Get Acquainted Info: High Speed Vehicles

This article is for people who know little about high speed flight vehicles.  It gets across some key concepts about:

#1. frontal thrust density and top speed capabilities, 

#2. how the same inlet components are used quite differently in ramjet versus turbojet installations, 

#3. why achieving combined cycle engine designs can be so difficult,  and

#4.  how heat protection is the true driving issue for high-supersonic and hypersonic flight.

There are other articles posted here and available elsewhere,  that go into considerably more detail about these topics.  But this one tries to illustrate the basics,  to get started.

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Get Acquainted Info: High Speed Vehicles  

There are many concepts to understand about high-speed flight.  Frontal thrust density is a very important issue.  And,  there is no “magic” to waveriders.  See these 2 illustrations:

 

The number of propulsion nozzles at the back of a vehicle also seriously affects frontal thrust density.  This applies to both rockets and airbreathers (of any type).  See:

The over-simplified behavior of inlets on a supersonic ramjet vehicle is shown: 

 Bear in mind that pitot-normal shock inlets,  which have no shock-on-lip behavior,  actually have 6 behaviors to understand,  and external-compression feature-fitted inlets have 9 different behaviors to understand.   You do not initially need to understand all that detail!

But,  it is the basic as-illustrated inlet behavior above,  that drives supersonic ramjet performance.  Ramjet takeover from the booster needs to occur no lower than shock-on-lip speed.  The lower the shock-on-lip speed is,  the smaller the booster can be,  leaving more room for ramjet fuel and the nonpropulsive items.  Considerably higher speed is still efficient:

For supersonic flight,  gas turbine engine installations use the same supersonic inlet components,  but they use them quite differently!  These are usually low-bypass “turbojets”,  and they are usually fitted with afterburners. 

Unlike the ramjet,  which when operating properly,  accepts a fixed scooped air massflow from the inlet,  the turbojet demands a variable air massflow corresponding to its rotor speed(s),  determined in turn by the throttle control setting.  The turbojet inlet has to vary the captured air massflow to match engine demand,  which inherently requires subcritical inlet operation,  with variable-but-significant amounts of spillage around the cowl lip. 

The dominant pressure-rise feature in a turbojet installation is the compressor,  not the inlet!  (The only pressure rise feature in a ramjet is the inlet.)  See:

High speed flight involves lots of aero-heating.  Adjacent and captured air temperatures are high.  As you go hypersonic,  shock impingements multiply heating rates substantially.  See:

Shown just below are the heating rates to,  from,  and within,  any given piece of exposed material.  There is steady-state equilibrium (applicable to hypersonic cruise),  and there is transient behavior (applicable to atmospheric entry),  to worry about. 

Radiation occurs only when there is a view of something hot or cold from the affected surface.  The emissivity “e” can make radiative transfer either inefficient if low,  or efficient if high.  It varies between 0 and 1.  (The sigma represents Boltzmann’s constant.)

For convective transfer,  heating rates can be to,  or from,  the surface.  The “film coefficient” h is larger near stagnation zones,  and smaller on lateral skins.  The values of h all decrease as the air thins drastically at very high altitudes. 

Thermal conduction can be to,  from,  or within the piece.  The conduction within acts to set the temperature distribution of the piece from one end to the other.  The other two determine how much heat enters or leaves the piece.  See:

It should now be obvious that the main enabling factor for high supersonic,  or especially hypersonic,  flight is really thermal management,  more so even than propulsion.

And “scramjet propulsion”,  whether combined-cycle or not,   does not make your job any easier,  because it is geometrically incompatible with ramjet and gas turbine,  including even most of the inlet.  In fact,  combining any of these propulsive cycles,  including rocket,  is difficult at best,  because of the severe geometric incompatibilities,  not to mention the speed-of-application differences.  See:

The two that do combine well are rocket and ramjet,  for the “integral rocket ramjet” (IRR):

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Air Launch to Low Earth Orbit

There is a conundrum associated with launching to low Earth orbit from an airplane.  The illustration tries to sum up the various parts of it.  That is not to say that it cannot be done,  because it already has.  But,  it may,  or may not,  be an attractive way to do the mission.

The first part of this conundrum is the low speed of the launch aircraft (which for the Pegasus system is a wide-body subsonic airliner).  That forces the dropped rocket vehicle to be at least two-stage,  despite the advantage of the low stratospheric launch altitude.  As it says in the illustration,  speed at drop is the biggest influence on the rocket vehicle design,  and altitude the least,  although both are beneficial.  Mach 0.85 at 45,000 feet is but 822 feet/sec (0.25 km/s).  The drag loss of the rocket vehicle is (at least theoretically) less,  because it starts in thinner air up high.

The second part of this conundrum is not so obvious:  the level path angle of the carrier airplane at the drop point.   A low-loss non-lifting ballistic trajectory begun at stratospheric altitude would need a path angle at ignition on the order of 45 degrees,  maybe even a little more.  So,  either the carrier airplane,  or the rocket vehicle,  has to pull up rather sharply,  to reach that path angle from level flight.  One or the other must do this!

The usual airplane flying high in the stratosphere is at or near its “service ceiling”,  where there is barely enough wing lift being produced at an efficient angle of attack,  to hold up the weight,  and essentially all the thrust the airbreathing engines can make is just overcoming drag at the flight speed!  The airplane can neither accelerate path-wise,  nor can it climb!  That is the definition of “service ceiling”,  and for most planes,  it falls in the 45,000-55,000 foot altitude range,  at high subsonic speeds.  There have been exceptions:  the U-2 variants and the SR-71 variants could fly higher,  being very specialized designs.

Left unaddressed in the airplane,  the service ceiling problem puts the sharp pull-up task squarely upon the rocket vehicle to be dropped.  There are only two choices:  put wings on the rocket vehicle,  or fly it at very large angles of attack,  so that the cross-path vector component of its thrust is effectively a large lift force. 

Pegasus used large wings,  on the first stage of a two-stage rocket vehicle.  Those add both weight and drag,  especially drag-due-to-lift at the large lift coefficient needed to pull up sharply.  That pretty-well eats up the advantage gained by launching the rocket at elevated altitude in the thin air.  The wings are bigger than you would want,  precisely because of that thin air!  And that problem is why there have just not been that many Pegasus launches.

Leaving the wings off of the rocket vehicle forces you to pitch it up to very large angles of attack,  in the 45-75-degree range,  to get enough of a cross-path vector component of the rocket thrust,  to serve as the necessary lift force for a sharp pull-up maneuver.  That reduces the path-wise vector component of thrust,  while at the same time greatly increasing vehicle drag.  So,  you accelerate slowly( if at all) in rocket thrust during the pull-up maneuver,  using up a great deal of rocket propellant that adds nothing to your speed.  That also eats up any advantage of launching in the thin air,  way up high!

The only other feasible alternative is to add another large source of thrust to the launch airplane,  so that it can execute the pull-up maneuver into a zoom climb,  without stalling and falling out of the sky,  out-of-control.  Generally speaking,  you would add a source of thrust immune to the service ceiling effect,  and that is rocket thrust!  Your launch airplane would have to be modified for mixed (parallel-burn) rocket and gas turbine propulsion,  somewhat similar to the NF-104 and some of the early high-speed X-planes. 

So far,  no air-launch carrier plane has had this design approach,  but it certainly would be possible!  And it would take care of the high path angle requirement that is second only to speed at launch in importance,  while keeping the wings on the airplane where they belong,  and not on the rocket vehicle!

That leaves speed at launch,  the most important variable affecting the rocket vehicle design.  There are (or have been) very few supersonic aircraft designs that are also large enough to serve as a drop aircraft for a rocket vehicle of any significant size.  Those would include the B-58 Hustler (long-retired,  and none are left),  the SR-71 (also retired,  but very expensive to operate indeed),  and the B-1B bomber (currently in service as a military strategic bomber).  

The modifications to include rocket propulsion to the SR-71 likely would not fit within its very-critical shape.  The M-21 variant that launched the D-21 drone was limited in payload size,  to the size of that drone (not very large).  A rocket might be added in the tail cone of a B-1B,  but its payload would be limited to that which would fit in its bomb bay.  That B-1B option would reach a low supersonic launch speed at the high path angle needed,  with a rather-dangerous zoom climb and recovery after drop.

That brings up the danger of supersonic store separation.  There is a very good reason that most military aircraft,  even those capable of supersonic flight,  are limited to high-subsonic weapon release speeds.  That is because the inherent wobbles of a released store will include pitch-up,  thus developing lift.  At high enough speeds,  that lift generated by the wobbling store will exceed its weight,  and it can easily fly up and collide with the drop aircraft,  before the store’s drag can pull it behind. 

It cost a destroyed airplane and the life of one of the two crew,  to learn this lesson with the M-21 trying to launch a D-21 drone (without a booster) at just about Mach 3.   That is why the drone was re-fitted with a big booster,  and launched subsonically from B-52’s instead.  It’s not that supersonic store separation cannot be done (because that booster separated at Mach 3 from the D-21).  But successful supersonic store separation is very difficult to achieve,  and the risks of doing it are inherently very high.

So how fast a drop speed can be obtained?  That depends upon the gas turbine engines powering the launch aircraft.  Those are seriously limited by the high air temperatures associated with capturing supersonic air.  Most are limited to about Mach 2.5.  There are a very few that went faster:  those powering the XB-70 at Mach 3,  those powering the SR-71 variants at Mach 3.2,  and the 500 hour short-life,  replace-don’t-overhaul engines in the Mig-25 at Mach 3.5.  So,  to have a wide range of possible engines available for new designs,  it looks like Mach 2.5 at drop is “about it” with gas turbine.  Maybe Mach 3.

So,  the answer would seem to be a mixed-propulsion airplane with gas turbine propulsion,  augmented by parallel-burn rocket propulsion,  added to enable the zoom-climb by a sharp pull-up maneuver.  This would be at high altitude near 45,000 feet,  for the drop of the rocket vehicle.  To do this successfully,  the very difficult supersonic store separation problem must be very carefully addressed!  Both aircraft and crews are at serious risk.

Mach 2.5 at that altitude would be 2419 feet/second (0.737 km/s),  less than 10% of low circular orbit speed,  so one is still looking at a two-stage rocket vehicle to reach orbit.  Deliverable payload would be limited in size by the size of the drop aircraft,  since that in turn limits the size of the rocket vehicle it can drop.

In a word,  this has already been done with subsonic carrier aircraft,  although it has proven no more attractive than vertical rocket launch,  at best.  The supersonic release has yet to be tried,  and will prove both difficult and dangerous,  although the improvement in attractiveness may be worth that effort and risk.  No one yet knows. 

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Update 8-2-2025:  Please do not misunderstand,  air launch to LEO is possible and in fact has been done more than once!  It's just not easy,  because many of the problems associated with it are hard.  They are hard enough that the attractiveness of this approach is still in question,  relative to the tried-and-true vertical rocket launch. 

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Update 8-4-2025:  For an air launch-to-orbit carrier aircraft,  the gas turbine speed limitation could be gotten around by instead using ramjet propulsion,  which for a true high speed design might reach speeds between Mach 3 and Mach 4 in the stratosphere,  limited mainly by atmospheric drag of something inherently not a “clean” missile shape. 

One would still need the rocket component of a mixed-propulsion parallel-burn scheme to achieve the necessary climb angle at launch of the rocket payload,  and one would still need to solve the dangerous supersonic store separation problem.  But this would get the highest possible speed at launch,  at the right launch angle,  and at an altitude high enough to be beneficial.

The downside is that ramjet has no static thrust!  You will need some sort of booster to reach ramjet takeover speed,  and the necessary high-speed ramjet design is going to have a takeover speed in the Mach 1.8 to 2.5 range.   Given that rocket is needed to reach the high climb angle at launch,  that same rocket is likely the propulsion needed to reach takeover speed. 

Speeds will be limited by the percentage of frontal blockage area occupied by each of the two propulsion systems.  The airbreather is fundamentally lower in frontal thrust density than is the rocket,  so it needs to occupy the larger fraction of the total frontal blockage area. 

Being a lower percentage of vehicle frontal blockage area than the ~100% of a “clean” missile design,  the max possible speed capability of a ramjet (near Mach 6) cannot be reached with this kind of a vehicle.  But the ramjet weighs far less than any possible turbojet propulsion!  That makes a smallish rocket system feasible for getting off the ground with wings,  and reaching Mach 1.8 to 2.5 takeover speed at relatively low altitude. 

From there,  you climb in ramjet to high altitude at speeds near Mach 2.5,  and pull over level to accelerate to top speed in the thin air.  Fire up the rocket to climb steeply for the supersonic store separation,  then shut down the rocket and throttle-back the ramjet to execute a zoom climb and descent back into air dense enough to support controlled flight.  Cruise back in ramjet,  then glide to a landing with the rocket in reserve for go-around capability.

The real trade-off here,  yet to be evaluated,  is whether to integrate the two propulsion systems into some sort of combined-cycle rocket-ramjet,  or leave them as separate systems to be operated entirely separately.  Combined-cycle usually seriously compromises the performance of both components,  while parallel-burn does not,  instead running into the fraction-of-frontal area problem. 

And there is also the problem of there being “no such thing as cooling air” above about Mach 3 to 3.5 in the stratosphere.  Vehicle designs flying faster than that will need one-shot ablatives for their ramjet combustor and nozzle heat protection.  Which means you must swap-out the entire combustor and nozzle unit after every flight!  Given that eventuality,  you could do a solid propellant integral booster in the combustor and nozzle unit,  like a great big JATO motor,  for the initial takeoff.  That reduces the volume (and cross-sectional area) of the on-board propellants for the liquid rockets.  

None of these issues have been resolved for an air launch-to-orbit application. 

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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!