Launch to Low Earth Orbit: 1 or 2 Stages?

Update 5-6-2026:  I have created a simple spreadsheet with which anyone can rough-size Earth orbit launch vehicles and generate a preliminary weight statement.  It handles both SSTO and TSTO.  It uses a factored-up mission dV (and staging V as applicable),  assumed stage inert mass fractions,  and assumed stage Isp values to do this.  It does not verify the assumed inert or Isp values,  and it does not size engines or check that they fit behind the stages.  The better your assumptions about these values,  the better your results,  simple as that.  There is no user manual,  the instructions are in the worksheets themselves. Watch this site for an article to be titled "Launch Vehicle Rough Out",  to be posted sometime during May 2026.  It will tell you two different ways to get this spreadsheet file. 

Update 5-23-2026:  The article you were asked to watch for has been posted,  as two articles,  actually.  They are "Launch to Low Orbit Study" posted 19 May 2026,  and "Launch Vehicle Roughout",  posted 18 May 2026.  "Roughout" describes the spreadsheet well enough to be its user manual.  Low Orbit Study" describes the results of TSTO and SSTO configurations that I ran,  to bound possibilities and determine some sensitivities.  

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Update 10-26-2025:  I have noted a recent upsurge in readership of this article.  Please bear in mind it is not a final assessment,  I am still examining these issues.  I have since found the nominal 5% stage inert fraction used in this study to actually be quite variable with propellant density.  The 5% applies to LOX-RP1 and the room temperature storables.  LOX-methane is maybe a %-or-so higher,  but LOX-LH2 is likely really closer to 7-8%.  Keep that in mind,  as you look at what I found here,  using the simpler assumption that has since proved wrong.

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Although I have examined this question before,  I wanted to look at it again,  because there is still enthusiasm for the single-stage notion using chemical propulsion.  The problem with that is achieving a very high specific impulse (Isp) across a broad range of altitudes with the stage engines.  These must have adequate thrust at sea level,  but also average a high Isp all across the ascent.  Those requirements are in conflict because of fundamental physics.

The two-stage notion does not face that quandary as directly.  While the first stage engines show the reduced Isp typical of a sea level design,  which does not improve much at all going to high altitudes,  that penalty is compensated by the first stage shouldering only a minority fraction of the total delta-vee (dV) requirement to low Earth orbit (LEO).  The second stage can be a “vacuum” design,  featuring much higher Isp,  with much-relaxed thrust requirements.

Fixed-geometry rocket engines provide the shortest list of possible failure modes,  compared to variable -geometry designs that compensate by deployable expansion bell extensions.  Fixed-geometry rockets also show much higher performance out in actual vacuum than any of the free-expansion designs,  because of the very high streamline divergence the free-expansion designs inherently suffer when out in actual vacuum.  (They work “best” in the lower stratosphere.)

Accordingly,  what I looked at here were entirely fixed-geometry rocket engines.  For the two-stage notion,  the first stage engines were sea level designs,  and the second stage engines were “vacuum” designs,  although,  strictly speaking,  there is no such thing as a “vacuum” design,  there are only practical design constraints on how big the expansion can actually be (it has to fit behind the stage).

The sea level designs size the expansion ratio to be perfectly-expanded at sea level for no pressure term penalty,  and its dimensions also size there,  to meet a sea level max thrust requirement. This is because the vehicle is the heaviest at ignition,  and yet adequate net acceleration upward against gravity (around half a gee net) must be obtained!  In addition,  the sea level engines were presumed to use kerosene-oxygen propellants,  in order to minimize first stage tankage volume and frontal area,  so that drag losses are minimized.  Not to do so makes the needed mass ratio even larger.

The vacuum designs for second stages (and for the single-stage design) were presumed designed for expansion just short of backpressure-induced flow separation at sea level, at a suitable part-throttle condition:  some 85% of max chamber pressure.  In that way,  the actual flight engines can be tested open-air nozzle at sea level,  at 85%-and-above chamber pressure,  drastically reducing development test costs!  Similarly, in flight,  thrust can be reduced to 85% chamber pressure levels from sea level on up,  without risking flow separation in the expansion bell.  

For the two-stage design,  a vacuum thrust requirement can be used to set dimensions.  This second stage was presumed to use oxygen-hydrogen propellants,  since the smaller stage volume is compatible with the same or smaller frontal area,  despite the low density of liquid hydrogen.  For the single-stage design,  a sea level thrust requirement must be imposed.   The single stage design needs a higher-energy propellant combination,  but also suffers greatly from the enormous tankage volumes and frontal area of a hydrogen design.  So,  a compromise was used:  methane-oxygen.  

The launch trajectory was presumed to be a thrusting gravity turn affected by atmospheric drag,  to LEO at low inclination eastward,  as shown in Figure 1.  For the all-expendable designs presumed here,  staging would be somewhere near 50 km altitude and about 2 km/s achieved speed.  Circular orbit speed near 300 km altitude is about 7.7 km/s achieved.  Assuming 5% each for gravity and drag losses,  the mass ratio-effective dV is about 8.5 km/s.  The loss to be overcome is thus about 0.8 km/s,  all assigned to the first stage of a two-stage vehicle as a decent approximation,  and all borne by the single-stage vehicle.

Figure 1 – Launch Requirements

I did not actually size engines for the kerosene-oxygen and hydrogen-oxygen engines of the two-stage design,  because I have done this before,  and my results match general industry experiences.  These represent only modestly state-of-the art designs:  330 s Isp for the kerosene-oxygen,  and 450 s Isp for the hydrogen-oxygen.  These would be for chamber pressures in the 2000-3000 psia range,  and maybe 2% bleed.

I presumed a very state-of-the-art methane-oxygen engine of full flow cycle so that bleed was zero,  with a very high max chamber pressure of 4000 psia and a rather-demanding pressure turndown ratio (P-TDR) of 3.  I also presumed I would size its expansion from 85% chamber pressure down to 3.3 psia,  with the separation-inducing backpressure set at 14.70 psia.  For initial rough-sizing purposes,  I simply presumed it would average 370 s Isp across its full ascent.

For vehicle rough-out sizing,  I presumed a 5% inert fraction (f_inert) for all stages,  as loaded with payload.  The payload was presumed to be a dead-head 100 metric tons,  streamline-shaped,  and mounted out in the open,  atop the launch vehicle.   The ratio of dV to effective exhaust velocity (Vex) determines the stage mass ratio (MR).  The propellant mass fraction (f_prop) of the loaded stage is then 1 – 1/MR.  And the payload fraction (f_pay) is thus 1 – f_prop – f_inert.  For the two-stage launch vehicle,  the first stage “payload” is the fully loaded and fueled second stage mass.

I used a very simply laid-out spreadsheet to calculate these numbers for the two designs,  using the presumed Isp values and the relationship Vex = gc*Isp/1000,  to get Vex in km/s to match the dV values.   Those initial results are shown in Figure 2.  Note that the one-stage design has about half the overall payload fraction and twice the launch mass of the two-stage design!  I used thrust-to-weight (T/W) ratios of 1.5 at liftoff for good ascent kinematics,  and a T/W just over 1 for the exo-atmospheric,  nearly-horizontal portion of flight near the end of the ascent.  These sized some stage thrust requirements for me.   I used only half-a-gee for the second stage of the two-stage vehicle.

Figure 2 – First Vehicle Rough-Out

               Revisiting the Rough-Out

I really had no questions regarding the feasibility of the presumed engine Isp levels for the two-stage design.  There was concern about the Isp = 370 s presumption for the one-stage design.  Accordingly,  I actually ran some engine sizing and performance estimates,  using a convenient spreadsheet tool.  The ascent-averaged Isp fell closer to 360 s than the initially-presumed 370 s.  This is illustrated in Figure 3 below.  That includes a sketch and notations,  plus some copied sizing and point performance data from the spreadsheet.  The predicted performance vs altitude plots from that same spreadsheet are given in Figure 4 below. 

To find the ascent-averaged Isp from the calculation block in the spreadsheet,  which is performance vs altitude,  I simply summed the 100% Isp values over the ascent,  and divided that by the number of entries in the table.   This is not the “right” average value,  because the vehicle does not spend equal amounts of time at each altitude,  but it is somewhere in the ballpark.  The Isp out in vacuum is pretty near the initial presumption of 370 s Isp,  but the low altitude values are much lower,  and the vehicle does spend a lot of time there,  since it is still moving slowly at low altitude.

Therefore,  I reran the vehicle size-out and thrust requirements for that one-stage vehicle,  with the nominally-lower presumed average Isp = 360 s.  That revised vehicle rough-out is depicted in Figure 5 below,  which is just Figure 2 edited in some places.  The edits are in red text.  The effect of the small Isp change is more dramatic on the one-stage vehicle than it would be for either stage of the 2-stage vehicle.  This is precisely because it is only one stage,  and the payload is a fixed number.

Figure 3 – LOX-LCH4 Engine Sizing (Re-scalable With Thrust Rating)

Figure 4 – Predicted LOX-LCH4 Performance Fell Short

Figure 5 – Revised Vehicle Rough-Out Reflects Revised Isp For the Single-Stage Engines

This second version of the vehicle rough-out is more reliable,  after revising the one-stage average Isp value.  The two-stage vehicle is probably “pretty close” as it is,  especially since the second stage Isp is likely a slight underestimate,  which would offset any over-estimate of the first stage Isp.

For the two-stage vehicle,  we are probably looking at 8 or 9 engines of some 220 metric tons-force thrust each,  in the first stage.  The second stage needs very little pathwise acceleration capability,  and most of that at ignition where it is heaviest,  so the same 220 metric tons-force of thrust would work,  although for redundancy,  I would recommend two engines of 110 metric tons-force thrust each.   That way,  it still flies adequately even if one engine quits.

For the one-stage vehicle,  the same engines burn all the way through the ascent,  only shutting down those that are not needed as weight decreases.  This is a compromise between too many engines and too much thrust late in the ascent.   What the figure shows is that 15-16 engines of around 250 metric-tons-force each,  will lift off well,  with only one of those still burning very late in the ascent.

Overall,  the message is clear:  to do this one-stage cuts the achievable payload fraction in half or less,  while increasing the liftoff mass by a factor a bit over 2,  all for placing the same payload in eastward,  low-inclination LEO.  Lower payload fraction and higher ignition mass increase cost!

The two-stage vehicle does better,  because its two stages address the wildly-different requirements of ascent out of the atmosphere and exo-atmospheric acceleration to orbit speed,  with two entirely-different engine designs and propellant combinations!  The one-stage design lacks that advantage,  and must push its engines to the very outer limits of the state-of-the-art.

Extending to Reusable Vehicles

To do this reusably just makes the vehicles somewhat larger.  For the two stage vehicle,  the first stage gets larger in order to have the extra propellant required to recover it and land it.  Up to this date,  there have been no demonstrations of any recovery of second stages at all.  This is the partial recovery path taken by SpaceX with its Falcon-9 and Falcon-Heavy vehicles.

The inert fraction of any recoverable second stage would be much larger than the 5% presumed here,  because it must be not just a stage,  but also a survivable orbital re-entry vehicle.  It might as well carry the payload internally,  which likely increases its inert fraction even more.  That path is the one chosen by SpaceX with its Starship/Superheavy orbital transport design.

As for making the one-stage vehicle reusable,  with only 4% payload fraction,  it could only have an inert fraction of 9%,  even if it carried no payload at all!  To make the stage also an entry vehicle,  and to carry the payload internally,  would seem to push well past the bounds of any reasonable assumptions at all,  with chemical Isp.  This is the path attempted without any success by the X-33 “Venture Star” project,  and it used hydrogen-oxygen,  the best chemical combination available!

               Summary Remarks

Because launch price is sensitive to payload fraction and ignition mass,  I cannot recommend the single-stage-to-orbit approach with any conceivable chemical propulsion,  even in expendable vehicles.  The numbers are just not there,  regardless of what kind of “trick” engines one proposes,  because such always have performance shortfalls somewhere across the ascent.  Two-stage to orbit,  using two different propellant combinations in the two stages,  is likely the best,  but SpaceX has already shown rather good results with the same propellant combinations in both stages.

To add reusability,  the best approach is still two-stage,  with either (1) an expendable second stage and payload riding atop it,  or (2) a second stage that is also its own entry vehicle,  with payload riding inside.  The first is still more mature than the second,  at the time of this writing.

Switching to all-hydrogen instead of the denser methane is not the solution to the single-stage problem,  because the far-larger tankage volume and frontal area will increase the drag loss,  raising the dV penalty,  and thus make mass ratio-effective dV requirement still higher.  Such acts to offset the effects of the higher Isp of the hydrogen,  which still has to be ascent-averaged.

If you really want to do single-stage to orbit,  the most fruitful thing to do would be developing into maturity a nuclear thermal engine of significantly-higher Isp and substantially-higher engine thrust/weight than the NERVA design that was ready to flight test,  when it was cancelled in 1974.  Such an option is very likely some sort of gas core design.  One needs at least about Isp = 1000 s or so,  to make fully-reusable stages that are their own entry vehicle,  and can contain the payloads internally.  The vehicle inert fractions will fall in the 20-30% range,  unless high engine weight drives it even higher.  The vehicle launches vertically,  and could land horizontally.  If clean,  dV ~ 8.5 km/s.

At 1000 s:  Vex = 9.80667 km/s,  MR = 2.3792,  f_prop = 0.5797,  guess f_inert = .25,  f_pay = 0.1703.  For W_pay = 100 metric tons,  W_ign = 587 m.ton,  W_inert = 147 m.ton,  and W_prop = 340 m.ton.  At liftoff T/W = 1.5,  the required liftoff thrust is 881 m.ton-force.  Burnout is about 247 m.ton,  for about 3.57 gees at liftoff thrust. The thing is likely winged,  or a lifting body shape,  to land on a runway or dry lake bed.

               Follow-Up on the Nuclear Single-Stage Notion

I created another spreadsheet worksheet to evaluate the possibility of a nuclear thermal one-stage design.  I made the inert fraction iterative,  with an R-value to estimate LH2 tankage inerts,  and an engine thrust/weight ratio to estimate engine inerts based on liftoff thrust required. 

This crude analysis includes nothing for on-orbit maneuvering,  or deorbit,  which would probably be storable propellants!  I made the inerts analysis iterative so that the overall inert fraction input would give a realistic airframe inert fraction,  that does not include the engine or the tankage. 

This one is a lifting body,  with an engine not all that far improved over NERVA,  and it would land dead-stick like the shuttle,  probably on a dry lakebed,  or a very long runway indeed.  It would likely touch down at around 200 mph. 

This one had the highest payload fraction I have seen yet,  and would likely be fairly cheap to operate,  as long as it proves tolerable to return the idled nuclear engine back to Earth.  (That is a really big “if”!)  See the spreadsheet image in Figure 6,  and a sketch of the vehicle concept in Figure 7 below.  

I only had to increase my assumed inert fraction a little bit to achieve an airframe-only inert fraction that I considered to be believable.  Even so,  the payload fraction is about twice the payload fraction of the two-stage expendable chemical vehicle,  and almost 4 times the payload fraction of the one-stage expendable chemical vehicle.  And the nuclear one-stage vehicle is entirely reusable,  but if and only if you can accept returning its engine to Earth!

Figure 6 – Spreadsheet Image for the Single-Stage Nuclear Vehicle

               Final Remarks

For the nearer term,  using only well-developed,  ready-to-apply technologies,  the highest payload fraction option is the two-stage vehicle,  which can readily adapt the designs of its two stages to the different circumstances of ascent out of the atmosphere,  and acceleration exo-atmospheric and nearly horizontal to orbital speed.  Making its first stage reusable would not cost that much payload fraction.

Trying to do this,  even if expendable,  as a one-stage vehicle with chemical propulsion,  is unlikely to provide a payload fraction high enough to actually pay off.  It will likely underperform the two-stage expendable in terms of payload fraction,  no matter what propellants might be used.  And it will be heavier at liftoff under any conceivable circumstances,  for the same payload.  Thus it will cost more.

Longer term,  a fully reusable one-stage vehicle of even higher payload fraction than the two-stage expendable chemical vehicle,  might be feasible with some form of nuclear thermal propulsion that performs only slightly better than NERVA.  Key to its viability will be the acceptability of returning and landing with that engine aboard.

Figure 7 – The Nuclear One-Stage Vehicle Concept

Update 3-6-2024:  

I went ahead and looked more closely at the engines for the two-stage vehicle.  These would be LOX-LH2 in the second stage with vacuum bell designs,  and LOX-RP1 in the first stage,  with something suitable as a sea level bell design.  Neither would push the state of the art the way the LOX-LCH4 engines must do,  in the one-stage vehicle.  I used very modest modern-technology characteristics for the engines of both stages:  2500 psia max Pc,  with only a P-TDR = 2.5,  and a dumped bleed fraction BF = 0.02.  They use otherwise the same 18-8^o bell profile and C_D = 0.995.

As Figure 8 shows,  the traditional sea level design with perfect expansion to sea level pressure from max Pc,  shows an ascent-averaged Isp shortfall relative to what I wanted for the first stage.  But when I used the “compromise design” approach (see Figure 9) to size those engines,  trading away unseparated sea level operation at min-throttle setting,  for more expansion ratio and higher vacuum and ascent-averaged Isp values,  that ascent-averaged Isp exceeded the assumptions used for roughing out the first stage. 

Elsewhere,  I had looked at vacuum designs for LOX-LH2 engines,  sized to arbitrary expansion ratios of A/A* = 100,  150,  and 200,  with those same modest modern-technology characteristics.  The min expansion version (Figure 10) gets you the smallest physical length and exit diameter,  and its vacuum Isp substantially exceeded what I assumed for the rough-sizing of the second stage.  So,  I revisited the vehicle rough-out with a somewhat-higher second stage Isp (Figure 11, blue edits).  That increased the payload fraction,  and reduced the launch weight,  both acting to lower costs. 

Figure 8 – Traditional Sea Level Sizing Falls Short of Desired Ascent-Averaged Isp = 330 s

Figure 9 – Sea Level “Compromise” Design Exceeds Desired Ascent-Averaged Isp = 330 s

Figure 10 – Vacuum Design at A/A* = 100 Substantially Exceeds Desired Vacuum Isp = 450 s

Figure 11 – Revised Vehicle Rough-Outs Show 2-Stage To Be Even Slightly Better

Update 3-7-2024: 

The question came up of whether I demanded enough dV of the vehicles?  I had added 10% to the 7.7 km/s orbital velocity for 8.5 km/s.  Here is what the size-out produces with 20% added,  for 9.2 km/s.  The “best” engines and nozzles that I found earlier were retained just as they were revised.  Only the velocity requirement was increased.  I put all the increased burden on the first stage of the two-stage vehicle,  precisely because it has the lower Isp,  as a worst case.  See Figure 12. 

 

Figure 12 – Revised Launch Requirements for Higher dV Values for Rough-Out

The resulting vehicle size-outs show larger vehicles and lower payload fractions,  to be sure exactly as expected!  However,  the SSTO is now worse by about a factor of 3,  not just 2,  than the two stage vehicle.  Both were considered to be expendables for this,  as before.  See Figure 13.  The engine count is getting to be something to worry about,  as well.  That cluster has to fit behind a slender tankage set.  If you make the tanks fatter and shorter to “cover” the cluster,  you are no longer “long and slender”,  and that increases your drag loss.   

One thing readers should consider is the requirement for adequate kinematics right off the launch pad.  You need half a gee or more,  of effective net acceleration beyond gravity,  to be efficient,  and not spend most of your propellant just climbing the first few thousand feet.  For an Earth launch,  that’s an ignition thrust/weight of 1.5 or higher. 

In the real world,  you can use more and/or bigger engines to achieve this,  or you can add some solids (always of much higher frontal thrust density than a cluster of liquids).  I chose to just use more and bigger engines.  Why complicate the study?

This is a very strong effect,  almost to the point of being overwhelming!  It is precisely why vehicles with low launch thrust/weight also have historically had low payload fractions.  The poor acceleration kinematics drastically raise the gravity loss,  making the dV requirement effectively much larger,  and THAT lowers payload fraction rapidly.  To be “efficient”,  you really have to scoot off the pad!  And THAT is exactly what I enforced in this study!

Figure 13 – Revised Rough-Out Results for Higher dV Requirement

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I should probably have followed my own recommendations and used the surface circular orbit speed of 7.9 km/s,  and not the speed at orbit altitude 7.7 km/s,  as the "ideal dV" to be factored up for gravity and drag.  But it really doesn't matter very much when doing a comparison analysis.  The factor would be 1.1 if one assumes 5% each for gravity and drag losses.  It is 1.20 if instead one assumes 10% each for gravity and drag.  7.7*1.1 = 8.5,  some 0.8 loss to cover,  while 7.7*1.2 = 9.2,  some 1.5 loss to cover.  If instead you use 7.9 km/s,  the numbers are only slightly different:  7.9*1.1 = 8.7,  for 0.8 loss,  and 7.9*1.2 = 9.5,  for some 1.6 loss.  

More important is arriving on orbit with something left to support doing rendezvous,  plus some sort of controlled de-orbit burn.  The former is likely on the order of 0.3-0.5 km/s,  and the latter is about 0.1 km/s,  for about an extra 0.5 km/s.  You add those unfactored to the total effective launch dV.  That would be around 8.5+0.5 = 9.0,  or 9.2+0.5 = 9.7.   I did NOT include anything like that in the dV requirements,  because I was only looking for relative trends.  

And those relative trends say the single-stage-to-orbit (SSTO) does factor 2-to-3 worse in terms of payload fraction and launch weight than the two-stage design.  That's for both designs being clean and slender for low drag loss,  and neither pushing the state-of-the-art on structure technologies (the fixed 5% inert in a loaded stage).  The 2-stage does not push the state-of-the-art on its engine technologies,  but the SSTO has to.  SpaceX has already had its troubles with that,  in its own LOX-LCH4 engines.

If you go to LOX-LH2 to improve past the Isp of LOX-LCH4 for the SSTO,  you will end up having to push the state-of-the-art on your structure technologies as well as your engine technologies.    And it may no longer qualify as "clean-and-slender,  so the drag factor may increase,  too. 

If you want something easily and less-expensive to develop,  then don't push the state-of-the-art.  If you do,  you will have higher development costs to amortize.  Everything is acting in the wrong direction on costs,  with a chemical SSTO. 

Update 6-8-2025:  This study was continued and expanded in scope,  in the article entitled "More Refined 1- vs 2-stage to LEO",  posted to this site 11 March 2024.  In it,  the actual trends of payload fraction and launch mass vs propellant combination were determined,  for both the TSTO and SSTO all-expendable scenarios.  If this article interests you,  you should go see that one as well.  

Tricky Landing

The “Odysseus” robot lander created by Intuitive Machines seems to have landed successfully on the moon,  although reports say it is on its side rather than upright.  Details as of yet are quite sparse,  but depending upon whose reports you read,  it would appear the lander had a non-trivial and unintended horizontal speed at touchdown.  Odds are,  it was also tilted a bit in the direction of that horizontal motion.  It seems to have “tripped” on one of its legs being somehow obstructed,  overturning the lander as it touched down.

This is always going to be a serious problem for a robot moon lander,  as opposed to a manned craft.  It is still difficult-to-impossible to program a robot to do what a human pilot can do,  and robot vision is still nowhere near as good as human vision. 

Consider what Neil Armstrong had to do,  landing the Apollo 11 lunar module.  The computer-controlled trajectory was taking the vehicle into a tightly-packed field of multiple boulders as big as houses:  a guaranteed fatal crash!  Armstrong had to take manual control,  stop the descent into an unplanned hover,  and then direct that hover toward a clear landing site nearby.  The depletion of his rocket fuel was but a single handful of seconds away at engine shutdown.  

The rule-of-thumb stability criterion used for all successful landing leg-equipped craft on the moon and Mars,  is that the span between foot pads at least equals the height of the craft center of gravity,  and preferably exceeds it. The Odysseus lander only just barely met this,  and the also-recent Japanese lander did not meet it,  and was photographed upside-down after its landing!

It is not yet known what “tripped” the Odysseus lander,  but the odds favor either a leg striking a fixed rock or similar obstruction,  or else a landing pad digging into the surface dirt.  The “fix” for this is two-fold:  (1) increase the pad span to center-of-gravity height ratio significantly,  and (2) hinge the pads on the ends of the legs,  and spring-load them to tilt upward toward the radial-outward direction at each leg.  The first decreases the net overturning torque of a “tripping” incident,  and the second acts to prevent a pad from digging-in. 

Seems “intuitive” to me.  Maybe we old farts still have things to contribute,  after all. 

Update 2-26-2024:  The quote below,  from a PBS NewsHour story published this date,  confirms what I hypothesized about the Odysseus lander.  It apparently will cease operations tomorrow for lack of sunlight on its solar panels,  according to the story.  Highlighting is mine.

“The lander, named Odysseus, is the first U.S. spacecraft to land on the moon in more than 50 years, carrying experiments for NASA, the main sponsor. But it came in too fast last Thursday and the foot of one of its six legs caught on the surface, causing it to tumble over, according to company officials.”

What I found about the Japanese “SLIM” lander is enlightening,  although it is still unclear just exactly how it ended up on its nose.  It was supposed to hover and then tip over onto its side,  with its landing legs extending out that side.  In the long dimension,  pad span exceeds cg height,  meeting the criterion.  From side-to-side,  it does not meet the criterion,  a very real risk. 

But it did not fall over to one side,  somehow it instead went tumbling end-over-end,  which is the only way it could have ended up on its nose!  Some stories mention a problem with a main thruster (there were two in its bottom).  Those should be “off” during the actual tip-over-and-landing because they are too powerful,  so any main thruster-related hypothesis would have to have occurred before that process.

One possible main thruster-related hypothesis is that it may have experienced suddenly-asymmetric thrust just as it approached hover for final tip-over-and-landing.  If so,  that could have sent it tumbling end-over-end while still aloft,  instead of hovering into a controlled tip-over. There should be marks in the regolith if that hypothesis is true,  marks where it hit while already tumbling end-over-end.  In the low gravity,  it would have continued to bounce end-over-end after hitting the surface.  It just happened to quit bouncing,  while on its nose.  Improbable,  but possible.  Still,  only a hypothesis. 

GW’s Ramjet Book Is Now Available!

This has been a long time coming,  because I originally finished writing the book back in 2017.  I offered it to a technical publisher,  who took over 2 years to decline publishing it as a hardcopy,  hardcover book.  It then languished as a back-burner item,  while I figured out how to really do this myself,  in between more pressing obligations.  But I knew that I really did need to get this book “out there”,  because I am an old retired person,  and so I will not be around for that many years yet to come.  I’d rather this knowledge and experience to not die with me.

This is not your usual academic tome.  It is more of a very extensive “how-to” compendium of the things that actually worked for me and my colleagues,  while actually doing real ramjet work.  The scope is subsonic combustion ramjet,  not combined cycles,  and not supersonic combustion ramjet (scramjet).  It covers mainly liquid-fueled and solid gas generator-fed ramjets.  It bears about the same relationship to ramjet engineering,  that Sighard F. Hoerner’s self-published books,  “Fluid Dynamic Drag” and “Fluid Dynamic Lift”,  bore to aerodynamical engineering.  No real publisher wanted to publish those books,  either,  but scads of people found them very useful anyway!  I hope you find my book useful. 

I now have an initial solution:  I can literally email the book as pdf files to those who want to buy it. 

It exists as some 27 pdf files:  one for the “up-front” stuff,  one each for all 22 chapters,  and one each for all 4 appendices.  Each chapter has its own page numbering,  its own figure numbering,  and its own reference list.  The “up-front” stuff includes a foreword,  biographical data,  a table of contents,  and (quite uniquely !!) another table of contents with a paragraph indicating content for each chapter!

If you want to buy the book,  just contact me,  email is best!  My email is gwj5886@gmail.com.  (I will need your email to send the files,  in any event.)  I will give you my physical address,  to which you can send the purchase amount by check or money order. 

When I receive it,  I will email the files to you in multiple emails,  since there are so many and they are large.  Plus,  I will follow up to make sure you get them all! 

Base price is $100 per copy.  Out here rural,  the Texas sales tax is only 6.25% (and I have a Texas sales tax certificate),  so the sales tax amount is $6.25. (SEE UPDATE 4-11-2025 JUST BELOW!!! That puts the total purchase amount at $106.25,  turn-key. 

That’s how I need to do this for now.  Soon I hope to be able to take credit cards by voice over the phone,  which would speed the process up for you.  But that is not ready yet.  Watch this space for updates,  I will add that capability soon. 

Eventually,  if I can find qualified help,  I hope to set up another site that automates the payment and send-out processes.  But that is for the future.

Update 4-11-2025:  

I still do not have a permanent site,  so I am still doing this as delivered pdf files from my home,  once I have the money in-hand.  

I have found out that foreign customers can use Western Union to send me the money for a physical pick-up.  I do not risk bank account information for direct-deposit on-line.  

I have figured out that I should be collecting McLennan county tax in addition to state of Texas sales tax.  Out here rural,  there is no city sales tax.  So the corrected invoice values are base price $100.00,  state plus county sales tax $6.75,  invoice total $106.75,  not the value shown just above.   

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As examples of my real-world experience,  I have included some pictures here.  I hope these help inspire in you enough confidence that I really know what I am talking about,  so that you will be more inclined to buy the book.

Figure 1 below shows the hybridized ground test hardware that I used to great advantage,  doing ramjet tests on the ground in a direct-connect facility,  long ago.  It coupled a heavyweight lab motor as a short-burn solid gas generator,  to a flight-weight combustor and inlets.  This hardware was extremely effective for testing experimental fuel propellants,  experimental combustor insulations,  and one experimental fuel flow rate control approach.

Figure 2 below illustrates what the exhaust plume looked like for one of these tests,  conducted “open-air nozzle”,  with both an experimental fuel and an experimental combustor insulation,  back in 1991.  Most of the sparkler streaks were from the insulation,  not the fuel! 

Believe it or not,  this particular test was the first time anybody ever burned high-percentage boron efficiently in a ramjet!  See the smoke-free clarity of the plume downstream of the fire as proof.  Even the metal oxide smoke is barely visible downstream.  However,  the incandescent glare from it (and some soot) is part of what makes the tailpipe flame opaquely brilliant.   

Figure 3 below shows a modern cutaway display model of the Russian surface-to-air missile known to NATO as the SA-6 “Gainful”.  It was a solid gas generator fed ramjet,  with an “integral booster”,  meaning the booster rocket was housed inside the combustor itself,  not a staged-off item.  As a young engineer,  I was the lone engineer among 3 propellant chemists who did the actual exploitation work on this foreign technology.  We duplicated the solid fuel-rich propellant and its processing,  tested it static and with air,  and I put together a computer trajectory model of the system,  which matched performance seen on the battlefield.  This knowledge used to be classified,  but no longer (not with public display models).

Figure 4 below is a two-view picture of an ASALM-PTV being launched from an A-7 Corsair-2.  It was a liquid-fueled ramjet with an integral booster.  I worked on ASALM,  which was a prototype for a high-altitude supersonic ramjet-powered cruise missile that (unfortunately in my opinion) never proceeded to operational status,  because of treaty limitations. 

It was flight tested 7 times,  and met or exceeded all objectives on 6 of those.  On the first of those tests,  it accidentally went hypersonic due to an assembly error in its fuel throttle controls.  Way back in 1980,  this thing accelerated in ramjet,  at low altitude,  to about Mach 6!   A different picture of it (not here) on the same airplane,  I consider to be a sort of “family portrait”.  I worked on ASALM,  and my father was lead engineering designer for the A-7. 

Figure1 – Hybridized Ground Test Hardware

Figure 2 – Typical Experimental Open-Air Nozzle Ramjet Test

Figure 3 – Modern Cutaway Display Article of the SA-6

Figure 4 – Two-View of ASALM-PTV Launched From A-7 Corsair-2

Swatting at Proxies is Pointless

There has been a lot of violence and danger in the Middle East in recent decades.  Most,  but not quite all of it,  is summarized in Figure 1.  This article is about things since about 1980.  For earlier history,  see “Israel vs Hamas:  It Is Worse Than You Think”,  posted 29 December,  2023,  on this same site. 

I drew that figure on 22 January.  Since I drew the figure,  there has been an attack by Iranian proxies on a US base in Jordan,  killing 3 of our troops.  However,  that still fits the same pattern shown!

Note that Western nations in general,  and Israel in particular,  have been combatting the proxies listed since about 1980.  There is however a common thread to all of that listed evil,  and that common thread is shown in the figure to be Iran.

Figure 1 – A Summary of Where Most (But Not All) Middle Eastern Violence Really Comes From

It is my contention that Iran is ruled by a terroristic dictatorship,  masquerading as a democracy.  The ruling figures pose as religious mullahs to justify what they do,  but their actions clearly make that claim false.  They can over-rule anything the “elected” officials come up with,  making it a sham democracy.  This group is propped up in power by the Iranian Revolutionary Guard,  which is essentially their private army that ruthlessly suppresses domestic dissent.  My contention cannot be far from the truth!

In point of fact,  there is very little operational difference between this situation,  and 1933 Germany,  with Hitler propped up by his private army,  the brutal and ruthless SA. And we all know where that led!  I did generalize this to a warning about leader cults,  published 13 February 2020 as “Beware of Leader Cults” on this site.  Such can be political,  religious,  or both.  To find any of these quickly,  use the navigation on the left.  Click the year,  then the month,  then the title if need be.

This terrorist government in Iran funds,  supplies,  and commands a bunch of proxy terrorist armies in multiple places.  Those proxies are killing and wounding lots of people,  and even killing and wounding US troops,  as noted.  Iran already has cruise missiles and drones,  as well as an army,  a navy,  and an air force.  It is going for a nuclear weapon,  and has been for some time now.  Iran is even launching shipping attacks from within its own territory now,  so their vile behavior is escalating. 

Striking at proxies has proven ineffective, because the outfit giving the orders does not suffer any consequences!  This is indicated in Figure 2,  where Russia has been unsuccessful for 2 years now swatting at the West’s proxy,  the Ukrainians.  We in the West are not generally terrorist dictatorships,  not yet,  anyway.  We should care a lot more about our proxy than any dictatorship ever would,  and therefore we all should see to it that they win.  Or overtly help them to win,  if needed.

Economic sanctions against dictatorships have also proven ineffective,  because those do not hurt the dictator,  only those oppressed under him,  and he cares not that they suffer!  Our experiences with Iran,  Russia,  North Korea,  and now China,  all prove that thesis.  This is also indicated in the figure.

Figure 2 – What Does and Does Not Work,  Dealing With Proxies,  Plus a Suggestion

My firm opinion:  there will not be peace of any kind in the Middle East until Iran is dealt with effectively.  Basically,  that government must fall!  And none of us want to invade and occupy Iran,  we’ve already had enough of that nonsense with Afghanistan and Iraq.

As the suggestion indicates,  one uses a surprise strike to kill as many of the ruling mullahs as possible,  in one fell swoop.  After that,  one then conducts strikes from long range to destroy as many of the Revolutionary Guard’s facilities and assets as can be found.  But you do not invade!  And leave the general infrastructure alone.  Just hit the Revolutionary Guard stuff,  and some of the military assets.

With the Revolutionary Guard thus weakened,  and the ruling mullahs in disarray or dead,  there can be a successful popular uprising,  like the one about a decade or so ago,  that Mr. Obama failed to support.  The Iranian people are actually good folk who would just as soon not be our enemies!  This would give them a chance to be free and become our friends (once again). 

Dealing with our multiple adversaries:

We the West face 4 really bad adversaries:  Iran,  North Korea,  Russia,  and China.  Iran is now escalating from using all proxies into overt attacks,  and they are close to having nuclear weapons.  They really do need to be dealt with immediately.  I just told you how.

North Korea is the one most likely to fling a nuke right now,  with Iran not far behind.  The North Koreans don’t have very many nuclear weapons yet,  so we can afford some damage to take on Putin’s Russia next instead,  by forcing their utter defeat in,  and complete expulsion from,  Ukraine,  any which way we can!  Putin will be overthrown from within if that happens,  although there is no guarantee his successor won’t be just as evil as he is.  However,  it will take time for the new one to consolidate power,  during which time we can act.

Putin’s defeat and overthrow will tend to deter Xi’s China,  perhaps preventing World War 3 from starting over Taiwan in the Pacific.  His country’s mounting economic stress (from going to a war production footing during peacetime without much excuse other than starting a major war that the Chinese people do not want) can possibly induce his overthrow from within,  especially if that economy continues to falter into serious recession. 

With Russia and China out of the way,  North Korea can be easily taken down.  South Korea and Japan will be happy to help.  That one IS an invasion!  It results in a reunified Korea,  too.

Final related remarks:

Do not be fooled by my inclusion of Israel among the nations of the West.  In the current war with Hamas,  they have used tactics and weapons that bespeak of a total disregard of Palestinian lives,  well in excess above the appalling casualties one would have to expect,  from striking at your enemy through their human shield.   It may actually qualify as some sort of war crime.

That disregard of Palestinian lives is driven by the far-right political coalition that currently governs Israel:  they do not want a 2-state solution,  they apparently want instead for there to be no Palestinians left to have a state at all.  Very typical of authoritarian hard-liners!  The Israeli people need to change that government,  before it becomes a dictatorship.  Netanyahu trying to “reform” the Israeli judicial system was actually him trying to enable his staying in power permanently.  Israelis,  you have been warned!

As for the UN looking at war crimes charges against Israel:  why are you not also looking at Hamas?  Using human shields is a war crime,  as is attacking civilians!  And Hezbollah,  for dropping rockets on civilians for decades now.  What’s good for the goose is good for the gander!  Hypocrisy at the UN stinks!

As for everybody else:  look out for your own right-wing extremists!  They are among you!  They are invariably very authoritarian,  and they invariably want to “eliminate” (kill) their opposition.  If they have committed any crimes,  jail them for it!  Even if not,  you need to vote them out,  not in!  Or else you will have to revolt after they have established their dictatorships over you.  Doing it at the ballot box instead,  leaves a whole lot less mess to clean up!

And when I point my finger at you all,  my thumb is pointing back at me!  We face the same peril here in the US,  with multiple failed attempts (including an insurrection) to set up a right wing extremist dictatorship,  precisely because we voted an authoritarian in,  instead of out,  and he did not want to give up power when his term in office was over.  And now he wants another shot at it!  Surprise,  surprise!

Trump Cult Warning

The following is the text of a signed letter I sent to PBS's NewsHour at their "viewermail" address.  The letter is a warning about the threat of a coming dictatorship in the US.  I am shouting from the rooftops about this threat!  As for the image,  some "peaceful tour or demonstration" that was!

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A much-edited version of this appeared as a column in the Waco,  Texas,  "Tribune-Herald" 30 January 2024

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I am still astounded that no one trying to responsibly report the news seems to understand where all the rabidly-loyal Trump voters are coming from,  and why they persist in their support,  despite the serious criminal trials of Trump that are coming.  They so very clearly want him,  even if he is in jail!

That’s because it is a fearless leader cult built around Trump in the run-up to the 2016 election,  from roots in the “Qanon” on-line conspiracy.  Cults are cults,  belief outweighs the importance of any facts!  They operate by brainwashing,  and the Trump cult has been brainwashing GOP voters since 2015. 

Our cowardly GOP politicians know this,  which is why they cravenly do whatever the brainwashed crowd wants,  no matter how nonsensical or evil.  They still outnumber the true Trump cultists in the GOP,  and yet they are utterly subservient to them,  because of those brainwashed voters.  That is what “primarying” really means!

The GOP has morphed from a largely corporate-friendly membership 3+ decades ago,  to a major percentage of uneducated blue-collar membership today,  precisely because uneducated people are far easier to brainwash!  The brainwashing is done by both the politicians themselves at their rallies and events,  and by the “social media” on the entirely unregulated internet,  which freely spouts all sorts of lies,  and even Russian (and other) propaganda!  If you don’t believe me,  go look for yourself! 

That unregulated lying mess is where most GOP voters get their “news” and their “facts”.  If you don’t believe me about that,  go ask any of them!  But that unregulated lying mess is also why they don’t believe any of the “mainstream media”,  which is you,  the responsible journalists still left in this world!  And I think you do know about that!

Political cult,  religious cult,  or some of both,  it does not matter.  All have a purpose,  and a top-of-the-list thing they want to do.  These are usually initially secret,  but they always come out.  Trump’s former advisor,  retired General Flynn,  spilled the beans in public about the Trump cult’s purpose,  some years ago during Trump’s term in the White House:  a dictatorship over the US,  with Trump at the top.  This was to start with the military being ordered to confiscate voting machines,  then re-running the election to get the outcome the Trump cult wanted.  (Updated in red 1-27-2024.)

Trump himself has made clear what his top-of-the-list priority is,  once he takes power: to kill all his opposition,  just not in those exact words.  His word is “retribution”.  But that’s what it ultimately means!  If you look at the Qanon roots of the Trump cult,  “the storm” is where they round up all who oppose them (termed “deep state”),  maybe (or maybe not) try them by a military tribunal,  not a real court,  and execute them.  That intent has not changed on the internet since 2016;  I have watched it.

Liz Cheney was,  and is,  correct:  this nation is sleepwalking its way into a dictatorship!  The GOP has absolutely no business running a multiply-indicted (and likely convicted) felon for the office of President,  or anything else!  Especially one so evidently guilty of fomenting an insurrection!  That they are running him is proof that the craven-coward politicians,  and the Trump cult members of Congress,  are together in total control of the Republican party,  which clearly is no longer a responsible entity!

All the responsible media,  NewsHour included,  should be screaming about this abomination from the rooftops!  I certainly am.

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I have written articles before,  on this site about the Trump cult.  The best one is "Beware of Leader Cults",  posted 16 February 2020.  Use the navigation tool on the left to find it quickly.  All you need is the date and the title.  Click on the year,  then the month,  then the title if need be. 

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Update 1-27-2024:  add another image as proof of roots.  Look at caps,  then at sign.

Update 6-6-2024:  Well,  "Teflon Don's" teflon now has at least one big hole in it:  he is now a convicted felon,  with 3 more felony trials looming!  And it's by a state court,  not federal,  so even if he becomes President again,  he cannot pardon himself of this!  He is a convicted felon who now wants to you all to re-elect him,  so he can become dictator over you.  Like he almost did before,  with the Jan. 6 insurrection he incited.

I reiterate:  the Republican Party has absolutely NO business running a convicted and multiply-indicted felon for President!  The President is supposed to be a role model for our children,  among many other things.  Donald J. Trump is NO role model of anything good!  That alone should disqualify him in the minds of all but the most brainwashed voters!  Not to mention his wannabee-dictator ambitions!

Immigration Crisis?

Yes,  there is one.  No,  it is not the fault of Presidential administrations of either party.  It is primarily the fault of a dysfunctional Congress not doing its sworn job.  See the figure.

This has been neglected since right after the end of World War 2,  except for one ineffective change that George W. Bush got through Congress about 20 years ago.  The public has become aware over the last 2 decades that there is a problem,  but Congress lies about whose fault it is,  instead of doing something constructive about it.

The guest worker quotas have always been set too low,  since 1945.  Congress sets the maximums for the worker visa quotas.  Administrations may issue less,  but not more. Those visas cannot be tracked effectively,  because Congress never appropriated the money to hire the people to do the tracking job.  Why should anyone be surprised that,  after decades of this mismatch,  there are something like 10 million illegal residents in the US?

Until about 2 decades ago,  the number of guest workers we had to deal with was very much greater than the number of asylum seekers we had to deal with.  Under federal law,  asylum seekers must be granted a hearing before an immigration judge.  The number of these immigration courts and their infrastructure depends upon what Congress funds.  They were barely adequate 2+ decades ago. 

The smugglers of drugs and people were only as numerous as they were 2 decades ago,  because of the illegal guest workers to be smuggled.  Our border patrol was roughly adequate to the task then.  No longer.

Since then,  a large number of failed states in South America,  the Caribbean,  and elsewhere have produced vast numbers of refugees seeking asylum,  far more now,  than we ever saw 20+ years ago!  The US has absolutely no control over the conditions forcing those people to flee.  And under federal law,  they are guaranteed a hearing before an immigration judge;  not entry,  just the hearing.  That law says nothing about how they crossed the border to come apply.  

Administration policies requiring deportations without that hearing are the Executive Branch literally violating federal law instead of enforcing it.  The wait time for an immigration hearing now is a few to several years,  because Congress has not funded an increase in the number of immigration courts to address the vastly increased demand.

Walls and barriers demonstrably do not work nearly as well as claimed.  Even when they do work,  their actual effect is to deny asylum seekers the hearing they are entitled to,  under our laws.  That denial is a violation of our laws.   So are the stay-in-Mexico policies,  and similar stuff.

What we need is a Congress that will update those laws and fund the infrastructure that enables Presidential administrations to enforce them faithfully. 

What we have is a long history of dysfunctional Congresses blaming administrations of the opposite party for the crisis,  just to drum up votes.  Playing politics is so very clearly prioritized way higher than actually doing the jobs they swore to do.  It also shows up in Congress not having passed a proper budget in almost 20 years!  Oath-breakers!

And bear in mind,  your own Congress has been lying egregiously about this immigration crisis (and many other things) to you,  the citizens,   for some decades now.  Both major parties do it,  but one is currently worse than the other about that.  I’ll let you readers guess which one. 

Hint:  the one that wants the border walls everywhere.

There is a “fix” for this,  and it is coming up this very November!  Throw the bastards out!  All of them!    They certainly deserve it for playing hardball politics instead of doing the jobs that they swore to do!  Try somebody new,  it does not matter who. 

You cannot do any worse than what you have now.  But you might do better.

Update 1-12-2024:  It nauseates me to see the House GOP controlled by Trump-cult extremists who freely abuse any lever of power to get what they want,  when they have not the votes,  all the while lying so egregiously about what they are doing.  My article above makes abundantly clear that the immigration crisis is the fault of Congress's dereliction of duty over many decades,  and not the fault of the current President or any of his predecessors.  Yet blaming Biden is the loudest noise being made by the Trump cult extremists dominating the House GOP. 

 

Airplanes on Mars?

In a word,  probably not. 

The mechanics required for steady flight are illustrated in Figure 1 below.  Basically,  lift must balance weight,  and thrust must balance drag.  For clarity,  the moment balance about the center of gravity is not depicted. 

Lift and drag are both proportional to the wind pressure and the wing area.  The coefficients of proportionality are the lift and drag coefficients.  Control of lift is by angle of attack (AOA),  and the usable lift coefficient only varies between zero and the stall value (a bit over 1).  For control purposes,  the same basic lift coefficient values must be used on Mars as on Earth.

The wind pressure (q, the dynamic pressure) is proportional to density and to velocity squared.  The density can be calculated as a density ratio (σ) multiplied by a standard density value (ρ_o).  Earth sea level density on a standard day is the usual value used for that standard density.  Values are shown. 

Under ideal gas assumptions (P = ρ R_univ T/MW),  the density ratio pretty much anywhere is the pressure ratio to Earth standard pressure,  multiplied by the molecular weight ratio to standard,  and divided by the absolute-scale temperature ratio to standard.  For typical pressures and temperatures on Mars,  density ratio is near 1% of Earth sea level,  but this is quite variable since the “air” pressure there is quite variable.  An average value is shown.  Surface gravity on Mars is 38% that on Earth.  

To design aircraft for Mars,  we need the surface density ratio divided by the surface gravity ratio.  The net effect is that the levels of the aerodynamic forces acting on a reduced weight on Mars, are about factor 35 smaller than here on Earth,  at otherwise the same AOA’s!  That factor can increase either the wing area or the square of the velocity,  or some of both,  to get the same balance for steady flight on Mars. 

Note that if you make the wing bigger,  it will be more massive in proportion to that increased area,  and therefore heavier,  even in the lower gravity of Mars.  The weight increase of more wing area will act toward overcoming any lower speed benefit.  That is because the density effect is much larger than the reduced gravity effect,  on Mars.

Velocity squared factored up by 35 is the same as velocity factored up by almost 6.  Example:  if landing and takeoff speed for some airplane design was about 100 mph on Earth,  it would be almost 600 mph on Mars for the same wing area as on Earth.  Such speeds that close to the surface are quite dangerous.  That is just not something to be attempted voluntarily. 

Double the pressure to 12 mbar in the Hellas Basin,  and the over-100 density reduction factor halves.  That density ratio divided by the gee ratio is now closer to 17 than 35,  and its square root is a velocity ratio a bit over 4.  It’s still a bigger,  heavier (and impractical) wing by a factor of 17 on wing area,  or else a speed near the surface exceeding 400 mph.  Or something in-between,  with an impractically-large wing and a speed that is still too high close to the ground to be safe.  Not at all safe to attempt. Plus,  you cannot fly it anywhere except down in that basin.

The same basic aerodynamic and weight-carried factors act on helicopter rotors in pretty much the same way.  This is why I think the use of airplanes (or helicopters) as we know them here on Earth,  at a size scale suitable for transporting freight or people,  are simply not technologically feasible in the extremely thin “air” of Mars,  despite the lower gravity. 

Not absolutely impossible,  but a practical design configuration is pretty much unimaginable. 

Figure 1 – First Cut Exploration of Aircraft Design Requirements for Mars

Second,  Closer Look:

Now,  looking at this issue a bit more closely,  let us explore landing and takeoff speeds that are practical,  and at lift coefficients that are high,  but with adequate stall margin,  sort of like what is required by the FAR’s here on Earth.  For that,  I presume 120 mph = 176 ft/sec = 53.6 m/s,  and a max lift coefficient at takeoff and landing of 1.0.  I also looked at high altitudes on Earth,  and at higher pressure in the Hellas Basin on Mars.  I did this with a spreadsheet,  as illustrated in Figure 2 below.

Those numbers for Mars might not seem too bad,  until you try to sketch what that kind of a change to an aircraft design might look like.  I did that in Figure 3 below,  holding the fuselage size constant,  and just up-sizing the wings and tails.  There is no way to get the required tail arm lengths for stability and control,  without also up-sizing the fuselage,  which drives up mass even further!  It would be the same with a swept-wing design for higher cruise speeds:  you still have to land and take off!  

That should indicate just how impractical it will always prove to be,  to design conventional airplanes capable of safe and practical flight on Mars,  regardless of the propulsion.  That “air” is just too thin!

Figure 2 – Sizing Wings for 120 mph Takeoff/Landing Speeds on Mars

Figure 3  -- Upsizing Aerosurfaces for Fixed Fuselages For Mars