Monday, October 23, 2023

Only Force Stops Bullies

Lost among all the war news from the middle east is more bullying conducted by the Chinese.  They are actually ramming vessels belonging to the Philippines,  according to news reports.  That risks lives,  and the longer this evil behavior goes on,  the more likely it is that people will die. 



They haven’t rammed our vessels yet,  but apparently feel no compunctions about ramming the vessels of a nation perceived as weaker.  This is classic bullying,  just like what happens among school children.  And only raw,  naked force stops it,  just like among school children.  The difference is that between nations,  the force is necessarily military action.

The worst offenders in recent years have been the Chinese,  the Russians,  the Iranians,  and the North Koreans.  You have to understand who and what these players really are.  All of these are brutal dictatorships masquerading as faux democracies.  Each dictator is the center of his own fearless leader cult.  Facts do not matter,  and all opposition is crushed,  creating the illusion of popular support.

These bullying dictators typically try to intimidate neighbors into letting them do whatever they want,  and if unopposed,  the offensive behavior always escalates.  If never opposed,  the bully eventually loses his fear of starting a war,  and starts one. 

Xi’s Chinese sail and fly too close to the ships and planes of other nations in the ocean regions they want to annex.  This has now escalated into ramming Philippine ships.  The Iranians under the mullahs are seizing ships in the Straits of Hormuz and have now conducted a major attack upon Israel with their proxy Hamas.  Kim Jong Un’s  North Koreans sank a South Korean ship a few years ago,  now they threaten dropping atom bombs on the South,  and on us and Japan.  It is all escalating.

Putin’s Russia first annexed part of Ukraine,  then sent a proxy army to cause death and destruction in eastern Ukraine,  and still being unopposed,  Putin is losing his fear of starting a war with NATO,  and has now invaded Ukraine,  committing all sorts of atrocities along the way.

If these ever-escalating bad behaviors sound familiar,  they should.  Nazi Germany was a dictatorship built around Adolf Hitler as the center of a fearless leader cult.  His offensive behaviors first included annexing the Rhineland,  then the Sudentland,  then all of Czechoslovakia and Austria.  Never opposed,  he lost his fear of war and invaded Poland,  starting World War 2 in Europe.  And we know all too well about what happened as a result,  and all the atrocities he committed.  

Xi’s China has also so far been unopposed with force.  The next step for them is invading Taiwan,  which could well start World War 3 in the Pacific.  Oh,  you heard about that?  Now you understand the seriousness of the pattern here,  because I just told you. 

Diplomacy and sanctions are no opposition for these bullying dictators.  Only raw naked force gets their attention.  Without it,  their escalating misbehavior does not change.  THAT is the lesson of history!  Learn the lesson,  or repeat the history!  Simple as that!

The next time one of these dictator’s ships endangers one of ours on the high seas,  fire a shot across its bow (the signal understood for centuries).  If they don’t adjust,  then sink them,  no if’s,  and’s,  or but’s.  The next time one of their planes endangers one of ours,  fire a stream of tracers across its path.  If they don’t adjust,  shoot them down.  It is that simple,  and that brutal.  There is no other way. 

Global war is now upon you very soon,  if you fail to learn the lesson of history! 

I have written about this problem before,  at greater length than here.  If you want more depth,  go here on http://exrocketman.blogspot.com and see either (or both) the articles “What To Do About Aggressive Behavior At Sea Or In the Air” dated 8 June 2023,  and “Bullying Demands Resistance”,  dated 8 June 2019.  There is a fast navigation tool on the left side of that page.  Click on the year,  then the month,  then the title if more than one article was posted that month.  

You will soon see that I have not changed my opinions about what has been happening,  or what is required to stop it.  The only thing different is the increasing urgency as this escalates into war.

If you end up agreeing with my assessment,  then contact your federal representation,  and tell them what you want done.  If they won’t do it,  then elect somebody else.  Simple as that. 

Sunday, October 22, 2023

On the Israel-Hamas War

This was originally written 10-18-2023:

To understand what is going on,  you have to understand who and what the players are.  We know who the Israelis are.  But many do not understand who and what Hamas (and Hezbollah) really are!  We need to include Hezbollah,  because very soon they might enter this war,  too.

These are terrorist organizations masquerading as religious jihadist groups,  that are really proxy armies for Iran,  and whose role is to cause chaos and death wherever the Iranian government wants it.  When I say “Iran”,  I am talking about their government,  a terrorist dictatorship masquerading as a democracy.  Not the Iranian people.

There are other similar terrorist organizations masquerading as religious jihadist groups out there (Al Qaeda and ISIS come to mind),  but it is Hamas and Hezbollah that belong to the Iranian government who largely funds them,  and certainly gives them training,  weapons,  and marching orders.  This has been going on for some decades now,  it is no secret.

I classify them as extreme terrorist groups,  because that is exactly what they do.  These groups kill anybody and everybody.  In point of fact,  they kill more Muslims than anybody else,  because those are the most numerous potential victims in the countries where they typically operate.  We’ve all seen these vicious crimes going on for many years,  and now Hamas terrorists beheading little babies in this war. 

What else is this but simple murderous terrorism?  It needs to be eliminated from the face of the Earth,  there is no question about that!

The start of this current war has Iran’s fingerprints all over it!  Iran is a sworn enemy of Israel,  but also a sworn enemy of Saudi Arabia (no secret there).  Israel and Saudi Arabia were getting close to a peace agreement that would have effectively put severe restrictions on Iran’s freedom-of-action,  so Iran had to start a war involving the Israelis to put a stop to that.  They did that by commanding Hamas to attack in great force,  which demands an invasion of the Gaza Strip as the response.

Hamas has been attacking Israel from the Gaza Strip for many years.  This usually takes the form of an unguided rocket barrage,  or a few terrorist troops crossing the border,  but rarely both,  and never before in the quantities and coordination seen at the start of this war.  That suggests the planning and supplies came directly from Iran!  Most of the weapons do,  we’ve already seen some stockpiles of them on TV.

As for the explosion at the hospital in southern Gaza,  consider that logically there are 4 possibilities:  (1) Israel did this deliberately,  (2) Israel did this accidentally,  (3) Hamas did this deliberately,  and (4) Hamas did this accidentally.  The point of such an attack,  if deliberate,  would be to stir up anti-Israeli sentiment among not just the Arabs,  but around the world.  Which we have seen! 

We have not seen any evidence as of yet,  regarding which of the 4 possibilities might really be true.  We have seen some suggestions that this was a misfired Hamas rocket (possibility 4). But no evidence has shown up yet in public. 

Instead consider motivations.  Why would Israel want such a thing to happen?  It could only stir up resentment against them.  Hamas,  on the other hand,  would like that resentment against the Israelis.  That suggests possibilities 1 and 2 are rather unlikely,  while possibilities 3 and 4 are rather likely.

So the odds favor that Hamas did this,  deliberate or not.  I cannot rule out deliberate,  because Hamas is the elected government (such as it is) of Gaza.  And yet Hamas has a repeatedly-demonstrated proclivity to use as human shields the very people it supposedly governs! 

Israel did not expect an attack on this scale.  That much is clear,  because it was absolutely not prepared ahead-of-time to invade.  In the past,  an air raid or two was sufficient response.  But not this time! 

I suggest that they invade,  kill all the Hamas fighters they can find,  and corral the civilians.  The women-with-children and old men can pretty much be presumed innocent civilians.  Younger men in the company of women-with-children are likely civilians,  too.  But young single men,  and single-women-without-children (a rarity in typical Arab cultures),  need close scrutiny! 

Why?  Because you do not want to kill innocent civilians,  but you do not want to take any Hamas prisoners!  Why waste the resources to keep alive that which you so sincerely want dead?  And if Hezbollah comes across the border from Lebanon,  don’t take any of them prisoners,  either!  This scourge needs to be wiped clean from the face of the Earth.

Update 10-22-2023:

4 days after this was originally written,  we have still seen no evidence in public about who really blew up that hospital in southern Gaza.  The motivations still point to Hamas doing it either deliberately or accidentally,  and some reports finger a subsidiary Hamas terrorist group as the perpetrators.

On the other hand,  terrorists are now firing rockets at Israel from the West Bank,  and Syria,  if reports are accurate.  Everyone fears a widening war.  It definitely appears that Hamas and its sympathizers are the ones widening it.

The recommended solution is still the same:  wipe these evil people from the face of the Earth.  All of them.  But,  while doing it,  try not to kill the innocent civilians!

Update 11-2-2023:

Israeli forces are now in the Gaza strip,  surrounding Gaza city,  and hitting what they claim are Hamas targets with bombing,  while causing casualties among the civilians in and around these targets.  Meanwhile Hamas is still firing rockets into Israel,  and so is Hezbollah in Lebanon.  Plus,  other Iranian terrorist proxies,  are firing directly at American forces in Iraq and Syria,  and killing some of them.  The war has already widened,  whether you like it,  or not!  There are two fundamental points to make about this,  which so far are not being addressed properly in the press reporting.

Point 1:  the ultimate culprit here is the terrorist “government” of Iran.  All these violent groups are their proxy terrorist armies.  The Iranian government funds them,  supplies them,  and gives them strategic direction.  So far,  the government of Iran has not been held accountable for any of this destruction,  despite their being fundamentally at fault for all of it!  That is a very serious foreign policy mistake being made by all the western governments,  collectively.  And this evil crap will not stop until the terrorist government of Iran is deposed!  

That government is terrorist dictatorship that masquerades as a religious group to justify itself to the people it rules,  and it operates a sham democracy where the ruling “mullahs” can override anything any elected body decides.  They ruthlessly oppress and kill any of their own citizens who dare protest or defy anything. This has been going on since they took over in 1979 after the Shah fled. 

You’d think the western governments would have done something effective about this before now,  but they have not.

Point 2:  the calls for a cease fire are well-meaning,  but are strategically very incorrect.  The reporting on this is based upon the massive death and destruction of civilians in Gaza that is right in front of everyone,  and not at all on what underlies that tragedy,  and which overwhelms that tragedy in importance. 

That mistake on the part of most of the reporters is understandable,  since reporting on what is right in front of them,  is usually exactly what they are supposed to do.  But,  focusing on the appearance is not what must be done by those who actually have to fight the war!  The few reporters I have seen who actually interview a real war-fighter about this issue,  do not seem to understand,  or even listen to,  the answers given by these war-fighters,  since these answers disagree with the appearances.  And that is a very serious mistake being made by the news media.  Dig deeper,  please!

Unlike previous Israeli responses to Hamas attacks,  this time the Israelis have made their top objective the ultimate destruction of Hamas,  despite the human shield behind which Hamas is hiding.  Why should it surprise anyone that there are civilian casualties,  when to win,  the Israelis must go right through that human shield to get at Hamas?  If they do not do this,  they lose,  and so do we all,  since the world must be rid of these terrorist groups!  The real war crime here is not the Israelis going through that human shield,  it is Hamas using a human shield in the first place! 

And I do not see that crucial fact being adequately reported.

Update 11-6-2023:  For those who cannot see past the civilian casualties in Gaza,  consider this.  Israel telegraphed the "punch" that was coming,  to give the civilians who constituted the human shield time to get out of the northern Gaza strip.  Very few did,  most did not.  Some might have since changed their minds,  worthy of a short pause to depart,  but only very short!  The Hamas terrorists simply cannot be allowed time to regroup. 

Update 11-30-2023:

Please see the column by Jonah Goldberg and titled “China deflects world’s attention to Israel”,  which was published this date in the Waco Tribune-Herald.  He hits the nail right on the head regarding the strategy China has been using to deflect away criticisms for the many evils it does. 

The misplaced support so many very young people show for the terrorist “government” in Gaza,  called Hamas,  traces directly to their use of the Tik Tok social media platform,  where anti-Jewish disinformation (among other things) gets spread by the Chinese government.  China is not the only one doing this,  but right now,  they are among the worst.

Thank you,  Jonah Goldberg,  for pointing this danger out in public.


Wednesday, October 18, 2023

Jim Jordan, Speaker of the House? NO!!!

I’m sorry,  but the record established by Jim Jordan as a representative from Ohio is much more an agent of chaos,  than anything one might construe as doing the people’s business in Congress.  He is an ardent Trump supporter,  a 2020 election denier,  and there is at least some reason to believe he should also be under indictment,  regarding the Jan 6,  2021,  insurrection at the Capitol.

This is absolutely NOT the man you want running the agenda for the House of Representatives,  who is also third in line to Presidency!

What you are seeing here is the Trump cult loud minority trying to find a way to rig things so that they can pull the levers of power in Washington,  despite not having the votes to get their way properly.  Failing that,  I predict (warn!!!) that they will continue to cause paralysis in the House,  causing the government to be dysfunctional,  and drive it into default on its debt.  This is deliberate sabotage!

The Trump cultists are hoping there will be an outcry from the people to “do something” if this chaos persists long enough and causes enough destruction.  Their hope is to topple our democracy and install a dictatorship in its place,  something espoused in public by former Trump advisor retired General Flynn (many have forgotten that,  but I did not!),  with Trump (or a younger Trump wannabee like Desantis) as dictator.

This is absolutely NOT the Republican party that I once knew and respected!  There are now no longer enough traditional Republicans to resist the Trump cultists.  This Trump cult group is now a direct,  clear,  and present danger to our republic.   Personally,  I see little difference between them,  and what happened in 1933 Germany with the Nazi takeover from within.  The Nazis were a Hitler cult.

Do not be fooled by what they say.  Look instead at what they actually do!  Which speaks volumes! 

My sincere recommendation:  vote these people out,  as fast and as decisively as you can!  It does not matter who the opponent is,  or what his party affiliation is.  You cannot do any worse than what you have right now!  You might do better!

You CANNOT say that I did not warn you!


Update 10-20-2023:  Jordan lost a 3rd vote (with fewer votes each time) and has been deleted as a GOP candidate for Speaker,  according to news reports.  Whew,  that's a relief!  Now we have to see who they might nominate instead.  The risk would be another Trump-cult agent of chaos.  

Update 10-23-2023:  The House GOP is now considering 9 candidates from which to select a nominee to be speaker.  I checked the news stories to find out who they are and a little bit about them.  7 of the 9 voted to decertify the 2020 election results after the Jan 6 2021 insurrection took place!  Of the other 2,  one supported the lawsuit in Texas to overturn the 2020 election results (Emmer),  and the other was a Jim Jordan supporter (Scott),  right up until he dropped out. 

As far as I am concerned,  the ties all 9 candidates have to the Trump-cult attempt to overturn the election and stop the peaceful transfer of power,   totally disqualifies each and every one of them as a credible candidate to be Speaker of the House!  They only have credibility with the Trump cultists.  I do not see in any of them,  a candidate that even might possibly prioritize actually doing the people’s business,  above their extremist political agenda.

My conclusion from all that is this:  any non-Trump-cult Republicans that still might remain in the House need to get with the House Democrats and do the suggested bipartisan deal.  I think we will soon see if any such still exist in the House.  If not,  get ready for long-lasting paralysis of Congress,  and a debt payment default that hurts us all,  plus a total calamity in our foreign policy during a time of multiple crises plus a war that seriously threatens to widen and engulf us all. 

That last aids and comforts our enemies,  and that is in the Constitutional definition of treason! 

Merrick Garland and the DOJ:  are you listening?  Did you hear what I just said? 

You need to do something about Trump-cult treason,  and you need to do it quickly!!!  You will have millions of eyewitnesses to these acts of treason,  witnesses who will have seen this on live TV.  One or more eyewitnesses to the act is a Constitutional requirement,  too.  And it will be satisfied.

Update 10-25-2023:  They selected Emmer as their candidate,  but he dropped out only hours afterward,  when both Trump and the Trump-cult extremists denounced him (as not being enough of a Trump supporter).  Now they have selected Mike Johnson of Louisiana,  one of the 7 who voted to decertify the election,  and a well-known ardent Trump supporter and Jordan supporter.  We will see where that goes!  

The choice seems to be to either give control of the House to the Trump-cult extremists (leading directly to the end of our democracy),  or simply continue the ongoing chaos and paralysis (leading perhaps to the end of our democracy).  Which is EXACTLY what I warned you readers about above! 

Late-breaking same day:  the non-Trump-cult Republicans gave up and let the House elect Mike Johnson of Louisiana as its Speaker.  That gives total control of 1 house of Congress to a bunch of radical extremists that are bound and determined to destroy our democracy and replace it with a dictatorship.  Expect nothing useful from Congress,  and thus our entire government,  from this point! 

Expect to see some non-Trump-cult Republicans assassinated between now and the 2024 election.  It's called a "purge".  We've seen this before,  with the Fascists,  the Nazis,  and the Bolsheviks,  as well as the Maoists.  

Expect also that they will attempt to install Trump as dictator,  via the 2024 election,  whether he is a convicted felon or not,  and whether he is behind bars or not!  

Better arm yourselves!  It is only a matter of time before these extremists come for you,  too!  

Friday, October 6, 2023

Two Funnies

Here are two funnies that my wife found on Facebook,  presented essentially without comment.  Enjoy!  (Youngsters might need to be reminded that the old man in the second picture is Dick Van Dyke,  who is 97 years old now.)





Sunday, October 1, 2023

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. 

 

Friday, September 1, 2023

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 3rd or 4th 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!