Rocket Hopper for Mars Planetary Transportation

The future presence of bases and settlements upon Mars brings the need for transportation of freight and people about the planet.  A little thought reveals the two categories,  freight and people,  are fundamentally different in their requirements.  Most freight is not time-sensitive,  while people are. 

Freight not time-sensitive needs to go by slow surface transportation,  without emplacing expensive and effort-intensive infrastructure to make that possible.   Such infrastructure is often very expensive here,  and the costs there are likely to be quite catastrophic.  Freight needs something similar to rail transport here,  but without the tracks.  A robot “truck train” on a graded dirt road is the answer.

People are time-sensitive,  and need to fly in order to cover large distances rapidly.  But physics in an atmosphere so thin,  that it is first cousin to the vacuum of space,  rules out air transport by airplanes or helicopters as we know them on Earth.  It also rules out any form of “lighter-than-air” transport,  since buoyant lift forces are proportional to differences in densities,  and those are so vanishingly-low on Mars.  That pretty much leaves suborbital rocket travel (the “rocket hopper”),  the topic of this document.  The same could be used for that tiny portion of freight that really is time-sensitive.

Suborbital Trajectories

I used my “orbit basics” spreadsheet,  “R V q orbits” worksheet,  to model suborbital trajectories about the planet,  using ellipses that lie mostly within the planet.  It was necessary to sharply limit the trajectory angle below local horizontal at entry interface altitude (135 km for Mars),  in order to limit peak entry deceleration gees and peak heating,  and to achieve altitudes from which rocket-braked landings were feasible in terms of timelines and deceleration gees.  The results I was able to obtain are shown in Figure 1.  The longest-range of these trajectories is very nearly antipodal (10,637 km). 

Figure 1 – Suborbital Trajectories

Entry,  Descent,  and Landing

I used the “entry spreadsheet” spreadsheet file,  worksheet “Mars variations”,  to compute estimates for the worst case (highest entry speed) entry trajectory,  using the old 1953-vintage analysis used for warheads by H. Julian Allen and his colleagues.  This stuff was declassified and taught in engineering schools in the late 1960’s.  It is not the most accurate thing to use,  but it gets you “well into the ballpark” with very simple,  essentially-by-hand,  calculations.  These are easily put into a spreadsheet.

The highest speed at entry is the most challenging,  since all the entry angles are about 15 degrees,  so that analysis is depicted in Figure 2.  It was crucial to get the hypersonic ballistic coefficient of the hopper vehicle down under 200 kg/sq.m,  and preferably under 180 kg/sq.m.  It proved feasible with the final design to get well under that requirement with the value shown in the figure,  although most design approaches will fail in that respect!  Getting the heating down to something easily handled required the largest-possible “nose radius”.  The value shown was dictated by the design approach taken here,  and is quite easily handled,  although it is too much for metal exposed at the stagnation zone. 

Figure 2 – Estimates for Entry Conditions

The hypersonic aerobraking is largely over once the vehicle has decelerated to about local Mach 3,  which is roughly 0.7 km/s speed in the Martian atmosphere.  Slower than Mach 3,  a blunt object is no longer hypersonic,  and the assumption of a constant ballistic coefficient fails.  It would be folly to continue the hypersonic estimate past that point,  for that very reason. 

Not included in the approximate analysis is the effect of trajectory “droop” to steeper angles due to gravity.  That mostly happens after the peak deceleration point,  which is actually rather close to the end-of-hypersonics (Mach 3) point.  Peak heating occurred slightly earlier.  For purposes of “reasonable approximation”,  I just used the hypersonic endpoint altitude as obtained,  but I presumed the trajectory was headed about 45 degrees downward at the Mach 3 point. 

Ignoring the effect of the potential energy associated with the Mach 3 point altitude,  it is the same Mach 3 point speed of 0.7 km/s that we have to “kill” with last-second rocket braking,  regardless of that altitude.  Appropriately factored for losses and maneuvering,  that is the rocket braking delta-vee (dV) that we must have.  I used factor 2,  and would never use less than 1.5 under any circumstances,  in order to account for losses,  plus hover and divert requirements.  The Mach 3 point altitude essentially determines how much time we have left before surface impact,  which sets the required average gees,  and thus the thrust required for any particular vehicle mass. 

I used simple high school-level geometry and physics/kinematics to establish the average deceleration gees during the rocket-braking landing.  This is a very simple hand calculation,  illustrated in Figure 3.  The 6 km altitude translates to an 8.5 km path length down a straight line at 45 degrees.  At an undecelerated constant 700 m/s,  we are about 12.1 sec from impact,  as shown.  Thus there is far too little time available to deploy a chute,  much less expect any deceleration from it. 

If we rocket-brake decelerate to zero,  the average velocity down the path is only 350 m/s,  and we have 24.3 sec to touchdown,  as shown.  The change in speed is the 700 m/s.  The change in time is the 24.3 sec.  Their ratio is the average deceleration required,  which is 28.8 m/sec²,  or some 2.94 standard gees.

Figure 3 – Hand Calculations for the Rocket-Braked Landing

Therefore,  we are looking at roughly a 3-gee rocket-braked landing,  with the gees felt over an interval 24-25 sec long.  That is easily handled by persons not trained in resisting gees,  if seated,  even more so if reclined.  Roller coaster riders endure worse all the time.

The hypersonic aerobrake peak gees fall in the 6.6 to 6.7 range,  but again for a short interval above 5 gees that is only around 20-25 sec long,  as well.  That is more difficult,  but it is endurable,  even by untrained persons as long as they are fully physically fit,  as also experienced by some roller coaster riders.  It is anticipated that passengers will be riding while wearing some sort of pressure suits.  It would help if these pressure suits had “gee-suit” features as well.  Otherwise,  some passengers might temporarily faint,  if sitting up.  Any crew must be trained to endure such gees,  and they must be wearing suits with “gee-suit” features.

“Rocket Hopper” Vehicle Design Concept and Estimates

I looked at 3 classes of possible design configurations trying to meet the requirements of low hypersonic ballistic coefficient and large “nose radius” simultaneously.  Only one approach satisfied those needs,  and still offered ways to mount landing legs for rough-field operations,  plus a simple unobstructed engine bay.  That was the cylindrical stack depicted in Figure 4,  but flown dead-broadside to the oncoming stream during entry! 

If the cylinder L/D ratio falls in the 4-to-6 range,  that is enough larger blockage area to greatly-reduce the hypersonic ballistic coefficient,  despite the low hypersonic drag coefficient of the cylinder shape.  That shape was required to keep tank construction lightweight.

As for the tanks,  these are main tanks that are integral components of the vehicle airframe,  but they also contain header tanks.  As the numbers worked out,  about 15% of the tank volume is in the headers,  for course correction and rocket-braking,  with the other 85% in the main tank volume for launch. 

Figure 4 – Sketch Layout and Characteristics of the “Rocket Hopper” Design Concept

As shown,  the smallest item was the engine bay,  and the largest item the cabin in which people ride.  The tanks are stacked in the middle,  so that center-of-gravity travel is not very large as the propellants burn off.  The figure shows the layout,  a weight statement,  seating arrangements,  the basic trajectory-related notions,  and some entry heat protection numbers. 

Most but not quite all of the surface of this craft could be exposed metal construction,  if something like a 316L stainless steel or an Inconel X-750 is used.   Only near the stagnation line on the windward side is something more heat-resistant required.  That could be a strip of ceramic tiles of some kind.  Even low-density alumino-silicate ceramics could be used,  if blackened for high emissivity,  as peak entry pressures are actually quite low.

Peak entry pressures are easily rough-estimated by simple hand calculations at the peak deceleration gee point in the hypersonic entry trajectory.  If you know the mass at entry,  the peak gees acting upon that mass give you the peak force decelerating the vehicle.  Dividing that force by the frontal blockage area gives you the average pressure applied to that area.  The peak is at the stagnation zone,  crudely twice the average value.

To run some of these numbers,  I did create a custom “rocket hopper” spreadsheet.  It has multiple worksheets,  of which two are relevant here.  Worksheet “veh” is set up to make the calculations illustrated in Figure 5.  Worksheet “sections” is set up to make the calculations shown in Figure 6. 

In worksheet “veh”,  user inputs are yellow,  significant outputs are blue,  and things requiring iteration or verification are green.  (The same color code applies to all my spreadsheets.)  It works in terms of mass ratio-effective dV,  which is the end-of-burn V multiplied by an appropriate factor to account for gravity and drag losses (about 1.02 on Mars).  

Figure 5 – Numbers Run for the Design Concept,  Part 1

The 3.6 km/s orbit speed at launch multiplied by that factor is the 3.672 km/s dV shown.  The course correction budget is 8% of the orbit apoapsis speed,  which is where corrections should be made.  For the highest-speed case,  that is the 0.215 km/s shown.  And at factor 2,  the 1.4 km/s dV is what the rocket-braking burn must be capable of,  the same for all cases. 

I used a launch liftoff 1.5 gees as required for initiating good ascent kinematics,  same as here on Earth.  0.1 gee for course corrections is probably just a lower limit.  I used 3.5 gees at landing to get some margin over the average 3 gees determined above.

The specific impulse input of 352 sec shown is justified by the analysis given below.  The sum of the dV values is the total dV to be delivered for the mission,  which sets vehicle mass ratio and propellant mass fraction.  1 – propellant fraction – inert fraction is the available payload fraction.

There is an “inert mass fraction build-out” block shown.  We can argue about the component inputs,  but their sum is likely “in the ballpark” no matter exactly what inputs one uses.  The same is true of the size payload block.  You are looking at the weights for a person,  his pressure suit,  a few hours worth of oxygen,  water,  and food,  plus some luggage.  It’ll be around 0.2-0.25 metric tons per person,  almost no matter what,  when you sum it up. That and how many people are aboard,  sets the payload mass,  which ultimately sets the weight statement.

The “heat shield re-radiation” block presumes convective heating is balanced by re-radiation from hot exposed surface materials.  It uses the peak heating from the entry analysis,  plus good guesses for surface emissivity and the effective temperature of the surroundings that must receive that re-radiated heat.  A highly-emissive surface is typically 0.8,  while low is 0.2.  400 R for the surroundings is -60 F.

The “run weight statement and size thrusts” block does exactly that.  Payload mass divided by payload fraction is ignition mass.  Ignition mass time inert fraction is inert mass,  and times propellant fraction is propellant mass.  Payload plus inert is burnout,  and burnout plus propellant is ignition.  Each burn has a dV that sets its mass ratio.  That in turn sets start and end-of-burn masses,  the difference being propellant used for that burn.  The sum of those propellant masses used must equal the total propellant mass already figured. 

There is a “check pressure on heat shield” block that uses the hypersonic ballistic coefficient and the hypersonic drag coefficient as inputs,  plus the initial mass at entry,  and the peak entry gees.  It computes the mass per unit blockage area from the ballistic coefficient and drag coefficient,  then the peak entry force from that and the entry mass and peak entry gees.  It then divides force by blockage area for average pressure,  and doubles that for the stagnation pressure estimate,  reported in a variety of units of measure.

The ”heating other locations” block gets you equilibrium temperatures in degrees F for stagnation,  “typical” lateral,  and separated wake zone locations.  The stagnation peak heating is reduced by a factor of 3 for “typical” lateral surfaces,  and by a factor of 10 for separated wake zone surfaces.

The only other block shows launch dV available as a function of percent max propellant loaded on board.  The course correction and landing dV values are not changed.  This would be useful trying to relate range to propellant load required.

Figure 6 – Numbers Run for the Design Concept,  Part 2

The “sections” worksheet works out the proportions of the engine bay,  tankage,  and cabin sections of the ship,  plus some other pertinent results.  It needs the r-ratio (oxidizer/fuel fuel mass ratio) for the engine,  and the specific gravities of the fuel and oxidizer materials.  It also needs as inputs the mass at start of entry (after course corrections from the weight statement),  and a hypersonic drag coefficient in crossflow for the presumed vehicle shape,  which in this case is a circular cylinder.

It also needs as inputs the propellant masses for each burn.  It works out from these the masses of oxidizer and fuel for each burn,  and their volumes.  This is done in an untitled block top center of the page.

There is an “engine resize” block that takes the engine characteristics modeled elsewhere,  and rescales them to the correct thrust size.  Those inputs are the modeled vacuum thrust,  the required vacuum thrust,  the throat and exit diameter sizes,  and the effective average half-angle of the supersonic expansion bell. 

There is a “tanks figured on totals,  with headers inside TBD” block.  It has vehicle diameter and a sort of interstage length between the tanks as inputs.  It works out all the lengths and L/D ratios,  and requires the “right” vehicle diameter to keep a full sphere as the smaller tank,  as well as to be consistent with the seating arrangements in the “cabin” block.    The seating is an input number per level,  and number of levels,  consistent with the total number of people.  There has to be room for seating at the input diameter in the “tanks” block,  and the input seat pitch is the spacing between levels.  Note how the empty main tank shells protect the propellants in the header tanks from the effects of entry heating.

The “engine bay” block takes the resized dimensions of the engine (overall rough estimate of length,  and the exit diameter,  and uses these with inputs for number of engines and the spacing requirements for gimballing,  to estimate min dimensions of the engine bay.  Its diameter should never exceed the input diameter in the “tanks” block.

From there,  the “overall vehicle” block puts together these results into estimates for the length and L/D ratio (which ought to be in the 4 to 6 range) of the entire vehicle stack,  and with inputs for entry mass and hypersonic drag coefficient,  estimates the broadside-entry ballistic coefficient. Too low an L/D will get you too low a blockage area and too high a ballistic coefficient.  Too high an L/D is a topple-over risk,  or at least a risk of bigger,  heavier landing legs.

Creating the Re-Sizable Engine Data

I used the “rocket nozzle” spreadsheet file,  worksheet “rocket noz”,  to rough-size a suitable engine and calculate a reliable performance estimate for it.  This was actually one of the first things I did.  This engine burns liquid methane fuel with liquid oxygen oxidizer,  similar to SpaceX’s Raptor and Blue Origin’s BE-4.  These propellants are thought to be manufacturable in situ on Mars.  This entire design study assumes that to be true.

I chose not to push the state of the art,  given the troubles SpaceX had getting to current Raptor-2 performance levels.  This engine is only sized for a chamber total pressure delivered to the nozzle entrance of 2000 psia,  and only a 3:1 pressure turndown ratio,  although this analysis does presume a full-flow cycle with no dumped bleed gas.  The nozzle is assumed to be an 18-8 degree curved bell,  with a throat discharge coefficient of 0.995.  Both c* and r are presumed functions Pc,  using the data shown in Figure 7 as the inputs.  Similar data for other propellant combinations are in the “prop comb” worksheet. 

Figure 7 – The Resizable Engine For This Study

The nozzle expansion was designed at full Pc = 2000 psia,  expanded to 5.97 psia at its exit plane.  This gave us a nozzle right at incipient separation when operated at 2/3 Pc,  at sea level on Earth,  allowing easy open-air testing on Earth.  It is unseparated for that power setting (or higher),  but cannot be operated at lower settings at sea level,  because the nozzle will separate. 

Thrust was sized at an arbitrary 10,000 lb in vacuum at full Pc.  Performance in the near-vacuum of Mars’s atmosphere is indistinguishable from true vacuum performance,  so the vacuum data were used for this study.  There is very little specific impulse variation from 1/3 to full thrust,  reflecting pretty much only the variation of c* with Pc. I used the 2/3 power value of 352 sec as “typical” of operation at any throttle setting.  Thrust and flow rates scale with throat area,  dimensions scale with throat diameter.

Final Note

Most of the spreadsheets used here are part of the course materials that I created for orbits and vehicle sizing.  Only the custom spreadsheet used for vehicle characteristics as calculated here,  is not part of those course materials.  Those course materials are available on the New Mars forums,  in the "interplanetary transportation" topic,  "orbit mechanics class traditional" thread. 

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. 

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.

Scariest Halloween Costume

 

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!  

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.)

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.