Monday, October 23, 2017

Reverse-Engineering the ITS/Second Stage of the Spacex BFR/ITS System

The “giant Mars rocket” proposed by Spacex has reduced in size somewhat since its first reveal at the Guadalajara meeting.  The term “BFR” is now beginning to refer to the first stage of the two-stage system,  which flies back and lands for reuse.  The term “ITS” more properly applies to the reusable second stage,  which apparently has two forms.  Those are the cargo/passenger craft that goes to destination after refilling on-orbit,  and a flyback tanker that provides the refill propellants on-orbit. 

Data published by Spacex at the latest meeting indicate a cargo/passenger vehicle that summarizes as given in Figure 1.  Grossly,  this is a 9 m diameter vehicle about 48 m long,  with a dry mass of about 85 metric tons,  and propellant tankage that holds about 240 metric tons of liquid methane and 860 metric tons of liquid oxygen.  Stated payload weights are 150 metric tons on ascent (and presumably to destination), and “typically” 50 metric tons on return.  Characteristics of the tanker form are less clear,  but it seemingly has a lighter dry weight of about 50 metric tons.


Figure 1 --  Estimated Characteristics of ITS Per 2017 Revelations

These two versions presumably share the same ascent propellant tankage and engine cluster.  Those engines include both sea level and vacuum expansion forms of the same Raptor engine,  with a nominal chamber pressure of 250 bar,  and deeply-throttleable to 20% thrust.  The cluster has 4 vacuum engines of 1900 kN thrust each at 375 sec vacuum specific impulse,  and two sea level engines of 1700 kN thrust each,  and specific impulses of 356 sec in vacuum and 330 sec at sea level.  Exit diameters are 1.3 m and 2.4 m for the sea level and vacuum forms,  respectively.  (I did not correct sea level thrust to vacuum.)

I am presuming here that second stage operation during launches to Earth orbit takes place in vacuum,  so I use the vacuum thrust data for both versions of the engine.  Each type’s thrust is therefore associated with a propellant flow rate via its specific impulse.  Summing these gets a total full thrust and a total propellant flow,  and thus an effective “average” vacuum specific impulse with all six engines running,  for an effective exhaust velocity of about 3.5762 km/sec.  That calculation summarizes as follows,  where effective cluster specific impulse is total thrust divided by total flow rate (Figure 2).

Now,  on the assumption that both forms of the vehicle have the same ascent propellant tanks and quantities (totaling 1100 metric tons of propellants),  the following weight statement and delta-vee table applies (Figure 3).  For the tanker,  the first-listed payload of 150 tons is assumed from the cargo passenger version.  The second is back-calculated from holding tanker delta-vee capability to be the same as the heavier ascent form of the cargo/passenger vehicle.   

To do that,  one finds the required mass ratio from the delta-vee,  then solves the mass ratio build-up for the unknown payload:

                Wpay = [Wp – (MR – 1)Wdry] / (MR – 1)





What I find very interesting here is that Spacex seems to have said it takes 6 tankers to fully refill an ITS on orbit for its voyage to destination.  If you look at the heavier tanker that gets the same 6.2 km/sec delta-vee as the fully-loaded cargo/passenger form,  then 1100 metric tons of propellant divided by an estimated 184.7 metric tons per tanker equals 5.956 (almost exactly 6) tankers required.  So the tanker at 50 tons dry weight seems to hold 1100 tons of ascent propellant,  and just about 185 more tons of propellant-as-payload with which to refill a cargo/passenger ITS on orbit.  It would appear this estimate is then just about right.  It does presume all 6 engines running all of the time.

Using BFR/ITR at Mars

For a trip to Mars from low Earth orbit,  the departure delta-vee for a Hohmann minimum-energy orbit to Mars is around 3.71 km/sec at average orbital conditions.  For a direct entry without stopping in Mars orbit,  you let the planet hit you from behind,  as the planet’s orbital velocity is faster than the transfer orbit’s aphelion speed.  Velocity at entry interface will fall in the 6 km/sec range,  and aerodynamic drag kills most of that to about 0.7 km/s coming out of hypersonics fairly deep in the Martian atmosphere.  Double or triple that for the landing burn:  about 1.5-to-2 km/sec delta-vee requirement. 

That’s crudely 5.21 to 5.71 km/sec delta-vee required to make a direct landing on Mars,  with just almost 6.2 km/sec available.  The difference can be used to fly a somewhat higher-energy transfer orbit,  for a shorter flight time than 8 months.  Faster is possible if payload is reduced.

To return,  the ITS is refilled with in-situ propellant production on Mars.  It will need around 6 km/sec delta-vee capability to launch and escape directly,  with enough energy to achieve the return transfer orbit.  We assume a direct entry at Earth,  which means in turn we run into the planet from behind,  since vehicle perihelion velocity is higher than Earth’s orbital velocity. 

It will be a very demanding entry interface speed (well above 11 km/sec):  this is what stresses the heat shield,  not entry at Mars.  But,  the vehicle will come out of hypersonics at about the same 0.7 km/sec moderately high in the atmosphere.  It will need at least 3 times that as the landing burn delta vee requirement,  because the altitude is higher,  and the gravity is stronger.  Call it 2 km/sec as a “nice round number” to assume.

The total delta-vee requirement to ascend from Mar’s surface and achieve a direct transfer orbit and a powered landing on Earth is therefore in the neighborhood of 8 km/sec.  That is just about what the ITS cargo/passenger version seems capable of,  if restricted to about 50 metric tons return payload.  Again,  that particular payload correspondence lends confidence to these otherwise-guessed numbers. 

It also points out how critical in-situ propellant production will be for using this vehicle on Mars.  Unless this vehicle is refilled locally with the full 1100 metric ton propellant load,  it is stranded there!  Each launch from Mars requires 240 metric tons of locally-produced liquid methane,  and 860 metric tons of locally-produced liquid oxygen.  Launch opportunities are 26 months apart.  Required production rates are thus 9.23 tons/month methane,  and 33.08 tons/month oxygen,  at a bare minimum,  per launch.

BFR/ITS For the Moon

Some have pointed out that this vehicle could also visit the moon.  To leave Earth orbit for the moon,  the delta-vee requirement about 3.29 km/sec.  The delta-vee to arrive into low lunar orbit is just about 0.8 km/sec,  or to land direct,  about 2.5 km/sec.  Those one-way totals are 4.09 km/sec to lunar orbit,  and 5.79 km/sec to land direct (remarkably close to the Mars value at min energy transfer). 

To return by a direct departure from the lunar surface requires about 2.5 km/s,  or from orbit about 0.8 km/sec.  Landing at Earth is largely by aerodynamic braking,  but requires about a 2 km/sec landing burn.  Therefore,  total delta-vee requirements to return are 4.5 km/sec from the surface,  or 2.8 km/sec from lunar orbit.

One could conclude that the ITS could ferry cargo to lunar orbit and return entirely unrefilled,  a trip requiring total 6.89 km/sec delta-vee capability.  This is not available at 150 metric tons of payload,  but it is available at something a little larger than 50 tons.  I get about 102 metric tons of payload. 

The requirements to land and return entirely unrefilled would be 10.29 km/sec,  which is out-of-reach even at only 50 tons payload.  To use the ITS on the lunar surface will require propellant production on the moon,  although likely at somewhat lower rates and quantities than at Mars.

Guessing Reusable Performance of BFR

A related point:  if we presume the fully-loaded ITS uses essentially all of its 1100 tons of propellant achieving low Earth orbit,  we can back-estimate the delta-vee that is actually available from its BFR first stage,  even allowing for flyback.  Earth orbit velocity is just about 8.0 km/sec.  Allowing 5-10% gravity and drag losses for a vertical ballistic trajectory,  the min total delta vee is about 8.4-8.8 km/sec.  About 6.1 of that is from the ITS second stage.  The first stage need only supply 2.3-2.7 km/sec,  which means the staging velocity is just exoatmospheric at around 2.5 km/sec.  It should easily be capable of ~5 km/sec,  so the difference is for flyback all the way to launch site,  and propulsive landing.

Suborbital Intercontinental Travel

Finally,  there has been some excited talk about using the BFR/ITS for suborbital high speed transportation across intercontinental ranges here on Earth.  That is a ballistic requirement similar to that of an ICBM.  The burnout velocity of the typical ICBM is around 6.7 km/s.  Allowing 5-10% margin for gravity and drag losses,  the delta-vee necessary to fly intercontinentally is 7 to 7.3 km/sec,  plus for the ITS,  about 2 km/sec for the landing burn.  Total is thus 9 to 9.3 km/sec delta-vee. 


This is way beyond the delta-vee capability of the ITS stage alone,  notwithstanding the fact that 4 of its 6 engines will not operate at sea level,  and even if they did,  total 6-engine thrust of the ITS stage (1100 kN) is less than its weight (1300 kN or more).  But this delta-vee is within reach of the two-stage BFR/ITS combination (6.2 to 7.9 km/sec ITS and ~2.5 km/sec BFR for 8.7 to 10.4 km/sec),  and likely with a little less payload than the 150 tons typical to Mars.  Maybe something in the vicinity of 100 tons. 

Final Remarks

These estimates are rough.  I did not correct sea level thrust to vacuum for one thing,  my delta vee requirements are approximate for another,  and I did not explore the effects of using only the vacuum engines for higher specific impulse out in space.  

Even so,  these results are very intriguing.  These calculations were made pencil-and-paper with a calculator.  Nothing sophisticated.  

Monday, October 16, 2017

ASUS Hardware, Windows Software? Never Again!

My ASUS X553M laptop with factory Windows 10 operating system is a low-quality,  unreliable piece of crap!  So is its operating system!  (Its predecessor was a Toshiba laptop running Windows 8/8.1.  The hardware failed at age 2:  the display hinges broke.  I hated Windows 8 from the moment I saw it.)

This ASUS machine/Windows software combination has several very serious issues that Best Buy’s Geek Squad cannot,  or will not,  help me with.  All these major issues are fatal,  as far as my estimate of quality is concerned.  That list follows below.

I would appreciate comments from readers as to what machines or operating systems might possibly be acceptable (since this machine and operating system are so very clearly not). 

I need to do word processing,  powerpoint-type slides,  spreadsheet work with plotting,  and a shell within which to run old-time DOS software.  I need something that can use wi-fi to access the internet and email.  I want a battery pack that I can pull,  to force a restart,  when all else fails.

ASUS X553M / Windows 10 Fatal Issues List:

#1. The screen dims and flashes or flickers,  when not plugged into the AC power supply.  This renders the machine unusable,  in spite of the battery being charged.  When the issue first started,  it did this with about 50% battery charge remaining,  as indicated on the display.  This rapidly got worse over a period of only months,  accelerated to starting the flicker at 90% battery indicated.  Now it will not run without flashing even at 100% indicated charge state.  Nothing in the Windows settings affects this. 

#2. The machine turns off its wi-fi device spontaneously,  without warning,  and for no perceptible reason.  This happens erratically and unpredictably.  The frequency with which it occurs is increasing as time goes by.  More of the time,  It still sees the wi-fi network,  and will reconnect if you command it.  But for a significant portion of the time,  it does not see the wi-fi network,  and so cannot be commanded to reconnect.  The only recourse in that case is reboot. 

#3. This machine on occasion locks up without warning,  rendering the keyboard and the mouse totally inoperative.  The only way to deal with this is a reboot.  It always loses all data up to the last save.

#4.  I cannot trust the reboot to be effective,  unless I unplug the AC power,  and either select full shutdown (not restart),  or else use the power switch.  I have noticed that the tiny indicator lights do not go out,  and that the issues the reboot was supposed to correct do not reliably get corrected,  unless I go for the complete shutdown with no AC connected.  There is no battery pack to pull,  as the battery is all-internal.  

#5.  The machine erratically and unpredictably ignores clicks of the mouse.  This problem comes and goes erratically. 

#6.  The keyboard has unreliable keys,  and a slow response to keystrokes.  You can type fast,  and it will miss a lot of letters.  Some are worse than others.  Those will often ignore slow repeated keystrokes,  even ignore continuous hold-down of the offending key.  Plus,  the symbols wore off the keys in only a year.

#7.  I haven’t seen a stable operating system out of Microsoft since DOS,  which would fit on a 1 megabyte floppy disk.  The entire fundamental Windows concept is flawed,  forcing people to learn a second language (icons),  which was (and still is) unnecessary.  The last DOS machine I had also had a little shell program (from a German company) that did a text-based point-and-click mouse controlled interface.  This interface did everything for file navigation that Windows ever did,  but would fit on another 1 megabyte floppy disk without even filling it. 

#8. Windows 8/8.1/10 are all useless pieces of crap totally bogged down with useless touch-screen crap that is totally inappropriate to an ordinary laptop.  That kind of marketing arrogance totally negates any possible past reputation Microsoft ever had for quality or for customer service. 

#9. All of the Windows operating systems are very hard-to-remove (you must wipe the hard drive),  behaving exactly like a virus or malware,  ever since Windows 95.  The last semi-stable version I had was Windows 3.1,  but it was nowhere near as stable as DOS 2 or DOS 6,  which never corrupted themselves or required reboots.


#10.  The Windows operating systems are all self-corrupting,  and they do not clean up the messes they make,  which clog up your hard drive memory,  and bog down your machine’s operating speed.  DOS did not do that.

Monday, October 2, 2017

Machine Guns in Las Vegas?

Update 10-3-17 in red text below.

Update 10-4-17:  in blue text below.

Update 10-6-17:  in purple text below.

Under federal law,  a “machine gun” is a firearm that shoots more than one bullet per trigger pull.  The synonym for this is “fully-automatic”.  A “semi-automatic” weapon is one that sends one bullet per trigger pull,  loading the next round automatically.  If it doesn’t load the next round automatically,  that means the user must operate some sort of manual bolt or other mechanism to load the next round.  Bolt-action rifles,  pump or breakdown shotguns,  and ordinary revolver handguns fall into that last category. 

The M-16 used by US armed forces is indeed a machine gun,  a fully-automatic weapon,  although it can be operated as a semi-automatic single-shot weapon as well.  The same is true of the Russian-developed Kalashnikov AK-47.  These are true “assault weapons” for military use precisely because they really can be machine guns.  A military unit not so armed is at a lethally-distinct firepower disadvantage when confronted by such weapons. 

The AR-15 (and most modern hunting and sport guns) is a semi-automatic weapon,  not a machine gun / fully-automatic weapon.  The fact that an AR-15 looks exactly like an M-16,  has absolutely nothing to do with its rate of fire.   Calling it an “assault weapon” is wrong,  because no military unit today would ever go into combat with the AR-15.  They would be totally outgunned by any group with fully-automatic weapons.  It’s not about what the gun looks like,  it is entirely about what the gun can actually do.  Simple common sense.

Civilians in this country currently can indeed own or possess machine guns,  but what devices they can own,  and what they can do with them,  is very,  very,  very severely restricted.  This began with the National Firearms Act (NFA) of 1934.  That law came about because the mafia was causing mass death in the streets with the venerable old “Tommy gun”,  which really was a machine gun.  It severely restricted civilian ownership of fully automatic weapons,  short-barrel rifles and shotguns,  and certain explosives.  It was amended in 1968 and again in 1986.

The 1986 amendment restricted civilian ownership of fully automatic weapons to only those made before 1986,  only with payment of a $200 tax along with an enormous and very invasive application,  and only with a very,  very thorough ATF background investigation,  plus requirements for notification of the ATF any time the owner traveled with any of those devices. 

Such devices could not be updated or repaired with modern parts.  Parts for such devices are largely out-of-reach of all but the richest today.  There are no exceptions to allow for the ownership of anything newer than 1986.  There are no exceptions to any of the other requirements.

This status was superseded for a while in 1994 to disallow entirely the civilian ownership of those pre-1986 machine guns,  short-barrel guns,  and devices,  but that restriction expired in 2004.  So,  we are still under the 1986 version of the law today.

In all 50 states,  it may indeed be legal to own machine guns,  but only in accordance with the federal law!  If the possession or use is not in accord with federal law,  then such possession or use is presumed illegal under state law,  period!  Some states impose further restrictions,  some do not.  And that federal law is exactly the 1986 update of the 1934 NFA law.  Period.  No exceptions.

Modifying a semi-automatic weapon into a full-automatic weapon is indeed possible,  but it is generally not very easy to do.  It requires appropriate tools and knowledge and experience.  It also requires testing.  This is already illegal under any circumstances,  no exceptions. 

Update 10-4-17 Two new technologies for increasing firing rate have come to light.  These are the "bump stock" and the "gat-crank".  These act to increase the firing rate of a semi-automatic weapon to that of a fully-automatic weapon,  without modifying the loading mechanism inside the weapon.  These are therefore technically legal,  but they definitely do violate the intent of the 1986 prohibition on all but grandfathered machine guns.  In my opinion,  this is cheating,  and should not be allowed.  

What the shooter in Las Vegas did,  and what motivated him,  are still the subjects of investigation.  Nothing is yet known with any certainty,  and such certainty is unlikely for quite a while yet. Update 10-6-17:  information in news reports keeps surfacing that point to mental illness of some kind in this shooter.  He got his guns legally,  because no judge ever had him committed.  If you look at the earlier article cited below,  that "leak" of guns into the hands of crazies is the most common cause of these mass shooting incidents!  

The best speculations are (1) he sneaked some 10 (weapon count has been climbing in subsequent reports,  both in the hotel and at his home) long-barrel weapons into his hotel room overlooking the outdoor concert venue,  (2) at least some of those weapons were machine guns based on the high rates of fire evident from the audio recordings of the event,  and (3) he fired into a dense crowd that could not move quickly,  so that without aiming,  he was certain to hit lots of people. 

Item 3 means that fully-automatic weapons are not required to exact a huge death toll,  but they do considerably raise it.  Not even semi-automatic weapons are needed.  A considerable death toll could still be expected with just single-shot,  bolt-action rifles.  So,  it’s not really about the gun,  it’s much more about the situation:  a densely-packed,  immobile crowd as the target from a nearby high place. 

Every time there is such a mass shooting event,  there is an immediate knee-jerk reaction:  a call for tighter gun control.  Always the same things are proposed,  and almost none of them would have prevented any of these events,  including this one!  The exceptions are (1) selling weapons too easily to crazy folks,  and (2) loopholes to the required background checks we already have. 

The problem here really isn’t so much the guns,  it is what motivates people to want to kill their neighbors.  What causes that?  I have never heard a good answer to that question.  Maybe it is past time to go find out. 

Update 10-3-17:  To find out what the gun violence is really trying to tell us,  go see my analysis of excerpts from the Mother Jones gun violence database.  It is not what you think!  This analysis is in the article titled "What the Gun Violence Data Really Say" dated 6-21-2016 on this website.  It has a list of titles and dates for other articles I have also written on this subject.  The navigation tool on the left gets you there most easily.  Click on the year,  then on the month,  then on the title. 

For those unwilling to go to the cited article and examine the data for themselves,  here is the short form of the message:  (1) we have a major "leak" of guns legally sold to people who are mentally ill,  but have never been so ruled by a court,  (2) we have a major problem with inadequately-defended (or entirely-undefended) gun-free zones,  which also invite terrorist attack,  and (3) the "usual" gun control proposals of "assault" weapons bans,  clip size limits,  and the like,  have already been tried and were already found to be ineffective.  

It's both that simple and that ugly.  Fix those two items properly,  and it looks to me like most of this problem goes away.  Item 3 tells you what not to do.  Update 10-4-17 I also recommend outlawing "bump stocks" and "gat-cranks".  That won't prevent the incidents,  but it will reduce the death tolls.  


Saturday, September 23, 2017

Why So Many Illegal Immigrants?

Depending upon whom you believe,  there are some 10 to 12 million illegal immigrants in this country.  Why?   (I’ll warn you ahead of time:  you won’t like the real answer.) 

Short form: 

This traces directly to inaction by Congress since the end of WW2,  when they ended the Bracero program with the mass deportation of Mexican agricultural workers.  

Long form follows:

There are H1A visas for technical people,  and there are H2A and H2B visas for unskilled labor,  intended to be work permits for mostly-Mexican laborers.  These H2A and H2B visas cover the laborers,  plus the dependents they bring with them.  H2A visas are specifically for migrant farm workers,  and H2B visas are for all the other migrant worker trades,  such as the truly grungy stuff at construction sites,  concrete work,  road work,  lawn care guys,  and toilet cleaners at motels,  etc.

Because these jobs are both low-paid,  and very hard and unpleasant work,  almost no Americans really try to apply for such jobs,  despite what some claim.  We are awash in fake news about this issue,  among many others.  You can recognize a fake news echo chamber by the lack of divergent opinions,  it really is that simple.

The low pay for the immigrant workers is a vicious cycle:  because most of the workers are illegally here,  their employers simply extort labor at very low pay from them.  This is immoral and unethical,  but VERY widespread.  If these workers were legal,  pay for that work would have to rise,  and more Americans might even apply for such jobs.

These workers are a huge factor in our economy:  reportedly around 15% of construction jobs,  and apparently almost all the crop harvesters we have ever had since WW2.  If you deport them all,  important sectors of our economy not only crash,  but you will go hungry because of high-priced foreign food imports.   Now that's the real facts,  unpleasant though they are.

Why are these workers mostly illegal and thus subject to extortion into wage slavery?  Because the worker permit visa quotas controlled by Congress are completely out-of-line with the "ground truth" of our economy.  The demand and corresponding need is there,  the accommodation is not.

According to the Brookings Institute,  the annual cap on H2A and H2B visas totals to about 125-150,000.  That's roughly a factor-of-100 out-of-balance with reality:  the 10 to 12 million that are here doing the work,  and paying taxes on their meager wages,  despite what some say.

What no one wants to hear (but the painful truth will set you free,  when political lies won’t):  we brought this on ourselves;  more specifically,  our Congress did,  with over 7 decades inaction on this issue.  That is utterly inexcusable

Worse,  some of them run for re-election promising to do the wrong thing about this problem!  But we keep electing and re-electing all the idiots that did this!


So,  stop re-electing them!  Elect instead somebody who will really fix this,  by actually doing something about the out-of-balance visa quota system.  You’ll see this problem melt away in a very few years,  if this imbalance is corrected. 

(And by the way,  fixing this permanently fixes the DACA problem,  as well.) 

Sunday, August 13, 2017

North Korea Has Come to a Head

Note:  this article appeared in a slightly shorter form as a guest column on the opinion page of the Waco "Tribune-Herald",  Sunday 8-13-17.

Update 8-19-17:  I have appended some very specific recommendations for what to do about this problem at the end of this article.

The North Korea atomic weapons crisis has come to a head.  Understanding this situation is a whole lot easier than many think.  Like a boil,  it must be lanced.

They now have the 4 elements needed to present a credible nuclear missile threat to the US and many other nations.  Those are a big-enough rocket,  a nuclear warhead small enough to ride that rocket,  a guidance system to get it near its target,  and a heat shield for the warhead to survive reentry. 

The recent high-arcing rocket tests demonstrate they have made sufficient progress on all four fronts.  The trajectory shows the capability of hitting the US if aimed differently,  the intelligence communities agree they have a bomb small enough to ride that particular rocket,  and the fact that these test flights have not gone astray shows that the guidance works.  “Something” from these rockets have been tracked to impact from these tests,  which very strongly suggests that the heat shield works. 

Whether this ICBM is actually reliable is beside the point,  same as it was with ours and Russia’s in the late 1950’s.  If they launched several,  at least a few would get to the target.  Now that he has a credible weapon,  Kim Jong Un is ready to play the age-old blackmail game.  This is a pattern known across millennia of history,  but most folks would recognize the name Adolf Hitler. 

The game is played thusly:  the aggressive one makes a threat to do something “unspeakable” unless he gets what he wants.  He must be willing to risk getting slapped down for it,  but throughout history,  most of those who are willing to make the threat,  have been willing to take that risk. 

Between the World Wars,  that “unspeakable” threat was to wage war at all,  based on the horrifying experiences of World War 1.  Since World War 2,  the “unspeakable” threat has been to wage nuclear war.  Notice how lots of conventional wars have been waged since then?  Only the technology deemed “unspeakable” has changed.  The game remains the same. 

Kim Jong Un may seem crazy to us,  but he is crazy like a fox.  It is not yet clear what he wants,  but he has already made the threat to nuke Guam.  His risk bet is that we won’t actually go to war over an island far from our shores.  That is why he has not yet threatened the lower 48 states. 

But as this escalates,  Hawaii and Alaska are at risk,  because of US military assets in both places,  plus our allies in the region.  Eventually,  he would attack the lower 48 as a final act of desperation.  We’ve seen this pattern many times before.

And escalate it will!  Just like with Hitler and the Nazis in 1930’s Europe.  This scenario has played out countless times over history.  Kim Jong Un is following a long-established pattern like it was a cooking recipe.  This is perfectly predictable. 

Of course,  there is no excuse not to pursue a diplomatic solution.  Basic humanity on our part demands it.  But,  don’t hold your breath for it to work!  It didn’t work with Hitler,  or his predecessors. 

What worked was raw naked force.  The only question is how much you have to use,  and that increases as time goes by.  This is very much like a boil:  the longer you let it fester,  the more it hurts when you lance it,  and more damage there is to heal afterwards.

It is very important that we not strike the first blow,  and that would be true,  even without any pronouncements from the Chinese as to whether they get involved or stay neutral.  It is also important that we not resort to half measures,  such as only striking test sites. 

This is the main lesson of World War 2:  you go “whole hawg or none”.  If North Korea strikes Guam or anywhere else,  we take out Kim Jong Un and his entire government.  Regime change or nothing.  Period. 

It would be nice if we could kill Kim Jong Un and all his government functionaries by destroying them in their big government complex in Pyongyang,  without killing all the civilians in the surrounding city.  Then there’s no need to send one tank or one soldier across the border,  or to commit genocide by nuking the city.

The size of that complex demands that we use a deep-penetrating “bunker-buster” projectile fitted with a small nuclear warhead,  exploded deep underground,  and turning the complex into a contained rubble pile in a pit,  too radioactive to enter.   For the most part,  the city and the people survive,  only Kim Jong Un and his government die.

But I haven’t ever heard that we actually have such a weapon!  North Korea has been festering since 1953,  so it’s not like we haven’t foreseen this problem coming.  This lack for so long a time makes me think we have spent an awful lot of money on the wrong weapons,  not the ones we really needed.

Think about THAT the next time you go vote.  Which is now too late to do anything about any of this.  


Meanwhile,  sleep tight!

Update 8-19-17:  Appended Specific Recommendations:

Specific Recommendations Regarding North Korea                                          

First,  privately among ourselves,  we must agree upon three things: 

(1) We will put an end to the regime if they launch any sort of weapon at any US territory or ally,  anywhere in the world. 

(2) We will accomplish this from a distance:  no invasion,  no occupation. 

(3) We would like to do this with minimal loss of civilian life on all sides,  but accomplishing an end to that ugly regime is higher priority than saving those lives.

Second,  we tell North Korea publicly that “we will put a permanent end to their regime if they launch any weapon toward any US territory or ally,  anywhere in the world”.  This should be calm,  quiet,  succinct,  and very much to the point.  No questions,  no discussion.  No bluster.  Just that fact.

Third,  we tell China very privately that we will put an end to the North Korean regime because they did not control the rogue regime that they created.  We tell them we will not invade or occupy,  because that is not in our interests.  It was in their interests to control what they created,  but they did not do their job. 

Our action will inevitably leave a failed state on their doorstep,  something neither of us wanted.  But because of them not doing their job,  it is only fair that they clean up the failed state mess that we leave for them.  No questions,  no discussion.  Not negotiable.  Best for them and for us.

Fourth,  among ourselves,  and probably in a deeply-classified information scenario,  we must address exactly how we will utterly destroy that regime from a standoff distance,  both “right now”,  and within the next year or so.  There will be no invasion (not even temporarily),  no occupation.  It is best to do this without even sending manned aircraft. 

We do this with standoff weapons,  and preferably not ICBM’s,  which could be mistaken for an attack on China.  Tactical (not strategic) weapon trajectories are an imperative here.

The goal is to suddenly destroy the entire governmental complex in Pyongyang,  in a completely-surprise attack,  at a time we choose,  not just an immediate knee-jerk response.  The hope is to catch Kim Jong Un and his top staff there,  and kill them all in the sudden utter destruction of that complex.  If we miss him,  then we target other installations where he might be,  in a similar fashion.  We keep up the strikes until we get him,  no matter how long it takes.  Then we quit.

A tactical missile with a nuclear warhead can do that job right now,  but with enormous civilian casualties and the destruction of much of the city.  That outcome would resemble Hiroshima and Nagasaki,  so it is imperative that they strike first,  no if’s,  and’s,  or but’s about that.  Such a weapon could be launched from Japan,  South Korea,  or a ship (or submarine) at sea close by.

However,  some sort of tactical missile might possibly be fitted with a deep-penetrating “bunker-buster” nuclear warhead.  It would likely be a larger tactical missile due to the weight of the Earth penetrator and the necessary speed at impact. 

Such a strike would excavate out a cavity under the foundations of the government complex,  shatter that complex into rubble,  and contain that radioactive rubble by its collapse into the excavation pit.  There would be some surface fallout,  but not nearly as much as the usual “city-busting” scenario.  In this underground nuclear scenario,  most of Pyongyang and its civilian population would survive in good shape.  That is the preferred scenario. 

The questions we must ask ourselves in this private,  classified discussion are two-fold. 

(1) Do we possess such a weapon?  If yes,  we’re “good-to-go” immediately.

(2) If not,  how soon could we have one?  And then get on with it as a “crash program”.  Speed is crucial.


Finally,  I would add that this crisis has been long foreseen.  If we have no such suitable weapon to end it with minimal civilian casualties,  why is that?  How do we fix that management lack?

(end update 8-19-17)

Update 8-23-17:  the same nuclear bunker-buster I suggested for decapitating the North Korean regime,  would work against the underground hardened nuclear production facilities in Iran.  That need would arise if  they choose to violate the agreement and start building bombs (a real risk).  I repeat: do we have such a weapon?  If not,  why not?

Update 9-19-17:  After thinking about it for a while,  I believe the real reason Kim Jong Un wants nuclear weapons is to extort the reunification of Korea on his terms.  The threat of nuclear attack "wherever" is the threat by which to ward off the counter-invasion that topples his regime.  I still say we do this by standoff strike,  not invasion.  We leave the failed state on China's doorstep to clean up.  It's only fair,  they created this abortion.


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Tuesday, July 4, 2017

Heat Protection is the Key to Hypersonic Flight

The problem is not so much propulsion as it is heat protection.  The reason has to do with the enormous energies of high speed flight,  and with steady-state and transient heat transfer.  Any good rocket can push you to hypersonic speeds in the atmosphere.  But it is unlikely that you will survive very long there

The flow field around most supersonic and hypersonic objects looks somewhat like that in Figure 1.  There is a bow shock caused by the object parting the oncoming air stream.  Then,  the flow re-expands back to near streamline direction along the side of the object.  Then it over-expands around the aft edge,  having to experience another shock wave to straighten-out its direction parallel to free stream again.  This aft flow field usually also features a wake zone of one size or another,  as shown. 


The conditions along the lateral side of the object are not all that far from free stream,  in terms of static pressures,  flow velocities,  and air static temperatures.  One can compute skin heat transfer using those free-stream values as values at the edge of the local boundary layer,  and be “in the ballpark”.  That is what I do here,  for illustrative and conceptual purposes. 


 Figure 1 – Supersonic and Hypersonic Flow Fields About All But the Bluntest Objects


Once flow is supersonic,  the boundary layer behavior isn’t so simple any more.  There is a phenomenon that derives from the very high kinetic energies that one simply does not see in subsonic flow:  energy conservation.  The value of that kinetic energy shows up as the air total temperature Tt,  which is the upper bound for how hot things could be.  Air captured on board by any means will be very close to Tt,  if subsonic relative to the airframe after capture.  This includes any “cooling air” one might use!

In addition,  there is “viscous dissipation”,  which has the effect of raising the actual (thermodynamic) temperature of the air in a max shearing zone within that boundary layer,  to very high temperatures.  The peak of this temperature increase is called the recovery temperature TrThe difference between this recovery temperature and the local skin temperature Ts is what drives air friction heat transfer to the skin,  not the difference between the air static temperature and the skin temperature,  as is typical in subsonic flow.  See Figure 2.  The temperature rise from static to recovery is around 88 to 89% of the rise from static to total,  in turbulent flow,  which this almost always is.  

 Figure 2 – Viscous Dissipation and the Recovery Temperature


Most heat transfer calculations for this kind of flow regime take the basic form and sequence illustrated in Figure 3.  “How high and how fast” determines the conditions of flow,  ultimately.  Total and recovery temperatures may be computed from this,  and total temperature is conserved throughout the flow field around the object,  regardless of the shock and expansion processes.  The flow alongside the lateral skin is not far from free-stream to first order,  and that may be used to find out “what ballpark we are playing in”.  Better local edge-of-boundary layer estimates must come from far more sophisticated analyses,  such as computer fluid dynamics (CFD) codes. 

In Figure 3,  the process starts by determining recovery temperature.  The velocity,  density,  and viscosity at the edge of the boundary layer won’t be vastly different from free stream,  unless you are really hypersonic,  or really blunt (detached bow shock).  The various correlations account for this.

Using whatever dimension is appropriate for the selected heat transfer correlation,  one computes Reynolds number Re.  Low densities at high altitude lead to low values,  and vice versa.  High speeds lead to high values.  Different correlations have the density and viscosity (and thermal conductivity) evaluated in different ways and at different reference temperatures.  You simply follow the procedure for the correlation you selected.  Sometimes this is neither simple,  nor straightforward. 

The complexity of these correlations varies.  My favored lateral skin correlations use a T* for properties evaluation that is T* = mean film plus 22% of the stagnation rise above static.  My favored slower than reentry stagnation zone correlation evaluates fluid properties at total conditions behind a normal shock.  In the stagnation case,  Reynolds number is based on the pre-shock freestream velocity.

The next step is the correlation for Nusselt number Nu.  This nearly always takes the form of a power function of Re (plus some other nontrivial factors),  usually with an exponent in the vicinity of 0.8 or so.  Nusselt number is then converted to heat transfer coefficient h,  using the appropriate dimension and the appropriately-evaluated thermal conductivity of the air,  for the selected correlation. 
The heat transfer rate is then as given in Figure 3,  which shows the Tr – Ts temperature difference.  

One should note that because both density (which is in Re) and thermal conductivity k (which is in h) are low at high altitudes,  the computed values of h will be substantially smaller at high altitudes in the thin air.  High speeds act to raise h,  and to very dramatically raise Tr and Tt.  That last effect is truly exponential.

Having the heat transfer rate is only part of the problem.  One must also worry about transient vs steady-state effects.  If the skin is completely uncooled in any way,  it is then only a heat sink of finite capacity,  with the convective input from Q/Aconv = h (Tr - Ts).  One can use material masses and specific heats to estimate the heat that is sinkable as skin temperature rises.  The highest it can reach is Tr = Ts,  where it is fully “soaked out” to the recovery temperature.  That zeroes heat transfer to the skin. 

The time it takes to soak out can be very crudely estimated as 3 “time constants”,  where one “time constant” is the heat energy absorbed to soak-out all the way from initial Ts to Tr,  divided by the initial heat transfer rate when the skin is at the initial low Ts.  

 Figure 3 – How Lateral Skin Heat Transfer Is Computed


More complex steady-state situations must find the equilibriating Ts when there is convective input from air friction,  conductive/convective heat transfer into the interior of the object (something not illustrated here),  and re-radiation from the hot skin to the environment.  In high speed entry,  there is also a radiative input to the skin from the boundary layer itself,  which is an incandescent plasma at such speeds,  and this is very significant above about 10 km/s speeds. 

Not covered here in the first two estimates are heat transfer correlations for nose tips and leading edges.  Those heat transfer coefficients tend to be about an order of magnitude higher than the coefficients one would estimate for “typical” lateral skin.  Stagnation soak-out temperatures should really be nearer Ttot than Tr,  although those temperatures are really very little different.

Suffice it to say here that if one flies for hours instead of scant minutes or seconds with uncooled skins,  they will soak out rather close to the recovery temperature Tr or total temperature Ttot.  That brings up practical material temperature limits.  See Figures 4 and 5. 

For almost all organic composites,  the matrix degrades to structural uselessness by the time it reaches around 200 F.  The fiber might (or might not) be good for more,  but without a matrix,  it is useless.  For most aluminum alloys,  structural strength has degraded to under 25% of normal by the time it reaches about 300 F,  which is why no supersonic aircraft made of aluminum flies faster than Mach 2 to 2.3 in the stratosphere,  and slower still at sea level.  Dash speeds higher are limited to several seconds.

Carbon steels and titaniums respond to temperature very similarly,  it is a very serious mistake to think that titanium is a higher-temperature material than carbon steel!  Titanium is only lighter than steel.  And you “buy” that weight savings at the cost of far less formability potential with titanium.  Both materials are pretty-much structurally “junk” beyond about 750 F.  Various stainless alloys have max recommended use temperatures between 1200 and 1600 F.  Inconel is similar to the higher end at about 1500 F.  There are a very few “superalloys” that can be used to about 2000 F,  give or take 100 F.

Figure 4 compares steady-state recovery (max soak-out) and total temperatures to material limitations on a standard day at sea level.  Max speed for organic composites are barely over Mach 1,  and just under Mach 2 with aluminum.  Steel and titanium are only good to about Mach 2.5,  unless cooled in some way.  Stainless steels can get you to about Mach 3.5-to-4,  the superalloys not much higher.  


Figure 4 – Compare Tt and Tr to Material Limitations at Sea Level

Figure 5 makes the same comparison in the stratosphere on a standard day,  where the static air temperature is far colder.  You are good with organic composites to almost Mach 2,  and to about Mach 2.2 or 2.3 with aluminum.  Carbon steel and titanium will only take you to about Mach 3.5,  unless cooled in some way.  The various stainless alloys cover about Mach 4 to 4.5,  and the superalloys cover to just above Mach 5.  All of that is entirely uncooled soak-out.

 Figure 5 -- Compare Tt and Tr to Material Limitations in the Stratosphere


One should note that stratospheric temperatures are only -69.7 F from about 36,000 feet altitude to about 66,000 feet altitude.  Above 66,000 feet,  air temperatures rise again,  to values intermediate between these two figures!  That lowers the speed limitation some,  for altitudes above 66,000 feet.

This steady-state soak-out temperature comparison neatly explains why most ramjet missile designs (usually featuring shiny or white-painted bare alloy stainless steel skin) have been limited to about Mach 4 in the stratosphere,  and around Mach 3.3 or so at sea level.  Those limitations on speed are pretty close to the 1200 F isotherms of total or recovery temperature.  Without re-radiation cooling,  the skins soak out fairly quickly (the leading edges and nose tips extremely quickly).

To fly faster will require cooled skins,  or one-shot ablatives,  or else the briefest episodes (scant seconds) of transient flight.  The nose-tip and leading edge problem is even worse!  That means for long-duration / long-range flight,  the skin must be cooled,  or else coated with a thick,  heavy,  one-shot ablative.  There are two (and only two) ways to do cooling:  (1) backside heat removal,  and (2) re-radiation to the environment.  Or both!

Backside heat removal must address (1) conduction through the materials,  (2) some means of removing the heat from the backside of the materials,  and (3) some means of storing or disposing of all the collected heat (what usually gets forgotten).   Liquid backside cooling using the fuel comes to mind,  with the heat dumped in the fuel tank.  However,  there are two very severe limits:  (1) the liquid cooling materials and media may not exceed the boiling temperature at tolerable pressures,  and (2) the heat capacity of the fuel in the tank is very finite,  and decreasing rapidly as the vehicle burns off its fuel load. 

Re-radiation to the environment requires a very “black” (highly emissive) surface coating,  and is further limited by the temperature of the environment to which the heat is radiated.  These processes follow a form of the Stefan-Boltzmann Law,  to wit:  Q/A = σ εs (Ts4 – Te4),  where σ is the Stefan-Boltzmann constant,  and the εs is spectrally-averaged material emissivity at the corresponding temperature.  Subscript s refers to the hot radiating skin panels,  and subscript e refers to the environment. 

While deep space is ~4 K,  earth temperatures are nearer 300 K,  and that is what most atmospheric vehicles usually “see”.  The material absorptivity is its emissivity,  which is why that value is also used for the radiation received from the environment.  A truly “black” hot metal skin might have an emissivity near or above 0.8.  This could be achieved in some cases by a metallurgical coating or treatment,  in others by a suitable black paint (usually one of ceramic nature,  and very high in carbon content).

One More Limitation to Consider

Once the boundary layer air is hot enough,  it is no longer air,  it is becoming an ionized plasma.  The kinds of heat transfer calculations that I used here become increasingly inaccurate when that happens,  and other correlations developed for entry from space need to be used instead.  As a rough rule-of-thumb,  that limit is about 5000 F air temperature. 

If you look at Figure 4 (sea level),  you hit the “not-air anymore” limitation starting around Mach 7.  In figure 5 for coldest stratosphere,  that limit gets exceeded starting around Mach 8.  The only calculation methods that “work” reliably above these limits would be CFD codes,  and even then,  only if the correct models and correlations are built into the codes.  That last is not a given!  “Garbage-in,  garbage-out”.  That expression is no joke,  it is quite real. 

With Re-Radiation Cooling at Emissivity = 0.80

This applies only to lateral skins,  not leading edges,  because the heat transfer rates are an order of magnitude higher for leading edges.  That effect alone changes the energy balance enormously. 

But for lateral skins,  the speed limitation occurs when the re-radiation heat flow equals the convective input to the skin.  The complicating factor is that convective heat transfer is a strong function of altitude via the air density,  while re-radiation is entirely independent of altitude air density.  There are now more variables at work on the energy balance than just ambient air temperature. 

That means two charts depicting the “typical” effects are entirely inadequate.  We need a sense for how this changes with altitude air density.  What follows is a selection of equilibrium re-radiating temperature versus speed plots,  at various altitudes,  in a US 1962 Standard Day atmosphere model.  Material temperature capabilities are superposed,  as before.

Figure 6 -- Lateral Skin Radiational Equilibrium at Sea Level



 Figure 7 – Lateral Skin Radiational Equilibrium at 20,000 feet


 Figure 8 -- Lateral Skin Radiational Equilibrium at 37,000 feet


 Figure 9 – Lateral Skin Radiational Equilibrium at 66,000 feet


 Figure 10 – Lateral Skin Radiational Equilibrium at 80,000 feet


Figure 11 – Lateral Skin Radiational Equilibrium at 110,000 feet


Tough Design Problem

How exactly one achieves this re-radiation cooling is quite a difficult design problem.  The skin itself will be very hot,  in order to re-radiate effectively.  Not only will it be very structurally weak,  there will be heat leakage from it into the vehicle interior.  This is inherent,  but by careful design,  can be limited to rather small (1-2%) values compared to the energy incident and re-radiated from the outer surface. 

There must be a sufficient thickness of low density insulation between that skin and the interior,  one capable of surviving at the skin temperature.  This insulation must be some sort of mineral fiber wool.  There are no simple glasses that survive at the temperatures of interest for hypersonic flight. 

The mountings that hold the skin in place constitute metallic conduction paths into the interior.  These must be made of serpentine shape,  of length significantly greater than the insulation thickness,  in order to effectively limit heat leakage by the metallic conduction path. 

Finally,  there is the issue of sealing the structure against throughflow induced by the surface pressure distribution relative to the pressure in the interior.  Because it is much easier to design seals that survive cold,  than seals that survive incandescently-hot,  it seems likely that the surface skins must be vented,  with the pressure distribution resisted by colder structures deeper within the airframe. 

Two Sample Cases

The SR-71 and its variants featured a “black” titanium skin,  cooled by re-radiation,  but nothing else.  The leading edges (at least very locally) would approach the soak-out temperature limits shown in Figures 4 and 5 above.  Typical missions were flown at around 85,000 feet,  with speeds up to,  but not exceeding Mach 3.3.  In the very slightly-colder air at 66,000 feet,  that leading edge limit was Mach 3.5. 

As figure 10 shows,  the lateral skins had a higher speed limit nearer Mach 4.  So we can safely draw the rough conclusion that the SR-71 airframe was likely limited by leading-edge heating to about Mach 3.5 or so,  at something around 80,000 or 85,000 feet. 

The X-15 featured skins of Inconel-X that were radiationally very “black”.  About the max recommended material use temperature is 1500-1600 F.  Leading edges might tend toward the local soak-out limit at about Mach 4 to 4.5,  unless internally cooled by significant internal conduction toward the lateral surfaces of a solid piece,  which these were.  Thinner air “way up high” might help with that balance,  by reducing both the stagnation,  and lateral,  heating rates. 

As shown in figure 11,  the re-radiation equilibrium limitation near 110,000 feet is closer to Mach 10 for the lateral skins,  and higher still at higher altitudes,  as the other figures indicate by their trends.   The fastest flight had a white coating,  which effectively killed radiational cooling.  For that,  the soak-out speed limit is closer to Mach 4.5 to 5.5,  based upon figures 4 and 5. 

Again, we might very crudely conclude the X-15 was limited by its leading edges to something between Mach 5 and Mach 10.  The fastest flight actually flown reached Mach 6.7,  without any evident wing leading edge or nose damage,  excepting some shock impingement heating damage in the tail section.

My Conclusions:

Most of the outfits claiming they have vehicle designs that cruise steadily at Mach 8+ (high-hypersonic flight) have not done their thermal protection designs yet. 

That lack inherently means they do not have feasible vehicle designs at all,  since thermal protection is the enabling item for sustained high-hypersonic flight. 

“Hypersonic cruise” (meaning steady state cruise above Mach 4 or 5 for extended ranges) is therefore nothing but a buzz word,  without an advanced thermal protection system in place. 

The faster the cruise speed,  the more advanced this thermal protection must be,  and the more unlikely there will be a metallic solution.

Practical Definitions:

Blunt vehicles = hypersonic Mach 3+

Sharp vehicles = hypersonic Mach 5+

Formally,  “hypersonic” is when the bow shock position relative to the vehicle surface contour becomes insensitive to flight speed.

A Better Leading Edge Model

That is entirely out of scope here.  It might consist of one solid leading edge piece,  to be assumed isothermal.  It would have a very small percentage of its surface area calculated for stagnation heat transfer,  with the remainder calculated as lateral skin heat transfer,  except as modified for convexity into the flow near the leading edge.  There would be no conduction or convection into the interior.  All surfaces would re-radiate to cool.

The next best model is a finite-element approximation,  which allows for temperature variations and internal conduction,  within the leading edge piece.  Adding conduction and convection paths into the interior is the next level of modeling fidelity.  None of this is amenable to simple hand calculation. 

Supersonic Inlet Structures

These are an even more difficult problem,  as the inner surfaces are (1) blocked from viewing the external environment for radiational cooling,  and (2) are exposed to edge-of-boundary layer conditions that are very far indeed from freestream conditions. 

Monday, June 12, 2017

Shock Impingement Heating Is Very Dangerous

The X-15-A-2 was rebuilt from ship #2 after a crash.  In October 1967 Pete Knight flew this craft to Mach 6.7 as part of a flight envelope expansion project,  with a dummy scramjet pod attached to the ventral fin stub.  There was severe heating damage to the ventral fin stub from spike shock shed from the from dummy scramjet pod.  The pod separated in flight.  Inconel-X skins suffered about 7 times-normal heating rate due to shock wave impingement. 


The first photo shows the vehicle about to be dropped from its mothership B-52.  Note the white heat protection coating applied to vehicle,  and the dummy scramjet pod attached to ventral fin stub.  The white heat protection coating did not prove to be successful.  This version of the X-15 had two big drop tanks of rocket propellants.  


The second photo is actually 3 images combined to get 3 views of damaged ventral fin stub.  It shows clearly the damage to the ventral fin,  obviously of a meltback nature.  The material was simply overheated by shockwave impingement.  These skins were Inconel-X,  with a listed max useful temperature about 1500 F,  and with meltpoint well beyond 2500 F but far less than 3000 F.


The third image is another view of the damaged ventral fin,  with damage to the aft fuselage also visible.  The separated scramjet pod was also recovered,  and is shown. 


What this proves is that the “parallel nacelle” arrangement is a really bad idea when flight speeds exceed about Mach 5 or 6,  varying with the toughness of the materials involved.   If you let this situation go on long enough,  the impinging shock wave will cut away all the adjacent structure that it strikes.

That is the fundamental reason there have been no successful hypersonic vehicles using the “parallel nacelle” arrangement.  The SR-71 and similar aircraft simply did not fly fast enough to incur this kind of damage.  The X-15 did,  and any entry vehicle far exceeds the heating risks that the X-15 saw. 

Schematically,  this is illustrated in the sketch.  The areas at risk are subject to direct impingement,  meaning the shock wave is “headed directly toward” the surface at risk,  as if that surface is “in the way” of the wave.  For waves that propagate 90 degrees away from the “headed toward” direction,  the effects are very much less.  That is why fins do not damage the surface from which they extend.  There can be a little local heating,  but nothing at all like direct wave impingement.  


As to when the damage occurs,  that depends upon the material and upon the flight speed.  Even the turbine blade superalloys fail by melting under 3000 F,  and fail structurally at temperatures not much over 2000 F.  For a steady state exposure,  the energy balance is convective input to the material,  balanced by internal convective cooling,  or by external re-radiation of heat to environment,  or by a combination of both.  If neither cooling occurs,  the material soaks out to the recovery temperature.

The convective input is driven by the difference between the recovery temperature and the material temperature.  The re-radiation ability is driven by the infrared (and optical) emissivity of the material and its temperature.  In the case of the X-15 flight,  there was no internal cooling,  and the white coating had drastically reduced the material’s emissivity (the normal surface finish was nearly black).
 
At Mach 6.7 and 100,000 feet on a 1962 standard day,  the turbulent recovery temperature that drives convective input calculates as about 3250 F,  well beyond the melting point of any superalloy,  much less its maximum use temperature.  With re-radiative cooling suppressed by the white coating (and no internal cooling),  it should not be surprising in retrospect that the test nacelle bow shock did extensive damage to the fin stub and aft fuselage. 


The only real surprise is that this X-15 survived that particular flight at all.  The exposure was brief enough that these effects did not have the time to sever its tail section.