Rocket Nozzles

This article is intended to acquaint the nontechnical or non-specialized person with the basics of compressible flow in rocket nozzles,  and how they are sized for rocket engines and rocket vehicles.  Scope here is limited to only conventional bell nozzles.

The author had two 20-year careers,  the first in aerospace/defense new product development engineering.  He is qualified!  The second was mostly teaching at all levels from high school to university,  but with some civil engineering and aviation work,  as well. 

Nontechnical and non-specialized people have difficulty with this topic,  because the behavior of supersonic compressible gases is quite foreign to their experience.  This paper attempts to address that,  as simply as is possible,  so that the behavior is not so foreign as to obscure what is needed to do the figuring. 

A familiarity with high school-level algebra is the only math required!  There are spreadsheet tools to do this kind of figuring,  but it really helps for the user to understand what the spreadsheet is actually doing for him or her.  That’s how to detect input problems.

The converging-diverging passage of a rocket nozzle is quite unlike the garden hose sprayer gun or spray nozzle that most people are familiar with!  On the subsonic side of the throat,  behavior is familiar,  because the flow accelerates in speed (and the pressure drops) as the passage narrows. 

It is the supersonic side,  downstream of the min-area throat,  where behavior is quite unlike common experience.  The supersonic flow continues to accelerate in speed (with further drop in pressure) as the passage grows larger!  Other than that,  the nozzle works to expel a fast jet that creates thrust,  by means of the large pressure drop from upstream of the nozzle out to ambient conditions.  That is grossly the same as the garden hose sprayer experience,  actually.  Just the supersonic-side details are different!

The gases cool off as they accelerate in speed,  because the sum of the heat energy and the flow kinetic energy,  anywhere in the nozzle,  is a constant that pretty much matches the heat energy of the almost-stationary gases upstream of the nozzle.  Energy conservation is not all that unfamiliar a concept,  even for nontechnical people.

Everyone is familiar with the reaction “thrust” of a garden hose,  or more especially that of a small fire hose.  That thrust is the momentum of the ejected stream of water.  The faster it moves,  the bigger the thrust.  The more water is ejected,  the bigger the thrust.  Simple!

In the compressible nozzle,  the momentum of the ejected stream of gas is also part of the reaction thrust,  but there are pressure forces that are also part of the thrust,  unlike the water hose.  The pressure of the gas just as it leaves the supersonic nozzle exit can be quite different from the surrounding atmospheric pressure!  The thrust of a rocket nozzle is the sum of the exit momentum and the pressure forces at the exit plane.  See Figure 1. 

Figure 1 – Fundamentals of Compressible Flow Nozzles

That difference in pressure between the exiting gas stream and the surrounding atmosphere leads to some behaviors of such nozzles,  that would otherwise look incomprehensible to the nontechnical or non-specialized person.  There is a force associated with the exiting gas pressure that adds to thrust,  and a force associated with the surrounding atmospheric pressure that subtracts from thrust.  Both of these pressures act upon the flow cross section area right at the exit plane. 

As shown in Figure 2,  when the exiting gas pressure is greater than atmospheric,  we say that the nozzle is “underexpanded”,  since expansion to just the right size larger exit area,  would reduce that exiting gas pressure to exactly atmospheric,  while at the same time increasing its speed still further.   This is the leftmost image in the figure,  corresponding to a high chamber-to-ambient pressure ratio.  The exiting plume actually spreads out wider after leaving the nozzle exit,  because its pressure really is higher than atmospheric.

For the same geometry,  the “perfect expansion” to atmospheric pressure,  at a slightly lower chamber-to-ambient pressure ratio,  is the second image in the figure.  That exiting plume neither spreads wider,  nor does it narrow,  after leaving the nozzle exit!  The pressure forces add to zero,  leaving only the momentum component of thrust.

The third image shows what happens when the exiting gas pressure is lower than atmospheric,  but not by too much.  We call this “overexpanded”,  because at this pressure ratio,  we would need less expansion of the nozzle passage than we have,  to bring the exit pressure back up to equal to atmospheric. The plume actually does contract some,  after leaving the nozzle exit!  Under certain circumstances,  the indicated oblique shock waves from the exit lip can actually be seen, often as the lead in a series of “shock diamonds”.

Figure 2 – Nozzle Behavior as Chamber to Ambient Pressure Ratio Reduces

Where one gets into trouble is illustrated in the 4^th and 5^th images in the figure,  where the chamber-to-ambient pressure ratio is too low for proper operation.  The oblique shocks first coalesce into a normal shock wave at the exit plane,  then move a bit upstream,  causing flow to separate-off of the inner wall of the nozzle!  The lower the chamber-to-ambient pressure ratio,  the further upstream this shock-separation phenomena moves!  Flow downstream of a normal shock is always subsonic (meaning very low speed),  so there is very little thrust,  once the shock is inside the nozzle and separating the flow from the wall.

The “trouble” one gets into is called “shock-impingement heating”.  Where the shock wave hits the nozzle wall (causing flow separation),  there is a large but very local amplification of the rate at which heat is transferred from the hot gas to the cool wall.  The nozzle can actually burn through and fail,  in a matter of only several seconds,  when this happens! 

The last (rightmost) image in the figure shows what happens when the atmospheric backpressure exceeds about 50-some percent of the chamber pressure.  The throat “unchokes” (goes subsonic),  and flow throughout the nozzle is subsonic.  There is no useful thrust when this happens.  There is almost no useful thrust even when choked,  if shock-induced flow separation occurs.  There is none when unchoked.

Most rocket engines have a set of turbopumps,  with pre-burners of one sort or another to create modestly-hot gases at high pressure,  which then get used to drive those turbopumps.  How this is done varies,  and is what we call the “cycle” of the engine.  

Those details do not matter to the functioning of the rocket nozzle!  All that stuff up to the chamber right before the nozzle entrance is just a “hot gas generator” that feeds the nozzle.  It is the nozzle that creates the thrust and its associated performance with that hot gas. 

The only effect of the engine “cycle” upon that nozzle behavior is whether-or-not any of the turbopump drive gas gets dumped overboard,  without going through that nozzle!  That does reduce the performance ,  even at the same thrust!  This is indicated in Figure 3,  among several other things.  

Figure 3 – How the Engine and Nozzle Work Together to Create Thrust

There are a couple of nozzle efficiency factors that depend upon the exact geometry going through the nozzle.  The effective flow area of the throat is slightly smaller than its geometric area,  because of “boundary layer displacement” effects.  This can be held to a minimal difference,  by using a smooth profile curve through that throat,  from ahead to downstream.  Effectively,  you just need the profile radius of curvature to be about the same as the throat diameter,  in order to get a good,  high discharge coefficient C_D. 

The shape of the supersonic expansion passage,  called the nozzle “bell”,  influences something called the nozzle kinetic energy efficiency factor η_KE.  Curved bells,  like that illustrated,  have half-angles that are large near the throat,  and smaller near the exit lip,  which need to be averaged.  Simple conical bells have only the one half-angle.  Curved bells require careful design using a computer program that does something called “method of characteristics” analysis.  Conical bells of half-angle equal to the average curved-bell half angle,  have exactly the same kinetic energy efficiency,  but are only somewhat longer than the curved bell.  They require no complicated analysis in order to lay out a design!

This η_KE factor measures the effect of having many of the exiting streamlines oriented not exactly aft.  There is a very simple empirical estimate of this efficiency,  computed with the bell average half angle,  as shown in the figure.  It applies to the momentum component of thrust,  but not to the pressure-forces component of thrust. 

One does need to address the subsonic contraction area ratio from chamber to throat!  If this is not large enough,  the flow Mach number at the nozzle entrance may be too high to use the measured chamber pressure as if it were the “total” or “stagnation” pressure for the nozzle flow.  There is a simple correction factor to increase measured chamber pressure slightly,  in order to have exactly the right “total” pressure for the nozzle thrust analysis.

Note in the figure that there is a nozzle massflow,  that depends upon both throat geometric area and its discharge coefficient.  That massflow may not be the massflow actually drawn from propellant tankage,  if there is dumped bleed from the turbopump drives!  It is the massflow drawn from tankage that affects rocket vehicle masses,  so for “rocket equation estimates” of vehicle performance,  the specific impulse needs to be computed from thrust using that total massflow,  not just the nozzle massflow! 

The other factor affecting calculation of the nozzle massflow is the “chamber characteristic velocity”,  usually denoted as “c*”.   That will be discussed below.  Just be aware that experimental values are far more reliable than theoretical thermochemical estimates.

In figuring all these things out,  one needs to be aware that there are two different design applications,  each with its own sizing methods.  Those are “vacuum design”,  for use outside the atmosphere,  and “atmospheric design”,  for use down in the atmosphere.  They are done differently using the same basic math,  just in a different sequence and with different constraints.  See Figure 4. 

We start by determining the “right” nozzle bell area expansion ratio.  For the vacuum case,  this number is assumed from the outset!  For the atmospheric design case,  this is determined by the pressure ratio at the exit,  in one fashion or another.  There are actually 3 distinct options to do atmospheric design sizing. 

Be aware that the very same math will analyze the chamber to throat contraction for us,  determining whether we need to factor-up the chamber pressure measurement. 

Figure 4 – Both Streamtube and Ratio Analyses Get Used First

Vacuum sizing is done to a presumed max expansion ratio, limited only by having the engine (or engines) actually fit behind the stage.  There is simply no such thing as a “vacuum-optimized” design!  Everything about it is constraint-driven,  and constrained even more if gimballing is needed for thrust vector control.  See Figure 5.

Figure 5 – Essentials of Vacuum Nozzle Sizing

Atmospheric nozzle sizing is done in one of three distinct ways,  starting with appropriate ratios of expanded pressure to chamber total.  These all use the same math,  just not in quite the same ways.  This is shown in Figure 6.  

Figure 6 – Three Options for Atmospheric Nozzle Sizing

The option on the left in the figure is “standard” sea level perfect-expansion sizing.  One knows a suitable chamber pressure.  One assumes the expanded exit plane pressure to be exactly equal to sea level atmospheric pressure.  That sets the ratio of expanded pressure to total.  From that comes the exit Mach number,  and from that,  the expansion area ratio.  These three items (and a nozzle kinetic energy efficiency) are needed to get a thrust coefficient,  in turn a way to book-keep where the thrust comes from.

Sea level nozzles have good thrust at sea level,  but their thrust does not increase much,  as you climb to higher altitudes.  Which in turn means the specific impulse does not increase very much with altitude.  They typically have rather low area expansion ratios. 

If you want to average a higher specific impulse as you climb to much higher altitude,  you can obtain it by sizing the expansion ratio to a higher altitude’s ambient pressure (top right),  or by sizing the nozzle to incipient separation at sea level (bottom right).  The penalty you pay for that higher average specific impulse during ascent,  is lower thrust right at sea level,  at liftoff,  when weight is largest!  So,  the design point selection is a tradeoff!  These do have somewhat larger area expansion ratios.

Clearly the compressible streamtube analysis math is crucial to running numbers for a nozzle.  This streamtube math is illustrated in Figure 7.  

Figure 7 – Compressible Streamtube Analysis

This is the analog to V₁A₁ = V₂A₂ in incompressible flow,  that many people have actually heard of,  or actually even used.  The equation is different,  but it is the same fundamental idea!  However,  everything is figured relative to the choked min area at the throat. 

One case of interest is finding the area ratio from a known Mach number.  That is a direct solution.  Just fill in the formula items,  starting with the gamma constants.

The other case of finding Mach number from a known area ratio has no direct solution,  because the equation is what they call “transcendental” in Mach number!  It is impossible to isolate Mach number in the equation,  because it appears in two places under very different mathematical circumstances (different exponents and functional forms). 

For that case,  there is only the iterative (trial-and-error) solution.  Keep guessing Mach numbers until the equation result is the area ratio you really want.  That is where spreadsheet-assist is so useful:  it makes such iteration very easy,  boiling down to just inputting the guesses in one cell and looking at the result in another cell.

The other piece of this math is the set of compressible flow ratios,  static vs total (or stagnation).  Those are shown in Figure 8.  These are “reversible” in the sense that a known Mach number gets you all the ratios,  and a known pressure ratio can be solved directly for a Mach number.  The basic math here is based on total/static ratios,  but their inverses are what we need for thrust coefficient and flow separation.  Those inverses are included.

Figure 8 – The Compressible Flow Ratios

We use the thrust coefficient form of this math to separate the variables,  allowing expansion ratio to be determined before actually sizing dimensions to meet a thrust requirement.  You cannot do that,  working directly in the primitive variables!  That thrust-sizing math based on thrust coefficient is shown in Figure 9. 

Thrust coefficient has two components,  the vacuum thrust coefficient,  and a correction term that reduces it somewhat to the thrust coefficient down in the atmosphere.  The vacuum thrust coefficient is actually independent of the specific value of chamber pressure!  The correction term depends directly upon chamber pressure and ambient pressure,  so that the down-in-the-atmosphere thrust coefficient is also dependent explicitly upon them,  as well.

Once you know the thrust coefficient,  you can use it,  your intended chamber total pressure,  and a thrust requirement,  to find the geometric throat area.  Knowing the expansion (and contraction) area ratios,  lets you define those chamber and exit areas from that throat area!  Very simple,  actually. 

Once you have a throat area,  you can compute nozzle massflow,  adjust it to total,  and compute specific impulse.  That is discussed below.  

Figure 9 – Thrust Coefficient Math Equations

The math for thrust-based sizing is a bit more complicated than simple performance of an already-sized configuration.  This is shown in Figure 10. 

Figure 10 – Thrust Requirement-Based Sizing of Dimensions and Flow Rates

By definition of the thrust coefficient,  thrust is the product of thrust coefficient,  chamber total pressure,  and geometric throat area!  Once you have a thrust coefficient defined,  you can size throat area from a required thrust value and your chamber pressure.  The contraction and expansion ratios then size those areas from your sized throat. 

You can use the sized throat area,  your chamber total pressure,  the c* model for your propellant at that pressure,  and your throat discharge coefficient,  to size the nozzle massflow.  That and the dumped bleed fraction define your total massflow drawn from tankage.  In turn,  that and your sizepoint thrust define your sizepoint specific impulse. 

Computing performance of an already-sized system is even easier,  as is also shown in the figure.  You compute the thrust from thrust coefficient at that altitude and your chamber pressure,  and you already know the total flowrate at that pressure.  Thrust at altitude divided by total massflow rate is specific impulse at that altitude.   Very simple indeed!

Be aware that all of these estimates are computed assuming there is no shock-separation going on in the nozzle bell!  So,  you must check for that!  If it occurs,  your calculated performance data are no good!  Do not use them!

The math predicting flow separation is an old correlation from designing tactical missile rocket nozzles.  It is slightly conservative.  The math is given in Figure 11.

Figure 11 – Math for Dealing With Flow Separation

The use of this empirical correlation is quite straightforward when computing performance vs altitude at any given throttle setting.  The nozzle expansion has a fixed ratio of exit plane pressure to chamber total pressure.  From that,  the correlation determines the ratio of separation backpressure to chamber total pressure.  That ratio and your operating chamber total pressure,  give you the value of backpressure that will risk inducing flow separation. 

If your ambient atmospheric pressure is less than,  or just equal to,  the separation pressure,  no separation occurs and your thrust and performance estimates are good.  If your ambient atmospheric pressure exceeds the separation pressure,  shock-separation will occur,  and your thrust and performance estimates are no good!  Simple as that!

When sizing an atmospheric nozzle for incipient separation at sea level (as discussed above),  you use the empirical correlation in reverse (which is also shown in the figure).  You know a suitable value of your chamber total pressure,  and you literally set the separation pressure equal to sea level atmospheric pressure.  Their ratio determines the expansion pressure ratio exit-to-chamber for your design process.  That gets you a Mach number,  and from that,  the expansion area ratio.  From them,   thrust coefficient is easy to find.

You have to think about your rocket vehicle and where it is flying,  to determine suitable thrust requirements.  Some items typical of launch vehicles are given in Figure 12.  Cases do vary,  though!

Figure 12 – Typical Considerations for Thrust Requirements

For launch vehicles,  you need to accelerate the vehicle at half a standard gee or more,  above the retarding effects of drag and the pathwise weight component.  Such would apply at vehicle masses appropriate to stage ignitions,  where vehicle weight is high.  The half-gee figure is only a rule-of-thumb minimum.  If you achieve lower,  you will definitely “dawdle around” at low speeds near the launch pad burning off lots of propellant,  without it actually buying you very much in the way of flight speed.  Higher gee is better,  but that requires more thrust,  and the engines might not fit behind the stage.  It’s a tradeoff!

Vehicle acceleration also has max values,  especially if crewed,  but a lot of potential payloads have similar acceleration limits.  Those limits might be roughly in the 4 to 6 gee range.  You can always turn off some engines while throttling others,  to stay within such limits.  They would occur when vehicle masses are low,  near stage burnout. 

The nozzle massflow equation uses characteristic velocity c* as the denominator.  You must have a suitable model for this value,  consistent with your propellant combination and design chamber pressure.  In the real world,  c* is weakly dependent upon chamber pressure as a power function.  This is shown in Figure 13.  

Figure 13 – About Chamber Characteristic Velocity (c*)

You must run a thermochemical code (computer program) on your propellant combination at your intended chamber pressure,  and your intended oxidizer-to-fuel ratio,  to determine the resulting combusted chamber temperature and gas properties.  These are theoretical values,  and from them a theoretical c* can be computed with the equation shown.  It will have a very weak power-function dependence upon chamber pressure. 

In the real world,  delivered test c* is always a little less than the theoretical value,  by a factor we call the “c* efficiency”.  This factor also typically has a weak power-law dependence on chamber pressure.  Therefore,  the actual experimental delivered c* is best modeled as a weak power-law dependence upon chamber pressure,  with an exponent that is usually crudely in the vicinity of 0.01. All of this is shown in the figure.

In Figure 14 is a table of values for PR = Pt/Pc vs Mach number,  including values for Ac/At,  created with the usual factors,  for gamma = 1.2 as “typical”.  Plotting Pt/Pc vs Ac/At reveals the importance of allowing for non-zero Mach number at station c (the aft “chamber”,  right before the nozzle entrance). 

Pc is always measured on real engines as a simple static pressure tap.  This is the total pressure fed to the nozzle only if the Mach number of the flow in the chamber is trivially close to zero.  For the recommended and often-observed Ac/At ratios,  this Mach number is simply not trivial,  so the Pt/Pc ratios are not trivially close to 1!  The error incurred by using Pc as Pt would seem to range from about 1% to 6%.  Pt = Pc * (Pt/Pc for the Ac/At ratio).

Figure 14 – Why Accounting for the Contraction Ratio Is Important

For an engine with a maximum nominal chamber pressure of around 3000-4000 psig in test,  one might select a pressure transducer of nominal 5000 psig capability at the very least,  which might have an accuracy of 0.25% of full scale.  That would be an expected error of 12.5 psi.  That is the inherent uncertainty,  within which one simply cannot distinguish measurements. 

For 3000 psig Pc,  that 12.5 psi is 0.42% error,  and for 4000 psig,  it is 0.31% error.  Most of the Pt/Pc error factors in the figure are very much larger than that,  so correcting for Pt/Pc before doing a nozzle analysis,  really is crucial for getting accurate results!

To Sum Up

Everything shown here is basically pencil-and-paper calculation stuff,  using the algebra equations given in the figures.  However,  this is better done with spreadsheet software,  to make iteration much easier!  In particular,  the computation of exit Mach number from the nozzle area expansion ratio is inherently iterative. 

The latest and best version of my own spreadsheet for this is the Excel spreadsheet file “liquid rockets.xlsx”.  It has 3 worksheets,  one the nozzle-sizing work space,  one has a compressible flow streamtube tool for relating Mach number and expansion ratio,  and there is one that is a propellant data library.  There is a “.PNG” file that goes with it,  as the template for your results report.  You just copy-and-paste your results into a copy of it. 

Figure 15 is an overall view of the nozzle-sizing worksheet,  where it is too small to read things in this view.  The main working area is top left across to the top center,  the results to be copied are top right,  and there are tables and plots of altitude performance across the bottom. 

Figure 16 shows the compressible flow tool worksheet that supports this.  You just iterate your Mach number until you get the desired area ratio,  then copy the pressure ratio for pasting into the main working space.   Figure 17 shows the propellant data library worksheet.  You just copy what you need,  and paste it in where it goes,  in the main workspace space. 

Figure 18 shows just that portion of the nozzle sizing worksheet where you actually do your sizing.  It is large enough to read easily.  Figure 19 shows just that portion of the nozzle sizing worksheet where your results are summarized.  This is what you copy,  and then paste it into the results report. 

Figure 20 shows an image of the “.PNG” file that you make a copy of,  and then paste your results into it,  and finally do some minor final edits as needed.  This “.PNG” file was drawn in the old 2-D Windows “Paint” software,  which is where I do my copying and pasting and editing. 

Figure 15 – Overall View of the Main Nozzle-Sizing Worksheet in the Spreadsheet File

Figure 16 – Image of the Compressible Flow Tool Worksheet

Figure 17 – Image of the Propellant Library Worksheet

Figure 18 – Image of the Main Working Area of the Nozzle-Sizing Worksheet

Figure 19 – Image of the Results Summary Block on the Nozzle-Sizing Worksheet

Figure 20 – Image of the “.PNG file” Results Report Into Which Results Get Pasted

Such spreadsheet tools already exist and are freely available to interested persons.  In particular,  a good spreadsheet embodying the rocket nozzle math calculations,  is available as part of the course materials included with the “orbits+” course materials on the Mars Society’s “New Mars forums” website.  These are available to anyone for free download.  That rocket spreadsheet is same “liquid rockets.xlsx” that was just described.

You go to the forums website newmars.com/forums/.  Go to the “interplanetary transportation” topic and select the “orbital mechanics traditional” thread.  The links to all sorts of lessons and multiple spreadsheets are in those postings.  These go way beyond just rocket nozzle sizing and performance,  to include orbital mechanics,  and even entry,  descent,  and landing.  All these materials are located in an online dropbox accessed by those links. 

The author has other materials and courses available directly from him.  Contacting him by email is preferred at gwj5886@gmail.com.  He has a blog site with all sorts of stuff posted,  much of it technical.  That is http://exrocketman.blogspot.com.  You may copy anything you like from that blog site.  He also has a presence on LinkedIn,  and another on Youtube under the name “exrocketman1”.  

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Search code DDMMYYYY format      01022026

Search keywords                                       space program

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Appendix – Where the Thrust Coefficient Comes From

The boundary layer displacement factors are all very close to 1 and so divide-out of all the Ae/At ratios.  It appears explicitly only in the nozzle massflow equation as C_D,  not in C_F.

An Australian’s View of Our Situation

My wife found this and sent it to me on the 18^th of January (2026).  It is quite accurate and quite good.  I cannot vouch for who this person really is or where this originally came from.  But it does seem to be quite to the point! 

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An Australian's view of our situation 

Volodymyr Vlad Kunko

Alright, I’m saying this as an Australian who is absolutely sick to death of watching the world hold its breath every time this blabbering blubbering blithering blustering buffoon opens his grotesque mouth.

You see folks, as far as I can tell, from the outside, this is what it looks like: America has elected a man who talks and behaves like a megalomaniac, and the rest of the planet is supposed to just trust that he won’t completely lose his grip on reality and drag us all into catastrophe.

You want to steal Greenland.

You want Cuba to “make a deal before it’s too late”. 

You talk about bombing or invading Mexico.

You kidnap a President and knock off the people’s oil in Venezuela.

You joke about annexing Canada like it should be a shopping centre car park you can just claim because you feel like it.

Do you have any idea how insane that sounds to the rest of us?

This isn’t tough talk. This isn’t strategy. This is a deeply unstable old man threatening sovereign nations like he’s flipping over a Monopoly board because he’s losing. This is not normal behaviour. This is not leadership. This is not strength. This is a walking, talking international crisis.

And Americans, this is where it comes back to you. Not just MAGA, not just the people who voted for him, all of you. Because when the President of the United States starts talking about kidnapping leaders, annexing countries, and issuing ultimatums like a mob boss, the rest of the world doesn’t get a vote. We just get the consequences.

You don’t get to shrug and say, “Well I didn’t vote for him.” That might fly at a dinner party, but it doesn’t fly when nuclear powers are watching this circus and recalculating their own red lines. This is your system. Your presidency. Your responsibility.

From the outside, it looks like America lit the fuse and then wandered off while everyone else stands around the bomb wondering who’s going to cut the wire.

And let’s be brutally honest. This man is nearly 80. He’s frail. He’s clearly deteriorating. He is not some long term visionary playing chess. He’s at the end of his lifespan and acting like nothing matters after him. That is the most dangerous type of leader there is. A man with nothing to lose and an ego that demands constant feeding.

Why should the rest of the world pay for that?

Why should families in Europe, Asia, Australia, South America, anywhere, have to worry about war, trade collapse, energy shocks, or global instability because America couldn’t get its own house in order?

This is not about left or right anymore. This is about basic sanity. This is about stopping a psychopath before he does something irreversible. Because once a war starts, once a country gets invaded, once alliances fracture beyond repair, you don’t get a reset button.

So yes, this falls on Americans. You got the world into this mess, and you damn well better roll your sleeves up and get us out of it. Impeach him. Remove him. Contain him. Do whatever your system allows, but do it fast.

Because the rest of us just want to live our lives, raise our families, pay our bills, and not wake up one morning to find out World War Three started because an unhinged old man wanted to feel powerful one last time.

This isn’t funny anymore.

It isn’t theatrical.

It isn’t tolerable.

Get this lunatic under wraps before he ruins it for everyone.

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Search code                  19012026

Search keywords         bad gov’t, idiocy in politics, treason

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Assessment of Completeness: Imposition of Trump Dictatorship

Everybody has seen the appalling misbehavior of ICE in Minneapolis,  and all over America.  Several people have been killed by them.  Nearly everything they do involves violence at one level or another.  ICE has been weaponized and expanded by Trump into what amounts to a secret police force,  to intimidate people and make some people (so far only the demonized immigrants) “disappear”. 

And there are “detention centers” that are really nothing but concentration camps,  specifically built to house those awaiting being “disappeared” by deportation.  Some inmates have died from the squalid conditions and the medical neglect in those camps.

Everyone has seen the giant corporate billionaire heads sucking up to Trump and going along with anything he wants,  no matter how outrageous,  so that he will not cause them trouble.  Musk,  infamous as he was with his destructive government job-cutting,  was a temporary exception,  but has since settled back into his same Trump-supportive role,  apparently to protect his businesses.

Everyone has seen National Guard troops sent to multiple cities by Trump,  ostensibly to help fight out-of-control crime.  But the crime statistics show that crime in those cities,  while bad,  was actually decreasing,  before the troops ever arrived.  Every one of those cities had leadership that were not Trump supporters!  No cities led by Trump supporters had troops sent to them!  Pretty telling,  is it not? 

Now Trump is threatening to send active-duty regular army troops to cities,  starting with Minneapolis,  because of the large-scale protests there.  Folks in that city are mostly against him,  his policies,  and his misbehaving secret police.  Surprise,  surprise!  Using the army to do police work and intimidate opponents is typical of dictatorships.

That’s all bad enough,  but it’s even worse than most of you know!  I personally have identified some 10 hallmarks of dictatorships.  7 of them are already fully in place in America right now!  The other 3 are partly or mostly in place.  Soon not just the demonized immigrants are going to be “disappeared”.  Mark my words!

Meanwhile our “fearless leader” has now been making real war in the Caribbean region,  and he is making economic war (with his tariffs) or threatening real war,  against our friends,  neighbors,  and allies,  to get whatever he wants!  He is doing all this evil without being held accountable by anyone!  Not Congress!  Not the Supreme Court!  Not the broadcast news media anymore!  No one!  Also typical of dictatorships.

Look at my assessment and judge for yourself.  It should scare the ever-loving hell out of you!  It does truly scare me! 

Be aware that I have repeatedly messaged my Senators and my Representative about this nearly-completed dictatorship.  To the best I can determine,  they have done absolutely nothing to stop this!  Apparently,  they value staying in office as part of the Trump dictatorial regime,  above their jobs protecting our freedom!  All 3 belong to a formerly-great political party that has since become nothing but a cult of personality around Trump,  so far as I can tell,  and I am not alone in that judgement!  Such a cult of personality is a thing we have seen before,  in 1930’s Germany!  And that turned out very badly for all concerned.

The mid-term elections are your last possible chance to remain free,  short of armed revolution in the streets!  Unless,  they successfully get stolen by the Trump-ordered gerrymandering that we have all already seen! 

Don’t ever say that I did not very clearly warn you! 

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Search code                  18012026

Search keywords         bad government,  idiocy in politics,  treason

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Recent Letters to Federal Reps

These are my most recent messages sent to my federal representation over the behaviors that I see done by the Trump administration.  These messages speak for themselves:

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Trashing allies, etc.                                                 169 words

Greenland demands?  I am quite tired of seeing Donald Trump trash our allies!  This threatens our NATO partners at a time when Putin’s Russia has become ever-more-ambitious to take back former Soviet Republics,  some of which are NATO members now.   Even just weakening NATO at such a time is treason of the aid and comfort type,  and you know that!  And Trump has already done that!  Now he threatens Denmark and Greenland,  for no good reason,  making that treason worse.  And,  he has been walking all over the Constitution,  consolidating all power into the Executive branch,  and weaponizing its various offices to persecute his opponents.   

You swore in your oath of office to protect and defend the Constitution,  against all enemies,  foreign and domestic.  We have a domestic enemy and evident traitor in the White House,  who therefore presents a clear and present danger to our government,  our Constitution,  and our democracy.  Fulfill your oath!  Do something about him!  This is not about politics!  The country must come first!

Verified all 3 got it                                                    sent 1-7-2026

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Secret police evils                                                   220 words

Trump has weaponized ICE into an aggressive secret police force that detains any Hispanic or black people it finds without due process,  and also anyone who so much as protests what is going on!  They just shot and killed a protester in Minneapolis,  whom they tried to drag from her car,  without even having been there a full 24 hours!

The alleged illegal immigrants (most are legal these days,  but that is ignored) are detained without due process,  and housed in concentration camps (a more precise name than “detention center”) awaiting deportation without due process.  Some have died from the squalid conditions in these concentration camps.  Those deported go to infamous foreign prisons,  with the intent that there,  they are to die.  There are still some roadblocks in only some courts,  but once those are overcome,  more than just immigrants will “disappear” that way!  Mark my words!

Secret police forces to “disappear” people,  and concentration camps in which to hold them,  are two of my 10 hallmarks of dictatorship,  and they are pretty much in place now!  I see no real difference between what is going on here and now,  and what went on with Stalin’s KGB,  or Hitler’s Gestapo and SS.

I want an answer from you!  Why have you not resisted the imposition of these evils of dictatorships?

Verified all 3 got it                                                    sent 1-7-2026

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Multiple Trump treasons                                      268 words

Trump took office,  stopped US aid to our ally Ukraine,  and removed all sanctions against Russia.  Russia has since pounded Ukraine,  committing war crimes of targeting civilians,  while Ukraine ran out of weapons,  since only Europe’s aid is not enough.  Now Trump’s “peace process” is forcing our ally Ukraine to surrender to Putin’s demands (Putin’s Russia being our ever-so-clear enemy).  How is that NOT treason of the aid and comfort type on Trump’s part?

Trump has been trashing our allies,  particularly our NATO allies in this term,  but also in his first term!  Weakening the NATO alliance in any way,  when we all together face Putin’s Russia as a threat,  as well as Xi’s China,  is doing what Putin wants to do but cannot:  destroy NATO.  How is that NOT treason of the aid and comfort type on Trump’s part?

Threatening to invade Greenland to take it from its people and from our NATO ally Denmark,  possibly by force,  is a direct attack upon our NATO ally,  and thereby upon the entire NATO alliance.  Such an attack would destroy it!  There is absolutely no excuse for this:  we could easily add more bases in Greenland,  in cooperation with our allies which would be to our mutual benefit,  against both Russian and Chinese expansion into the Arctic.  This is destroying NATO for Putin,  which is TREASON of the aid and comfort type on Trump’s part!  There is NO OTHER possible interpretation!

I want an answer from you!  Why do you continue to enable this very-evident traitor to commit multiple treasons?   Does that not render you complicit in his treasons? 

Verified all 3 got it                                                    sent 1-12-2026

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Trump administration lies                                   253 words

There are lies on US government websites about vaccines.  There are lies by both commission and omission on government websites about climate change.  There are similar lies on government websites about renewable cleaner energies.  Trump,  Noem,  Vance,  and others,  all lie in public about what just happened in Minneapolis,  despite the videos contradicting them!  Trump still lies about the January 6,  2021,  insurrection,  despite all the imagery available that contradicts him,  and he pardoned all the insurrection’s perpetrators,  some of whom have gone on to commit other crimes! 

Trump lied when he initially said the Venezuela incident was to stop drugs,  after he had just pardoned another country’s leader serving time for the same crime.   After exposure of that hypocrisy,  he now sort-of admits that the Venezuela thing was only about the oil. 

Why should we believe any person in this Trump administration who says anything about anything at all?  Lying as part of the control of all public information is one of my 10 hallmarks of dictatorship.  With all the corporate self-censorship now in place to please him,  that control of public information seems to be mostly in place.

As far as I can tell,  you have done absolutely NOTHING to stop any of this!  Indeed,  you evidently and repeatedly vote to enable him to do whatever he wants to do,  no matter how wrong it is! 

I want an answer from you!  Why do you enable Trump to do these evil things?  Does that not make you complicit in his crimes?

Verified all 3 got it                                                    sent 1-13-2026            

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Undeclared wars                                                      115 words

First there was Venezuela raid,  which turned out to be simple aggression to take the oil.  “Narco-terrorist” was a made-up lie of a term to “justify” doing it.  Now there are threats of war against Columbia,  Mexico,  Cuba,  Iran,  and even Greenland.  Only one of these is a terrorist nation (Iran),  and only Iran presents any possible threat of attack.  Except for Iran,  this is clearly very far outside any possible interpretation of any war powers act delegating the decision to wage war to the President!  Trump is already behaving like the dictator that I have repeatedly warned you about!  I want an answer:  when will you grow a spine and act to stop him?

Verified all 3 got it                                                    sent 1-13-2026            

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All of these evil behaviors point toward what the following cartoon illustration says.  Trump recently met with the other two dictators,  and no one knows what they really discussed.  They allowed no witnesses. 

I have repeatedly messaged my representation about Trump imposing a dictatorship upon America,  and about his multiple treasons.  They have done nothing to stop it,  so far as I can tell!  Which means they are part of the problem and are complicit in all these crimes. 

America,  wake up!  Rise up and overthrow these bastards before it is too late! 

You are now only months away from being out of time to act! 

You must outvote the gerrymandering that was intended to steal the November 2026 elections,  to stop this evil!  That is your very last chance!

Or else it will have to be armed revolution in the streets!

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Search code DDMMYYYY 13012026,  search keywords bad gov’t, idiocy in politics,  treason

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Update 1-15-2026:  This just below is a copy of the latest letter I sent.  Again,  it speaks for itself!  

You can do the same thing that I have done:  email your messages to your representation's Washington offices.  Just go to their official government websites.  The instructions for how to email a message are there.

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Treason over Greenland                                       195 words

Trump seems determined to take Greenland on the flimsiest excuse.  We do NOT need political control of that island!  We just need to negotiate with our friends and allies some more US bases in Greenland,  from which to project our power into the Arctic.  Which would also preclude any Russian or Chinese moves onto that island.  All without damaging our alliances!

Trump threatening to take Greenland by force from a NATO ally,  is quite literally the US threatening to make war against a NATO ally (Denmark).  Which if done,  would effectively destroy NATO!  Destroying NATO is something our enemy,  Putin’s Russia,  wants to do,  but cannot.  Nor could his predecessors in the old Soviet Union.

Here,  over Greenland,  Trump is quite apparently trying to destroy NATO for Putin!  That is so very clearly aid (and inherently comfort) to our enemy,  and THAT is TREASON,  of the aid and comfort type,  as defined in the Constitution!

Fulfill your oath of office!  Put a stop to this treason,  by law,  by impeachment and conviction,  or both!  Or else be complicit in Trump’s treason! 

And if you prove complicit,  know that I will not be silent about that!

Verified all 3 got it                                                    sent 1-14-2026

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About Venezuela

This was originally submitted 4 January 2026 to the Waco "Tribune-Herald" as a column on the op-ed page.  I am on their board of contributors.   They ran it Thursday 8 January 2026,  with very few edits.  The original as-submitted version is posted here:

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About Venezuela                      1-4-2026         

The surprise raid into Venezuela that captured Maduro has certainly created an uproar!  This was the final event of a pressure campaign to oust him.  It started with economic sanctions,  and recently escalated into drug-running boat strikes.  Then it escalated into sanctioned tanker seizures.  When those did not work,  a military raid ousted him.

Why oust him?  Optimists would point to (1) the end of a vicious dictatorship that ran a lot of drug smuggling to support itself,  or (2) enabling denial of Venezuelan oil to enemies like China,  Russia,  and Iran.  Or both.  Pessimists would say it’s simply about gaining control of Venezuelan crude oil.  Both are probably right,  to one extent or another.

Were these things the right things to do?  Now that’s the real question,  and it is very complex,  as are the answers.

Economic sanctions are quite legal under both US and international law,  and a lot of countries do this,  with varying success.  US sanctions against Venezuela were part of what drove Maduro to run drugs.  US sanctions against Russia over Ukraine were actually working fairly well,  until Trump abruptly removed them upon starting his second term (which is another topic for a whole different article).

Stopping drug smuggling boats at sea is quite legal under US and international law,  including the centuries-old so-called “law of the sea” regarding unflagged or false-flagged vessels.  It is legal only when done the way the US Coast Guard has done it for decades:  stop the boat,  board it,  and see who and what are in fact on board,  and then deal with that.   

The boats in question here may or may not be drug-runners (which if they are,  are criminal scum,  to be sure).  Most often,  they prove to be.  But not always!  And even if they are criminals,  they are civilians,  just like the Mafia and any other criminal organizations.   So,  destroying those boats on sight is a violation of US law,  international law (including the “law of the sea”),  and the US Code of Military Justice.  Killing survivors in the water ranks right up there with war crimes.  And that is exactly what happened on that first boat strike!

Some of those boats can now out-run the Coast Guard cutters!  The right way to counter that,  would be to pair the Coast Guard cutter on such duty,  with a Navy frigate carrying an armed helicopter.  The helicopter can easily catch the boat,  and can target its motors with machine gun fire to stop it.  Those motors are a legitimate target that is not civilians!

But that’s not the way it was done!  Killing people on sight with missile strikes is a whole lot more dramatic chaos to put on the evening news,  and a chance to get political faces before the cameras.  Killing people for political publicity!  How heinous is that crime?

Now,  the tankers were boarded from helicopters and stopped.  That was doing it “right”!  I suspect this was driven more by the size of those ships,  than by any desire to do this legally,  but that is just my opinion.

Now we come to the raid that captured Maduro.  This was executed very adeptly and quickly by the US military forces,  with few injured and no dead on our side.  It was “in and out”.  That’s a very well-executed mission,  and perfectly legal under US law and the US Code of Military Justice.  It is illegal under international law,  but we have done it many times,  especially in Latin America and the Caribbean.  We are not alone in doing this.

This raid captured Maduro and his wife,  and has brought them back to the US for drug charges and trials.  It did not topple any of the rest of Maduro’s government in Venezuela!  They are still in place,  and his vice president has been sworn in as their president, in an administration that is still a dictatorship.  We will see if that dictatorship is ever changed.

Meanwhile,  according to Trump’s press interview,  we are “sending in the oil companies” to run the Venezuelan oil industry.  That being the one big chunk of their economy,  you will effectively have corporations running the country.  Giant corporations tend to value money above all,  and by far,  as we all already know.  It is my opinion that this will not turn out well for the Venezuelan people.

And all of that is why my opinion is that this raid (and the entire pressure campaign) was more about the oil,  than anything to do with either freeing the Venezuelans from their oppressive dictatorship,  or with actually trying to stop the drug trade.

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search code 08012026

search keywords bad government,  idiocy in politics

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Landing Pads for Rocket Vehicles

For vehicle designs that do not meet rough-field criteria (Ref. 1),  they should not be sent to the lunar surface,  until a hard-surfaced,  strong landing pad surface has been constructed.  The same applies to Mars,  most of its surface is similarly weak. 

Such involves a deep excavation,  back-filled with size-graded rock of decreasing sizes toward the surface,  with the rocks in direct touching contact,  and the void spaces in each layer filled with appropriate hard-packed fines,  to include sands and dusts.  The last layer of fill is gravel with sand and dust fines,  on top of which the final finished paved surface is laid.  This is shown in Figure 1: 

Figure 1 – How Roadbeds and Foundations Are Supported Upon Softer Ground

There is a load-spreading effect of the backfill-rock substrate,  which is how you spread a concentrated large force on the surface,  onto a much larger area at the bottom of the excavation.  This behavior reduces the applied bearing pressure at the surface,  to what the regolith or soil below the excavation,  can actually withstand. 

Estimates of the proper load spreading angle vary,  but the usual civil engineering practice assumes angles from about 30 degrees to as much as 45 degrees,  with the usual default being 34 degrees.  Angles as low as 26 degrees have been seen experimentally,  but are not common. 

For this rocket landing pad application,  the author recommends (in the absence of any real off-world experience) something like 30 degrees,  and an allowable soil bearing pressure that is around factor 2 below measured failure pressures.  That sets the required excavation depth for a given load force with a certain surface footprint,  as Figure 2 shows:

Figure 2 – Excavation Depth Depends Upon Pressure Reduction Ratio and Spread Angle

Bear in mind the virtually all the regolith on the moon resembles nothing so much as “sand-dune sand” here on Earth.  Fine dry loose sand here on Earth has a minimum allowable bearing pressure of about 1 US ton per square foot,  equal to about 0.10 MPa.  The max allowable value is only twice that,  and the safety factor below failure is also only about 2 (meaning the 0.1 MPa allowable fails at about 0.2 MPa,  and the 0.2 MPa allowable fails at about 0.4 MPa).  Most of Mars’s regolith is similar.  The rocks embedded in these regoliths generally do not touch,  and so offer no reinforcement,  unlike a properly-built roadbed.  

These heavy load-bearing pad foundation construction techniques described here,  were developed and used with great success by the Romans building roads,  and are still used today for Earthly road-building.  Unfortunately,  doing it "right" is quite expensive,  so today our roads are built with inadequate excavation and inadequate quantities and size-grading of the rock fill underneath the paved finish surface. 

So,  most roads today do not hold up nearly as well as the old Roman roads.  Big heavy trucks do the most damage,  by crushing the inadequate roadbed (and pavement) down where the wheels track,  one after the other,  thus "rutting" the road.  Rain fills these ruts,  presenting a loss-of-control danger to automobiles,  if the water depth exceeds the tread depth on the tires.  This kind of roadbed damage is illustrated in Figure 3,  and is not properly repaired by simply resurfacing the pavement:

Figure 3 – What a “Crush Rut” Looks Like

The photo was taken right near my driveway on the country highway that runs by my house and farm.  It has so very clearly never been properly repaired!  This highway is posted as “58,420 lb max gross weight” (about like a 10-wheel dump truck),  but I see 18-wheel big-rigs out here all the time,  and the big-rig grain trucks during harvests appear to far exceed the statewide 80,000 lb gross weight limit!  A rough guess puts them in the 100,000-120,000 lb range,  pretty close to the original factory gross weight limits for most of them.

This kind of back-filled excavation construction,  whether here on Earth,  or off-world on the moon or Mars,  is all "dirtwork" to well-known civil engineering standards,  except for the final pavement finish surface.  To land rockets,  that finish pavement must be both heat-resistant and blast-erosion resistant!  Concrete usually requires some repair after a rocket landing because of heat-induced spalling,  but concrete as we know it is simply unavailable on the moon (or Mars). 

Some sort of tough,  resistant “tiles” laid like close-fitted flagstones might work on the moon or Mars.  But they need to be thick,  and as heavy as possible,  in order not to get ripped away by jet blast shear forces!  It would help if there were projections from their bottoms that penetrated into the top gravel-and-fines layer of the bedding fill.  This is an approach option that needs development:  it is not experience-proven,   and therefore not yet ready to apply!

However,  laying such “tiles” directly upon the weak regolith will NOT work!  They will simply be crushed down into it by the large concentrated load forces,  and also tilted by those same forces acting off-center!  That kind of behavior is just unacceptable,  especially since a rocket that topples over is a rocket that fatally explodes!

References

(1 (1)    “Criteria for Rough-Field Landings” by GW Johnson,  posted 12-01-2025

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Search code                  01012026

Search keywords       space program, Mars

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Update 2-1-2026:  In response to questions from friends,  here is another representation.  The excavation angle has nothing to do with the landing load-spreading angle.  That is why the allowable landing area is less than the paved area over the excavation.  Changes are in red.