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Those Isp charts are marketing hype.  I first saw them about 50 years ago.  No one design will ever follow any of those curves,  even at low altitude,  which low altitude is what the T/W ratio chart really is. 

I have said it before,  and I will say it again:  ANY airbreather of any type whatsoever,  has a service ceiling!  This is because ALL airbreathers (of any type whatsoever !!!) have a combustion chamber pressure that is pretty much fixed as a ratio to the local atmospheric pressure.  That combustion chamber pressure ratio to ambient is pretty well proportional to the engine thrust,  whatever type of airbreather it is.  That's just basic thermodynamics,  a subject few ever take.  I majored in it,  among other things. 

At very high altitudes,  thrust is low because ambient atmospheric pressure is low.  That is INHERENT with any type of airbreather whatsoever.  This has been known since the end of WW1 (yes,  I said WW 1 !!!) and there have been no violations of that trend since then. Only the ratios vary with engine type.  But once you are high enough,  there is no significant thrust,  because your ratio multiplied by essentially nothing for an ambient pressure is essentially nothing as thrust. 

The highest airbreathing engine operation ever achieved was in a French ramjet test many decades ago,  at 125,000 feet.  I am entirely unsure whether thrust was greater than drag up there,  but I am entirely sure that thrust was less than weight.  This was a zoom climb test that apogeed out at no speed,  and fell back.  Even scramjets are VERY UNLIKELY to develop significant thrust at such an altitude. 

Service ceiling is defined by a 200 fpm climb rate under the FAR's,  but effectively it is the altitude at which your design is barely generating lift equal to weight at a relatively-efficient angle of attack near that for high vehicle L/D,  and your thrust,  being all you can deliver,  is essentially just barely equal to your drag.  You cannot accelerate to higher speed,  and you cannot climb at any humanly-sensed rate.  PERIOD.  End of issue. 

Rockets are not subject to that limitation,  since their chamber pressure is utterly independent of the ambient atmospheric pressure,  at any altitude whatsoever.  You cannot presume that a ramjet or a scramjet is going to give you enough thrust to both climb and accelerate at altitudes in the 100,000-125,000 foot range.  If you don't have thrust to accelerate your vehicle mass,  Isp is worthless BS. Simple as that!

Do not be fooled by names:  an "air turborocket" (ATR) is an airbreathing engine,  not a rocket,  and not a very efficient airbreathing engine at that.  I know,  I literally have worked on air turbo rockets,  as well as ramjets and gas turbines,  and of course piston engines. 

There is no "magic" here with any kind of airbreather,  ramjet,  scramjet,  or anything else remotely conceivable!  It has a speed limit beyond which efficiency and Isp reduce.  But the altitude limitation for ANY of them is down nearer 100,000 feet (30 km),  than anything you might ever need to reach orbit.

Second point I have covered before:  the Skylon airframe will NEVER survive reentry,  not with wingtip-mounted engines!  No entry spacecraft has EVER featured parallel-mounted nacelles,  and no entry spacecraft ever will!  That answer has been known since the 1968 X-15A-2 flight that reached Mach 6.67 at about 100,000 feet altitude.  It is called "shock impingement heating",  and it is fatal,  even at low hypersonic speeds. 

Those who fail to learn from history are doomed to repeat history's failures.  PLEASE wake up and smell the coffee!  Talk to some of us oldsters who were there,  when the mistakes and the successes were made!  Not everything was ever written down in the final reports,  not by a long shot!

GW

What I showed was an all-expendable SSTO could be built,  with the best-performing version using LOX-LH2,  and plain-vanilla metal tankage of about 5% stage inert mass.  I also showed that the dominant effect is raw Isp,  not density impulse (although that does act in the right direction).

The biggest problem is getting engines of a chamber pressure high enough to reduce their dimension enough so that enough of them would actually fit behind the stage at both an acceptable stage L/D ratio (something in the 6 to 10 range or else you need to double the 5% drag loss you assumed),  and an acceptable takeoff thrust/vehicle weight ratio (something above 1.5,  or you need to double the 5% gravity loss you assumed).  I could not achieve believable engines that would fit,  with methane. 

This thing had roughly the same payload fraction (about 6-7%) as an all-expendable TSO using LOX-LH2 in the upper stage,  and pretty much any combination you desire in the lower stage.  The real problem is the all-expendable design.  You lose your engines every time you fly,  and these will have to push engine state-of-the-art VERY hard,  so they will be very  expensive things to lose. The economics would be horrible,  when by payload reduction to about half,  you can recover the booster of a TSTO,  leaving the rest of the design expendable.  That is a fairly easy way to get far better economics,  as we have all seen,  here in recent years. 

There is no "lower thrust/weight" ascent trajectory for vertical launch.  You either dawdle at lower net effective acceleration and use most of your propellant in the first 30,000 feet,  or you accelerate much harder and use your propellant more efficiently.  You need at least 0.5 net gee upward off the pad,  for a thrust/weight ratio of at least 1.5.  We've already seen it many times since the 1950's.  That effect is just no longer debatable.

Making an SSTO into a reusable craft is just NOT going to happen at a stage inert fraction in the 5-10% range!  Neither will be making a TSTO upper stage reusable (something SpaceX is attempting with its Starship upper stage,  and they are not yet successful).  These things,  to be reusable,  must also be fully-qualified reentry vehicles,  and must also be fitted out to land,  either vertically or horizontally.  That costs added mass,  period!  It is unlikely in the extreme to even happen nearer 15%.  Most aircraft have inert mass near about 40% of max takeoff mass.  Using composites reduces that below that notional 40%,  but you cannot use them everywhere.  Nowhere that gets really hot,  for sure!

You run the rocket equation for yourself,  at any Isp you think models a propellant combination you like,  but with a ~25% inert mass fraction.  If you get a positive payload fraction without using some sort of gas core nuclear,  I'd like to hear about it.  I typically get around 1300 sec Isp min. Higher if you want significant payload fraction.

Airbreathers reaching a practical staging speed or transition-to-rocket speed in the 1-2 km/s range,  are simply not a practical way to approach this.  The air at the requisite staging or transition altitude is just too thin,  you are 40+ km up!  Maybe 60+ km up!  ALL airbreathers (no matter WHAT they are!!!) have a thrust level that is more-or-less proportional to the atmospheric pressure in which they are flying.  Up there,  5-to-15 times nothing is still nothing!  No significant thrust to push considerable mass!  You will neither accelerate nor climb!  It is called the "service ceiling" effect.  Only rockets are immune to it.  Because they do not breathe air.

GW

Kbd512:

I didn't say there was anything wrong or bad about composites.  I just pointed out the impact damage vulnerability using carbon fiber or cloth.  That results from the low elongation capability of carbon fibers.  It is inherent.  The other materials do not have the strength and stiffness needed for that option,  but at least one of them is very resistant to impact and puncture damage.  That is the kevlar-vinyl ester material used in airliner interiors,  especially the floor deck panels.  They found out back in 1958 not to use aluminum alloy floor panels:  ladies' spike heels poked holes through those panels,  simply walking.  The kevlar-vinyl ester panels have successfully resisted that ever since.

I did point out ways that a composite overwrapped steel tank might fail.  The ways I pointed to are defects in the metal weld zone,  not the composite,  which gets added later in the manufacturing process.  Could be a weld defect,  could be a bad joint design with too little added thickness near the weld.   Some steel with a lot of elongation would survive only a single handful of pressurizations,  before cracking apart,  without the extra thickness to "sop up" the bending stresses coming from the radial displacement mismatch at the cylinder-to-head joint.  A more "brittle" steel would fail immediately. 

My guess is that these newbies at SpaceX (none over 40-45 years old,  most are under 25-30) are welding as-supplied stock sheet metal together without any added thickness at the joint.  With a single handful of fatigue cycles available at the weld joint in a pressure vessel,  at the cylinder-head joint,  "unexpected" failure is inevitable!  The overwrap cannot prevent that,  even if you lap it over the joint a bit!  They need to use the weld joint shapes in the ASME boiler code. 

And this same design flaw applies to a lesser degree to all the welded ring joints in the Starship and Superheavy hulls.  Those are all heat-affected zones that are also affected by weld physical chemistry.  They have less tolerance of strain than the base metal,  even if you get full weld strength by doing electron beam welding,  which SpaceX is NOT doing!  I've seen the videos,  they are stick-welding those hulls.

Makes you wonder where some of the methane (and maybe oxygen) leaks have come from,  does it not?  Maybe where all the ice particles came from,  inside the cargo bay during that last flight?  Since there was a LOX header tank in the nose,  adjacent to a nitrogen COPV.  Any sort of tank flaw,  or any sort of plumbing defect,  could cause such leaks.  And many others not well understood up to now. 

Just food for thought. 

By the way,  I actually like composite materials.  I've built a lot of them with my own two hands,  many years ago.  Every material has a "right" application,  and a "right" way to be processed.  And a "right" way for the application to be designed,  for that matter.  You do it "wrong" at your peril. 

GW

The single-click link is to my article "More Refined 1- vs 2-Stage to LEO",  posted 11 March 2024,  to which I just added a search code 11032024,  based on the date of posting in DDMMYYYY format,  all as one number.  The most telling plot of trends is in Figure 25,  pretty near the end of the article,  in one of its updates. 

The SSTO is far more sensitive to the exact values of engine performance parameters,  and only results in overall payload fractions comparable to TSTO,  when you use LOX-LH2 as the propellant combination.  The TSTO is far less sensitive to such details,  and has ballpark-similar overall payload fractions for pretty much any modern propellant combination in the first stage,  as long as you select LOX-LH2 for the second stage.

GW

I've already answered that question using the spreadsheets and other "orbits+" course materials.  Yes,  an SSTO can be built,  and if LOX-LH2-powered,  it can pretty much equal the performance of a TSTO based on LOX-RP1 in the booster and LOX-LH2 in the upper stage.  That answer is already either posted or referenced here on these forums.  And I have had it posted for some time on "exrocketman". 

That was for all-expendables,  by the way.  Reusable is quite the different story.  It is easy to reuse lower stages.  It is very hard to reuse upper stages,  and even harder to reuse an SSTO,  because it must survive by the same means as the so-far-mythical reusable upper stages.  That is neither lightweight nor cheap,  no matter how one attempts to do it. 

GW

What you put into the rocket equation is a dV that has been increased to cover gravity and drag loss effects.  I have been calling that the mass ratio-effective dV.  Those corrections can be rather substantial for launch to LEO. 

The other thing the rocket equation requires is a realistic Isp from which an effective Vex can be determined.  That is the other reality check:  picking an Isp out of published comparison tables is too inaccurate to serve.  You must actually do the ballistics of the engine to get a reliable figure.

One of the things the rocket equation completely ignores is thrust versus weight.  Your results cannot be realistic until and unless you investigate that,  with realistic criteria by which to judge.  The normal Earth launch gravity loss is around 5% of surface circular orbit speed,  but that is only true if your net upward acceleration exceeds half a gee,  meaning takeoff thrust to weight exceeds 1.5!  Fail to achieve that,  and your gravity loss correction could easily double or triple!  Those loss figures are just empirical correlations,  by  the way.

The other thing the rocket equation completely ignores is whether the engines actually fit behind the stage without sticking out laterally into the stage slipstream.  If they fit,  then for an aerodynamically "clean" shape of L/D 6 to 10,  the drag loss is typically about 5% of surface circular orbit speed.  If they don't fit,  the extra drag can easily double or triple your drag loss.  The same is true if your vehicle L/D falls outside the 6 to 10 range,  or the shape has bulges,  protuberances,  or large changes in diameter.   

I know it is complicated.  But you have to investigate such items to get reliable results!  THAT is the lesson of history here!  And it is why I do not use the little on-line calculator offerings,  as typically,  these crucial items are NOT included in those models. 

GW

That patent was for adapting a simple showerhead injector whose ports were the gas generator throat for a fixed flow design,  to the presence of a throttle valve upstream as the gas generator throat in a variable-flow system capable of arbitrary fuel flow commands. 

I had to maintain choked flow at the ports of the injector while avoiding flow acceleration on the way to the next ports.  The fixed-flow form had a very subsonic Mach number in the injector.  For the variable flow form I had to step the ID at each set of ports to maintain a constant high internal Mach near 0.8 to 0.9.  The port sizes had to be large enough not to unchoke the throttle valve at its max area,  but also small enough to still choke at the min valve area.  And it had to do this despite the intensely 3-D supersonic expansions and shock-downs just downstream of the throttle valve throat. 

That throttle worked as a side-inserted pintle into a throat blast tube.  I played a key role in making that throttle valve item work,  too,  to include working out the real-world ballistics of a solid propellant device with such a variable throat,  which showed why linearized throttle control logic systems always failed (those motors invariably blew up).  Those ballistics were unbelievably non-linear in nature.  Once we had the nonlinear adaptive gain determined,  we never lost another motor!

My injector patent was assigned to Hercules Aerospace,  where I worked at the time in their McGregor plant (it had been Rocketdyne Solid Rocket Division when I first went to work there).  This thing was verified extensively in live fire ground tests and was ready to fly when the McGregor plant was closed.  The JV partner ARC put it into their Coyote drone for the Navy.  It was originally intended for a ramjet upgrade to the AIM-120 AMRAAM.  USAF never fielded that upgrade (and there is a rather sordid story behind that failure),  although the Europeans have fielded their version of the very same idea:  Meteor. 

--  GW

There were two variable throat area technologies that I worked on long ago. 

One was the rotating "lollipop" for the ASALM variable geometry nozzle option that was not flown.  It could have,  but the prime did not choose to do that.  That is the technology described in the posts just above.  It was survivable at ramjet throat conditions,  but would not be survivable at rocket throat conditions,  where the higher pressure drop would drive larger shear forces that would strip the silica phenolic ablative right off the steel.  This also shows up in the fact that monolithic silica phenolic nozzles work well in ramjets,  but not in rockets,  which needed a hard graphite throat insert instead.

The other was a side-inserted pintle into a throat tube,  for the fuel-flow throttle valve of a gas generator-fed ramjet.  The fuel-rich solid propellant's effluent stream was the fuel to be burned with air in the combustor.  This was a successful technology,  and while ours did not fly in a ramjet AMRAAM,  something similar to it is flying today in the European "Meteor" missile,  which is a very similar gas generator-fed ramjet.  Ours did fly in the USN "Coyote" gunnery target drone,  after our plant got closed.

It was the relatively cool and reducing environment of the fuel stream that allowed us to make the pintle and the throat tube out of TZM alloy,  despite the high solids content and its gritty erosive nature.  There was a sort of tower out the side of the throat tube that contained a stack of graphite heat sink rings,  which pulled enough heat out of the pintle to allow a gas seal to survive at the cool end of it.  This tower's shell was part of the pressure vessel.  This thing worked on a transient only,  with about a 2 minute capability,  at 1700-2500 F gas temperatures,  and upstream chamber pressures from 50 to 2200 psia.  The cool end of the tower is where the motion servo and measuring gear were mounted.  The TZM had a ~4000 F meltpoint,  but would oxidize away rapidly if there was any oxygen present. 

This was a fuel throttle for massflow control of the solid gas generator burn.  It had nothing to do with producing thrust.  The smaller the net throat area,  the higher the equilibrium pressure,  and the higher the flow rate.  The flow about the pintle was wildly 3-D,  with a wake zone and oblique shocks.  The shock-impingement and associated amplified heating upon the throat tube were handled by the TZM,  but there was silica phenolic ablative between it and the surrounding pressure shell.  This thing led to a showerhead-type fuel injector,  which had to be specifically designed for very high subsonic internal flow speeds, in order that the hole sizes would still help direct how much fuel effluent went where.  I got the patent for that.

This sort of thing might be at least theoretically used to vary the throat area of a rocket,  but the cooling requirements will be enormous.  The gas temperatures are well above the meltpoint of TZM,  and there will likely be oxygen present at low concentrations,  ruling out the use of that alloy.  The very high chamber pressures (3000-5000 psia) will stress the thing severely.  And there is the wildly-3-D flow field downstream of the pintle.  That will really mess up the expansion-for-thrust in the bell.  And if the pintle wake does not close before the exit plane,  you have the same massive thrust inefficiency problem that I already described for the ASALM lollipop.

The pintle throat was never developed or tested for rocket nozzle application,  only the fuel effluent throttle for a fuel-rich solid propellant gas generator (which is a misnomer because of the high solids content in the effluent).  The "lollipop" was tested,  but only at ramjet conditions.  It was developed to the point of readiness for experimental flight test.  The pintle was also developed to the point of readiness for experimental flight test,  but only at those gas generator conditions,  and for a showerhead injector,  not a thrust-producing expansion.

Both of these were "one shot" missile designs,  not anything to be reusable.  These technologies were very difficult development items,  even though they were restricted to their less challenging applications.   

GW

ASALM was a ramjet.  When you lean down to lower thrust for efficient cruise,  the combustor pressure drops a little,  which means the inlet pressure drops a little.  When that happens,  the terminal inlet normal shock lies deeper down the inlet's divergent diffuser section,  where it takes place at a higher Mach number and is therefore stronger with a larger total (stagnation) pressure loss.  That lowers cruise Isp a little from the higher level that leaning-down provides.

The sketch showing flow "clinging to the walls" is not quite right as it is drawn.  There is a "cling to the walls" effect,  but there is also a separated wake closure effect that is not at all depicted in the sketch. 

This is because of Prandtlt-Meyer expansions and oblique shock compressions and changes of direction.  It will over-expand around the obstruction,  then where those flows collide on centerline,  oblique shocks straighten the flow back out to axial.  The more 3-D the obstruction shape,  the more complicated the flow pattern.

If you can achieve obstruction wake closure before reaching the bell exit plane,  your nozzle kinetic energy efficiency stays high,  although not quite as high as a "clean" nozzle with no throat obstruction to create a wake.  If you do not achieve closure before reaching the exit plane,  your nozzle kinetic energy efficiency drops precipitously! 

The low kinetic energy efficiency multiplies the Mach number squared term in the CF equation,  which is where most of your thrust comes from.  We verified this in flow visualizations,  cold flow tests,  and hot firing ramjet tests with Shelldyne-H fuel (also known as RJ-5) and heated air. 

Injecting fuel near a ramjet throat has no chance of being successful!  You might as well just dump it overboard,  because it has no chance to burn.  The combustor residence time of 2 to 3 msec is just barely enough to get around 95% of the fuel injected in the inlet burnt.  From throat to exit plane the residence time is a tiny fraction of a msec. 

Besides,  the injected fuel streams will have no perceptible effect on the gas flow pattern through the throat,  for two reasons:  (1) the fuel mass flow is tiny compared to the air mass flow,  even if you inject ALL of the fuel there,  which you cannot,  and (2) the volume of the fuel stream is exceedingly tiny compared to the volume of the air stream,  precisely because the density of the liquid is much higher than the gas,  and the mass flow of fuel is so small compared to the air.

GW

Basically,  for things like helicopters and rotor drones,  plus chute openings,  and small conventional airplanes,  if you can design it to work without using atmospheric oxygen and operate at about 110,000 feet here on Earth,  it will work on Mars. 

There is an issue of how things scale here.  Mass increases as dimension cubed,  while area increases as dimension squared,  all else equal.  Weight to be held up by thrust or lift increases as the cube of dimension,  faster than any wing or blade areas,  which scale up only as dimension squared.  That means it is easier to build very small things that fly than it is to build very large things.  And THAT is Ingenuity could fly on Mars,  when an electric Bell Jet Ranger probably could never be made to fly in air that thin!  The Bell has trouble flying at only 30,000 feet. 

Kbd512 is right,  it's very complicated.  There's more than just aerodynamics or propulsion at work here.  That scaling effect is VERY real,  too!

GW

Just remember,  when in development flight tests,  projected operational payload capacity figures to LEO are speculative guesses,  spelled "BS".  Once this vehicle starts making survivable landings from orbit,  we'll have a better idea what that payload might really be.  They have a lot of changes to make yet,  to solve a lot of fatal problems they still face.  And nobody yet knows what those changes really are.

As a first guess toward tanker flights to effect a full Starship refill on orbit,  you need the tank capacity,  and the mass of propellant deliverable as payload on-orbit.  Starship v.1 had 1200 metric ton propellant capacity.  If its operational deliverable propellant payload was 200 metric tons,  it would take 1200/200 = 6 tanker flights.  If its deliverable propellant is 150 tons,  it would take 1200/150 = 8 tanker flights.  If its deliverable propellant were 100 tons,  it would take 1200/100 = 12 tanker flights.  Simple as that! 

Starship v.2 has 1300-something tons of propellant capacity.  Maybe.  We'll see how it really changes in order to survive a test flight.  It'll take more tanker flights,  at the bigger capacity,  presuming the same range of payload figures.  And to go to the moon or anywhere else outside LEO,  you need to do a full refill on-orbit!

as for the alternate lander and mission:

The alternate mission profile makes good sense to me,  except that whoever created that illustration still calls out that crazy lunar halo orbit.  It is pretty clear there is not going to be a Gateway station,  so why retain an orbit that adds 50% or more to the propellant capacity needed of the lander? (***) If instead you do a relatively low orbit,  you can carry more lander payload if you need less lander propellant.  But beware,  your lander is not reusable unless it is 1-stage,  and it is refilled on-orbit about the moon. 

*** Answer:  SLS/Orion using the interim upper stage cannot send an Orion into low lunar orbit and still get back out to come home.  Orion's service module is too small for a capsule that size.  You do have a bigger dV getting into low lunar orbit compared to that crazy halo with its periapsis so high above the moon.  Earlier mistaken decisions do have a habit of coming back later,  to bite you in the rear,  do they not?

answer to that *** answer:  Delete SLS/Orion as too expensive and too incapable.  Do it instead with a Dragon atop a Falcon-Heavy,  plus another unladen Falcon-9.  Dragon's good for 2 weeks life support,  all you need for this.  Dock the unladen Falcon-9 upper stage (which has the most unused propellant aboard) to the nose of the Dragon,  and use that for trans-lunar injection.  Use the Falcon-Heavy upper stage for the return to Earth.  You should be able to accomplish that from LLO,  not that crazy halo.   

Use the extra tank volume left over in the lander that was designed for the higher 2-way dV,  for getting into LLO instead of the halo orbit.  Then you can still carry more payload than you previously thought to the moon,  because the propellant you still have is more than enough for the lower dV requirement.  You set your LLO altitude just high enough to make this work,  but nowhere near as high as that 3000 km periapsis of that crazy halo.

BTW,  that crazy halo was unstable:  it had a 70,000 km apoapsis,  when the stability limit Hill sphere radius was only 60,000 km.  That's what drove periapsis speed to only a snit lower than lunar escape.  In turn driving up the 2-way dV requirement to land by more than 50%.

GW

1.2 m dia is 0.6 m radius.  Tip V = R w,  where w is the rotation rate in radians/s.  At 2900 rpm,  w = (2900 rev/min) * (2 pi rad/rev)/(60 sec/min) = 303.7 rad/s.  Tip V = R w = 182.2 m/s.  If the speed of sound c is about 240 m/s on Mars,  then tip Mach M = tip V/c = 0.76. 

GW