristics for a Blunt Shape in Entry Hypersonics

The same tumble-home angle limits the achievable AOA to no more than the tumble-home angle,  because otherwise,  the flow would re-attach on the more-windward side,  leading directly to very much higher heat transfer coefficient “h”,  due to the scrubbing action. 

Otherwise,  the lateral sides of the capsule are within the wake zone,  where velocities relative to the surface are quite low,  and so there is little scrubbing action.  That means heat transfer coefficients “h” are low,  relative to those on the other surfaces.  These lateral sides therefore receive the least heating rates,  far below any of those seen on the heat shield surface.  They could cool by re-radiation,  if the local equilibrium material temperature is low enough to be tolerable for the material. 
 
The situation for “pointy” shapes at high angle-of-attack is actually rather similar,  as illustrated in Figure 4.  If dead broadside,  there is a stagnation line along the belly.  If otherwise high AOA,  there is a stagnation point near the nose end of the belly,  with near-stagnation conditions along what otherwise would have been the stagnation line along the belly. 

Either way,  it is the crossflow picture that is informative.  While the effective cross section shape varies with AOA,  the basic conditions are otherwise similar,  as illustrated in the figure.  The sonic line delimiting the subsonic region is much closer to the stagnation point or line,  with supersonic flow over much of the windward side.  The resulting heat transfer coefficients are higher than one might otherwise expect,  due to the larger supersonic scrubbing action,  in spite of the lower pressures. 

Figure 4 – Typical Flow Field Characteristics for a “Pointy” Shape at High AOA in Entry Hypersonics

The point at which flow separation typically occurs in turbulent flow is at (or just past) the maximum cross section width,  as shown.  Conditions in the separated wake zone are very low velocity,  with low scrubbing action,  and low heat transfer coefficients. 

If flow were instead laminar,  the separation point would occur somewhat upstream of the location of maximum width.  However,  that would obtain only on very small objects.  Otherwise,  the conditions are pretty much similar to what is pictured in the figure. 

Bear in mind that hypersonic heating is both convective and radiative.  The convective heating varies with velocity cubed,  and dominates the picture at speeds below 10 km/s in air.   Radiative heating comes from the incandescent plasma that is the shocked flow surrounding the object.  This effect varies as velocity to the 6th power,  and dominates the picture above 10 km/s in air.

Even if the atmospheric gas is not Earthly air,  there is not a lot of difference,  qualitatively.   Specific heat ratio and Prandtl number are different,  so the numbers are a little different.  

On the windward side,  there must be some sort of ablative or refractive heat shield material,  in direct contact with a significant mass of structure within the object.  That structure is the heat sink,  into which the heat conducted inward must be deposited.  The whole process is a short transient,  only minutes in duration.  And THAT is why entry heat protection is fundamentally a transient heat-sinking process quite distinct from sustained hypersonic atmospheric flight!

Because of the far lower heating,  the lateral-side heat protection problem is quite different,  as illustrated in Figure 5.  If the entry situation is not too demanding,  and the lateral wall material can survive the high equilibrium temperatures,  then bare metal sides can be used,  as in the old Mercury and Gemini capsules returning from low Earth orbit at about 8 km/s speeds.

If the situation is a little more demanding,  similar to Apollo returning from the moon at just under 11 km/s,  there must be some heat shield ablative or refractory over the structure of the lateral sides.  This is also shown in the figure.  That substructure is the heat sink for the lateral heat shield material. 

This kind of “backshell” construction (whether it needs heat shielding or not) is required in order to protect cargo within that is “delicate”,  in the sense that its temperature may not be allowed to go high enough to re-radiate.  Such is typically in the vicinity of 1000+ F = 811+ K for steels and other alloys.

On the other hand,  the cargo might be “tough”,  in the sense that it can withstand getting hot enough to re-radiate effectively all by itself.  In that case,  there is no need for any backshell at all,  only a windward-side heat shield is required.

For re-radiation to work as the only cooling,  then the material temperature and spectrally-averaged emissivity must be high enough for that re-radiation to effectively balance all of the convective and radiative heat inputs at their peak values,  and to do this at an acceptable material temperature.

For ablative heat shields,  the heat balance for design purposes is effectively that the convective and radiative inputs must balance the re-radiative output plus the conduction inward plus the energy consumed to pyrolize.  The surface temperature (in part governing conduction inward) is effectively that at which the material has just fully charred. 


Figure 5 – Technical Solutions For Heat Protection During Entry

For refractory heat shields,  the surface temperature may freely “float” to equilibrium.  Only practical material service temperatures limit this.  Otherwise,  the balance is the same as for ablative heat shields,  except that there is no energy consumed by pyrolysis. 

Minimum conduction inward occurs when the heat sink temperature has maximized.  The temperature rise of the heat sink,  its specific heat capacity,  and  the mass of the heat-sink substrate,  must together be enough to contain all of the heat conducted into it,  during the total entry heating transient.

Steady Low-Hypersonic Flight:

For analyzing steady cruise up to about Mach 6 in the atmosphere,  the heat protection problem tends to become a steady-state issue,  not a transient heat-sink issue.  This is because the time scale is so much longer:  several minutes to a few hours. 

The same basic ideal-gas compressible-flow analyses apply,  except that your heat sink “gets full” quicker than you can reach your destination.  That means there are two,  and only two,  practical means to deal steady-state with the heat energy you continuously absorb:

(1)    Re-radiate the energy away to the environment
(2)    Put the absorbed energy into the propulsive fuel,  so that it ultimately exits the tailpipe

To radiate away the energy means the radiating surface must get hot,  it must have good spectrally-averaged thermal emissivity to be efficient,  and it must have a direct view of the environment.  The Earthly environment has a warm temperature,  which reduces the energy radiation rate somewhat.  A form of Boltzmann’s Law applies to the re-radiated energy rate:

Q/A,  BTU/hr-ft2 = e σ (T4 – TE4) for T’s in deg R and σ = 0.1714 x 10-8 BTU/hr-ft2-R4

where T is the material temperature,  TE is the Earthly environment temperature (near 540 R = 300 K),  e is the spectrally-averaged emissivity (a number between 0 and 1),  and σ is Boltzmann’s constant.

If instead you “dump” the heat into the fuel as it is used,  it will get very hot,  and you must prevent that fuel from boiling,  which produces vapor lock,  that stops the propulsion.  That requires very high fuel delivery pressures,  especially in the passages where it is the coolant for the aeroheated part.  

Depending upon the nature of the fuel,  there is also the risk of “coking” deposits,  which will plug up small passages very quickly,  even if boiling is successfully avoided.

Above Mach 6,  the compressible flow and heat transfer relations have to be replaced by their non-ideal gas equivalents,  but Boltzmann’s Law still applies for re-radiation. It’s still the same steady-state heat balance for each and every part of the vehicle.

Airbreathing Engine Cycle Analysis Applications:

Gas turbine engines of multiple types can be modeled fairly accurately with simple “pressure ratio” models,  because the compressor pressure-rise and turbine pressure-drop dominate the cycle pressure picture by far,  over all the other effects.  Those “others” would be the inlet pressure rise,  and the pressure losses associated with all the other components.  These are usually input as fixed ratios,  because the variations with operating conditions are quite small compared to compressor and turbine pressure-rise and pressure-drop effects. 

That last becomes increasingly inaccurate as flight speeds get hypersonic,  because the variations of component performance with operating conditions are going to get far more important as conditions get more extreme.  Offsetting that is this simple fact:  so far,  there are no turbine engines that have ever been operational,  which flew any faster than about Mach 3.5.

Those same pressure ratio models can be used to model subsonic combustion ramjet engines,  but this is far too imprecise to be a useful design analysis!  There are no compressor pressure-rise and turbine pressure-drop phenomena in a ramjet.  The only pressure-rise item is the inlet,  and its variation with conditions and its interplay with the pressure drops of all the other components,  dominates ramjet behavior.  These things simply cannot accurately be modeled as “typical constant ratios”. 

At the other end of the spectrum is finite-difference computer fluid dynamics modeling.  This is accurate to the extent that the turbulence model,  the combustion models,  the flow separation models,  and the ionization/non-ideal gas models are all accurate (not all codes have such).  Such analyses require great effort to set up and to interpret the results.  One analysis for one situation in one design means the investigator must run a lot of them,  for just the one design.  However,  this is about the only realistic way to model supersonic combustion ramjets (scramjets),  especially at speeds well above Mach 6.

In between these two modeling extremes are the quasi-1-D ideal-gas compressible flow-based models of subsonic combustion ramjet cycle analysis.  These are quite accurate,  up to the Mach 6 point where the ideal gas model fails,  and they require a lot less effort to set up,  and very little to interpret. 

These can be tailored to provide sizing or performance,  and for repeated performance runs across the flight envelope.  They provide fluid flow state information at every modeled location within the engine.  Those are all very distinct advantages.  But they inherently do not provide accurate results past about Mach 6. 

Recommended Simple Heat Transfer Models for Back-of-the-Envelope Stuff:

These divide into what applies in when compressible fluid mechanics is “good”,  and what applies when it is “not good”.  That changeover is about Mach 6.

               Supersonic to About Mach 6

These take the forms of lateral surfaces,  stagnation zones,  and internal duct flow (for propulsion items such as combustors and subsonic ducts).  You look up gas properties from standard tables,  or else estimate them with empirical equations. 

Turbulent flow with compressibility and viscous dissipation on a flat plate parallel to freestream;  applicable to exposed skins in high speed flight at speed V

Need:                   total Tt,  and static T,  plus fluid Prandtl number Pr and plate surface Ts
                              plus density rho and velocity V at edge of boundary layer,  and length L

Calculations:      recovery factor r = Pr1/3
                              recovery temperature Tr = r (Tt – T) + T
                              ref temp. T* = 0.5(T + Ts) + 0.22(Tr – T)   this models compressibility
                              evaluate properties at T*
                              ReL* = rho V L / mu   (properties at T*,  V = freestream/edge of boundary layer)
                              average NuL* = .036 ReL*0.8 Pr1/3
                              average h = NuL* k/L   (k at T*)
                              Q/A = h(Tr – Ts)   this models the viscous dissipation, positive to surface for Tr>Ts

Source:                Chapman (ref. 2) eqn. 8.41,  attributed therein to Eckert

Stagnation-Point heating in very high speed flow (supersonic and hypersonic)

Need:                   stagnation Tt2,  Pt2,  kt2, mut2,  Prt2,  and rhot2 behind the shock wave,  surface Ts,  freestream V and rho;  diameter D = 2 Rn,  where Rn is the nose radius

Calculations:      Rpt = Pt2/Pt1 = (N1/D1)E1*(N2/D2)E2 where
                              N1 = (γ + 1)M2,   D1 = (γ – 1)M2 + 2,  and E1 = γ/(γ – 1)
                              N2 = γ + 1,    D2 = 2 γ M2 – (γ – 1),  and E2 = 1/(γ – 1)
Pt2 = Pt1 Rpt  (this procedure is total pressure ratio across a normal shock,  any γ)
ReD = rhot2 V D / mut2
                              Cylinder:  NuD = 0.95 ReD1/2 Prt20.4 (rho/rhot2)1/4  applies to leading edges
                              Sphere:    NuD = 1.28 ReD1/2 Prt20.4 (rho/rhot2)1/4  applies to nose tips
                              h = NuD kt2 / D
                              Q/A = h(Tt1 – Ts)    where Tt1 = total ahead of wave = Tt2 behind wave

Source:                Chapman (ref. 2) eqn. 8.45,  see also ref. 1 for total pressure ratio across shock wave

Turbulent flow inside a pipe or duct or tube,  with a nontrivial difference between fluid T and surface Ts;  applicable to combustor and subsonic inlet air duct inside film coefficients

Need:                   flow rate w,  duct diameter D,  fluid static T,  and surface Ts

Calculations:      evaluate all properties at bulk T fluid, plus a second mus at Ts
                              ReD = rho V D / mu = 4 w / pi D mu             (second form very convenient!)
                              NuD = 0.027 ReD0.8 Pr1/3 (mu/mus)0.14       (“Seider and Tate”)
                              h = NuD k/ D
                              Q/A = h(T – Ts)                  positive to surface for T > Ts

Source:                Chapman (ref. 2) eqn. 8.16,  attributed therein to Seider and Tate

               Above About Mach 6

This takes the form only of stagnation heating.  The lower values farther away from the stagnation zone must come from experimental data for each shape and situation.  However,  for a blunt capsule heat shield,  a first-cut over-design is to size the heat shield to the stagnation zone requirements.  It must be “that thick” there,  and can be about half that thick near the sonic line.

The stagnation point heating model is proportional to density/nose radius to the 0.5 power,  and proportional to velocity to the 3.0 power.  The equation used here is H. Julian Allen’s simplest empirical model from the early 1950’s,  converted to metric units.  It is:

q, W/sq.cm = 1.75 E-08 (rho/rn)^0.5 (1000*V)^3.0,  where rho is kg/cu.m,  rn is m,  and V is km/s.  The 1000 factor converts velocity to m/s. 

The source for this (that I have in my possession) is a US customary units form of the same equation,  obtained from ref. 3.

Getting Gas Properties

If you cannot obtain more accurate data from tabulations in various references,  there are some empirical estimating relations that will get you “into the ballpark”.  These are from the “grab bag” chapter of my yet-to-be-published book on ramjet propulsion,  ref. 4.

It is always preferable to look up the properties of real gases and liquids in standard references.  For hot combustion gases,  this is often problematical.  However,  it is possible to approximate the properties from simple inputs.  I obtained these correlations informally from a colleague,  James M. Cunningham,  who was the head thermal analyst at Rocketdyne/Hercules in McGregor,  Texas,  about 2 to 4 decades ago.  These also work reasonably well for air itself,  although real data tables for air are better.  Choose a gas MW and γ appropriate to the temperature range you are working in.  Those and the temperature are all you need to estimate realistic properties for heat transfer purposes.  Ideal gas behavior is inherently assumed.

Input items as constants (not very dependent upon temperature at all):

Gas molecular weight MW           (can be summed up from the chemical balance equation)
Gas specific heat ratio γ                (usually in the vicinity of 1.2 for real combustion-product gases)

Functions of inputs but not very dependent upon temperature:

Specific heat at constant pressure cp = 1.987 γ / [(γ – 1) MW]    units will be BTU/lbm-R
Prandtl number Pr = 4 γ / (9γ – 5)                                                          dimensionless
Gas constant   R, ft-lb/lbm-R  =  Ru/MW               where Ru = 1545.4 ft-lb/lbmole-R

Functions of inputs and strongly-dependent upon temperature:

Viscosity  µ, lbm/in-sec = 46.6 x 10-10 MW0.5 (T, R)0.6  or µ, lbm/ft-sec = 5.592 x 10-8 MW0.5 (T, R)0.6
Thermal conductivity k, BTU/hr-ft-R = [1 x 10-4 (9γ – 5) (T, R)0.6] / [(γ – 1) MW0.5]

General Remarks:

None of these above are considered to be significantly pressure-dependent at all.  The property that is strongly pressure-dependent is density.  The ideal-gas relation to define density is:

               rho,  lbm/ft3  =  (P, psfa) / [(R, ft-lb/lbm-R)*(T, R)]             (“psfa” is lb/ft2,  absolute)

If your situation is not quite amenable to the ideal gas model,  you can still use P = Z rho R T,  where Z is an empirical function of P, T,  and the critical Pcrit and Tcrit for your gas.  Reference 5 is an old thermodynamic textbook that contains a universal approximation chart for Z.  Any modern text should contain the same chart.  This is more applicable to cold conditions approaching the triple point.

It should be noted that the usual Mach number formulation of compressible flow analysis does in fact assume both adiabatic and ideal-gas behavior!

References:

There are many references for classical compressible fluid mechanics.  But fundamentally,  virtually all of the basics in any of them,  trace back to the famous old NACA report number 1135:

#1. NACA Report 1135,  “Equations,  Tables,  and Charts For Compressible Flow”,  Ames Research Staff,  1953.

There are many books available on heat transfer,  covering a variety of situations with empirical correlations for each.  My reference is an old college textbook on the subject:

               #2. Alan J. Chapman,  “Heat Transfer” second edition,  MacMillan,  1967.

There is a variety of good information on very many topics in the following reference.  I cite it for the simple entry stagnation heating equation attributable to H. Julian Allen,  equation 4B-4 page 520.  In the reference,  this is given in US customary units.  I converted this to metric,  specifically for entry calculations using speed in km/s and heating rates in W/cm2. 

#3. “SAE Aerospace Applied Thermodynamics Manual”,  second edition,  Society of Automotive Engineers,  1969.

The next reference is not yet available,  but soon should be.  AIAA has chosen not to offer it,  so that I must self-publish it.  This reference is now available directly from the author.  Contact him by email. 

#4. Gary W. Johnson,  “A Practical Guide to Ramjet Propulsion”,  yet to be published,  but copyrighted as of 2017.  This reference has been in self-publication since Feb. 2024,  similar to the self-published “Fluid Dynamic Drag” by Sighard Hoerner.  Contact the author to buy it.

 This one is just another old textbook on classical (not statistical) thermodynamics.  Any modern classical thermodynamics textbook should have the same information in it.

#5. Gordon J. Van Wylen and Richard E. Sonntag,  “Fundamentals of Classical Thermodynamics”,  John Wiley and Sons,  1965.


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This article was originally posted 2 January 2020.  It was taken down by blogger 8-17-2025 as “not meeting their guidelines” in some way,  but they utterly failed to tell me what it actually was,  that violated their guidelines!  I looked at the guidelines,  and as near as I can tell,  this article violated nothing!  This is a simple technical article,  based on open sources,  and some of those have been available for over 6 decades.  All I could find that was not still completely correct was the status of my ramjet book,  reference 4 in the list,  which is now in self-publication.  So,  I corrected that status,  in red text,  marking out the errors,  but leaving them in place for comparison.  I had recently also added a search code,  and I repeated that addition just below,  also in red text.  

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Search code 02012020,  search keywords: aerothermo,  airplanes,  launch,  ramjet, space program

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