Entry Concept Screening

 Below is the text paper form of the presentation I gave at the Carbon Society meeting at NC State (see "Presenter at Workshop" posted this site 4-23-2024).  It was one of 3 presentations I brought to the meeting.  The others I may also post here in the future.  

This presentation was really about using the old,  approximate by-hand design analyses as a fast and inexpensive means to screen concepts.  That allows using the brainstorm process to generate many concepts,  raising the probability of eventual success,  but without breaking the budget and wrecking the schedule.  

Today's design analyses with software packages require much more than a notional design to support putting together much more detailed models for analysis.  That is inappropriate at the concept screening stage.  But,  today,  few young engineers fresh out of school can do the old by-hand analyses any more.

The example used in this presentation was rapid estimates of atmospheric entry,  by means of a 1953-vintage by-hand analysis used then for warhead entry.  The analysis is very simple,  and was rendered extremely rapid by embodying it in a spreadsheet to semi-automate design iterations.  

The spreadsheet I used for developing this presentation,  and a recent upgrade to it,  are available for free at the Mars Society's New Mars forums site newmars.com/forums/.  

For the original,  scroll down to the Acheron Labs section and select the Interplanetary Transportation topic.  Scroll down a page or two to the thread titled Orbital Mechanics Traditional,  and scroll down to post # 16 regarding lesson 7.  There is a link there for the spreadsheet file https://www.dropbox.com/scl/fi/9xjaw3m6 … d03mf&dl=0  and for the user’s manual that goes with it https://www.dropbox.com/scl/fi/rdqawq8z … y27y8&dl=0.

For the upgraded spreadsheet,  go to newmars.com/forums/ and the Meta New Mars section.  Go to the topic titled GW Johnson Postings and exrocketman1 You Tube videos.  Select page 12 of that thread and scroll down to post 287.  The link to the updated spreadsheet is there as https://www.dropbox.com/scl/fi/9nqdv47z … f6avf&dl=0.  The link to the user's manual is there as https://www.dropbox.com/scl/fi/dw1o8end … 0c208&dl=0.

The original had worksheets representing the atmospheres of Earth,  Mars,  and Titan.  It only estimated convective stagnation heating.  The upgrade adds a worksheet representing the atmosphere of Venus,  and it has added a stagnation heating model for plasma radiation heating,  important at entry speeds exceeding about 9 or 10 km/s. 

Here is the text of the presentation paper:

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Early Ballpark Analysis: Entry   

G. W. Johnson,  PE(ret.), PhD      2 Jan 2024             

Abstract

New product development often starts with the brainstorming of several candidate concepts and ideas.  Full modern engineering design analyses mainly use finite element computer software.  These are expensive in terms of effort and schedule time,  because the computer models require very large data sets,  which in turn have to be verified before use.  There is rarely enough budget and schedule time to do this for all the concepts and ideas. 

Guessing the “winner” among them is low-probability,  as is getting a larger budget and longer schedule in order to enable doing all of them “right”.  What is needed are simple,  quick analyses that are “ballpark correct”,  for screening the candidates down to the winner.   The old by-hand,  pencil-and-paper analyses used long ago,  but updated and automated with modern spreadsheet software,  provide the necessary screening tools.

 The examples presented deal with entry analysis as it is used to design heat shields. 

Background

Many new product development efforts are going to start with some sort of brainstorming to generate several possible design concepts or ideas.  However,  there will usually only be enough budget and schedule time for a team to do real engineering design analysis on one (or maybe two) of them.  Just arbitrarily selecting,  or guessing,  the “winner” from among those candidates has a rather low probability of success,  as does begging for more budget and schedule time to enable “doing this right”.

What you really need up front in this process are some ballpark-correct,  but small,  fast,  and simple design analyses with which to screen your candidate ideas and concepts.  You use these to screen down to the one or two “winners” that are actually worth the significant investment of effort,  resources,  and time,  that real engineering design analyses inherently consume.  See Figure 1.  

Figure 1 – Approximate Analysis for Screening,  Rigorous Analyses for “Winner”

That inherent high cost of real design analysis is because today those are typically done with multiple sophisticated finite-element computer models of several different kinds.  These typically have large input data-gathering requirements,  and there is significant debugging time associated with those massive sets of inputs.  However,  experience clearly shows the results are more reliable,  by far,  when done right.

As it turns out,  the best candidates for such ballpark-correct fast-but-simple analyses are what engineers used to do long ago before the advent of desktop computers,  with pencil-and-paper,  by-hand methods.  (Back then,  the only computers were mainframes,  using card batch inputs,  with long turnaround times.)  Unfortunately,  the career training at most engineering schools now greatly emphasizes the use of computer programs over any significant training in the old by-hand methods.  Note also that,  assisted by modern technology such as spreadsheets,  those old methods now require far less effort and time to execute than they did back then.

What I just said applies in pretty-much all engineering topic areas and disciplines.  The example illustrating it here is the topic of heat shields for atmospheric entry,  to be relevant at this meeting. 

Usually what is most important are the influences of peak surface temperatures and pressures upon choices of heat shield type,  and for the selection of specific materials with which to construct that heat shield.  Generally speaking,  in today’s world,  the overall scope of this includes refractories and ablatives.  Exposed heat sinks long ago proved unpromising,  being too heavy.  See Figure 2.  

Figure 2 – Application In General and Specific Application to Entry Heat Shields

Entry is Complicated,  But Is Also The Source of the Design Criteria

Actual atmospheric entry is complicated,  and requires analysis methods that are generally outside the experience of more Earthly topics.  The mass,  size,  and shape of the object,  plus its speed and angle-below-horizontal at start of entry,  are what determine its entry trajectory.  That trajectory results in time histories for speed,  deceleration gees,  and the measures of air friction heating,  of which heating at the stagnation point or zone is the most important.  See Figure 3. 

Figure 3 – Entry Is the Complicated Source of the Necessary Temperature and Pressure Loads

One must obtain “from somewhere” estimates of peak deceleration gees,  and of peak stagnation heating.  The peak gees essentially determine how much aerodynamic pressure gets applied to the heat shield material.  The peak heating goes into one or another kind of heat balance that determines the peak surface temperature.  It is peak surface temperature and pressure that determine what materials might be feasible for any given entry scenario.

It sure would be nice to have some simple,  fast means to determine ballpark-correct values for the peak deceleration gees,  and for the peak stagnation heating,  for any given entry scenario.

Old Simplified Analysis as the Solution

As it turns out,  there really is a ballpark-correct entry analysis tool.  It is the old 1953-vintage analysis attributed to H. Julian Allen,  and used by him and his colleagues to estimate re-entry of ballistic missile warheads throughout the 1950’s,  and into the early 1960’s.   Back then,  this was security-classified information.  But by the late 1960’s,  it had been declassified,  and was taught in aerospace engineering classes for high speed aerodynamics at the graduate school level.

This analysis was simplified to a form that could produce a closed-form equation for the variation of object speed with altitude.  From that,  it is easy to estimate deceleration gee history.  And coupled with some object geometry plus an old empirical stagnation heating correlation,  it is also easy to estimate stagnation heating history.  Analysis starts at an entry interface altitude,  with a speed at interface,  and that angle-below-horizontal.  

The analysis is two-dimensional,  and formulated in Cartesian coordinates,  meaning you must “wrap” its approximate results around the curve of the Earth’s surface.  It uses a simplified exponential distribution of density with altitude.  It assumes a constant trajectory angle below horizontal,  which you must “wrap” around the curve of the Earth to represent a constant angle below local horizontal.  It presumes the object has a constant mass,  and that its hypersonic drag coefficient is a constant value. 

The results are only ballpark-correct,  but it is astonishing just how correct they usually are.  Atmosphere models now exist for this analysis tool,  beyond just the original Earth’s atmosphere model.

If you add to this a couple more items,  this becomes a tool good enough to use in entry concept screening analyses.  You need a model for radiative heating from the glowing plasma sheath about the vehicle,  something that gets important for entry speeds at interface above about 10 km/s.  You also need some rule-of-thumb means to estimate heating items at other locations than the stagnation zone. 

Those usually just scale from the stagnation value in a simple way,  as indicated in Figure 4.

Figure 4 – How the Old By-Hand Analysis Worked

In the old days,  this was all done by hand,  pencil-and-paper,  with slide rules.  Pocket calculators speed this up only a little bit.  But it is the spreadsheet technology available today,  that really drastically speeds this up!  Once you have such a worksheet formulated,  and every cell calculation verified,  then all you need for running many variations,  are sets of only 4 inputs at any one planetary body with an atmosphere.  Those are the object’s ballistic coefficient and “nose” radius,  and its speed and angle at entry interface.  The other advantage of using spreadsheets is the ability to do easy data plotting. 

How Best Done In a Spreadsheet

Figure 5 shows an annotated image of the Earth worksheet in an entry spreadsheet that the author set up and debugged a few years ago.  The things highlighted yellow are the user inputs,  with the object’s 4 data items circled and noted.  The other yellow inputs relate to the model of the Earth’s atmosphere.  Other worksheets in this same spreadsheet file are set up for Mars,  and for Saturn’s moon Titan.

The items highlighted brown are for calculations that the author found were incorrect,  probably due to units conversion errors,  so he did not use them.  He substituted numerical integration and differentiation for what those formulas were supposed to do.  Actually,  as it turns out,  the closed-form peak gee and peak heat rate estimates actually work.  It is the peak heat absorbed that had serious problems.  

Figure 5 – Image of the Author’s Earth Entry Worksheet In His Entry Spreadsheet File

The leftmost column contains altitudes z,  in km,  starting from entry interface altitude at the top.  Altitude is a true independent variable in this analysis.  You may have any numbers you like in these cells,  as long as they steadily decrease down the column.  One may revise this list to get lots of data points where any of the other things are changing rapidly.  Changes happen very slowly early in the descent.

You will probably want to pick one altitude for iteration to a specific endpoint velocity.  That entire row in this example has been highlighted green.  The specific velocity you want is for local Mach 3,  the lowest speed considered to be hypersonic for a blunt object.  Below that,  the analysis assumptions are violated,  because drag coefficient,  and the corresponding ballistic coefficient,  are no longer closely constant.  For Earth,  this speed is 1 km/s.  It’s closer to 0.7 km/s on Mars.

The author wants to call your attention to seven columns for plotting.  Those are the altitude (z, km),  the range (R, km),  the time from interface (t, sec),  the deceleration gees (decel gees),  the speed (V, km/s),  the stagnation heating flux (q, W/sq.cm),  and the stagnation heat flux integral with time (Q, KJ/cm²).  You will want to make 4 plots.  Plot only the data down to your end-of-hypersonics local Mach 3 speed row.  Leave the rest out,  they are incorrect,  meaningless,  and only serve to screw up the graph scales.

Figure 6 shows a single sheet presentation of the four recommended data plots for a scenario.  

Figure 6 – Presentation of An Entry Scenario’s Results As Four Data Plots

The first is range vs altitude,  which verifies “no problems” when it plots as a straight line,  whose slope is the tangent of the entry angle.  The second is time vs altitude,  which relates those two variables graphically for you.  It goes significantly nonlinear at the end of the trajectory,  as the velocity sharply drops.  The third is speed and deceleration gees vs time,  which give you plots of those histories.  The fourth is stagnation heat flux and its integral vs time,  which gives you plots of those histories. Note that the peak heating always occurs at a time earlier than peak deceleration gees.  Those two peaks are not simultaneous,  contrary to most preconceptions!

The four plots just described are easily made in the author’s version of the spreadsheet,  which was done in Microsoft’s “Excel” software.  These plots can be copied and pasted into Windows “Paintbrush” or something similar,  to create a single-sheet representation of everything anybody would want to know about any one entry scenario calculation.  As you change one vehicle input data variable at a time,  you can create a new plot sheet for each such scenario,  and you can record the pertinent peak data and endpoint altitude data,  into a running table,  from which you can also plot sensitivity trends. 

Accumulated Results: Trends

Figure 7 is what plotting trends of peak gee,  peak heating,  and end-of-hypersonics altitude look like,  versus speed at interface,  entry angle,  and object ballistic coefficient.  The only direct influence of object nose radius is upon peak heating,  which was not included in these plots.  Heating varies in inverse proportion to the square root of that nose radius.  It also affects hypersonic drag coefficient,  but only slightly,  for fairly significant changes in radius. 

Figure 7 – Obtaining Sensitivity Trends By Plotting Accumulated Data

Max Pressure and Surface Temperature Estimates

Getting a ballpark max pressure upon the heat shield is actually quite easy.  All you need are the peak gees from the entry scenario,  and the object mass and blockage area that went into its ballistic coefficient.  These combine as shown into a very accurate figure for the effective average pressure upon the heat shield,  since the ambient atmospheric pressure is quite low at entry altitudes.  Since pressure is high at stagnation,  and low at the edge of the heat shield,  doubling the average is a decent ballpark estimate for the max value of pressure acting at stagnation.  Any material that can take your scenario’s max pressure is thus a feasible candidate.  See Figure 8 below. 

It is a bit more complicated doing the heat balance necessary to find the surface temperature on the heat shield at the stagnation zone,  where it is usually highest,  or at any other locations.  This depends upon whether the shield is refractory or ablative,  and upon whether speed at entry is high enough to make the plasma sheath radiation significant,  and also opaque to re-radiated infrared.

There are 5 significant heat fluxes to balance:  convective,  radiation,  re-radiation,  backside conduction,  and ablative.  Usually,  they don’t all simultaneously play a role.  With significant low-density insulation behind the heat shield,  backside conduction can be made trivial.  Otherwise,  backside conduction,  and thermal re-radiation,  are explicitly functions of surface temperature.  Convective heating comes from the entry analysis,  and plasma radiation heating from that model at each speed.  Plasma sheath opaqueness will zero any thermal re-radiation.  Crudely,  that happens at about the same speed as the speed where plasma radiation heating becomes dominant.  See Figure 9 below.  

Figure 8 – Obtaining a Max Pressure Estimate Using Peak Entry Gees

Figure 9 --  Basics Of the Heat Balance

Now,  the details can vary greatly within the heat balance framework,  as indicated in Figure 10.  For a refractory ceramic heat shield,  there is no ablation.  There cannot be plasma radiation heating,  or else the plasma would also be opaque to the thermal re-radiation.  Refractories cannot work at all in such circumstances.  Otherwise you simply balance the convection against the conduction and radiation,  by varying the surface temperature until balance is achieved.  That is really easy to do in a spreadsheet,  whether or not the conduction is made trivial by insulation. 

Ablation is the odd one.  It may or may not be a function of surface temperature.  If the carbonaceous char erodes away as fast as it forms,  the surface temperature may in fact actually be that value at which material pyrolysis is completed!  In that case,  any conduction and re-radiation heat fluxes are fixed by that value,  and the ablation heat flux is “whatever is left” directly from the heat balance,  as shown.

That ablative flux drives the shield “erosion” rate,  using shield material density and heat of ablation values.  However,  it is really just the speed of the pyrolysis front.  If the char is relatively weak enough to be scrubbed away as fast as it forms,  then it is also the surface regression rate.  Otherwise,  not.

By using convection and radiation heat fluxes scaled to other locations than stagnation,  you can do these same kinds of heat balance analyses at other typical locations around the vehicle.   The lateral or leeside surfaces typically need less protection,  and in some cases under 8 km/s entry speeds,  bare re-radiating metals are feasible.  Such was true with the old Mercury and Gemini capsules in the 1960’s. 

Figure 10 – Heat Balance Variations For Refractories and Ablatives

Concluding Remarks

All of the above is how one gets “into the ballpark” with entry calculations,  but with little effort and time expended upon each of many candidate concepts and ideas.  The better answers come from the full engineering design analyses using finite element software packages.  Those require much more time and effort,  but need only be done to the winning concept,  thereby generating data you can trust for detailed design.  That is how you stay on schedule and within budget for a new development!

References

The author used two sources for his spreadsheet formulation of the old H. Julian Allen entry analysis.  One was a second edition of the “SAE Aerospace Applied Thermodynamics Manual”,  published by the Society of Automotive Engineers (SAE),  originally in 1960,  and the second edition in 1969.  This had good information for the scaling factors of heating away from the stagnation zone,  and a version of the simple stagnation heating correlation in US customary units,  similar to Allen’s original. 

The second source was “Atmospheric Environments for Entry Descent and Landing (EDL)” by C. G. Justus and R. D. Braun,  a conference paper presented June 2007 at the “5^th International Planetary Probes Workshop and Short Course”,  in Bordeaux,  France.  This described Allen’s analysis in sufficient detail to duplicate it,  although they had converted his original US customary units to metric. 

The author believes the huge errors he saw in in the closed form equation for the time integral of heat flux may be due to an incorrect units conversion.  That is why he resorted to finite-difference integrations and differentiations in his spreadsheet.  While initially suspect,  the peak heating and peak gee closed-form equations ultimately proved correct.

That same second source also has the basic atmosphere models in the same basic scale height format that Allen’s original analysis used,  for all the planets and moons with significant atmospheres.  Those would be an entry interface altitude,  a scale-height type of exponential density distribution vs altitude model,  and the altitude limits for the density model.  From those many models in the Justus and Braun paper,  the author created worksheets in his spreadsheet file for Earth,  Mars,  and Titan.  He did not create worksheets for Venus,  Jupiter,  or Saturn,  although that could easily be done.

The original H. Julian Allen publication after its declassification is somewhat hard to acquire.  It was NACA TN-4047 “A Study of the Motion and Aerodynamic Heating of Missiles Entering the Earth's Atmosphere at High Supersonic Speeds”,  dated October 1957,  with Allen and A. J. Eggers, Jr.,  listed as authors.

About the author

The author had a 20 year career in aerospace defense doing new product development design,  analysis,  test,  and evaluation.  He first entered the workforce in the slide rule days,  transitioning to then-expensive pocket calculators,  with desktop computers still several years away. 

This first career was mostly (but not entirely) in rocket and ramjet missile propulsion.  That ended with a plant shutdown and layoff,  just when the industry was shrinking drastically.  His second 20 year career was mostly in teaching (at all levels from high school to university),  plus a little civil engineering and aviation work.  He is now retired.  

Presenter at Workshop

I attended the American Carbon Society Symposium and Workshop on thermal management,  held at North Carolina State University,  March 18 and 19,  2024.  I was an invited speaker at that conference,  and I took 3 presentations,  ready to present.  Only one was “live”,  we turned the other two into poster presentations on-site. 

The live presentation (photo) had to do with old-style by-hand methods of design analysis being used up-front for concept screening,  to enable efficient use of the concept brainstorming process to increase chances of project success.  That enables concentrating the real design efforts and heavy-duty design analyses with software packages,  to be reserved for only the one or two best concepts,  thus using resources and schedule time efficiently.   Analysts who can do this sort of by-hand analysis can also more readily-recognize “garbage-in,  garbage-out” problems with software packages!

The specific example used for this presentation was the old H. Julian Allen by-hand simplified re-entry analysis,  used for warhead design about 1953,  and declassified in the late 1950’s.  I have taken that analysis and re-implemented it in the form of an Excel spreadsheet file,  with worksheets representing the atmospheres of Earth,  Mars,  and Titan.  Those models came from the Justus and Braun paper regarding entry,  descent,  and landing,  presented several years ago. 

There are only 4 easily-estimated pieces of data required to represent the entering object:  its speed at entry interface,  its trajectory angle below horizontal at entry interface,  its hypersonic ballistic coefficient,  and its effective nose radius which determines how bad the stagnation heating will be.  The altitude at entry interface is part of the atmosphere model.  My spreadsheet creates plots,  the most useful of which tell you the peak heating rate,  followed closely in time by the peak deceleration gees. 

Those lead easily and immediately to the peak pressure on the heat shield material,  and (by way of a thermal balance) the surface temperature that must be withstood.  Those in turn constrain your material selection.

The other two presentations were about a unique ceramic composite heat shield material I created out of essentially hardware-store materials,  decades ago,  and about the ramjet combustor ablative materials I tested decades ago,  in a particularly-productive direct-connect test series.

The spreadsheet entry analysis,  and others about orbital mechanics,  compressible flow,  high speed heat transfer,  and rocket engine performance,  are all things I can make available.  Contact me.

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Up to this point,  I was able to post the same remarks on LinkedIn and stay within a 400 word limit.  Here on “exrocketman” I can say more and provide more informative detail. 

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The entry spreadsheet uses worksheets with the atmosphere models already set up for each of three worlds:  Earth,  Mars,  and Titan.  All use the same stagnation heating model.  There are only 4 inputs needed to model an entering vehicle. It generates plots automatically,  but you need to make sure the altitude data in the worksheet do not go past something very close to the Mach 3 point.  Or else you would have to recreate the plots from scratch,  limiting what data you select for plotting to the Mach 3 point,  in order to prevent extreme scale distortion.   This is what the Mars entry worksheet looks like:

This old model is 2-D Cartesian (you have to “wrap” its results around the planet).  The trajectory has a constant angle Ɵ with respect to horizontal,  making it a simple straight line (in the real world,  it will “droop” significantly after the peak deceleration pulse).  It uses a very simple scale-height type of exponential model for density variation with altitude:  ρ = ρ₀ exp[h/h_scale],  where ρ₀ and h_scale are merely the curve fit constants for modeling density in the altitude range of interest.  It presumes a constant hypersonic ballistic coefficient β = M_entry/(C_D A_block),  which for blunt shapes means the entry analysis math assumptions are violated below local Mach 3.  Allen came up with a simple closed-form double-exponential equation modeling speed versus altitude,  under these particular assumptions: 

V = V_atm exp{-C exp[h/h_scale]}, 

where V_atm is the object’s speed at entry interface,  C = 1000*ρ₀*h_scale/(2*β*sin Ɵ),  and the analysis starts downward from h = h_atm,  the altitude for entry interface (a property of the atmosphere model along with ρ₀ and h_scale).  The factor of 1000 converts the customary km units of h_scale to m.  While the equations create results at speeds under local Mach 3,  they are in error for not being hypersonic (β is no longer constant),  and those points should not be included in any reported results or plots.  

Allen used a stagnation convective heating correlation that is surprisingly accurate,  even today.  It is q = Q/A = 1.75 x 10^-8 (ρ/R_N)^0.5 (1000*V, km/s)³,  where ρ is measured in kg/m³,  and R_N is the effective nose radius in meters.  The value of Q/A = q  is measured in Watts/cm².  Its integral with time is in the spreadsheet.  This is convective heating only,  one would have to add a model for plasma sheath radiation heating,  for speeds at entry exceeding about 9 km/s.  That is currently not in the spreadsheet,  but is considered to be negligible at entry interface speeds of 8 km/s and less.  The analysis is summarized in this figure:

Where Do-It-Yourselfers Can Obtain Such Materials

At least the entry spreadsheet,  the orbital mechanics spreadsheet,  and one version of the rocket engine performance spreadsheet,  can downloaded for free,  using links that are on the Mars Society’s “New Mars” forums site:  newmars.com/forums/ 

These are located on that forums site in the “Acheron Labs” section,  under the topic “Interplanetary transportation”.  Scroll down a page or two,  to the thread titled “orbital mechanics class traditional”.  The list of available lessons is in the first posting there.  Subsequent posts have the links to all the lessons,  which are actually located in a drop box on-line.  All three named-above spreadsheets are available from that drop box,  as part of the supplied class materials for this course.  

The course comprises multiple lessons that acquaint the student with classical 2-body orbital mechanics of elliptic orbits,  to include interplanetary transfers,  adds in empirical corrections for losses during launch and when 3 bodies are involved,  acquaints you with entry,  descent,  and landing issues,  then takes up rocket vehicle performance estimation (and the rocket engine performance estimation methods to support it).

Be aware that I have two other courses not available from this New Mars forums site,  but instead directly from me.  One is about compressible flow,  to include flow with losses and with heat addition,  as well as shock waves and expansion fans,  plus the same rocket engine performance estimations as are in one of the orbits course lessons.  The other has to do with high-speed heat transfer,  complete with recommended models for various situations.  Both of these courses are associated with spreadsheets as part of the class materials. 

All these class materials include pdf documents that are essentially texts from which to teach yourself how to do these things.  They include demonstration problems with solutions,  and assigned problems to be worked,  plus solutions to those assigned problems,  for comparison afterwards.   For the already-adept,  there are also slide shows from which you can teach others.

GW’s Ramjet Book

Also be aware that I have offered my ramjet book “A Practical Guide to Ramjet Propulsion” as a self-published item.  Just contact me by email,  it currently comes as a series of pdf files,  which I email to you upon receipt of payment.  I hope to soon have a fully automated site,  with a final single download file for the book.  This is not an academic work,  it is a real “how-to” guide written from my direct experiences doing that kind of work in the aerospace/defense industry long ago.  It deals with plain subsonic-combustion ramjets,  to include integral boosters,  but not ejector ramjets,  combined cycles,  or supersonic combustion.  If that interests you,  please contact me (email preferred).

Other Technical Articles Posted On “Exrocketman”

There are many technical articles on a variety of topics posted here on “exrocketman”,  along with a few things posted on youtube under the channel name “exrocketman1”.  Here on “exrocketman” the blog site,  there is a catalog article posted,  that I try to keep current,  which has these things as a list for each one of multiple topic areas.  This is the article “Lists of Some Articles by Topic Area”,  posted 21 October 2021. 

All you need are the posting date and title of the article you seek,  to find anything quickly on this site,  using the blog archive tool,  left side of page.  Click on the year,  then the month,  then the title if need be (such as if multiple articles were posted that month).  Just peruse the lists and jot down the dates and titles you want to see,  then use the archive tool.

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Thoughts on Multiple Bad Things

There’s lots of bad things going on the world,  notably in the middle east and Ukraine.  And there’s no clear “good guys vs bad guys” about the middle east,  despite so many claims otherwise on both sides.  There’s plenty of blame to go around there.  But not so much in Ukraine.

One thing has finally begun to become clear in the news reporting:  most of the death and destruction in the middle east is being done by proxy terrorist armies that are funded,  supplied,  and given marching orders by Iran.  These would include Hamas and Hezbollah,  the Houthis in Yemen,  plus some others in Iraq that have injured and killed US troops.  Here is the sense of a list of Iranian proxies that I got from the US State Department:

To this we need to add the following:  (1) the current direct Iranian attack upon Israel,  and (2) its Revolutionary Guard,  which has also directly attacked international shipping,  as well as being the private army that keeps the ruling mullahs in power in Iran.

The common thread here is Iran:  they have been ordering all this death and destruction,  and until recently,  have let their proxies do it for them.  The western nations have been striking back at the proxies,  but without any success at stopping the death and destruction,  not in about 4 decades! 

Iran itself has suffered no punishment whatsoever for doing all these evils,  mostly because the western nations do not want a general war in the middle east with Iran.  That has apparently been a policy mistake,  and needs to change.  And the mass attack upon Israel shows that the Iranians have finally been emboldened into acting directly,  instead of through their proxies,  likely precisely because they have never been punished.

Now,  don’t get me wrong:  the Iranian people are good people,  and have been our friends before,  and could be again.  They live in a sham democracy,  where the ruling mullahs can over-rule anything the elected people decide.  Those ruling mullahs are propped-up by a private army that ruthlessly suppresses dissent.  The mullahs themselves masquerade as religious leaders,  when they are in fact extremist terrorists who misuse and abuse religion to “justify” the evils they do. 

In point of fact,  there almost was a revolution in Iran about a decade ago,  but it failed for lack of outside support from us.  They had no chance against the private army (the Revolutionary Guard).

Now what Israel does is not under US control,  let that be perfectly clear!  They are a valued ally and friend in the middle east,  and one of the few democracies in the region that is not a sham democracy,  at least not yet.  And the US is sworn to help defend them when they are attacked,  that is also clear.  And we just did that,  helping to thwart the Iranian attack.

But,  the current elected government of Israel is a re-elected right-wing prime minister (Netanyahu) who this term leads a far-right coalition that is demonstrably a bit extreme.  This shows in the policies and strategies Israel has used in its Gaza war against Hamas,  that has led to incredibly-massive civilian casualties,  plus the approaching mass death-by-famine there. 

One might conclude that the overall goal here is that there be no Palestinian state,  because there are no Palestinians left to populate it.  And,  the current attack from Iran came about because (intentionally or not) the Israelis bombed an Iranian embassy in Syria. 

That being said,  Hamas is far worse!  That is a known terrorist organization that became the government in the Gaza strip,  in an armed takeover.  They give the people of Gaza just enough food to make them think that Hamas is their friend,  but then created a network of tunnels under every populated place in Gaza!  They hide behind a human shield at all opportunities,  and in fact prevented those civilians who were shielding them,  from evacuating before announced Israeli attacks!  No real government would do that,  but evil terrorists certainly would!  And did!

Now,  bear in mind another thing that must be made perfectly clear:  when you decide to attack an evildoer who hides behind a human shield,  the only way to strike him is through that shield!  There will be high civilian casualties when you do that,  it is inherent!  Using a human shield violates international law and anybody’s rules of war,  and that is exactly what the Hamas terrorists did. 

But the civilian casualties among the Palestinians in Gaza have been much higher than they needed to be,  and that’s the result of the policies of the right-wing extremist government of Israel.  So,  there really is plenty of blame to go around!  Israel needs to change-out its government,  that much is for sure!  Extremism is the true evil here;  right wing,  left wing,  makes no difference.  Both end up doing the same needless death,  destruction,  and oppression.  They both look the same to me!

 I think the wish to avoid a general war with Iran is the right thing,  but no consequences for Iran is the wrong thing! 

Here is an out-of-the-box idea:  what if Iran were to be struck,  but NOT invaded?  Struck in such a way as to enable the Iranian people to rise up and overthrow the mullahs?  The mullahs that oppress them,  and who committed all this death and destruction all these decades?  What if the strike were to attempt two things:  (1) kill most or all of the mullahs,  decapitating that government,  and (2) destroying as many combat assets as possible,  of the Revolutionary Guard?  But without any invasion at all!  None!  Simply enable the people of Iran to do their own revolution.

I would predict that the terrorist proxies would slowly go away over time,  should we be successful.  They are currently funded and supplied massively by Iran,  and if Iran no longer did that,  their means to cause death and destruction would dry up. 

Iran has been supplying Putin’s Russia with weapons for its Ukraine war, too.  If that were to stop,  Ukraine would have a better chance to defend itself.  You need to understand,  Ukraine is the west’s proxy in the war against Putin’s Russia,  who will next attack NATO members in eastern Europe,  if he succeeds in Ukraine.  It was that way with Hitler in the 1930’s,  it is that way with Putin today.  History says all these dictators are pretty much alike. 

Ukraine has run short of weapons and ammunition,  which is partly stalled by the GOP in the US House of Representatives.  We’ve all seen that on the news.  They are now losing to Russia as a result. We have all seen that,  too.

If Ukraine loses,  we lose,  and thereby will eventually face World War 3 in Europe,  when an emboldened Putin tries to rebuild the old Soviet empire in eastern Europe,  out of countries now NATO members.  Plus,  that other evil dictator in China,  Xi Jinping,  will be emboldened to invade Taiwan and start World War 3 in the Pacific,  if Russia is successful in Ukraine!  So,  Ukraine cannot lose!  Period!  End of issue!

One GOP representative in the US House has publicly said he has heard colleagues spouting Russian propaganda on the floor of the US House.  That propaganda is aimed at stopping aid to Ukraine,  so that Putin can win.  I submit to you that voting against Ukraine aid,  is giving aid and comfort to Putin’s Russia,  which is clearly America’s enemy here!

It says in the US Constitution that one definition of treason is “aid and comfort to the enemy”,  and the standard for conviction requires only two witnesses in court to the act.  I wish the Justice Department would do something about what looks to me,  to be an awful lot like treason,  going on in the US House!

Defeating Putin’s Russia in Ukraine might possibly lead to one other good outcome for the US and the world:  he might be overthrown!  There’s likely a lot of Putin clones waiting in the wings,  but if the Russian people can get rid of them,  they might once again set foot on the path to a not-sham democracy.  They are good folk,  and could also be our friends once again.

Update 4-29-2024:  There are two additional facets to what I just said above.  There are pro-Palestinian demonstrations disrupting US college campuses,  with elements of anti-Semitism sneaking into some of them,  and the US Congress finally passed an aid bill for Ukraine,  although it is damagingly late doing so. 

Relative to the pro-Palestinian demonstrations,  I offer these opinions: 

First:  there is a portion of these demonstrators who are sincerely disturbed about the death toll so far in Gaza,  and the much larger one that looms due to approaching famine.  So am I.  There are also some outside agitators who have infiltrated onto these campuses,  stirring up the tendency to violence,  and stirring up the anti-Semitism,  while at the same time depicting the evil terrorists that are Hamas,  as innocent.  My hunch is that these outside agitators were sent here from outfits like Hamas and Hezbollah,  acting under marching orders from Iran.  This crap is massively on social media,  too,  in an internet totally unpoliced for truth.  What did you expect?

Second:  much of the reason for these excessive civilian casualties in Gaza lies with the far-right coalition that is the current government of Israel.  That does not mean all of Israel is like that,  but enough were of similar mindset to elect them.   Israel is our ally and friend and deserves our help.  But,  maybe not a totally free hand with the aid we give them,  until Israelis see fit to replace that far-right government with something not so inclined to kill civilians needlessly.  Unlike what the demonstrators seem to think,  the US does not control Israel’s actions.  All we can do is exert what influence we can.

Relative to the Ukraine War and belated aid from Congress for our proxy Ukraine:

Senator Mitch McConnel admitted on “Face the Nation” 4-28,  that the feuding Republicans are at fault for the defeats Ukraine has been suffering lately,  by delaying aid and weapons for too many months.  I actually agree with that,  but I go further.  There are two irreconcilable factions within the party,  which have successfully paralyzed much of our government for some years now.  That chaos and paralysis is actually the intent of one of those factions:  the so-called “MAGA Republicans”.

If you investigate the sites favored by such people,  you find out that the things they apparently believe and strive for,  overlap very strongly with the Q-Anon conspiracy theory.  The most well-known items include things like the “deep state” to be overthrown,  and the claim that Trump actually won the 2020 election,  but was denied his win by massive election fraud. 

Some of the other less-well-known things are actually rather frightening.  One is “the storm”,  which is the conflict that overthrows the “deep state”,  and in which the people of the “deep state” are rounded up and eliminated.  Specifications for this purge vary from site to site,  but the sense is that the “deep state” is actually everybody who opposes them,  which is more than half the country.  THAT is who they want to get rid of!

The most frightening thing relates to the chaos and paralysis they have been causing in our government.  If our government fails to function long enough,  the people will supposedly be more open to the alternative they offer,  which is a military-supported dictatorship,  precisely per the figure above.  (Trump’s advisor General Flynn,  advocated this in public during Trump’s term as President.)  Bear in mind that the Q-Anon community evolved into a fearless leader cult about Donald Trump almost a decade ago.  He is the dictator that they offer us.

The most treasonous thing they offer (besides the overthrow of our democracy) is the extreme isolationism denying all aid and cooperation with our allies,  in a time when we face major threats from Putin’s Russia,  Xi’s China,  the mullahs’ Iran,  and Kim’s North Korea,  plus all the terrorist proxy armies run mostly by Iran.  Denying aid and weapons to our proxy Ukraine (in the war against the expansionist aims of Putin’s Russia) is the way to see Ukraine defeated and Putin winning,  also encouraging Xi to invade Taiwan.  Aiding the enemy is the treason I speak of.  World War 3 is the ultimate consequence of that treason.

You have been warned (multiple times,  in my articles here on this site).  Now I urge you to rise up and do two things:  (1) vote these traitors out of our government,  and (2) demand that the DOJ prosecute them for their treason.

Update 5-6-2024:  The pro-Palestinian protests continue,  edging across the line into doing damage and committing crimes in some cases.  I think if you follow the money,  the students are too poor to have bought all that camping equipment,  Palestinian-style headgear,  and signage.  That's where the "outside agitators" come into this.  They provided the money and supplies,  and took advantage of mob psychology to stir protests into serious misbehavior.  Psychologically,  lynch mobs work exactly the same way.

The "outside agitator" effect is also a part of what these students see on their social media,  which is unfortunately pretty much the place where today's young people get their supposed "facts" and "information".  The internet is unpoliced for any sort of truth,  which is why should it surprise no one that social media is rife with misinformation and disinformation,  much of it emplaced there by this country's multiple hostile adversaries,  to include the terrorist organization Hamas itself.  That is exactly how the anti-Semitism is getting into this unrest!  Why would you expect anything different?

That being said,  look at what Netanyahu's far-right wing Israeli government is doing.  The ceasefire negotiations were effectively sabotaged by Netanyahu insisting that he was going to attack Rafah.  While they distributed leaflets warning civilians to evacuate,  I'd bet money they will start the bombing without actually trying to move anybody out of the way!  And because Hamas was stupid enough to attack a border crossing where food comes across for the starving civilians,  Netanyahu has closed that crossing,  which pretty much guarantees that lethal famine will spread quickly.  Far-right Israelis don't care about Palestinian lives,  that much is clear.  This may well be attempted genocide,  or at least a war crime.  Which is why Israelis need to replace their government,  and soon!

Hamas has had years to build tunnels under every place in Gaza where civilians live.  The results uncovered so far verify that they did exactly that.  Netanyahu is therefore probably correct in saying Hamas is hiding underneath Rafah.  He's willing to kill the civilians in the human shield to get at Hamas,  while making no real attempt to save any of them.  That's the proof of my characterization of him and the far-right wing government he leads.

Hamas also quite clearly does not care for the civilian Palestinian lives that it supposedly represents as their government,  since it invariably uses them as a human shield,  and has done nothing for them but bare subsistence,  and even that stopped with the war following the infamous October 7 attack!  All of that would be entirely expected of a terrorist organization and terrorist proxy army,  deserving only to be wiped from the face of the Earth!  QED.

Meanwhile,  the terrorist fake mullahs that rule Iran have still suffered zero consequences for waging proxy war against Israel and the rest of the west,  with their Hamas,  Hezbollah,  and Houthis,  plus some others less well known in Iraq and Syria (that have killed US troops).  That needs to change,  or there will never be any peace in the middle east!  They've been the chief problem since shortly after taking over from the Shah. 

Some of the disinformation and misinformation that the protesting students get from social media was placed there by Putin's Russia.  I suspect Iran and China placed some there,  and I wouldn't put it past some of the proxy terrorists to have done so as well.  It is way past time to find some equitable way to stop the disinformation and misinformation that is so rampant all across the internet.  

This should also apply to radio and television.  I just haven't seen anyone in,  or running for,  Congress in the last 20-or-30 years that I consider smart enough,  and with enough honesty and integrity,  to actually do it!  Think about THAT the next time you vote!

Meanwhile,  Putin has taken full advantage of the unconscionable delays by the US and NATO at getting weapons to our proxy Ukraine in the war to thwart Putin's thirst for expansion and conquest.  The fault for that in the US (the extremist faction of the GOP misbehaving) was discussed just above,  and so far,  no one has been called to account for that!  That needs to change!  Right now!

Weapons are now finally on the way to Ukraine,  and suddenly Putin is barking threats to use nuclear weapons again!  Did nobody else notice the close timing of those two things?  His past pattern is to squawk and threaten,  whenever anybody in the west does anything that might thwart his expansionist plans.  I think we are seeing exactly that pattern again.  Which simply means massively arming Ukraine and ensuing their victory is PRECISELY the right thing to be doing!  Even if NATO has to go in there and help them!

Update 5-11-2024:  A couple of things seem to be coming to head,  with regard to the Israel-Hamas war and the protests it has sparked.  

First:  the administration has had a report done,  examining whether the Israelis violated US laws and regulations,  regarding the use of the weapons and equipment we gave them.  Meanwhile,  it has paused the delivery of 2000 lb and 500 lb bombs,  while this report was being produced.  The idea is that the US should not be complicit in any Israeli activities that the world may eventually deem to be war crimes.  This seems to me like the prudent thing for the US to do.  

The reader should note that Netanyahu and other far-right figures in Israel are quite publicly angry about the US pausing those bomb deliveries.  However,  more moderate figures in Israel are not!  Further,  there is considerable unrest and protest in Israel over the conduct of this war.  Given my assessments given above of the current Israeli government,  this outcome should surprise no one. 

The gist of the report is very critical of the Israelis for the vast number of civilian casualties they have caused in Gaza so far,  but not that our laws or regulations have actually been violated.  Dropping big bombs on a city densely full of civilians is certainly not something we in these modern times would want to do,  without making some serious effort to move them out of the way.  

All that being said,  I suspect the weapons deliveries to resume soon,  which will probably spark more protests here.

Second:  as described above,  I believe that the bulk of the actual students out protesting have been misled and stirred up by disinformation on social media,  that being the only thing they look at for their information,  or any other purposes.  That disinformation was put there by our adversaries.  The authorities would be wise to look closely into that,  and consider how best to police the internet for truth.  The free speech right in the First Amendment is NOT an absolute right:  no one is allowed to yell "fire" in a crowded theatre,  unless there really is one!  And inciting riots is a crime,  and quite properly so!

 Also as described above,  I believe that non-students have been leading these protests and supplying the money and means to do them,  especially the encampments and barricades.  Students are generally too poor to have bought all those tents,  for one thing!  The authorities would also be wise to look into that possibility.  If such outsiders are among the protesters arrested,  laws regarding incitement to riot have been violated,  along with laws about trespass and destruction of property.  If the outsiders prove to be foreigners,  deportation would also be appropriate,  but only after serving the appropriate sentences.

Tornado Precautions?

My wife found this on her Facebook.  We both thought it was hilarious,  primarily because it is close to the truth. 

Many years ago,  before we went to Minnesota for my first formal teaching job,  we did just about what is pictured for Texans.  Except,  we were sitting in lawn chairs,  eating and drinking,  just watching the show.  That show was multiple little F1’s spun up out of nothing,  about a thousand feet away or so,  out here on the farm.  They got bigger as they moved downwind.   

The nearest town is 4 miles away line-of-sight,  but there were no tornadoes over there,  so there were no sirens to ignore.

Ascent Compromise Design Trade Study

Update 4-8-2024:  Should any readers want to learn how to do what I do (estimating performance of launch rockets or other space vehicles),   be aware that I have created a series of short courses in how to go about these analyses,  complete with effective tools for actually carrying it out.  These course materials are available for free from a drop box that can be accessed from the Mars Society’s “New Mars” forums,  located at http://newmars.com/forums/,  in the “Acheron labs” section,  “interplanetary transportation” topic,  and conversation thread titled “orbital mechanics class traditional”.  You may have scroll down past all the “sticky notes”. 

The first posting in that thread has a list of the classes available,  and these go far beyond just the two-body elementary orbital mechanics of ellipses.  There are the empirical corrections for losses to be covered,  approaches to use for estimating entry descent and landing on bodies with atmospheres,  and spreadsheet-based tools for estimating the performance of rocket engines and rocket vehicles.  The same thread has links to all the materials in the drop box. 

The New Mars forums would also welcome your participation.  Send an email to newmarsmember@gmail.com to find out how to join up.

A lot of the same information from those short courses is available scattered among the postings here.  There is a sort of “technical catalog” article that I try to main current.  It is titled “Lists of Some Articles by Topic Area”,  posted 21 October 2021.  There are categories for ramjet and closely-related,  aerothermodynamics and heat transfer,  rocket ballistics and rocket vehicle performance articles (of specific interest here),  asteroid defense articles,  space suits and atmospheres articles,  radiation hazard articles,  pulsejet articles,  articles about ethanol and ethanol blends in vehicles,  automotive care articles,  articles related to cactus eradication,  and articles related to towed decoys.  All of these are things that I really did. 

To access quickly any article on this site,  use the blog archive tool on the left.  All you need is the posting date and the title.  Click on the year,  then click on the month,  then click on the title if need be (such as if multiple articles were posted that month).  Visit the catalog article and just jot down those you want to go see.

Within any article,  you can see the figures enlarged,  by the expedient of just clicking on a figure.  You can scroll through all the figures at greatest resolution in an article that way,  although the figure numbers and titles are lacking.  There is an “X-out” top right that takes you right back to the article itself. 

----------     

I updated the “compressible.xlsx” spreadsheet file as “liquid rockets.xlsx”,  and deleted the extraneous worksheets.  I added a convenient block of relevant outputs that requires no new inputs other than a name for the propellant combination.  I developed a “Paintbrush” file “engine sizing report.png” on which to copy and paste the convenient outputs block in one fell swoop.  You need only adjust the name text above the engine diagram.  See Figure 1 for what this looks like.  

Figure 1 – Image of What the “Engine Sizing Report” Format Looks Like

This is all you really need,  to understand what the engine can do,  except that you must look at the green-highlighted separation limits data,  and understand that the design shown is unseparated at sea level for full throttle,  and part-throttle settings (in this case 80% Pc).  This example has a backpressure-induced flow separation in the bell at min throttle,  below very near 12.6 kft.

You still have the two performance vs altitude plots already made by the “r noz alt” worksheet.   If you want to use them,  I  recommend you copy and paste them to a “Paintbrush” png file,  then annotate them for separation.  Such is illustrated in Figure 2 below.  These are located just to the right of the altitude performance calculation block. 

When evaluating flow separation in any of the calculation blocks,  note that the pressure in the standard atmosphere was modeled,  for purposes of quick and easy estimates of the altitudes below which to expect separation.  That model was reversed to altitude as a function of Pa,  plotted,  and a 4^th-degree polynomial trend line developed with the spreadsheet software.  The quality of the fit was excellent.  But,  because of the nature of the fitted curve shape,  using this on pressures above sea level standard 14.696 psia produces nonsensical results.  See Figure 3 below for why.

Figure 2 – Example Plots,  Showing How to Annotate for Flow Separation

Figure 3 – When and How to Use the Estimates of Separation Altitude

               Using the spreadsheet

To obtain such results quickly and conveniently,  I added an automated determination of the expansion-design value of Pe appropriate to compromise-ascent design,  once the design Pc has been selected and input.  Just copy and paste-123 the design Pe value into the indicated input cell for it.  I am recommending that you use 80% Pc for this purpose,  and that you size for thrust at sea level,  using the sea level C_F for that input.

If you are doing a traditional sea level-optimized design,  I recommend you use max (100%) Pc,  and the sea level standard 14.696 psia as your design Pe.  Again,  you can just copy and paste-123 the values into the cells quickly.  I recommend that you use the sea level C_F for sizing to your thrust. 

If you are doing a vacuum design,  there is some known expansion area ratio A/A* to which you are designing.  I have retained the “compr flow” worksheet for this purpose.  Go to it,  and make sure you have the correct specific heat ratio selected.  Then in the indicated input cell,  iteratively adjust exit Mach number Me until you hit exactly the desired value of A/A*.  Read the pressure ratio PR at that Mach,  and go back to the “r noz alt” worksheet and input that PR value, almost top right. 

Input PR in “r noz alt” where shown,  and the appropriate design Pe will appear,  to be used with your input expansion design Pc.  Copy and paste-123 that design Pe value into the appropriate input cell.  I also recommend that you copy and paste-123 the vacuum C_Fvac to size vacuum thrust for a vacuum design,  which in all probability cannot be unseparated at sea level,  even at full throttle.

               Trade Study for Throttle Setting to Use for Ascent Compromise Design

For the purpose of determining what throttle-setting Pc-value to use for ascent-compromise designs,  I ran a trade study.  I ran ascent-compromise designs at Pc values from 60% to 95% max Pc,  by increments of 5%.  This was for a liquid oxygen-liquid methane (LOX-LCH4) propellant combination,  in an engine technology characterizable as “low-tech”. 

Max Pc was assumed to be only 2000 psia.  I ran a constant pressure turndown ratio (P-TDR) of 2,  which set the min Pc to 50% of max,  or 1000 psia.  The intermediate throttle setting is what I varied.  I ran this with an 18^o-8^o curved bell,  a throat discharge coefficient C_D = 0.995,  and a dumped bleed fraction BF = 0.05.  All of this assumes a gas specific heat ratio of 1.20. 

For comparison,  I also ran a traditional sea level-optimized design,  and two vacuum designs at A/A* = 100 and 300.  The results were graphed in 4 different plots,  presented as annotated in Figure 4 below. 

Top-left of the figure,  the plot shows how sea level,  ascent-averaged,  and vacuum specific impulse (Isp) vary versus the range of throttle settings investigated.  The ascent-averaged Isp trend is not linear,  and I show a sort of “aft-tangent”  determination of the rather weak knee in this curve near 80% throttle setting. 

Top-right in the figure is the same basic plot,  but to a different scale,  showing the ascent-compromise trends and the bounds represented by the sea level and the two vacuum designs.  All of the ascent-compromise ascent-average Isp values beat the sea level design’s ascent-averaged Isp value.  They even beat the sea level design’s vacuum Isp value!  They are not significantly far below the vacuum Isp value for the A/A* = 100 vacuum design,  which in turn is not far below the vacuum design for A/A* = 300!  

Figure 4 – Trade Study Plots

Bottom left is a plot of estimated expansion bell lengths (L_bell) vs the throttle setting.  These are crudely estimated as L_bell = (De – Dt)/(2*tan(avg a)),  where avg a = 0.5*(a1 + a2).  The point here is twofold:  (1) the 80% or maybe 85% values for L_bell are halfway between the sea level and the vac-100 (A/A*=100) designs,  and (2) the trend is flat enough that none of the compromise choices are far from that “halfway-between” point.

Bottom-right is a plot of A/A* vs throttle setting,  quite similar to the L_bell plot.  In this case,  the 80% point is about a quarter of the way up between the sea level and vacuum A/A*=100 designs.  The trend is flat enough that no power setting investigated is far from that point.

               Recommendations for sizing engines

For the “traditional sea level” designs,  size the expansion between max Pc and Pe = Pa = 14.696 psia (1 standard atmosphere). That produces a sea level thrust coefficient C_F,  which you use with a sea level thrust requirement to size dimensions and flow rates.

For the “vacuum designs”,  there is some max expansion ratio,  allowable in terms of fitting the engine into the available space for it,  aboard the vehicle.  Determining that fit may well be iterative!  Size the expansion area ratio to that max area ratio A/A*,  at max Pc,  which produces a vacuum thrust coefficient C_Fvac,  once you translate A/A* into a design Pe value in the spreadsheet.   Use that C_Fvac and max Pc to size the flow rates and dimensions to a vacuum thrust requirement.

For the ascent compromise designs,  determine separately what throttle setting (percent of max Pc) will be used to size the expansion.  The recommendation here is 80%,  although variations of 5% up or down from that make very little difference.  I would not recommend less than 75%,  nor any more than about 85%,  though. 

Higher setting is higher vacuum Isp but lower sea level Isp.  Lower setting is lower vacuum Isp but higher sea level Isp.  The increase in ascent-averaged Isp with increased setting is almost negligible,  because of the offsetting effects on vacuum and sea level Isp.  But using near-80% setting gives you more “room for error” in a sea level open-air nozzle test,  where you need to ignite at a low setting,  and then throttle-up rather quickly above the separation-point setting,  before any damage is done.

               What this spreadsheet does not do

This spreadsheet is for calculating good estimates of performance for liquid rocket engines of fixed nozzle geometry.  It does not do variable geometry notions such as bell extensions,  excepting as separate estimates for the two geometries as if they were fixed.  It does not do free-expansion designs at all.  Those would include both coaxial and linear aerospike geometries,  expansion-defection designs,  or any exit stream with both a free surface and contact with a physical surface.

While it provides very good performance estimates of fixed bell geometry designs,  it does not model the “cycle” that powers the turbopumps.  One does not need to do that,  to model thrust and specific impulse,  as long as one has a good estimate of the dumped bleed gas fraction representing the cycle.

               Availability of the spreadsheet

I would be happy to share this spreadsheet.  Simply contact me to make the request. There is no user’s manual (see #1 Update 4-4-2024),  although its basic operation is described in this article and another on this site. User inputs are highlighted yellow.  Significant results are highlighted blue.  Things you need to check or to iterate are highlighted green.  The Excel “copy” command,  and the “paste-123” command are the best way to transfer numerical data from one cell to another.

#1 Update 4-4-2024:  This document was originally written during 12 through 16 March,  2024.  There is now a user’s manual,  available as a pdf document,  along with the spreadsheet file “liquid rockets.xls”.   The “Paintbrush” file “engine sizing report.png” is also available as a convenient tool for reporting results.  Open it in “Paintbrush”,  cut the block of data out of it,  and copy and paste the new block from the spreadsheet into it.

               Miscellaneous things to know about

Be aware that off to the right on the “r noz alt” worksheet are some other data and plots that I used deciding how to correlate Pa vs altitude for purposes of determining the altitudes where separation might occur.  These would be of little use to any user.  Just ignore them.

That does bring up the separation backpressure estimate,  which is entirely empirical,  and was developed originally for the straight conical nozzles seen in missile solid rocket motors.  It is slightly conservative for curved bells.  It takes this form:

               Psep/Pc = (1.5*Pe/Pc)^0.8333

The ratio Pe/Psep is a simple function of the nozzle area expansion ratio.  Psep is thus an easily-computed constant times whatever your operating Pc might be.  Whenever the ambient atmospheric pressure Pa equals Psep,  separation is likely.  When Pa exceeds Psep to any noticeable extent,  separation is certain! 

There are shocks that touch the inside bell surface when separation occurs.  These greatly amplify the localized heating at the impingement location,  leading to burn-throughs and destruction in only several seconds.  That is why separation is to be avoided.  See Figure 5.

Figure 5 – Sketch of Separation Phenomena in a Bell Nozzle

#2 Update 4-4-2024:  There are two very closely related articles on this site that this document and its partial throttle setting trade study supports.  They are

“Bounding Calculations for SSTO Concepts”,  dated 4-2-2024

“Bounding Calculations for TSTO”,  dated 4-3-2024 

Both of these have reference lists of other closely-related earlier articles on this site,  including two where I investigated free-expansion nozzle design approaches,  among other things. 

In the performance of the trade study,  I sized multiple engines with the “r noz alt” worksheet,  and reported those results (rather easily and quickly) using the “engine sizing report.png” Paintbrush file.  Those sized engine results follow,  as a collection of unnumbered and untitled figures.