Basic Thermal Results for High Speeds

This article is a direct follow-on to the updates posted to “Purported SR-72 Propulsion”,  posted 1 September 2023.  As I have said there,  and multiple places and times elsewhere,  if you do not have a thermal management design concept,  you do not have a feasible hypersonic flight concept!  This article attempts to put some bounds on that problem.

Lateral Skin Study

The following is a simplified equilibrium skin panel surface temperature estimate for lateral-facing skin panels.  These could be on aerosurfaces (wings and fins),  or on the sides of a fuselage body.  I did not consider any conduction inward or to adjacent panels.  I did not consider any active cooling.  There is convection to the panel,  and thermal re-radiation from it.  It soaks out hot enough to balance the two. 

I did this for Mach numbers from subsonic to Mach 7,  using standard compressible flow methods and the high-speed heat transfer models that are based upon it.  I used free-stream conditions as the good approximation that they really are,  for local edge-of-boundary layer conditions.  I did not analyze past Mach 7,  because the fundamental assumptions underlying compressible flow analysis methods are breaking down,  due to ionization into something that is no longer air as we know it.

I show temperature curves in Figure 1 for air total temperature,  boundary layer recovery temperature (the driver for heat transfer to the panel),  and equilibrium panel soak temperatures for low and high thermal emissivity.  The service temperature limits for a variety of materials are also shown.  Figure 2 shows the film coefficient trends vs Mach at 40 kft,  for low and high emissivity.  Beyond about Mach 3 or 4,  these are pretty constant.  Data in the same formats for 85 kft are in Figure 3 and 4,  and for 130 kft Figures 5 and 6. 

Figure 1 – Skin Panel Soak-Out vs Mach at 40 kft

Figure 2 – Film Coefficients vs Mach at 40 kft

Figure 3 – Skin Panel Soak-Out vs Mach at 85 kft

Figure 4 – Film Coefficients vs Mach at 85 kft

Figure 5 – Skin Panel Soak-Out vs Mach at 130 kft

Figure 6 – Film Coefficients vs Mach at 130 kft

Skin Study Correlation:

Recovery temperatures do not change so drastically with altitude,  unlike film coefficients.  See Figure 7.

Figure 7 – Replots of Film Coefficient and Soakout vs Altitude at Mach 5

As the figure shows,  the result is a drastic change in soakout temperatures,  driven by drastically lower film coefficients at extreme altitudes.  The recovery temperatures all fall between 3800 and 4500 F at Mach 7,  as shown in Figures 1, 3,  and 5 above.  This suggests that a single analysis could establish a representative film coefficient value insensitive to changes in speed,  at Mach 4+ and some altitude,  which could be quickly scaled to other altitudes.  Calculating recovery temperatures at each flight condition is a far easier thing to do.  The correlation supporting that shortcut is given in Figure 8.  Doing it that way is only a ballpark estimate that supports better,  more detailed analyses later.  But it is useful. 

Figure 8 – Correlating High-Speed Film Coefficient vs Altitude

Leading Edge Stagnation Study

There is a compressible flow-based heat transfer correlation for stagnation zone heating.  It exists in two forms,  determined by a coefficient on the Nusselt number expression:  C = 1.28 for nose tips,  and C = 0.95 for aerosurface leading edges.  I looked at leading edges for this study,  so bear in mind that nose tips will run a little hotter still.   

In this Nusselt correlation,  you evaluate boundary layer properties at the total pressure and total temperature properties behind a normal shock at flight conditions.  I used the NACA 1135 tables for this.  It also uses a second viscosity evaluated at the flight conditions.  I did this for Mach 2 to Mach 7,  at the same three altitudes as the skin panel study.  The idea was to balance convective heating against thermal re-radiation,  with no conduction or active cooling,  as in the skin panel study. 

The results at 40 kft are given in Figures 9 and 10.  Figure 9 shows trends of total temperature,  and two local stagnation-region equilibrium temperatures,  one at low emissivity,  one at high emissivity.  Figure 10 superposes material service limits on the same curves.  The same data in the same format is given in Figures 11 and 12 at 85 kft,  and Figures 13 and 14  at 130 kft. 

Figure 9 – Stagnation Region Soakout Results vs Mach at 40 kft

Figure 10 – Soakout at 40 kft with Service Limits,  and a Speed Limit Indicated with Inconel X-750

Figure 11 – Stagnation Region Soakout Results vs Mach at 85 kft

Figure 12 – Soakout at 85 kft with Service Limits,  and a Speed Limit Indicated with Inconel X-750

Figure 13 – Stagnation Region Soakout Results vs Mach at 130 kft

Figure 14 – Soakout at 130 kft with Service Limits,  and a Speed Limit Indicated with Inconel X-750

In Figures 10,  12,  and 14,  I have included data for the service temperature limits and tensile strength at those limits,  as part of the figure.  Of the metals possibly useful for these high speed exposures,  Inconel X-750 is by far the strongest,  leading to thinner parts of lower weight.  So,  I used it as the selection here,  for “best” performance.  Under the earlier name “Inconel-X”,  this was in fact the skin material and leading edge for the X-15 rocket plane,  which skin was a major load-bearing portion of its airframe. 

Even so,  the speed limit for Inconel X-750 in a stagnation zone is only about Mach 4.9 at 40 kft,  about Mach 5.2 at 85 kft,  and about Mach 5.8 at 130 kft.  For lateral skins,  this was nearer Mach 6 at 40 kft,  Mach 7 at 85 kft,  and likely near or above Mach 8 at 130 kft,  because the convective heat to be reradiated is far lower for lateral skins,  compared to stagnation zones. 

A good guess says the stagnation limit for Inconel X-750 is about Mach 5.5 at 100 kft,  which neatly explains why the X-15A-2 with the drop tanks was coated all-over with an ablative for its flights to Mach 6 and beyond,  despite the indicated survivability of its lateral skins at Mach 7+,  near 100 kft.  

The craft reached Mach 6.7 at 99,000 feet on flight 188,  and suffered shock-impingement heating damage to the underside of its tail,  to both lateral and stagnation surfaces.  That phenomenon drastically raises the local heating rate,  but not the actual gas temperatures,  as described in another of my articles on this site:  “Shock Impingement Heating Is Very Dangerous”,  posted 12 June 2017.  See also NASA TM-X-1669 ““Flight Experience With Shock Impingement and Interference Heating on the X-15-2 Research Airplane”,  dated October 1968,  and written by Joe D. Watts,  at the Flight Research Center,  Edwards,  CA.  This document is publicly available over the internet.

Stagnation Study Results:

Use no metals for leading edge stagnation zones that are cooled only by re-radiation,  past about Mach 5.5,  and then only above 100 kft.  You must instead use ablatives,  or apply massive active cooling.  See Figure 15.  

Figure 15 – Results for Stagnation Zone Equilibrium

Nose tips will run slightly hotter than leading edges (higher h values at the higher C raise Tsurf),  thereby have a somewhat lower speed limitation than leading edges.  The risk with both locations is distortion and collapse of the parts,  as they weaken rapidly with increasing overheat. 

Alloys like Rene 41 and Alloy 188 can take slightly higher temperatures than Inconel X-750,  but are inherently weaker structurally by around a factor of 2.  This is a crucial consideration,  because stagnation zones see the highest positive surface pressures on the airframe.  Distorted or failed leading edges lead to higher drag,  loss of lift,  and intrusion of hot gas inside the aerosurface,  something to be assiduously avoided.  In general,  weaker is thicker,  which is heavier. 

Lateral Skin Results:

Speed limits versus altitude for Inconel X-750 lateral skins are about Mach 6 at 40 kft,  a bit over Mach 7 at 85 kft,  and likely above Mach 8 at 130 kft.  This is complicated by the risks of shock impingement heating,  which occurrence is complex and difficult to predict,  and which can do fatal damage at much lower speeds nearer only Mach 6.  See Figure 16.  Bear in mind that the analysis method is invalid above about Mach 7,  although the prediction is likely still crudely true. 

Figure 16 – Results for Lateral Skin Equilibrium

As with stagnation zones,  there are alloys that will go a little hotter,  but at far lower strength.  This is a crucial consideration,  because in monocoque construction,  the skins are an integral part of the airframe structure,  bearing much more than just local surface pressure loads.  Weaker is thicker,  which is heavier.

Remarks About Airbreathers:

Components associated with airbreathers (of any type) were not studied here.  The X-15 was a rocket plane.  The results above apply to both rocket-powered hypersonic vehicles,  and to hypersonic gliders. 

All airbreathers will have some sort of supersonic inlet capture structures,  some sort of post-capture air ducting that leads to the engine device (whatever it is),  and that engine device and its nozzle.  The ducting,  engine device,  and nozzle might be either buried inside the airframe,  or exposed as part of the airframe.

               Air Inlet Components

Inlet capture features suffer worse heating effects than leading edge (or nose tip) stagnation surfaces,  This is because they are heated (unequally) on both outside and inside surfaces,  but can re-radiate to cool from only the exterior surfaces,  with very localized stagnation soak-out on leading edges that must stay thin and sharp,  in order to function properly.  There is little opportunity for any conduction-as-cooling,  and not much opportunity for any active cooling.  They must also contain serious internal pressures without shape distortion. 

Buried subsonic inlet ducts will inevitably soak out to essentially the full air recovery temperature,  or else  they must be actively cooled.  They cannot re-radiate,  being buried inside the airframe.  They must be externally insulated to protect the rest of the airframe and its contents. 

Exposed inlet ducts are unlikely in hypersonic designs,  as too much airframe drag gets added.  However,  these are also internally heated,  and can only re-radiate to cool from that portion of the outside surfaces not inside a fairing or facing the fuselage.  They will still tend to approach air recovery temperature soak-out,  although not as closely as buried ducts. 

               Combustor and Nozzle Components

Buried or exposed combustors eventually soak out to something in between the external and internal recovery temperatures,  and will likely need active cooling.  The buried combustor will take a longer time to equilibriate,  because it starts off exposed to low airframe internal temperatures,  with a relatively low thermal conductivity for the free convection or insulated interfaces between it and the skin.  But it will soak out very hot! 

An exposed combustor can re-radiate directly to the surroundings,  while the buried combustor cannot (while the airframe skin can),  so the exposed combustor may possibly equilibriate a little cooler than the buried combustor.  But neither has a cold “sink” to dump heat into.  They both get very hot! 

The same applies to propulsion nozzle structures,  whether buried or not. 

               Turbomachinery

As for turbomachinery (compressors and turbines),  these must be isolated completely from hot intake airflow above about Mach 3 to 3.5.  Beyond that speed,  the very intake air temperature exceeds the turbine inlet temperature limits of almost any conceivable design.  The main flying examples of these speed limitations were the XB-70 (Mach 3.0),  the SR-71 (Mach 3.2),  and the Mig-25 (Mach 3.5).

               (Subsonic-Combustion) Ramjet

Ramjet can fly faster than turbine,  before hitting overheat speed limits.  Flight tested but not fielded as operational,  the ASALM-PTV test vehicle was designed to cruise steady state at Mach 4 and 80 kft,  followed by an average Mach 5 terminal dive onto its target.  It did so successfully in flight test. 

In one test of ASALM-PTV,  an assembly error led to a throttle runaway incident,  with the vehicle accelerating to fuel exhaustion at Mach 6 at low altitude (near 20 kft).  It suffered airframe overheat damage,  but actually survived the short transient flight and was recovered after it crashed. 

If designed for it,  ramjet could conceivably be made to work steady-state at Mach 6,  or even a bit faster,  perhaps.  The internal air duct and combustor/nozzle will require active cooling for a long flight.  The inlet cowl lip surfaces will likely need to be made of a really high-melting metal,  like tungsten or columbium,  so that they remain both sharp and thin,  without distorting.

               Supersonic-Combustion Ramjet (Scramjet)

Scramjet can fly faster still than ramjet,  but faces similar overheat risks for its inlet capture and supersonic isolator duct,  and its combustor and nozzle structures.  These get ridiculously difficult to design for,  as speeds increase beyond Mach 7.  The same can be said for airframe stagnation surfaces and lateral skins.  Short transients and ablative materials make such flight possible,  but those are neither reusable,  nor are they long-range. 

               Altitude Limits

The problem with all airbreathers,  of any type whatsoever,  is the “service ceiling” effect.  These devices produce an altitude-dependent characteristic trend of thrust versus speed,  with lower thrust levels in the thinner air at higher altitudes.  Roughly speaking,  thrust is proportional to the ambient atmospheric pressure at altitude.  So is drag.  But weight does not vary with altitude,  only with time as fuel burns off.

The vehicle requires enough lift to offset the perpendicular component of its weight,  as it tries to fly up an ascending path.  It also requires enough thrust to offset the sum of drag and the pathwise component of its weight.  See Figure 17.

Figure 17 – Why There Is an Altitude Limit for Airbreathers

There is an altitude at which there is insufficient thrust to overcome drag and the weight component,  regardless of any wings that might solve the lift problem.  Above that altitude,  it cannot even fly level steady-state,  at all.  As a rule-of-thumb at speeds in the Mach 5 to 7 range,  that’s around 130 kft,  almost no matter what sort of airbreather you might design.

Remarks on Active Cooling

This can be done reusably with a dedicated liquid coolant,  or it can be done regeneratively with the fuel.  For rocket systems,  the oxidizers are not generally very good coolant materials,  while the fuels generally are.  Either way,  the coolant may not be allowed to boil inside the cooling passages,  because that leads to vapor lock and a stoppage of coolant flow.  That in turn requires you to operate your coolant passages at very high pressures to avoid boiling,  which costs weight,  and power to run. 

However,  even if you deliberately allow boiling,  that reduces heat transfer capacity of the coolant,  because the gas density is so much lower than the liquid density,  for all known coolant materials.  This is really a per unit volume problem,  rather than a per unit mass problem,  because the passage sizes are pretty much fixed. 

Final Remarks

What I have done here is bound the problem for rocket-propelled vehicles,  or gliders,  that fly hypersonically.  I did this in terms of steady-state equilibrium surface temperatures,  for lateral skins,  and for stagnation zones on nose tips and aerosurface leading edges. 

I have provided some discussions,  but no numbers,  for the airbreathing propulsion components that might be applied to hypersonic vehicles.  Those are worse to thermally-manage than stagnation zones.

I have commented upon the “service ceiling” effect that applies to any airbreather of any kind at all.  This is related to the narrow flight corridor to orbit,  that resulted from the X-15 program.  See also “About Hypersonic Vehicles”,  posted 1 June 2022,  on this site.  Plots of that corridor are in that article.

And I have commented upon the difficulties faced by any actively-cooled designs.  

Note:

This article has been included in the catalog article,  under the topics “aerothermo” and “ramjet”.  That article is “Lists of Some Articles by Topic Area”,  posted 21 October 2021.  The fastest way to reach it is to use the navigation tool on the left side of this page.  To use it,  you need the article posting date,  and its title,  so in general,  jot that stuff down.  Click on the year,  then on the month,  then on the title if more than one item was posted that month.  Simple as that. 

 

Purported SR-72 Propulsion

For some years now there have been marketing-hype disclosures about Lockheed Martin’s efforts toward the “SR-72”,  an intended follow-on to their famous SR-71 “Blackbird”.  The hype was about hypersonic speeds above Mach 5,  and some hand-waving about an advanced engine,  usually supposedly a combined-cycle gas turbine and scramjet (supersonic-combustion ramjet) engine.

I knew the hand-waving about combined-cycle turbine-scramjet was BS,  because about the fastest practical speed for gas turbine is about Mach 3.2 to 3.3 due to overheat damage,  and about the min takeover speed for scramjet is Mach 4.  Plus,  the inlet and nozzle geometries are utterly incompatible. 

What that really means is that your propulsion unit has to operate first as a gas turbine to take off and climb and accelerate to ramjet takeover speed at about Mach 2.5,  then operate as a (subsonic-combustion) ramjet to accelerate above Mach 4,  then finally operate as a scramjet to “fly hypersonically” at or above Mach 5.  The ramjet and the gas turbine share similar inlet and nozzle geometries,  but the scramjet is still utterly incompatible geometrically with the other two.  And,  you must change engine type in order to slow down for a more economical cruise. 

My suggested solution has,  up to now,  been “parallel-burn” propulsion:  do not try to combine the various propulsion types into one design,  instead install all 3 separately,  each optimized for what it is.  (Combined,  it is inevitable that performance of each component suffers greatly.)  But,  a major problem with parallel burn at higher speeds (where drag is high),  is that no one of these propulsive items is a large enough fraction of the vehicle frontal cross section area!  That severely limits the max speed attainable,  likely to less than hypersonic,  which eliminates any reason to have the scramjet at all!

Concept for Combining Gas Turbine with Ramjet and Scramjet

I have since had a sort-of hybrid idea.  The 3 systems can share one common supersonic inlet capture installation,  but nothing else!  The post-capture channels of the inlet must be made variable geometry,  so that the gas turbine and the ramjet can be fed subsonic air in a diverging channel,  while the scramjet is fed supersonic air in a constant-area channel.  The supersonic channel to the scramjet must be “straight through”,  you absolutely cannot divert a channel carrying supersonic flow,  because the turn always causes shock-down to subsonic flow!  Anybody who claims otherwise is spouting pure BS!

The gas turbine needs to be a low-bypass ratio afterburning design suitable for supersonic flight,  and also be fitted with air bypass tubes around its core big enough so that they can carry 100% of the air flow,  tapped off ahead of the compressor face,  and going directly to the afterburner.  (In the SR-71,  those engines had 25% max air bypass,  tapped from the 3^rd or 4^th stage of the compressor.)   In that way with 100% bypass,  the afterburner can also serve as the subsonic-combustion ramjet combustor,  using the very same post-capture subsonic inlet air channel as the turbine uses.  But,  we do need to stop the airflow into the compressor,  to avoid overheat damage!  And we need to stop backflow from the afterburner into the turbine!  Ramjet combustor gas temperatures are far higher than any allowable turbine inlet temperatures,  and “leaks” lower the ramjet pressure,  lowering performance drastically.

Therefore,  it is a key requirement here,  when operating as a ramjet,  to stop the backflow from the afterburner chamber from going up through the turbine into the turbine engine.  That is a serious and extremely difficult design problem to solve!  But it must be solved,  to prevent turbine overheat,  and to raise the achievable chamber pressure of the ramjet,  in order to preserve its performance.  Leaks are low chamber pressure,  and low pressure is low performance.  Period.  That was settled long ago in tests.

What you “buy” with the 100% bypass and the backflow stoppage complications,  is a gas turbine and a ramjet that share the same portion of the vehicle frontal cross section,  which then can be a much larger fraction of vehicle frontal cross section,  so that the top speed in ramjet can be higher,  reaching the scramjet takeover range at Mach 4+. 

For scramjet takeover,  you must suddenly change the inlet post-capture channel geometry to a long,  straight supersonic feed to the scramjet,  that is also the “isolator duct” required for stable scramjet operation.  This scramjet must be parallel-mounted to the rest of the propulsion,  and must be completely separate,  except for sharing the supersonic capture features.  It lets you put the scramjet on the belly of the aircraft,  and to use the vehicle aft underside as a free-expansion nozzle surface. That reduces (but does not zero) the scramjet’s fraction of the vehicle frontal cross section,  as opposed to that of the turbine/ramjet,  to about a 50-50 split.  That highly-integrated geometry in turn increases the max scramjet speed against drag,  making more-than-minimum (Mach 5) “hypersonic speed” feasible.

Doing these required design features is a hellaciously-difficult problem,  but does offer a potentially-feasible solution for hypersonic flight that does not involve rocket thrust to takeover speed.  I have not even touched on the thermal management issues,  which may,  in point of fact,  be fatal to the concept!  Suffice it to say the usual construction techniques for the afterburner and its nozzle cannot be used,  because for Mach 3.3+ speeds,  there is no such thing as the cooling air that those technologies require.

Finally,  if the marketing hype you see does not include a propulsion system that addresses the issues I have raised here,  and a thermal management scheme that addresses the propulsion and the inlet and the airframe,  then I suggest that you dismiss it as the BS that it quite evidently is!

A cartoon sketch of my scheme is given here as Figure 1.

Figure 1 – A Possible Means to Combine Gas Turbine Takeoff and Landing with Scramjet Dash

Rocket-Boosted Ramjet Is a Much Better Way

Actually,  I still prefer my parallel-burn,  completely separate,  rocket and ramjet solution,  and just forget the scramjet!  To take off,  climb,  and accelerate to around Mach 2.5 does not require all that big a rocket engine,  or all that much propellant.  The subsonic-combustion ramjet takes over at about Mach 2.5,  and supports supersonic cruise much more economically in the vicinity of Mach 3,  but with enough frontal cross section fraction to support supersonic dash speeds to Mach 5,  or possibly even Mach 6.  And that is hypersonic!  No scramjet required!  It just has lower specific impulse at hypersonic speeds,  as does the scramjet.  However,  you do not have to change propulsion to slow down to cruise!

If you include some small liquid rocket propulsion,  your landing is not entirely “dead-stick”.  Just fire up the liquid rockets to divert or go-around.  I find that to be a far safer and more practical solution,  manned or unmanned!

The main mass of booster propellant to reach ramjet takeover,  is likely a solid packaged within the ramjet combustor as an “integral rocket ramjet” booster (IRR booster).  There are two reasons for this:  (1) the booster needs to be big to have the very high thrust to accelerate very quickly to ramjet speed,  to reduce the aerodynamic drag losses to tolerable values,  and (2) there are no air-cooled technologies available for the combustor and nozzle internal heat protection at these flight speeds,  since there is no such thing as “cooling air” above about Mach 3.2 to 3.3;  thus the only technological solutions for combustor and nozzle are one-shot ablatives.  The IRR is proven,  existing 1-shot missile technology. 

That last says you need to pull the entire ramjet combustor unit out,  and replace it,  after every flight!  It therefore might as well contain an integral solid booster,  just like what has proved so successful in missile work.  You need the big boost to ramjet speed only once per mission!  The smaller liquid rockets let you fly the plane at speeds below ramjet speed,  for the approach and landing.

See Figure 2. 

Figure 2 – Rocket-Boosted Ramjet as a Means to Achieve Hypersonic Dash

Figure 3 shows some details about how the cartridge-loaded ramjet combustor and nozzle is also its own  integral rocket ramjet (IRR) booster.  The craft need accelerate only once to ramjet takeover speed,  and the IRR booster does that job,  then transitions to ramjet thrust in about 0.1 sec (as demonstrated by ASALM-PTV in flight).  The liquid rockets are much smaller,  and mainly serve to keep the descent and landing from being totally “dead stick” (with no go-around or divert capability).

Combustor and nozzle heat protection is by ablative materials,  which cannot be re-used.  So,  the IRR unit must be replaced for every flight.  In this concept,  there must be airframe structure to support the vertical tail,  so the IRR unit resides inside this airframe,  not exposed to hypersonic external aeroheating.  That greatly simplifies the thermal management,  to something the ablatives can easily handle for very long burns.  The case can be power-washed out,  refitted with ablatives,  and cast with another propellant charge.  On-pavement recovery has little in the way of risk to support this kind of reuse.

By making the bottom flat with the bifurcated inlet ducts,  there is little need for wing area in supersonic flight above about Mach 3,  but there is room for the small liquid rockets aft of the inlets ducts!  The wing is really sized for a tolerable landing speed,  with the delta planform allowing high angle of attack without stalling.  It is mostly just parasite drag at high speeds,  so there are many design tradeoffs here.  However,  at very high altitudes in very thin air,  the wing allows sufficient lift generation at lower angles of attack that correspond to lower drag-induced-by-lift.  This may help extend cruise range,  and certainly might help extend the service ceiling.   The “right” wing is quite likely smaller than the one sketched on the figure.  

Figure 3 – Cartridge-Loaded Ramjet Combustor with IRR Booster

In cruise at about Mach 3,  the ramjet specific impulse (Isp) should be in the neighborhood of 1000-1300 secs.  Running richer at full ramjet thrust for Mach 5+ dash,  the ramjet Isp is likely nearer only 700-800 sec.  The liquid rockets are lower-pressure units that are simply pressure-fed the LOX,  and little bit of the same thermally-stable kerosene that the ramjet uses.  It would be realistic to expect about 300 sec of Isp out of them.  The solid booster,  at about 85-87% solids,  would achieve a sea level Isp near 250-255 sec.

This plane could actually take off using the small rockets,  like the “rocket racer” did,  although zero-length launch from a ramp is also very feasible,  since the integral rocket booster accelerates the airplane at 5+ gees.  Once leaving the pattern,  you pull up sharply,  fire up the solid booster and shut down the small rockets.  Seconds later,  you do ramjet takeover at about Mach 2.5 while climbing very steeply,  and at much higher altitude.  The ramjet then takes you to cruise conditions,  and also hypersonic dash. 

At mission’s end,  you start your approach in ramjet,  but shut it down as you decelerate below Mach 2.5,  making most of the rest of the approach in glide.  As you near the field,  use the small liquid rockets as necessary to divert or to go around for a missed approach.   There is only one boost to ramjet takeover per mission,  but the small rockets can be used multiple times for multiple purposes in a mission. 

You swap out the spent combustor unit for a fresh one,  and refill the kerosene and oxygen tanks.  With on-ramp recovery,  spent combustor refurbishment is also a very low risk possibility.  Easy!

None of these considerable existing-technology advantages obtain with the sort-of combined-cycle gas turbine/ramjet/scramjet craft described above.  There are still missing-technology items with it,  but not with this rocket-ramjet airplane.

Related Information:

If you want to see more about how supersonic inlets really work,  and how they are adapted to ramjet versus gas turbine,  please see on this site “Fundamentals of Inlets”,  posted 9 November 2020. 

If you want to see more about how (subsonic combustion) ramjets really work,  please see “How Ramjets Work”,  posted 1 December 2022,  and “Primer On Ramjets”,  posted 10 December 2016. 

The general issues that must be addressed for hypersonic vehicles are discussed in “About Hypersonic Vehicles”,  posted 1 June 2022.  A peculiar problem with high hypersonic flight is discussed in “Plasma Sheath Effects in High Hypersonic Flight”,  posted 18 September 2022,  which debunks some of the widely-circulating myths about “unstoppable” hypersonic missile weapons.

If you want to see what an integral solid booster is,  please see “Solid Rocket Analysis”,  posted 16 February 2020,  and concentrate on the low L/D keyhole slot grain design therein.  How the internal ballistics of solid propellant devices work is well-explained.  There is also information on achievable burn rates,  and on safety sensitivity data.

The thermal management issues are discussed in more detail in “On High-Speed Aerodynamics and Heat Transfer”,  posted 2 January 2020,  “Heat Protection is the Key to Hypersonic Flight”,  posted 4 July 2017,  and “Shock Impingement Heating Is Very Dangerous”,  posted 12 June 2017.   

Flameholding in the ramjet wasn’t an issue discussed here,  but if you are interested,  that is discussed in “Ramjet Flameholding”,  posted 3 March 2020.  Something similar applies to scramjet,  and something somewhat different (but still similar) applies to gas turbine can combustors.  That article makes clear why the usual V-gutter and can stabilizers cannot work at speeds past about Mach 3.3,  and what will work.

There is a whole catalog article,  sorted by topic area,  of many of my technical articles posted on this site.  It is “Lists of Some Articles By Topic Area”,  posted 21 October 2021.  There is some duplication from list to list,  where the topic areas overlap.  It does have topic areas for ramjet,  for rocket stuff,  and for high-speed aero-thermo-dynamics and heat transfer.  I do try to keep that article updated and current. 

You can use the navigation tool on the left side of this page to access any of these articles very quickly.  Just jot down the titles and dates.  Then click on the year,  the month,  and finally the title if more than one was posted that month. 

One Final Note:

All of this was done with open sources!  I have seen no classified information for nearly 3 decades now,  since I last held a clearance and had a need-to-know.  But it is quite likely that any “real” SR-72 vehicle will be considered a classified design by the government,  much as the SR-71 was.  About 4 decades ago,  I roughed-out a vehicle somewhat similar to the rocket-ramjet hypersonic craft outlined here,  from only open sources.  (If you really know what you are doing,  open sources are all you need.)  That design concept was confiscated by the FBI and classified by the Pentagon.  They were exploring SR-71 replacements,  even way back then.  If this current one disappears off my site,  then it happened again.

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Update 9-5-2023:  I took some time to rough-out the characteristics of a rocket ramjet airplane design,  and along the way found a major choice to be made.  Since this was not already done in the original article,  see first the intended flight profiles,  given in Figure 4.  The plane could take off from a runway using its small-rocket power,  leading to the big solid booster ignition away from the airport,  or it could be launched zero-length from an inclined ramp,  directly with the big booster.  Climb and acceleration to cruise speed (and to dash speed) is by the ramjet.  Most of the approach to landing is “dead stick” glide,  but with the small liquid rockets available,  to divert,  or to go around for a missed approach.

Figure 4 – Concept Flight Profiles

I literally sized a paper liquid rocket design that uses LOX and the ramjet fuel (thermally-stable kerosene),  but is a very simple pressure-fed system.  The design goal here was simplicity above all else,  so that reliability would be highest.  This kind of thing should be utterly trouble-free,  at the cost of somewhat lower performance.  I did not choose a specific igniter,  but I did indicate that the igniter is linked to the on-off valves for the propellants.  It fires when they flow,  for some small set time interval.

The pressurant for the propellant is dry nitrogen,  commonly available in 2200 psig bottles.  It is likely an airframe-mounted vessel that is filled on the apron from standard gas bottles.  The regulators are set to deliver 700 psig to the propellant tanks,  so that a bit over half of the gas vessel pressure drop is available during the mission.  Assuming the pressure drop through the passages and injector plates is about 200 psi,  a max chamber pressure of 500 psia seems reasonable.  2:1 pressure turndown is easily achieved.   

The 15 degree conical nozzle is designed for expansion to 11.2 psia,  so that the expected separation backpressure at half pressure is still very slightly above sea level atmospheric.  That way,  nozzle flow separation is never a concern!  Expected performance data is shown in Figure 5,  including the small-rocket frontal thrust density value,  based on its exit area.

Figure 5 – Roughing Out a Small Liquid Rocket System Emphasizing Simplicity Above All

I had some old ramjet data predicted for a design with inlet shock-on-lip Mach number 2.5,  using kerosene fuel at equivalence ratio ER = 1.10 for max thrust without excessive waste. These data were for Mach numbers from 2 to 6 at 40,000 feet (40 kft) on a US 1962 standard day.  I curve-fit the variations in thrust and specific impulse vs Mach number at 40 kft,  and recorded the key area ratios and size of the sized engine.  I had no data at sea level or at 85 kft,  but instead just ratioed the thrusts by the ratio of atmospheric pressures.  That is not “right”,  but it is pretty close.  It was easy to divide the installed ramjet thrust by its nozzle exit area,  to get the frontal thrust density for the design study.  I took an educated guess for the leaned-back cruise specific impulse at Mach 3 cruise,  at 85 kft.

I also had some old vehicle drag data based on information from Hoerner’s old “drag bible”.  It includes nose pressure drag,  lateral skin drag,  aerosurface drag,  and base drag effects.  It is uncorrected for the drag area reductions associated with the chin inlet mounting,  and for the propulsion plumes coming from the base.  That makes these drag values a probable over-estimate by a few-to-several percent,  but at least the trend with Mach number is correct.

The drag and ramjet thrust density and specific impulse data are given in Figure 6. 

I had an old IRR booster grain design in my records.  It is for the wrong size,  but the L/D proportion is not too far wrong.  It was easy to compute its thrust per unit exit area,  for a scaleable frontal thrust density F/Ae = 18,350 psf to use in this study.  The detail internal ballistics are not quite right,  but the frontal thrust density is in the ballpark,  regardless.  Some selected data are shown in Figure 7.  

Figure 6 – Rescaling Ramjet Performance From Some Old,  Limited Data

Figure 7 – An Older Grain Design Used To Rescale IRR Booster Performance

The original notion of the flat-bottomed airframe with the bifurcated inlet,  finally sized-out capable of reaching Mach 5,  with the ramjet exit area A6 proportion to the vehicle frontal blockage area Sx reaching A6/Sx = 0.623,  as indicated in Figure 8.  This is less ramjet frontal thrust density than originally desired,  which is what limited the max dash speed to Mach 5.  The data include a preliminary weight statement and some estimated component lengths.  Gross cruise range exceeds 3000 nmi,  at 85 kft. 

Figure 8 – Results for the Flat-Bottomed Airframe With Bifurcated Inlet

The radial distance from vehicle outer mold line to the case or fuel tank OD is a critical variable,  as well.  There must be some such distance,  to isolate thermally the hot lateral skins from the vessels containing fuel or solid propellant.  That would include some high-temperature mineral wool insulation. 

Initially I set this at 6 inches,  and could not exceed Mach 4.  Setting it to 3 inches got me not quite to Mach 5.  Resetting it to 2 inches actually got me to Mach 5.  But that is about all I can realistically squeeze out of this design concept!  The strakes containing the bifurcated inlet and small liquid rocket equipment are just too large,  driven by the required air inlet duct branch sizes. 

That trend illustrates the crucial role frontal thrust density plays in high supersonic,  low hypersonic flight.  There is no getting around this,  it is quite fundamental.

An alternative design concept would not bifurcate the inlet.  Instead it would pass through the fuel tank on its way to the engine,  within an airframe of round cross section.  That makes the tank longer.  There would be no plenum,  but there would need to be a space in which to S-duct the inlet from the bottom up to the central axis.  The wing would have to move up to a mid-wing mount,  likely just a double delta planform.  The small rocket system would have to be mounted in the base of the vertical tail fin,  much like the one used in the NF-104 design.   

I re-ran this alternate configuration,  getting the results shown in Figure 9.  The top dash speed reached Mach 5.5,  reflecting the much larger ramjet frontal thrust density associated with A6/Sx = 0.844.  It packages less fuel mass,  but it also has less cross section area producing drag,  so the drag (and thrust requirement) is lower.  The gross cruise range figure is then just about the same,  as a result. 

If the ramjet propulsion were exposed at the rear,  being all of the aft airframe cross section,  A6/Sx would be a bit higher still (very nearly 1.0),  and the top dash speed would then approach Mach 6,  the same way it did with ASALM-PTV on the one flight test in 1980.  But such exposed propulsion is a much tougher thermal problem to solve for long-duration burns.

Figure 9 – Results for the Round Section Mid-Wing Airframe with Inlet Through Fuel Tank

Bear in mind that all of these are crude estimates,  only within about 10%,  at best.  However,  that is good enough to determine that dash speed nearer Mach 6 will trade off against the far-more severe thermal management problems with exposed propulsion.  Meanwhile,  if Mach 5 dash is “good enough”,  the flat-bottomed low-wing airframe with the bifurcated inlet is quite feasible. 

Or if Mach 5.5 dash is absolutely required,  the better choice is the round airframe with center-duct inlet and a mid-mounted wing.  That one will be somewhat more challenging to detail-design,  and it will have less volume available within its nose.  (You get what you pay for.) 

Also bear in mind that the next most important feasibility item is thermal management.  Those calculations have yet to be explored.  

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Update 9-18-2023:  As it says in the previous update,  the thermal management issues still need exploration,  in order to determine feasibility.  Here is an initial exploratory look. 

First,  look at “typical” lateral skins parallel to the oncoming stream.  These could be on aerosurfaces away from leading edges,  or on fuselages away from nose tips and inlet capture features.  This uses a flat plate convection model that accounts for both compressibility and the effects of viscous dissipation.  Overall setup and results are given in Figure 1.  Conditions at the edge of the boundary layer would not be very far from freestream conditions,  not enough to make a great deal of difference in the film coefficient,  so this analysis just uses free stream.  

Figure 1 – Thermal Analysis of a “Typical” Lateral Skin Panel

In the figure are plotted total temperature Tt,  recovery temperature Trec,  two curves representing equilibrium panel temperatures,  and the recommended max service levels for several possible panel materials. 

The analysis included not only convection to the panel,  but also thermal re-radiation from the panel,  as its primary method of cooling.  This was done for a typical low emissivity,  and a typical high emissivity.  Also included were two paths for minor cooling effects due to conduction into the interior.  One was through a low density mineral wool insulation layer,  occupying nearly the same area as the panel.  The other was through a minor area representing the conduction path through whatever structures attach the skin panel to the rest of the airframe,  presumed metallic,  and of a length comparable to the insulation thickness.

For reference,  a completely uncooled panel would soak out to the recovery temperature.  At speeds under roughly Mach 4,  the panel’s surface thermal emissivity does not make much difference,  since the temperatures are low enough that there is not much thermal re-radiation.  However,  above Mach 4,  the panel emissivity makes a great deal of difference,  with high emissivity (dull black surface) much better.

Note how organic composite panels are no good above (at most) Mach 2,  and that presumes adequate strength at the max temperature of about 200 F,  which presumption is seriously in question.  Aluminum is useless above about Mach 2.5,  which explains very well why most fighters made of it,  have max dash speeds of only just about Mach 2.5.    

A lot of folks think titanium is a high temperature material,  but that is mistaken.  Its max service temperature is 600 to 800 F (800 F shown),  which is good to a most about Mach 3.5-ish,  presuming a highly-emissive surface.  That explains very neatly the max flight speeds of about Mach 3.2 for the SR-71,  which had a dull black finish. 

Above 1500 F capability,  there are only some stainless steels,  and 3 exotic alloys that are not steels.  Of these,  only one has truly high temperature capability at 1800 F plus high tensile strength:  Inconel X-750 (formerly simply known as “Inconel-X”).  Which neatly explains the choice of “Inconel-X” skins on the X-15 rocket plane.  The difference between the low and high emissivity effects is the difference of about a full Mach number for survival of lateral skins at full strength:  Mach 6 if high emissivity,  only Mach 5 if low.  Which in turn neatly explains why the X-15 had a dull black finish.

Thermal analysis of nose tips and leading edge pieces is much harder to approximate with these simple by-hand techniques.  The actual stagnation zone seeing full stagnation heating is quite small.  The large lateral areas also see convection approximatable with the flat plate model,  but at edge of boundary layer conditions crudely approximated as those behind the oblique shock corresponding to a 10 degree flow deflection.  There is thermal re-radiation cooling from both the stagnation zone,  and the lateral surfaces.  There is even conduction cooling through the thickness of the part,  moving toward where it attaches to the rest of the structure. This concept is illustrated in Figure 2.  

Figure 2 – “Typical” Thermal Equilibrium Considerations for a Leading Edge Piece

The results did not validate the equilibrium model.  In all cases attempted,  the convection into the lateral surfaces (both top and bottom together) simply overwhelmed the effects of stagnation heating convection,  and also the numbers for all three of the cooling paths.  The “equilibrium” temperatures to balance the mathematical model were above the oncoming stream total temperature,  which is the maximum soak-out temperature the part could see.  We must therefore conclude that in the absence of active cooling means,  these leading edge parts will rather quickly soak out to the oncoming stream total temperature,  or very near to it. See Figure 3.  

Figure 3 – Leading Edge Piece Results

The Inconel-X material as a leading edge piece may or may not need its full strength to withstand the local wind pressures upon it.  Roughly speaking,  it reaches its max service temperature limit,  or a bit above,  at about Mach 5.  Mach 6 is very near the melting point for the material. This very neatly explains why the X-15A-2 vehicle was coated with a pink silicone rubber ablative and white ceramic paint topcoat,  for high-speed flights past Mach 5.  On flight 188,  with Pete Knight flying it,  it reached Mach 6.7.  There was extensive airframe damage from simple overheat in multiple stagnation regions,  and near-fatal shock-impingement heating underneath the tail section. 

What that really tells us is that for long flights beyond Mach 5,  one must either do high-capability active cooling,  or else use ablative materials for the leading edges and nose tips.  Active cooling will be very heavy,  and very expensive in terms of the power to run it.  Ablatives will require replacement,  at worst after every flight,  or at best after every few flights.  The ablative approach is exactly what was done with the Space Shuttle and its derivative the X-37B,  and also the old X-20 design never built.

Remember:  if you have airbreathing propulsion,  the inlet capture features are even more challenging than leading edges and nose tips,  and the buried ducts simply will require active cooling. 

If you have no thermal management solution,  you do not have a viable design for hypersonic flight!

Famous Quote Is Still True

“Politicians and diapers must be changed often,  and for the same reason” --  Mark Twain

(Everybody knows what these are full of.)

(He is just one of very many,  all full of the same thing as those diapers.)

Two More Fermi Paradox Answers

 Here's a couple more reasons why the aliens do not stop to talk to us.  Answers to the Fermi paradox,  they are.  

Note in the first one that it is "chicken-flavored" but labeled as "ham",  when it is in fact made of vegetable material.  The second one is self-explanatory. 

Alternate Solution to Fermi Paradox?

Here is an alternate solution to the Fermi paradox,  different from the one I posted here 7-16-23.  

For those who don't know,  the paradox asks why,  if there are so many inhabitable planets,  do the aliens not make contact with us?

Trump as Target of DOJ Jan 6 Investigation

Trump "says" he got a letter from Jack Smith about being the target of the Jan 6 investigation,  and he "says" he expects another indictment.  He "says" he got the letter on a Sunday.  He said this on his “Truth Social” network,  which in point of fact is anything but truthful. 

Since nearly everything Trump has ever said has been a lie before,  during,  and after his presidency,  why would you believe him now?  There was and is no US postal delivery on Sunday.  It would either be a lie,  or else a special courier delivery.  Do not believe any of this until Jack Smith himself addresses it,  or until the letter itself is produced in front of the public.   

Myself,  I do expect there to be an indictment of some kind related to the Jan 6 insurrection,  and I do expect it to be felony level.  I also expect to see a felony-level indictment issued from Georgia for election interference there.  Those expected two indictments,  plus the classified documents case and the NYC hush money business fraud case,  make a total of all 4 of the originally-anticipated felony indictments against Trump. If he's in court defending himself against any of these,  he will be too occupied to run for office,  and he (and his lawyers) know that.  Expect delay-delay-delay,  on any grounds at all,  no matter how flimsy.

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Update 7-28-2023:  the classified documents indictment just got some charges added,  and a third defendant added.  Still no indictment yet for the Jan.6 thing.   Or election interference in Georgia. 

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The fact that his polls and his fundraising go up at each indictment verifies my contention that this man is the center of a personality cult-of-belief.  I am talking about a cult-of-personality exactly like that of Adolf Hitler and his Nazis,  exactly like David Koresh and his Branch Davidians,  exactly like Lenin and his Bolsheviks,  etc,  etc,  etc.  Facts do not matter to cult believers.  You cannot argue facts with them,  facts are unimportant.  Only belief matters,  no matter how mistaken it might really be.  We’ve recently already seen this with the Taliban,  Al Qaeda,  ISIS,  and many more.

These cults are quite dangerous.  Many of these cults ended in disaster,  some not yet,  and this one will,  too.  And polls indicate that at least 40% of Republican voters are such cult believers blindly supporting Trump,  no matter how many egregious crimes he is accused of.  That party has clearly been hijacked by an extremist cult.  It is now a clear and present danger to our democracy,  and has been,  since before the 2020 general election.

According to testimony aired by the House Jan 6 committee,  Trump wanted to go to the Capitol and lead the insurrection himself on Jan 6,  but his secret service agents took him instead to the White House,  making him very angry.  His idea was to lead the insurrection into massive violence,  justifying a presidential declaration of martial law.  With enough support from high-ranking cultists in the military leadership,  that martial law gets turned into a military dictatorship with Trump as the dictator,  which is what the Trump personality cult really wants.  That is a key part of their belief system,  long posted on Qanon and other far-right sites.  Go see for yourself.  His advisor General Flynn even said so,  in public. 

In the picture below,  note the partially-obscured Qanon flag lower left.  This was taken at the rally on the Ellipse,  right before the insurrection started,  January 6,  2021. 

And it is this intent to overturn his own government and become a military-supported dictator,  that I really hope the Jack Smith investigation and indictment(s) are all about!  As far as I am concerned,  this insurrection plan leading to martial law and dictatorship,  was treason.  Even more so than the Confederates ever committed,  by waging war on the US to secede. At least they never tried to actually topple the government,  they just tried to get out from under it. 

Update 1 Aug 2023:  one shoe just dropped,  the DOJ indictment for the Jan 6 thing.  There was no sedition charge as best I can tell,  but the counts were all very serious federal felonies.  Trump has been summoned for arraignment Thursday (3 Aug).  That leaves the Georgia thing yet to come. 

Update 3 August 2023:  Mr. Trump has been arraigned today on the DOJ Jan 6 charges.  I downloaded and read the indictment.  It is very detailed,  and includes lots of supporting evidence.  The sooner this goes to trial,  the happier I will be,  and the better off we all will be.  

Update 16 August 2023:  The "fourth shoe finally dropped",  and a few days earlier than "everybody" expected.  Fulton County Georgia just issued an 41-count felony indictment late last night,  against 19 defendants.  13 of those counts are against Donald Trump,  and a couple of those have a mandatory sentence of 5 to 20 years if convicted.  

That makes 4 felony indictments against Trump,  with trials looming.  Two are federal cases,  two are state cases (New York and now Georgia).  He could be a convicted felon by the time of the 2024 election,  perhaps multiply-convicted.  

Second on the list of defendants in the Georgia indictment is Rudy Giuliani.  Included among them are Trump's Chief of Staff Mark Meadows,  several lawyers who helped engineer the multiple attempts to stay in power,  and Jeffrey Clarke,  a rabid supporter that Trump wanted to put in as Attorney General,  stopped only by the mass resignation threat from DOJ.  All 19 defendants have 10 days,  until 25 August,  to surrender to Fulton County authorities for arraignment.  

The Republican Party has no business running a 4-time indicted felon for President,  and anybody with any critical thinking skills knows that!  It may be legal,  but it is not right!  Yet,  they have been doing exactly that in Texas for multiple years now,  with indicted felon Ken Paxton re-elected as the state AG.  (He is out of office now,  under impeachment,  and his trials loom in the courts and the Texas Senate.)

That is what you get after 40-some years (standardized testing began in 1979) of dumbing-down public school education,  with school funding tied to a low-bar standardized test:  no critical thinking skills,  leading to the widespread belief in lies and conspiracy theories,  instead of actual facts.  And "right-wing media" (of multiple kinds) amplified the spread of this crap with their lies and echo-chambers. 

Update 25 August 2023:  Yesterday,  Trump was processed and posted bond for the Georgia indictment.  Unlike the other 3,  they did fingerprints and a mug shot.  They processed him at the jail,  not the courthouse.  One of his co-defendants failed to come up with a bond agreement before surrendering,  and ended up staying in jail.  The mug shot was probably the first time he could not control the circumstances of any publicity about him.  His expression certainly reflects that. 

Update 8-28-2023:  Tentative dates for Mr. Trump's trials have been proposed by the appropriate judges,  except not quite yet in Georgia.  The Georgia prosecutor has asked for October 2023,  but the official arraignments aren't scheduled until Sept 6,  2023,  so that date is not set yet,  even tentatively.  

The federal case for the January 6 insurrection,  and the NY state case for financial fraud are both scheduled for March 2024.  The federal case for the classified documents is scheduled for May 2024.  Spring 2024 is likely going to be a very busy time for Mr. Trump and his lawyers. 

Meanwhile,  Mr. Trump is using his Georgia mug shot to raise money.  He says $7 million so far.  How crass is that?