Rocket Engine Calculations

Update 5-31-2025:  I have since replaced the calculation spreadsheet used here in this article with a better version.  It does the same things,  but is reorganized to make results reporting easier.  It is "liquid rockets.xlsx",  available for free download,  along with its user manual,  from the Mars Society's New Mars forums,  at New Mars.com/forums/.  Look in the "Acheron Labs" section,  "Interplanetary Transportation" topic,  and scroll down to the "Orbital Mechanics Class Traditional" thread.  The first several postings there have links to this rocket spreadsheet stuff,  and a whole lot more!  The rocket engine spreadsheet is just a part of a whole self-taught class on 2-body orbital mechanics of ellipses,  empirical stuff,  velocity requirements,  engine performance,  and vehicle sizing.  Even a simple spreadsheet model for reentry is part of that.  

Update 11-24-2023:  corrected an error in figure 7 brought to my attention by a commenter. 

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These are simple formulae,  spreadsheet-automated for easy iteration.  Anyone can do this,  if they have a proper guide.  The actual sequence of use is not obvious from typical textbook presentations,  but that is explicitly covered here.  These formulae were arranged in the proper sequence and automated with an Excel spreadsheet file named “liqrockets.xls”. 

There are several worksheets in this spreadsheet file.  Some are data libraries,  others are parts of the calculation sequence.  The best worksheet for either sizing,  or reverse-engineering,  rocket engines is “allin1des”,  so named to recognize that all of the calculation sequences are in the one worksheet.

The examples used here are calculations done while reverse-engineering the SpaceX Raptor 1 and 2 engine versions,  both the sea level and vacuum variants.   The addendum addresses a -2 vac variant.

Basic Notions                   

The typical liquid-propellant engine whose ballistics need calculating comprises a chamber,  a contraction-to-a-throat,  the min-area throat itself,  and an expansion bell,  as shown in Figure 1.  Not shown is the turbopump assembly and pre-burners that drive it.  The chamber pressure of interest is the stagnation pressure just ahead of the contraction.  

Figure 1 – Basic Notions

All the turbopump-related stuff is higher-pressure,  and located upstream.  The exact “cycle” of the turbo-pump assemblies and their drive systems are just not applicable to the engine performance ballistics,  with one exception.  Some cycles tap gas,  drive the turbopumps with it,  and then dump that gas overboard,  without it going through the nozzle.  Others more recently do not. 

We need a figure for the percent of propellant drawn from the tanks that is dumped overboard instead of going through the engine nozzle.  For the rocket equation to work correctly estimating vehicle performance,  the engine specific impulse (Isp) must reflect the propellant massflow drawn from the tanks,  not just the massflow that went through the nozzle! 

The engine performance ballistics then simply reflect the nozzle area ratios and dimensions,  the chamber area and dimensions,  and the expanded pressure at the nozzle exit versus the ambient atmospheric back pressures.  There is a nozzle massflow associated with that,  and you must account for the bleed gas dumped overboard,  to actually get the massflow drawn from the tanks,  which is what you need for calculating the correct value of Isp.

There are also some empirical rules of thumb for some of the less important variables.  These get you into the right ballpark.  They do not really affect thrust and Isp much at all,  but they do get you fairly realistic dimensions.  What I show here is how you rough-out a design for more detailed analysis!

Nozzle Analysis               

We start with nozzle analysis.  These calculations are based on the compressible isentropic flow of an ideal gas.  This is the Mach number – area ratio stuff that is so well documented in NACA Technical Report 1135 “Equations Tables and Charts For Compressible Flow” (1953) for air.  We cannot use the NACA 1135 tables for rocket engines,  because our hot combustion gases have a different specific heat ratio than air does.  So we have to use the equations for compressible flow,  with an appropriate specific heat ratio,  and do the calculations directly.  See Figure 2.

In the figure,  the equations for the static temperature and static pressure distributions are shown in terms of Mach number down the nozzle (assuming choked flow Mach 1 at the min area throat).  The compressible streamtube-area equation is also shown,  which is how one relates nozzle local area to local average flow Mach number. 

Note all the factors made up from specific heat ratio g in the figure,  used as coefficients and exponents.  You need a good value,  and you cannot use air’s g = 1.40.  This is best computed from a thermochemical calculation for your propellant combination,  at your intended chamber pressure level.  However,  for nearly all rocket propellant combinations,  a guess of g = 1.2 is a very,  very close guess!

The definition of the thrust coefficient C_F is the nozzle thrust divided by the chamber (stagnation) pressure Pc and min throat geometric area At.  There is a momentum term and a two-part exit plane pressure term.  The two parts of the pressure term involve the expanded static pressure at the exit plane,  and the surrounding ambient atmospheric pressure,  most often termed the “backpressure”. 

If you have used the compressible flow analysis,  you know the exit plane Mach number,  and the ratio of exit plane static to chamber pressure.  You also know your expansion area ratio Ae/At,  and the atmospheric backpressure.  You end up with an equation for the vacuum thrust coefficient C_Fvac which is independent of atmospheric and chamber pressures,  and a correction term involving the actual chamber and atmospheric pressures.  The difference shown is the operating thrust coefficient C_F.

As indicated in the figure,  you also have to modify your nozzle analysis for two real-world effects:  (1) the boundary layer along the wall reduces the effective flow area slightly below the geometric value,  and (2) the exiting streamlines of the flow are not all parallel to the nozzle centerline. 

Because the ratios of effective to geometric area are so similar at throat and exit (and everywhere else),  they “divide out” of the area ratio,  as indicated in the figure,  and so you can just use the geometric area ratio for your calculations,  at any station down the nozzle.

The off-centerline streamline directions do not cancel out.  Things are “perfect” on the nozzle centerline,  and “worst” right at the nozzle wall.  Momentum is a vector quantity in physics,  so the cosine component notion applies here.  As it turns out,  the average of 1 and the cosine of the nozzle wall angle is a very,  very good empirical estimate of the streamline divergence factor we need to apply to the momentum term in the thrust,  as indicated in the figure.  It does not apply to the two-part pressure term in thrust,  which is why it is located where it is,  in the C_Fvac equation.

Figure 2 – Nozzle Analysis Using Compressible Isentropic Flow Analysis

The boundary layer displacements cancel-out in the area ratio,  as indicated,  but not in the massflow equation that involves Pc,  At,  and the ratio of effective to geometric area at the throat.  This effective area ratio is termed “discharge coefficient” (C_D),  and is determined experimentally in calibration flow tests.  It is usually quite high for a “well-designed” nozzle:  in the 0.98 to 0.995 range.  The massflow equation where this is used is discussed below.

The nozzle half angle “a” is a simple constant value in conical nozzle designs.  In curved bells,  it is usually computed as the average of just-past-throat and exit-lip values.  Thrust will vary with altitude because of the backpressure portion of the pressure term in thrust.  This term acts to reduce thrust,  but it zeroes as you go into vacuum.  At low altitudes there is another real-world limit,  when the backpressure is excessive relative to the exit plane static pressure.  If the backpressure is too high,  the flow separates (detaches from the wall).  This not only sharply reduces thrust,  it also endangers the survival of the engine from a regenerative cooling/heat transfer point of view.  It is imperative to avoid separation.

There are many empirical ways to estimate the separation backpressure for a design.  I use a very simple correlation developed for the conical nozzles used most often in solid rockets for missiles.  It is only slightly conservative,  for those designs.  Curved bells are a bit more resistive to separation than straight conical bells,  because the exit lip angle is lower for the curved bell design.  So my simple correlation is a tad more conservative for curved bells,  but still in the ballpark.  The proof is experimental test!

               Psep/Pc = (1.5 Pe/Pc)^0.8333             empirical separation criterion

If you know your operating Pc,  and you know Pe/Pc from your nozzle analysis,  then you use the separation criterion to estimate Psep/Pc,  and thus from it and Pc the expected separation backpressure Psep for your design.

Nozzle Massflow Model

The nozzle massflow equation,  which presumes a choked throat (Mach 1 at At),  was not given in any of the figures,  but is given here:

               w  =  Pc C_D At g_c / c*,  where g_c is the gravity constant that makes the units consistent

In this equation,  c* is the chamber characteristic velocity,  which is computed from chamber stagnation temperature and gas properties as indicated in Figure 3.  There is also a c* efficiency,  usually quite high,  that causes real-world c* to be a few percent short of the values computed by theoretical thermochemical methods. 

Both the theoretical c* and the c* efficiency are pressure-dependent upon the value of Pc.  The best empirical model of this,  is the power function of pressure as indicated in the figure.  Experimental test is the best guide to c* values.  Done at multiple pressures,  the exponent in the power function can be determined.  Thus experimental c* varies with chamber pressure Pc in an easily-computed way.

Not shown in the figure is a model for r,  the ratio of oxidizer massflow to fuel massflow,  in the propellant combination.  That value shifts weaky with pressure experimentally,  which I modeled as a simple linear variation.  I did not include it in the c* model,  precisely because values of r are already experimentally-optimized versus Pc levels,  in testing.

What will happen in the ballistics calculations,  is that you have a Pc and a desired thrust level,  and your nozzle analysis has determined your thrust coefficient C_F.  You use the thrust equation F = C_F Pc At to size At.  Then you use that throat ,  your Pc,  your value of c* at Pc,  and your estimate of C_D to determine the nozzle propellant massflow by means of w = Pc C_D At g_c / c*.  From there,  use your geometric ratios to determine all the other areas and associated dimensions.  And the total massflow.

Once all that is done,  you are ready to do the performance calculations versus altitude.  The only problems are allowing for nozzle separation,  and engine throttleability.  That is what complicates the overall analysis,  breaking it into a nozzle design sized at min Pc,  an engine ballistics design sized at max Pc and max required thrust,  and finally the performance-versus-altitude calculations.

Figure 3 – About Characteristic Velocity c*

Calculational Logic         

The resulting layout of the calculation sequence is illustrated in Figure 4.  There are the indicated 3 analyses:  nozzle sizing,  engine ballistic sizing,  and performance versus altitude.  You go into the nozzle analysis with your max Pc,  the pressure turndown ratio (P-TDR),  your specific heat ratio g,  the average half-angle “a” for the bell design approach you want to use,  and your design expanded exit plane pressure.  The calculation determines expansion ratio Ae/At from the exit plane pressure input,  and a min Pc computed as max Pc / P-TDR.

There is an option here if you want to design to a fixed expansion ratio Ae/At,  instead of an input expanded exit plane pressure.  Because this is a spreadsheet,  it is quite easy to iterate.  Simply iteratively change your input exit plane pressure,  until the output Ae/At is the value you want.

You come out of the nozzle analysis knowing the min Pc,  the exit plane Mach number Me,  the bell expansion area ratio Ae/At,  the vacuum thrust coefficient C_Fvac,  and the separation pressure ratio Psep/Pc.  Because you already know max and min Pc,  you thus know the actual separation pressure values Psep at max and min Pc.  And,  the analysis figures the Pc value required,  so that Psep is the ambient atmospheric pressure Pbaro at sea level.

The engine ballistics and sizing block defines flow rates and all the areas and dimensions from the required value of max vacuum thrust Fvac at max Pc. 

You can iterate input Fvac levels to hit a desired throat dimension and flow rate!  That is important if you wish to use the same gas generator power head with different bells for sea level and vacuum variants,  of otherwise the same engine design.  If that is indeed the case,  then design the vacuum variant first,  and then just iteratively choose the Fvac level for the sea level variant,  such that you get the same throat dimension and flow rate as was obtained for the vacuum variant.

The c* and r models,  the throat C_D,  and the dumped-mass bleed factor all get input into the engine ballistics block,  along with ballpark values for chamber contraction ratio Ac/At and chamber L*.  What comes out is the massflow scale-up factor,  max and min flow rates (both through the nozzle and from the tanks),  and all the engine dimensions,  excluding the turbopump portion.  

Figure 4 – Calculational Logic

The estimated performance block uses these results,  without further user inputs,  to determine engine performance versus altitude,  at max Pc and also at min Pc.  These outputs show up as both data tables and automatically-generated plots.  The data comprises actual operating thrust coefficient C_F,  engine thrust F,  and specific impulse Isp based on the massflows drawn from the tanks.  These are all given versus altitude,  at each of the two Pc levels.   

You may interpolate linearly between the C_F,  F,  Isp,  and w values corresponding to the min and max Pc values,  for other chamber pressure settings Pc,  as long as the exit bell flow is not separated!  The data tables include values for ambient atmospheric pressure Pbaro versus altitude.  Using the Psep values output from the nozzle analysis block,  you need to exclude any altitude whose Pbaro exceeds the appropriate Psep value!  I recommend that you highlight those excluded points. 

Calculation Block Details

For the nozzle analysis calculation block,  all the calculations are defined for every cell,  in Figure 5.  The figure is quite self-explanatory,  and not discussed further.  Similarly,  the calculations for every cell in the engine ballistics calculation block are defined in Figure 6,  again self-explanatory.  The performance versus altitude calculations are defined for every cell in Figure 7.  

Figure 5 – All the Details in the Nozzle Sizing Block

Figure 6 – All the Details in the Engine Ballistics Block

Figure 7 – All the Details in the Performance Block (corrected 11-24-2023)

The worksheet also makes performance plots automatically.  These are illustrated in Figure 8.  As noted,  if you copy this worksheet to another worksheet,  the plots will no longer update at all!  That is just a foible with the Excel spreadsheet software.  Use the nonfunctional plots as templates to create your own plots in the new worksheet,  then delete the old nonfunctional plots.  Simple as that.  

Figure 8 – About the Automatically-Generated Plots

Modeling SpaceX Raptor 2 Engines in 2022

Starting with the SpaceX Vacuum Raptor 2,  I sized the nozzle to a nominal 150:1 area ratio,   per “hearsay” from SpaceX.  I sized it to a 551,000 lb vacuum thrust level,  also per “hearsay” from SpaceX.  I did this at the 4400 psia max Pc that “hearsay” from SpaceX indicates they are now achieving with the new redesigned turbopump assemblies.  That thrust level nominally equates to a 250 (metric) tons-force level,  which is not an SI-metric unit,  but seems to be what SpaceX likes to quote.  Note that very little reliable information is available on the Raptor engine designs on the SpaceX website anymore,  unlike a few years back.  My results tables are in Figure 9.  

Figure 9 – Results Tabulated For Vacuum Raptor 2

The sea level Raptor 2 I sized to a nominal 40:1 area ratio,  per “hearsay” from SpaceX.  I sized iteratively to a Fvac level that produces the same flow rate and throat dimensions as those I got for the vacuum Raptor 2.  These results tables are given in Figure 10. 

I put the plotted performance results for both the sea level Raptor 2 and the vacuum Raptor 2 in Figure 11,  for a direct visual comparison.  First,  note that the sea level Raptor 2 has a smaller change in thrust  from sea level to vacuum than the vacuum Raptor 2.  This is because (1) the sea level Raptor 2 has a lower Ae/At,  reducing the effects of the backpressure term,  and (2) because the vacuum Raptor 2,  while possibly not separated near sea level,  is very definitely adversely affected by the large adverse backpressure term below the perfect expansion altitude. 

The sea level Raptor 2 can be fired at about 41% Pc at sea level,  without any separation risk,  as computed with my conservative separation criterion.  In contrast,  the vacuum Raptor 2 may (or may not) separate at sea level,  even at 100% Pc.  My separation criterion says it will separate,  but as I indicated,  that criterion is conservative,  and especially so for a curved bell.  Fully throttled down to 20% Pc,  it seems rather likely that the vacuum Raptor 2 will flow-separate at altitudes near 40-50,000 feet.  Perhaps SpaceX has actual test data on this.  I do not. 

Figure 10 – Results Tabulated for Sea Level Raptor 2

Figure 11 – Plotted Results For Both Sea Level Raptor 2 and Vacuum Raptor 2

There is one definite conclusion here:  even if the vacuum Raptor 2 does not separate at sea level and full throttle,  it is not an engine one would want to use at low altitudes!  The adverse backpressure term below around 50-60,000 feet sharply reduces thrust and specific impulse.  While such a design is convenient for ground verification testing,  it is demonstrably inadequate for actual vehicle ascents in the atmosphere.  The sea level Raptor 2 is much better for such ascents in the atmosphere.   

Compare Raptor 2 to Raptor 1  

I had reverse-engineered Raptor-1 (sea level and vacuum) about 2 years ago,  using the then-projected full 4400 psia Pc as my max Pc for calculation.  According to the SpaceX “hearsay”,  those engines never actually achieved the full intended operating pressure,  so they never achieved the full intended thrust and Isp levels in test.  They were adequate for the earlier “Starship” single-stage flight tests,  but were not adequate for any full “Starship/Superheavy” two-stage flights. 

According to the SpaceX “hearsay”,  the Raptor-2 turbopump design has a higher flow capacity,  which seems to enable it to achieve the full 4400 psia max operating pressure,  and perhaps just a bit more.  The same SpaceX “hearsay” hints that the Raptor 2 gas generator has a slightly-larger throat diameter than Raptor 1,  which is exactly what I found here,  running those estimates.  That corresponds to a higher flow rate,  which is also what I found.  There’s not any significant visual distinction grossly apparent to the eye,  in the bell diameters that I found.  See Figure 12 for a dimensional comparison.

Figure 12 – Comparison of Dimensions and Flow Rates For Raptors 1 and 2

I have meanwhile revised my 2020 estimates of Raptor 1 performance,  in the light of SpaceX “hearsay” regarding “finally beating the Russian RD-180 engine’s Pc level of 268 bar”.  That would correspond to the Raptor 1 gas generators operating somewhere in the 80-90% percent range,  of the intended max Pc of 4400 psia = 303 bar (nominally “300 bar”). 

I copied those data for both Raptor 1 designs,  and added a fourth table of performance interpolated between the max and min Pc values,  for the 80 and 90%-of-Pc levels. 

I did this for the vacuum Raptor 1 in Figure 13,  and the sea level Raptor 1 in Figure 14.  Note that the Raptor 1 bells were sized for a 4400 psia Pc level that was never actually achieved!  This is attributed by me to a shortfall in the Raptor 1 turbopump design capacity,  but only SpaceX “knows for sure”!  

Figure 13 – Revised Vacuum Raptor 1 Estimates for 2022

Figure 14 – Revised Sea Level Raptor 1 Estimates for 2022                                          

The thrusts available with the Raptor 2 designs are significantly higher than those that were available with the Raptor 1 designs.  Those larger thrusts (and the higher Superheavy engine counts) come a lot closer to meeting a lift-off thrust to weight ratio T/W = 1.5,  which according to the SpaceX “hearsay”,  they really want.  Such does greatly improve the takeoff kinematics,  and decrease somewhat the propellant mass consumed getting initially clear of the launch pad.  Basically,  you end up with a slightly higher staging speed capability,  all else equal. 

Concluding Remarks

Contact me if you want a copy of this Excel spreadsheet file.  It is named “liqrockets.xls”.  It comes with a user manual document.  What you want to use is the “allin1des” worksheet,  plus the “combinations” worksheet for the database on c* and r models. 

Addendum:  Vacuum Raptor-2 with Shorter Nozzle Bell

My friend Bob Clark,  who has the https://exoscientist.blogspot.com site,  asked me about a variant of the Raptor-2 vacuum engine with a shorter bell at only Ae/At = 107.  Supposedly,  this engine can be fired at full thrust in the open air at sea level without separating.  I ran that in my spreadsheet-based analysis,  iterating expanded pressure to hit Ae/At = 107,  then iterating vacuum thrust to hit exactly the same throat diameter and nozzle flowrate that I had for the earlier Raptor-2 estimates. 

My analysis still indicates a sea level separation risk,  even at full throttle,  although my separation criterion is conservative.  It does seem fairly likely that this variant of the vacuum Raptor-2 engine could be tested for verification in the open air at sea level.  However,  it suffers the same kind of severe loss of performance due to high backpressure,  that the 200:1 version shows.

Those results are given here as Figures 15 and 16. 

Figure 15 – Tabular Results for Vacuum Raptor-2 with Smaller Expansion

Figure 16 – Plotted Results for Vacuum Raptor-2 with Smaller Expansion

 

Bad Day

 No comment necessary.

Plasma Sheath Effects in High Hypersonic Flight

The figure indicates what is happening for a coasting body at higher hypersonic speeds.  If propelled,  the propulsion stream replaces some or all of the recirculating wake zone.  For purposes here,  “high hypersonic” is roughly Mach 8 or more.

The bow shock is close to the body surface (that is the definition of “hypersonic”).  Between it and the body there is shocked air,  and there is a sort of boundary layer sheath affected by friction,  that wets the body.  Because of friction dissipation effects,  this boundary layer is hot enough to show some ionization,  even at lower hypersonic speeds (about Mach 6 or 7).  The shocked air just outside it will eventually also show ionization,  but only at much higher speeds. 

The faster the speed,  the more ionization there is.  The more ionization there is,  the brighter the plasma sheath glows,  and eventually also the shocked air.  The brighter the plasma glows,  the more opaque the plasma sheath is to radio,  radar,  infrared,  and visible light.  That greatly affects what on-board guidance approaches will be feasible,  as well as communications to and from the body,  and also the visibility of the body and its flow field to sensors on the ground.  

Inertial guidance of high quality can take your hypersonic missile to a fixed target quite accurately,  as long as the flight time does not exceed about a quarter hour.  But hitting a moving target will be a severe problem,  especially if it is fast-moving.  The missile would have to slow down enough to dissipate the plasma sheath,  in order to use radar,  optical,  or infrared guidance to find its target.  The same would be true for radio command guidance,  from the launch (or some other) site.

Radar on the ground will not see the body itself,  but it will see the plasma sheath and the wake flows,  as these are electrically conductive,  rather like a metal.  Because they glow from incandescence,  they emit light and heat (infrared).  This shows up as a glowing streak across the sky,  of some length corresponding to how quickly mixing and energy emission cool the plasma back to non-incandescence.  The glowing streak persists for minutes at entry altitudes,  only seconds much lower down. At Mach 6 to 7,  with only about 1 second persistence,  the glowing streak is still about 2 km long!

Radar is not like human vision:  it sees only the relative brightness among discrete pixels that represent its field of view,  with a timed range that is accurate regardless.  If the radar system is capable of being programmed to track the leading tip of the moving bright streak across the sky,  then effectively it is tracking the body.   If not,  then it cannot accurately track the body.  A similar thing applies to reticle-type infrared tracking.   Visible or infrared imaging will see the leading tip of the streak more-or-less the same way the human eye does:  quite effectively.

The plasma sheath is turbulent,  and moving at rather high speeds relative to the body surface.  Between that relative motion and that turbulence,  plus the obscuration of the body itself,  a doppler radar will inherently obtain the wrong speed for the body,  if it can sort anything at all out of a very confused signal.  So if the target tracking is based on a doppler-derived velocity,  it will sooner or later lose track,  by grossly mis-predicting the next location. 

But with the right signal processing algorithms in the radar system,  looking at the motion of the leading tip of the streak instead of doppler,  the glowing plasma sheath is NOT a “cloak of invisibility”,  as is often claimed!  

To imaging systems (optical or infrared) that “see” the way the eye does,  there is no “invisibility” at all,  quite the opposite,  actually!

Nuclear War Warning

Well,  when this Ukraine war started,  like most folks,  I expected Russia to over-run Ukraine in a matter of days.  That obviously did not happen!  The war has see-sawed back-and-forth some months now,  and here of late,  it can only be said that Ukraine is winning with Western help.  I did not expect that at the outset,  but I am glad to see it,  because I am no fan of Putin in Russia! 

We have not seen the end of this yet.  Russia may again counterattack,  and conquer territory again.  You have to be prepared for that.  But,  if the current trend continues through the next couple of months,  it would seem that the Russians are headed for complete defeat.  And Ukraine may yet eject them from all its territory,  including the Crimea that Russia stole 8 years ago.

You really have to understand what that prospect portends.  In reference 1,  I compared Putin to Adolf Hitler,  and indicated that this invasion of Ukraine is the start of World War 3 in Europe.  I stand by that assessment.  The parallels to 1930’s Europe are just too close.  Think Czechoslovakia.

The problem is a longstanding military policy of the old Soviet government in Russia,  that tactical nuclear weapons are to be used to avoid defeat on the battlefield.  Putin is well-known to wish to restore the old Soviet empire,  and he was a functionary in the old Soviet secret police,  the KGB.  Why would he not want to continue that policy,  especially now,  facing defeat on the battlefield by the Ukrainians?  You need to face that prospect,  unpalatable as it is.

Nuclear war warning #1:  if this drags on another month or two in Ukraine’s favor,  expect the Russians to use tactical nuclear weapons on the battlefield in Ukraine!  The effects of that will be felt throughout Europe,  mostly radiological.  These will be low-altitude air bursts,  and even surface bursts,  of weapons in the several kiloton range.  NATO will be forced to intervene,  to stop the radiological damage to its European members,  and that might well start the general war that becomes World War 3.

If Putin fails to use tactical nuclear weapons in Ukraine,  he faces two,  and only two,  outcomes that he cannot abide!  He will either be defeated in Ukraine,  whereupon he will be deposed by his own military and his people,  or he will “mobilize his full military might”,  meaning he drafts everybody of age in Russia into the army to conquer Ukraine.  Whereupon his people sooner or later will rise up and depose him,  assisted by his military.  Either way,  he falls and dies.  So he will use them in Ukraine!

Nuclear war warning #2:  if Putin falls,  he will lash out at the West!  This will take the form of at least a limited strategic nuclear weapon strike at Europe,  and quite probably the US as well.  It could be a massive strike,  he really is that dangerous!  Either way,  there will be atomic attacks in the multi-megaton range,  and the bigger scenario could end all life on the planet. 

Putin will not care about that!  Either he lives and remains in power,  or he is deposed and dies.  He cares not for anybody else!  The old “mutual assured destruction” (MAD) deterrent to the big strategic strike does not apply with a madman Hitler clone like Putin!  He is quite unlike Yeltsin,  Gorbachev,  or even Kruschev.  I knew he was evil,  even way back in the G. W. Bush days (“rootin tootin Putin”).

Somebody,  somewhere,  outside Ukraine,  will get A-bombed by Putin at one level or another,  before he falls.

Nuclear war warning #3:  if on the other hand,  things go against the Ukrainians,  and Putin succeeds in conquering the little country,  that will embolden another Adolf Hitler clone in China:  namely Xi Jin Ping.  He will then invade and conquer Taiwan as quickly as he can,  which will start World War 3 in the Pacific between China and the US,  very much like the Pearl Harbor attack started World War 2 in the Pacific for the US versus Japan. 

If we intervene for Taiwan,  what starts as a conventional war between the US and China will rapidly escalate!  And that war will go tactical nuclear rather quickly!  Then it will rapidly escalate into strategic nuclear war,  quite probably ending life on this planet!

If we do not intervene,  then China will go on a conquering-territory rampage in the western Pacific,  just like the Japanese did after Pearl Harbor!  Either way,  it is World War 3!  And strategic nuclear weapons WILL be used!  To stop this,  we must stop Putin in Europe to deter Xi!

Bottom line:

Stopping Putin means he must fall,  and we are going to be A-bombed at one level or another as he falls.  That is inevitable.  But it is required to stop Xi,  who will otherwise eventually try to destroy us all.  He has the economy and military might to do so,  if undeterred.  Russia does not.

You have been warned!

 

References

#1. G. W. Johnson,  “What the Ukraine Thing Is Really All About”,  20 February,  2022,  article posted by the author on http://exrocketman.blogspot.com

#2.  G. W. Johnson,  "Mishandling Classified Materials is a Very Serious Crime",  1 September,  2022,  article posted by the author on http://exrocketman.blogspot.com

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Update 9-16-2022:  the timeline for all this war risk overlaps with the timeline for the insurrections and uprisings that I fully expect will follow the indictments and trials of key "Trumpworld" figures.  I expect those indictments to start in the month or two after the November election,  which is also pretty close to the time I expect to see Putin use tactical nuclear weapons in Ukraine (assuming the current war trends against the occupying Russian army continue without change for another month or two).   See ref. 2 for a discussion of only part of why I think those indictments and arrests are coming. 

There's no point denying that these "Trumpworld" uprisings will happen,  we've already seen a smaller one Jan. 6,  2021,  at the Capitol.  "Trumpworld" is a cult,  and facts do not matter to cult believers.  There is no talking them out of this,  their belief system includes a need to oppose by force all who do not believe with them.  There's more than one key cult leader now (there are several,  actually). 

Indictments and arrests of any of them will start the uprisings.  These will be armed insurrections,  and they will be killing lots of people.  They will try to stage attempts at an armed coup to take over the country and install one of their key cult figures as a fascist dictator,  which will require our regular military,  to put these coup attempts down. 

We in the US are in for some really bad times between about November's election and maybe (at the earliest) sometime in the spring,  putting down the armed "Trumpworld" revolts.  If either of the European and Pacific war scenarios detailed above also come to pass,  and escalate,  then we may not survive this at all!  THAT is what I am trying to warn you about! 

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Update 10-5-2022:  I see other public figures are now beginning to warn of Putin possibly using nuclear weapons in Ukraine,  and where that might lead.  So if you didn't believe me before,  you really ought to reconsider.  

Note that Putin cannot win territory with nuclear weapons that he could not win with an army!  This will be a revenge attack out of desperation,  and no one can predict where that will lead.  We don't even know for sure that he would only strike Ukraine.  Desperation is fundamentally irrational.

The only thing we currently know for sure,  is that he cannot be allowed to get away with using even small nuclear weapons in Ukraine.  That would embolden too many other would-be Hitlers,  like Kim Jon-Un and Xi Jinping. 

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Update 10-26-2022:  

The threads are coming together.  The news reporters have yet to put this together all the way,  but I have.   Don't say I didn't warn you!

There's mysterious "construction" activity at the Russian-controlled Ukrainian nuclear power plant that inspectors are not allowed to see,  there's allegations by Russia that Ukraine is going to use a "dirty bomb",  there's ongoing Russian retreat even without a major Ukrainian offensive in the Kherson region,  there's Putin's threats to use nuclear weapons if this-or-that does-or-does-not happen (the "reasons" don't matter,  but the threat does),  there's Putin's very serious difficulties sustaining his invasion and war (such as resorting to Iranian-supplied suicide drones instead of real military missiles),  and there's much talk about false flag attacks.   

Putin's war is failing.  He's unable to solve the logistics to avoid defeat,  and he wants revenge on the Ukrainians.  But he knows overt war with NATO is a total crushing defeat for him.  The "construction" activity at the nuclear plant is the construction of dirty bombs using conventional warheads plus nuclear waste from the plant.  This dirty bomb (or bombs) will be used in Russian-held Ukrainian territory in a false flag attack,  and blamed on the Ukrainians,  providing a thin excuse for Russian forces to use a tactical nuclear weapon (or weapons).  I cannot say what target will be nuked,  but if the previous pattern of extreme brutality holds,  it will be a Ukrainian city,  not a military target.  Casualties and devastation will resemble Hiroshima and Nagasaki. 

The fallout will damage NATO member countries.  That requires a NATO response,  meaning getting into the war,  and that includes us (it's an Article 5 thing).  This would be the time to destroy all Russian assets and forces throughout Ukraine,  including the Crimea.  

If we have the stomach for it.  Because Putin will likely fling more nukes when we do.  And when he does,  the only remaining choice is to go after him in Russia.  

It's coming soon!

Update 11-22-2022:  

Whatever that was,  that fell in Poland and killed 2 civilians,  it came closer to starting direct war between Russia and NATO,  than anyone wants to admit in public.  There is some reason to believe the story that this was a Russian-made air defense missile fired by Ukraine that went astray,  and there is also some reason not to believe it.  Either way,  something like this is liable to start the war that goes out of control.  

I think pressuring Ukraine to negotiate with Russia is misguided at best,  and probably morally wrong.  Russia hardly ever negotiated in good faith as the Soviet Union,  and it is still behaving that same way under Putin today.  Nothing Putin (or his minions) says can be trusted,  that much we know for sure,  given the last 8 years' history regarding Ukraine.  

I would recommend a 3-fold ultimatum to Putin instead.  (1) If a Russian-made weapons falls in a NATO country again,  regardless of whoever fired it,  then NATO is at war with you. (2) If any shells hit that nuclear power plant in Ukraine,  regardless of who fired them,  then NATO is at war with you.  (3) If you continue committing war crimes in Ukraine by targeting civilians and civilian infrastructure,  deliberately or not,  then NATO is a war with you.  

Then move the armies into place on the relevant borders to enforce it.  Do that,  and I think you will see Putin stand down and withdraw from Ukraine.  

Otherwise,  you will not see him withdraw,  without that overt threat of his own destruction.  And the longer this goes on,  the more likely this war will get out of control as Putin gets ever more desperate to avoid defeat on the battlefield,  and the more likely it will go nuclear. 

Two-Stage Reusable Spaceplane Rough-Size

I did this study without much forethought,  because of all the hypersonic craft and spaceplane stuff I have been seeing on LinkedIn.  Much of that stuff ignores the issues that (1) without a heat protection solution,  there is no credible hypersonic design,  and (2) combined-cycle propulsion is still at the concept and early test stage,  and scramjet s not quite yet truly ready for application. 

What I show here seems to be feasible,  although it is not optimized.  This is a study of a two-stage vertical takeoff,  horizontal landing system,  to be powered by liquid rocket engines approximating the performance of SpaceX’s Raptor-2 designs.  Each stage is a flat-bottomed wave-rider aircraft with a delta wing,  a butterfly tail,  and retractable landing gear.  The second stage mounts on the first stage,  belly-to-belly.  As the vehicle leaves the sensible atmosphere at only Mach 2,  there is no danger from shock impingement heating between the two parallel-mounted airframes. 

The first stage booster aircraft has initial thrust/weight of 1.5,  and flies very nearly vertically to the staging speed,  achieved well exoatmospheric,  then it coasts to a very high altitude (probably beyond orbit altitude),  and finally falls back.  It performs an entry burn to reduce its speed to about Mach 2 at around 130,000 feet,  where the sensible atmosphere begins.  It then belly-flops to subsonic,  goes nose first,  pulls out of the dive,  and glides back to the base from which it was launched.  A short entry transient at only Mach 2 allows the use of organic composites for the bulk of its airframe,  and it needs no heat shield at all.  It retains just enough propellant to make a go-around burn at landing.

The second stage has a similar shape,  just smaller.  It carries 5 metric tons of cargo internally,  for delivery on-orbit.  The system is sized to reach low-inclination low Earth orbit.  It has an ignition thrust/weight of only 1.05,  so that the gravity turn effect has serious effect early in the ascent burn.  It makes that ascent burn,  then coasts to orbit altitude,  where it makes a circularization burn.  End-of-mission,  it makes a de-orbit burn,  then aerobrakes at high angle of attack to about Mach 3 at 13,000 130,000 feet (corrected 9-26-2022).  From there it belly-flops subsonic,  and then glides to an approach to its landing.  It retains a bit of propellant to enable a go-around at that landing.  This sizing includes carrying the entire cargo mass back from orbit.

The basic concept is illustrated in Figures 1 and 2.  As it turns out,  no solid booster rockets were necessary.  Figure 3 illustrates the approximations I used for the go-around capability.  Figure 4 illustrates most of the other assumptions I made.  Figure 5 has the results.  Note that both craft have inert masses that are 15% of their ignition masses!  These craft both have wings and landing gear,  unlike anything else flying into space today.  The second stage orbiter must have a heat shield and largely-metallic construction.  The first stage booster must have the structure and attachments to carry the second stage at some large gee values. 

It would be quite unrealistic to assume anything less than 15% inert fractions for the two stages.  However,  anything significantly larger would render the concept infeasible!  Note that the 5 metric tons of cargo is just about 1% of the cluster gross mass at liftoff.  Expendable and semi-reusable vertical launch rockets carry larger payload fractions than that,  which explains their overall popularity over the decades.  Per flight cost must be lower,  to make the low payload fraction attractive.

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Update 8 Sept 2022:  What this study explores is almost exactly the original design concept for the Space Shuttle, which originally was a 2-stage spaceplane vertically-launched,  with both stages landing horizontally,  using wings.  The Shuttle was fueled with hydrogen,  leading to bulky fuel tanks and sizes,  and the resulting very serious aerodynamic drag problems.  Shuttle stages in that original concept did not have go-around capability at landing.  They were "dead stick" gliders.  (We all know how that concept got changed to the semi-reusable cluster that actually flew,  for budgetary reasons.) 

My study here is methane-fueled,  avoiding most of the bulkiness and drag problems (and the notorious hydrogen leak problems).  I did allow for a minimal go-around capability at landing,  with both stages.  What I noticed was the criticality of selecting the "right" staging speed,  and the very narrow window of feasible inert masses in both stages!  

Most people use too low an inert mass fraction to be realistic,  and the resulting performance results fool them into thinking they have a feasible design with breakthrough performance.  Nothing could be further from the truth.  Even my 15% inert fractions may be too low in terms of realism,  but if any higher,  the feasibility goes away almost immediately as deliverable payload zeroes.  

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While you cannot really do this in the real world,  this study is simple enough that everything (masses and thrusts) scales proportional to delivered payload mass.  Example:  if 10 tons,  double everything.

 

Figure 1 – Basic Two-Stage Spaceplane Flight Plans for Vertical Takeoff,  Horizontal Landing

Figure 2 – Basic Two-Stage Spaceplane Shapes and Inboard Layouts

Figure 3 – Outline of the Go-Around Approximation

Figure 4 – Most of the Remaining Assumptions Illustrated

Figure 5 – Summary of the Results Obtained,  Not Optimized,  Just Feasible

Values Used for Propulsion

The SpaceX Raptor-2 engines provided the Isp ranges used here.  I did not specifically use the SpaceX thrust values,  nor did I size engine counts.  The vacuum and sea level designs share the same power heads,  but with different expansion bells.  The sea level engine has a 40:1 expansion ratio (curved bell).  The vacuum engine has a 150:1 expansion ratio (curved bell).   Performance is listed at full chamber pressure 4400 psia.  It is lower,  if throttled down.  Update 10-5-2022:  had to correct the table --  had the sea level and vacuum numbers swapped for the sea level design.  

References:

#1. G.W. Johnson,  “Rocket Engine Calculations”,  paper yet to be posted here on “exrocketman”,  which shows how to get close estimates of liquid engine performance,  and uses the SpaceX Raptor-2 sea level and vacuum engines as examples.  Update 10-5-2022:  this article now posted as of 10-1-2022,  under the indicated name.  

#2. Pratt & Whitney “Vest-Pocket Aeronautical Handbook”,  12^th edition,  21^st printing,  Dec. 1969,  for the US 1962 standard day atmosphere data within.

Mishandling Classified Materials is a Very Serious Crime

Update 1-13-2023:  It appears that Joe Biden also has had some problems handling classified documents.  I see two offenders,  and I see two special prosecutors investigating the two cases.  So far,  the process of doing justice looks pretty even-handed to me.  

The natures of the two cases are quite different.  One offender is very unrepentant,  and was very uncooperative throughout.  The other offender is repentant and very cooperative.  So I would expect different outcomes,  if justice is properly done.  

I hear a lot of noise in the media and on the internet about this,  especially from what we call "right wing"-slanted sources,  yammering about how unfairly their favorite offender was treated.  

All of that is utter bullshit!  

No one should care what the media,  the pundits,  or the politicians think and say about these cases.  I certainly don't!  The only thing of substance here will be the outcomes of these two cases in the courts.  That's going to take a while.

Update 1-25-2023:  And it appears Mike Pence has also had a problem with classified documents.  He is repentant and cooperative,  like Mr. Biden.  I would suggest that all former Presidents and Vice Presidents,  their Cabinet officials,  and all members of both houses of Congress be searched.  I would hazard the guess that there is a lot more improperly-possessed and stored classified material out there!

Part of my thesis is that the people in powerful positions of government are held to a different standard than ordinary folks,  when it comes to handling classified material.  Repentance and cooperation should not be part of the charging decision,  only the sentence imposed,  as it is with ordinary folks.  My point is that no one is above the law,  we should all be handled the same way.  

We will see if DOJ can do its job.

Update 1-30-2023:  It appears that the National Archives agrees with me that other former officials might have stuff that is not legal.  They have asked half a dozen former Presidents and Vice-Presidents to search their files for classified documents.  I still think current members of both houses of Congress would be a good target for such investigative searches.

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original article:

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There is nothing unexplained about the Mar A Lago raid!  There was a very explicit,  court-approved warrant with supporting affidavit,  preceded by subpoenas and other requests that were ignored or illegally denied,  plus a prior recovery of improperly stored classified materials last January.  There is a pair of signed (by Trump lawyers) inventories of items taken by the FBI in August.  Among those items (and dominating them in importance) are various additional classified materials. 

That issue of improperly-handled classified materials is the only issue I explore here.

These classified documents included confidential,  secret,  top secret,  top secret/special access required (SAR),  and top secret/sensitive compartmented information (SCI) materials,  among some other special categories.  SAR means you must have a justified need-to-know to even see the document at all,  regardless of your confidential,  secret,  or top secret clearance.  SCI requires armed guards watching over you in a properly-secured location (like a vault or military base),  as you view the document.

None of those classified materials taken from Mar A Lago was secured in any kind of safe,  much less the government-approved safe that is the only approved thing to be used for such purposes!  They were laying about in boxes!  Mar A Lago is not an approved,  registered site for such documents to be stored,  even if a proper safe were on the site (which Mr. Trump’s wasn't). 

And,  there is absolutely nothing about Mar A Lago that makes it a candidate for viewing SCI materials,  after he left office.  There was a SCIF (Secret Compartmented Information Facility) there,  during his presidency,  but it was removed when he left office.  Which means no SCI documents can currently be viewed there,  nor can any be stored there.

All the hoopla over making public the affidavit and warrant is irrelevant legal maneuvering to avoid facing justice.  All the noise about whether this was a properly ordered raid is irrelevant propaganda to avoid facing justice.  There are two (and only two) things that are relevant here:  (1) documents marked classified were left unsecured in an unapproved location,  and (2) Donald Trump had effective possession of them,  they being within his residence.  Those facts are essentially self-proving,  and they constitute multiple very serious violations of federal law,  at the felony level.

There are still some real issues to decide.  The most important is:  were these documents with classification markings actually classified materials?  Some person or office originally classified these things,  which under the law then require proper handling,  subject to a penalty if mishandled.  Such can become declassified,  and not all the copies originally distributed may have been re-marked as declassified.  That happens quite frequently,  actually.  Once actually declassified,  they can legally be kept by persons without security clearances,  and be stored unsecured,  even in private residences. 

In prior decades,  there was a routine classification downgrade schedule for many classified documents (not all of them),  usually on a 12-year cycle from the publication date.  Such classified documents had exactly that marking on their front page or cover.  Secret reverted to confidential after 12 years,  then to unclassified 12 years after that,  and so forth. 

That changed during the Reagan administration,  which essentially means all classified documents generated since then remain classified “forever”,  unless explicitly declassified by the originating agency,  or by the president.  Whether that is the right policy is debatable (military secrets being the most fleeting of all secrets).  But,  it is the policy in place.

A sitting president can indeed declassify things all by himself,  something done before (for one,  George W. Bush with intelligence regarding Iraq weapons of mass destruction),  and upheld by the courts.  But the way this must be been done generates a paper trail:  a document written and signed by the president that he actually did declassify something,  and (critically) a description in that declassification record document specifying exactly what he declassified.  This implies that anything not so specified is still classified.  Just his verbal word is not enough!  And that authority goes entirely away when he leaves office.  Period!

Either that presidential declassification paper trail exists for the documents found at Mar A Lago,  or it does not!  If not,  the marked documents were mishandled:  an open-and-shut case against somebody!  Period!  Claims otherwise are bullshit,  to borrow a coarse but accurate term from former attorney general Bill Barr. 

Those violations rate up to 10 years in prison per offense (and each and every single document left unprotected is a separate offense under the law)!  If I had mishandled so many classified documents when I was dealing with them 40-50 years ago,  I would still be in jail today,  without any hope of ever getting out.  Intention or not to do harm doesn't matter under the law.  Only improperly handling documents matters,  as demonstrated by many cases against ordinary persons like me over the decades.

The only other issue to resolve is who actually caused the marked documents to be boxed up and sent to Mar A Lago illegally,  when Mr. Trump left office.  Under the law,  the person who ordered this action bears prime responsibility,  but those who carried out his instructions also bear responsibility.  The person who owns and resides at Mar A Lago (Mr. Trump) also bears responsibility no matter who ordered this,  since the mishandled documents were inside his place of residence!  So,  if justice is to be done correctly,  there are multiple cases against multiple individuals here.  It is not about who you should charge with a crime and who you should not.  They all must be charged!

There is a double standard of justice in this country,  though!  You apparently get all the “justice” your money and your political power can buy.  The Justice Department often chooses to let powerful public figures off with lesser punishments,  or even none at all,  using "no intent to do harm" as the excuse.  

They did exactly that with Hillary Clinton’s use of unsecured private phones for State Department business calls,  some of which were actually classified;  in part because she quit doing that,  after being called to task for it.  Mr. Trump (and several others) should be going to jail for what he and his people did,  for a very long time indeed,  but they won't do that to him!  Money and power talk. Unfortunately.

However it is very clear that he (and they) should serve some significant jail time,  plus the associated penalty (under the law) of never again holding any federal office.  That is what is done with ordinary people like me,  and Mr. Trump must not be above the law,  despite his being a former president!

Mr. Trump quite-apparently committed multiple counts of federal felonies.  In my opinion,  he’s pretty much already convicted himself,  as demonstrated by the facts uncovered in the raid.  However,  we will see if justice is really done.  It will happen slowly,  so be patient. 

“Trying” him quickly in the press or social media is irrelevant.  Let the Justice Department do its job,  and let them get this “right”,  something the press and social media rarely achieve.  But feel free to publicly encourage the Justice Department to do their job more swiftly.  This outcome will affect who can,  and cannot,  run in future presidential elections,  and it will impact future midterm elections.

They have to address the espionage act violations,  plus the issues of mishandling presidential records,  and any obstruction of justice items (per the warrant).   It’s a big job all together,  but the espionage act violations should come first,  being the most serious.

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Update 7 Sept 2022:  A federal judge has ordered that a "special master" be appointed to review the materials confiscated from Mar A Lago,  which will slow down DOJ's investigations.  Many experts question whether that "special master" is an appropriate action at all.  This is not the judge and court that authorized the search warrant,  but this judge is a recent Trump appointee.  That does suggest "judge shopping",  which is not exactly illegal,  but it is unethical.  It also suggests this particular judge may prioritize returning the favor to Trump above upholding the law equally for all.  If that proves to be the case,  it is a violation of her oath of office,  and thus an impeachable offense.

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Update 10-5-2022:  It would appear that Judge Aileen Cannon,  the Trump appointee who ordered the special master,  fairly consistently sides with the Trump lawyers.  That is prima facie evidence of political considerations prioritized by her above doing her sworn job of justice for all.  That is grounds for impeachment.  

Meanwhile,  Trump did not get what he wanted from the "special master" that he and DOJ agreed upon,  so he has now gone to the Supreme Court,  to see if his 3 appointees (plus the 3 somewhat like-minded conservatives there) will do what he needs to avoid jail.  If they do,  they will have violated their oaths of office to do equal justice for all under the law. 

It is becoming painfully clear that the Trump legal team is desperately grasping at any straw,  no matter how dubious,  to delay or prevent the prosecution of Mr. Trump for some rather serious crimes. That alone should speak volumes about what is really true here!

Update 11-22-2022:  It now appears that former vice president Mike Pence agrees with me:  Trump had absolutely no excuse for the presence of classified materials at Mar A Lago (or any other site he possesses).  Trump is only a year younger than Biden;  any questions about Biden being too old for another term also apply to Trump!  In my opinion,  the real reason he is running for president again,  is to forestall DOJ indictments for the classified materials mishandling,  and for inciting the Jan 6 insurrection (the House committee did a lot of DOJ's work for them).  He hopes the presidential politics of being a candidate will cause DOJ to hesitate.  I'm hoping the special prosecutor Garland just appointed will be tough enough to just get on with the job,  in a timely fashion.  It is simply past time Trump went to trial for these crimes he so apparently committed.