Thursday, July 1, 2021

Another Ramjet That I Worked On

This adds to the discussion in Ref. 1 about ramjets on which I have worked.  The topic here is "ASALM-PTV".  The topic in Ref. 1 was the Russian surface-to-air missile known to NATO as the SA-6 "Gainful".  I had the experience of doing the foreign technology exploitation work on the SA-6's fuel and ramjet engine.  ASALM was a US effort that I worked on.

ASALM is an acronym for Advanced Strategic Air-Launched Missile,  and the PTV stood for "Propulsion Technology Validation".  This ASALM-PTV was a propulsion verification test article for a supersonic strategic cruise missile to be known as ASALM.  That weaponized-design cruise missile ASALM was intended to carry the same 1000-lb conventional or variable-yield nuclear warheads as the Tomahawk cruise missile,  just 5 times faster and some 16 miles up instead of 200 feet,  making it essentially invulnerable to all known defenses. 

The ASALM-PTV test vehicle was somewhat heavier in construction,  and designed for shorter endurance and range,  but otherwise demonstrated all the key features of the ASALM weapon design.  These were the chin inlet,  the short S-duct turn,  the coaxial sudden-dump combustor,  the integral booster and transition scheme,  the fuel injection aerogrid device,  the fuel control,  and the internal heat protection and booster propellant bonding scheme.  See Figure 1. 

Figure 1 -- Comparing ASALM-PTV to ASALM And Its SLAT Derivative

ASALM-PTV flew 7 times in flight tests at Eglin AFB in the 1979-1980 time frame.  The first test experienced a throttle runaway incident,  and so it unintentionally set a hypersonic speed record for vehicles powered by airbreathing propulsion,  and furthermore it did that at low altitude!  That speed record stood for nearly a quarter century,  until NASA broke it with its X-43A scramjet test article in 2004,  at very high altitude with a brief 3-second airbreathing burn,  rocket-boosted all the way to test speed at Mach 7. 

ASALM-PTV accidentally reached about Mach 6 in that runaway ramjet burn,  starting from a Mach 2.5 ramjet takeover at end of rocket boost,  after a 20,000 foot launch for that first test.  The original intent for the first test was for the vehicle to fly a racetrack pattern,  at 20,000 feet and a sedate Mach 2.5,  to fuel exhaustion,  using simple timed turns,  in order to check out the ramjet systems.  Because of the throttle runaway problem,  it left the range and reached fuel exhaustion at hypersonic speed,  before the first timed turn could occur. 

We found it 3-4 days later,  stuck like a big steel dart,  in a farmer's field,  about 10 miles outside the airbase.  The final telemetry from the vehicle just before we lost it,  translated as "I am at Mach 6 and still accelerating as my skin begins to melt.  I just ran out of fuel.  Goodbye."  Well,  at least the other ramjet systems besides the throttle control worked just fine,  obviously.  So we counted that one as "half-successful".   

The other 6 ASALM-PTV flight tests were letter-perfect,  including the design cruise missile mission:  subsonic air launch,  supersonic climb to cruise altitude (80,000 feet),  high supersonic cruise (Mach 4) for a long range,  and high-supersonic dive (terminal about Mach 5) onto its target.  With the first one "half-successful",  that made us 6.5 for 7.  Not too bad!

Unlike what most internet sources say,  the program was really cancelled because of SALT-II treaty limitations on allowable numbers of strategic cruise missiles,  with the already-fielded Tomahawk entering full mass production.  See Figures 2 and 3 for what the ASALM-PTV test vehicle actually looked like.  It was 20 inches outside diameter and 14 feet long overall.  And it was 2500 pounds at launch. 

Figure 2 -- ASALM-PTV Flight Test Article Underwing On an A-7D

Figure 3 -- ASALM-PTV Dropped From A-7D,  Igniting Booster Well Away


I like to consider the images in the two figures to be a sort of "family portrait".  I worked on the ASALM-PTV vehicles,  while my father was the chief designer of the A-7 Corsair-II aircraft.  

 The vehicle prime contractor (to USAF) was Martin Orlando (from the Martin plant in Orlando,  FL,  that is now closed).  That included the inlet and duct as part of the vehicle.  The subcontractor for the ramjet engine,  fuel system,  and inlet duct port cover was The Marquardt Company of Los Angeles,  CA,  also now closed.  The subcontractor for the integral booster and ejectable booster nozzle was Hercules-McGregor (formerly Rocketdyne-McGregor) of McGregor,  TX,  now closed,  under the final ownership name ATK in its last months. 

I worked for Rocketdyne/Hercules-McGregor for many years,  including early-on,  when ASALM-PTV was underway.   I had roles on the main contract assisting with booster internal ballistics,  and assisting with the heat protection for the ejectable nozzle,  and helping to investigate a possible variable-geometry option for the ramjet nozzle (on an accompanying small R&D contract),  plus running point performance and trajectory simulations on IR&D.

While the ASALM cruise missile was never built,  it was redesigned a bit and entered service for the US Navy as the SLAT gunnery target drone.  It provided a sea-skimming Mach 2.5 target,  as did the Vandal (converted from the shipboard surface-to-air ramjet Talos) before it.  The Navy never really liked either one,  because they had nothing that could shoot them down.  They still don't.


What I hope to do in this article is add some detail,  and correct some misinformation in the published stuff on the internet.  While much of this stuff was originally classified Secret and Confidential,  the 12-year downgrade periods have long since passed,  and everything I discuss here has been on the internet in one form or another for some time now.  This article should be safe to publish,  as the program and flight tests ended some 31 years ago,  as of this writing.

ASALM-PTV was a flying example of an "integral rocket-ramjet" (IRR) or "integral booster" ramjet.  The first such flying example was the Russian SA-6 "Gainful" as it was referred to by NATO (which I was able to help exploit,  the main topic of Ref. 1).  The first such US examples were ASALM for USAF and ALVRJ (Advanced Low-Volume Ramjet) for USN.  It is safe to say that the use of the then-new IRR technology in the two American programs was inspired by its success in the Russian weapon.  IRR became the basis of the series of designs pursued as a propulsion upgrade for AMRAAM,  too.

In this IRR technology,  the rocket booster propellant is packaged within the ramjet combustion chamber,  with the inlet or inlets blocked off,  and a smaller-throat,  larger-expansion rocket nozzle added.  The booster rocket nozzle and inlet blockages are ejected at the transition from rocket to ramjet.  ASALM-PTV demonstrated that transition to be quite rapid at only about 100 milliseconds in duration,  from rocket thrust to ramjet thrust. 

A variation on this IRR technology is the "nozzleless booster",  which deletes the ejectable booster nozzle at the expense of a booster performance loss,  but still has to transition the inlet blockage devices.  With flameholding fuels like the liquid fuels and the "hydrocarbon" gas generator solids,  there is also a required combustor fuel-air igniter,  regardless whether eject-nozzle or nozzleless.  Discussions regarding flameholding are part of Ref. 1,  and the main topic of Ref. 2.

An illustration of IRR technology is included with a representation of the ASALM cruise missile in Figure 4.  This shows an inboard profile image at start of booster burn,  at end of booster burn (when the propellant is mostly gone),  at transition with the gear being ejected,  and during the ramjet burn (with open inlet and a wide-open ramjet nozzle).  Bear in mind that some of the details of the transition gear are not accurately depicted.  That is quite common among the published stuff I found on the internet.

Figure 4 -- Integral Rocket-Ramjet Technology


Combustor Insulation and Propellant Bonding Technologies

The ASALM-PTV combustor was made of a thin-wall heat-treatable high-alloy stainless steel,  with a separate forward dome and an integral forward attach skirt,  terminating aft in a configured ramjet nozzle shell.  There was a large inlet port centered in the forward dome.  The insulation was a fiber- and particle-loaded silicone rubber from Dow Corning known as DC 93-104,  installed after the ramjet nozzle parts were installed.  Marquardt brought the knowledge of this insulation material to the team.  It was previously not among the insulation solutions common to solid rocket work. 

DC 93-104 is a thick,  thixotropic liquid that is pressure-cast into the case (or troweled-in and packed by hand) around a hard mandrel that is withdrawn after the cure.  Rocketdyne/Hercules was the only solid rocket manufacturer adept in pressure-casting such thixotropic materials,  which is a crucial expertise that we brought to the team.  There is also a Japanese equivalent material called Type 0 Shin Etsu,  which I tested on company IR&D some years later.  It performs very nearly as well as the Dow Corning material,  which is still the very best known material for the ramjet insulation application,  but whose export is forbidden by ITAR (International Trade in Arms Regulations) restrictions.

What made ASALM-PTV unique was the need to positively retain the entire insulation char layer,  for burns far longer than the time to char-through the silicone.  Marquardt and Rocketdyne/Hercules working together came up with an elegant engineering solution:  a series of axially-oriented kinked-ribbon stainless steel strips,  spot-welded to the inside of the case.  See Figure 5.  

The insulation was cast around these kinked ribbons,  so that they were firmly embedded within the insulation,  and thus within the char,  once the insulation charred through.  Without them,  the bond between the insulation and the case wall fails once the insulation is charred through,  and the char departs from the wall in chunks and pieces,  leaving the steel bare.  Enough ribbons spaced closely enough will hold the entire char layer in place despite the loss of the bond.  Being embedded down inside the char,  the ribbon does not get too hot and melt.  You cannot do this job with a fabric "pre-preg" material,  you can only do it with a castable material that will flow around the kinked ribbons.

Rocketdyne/Hercules had to find some way to bond a hydrocarbon polymer-based composite propellant to this silicone rubber binder.  Chemically,  the two materials are utterly incompatible!  Each poisons the other,  and in a fairly short time!  The solution was to use an inert Teflon-type material as an isolator between the two types of rubber. 

Thin Teflon sheet (essentially a commercial form of Saran Wrap),  but appropriately acid-etched on both sides,  could be bladdered-in and bonded to the cured DC-93-104 insulation,  using the correct primer from Dow Corning.  "Bladdering" is using an inflatable mandrel,  so as to apply pressure to the bond.  You wrap the deflated bladder with the material,  and then pressure-it-out against the surrounding insulated case;  something already a common practice with most rocket motor insulations.

Then the surface of the isolator sheet facing the booster propellant could be primed for that binder system polymer,  and thus support a properly case-bonded propellant charge,  with a long and reliable shelf life and very good bond strength.  My friends and colleagues at Rocketdyne/Hercules,  Bill Hill,  Marshall Mabry,  and Scottie Scott,  came up with that combination of materials,  and the detailed processing that made it work.  All of this plus the kinked-ribbon char retention allowed thinner ramjet insulations to be used,  despite the very long burn times.  This design became the standard in all ramjet efforts at Rocketdyne/Hercules after that.  See again Figure 5. 

The ramjet nozzle had a shell with the convergent-divergent shape built in simple conical forms.  Inside this shell,  the nozzle was built up from machined silica-phenolic piece-parts bonded in place.  This all-silica-phenolic nozzle construction was a new technology,  unique then to ASALM-PTV.  Prior ramjet nozzles had graphite throat inserts,  much like solid rockets.  But in the ramjet environment at far lower ramjet chamber pressures,  the graphite throat complication is actually unnecessary.  Marquardt and Rocketdyne/Hercules developed this technology together and demonstrated it.  It was then applied to all other subsequent ramjet efforts at both companies. See also Figure 6

Figure 5 -- Case Insulation,  Propellant Bond,  and Booster Construction Technologies

Ejectable Booster Nozzle Technologies

The ejectable booster nozzle had an aluminum outer shell for the flow passage,  plus a conical skirt that held it in place against a snap ring protruding from the inside surface of the ramjet nozzle,  near its exit lip.  The nozzle inside this shell was built up from silica-phenolic pieces bonded in place inside the shell.  Being a rocket nozzle,  there were graphite throat insert pieces included in this nozzle buildup.  Lightly bonded into its exit cone just downstream of the throat was a silica-phenolic weatherseal closure,  that also held the igniter for the booster propellant charge.  All told,  this booster nozzle assembly weighed about 15 pounds.  See Figure 6

About the last 3/4 inch of the ramjet nozzle exit cone was bare steel shell partly machined to the exit profile,  not a silica-phenolic insert.  A snap ring groove was machined into it,  in which was placed a detonation cord charge underneath the installed snap ring.  At rocket to ramjet transition,  the detonation cord was initiated,  and its explosion compressed the snap ring inward,  clear of its groove.  This was done as the booster pressure decayed to about 200 psia.  The residual booster pressure pushed this ejectable nozzle assembly aft,  out of the ramjet nozzle,  to which it had sealed with an O-ring in the ramjet throat. The event was over before pressure had decayed under 150 psia.  See again Figure 6.

The flow out of the slot in the booster propellant grain had a tendency to erode that part of the booster nozzle entrance lip that was directly in line with the slot.  This was resolved by increasing the entrance lip size just enough to prevent the erosion damage from getting near the throat.  This was carefully done with thermal/structural analysis,  and verified in experimental test.  I participated in both of these efforts.

The critical difficulty with this design became apparent early in the ground tests of the booster and nozzle ejection,  and this difficulty was successfully resolved before any ground tests of the ramjet were ever conducted!  The explosion of the detonation cord had to be very,  very uniform around the circumference of the snap ring groove,  or else the snap ring would fail to be compressed clear of the groove at the weakest point of the cord explosion.  Only detonation cord meeting the very highest quality control specifications proved to be suitable for this application.  Should the snap ring fail to clear the groove,  the booster nozzle would fail to eject,  and the transition to ramjet operation would therefore fail.  But with highest-quality detonation cord,  this difficulty went away,  never to be seen again.

There was another difficulty encountered,  when the transition to ramjet was first tested in the Martin Orlando "Conflow" facility,  as a direct-connect test complete with a booster.  If the test article was strapped down too tightly to the test stand,  the case,  including the nozzle shell,  would get slightly ovalized by the tie-down forces.  An ovalized ramjet nozzle would cause the ejectable booster nozzle to become jammed in the ramjet throat,  thus failing to eject. 

Several ground test failures in the "Conflow" facility occurred due to this problem,  which Martin Orlando wanted to blame on the snap ring design.  However,  no snap rings were ever found jammed in the snap ring groove after these failures,  which finally forced them to look at the ovalization risk,  as presented by Rocketdyne/Hercules.  When the tie-down was revised to prevent any possibility of ovalizing the nozzle shell,  this problem went away,  permanently.  I assisted that structural evaluation which identified the ovalization risk,  as well.

Figure 6 -- Ejectable Nozzle Design


Inlet Port Cover Technology

Marquardt developed the frangible glass port cover used in ASALM-PTV.  It was cast from frangible glass as a round dome shape about an inch thick.  There was an O-ring seal around its periphery to the inside diameter of the inlet duct,  although I no longer remember whether the O-ring groove was in the port cover or in the duct structure.  It had a seating place machined in the duct dump location,  such that the port cover could not move up further into the inlet,  only downstream into the combustor. 

This assembly had a layer of rubber insulation on the combustor-side surface to protect it from hot booster gas exposure.  There was a pyrotechnic explosive charge mounted to the inlet-side surface,  initiated at the same time as the ejectable nozzle detonation cord.  I no longer remember how that charge attached to the port cover,  or any design details about that charge assembly. 

The explosion of that charge triggered the shattering of the port cover into 1-inch size fragments,  consistent with its thickness.  Those fragments plus the remains of the insulation layer,  go through the ramjet nozzle quite easily,  just after it is vacated by the ejectable booster nozzle.   This shattering into fragments of a size roughly equivalent to the original part thickness is typical of "frangible glass",  which is a tempered material that puts its outer layers in tension,  while its inner core is in compression. 

See Figure 7,  which shows the basic idea,  plus my own choices for some of the details.  The actual details used in ASALM might have been different,  but only somewhat.  

Figure 7 -- Frangible Glass Inlet Port Cover


Fuel Injection/Aerogrid and Flameholding Technology

ASALM-PTV (and the ASALM weaponized design) featured a device termed an "aerogrid" very near the sudden dump into the combustor.  This was actually both an aerodynamic device and the physical support for all the fuel injection locations and circuits.  As an aerodynamic device,  the prime function was as a flow straightening grid,  with a secondary function as an additional turbulence generator,  for enhancing the mixing rates in a fairly short combustor.  It would be incorrect to assume that it also functioned as a flameholder,  for the forward dome face and sudden dump entry performed that function,  while the aft surfaces of the aerogrid were actually a few inches upstream of the dump. 

Another function that similar aerogrid devices can perform is a terminal shock position limiter in the inlet divergent diffuser,  which comes into play if flow also chokes at the min passage area around the aerogrid.  That fixes the inlet diffuser terminal shock position,  and the corresponding shock strength and pressure drop,  while introducing a second terminal shock and further pressure drop in the flow passages about the aerogrid.  This function does not seem to be necessary for the ASALM application,  but has been used with good effect in some other applications.

More information on exactly how an aerogrid works as a flow straightening grid is given in Ref. 3,  particularly in its Figure 12.

ASALM's aerogrid was also the fuel injection location,  which is just upstream of the sudden dump,  which was the actual flameholder.  The fuel was RJ-5/Shelldyne-H,  which is a synthetic material of physical properties fairly similar to kerosene,  except that its density was very slightly greater than that of water.  It did eventually prove to have too high a freezepoint,  during the testing conducted for ASALM-PTV.

The fuel is injected as a spray pattern of fine droplets,  spread as uniformly across the inlet cross section as is possible.  In supersonic flight,  the inlet air has compression heat in it,  which can serve to vaporize those fine droplets before they reach the end of the recirculation zone.  That way,  fuel-as-vapor can be entrained into the actual recirculation,  which makes combustor ignition feasible.  Fuel-as-liquid into the recirculation zone is not very flammable,  and will "suck in" heat in order to vaporize,  thus tending to quench any chemical reactions your combustor igniter might provide.  Once the combustor is actually lit,  radiant heat from the flame greatly enhances liquid fuel vaporization rates;  the real difficulty is getting the flameholding recirculation zone ignited,  with only the hot air to drive the vaporization.

The coaxial sudden dump is a well known,  well-proven flameholder system for a variety of liquid and gaseous fuels.  Its lean and rich flameout limits are fairly well-defined in terms of an easy-to-use empirical correlation parameter that incorporates inlet flow pressure,  temperature,  and velocity,  as well as a measure of the size of the recirculation zone.  These considerations are well-documented in Ref. 2. 

One key takeaway regarding recirculation zones and flameholding is that your combustor igniter device specifically needs to ignite the actual recirculation flow itself.  If that recirculation zone is not ignited,  the combustor will inevitably flame out the moment the igniter ceases firing,  if indeed you get any discernable combustion at all.  In the coaxial dump combustor of the ASALM-PTV,  that zone is depicted in the sketch of Figure 8

Perhaps the easiest locations to mount an igniter would be on the forward dome,  firing directly into the recirculation vortex that is coaxial to the entering inlet air jet.  ASALM-PTV used magnesium flares mounted in the center of the aft face of the aerogrid/fuel injection structure.  For this location to work reliably,  the magnesium flare must be physically contained,  so that its still-reactive hot output forms a jet that can be aimed.  It must be aimed not straight aft,  but angled across the inlet air jet to hit the recirculation vortex,  as indicated in the figure.

Figure 8 -- Coaxial Dump Flameholder of the ASALM-PTV


The ASALM-PTV combustor was fairly short,  in that it was only about 2 diameters long.  This barely gave the recirculation flow time to attach to the sides and turn back forward,  before the flow began entering the nozzle contraction.  This is also shown in Figure 8. 

The entering air jet comprises essentially the same fuel/air mixture ratio as the recirculation zone flow,  as there was no dome fuel injection to enrich that zone,  relative to overall. 

The upstream end of the recirculation zone (at the edge of the dump) is the point of continuous ignition applied to the periphery of the main entering flow.  From there,  flame propagates radially inward at the turbulent flame speed,  while simultaneously traveling downstream at the overall flow speed.  This results in a rather gradual velocity triangle,  as shown in the figure,  that must reach flow centerline before that flow enters the nozzle,  or else there will be serious combustion inefficiency.

Having the aerogrid structure shed additional turbulence (calculable from its drag) right into the core inlet jet,  is a way to have a higher effective turbulent flame speed,  and thus help burn out the core flow faster before it reaches the ramjet nozzle.  That secondary function of the aerogrid (generating turbulence) is quite important to achieving good efficiency,  in a combustor that short.  This approach worked rather well in ASALM-PTV:  its demonstrated combustion efficiency was quite high despite the short length.

Inlet and S-Duct Technology

ASALM-PTV featured a "chin inlet" supersonic inlet design,  leading to a noncircular subsonic duct in the belly region of the vehicle.  There is an S-duct double turn that not only offsets the flow axis up to the vehicle centerline,  but also converts it from a noncircular cross section to a circular cross section at the dump entry.  This is correctly depicted in Figure 1 above.  Be aware that the flow in the belly duct and S-turn duct is well-subsonic in speed.   Otherwise the flow losses would have a catastrophic effect upon the total (stagnation) pressure delivered to the combustor entrance.

A chin inlet is like a sector of a nose inlet.  The inlet scoop is only on one side,  instead of extending all around the circumference.  A portion of the vehicle nose performs the same external shock wave compression function as the center spike in a nose inlet.  However,  the asymmetry of this geometry confers some of the advantages of a two-dimensional inlet,  at high positive angle-of-attack. 

At zero angle of attack,  the performance of a chin inlet very strongly resembles the performance of a nose inlet.  In this context,  we are considering total pressure recovery and captured streamtube recovery.  As angle of attack increases,  with a nose inlet,  there is little impact on pressure and streamtube recovery out to about 10 or 15 degrees,  then both begin to fall,  particularly the streamtube recovery.   But as angle of attack increases,  with a chin inlet,  while pressure recovery reduces beyond around 10 degrees,  the streamtube recovery actually increases,  much like a properly-oriented two-dimensional inlet.   See the discussions in Ref. 2 for more detail about supersonic inlets,  how they work,  and how they must be designed differently for a ramjet application,  compared to a gas turbine application.

This being a ramjet application,  better streamtube recovery is higher massflow ingestion,  and in a ramjet,  higher massflow ingestion has a bigger positive effect on engine performance than any losses due to lower pressure recovery (totally unlike a gas turbine application).  Therefore,  a chin inlet is a very attractive design candidate for any ramjet vehicle that will fly at significant positive angle of attack.  And wingless vehicles do exactly that.

The other impact of this choice is how vehicle turns are made.  For a symmetric vehicle,  "skid-to-turn" is usually employed as the simplest and easiest-to-implement.  For an asymmetric vehicle like ASALM-PTV,  "bank-to-turn" is more suitable:  you roll toward the turn direction you desire,  then pull higher angle-of-attack in that rolled pitch plane,  so that the increased lift,  aimed toward in the turn direction,  then causes the vehicle to turn.  If you have a chin inlet whose mass ingestion improves as you increase angle-of-attack,  then your ramjet thrust actually increases as you turn,  thus better offsetting the increase in vehicle drag at higher angle-of-attack (drag-due-to-lift increase).

Thus the choice of vehicle asymmetry,  the choice of chin inlet,  and the choice of bank-to-turn,  are not arbitrary choices for ASALM-PTV.  These really do work together to confer better performance overall.  Amateurs at this kind of vehicle design are unlikely to achieve results like this,  because they are unlikely to be aware of all these nuances,  and especially how they interact.  This is not simple stuff!  You don't learn this stuff in school by simply feeding inputs to a computer program whose internal details you do not know!

Booster Propellant and Grain Design Technologies

Many folks have a nodding familiarity with the composite propellant used in the space shuttle solid rocket boosters (SRB's).  That was an AP-oxidized (AP being ammonium perchlorate) composite,  metallized with about 20% aluminum by mass,  and using a PBAN (polybutadiene acrylonitrile) polymer as the binder system.  The propellant used for the ASALM booster was quite similar,  except that we at Rocketdyne/Hercules used an HTPB (hydroxy-terminated polybutadiene) polymer for the binder system,  and we probably had a higher solids loading,  being the plant that was adept at processing very thick propellants.  Memory fails,  but it was probably near 86% solids. 

ASALM,  like most tactical military ordnance items,  had to pass the "shake/rattle tests" at the extreme environments specified by Mil Std 210.  In other words,  it had to work "right" from -65 F soakout to 145 F soakout.  You cannot get the ballistics and structural properties out of a PBAN system for those kinds of extreme temperatures,  but you can,  out of HTPB and CTPB (carboxy-terminated polybutadiene).  The shuttle SRB's,  and most of the strategic ICBM's,  never see such extremes.  The booster propellant we used in ASALM was essentially the same as what went into many of our tactical missile motors.  We had a great deal of experience making it,  and applying it,  very successfully.

Ref. 4 contains discussions about all sorts of solid propellant types,  and the typical burn rate data,  as well as discussions on multiple solid propellant grain designs,  plus a tutorial on how solid propellant rocket internal ballistics are computed.

The ASALM booster had to fit within a combustor case with a length/diameter (L/D) ratio near 2,  which was half or less the usual value available in a tactical motor.  That booster needed a fairly neutral thrust-time trace,  it had to be an internal burner (not an end-burner),  and it had to be case-bonded,  not cartridge-loaded.  The usual slotted-tube designs for L/D > 5 or 6 would not serve,  and a simple cylindrical tube design would require two segments to provide neutrality (such a design being like the shuttle SRB).  That two-segment design cannot be had in case-bonded form without using a segmented case,  which ASALM could not have.  You cannot extract cast tooling shaped that way,  once the propellant has cured. 

The design solution was the "keyhole slot" grain design,  which was a tube with one full length slot on one side.  My colleague W. T. Brooks at Rocketdyne/Hercules,  came up with this design.  He was my mentor in internal ballistics,  and I helped him run those ballistics for this new design.   It proved to have even better neutrality than a two segment tube would have had,  and can be cast in the case with very simple tooling,  tooling very easily pulled after cure.  Brooks was the author of the NASA Monograph on solid propellant internal ballistics,  by the way.

In ASALM's case,  we had a wide-open forward end,  and a built-up nozzle with a wide ramjet throat aft.  We installed the grain face-forming tool and bore/slot mandrel from forward,  and cast the propellant into the case in a ramjet nozzle-up orientation.  After cure,  you pull the face-forming tool and the cast mandrel out the wide-open front end,  then you install the forward closure with the port cover and its pyrotechnic charge already in place.  The last step installs the booster nozzle into the ramjet nozzle,  with the weatherseal/booster igniter assembly already bonded in place,  and then lock it in with the detonation cord and snap ring.  This sounds more complicated than it really is,  but we were trying to provide a mass-producible design,  and we succeeded.  See Figure 9.

Because most other IRR-type ramjets have relatively short cases in the 3 < L/D < 4 range,  this "keyhole slot" grain design can serve all of them,  providing high cross sectional loading and good neutrality,  in an easily-fabricated design.  That is why it is my "go-to" choice for IRR ramjet booster designs. This design is illustrated,  with typical data presented,  not exactly that for ASALM,  in Ref. 4. 

Figure 9 -- Keyhole Slot Grain and Burning Surface


Variable-Geometry Nozzle Technology

While the main ASALM-PTV effort was underway,  we at Rocketdyne/Hercules had a small contract with Martin to support their efforts at identifying upgrades to the design.  ASALM itself,  like all the other operational ramjets,  was a fixed geometry design.  Martin contracted with us to look at ways and means of supplying variable nozzle geometry (VGN) to the design.  They had already ruled out variable geometry inlet (VGI) as less probable to provide benefit,  and as also requiring VGN,  in order to work at all with a ramjet,  unlike a gas turbine application.

This was the effort where I had the most work experience with ASALM,  and being new on the job,  I was not the lead engineer,  except in the cycle analysis and trajectory work.   The lead was my good friend and colleague Jim Cunningham,  who is now deceased.  Jim was the company expert in heat transfer,  compressible flow,  and internal ballistics as affected by compressible flow.  Among other things,  he was my mentor in the hydraulic analogy,  and also together we developed the best ramjet direct connect test analysis techniques in the industry,  which I then automated with software that I wrote. 

What Rocketdyne/Hercules provided to Martin was a combination of nozzle flow visualization using the hydraulic analogy,  thermo-structural design analysis for the VGN nozzle (and the greatly-revised ejectable booster nozzle that had to go with it),  and some full-scale VGN test article cold flow testing on a thrust stand with 6 degree-of-freedom measurement capabilities,  located at Rocketdyne Canoga Park,  in California.  These contract efforts were well-supported with IR&D efforts to enable our team to come up to speed in this ramjet work quickly.  (ASALM was not the only effort going on at the time at Rocketdyne/Hercules:  there was also work aimed at a ramjet upgrade to AMRAAM,  plus the foreign technology exploitation of the SA-6 that is described in Ref. 1.)

This work led to live-fire direct-connect ground tests of a VGN nozzle assembly on an ASALM combustor at Martin's Conflow facility.  The final test modeled the design mission.  The VGN began wide open,  then closed for cruise after the simulated climb,  then opened again for terminal dive,  after a 900 second burn.  Despite the ugly eroded appearance,  the nozzle efficiencies looked just about as good as they did from the cold flow testing. 

We did learn from the visualization work that the "lollipop" wake,  when the "lollipop" was oriented broadside,  needs to close before it leaves the surrounding exit cone,  in order for it not to respond to backpressure as an expansion-deflection nozzle.  That would induce lower nozzle efficiencies,  because of the large off-axis angle of the flow streamlines enclosing the wake zone.  Done properly with closed wakes inside the exit cone,  the nozzle efficiency of the VGN was about 94%,  as compared to about 98% for the plain clean nozzle.  The rather large inefficiencies of off-angle streamline orientation are described for other free-expansion designs in Ref. 5.  Those same risks applied to the ASALM VGN design.  With "lollipop" wakes closed prior to the exit plane,  the efficiency decrement with the ASALM VGN was traceable mostly to the stagnation pressure losses of the extra oblique shocks which actually closed the "lollipop" wakes,  not excessive streamline divergence.

This device is sketched in Figure 10.  It takes the form of a "lollipop"-on-an-axle across the ramjet throat.  Held streamline to the flow,  the ramjet throat area is its largest value.  Turned broadside,  the ramjet throat is its smallest value.  The degree of area modulation is very modest,  being only that needed to bring the inlet capture area / nozzle throat area ratio nearer to an efficient balance,  when the engine is leaned back to hold a steady cruise speed,  which in turn is much higher than the design point speed.  This variation in ramjet throat area reduces an otherwise large inlet supercritical margin in leaned cruise,  thus acting toward raising cruise specific impulse,  and consequently cruising range.  (Its weight,  modest as it was,  acted to shorten cruise range,  of course.)  The "lollipop" was a steel core covered with silica phenolic ablative. 

This design approach is just not suitable for the very large geometry changes between booster and ramjet operation.  For one thing,  the booster pressures are simply too high (approaching 2000 psia for a hot-soaked propellant grain),  while the ramjet pressures were always under 200 psia,  the max value occurring at max speed at sea level.  There was no feasible structural solution for that.  For another thing,  the higher booster pressures made local flow pressures higher all around the "lollipop",  thus creating unsurvivable heat transfer coefficients. 

While it would have worked for ASALM in cruise,  Martin and the USAF did not select VGN for the ASALM-PTV demonstration,  opting instead for the baseline fixed geometry.

Figure 10 -- Sketch Of VGN Nozzle As Designed For ASALM


To help support these efforts,  I was tasked on supporting IR&D funding to model the engine-inlet-nozzle combinations with USAF-supplied cycle codes,  and to conduct trajectory analyses.  I used inlet data and vehicle aerodynamics data supplied by Martin for this.  To understand what I actually did,  you have to understand what a "cycle code" is,  in the context of a ramjet engine application.

A "cycle code" is a means of predicting the performance (thrust and specific impulse) of an engine at any given flight condition.  It can be a standalone program for point performance calculations,  or it can be a propulsion model subroutine inside a trajectory code.  The word "cycle" is a reference to the classical thermodynamics text cycles that model heat engines:  things such as Brayton Cycle,  Rankine Cycle,  Otto Cycle,  etc.

There are some rather accurate predictive models for gas turbine engines that use typical pressure ratios,  input as constants,  to model various components in the engine,  plus an operating mixture ratio and a releasable heat from the fuel.  These models work well for gas turbines,  because the compressor pressure rise ratio and turbine pressure drop ratio are rather well-understood,  and they dominate over all the other pressure ratio factors by far.

These pressure ratio models can be used for ramjet,  but they do not supply reliable or realistic results!  This is because there is no compressor or turbine,  whose pressure ratios dominate the model.  That makes the ratios of the other components crucially important,  particularly the inlet,  which is then the only pressure-rise component in the model.  That in turn makes "typical constant values" inappropriate,  because all of these components' pressure ratios depend very strongly upon the state of the compressible flow entering them.

The "cycle code" models of ramjet that are successful are those that use the mathematics of compressible fluid flow to compute the actual flow states at every station through the ramjet engine,  using a series of empirical and theoretical component models strung together.  The details of this are well-explained in Ref. 7.  Of particular note is the iteration required to "balance" the engine massflow:  the captured massflow of air plus injected fuel for a current value of "inlet margin" can be delivered to the nozzle entrance at a certain pressure determined by the mixture,  combustion efficiency,  and component losses. 

At that pressure and those delivered conditions,  the nozzle can only flow a certain massflow.  For the engine balance to be converged,  those two massflows must be the same!  If they are not,  then one adjusts the "inlet margin",  and runs the entire calculation again.  There is a caveat:  "inlet margin" can mean either supercritical pressure margin or subcritical spillage margin (but these both cannot be nonzero simultaneously),  and you cannot jump back and forth between those two kinds of operating conditions (Ref. 3 covers what those conditions mean).

That ramjet massflow balance is totally unlike the behavior of a gas turbine system,  even one using exactly the same inlet hardware.  It is the rotation speed of the turbine core(s) at any given altitude and day type that determine engine massflow in a gas turbine application,  for which the inlet simply responds appropriately,  if it can.  That situation is totally unlike what happens in a ramjet application.  This topic is covered extensively in Ref. 3.

Early in my career when ASALM and those other efforts were underway,  I would size a ramjet engine and inlet with a sizing map like that depicted in Figure 11.  This was before I understood the additional constraints on throat area proportion imposed by flameholding considerations and by practical inlet duct sizes.  The sense of the figure is clear:  any thrust coefficient above the factored vehicle drag line is "feasible",  and the operating mixture strength and throat can be read for any such point from the point performance calculation that produced it.  The point performance results that produced this plot also produce specific impulse,  so that the "best" (highest-specific impulse) such solution can be selected.  Inlet duct size is understood as just being part of the set of inputs that produced this plot.  You have to revisit the duct sizing many times as performance is explored across the flight envelope,  because of infeasibly low or high duct velocities.  And if you explore flame stability across the flight envelope,  the number of necessary iterations gets worse. 

But,  as I learned later,  you cannot really do it very effectively this way!  (1) There are very severe limits on max throat proportion imposed by flame stability at design,  and even more so off-design.  (2) There are also very practical limitations on inlet duct size to prevent overspeed at cold flow ignition,  and underspeed,  producing flashback damage.  (3) Further,  the duct physical size also impacts flame stability directly,  especially in the coaxial dump ASALM configuration.  Note also that with side inlets,  vehicle drag varies more directly and more strongly with duct size,  than it does capture area size.

Today,  knowing what I now know about flame stability and mixing,  I just set the throat proportion to its maximum at 65% of combustor flow area for flameholding systems,  or at about 90% for hypergolic magnesium systems that only require mixing.  The inlet duct gets set (and likely revisited only once or twice) between about 40% and 50% of the combustor flow area.  Then thrust-over-drag margin just is what resultsand the higher it isthe better

I do this at the richest mixture expected (usually about 110% of "perfect"),  so that leaning-back just increases supercritical margin,  thus never incurring spillage at nonzero spillage margin.  I usually use a design point at the shock-on-lip Mach number for the inlet design,  in the stratosphere for the coldest,  densest air delivery to the combustor,  to have the max delivered air massflow.  Then warmer air at lower altitudes never drives the inlet subcritical,  causing spillage,  unless you try to fly below shock-on-lip Mach,  which you should never do. 

Thus,  in one or two sizing runs,  I get to a workable,  properly-sized answer,  that used to take me multiple sizing map iterations when I first got started doing this!  Plus,  I have a better grip on actually having adequate flame stability throughout the flight envelope.  That's a lot better results for a whole lot less work.

About the time of the end of the ASALM program,  I obtained the "seminal" works on flame stability.  For the coaxial dump,  this was the dissertation of E. Tom Curran at WPAFB,  and for blockage-element flameholders,  this was a report from Marquardt written by Robert Ozawa.  The side dump flame stability criteria and the hypergolic magnesium mixing knowledge,  I learned from long years of test experiences at Rocketdyne/Hercules.   I put a distillation of all this knowledge into Ref. 2.

Figure 11 --  Sketch of Typical Early Sizing Map


Heat Protection Issues for Airframe and Inlet

There are two things to worry about when doing heat transfer models:  (1) good engineering models for all of the heat transfer processes and all the fluid and solid physical properties involved,  and (2) establishing a steady-state balance among all the heat transfer processes taking place (which is just conservation of energy).  The simplest case is a lateral skin panel,  which can receive convective heating from the high-speed slipstream adjacent to it,  can radiate heat to the surroundings,  and can conduct heat to internal structures or items that can act as heat sinks,  at least temporarily. 

Skin panels receive convective heat transfer on only the outer surface,  radiate heat from only that outer surface,  and usually have very restricted conductive paths for heat flow from the panel into the interior.  The convective heating rate to the panel is rather high at low altitudes where the air stream is dense,  and low at very high altitudes,  where density is low.  This is because high density leads to high Reynolds number,  which leads to high Nusselt number,  and thus high heat transfer coefficient.  The radiative and conductive transfers do not depend upon air density.  See the discussions in Ref. 6 for more detail on exactly how this works,  and how it is calculated,  with examples. 

Nosetips and leading edges are similar,  except that the geometry is not planar,  and the heat transfer models for stagnation zones,  and regions close by,  lead to very much higher heat transfer coefficients.  The convective driving temperatures are the same,  so it really is the higher heat transfer coefficients that cause the far higher heating rates.

Air inlet structures present special problems of much more severe heating.  This is because things like inlet cowl lips are heated convectively on two sides (and not by the same amount),  while they are only able to shed heat radiatively on the one side that faces the surroundings.  They will equilibriate at higher temperatures just because of the 1-surface vs 2-surfaces effect.  Paths by which to shed heat conductively are extremely limited,  or may not exist at all. 

For ducts in the interior of the vehicle,  there is usually convective heating on one surface (inside the duct),  and no chance to shed heat radiatively to the surroundings from an outside surface.  There may or may not be paths by which to shed heat conductively to adjacent structures.  The upshot here is that inlet structures will often equilibriate at higher temperatures than even nosetips and leading edges,  because of an inability to shed heat at all.  Any surface unable to shed heat will equilibriate at the driving temperature for convective heating,  which is the recovery temperature in the thermal boundary layer.  Again,  see Ref. 6 for details.  Recovery temperatures are very nearly stagnation temperatures.

For equilibriation purposes,  the recovery temperature that drives convective heat transfer is set by the compressible flow conditions.  The surface temperature that drives re-radiation is actually your variable for iteration purposes!  The temperature of the surroundings is pretty much a constant,  as is the heat sink temperature for conduction.  You simply iterate values of surface temperature until the heat energies balance.  Computer codes do this internally quite automatically (because they are programmed to do so),  but you can also do it manually in a spreadsheet.  Just input a range of surface temperatures and do the calculations automatically with all of them.  With the one calculation that comes closest to balance as a startpoint,  use trial and error to converge that one calculation as close as desired.

In the case of ASALM,  at low altitudes the Mach number is rather low:  around 2.5 to 3.  The higher cruise Mach number of 4 takes place only in the thinner,  colder air up around 80,000 feet.   On a "standard day",  at 20,000 feet Mach 2.5 the worst case is soakout to the recovery temperature,  which is very near the stagnation temperature of 547 F (286 C).  At 80,000 feet Mach 4,  it is around 1211 F (655 C).  These are temperatures that a Martensitic stainless steel can handle without too much loss of strength.  However,  at Mach 6 and 20,000 feet for the throttle runaway incident in flight test 1,  these temperatures were quite unsurvivable for steady-state exposure,  at 3209 F (1765 C),  which neatly explains the telemetry about the skin beginning to melt during this brief transient event.

Final Remarks

When I first started work in the industry,  it was not long at all before I began doing ramjet work.  At that time,  there were no desktop  or laptop computers,  and even scientific pocket calculators were uncommon.  The only computers were giant "mainframe things" requiring tons of air conditioning,  that you input with steel trays of punched cards,  up to 2000 cards in a tray.  That was reserved for only the very hardest problems that you could not approach otherwise,  because that same computer was usually tied up all day by the accountants running payroll,  and payroll was much more important to management.  There was no "spreadsheet software" of any kind.

So,  we usually ran repetitive engineering calculations entirely by hand,  organized and laid out on a great big piece of paper,  but pretty much the way spreadsheets work today.  Those calculations were done manually,  pencil-and-paper,  assisted by slide rules,  and by adding machines that resembled old-fashioned typewriters.  Those tools were replaced by scientific pocket calculators,  once real scientific pocket calculators became available,  in the first few years of my career. 

Many of you readers will not even know what a slide rule was!  The slide rule served as the "scientific pocket calculator" for about 3 centuries,  before real scientific pocket calculators were invented.  There's a picture of my own personal slide rule in Ref. 8.  I designed my first airplane and my first 6 supersonic missile propulsion systems with it.

The scales on a slide rule were marked logarithmically,  so that when you added with those scales,  you were adding logarithm to logarithm.  Mathematically,  that literally is multiplication!  Differencing logarithms is division!  There were other scales that would do powers and roots,  and trig functions.  If you really understood that kind of math,  then learning slide rule was easy.

The first ramjet work I did was in 3 areas:  (1) ASALM,  which was a liquid fueled ramjet,  (2) gas generator-fed ramjet work aimed at an upgrade for AMRAAM,  and (3) exploitation of the Russian SA-6,  which was a gas generator-fed ramjet.   Every one of these was an IRR.  I also used the ASALM technology for a ram-fed hot gas generation device that burned a variety of gaseous and liquid fuels,  when I worked for what was then Tracor Aerospace (now BAE Systems) in Austin,  TX.  That was for an advanced-technology infrared decoy.

This article covers what I remember of the ASALM work.  Ref. 1 covers mainly the SA-6 exploitation work,  with some discussions of the AMRAAM-targeted work.  If there is enough interest,  I may write up that AMRAAM-targeted work in much more detail in a future article,  and possibly the hot gas decoy device in another.  

I have also noticed some readership of the solid propellant rocket ballistics article,  which would apply to IRR boosters,  space launch stages or strap-ons,  as well as solid rocket missiles and applications in general.  And,  the several high speed aerodynamics and heat transfer articles seem to have had some interest.  Plus the inlet fundamentals article,  Ref. 3.  These apply to missiles or those other vehicles,  whether ramjet or rocket,  and high-speed airplanes,  no matter how powered. 

Please feel free to leave comments in any event.

References (all located on this site):

To find these references,  the easiest procedure is to use the navigation tool left side of this page.  Write down the year,  month,  and title on a scrap of paper.  Click first on the year in the navigation tool,  then on the month,  and if need be,  on the title.  Simple as that.  I wrote all of these articles.

#1. 4 February 2020,  "One of Several Ramjets That I Worked On"  [article describes SA-6 exploitation in great detail,  plus descriptions of ASALM,  the AMRAAM ramjet upgrade projects,  USN's AAAM project,  and the IR decoy combustor]

#2. 3 March 2020,  "Ramjet Flameholding" [primer on flameholding how-to,  scope includes liquids,  "hydrocarbon" gas generator solids (which would include modest metallization with aluminum,  magnesium,  and boron),  and "hypergolic" gas generator solids (which are effectively only high-magnesium)]

#3. 9 November 2020,  "Fundamentals of Inlets" [primer for pitot/normal shock inlets and both types of supersonic inlets,  relating to both ramjet and gas turbine application]

#4. 16 February 2020,  "Solid Rocket Analysis" [physics and design analysis models for solid propellants and the devices that contain them;  interior ballistics]

#5. 12 November 2018,  "How Propulsion Nozzles Work" [physics and engineering how-to for nozzles]

#6. 2 January 2019,  "Thermal Protection Trends for High-Speed Atmospheric Flight" [heat protection issues]

#7. 21 December 2012,  "Ramjet Cycle Analyses" [how to model ramjet engines for reliable and accurate performance prediction]

#8. 16 March 2019,  "This Is A Slide Rule" [image plus some history]

Tuesday, June 15, 2021

Landing Legs Concept 2

I looked at a very simple adaptation of the Spacex Falcon-9 booster landing legs scaled up and adapted to the Spacex Starship,  in Ref. 1.  I did this adhering to the criteria outlined in Ref. 2.  The results met the criteria for clearance skirt-to-ground,  and for the worst-case total landing pad area as driven by the Mars takeoff scenario,  with a center-of-gravity height to stance ratio very near to satisfying that criterion.  It featured a hinge location at the edge of the aft skirt,  much like on Falcon-9.  I now call this "Concept 1".

However,  dimensional feasibility of the hydraulic cylinder required to extend and retract the legs led to a mid-span attach point on the leg.  That in turn led to a large bending moment in the leg near that attachment point,  with the requirement for a rather large section modulus.  The hydraulic cylinder itself was driven to very high pressures at a rather large piston diameter by the force required to hold the leg extended under the applied loads.  Accordingly,  I wasn't pleased with this design concept,  as was indicated in Ref. 1.

Hinging at the top of the leg instead did not really help,  as the cylinder attach point cannot be near the end of the leg,  which must then be extended to get the ground clearance.  That left me with bending moment and section modulus problems,  as well as a limited stance dimension that failed to meet stability requirements.  That approach I abandoned as no better than the bottom hinge design,  and quite likely worse. 

Therefore I looked at moving the leg outward and downward on two link bars as illustrated in Figure 1 (see below at end of article).  This produces a rectangle of the two link bars,  the side of the ship,  and the upper part of the landing leg.  The remainder of the leg extends below the rectangle and below the ship aft skirt.  Its vertical orientation eliminates bending in favor of simple compressive loading.  All this is shown in the figure.

The hydraulic cylinder that extends and retracts the leg becomes a diagonal member in this geometry,  as illustrated.  It is relieved of most stroke versus retracted length limitations,  and is a tension member,  not a compression member.  It extends the leg by retracting its rod.  That rod can include a coil spring-over-shock absorber as part of its length,  as shown.  That directly addresses the need for shock absorption identified in Ref. 2,  unlike Concept 1. 

The difficulties with this geometry are too much ground clearance under the aft skirt,  and too little capability for stance relative to center-of-gravity height.  Although,  the height/stance ratio (and landing pad area) is much better than the Starship prototypes currently flying in tests,  with the 6 small,  stubby legs.

The pad fold-out mechanism illustrated here in the figure could be applied to the Concept 1 design as well.  The pad is carried inside the leg,  slides down as the leg extends,  then rotates roughly 90 degrees to the touchdown position.  Very low forces are required for these motions,  which could be light spring forces.  There is essentially zero hinge moment at pad center,  and the bending in the pad itself is around 4 times lower than the Concept 1 values.

Included in the figure is a sketch of the free body diagram (FBD) that I used to determine the pin reactions,  and on which I included the member forces from a two-dimensional truss analysis by the method of joints.  There is also a plan view sketch of the footprint,  showing the pad span and stance dimensions for the 6 legs.  The ratio of stance to span is 0.866 for 6 legs;  for 4 legs it is 0.707.

This is not a bad design,  although it fails to fully meet the height/stance criterion set out in Ref. 2.  One could reduce the clearance height by not folding out fully to the side,  although this also reduces stance further. 

Alternatively,  one could angle the legs outward at their tips by using link bars of unequal length (shorter on top,  longer at the bottom).  That would put bending moments (and required higher section modulus) requirements back on the legs.   However,  it would simultaneously buy a wider stance and a lower aft skirt ground clearance. 

Achieving the design goals versus incurring leg bending difficulties is an inherent design tradeoff the Spacex designers can make.  Concepts 1 and 2 sort-of bound this design tradeoff space:  Concept 1 having legs mostly loaded in bending,  while concept 2 has legs loaded only in compression. 


1. Johnson,  "One Concept for Landing Legs",  posted 8 June 2021 this site.

2. Johnson,  "Evaluations of the Spacex Starship/Superheavy",  posted 15 May 2021 this site.


Figure 1. -- The Concept 2 Landing Leg Design Approach

Tuesday, June 8, 2021

One Concept for Landing Legs

This article extends the landing leg-sizing sub-topic of the article titled "Evaluations of the Spacex Starship/Superheavy",  dated 15 May 2021,  on this site.   I have also updated that article to show this one in its list of references.  You can also find a reference to the soil mechanics data in that article as its reference 11.


I looked at a basic,  straightforward concept for landing legs for the Spacex Starship.  The idea is based on the Falcon-9 booster landing legs,  modified to replace the one-shot extension tubes with a hydraulic cylinder.  The idea is to hydraulically extend the legs for landing,  and then hydraulically retract them after launch.  Falcon-9's leg design cannot do that retraction after launch.  This concept is sketched in Figure 1 (all figures are at the end of this article).

This concept provides a ready means to get clearance between the surface and the aft vehicle skirt to protect the engine bells from debris damage.  It also provides a very-ready means to obtain a wide stance (for the landing pad polygon) relative to vehicle center of gravity (cg) height,  for robust stability on rough,  uneven,  and significantly-sloping ground.

The actual landing pads must also fold out so that a large pad bearing area can be obtained.  I looked at the hydraulic cylinder location and sizing to fold out the legs,  but not at the pad fold-out mechanism details.

Concept Design Analysis

The idea was to mount legs to the aft surfaces of the Starship vehicle.  Those on the windward side would have a coating of heat shield tiles on the outer surface,  with the skin underneath the leg bare.  Those on the leeward side could be bare,  like the leeward skins.  The windward legs thus become part of the Starship windward side heat shield.  Hinge line was at the aft skirt,  with fold-out pads mounted on the inside surface of the legs.

The "trick" with rough field overturn stability is a cg height/stance ratio near 1,  as demonstrated to be successful by several lunar and Mars probes,  and by the lunar lander used during Apollo.  Stance is the minimum dimension across the polygon defined by the centers of the landing pads.  If the vehicle weight vector (in three dimensions) falls outside that polygon for any reason whatsoever,  the vehicle topples over,  with fatally catastrophic results.  If it falls within the polygon,  it will not topple over.  This is basic statics. 

The "trick" with sizing the areas of the landing pads is not exceeding the bearing pressure strength of the soil you are landing upon,  no matter the circumstances.   There is "allowable soil bearing pressure",  and there is "ultimate soil bearing pressure",  which is usually factor 2.5 to 3.5 higher than allowable.  This is reported for a variety of Earthly soils in a variety of references,  as ranges of allowable soil bearing pressure versus soil types. 

While this data is primarily for foundation design in Earthly civil engineering,  it also applies directly to the spacecraft landing pad design problem.  The regoliths on the moon and Mars resemble nothing else so strongly as they do "loose fine sand".  For the static problems of after-landing and before-takeoff,  you may not exceed the allowable bearing pressure,  because of the long exposure times to the applied load.  There is time for settlement and compaction to occur.   For the transient of touchdown with factored-up weights,  you may use the ultimate bearing pressure,  because the soil does not have time to fail by settlement and compaction.  It instead fails by direct penetration. 

If you have no soil strength test data (and we do not,  for the moon or Mars),  then you use the minimum strength for the reported range of strengths,  for the soil type (in these off-world cases "soft fine sand" at 0.1 to 0.2 MPa allowable means you use 0.1 MPa).  For Earthly abort landings,  you will not be able to pick your touchdown location,  which means you must deal with the possibility of landing on "soft fine sand" or "soft clay" (0.1 MPa allowable),  both of which share the same low allowable bearing pressure in the absence of actual on-site test data.  Mud flats are even worse.

There is the static weight of the vehicle bearing down on the soil after landing.  There is vehicle weight multiplied by a dynamics factor as the applied force during the transient of touchdown,  and,  there is another dynamic factor applied to static weight that accounts for hitting on one leg first,  when the ground is uneven.  Weight at takeoff is higher,  because the fuel tanks are usually refilled for this event,  although this is another static case.   Weight depends upon both mass and the local gravity (at issue here is Earth,  Mars and the moon).

Relevant Missions

Different things are required of the different mission scenarios.  Starship is initially intended for travel to low Earth orbit and back,  plus suborbital flights point-to-point.  The intended landing place is always a site where there are thick pads of reinforced concrete to support the ship.  But presuming this is always so ignores the very real possibility of an off-site emergency or abort landing!  Most of the Earthly soils are far softer than a concrete pad,  and some are quite soft indeed,  such as sand dunes,  soft clay,  plowed fields,  and mud flats.  You must plan for that.  Eventually,  it will happen.

Eventually,  Starship is to be refilled on-orbit,  so that it may haul payload to the moon or Mars.  Missions to the moon presume no refilling is available there.  Missions to Mars presume refilling on Mars,  in order to enable a return to Earth at all.  Both have surfaces that are dominantly regolith,  which is rocks of many sizes dispersed in a range of sands from fine to coarse,  with no adhesion at all between the sand grains,  or between the sand and the rocks.

Doing the Analysis

There are 9 scenarios to examine,  3 at each of 3 possible landing sites (Earth,  moon,  and Mars).  At each site,  you look at pad sizing for static post-touchdown,  for the transient dynamics of touchdown,  and for static pre-launch.  The two static cases use allowable bearing pressure,  and the dynamic case uses ultimate bearing pressure.  I used for the dynamic case weight factored up by 2 for the dynamic effects,  and by another factor of 2 for the uneven ground effects.  Those factors could be higher,  but even when only set to 2's,  the weight gets factored up by 4.

I put this analysis together as a spreadsheet worksheet.  There's a block of common data,  and a block for the Earth landing/takeoff,  a block for the lunar landing/takeoff,  and a block for the Mars landing/takeoff.  In the flyout after an Earth abort landing,  the refill for takeoff is only a modest small percentage of the propellant capacity.  The ship has insufficient thrust to lift off against fully-refilled Earth weight.  I did not include thrust/weight analysis.

An image of the common data and the 3 Earth abort cases is given in Figure 2.  An image of the 3 lunar landing cases is given in Figure 3.  An image of the 3 Mars landing cases is given in Figure 4.  The worksheet is its own user's manual,  because of the text notes I made upon it.  Those are shown in Figure 5,  which defines all the relevant variables,  and lists all the relevant assumptions.  All this content is one worksheet in the spreadsheet software.

The results quite clearly show that the Mars pre-takeoff static case is the worst of the 9 cases,  and by far.  This is because of the large fully refilled mass,  despite the lower gravity on Mars.  The Earth abort scenario transient touchdown is the second-worst case,  and the lunar landing transient touchdown is by far the least demanding case.

What one does in this spreadsheet is input the data,  then look through the 3 sized pad area cases for the Earth abort scenario,  pick the largest,  and re-input that pad area for sizing the pad dimensions and the stability ratio criterion.  Then one does the same for the lunar scenario,  and again for the Mars scenario.  The largest pad area of the 3 scenarios governs,  for any design considered to be capable of use in all 3 scenarios (Earth abort,  lunar landing,  and Mars landing). 

What I did next was use the worst-case sized-pad scenario for Mars takeoff,  and run a stress analysis on the concept leg design.  I did this pencil-and-paper,  totally by-hand,  with a calculator.  It took 3 pages to do,  reproduced here as photos of those pages,  Figures 6,  7,  and 8.  These force and moment analysis numbers converge to the nearest 0.001 MN or MN-m.  This is not software,  this is just a well-defined procedure that you run,  getting numbers with equations,  which I have done for almost half a century now.  Before there were calculators,  I used a slide rule for this.  Done correctly,  it gets very good answers,  regardless of the calculation tool.

Figure 6 starts with a sketch of the leg design and the definitions of the variables in it.  Note that the initial attach point at mid leg span proved incorrect:  I reduced it twice before I got a retracted cylinder length greater than the cylinder stroke.  The second calculation determines the cylinder force angle relative to the leg,  from geometry.  This got revised after I finally found the feasible cylinder attach location on the leg.  The third calculation is a freebody diagram and analysis to find the fold-out pad hinge force and hinge moment.  I did not look at the details of the fold-out mechanism.

Figure 7 shows the freebody diagram and associated analysis of the leg,  with the pad forces applied,  and the cylinder and vehicle base hinge forces to be found.  It is standard freebody sums of forces and moments,  but includes a determination of tensile and compressive forces in the two regions of the leg.  At the bottom of the page,  I took a look at cylinder pressure and piston size,  as a function of the hydraulic pressure.  I did this in US units,  but converted the results to metric.   For this straightforward concept,  the cylinder sized alarmingly large,  and at alarmingly-high hydraulic pressure.

Figure 8 shows the leg bending analysis,  as the sequence of a load diagram,  a shear diagram,  and a bending moment diagram.  Unsurprisingly,  the max bending moment to be resisted occurs at the cylinder attach point on the leg,  and is more than a factor of 3 higher than the required hinge moment holding the fold-out pad level on the ground.  Units shown are metric. 

At the bottom of Figure 8,  I added a calculation of the required leg section modulus to resist the max bending moment without yielding the leg material.  If the leg yields,  it will not retract fully,  which guarantees a fatal catastrophic failure of the heat shield at the next entry!   Being more familiar with US units,  I converted a typical US units yield stress to metric,  and then calculated the corresponding section modulus in cubic meters,  then converted that back to US units of cubic inches.  Either way,  it is a very large number,  something inconsistent with the largest leg cross section dimension being lateral,  not vertical,  when deployed. 

Results and Conclusions

Between this section modulus result and the high hydraulic pressure result,  it is very clear that the simplest,  most straightforward update of the Falcon-9 folding leg design to Starship is NOT the right way to do this!  We need a better retractable leg design concept,  one that couples the actuator system much nearer the tip of the leg.  That will require some sort of compound link system to accomplish.  Not being a landing gear designer,  I am not the person to come up with that rig.  I would appreciate input from real landing gear designers about this,  by comment or by email!

Overall,  I would venture to say that any design that achieves both the reduced soil bearing pressures,  and the wide stance necessary for rough field stability,  is going to cost some extra inert weight,  but,  you will get what you pay for!  The "trick" will be designing the compound linkages that let us reduce leg bending moment closer to the level of the pad hinge moment.  Another "trick" will be finding some alternate way to fold out the large pad areas that we will have to have,  and then restrain them level to the ground,  but with a lower hinge moment. 

Figure 1 -- Sketch of the Basic Straightforward Concept

Figure 2 -- Spreadsheet Image for Common Data and the 3 Earth Abort Cases

Figure 3 -- Spreadsheet Image for the 3 Lunar Cases

Figure 4 -- Spreadsheet Image for the 3 Mars Cases

Figure 5 -- Spreadsheet Images for the Notes and Variable Definitions

Figure 6 -- Image of Hand Calculation Page 1 of 3

Figure 7 -- Image of Hand Calculation Page 2 of 3

Figure 8 -- Image of Hand Calculation Page 3 of 3

Saturday, May 15, 2021

Evaluations of the Spacex Starship/Superheavy

Over the last few years,  I have done several reverse-engineering evaluations of the Spacex Starship/Superheavy design,  as it has evolved into what is being test-flown as of this writing.  All of those evaluations are documented in articles posted on this site.  Here is a list,  from latest to oldest.  I have included evaluations of some test flights in this list,  but not the descriptions of the analysis techniques that I used.  

UPDATE 5-21-21:  I added another reference (#18) where the reduced payload/reduced tanker flights option was explored,  done with the best rocket performance estimating spreadsheet yet.  

Update 6-7-21:  I added another reference (#19) where the details of the simplest,  most straightforward landing leg concept were explored.  This was a retractable variant of the Falcon-9 legs,  to get a wide stance,  but also with a fold-out pad area to achieve low bearing pressures.  

Update 6-15-21:  I added a second landing legs article as another reference.  This is again a retractable variant of the Falcon-9 legs,  but done with link bars to get vertical leg orientation with no bending.

Ref.        date                      title [comments]

#1.         3-23-21                Third Spacex Tanker Study [found practical approach to refilling lunar missions]

#2.         3-21-21                Second Spacex Tanker Study [investigation of lunar mission refill feasibility]

#3.         3-17-21                Spacex Tanker Investigation [initial investigation of lunar mission refill;  includes capabilities to low circular orbit]

#4.         3-15-21                Reverse Engineering Estimates: Starship Lunar Landings [determining elliptic departure orbits to make lunar nearside landings feasible with 2021vehicle estimates]

#5.         3-9-21                  Reverse-Engineering Starship/Superheavy 2021 [estimated performance to low circular orbit with best 2021 vehicle data and techniques,  including booster fly-back]

#6.         12-10-20              Spacex Test Flight Results In Explosion

#7.         7-13-20                Non-Direct to the Moon with 2020 Starship [looking for ways to make lunar landings feasible with 2020 vehicle estimates but without penetrating into the Van Allen radiation belts]

#8.         7-5-20                  2020 Starship/Superheavy Estimates for the Moon [found to be infeasible from departure orbit that does not penetrate into the Van Allen radiation belts]

#9.         6-21-20                2020 Starship/Superheavy Estimates for Mars [found to be feasible from low circular orbit with 2020 vehicle estimates,  including faster transfer orbits]

#10.       5-25-20                2020 Reverse Engineering Estimates for   Starship/Superheavy [payload to low circular orbit with 2020 vehicle estimates and techniques,  including booster fly-back]

#11.       10-22-19              Reverse-Engineering the 2019 Version of The Spacex “Starship” / “Super Heavy” Design [first attempt at performance estimates to orbit,  with staging assumptions and crude booster fly-back,  using 2019 version of design;  updates included evaluations of overturn stability and soil bearing strength effects,  plus trips to Mars and to the moon,  plus proper landing engine choices]

#12.       9-26-19                Reverse-Engineered “Raptor” Engine Performance [evaluations of sea level and vacuum-bell engines,  complete with part-throttle vs full-throttle data based on chamber pressures]

#13.       9-16-19                Spacex “Starship” as a Ferry for Colonization Ships [an alternate use scenario]

#14.       2-4-19                  Designing Rough Field Capability Into the Spacex Starship [serious look at rough-field landing issues with 2019 version of the design]

#15.       4-17-18                Reverse Engineering the 2017 Version of the Spacex BFR [earlier look at the 2017 version of Starship with the projected 85-ton inert mass;  includes estimates to orbit and to Mars,  includes a look at rough-field landing issues and at the tanker issue;  a revisit of Ref. 16]

#16.       10-23-17              Reverse-Engineering the ITS/Second Stage Of the Spacex BFR/ITS System [an earlier look at only the 2017 version of the Starship second stage vehicle,  diameter reduction to 9 m]

#17.       10-2-16                Elon Musk Reveals His Plans for Mars [very first armchair look at the 12 m diameter Starship concept,  not a reverse-engineering evaluation;  some significant issues identified]

#18.        2-9-21                Rocket Vehicle Performance Spreadsheet [descriptive information that is essentially a user's manual for the spreadsheet,  plus the example of SS/SH to Mars for 2021 at max payload,  and at reduced payload for reduced on-orbit refill requirements]

#19.       6-7-21                  One Concept for Landing Legs [spreadsheet pad sizing and by-hand concept design analysis of a simple retractable landing leg concept of wide stance,  with large fold-out landing pads to reduce bearing pressure]

#20.        6-15-21                Landing Legs Concept 2  [legs fold out on two link bars to achieve vertical leg orientation with no bending,  slide-out pads that attach at their centers to legs]

These articles are most easily found by using the navigation tool on the left of the page.  Record the dates and titles you want to find on a piece of scrap paper.  Click on the year,  then click on the month,  then if need be on the title.  

Figure 1 -- Brief Summary of Results

Best of the Various Estimates

For a mission Starship to low circular Earth orbit,  the most realistic reverse-engineering estimates that I have are given in Ref. 5,  for a 9 m diameter system with inert masses of 120 metric tons for Starship and 180 metric tons for Superheavy,  as they are best understood in early 2021.  These include my best estimates of staging velocity and booster flyback,  which has some impact on payload to orbit.  The vehicle acceleration impacts of thrust levels are included,  along with my best available estimates of the landing after the belly-flop maneuver.

For a mission Starship to elliptical orbit for lunar landing missions,  the most realistic reverse-engineering estimates are given in Ref. 4,  which includes the analysis of direct landings on the lunar nearside.  This is for the Starship/Superheavy as it is understood in early 2021:  9 m diameter,  with 120 and 180 metric ton inert masses.  Thrust effects are included.  The lunar departure is from an elliptic orbit with its apogee inside the Van Allen radiation belts.  It must be fully-refilled at departure.

For missions from low circular Earth orbit to Mars (and back),  the best reverse-engineering estimates available are given in Ref. 9,  for the same 9 m diameter Starship of inert mass of 120 metric tons.  The data are as understood during 2020,  and could be updated for better precision,  although the older booster unknowns (such as inert mass) are not a major impact on overall results.  Both Hohmann min-energy transfer and faster transfer orbits were evaluated.  Payloads are smaller than could be lofted to low Earth orbit. That reduces the refill requirements (and the number of tanker flights) to depart.

Update 5-21-21:  Ref. 18 has the 2021 spreadsheet results for the Mars mission from LEO,  at full payload,  and for a reduced payload that reduces on-orbit refill requirements.  Scope includes both Hohmann transfer at average planetary distances,  and a 2-year "abort" orbit at average planetary distances.  These really are the best available estimates based on the best available data as the SS flight test program proceeds (up to SN-15).  

For tanker capabilities to low circular orbit,  the best reverse-engineering estimates are given in Ref. 4.  They include withholding adequate landing propellant allowances under different constraints than would apply to mission Starships.  Both rough-estimated “dedicated” tanker designs,  and “ordinary” Starships used as tankers,  are covered.  Estimates of tanker capabilities to the feasible lunar departure elliptic orbits are also given (these are quite low in comparison).  Thrust effects are included.

The capacities and mission strategy for tankers to support lunar missions are given in Ref. 1.  These reverse-engineering estimates minimize the number of tanker flights for a single mission to a lunar landing.   Thrust effects are included.  This best scenario does most of the refilling in low Earth orbit,  with the mission Starship and one refilled tanker sent to the elliptic lunar departure orbit. 

The best Raptor engine performance characteristics are given in Ref. 12.  Although those data reported are given in US customary units,  they are easily converted to metric using  4.44822 N = 1 lbf for thrust data.  There is no need to convert seconds of specific impulse. 

Scope includes both the sea level and vacuum-bell Raptor engines,  and full data at both 100% and 20% chamber pressures.   You may scale linearly between thrusts and specific impulses at 100% and 20% chamber pressure.  You may not scale linearly between vacuum and sea level performances.  The reference provides performance vs altitude lists for both sea level and vacuum-bell designs,  at both throttle settings. 

I don’t see much reason to keep updating these reverse-engineering estimates until after the Starship and Superheavy flight tests are completed,  and the system has begun flying to low circular orbit.  At that time,  the inert masses and the propellant capacities of the two stages will be known far more clearly,  as will the number of engines in the booster,  and the best practices for landing the upper stage spacecraft.  Not to mention many important details,  like the landing legs and the heat shield.

Beware the Unaddressed Issues

These estimates that I made do not address all the issues that must be resolved before this system can do any of the projected missions!  Some of those issues have been anticipated,  such as rough-field landing capability.  Others are becoming apparent during the early Starship flight tests!  All are potentially-fatal problems that must be resolved,  before the system can become operational.  The performances I have identified are certainly attractive enough to warrant the massive efforts needed to resolve those problems!

One should be aware that Spacex has taken a far different approach to that of NASA,  in designing its large lifter-to-space.  There are a whole host of risky new technologies embodied in the Starship/Superheavy design.  These are what must be included to get large capabilities along with low costs.  The NASA approach (as embodied with SLS) is very much lower-risk approach (a new combination of things that have been used before),  but that is already known to be inherently very expensive. 

What Spacex did with its Falcon launch vehicles lies sort-of “in the middle” of that high-risk/low-cost to low-risk/high-cost spectrum.  Those vehicles flew conventionally first,  then added new technologies one or two at a time to get reusability and lower costs.  This was successful,  although Spacex nearly went bankrupt at first,  learning how to fly and stage supersonic vehicles.  They are now the low-price leader in the launch industry,  and some of their competitors are beginning to move toward reusability as well.  However,  while leading the pack,  Spacex is also encountering problems to solve that no one has ever addressed before.

Problem to Solve:  Rough-Field Landing Capability

There are three separate aspects of this.  All three require effective solutions.  They are (1) overturn stability,  (2) safe bearing pressure exerted on soft substrates,  and (3) a telescoping capability to address surface contour roughness and shock absorption.  The landing legs we have seen so far on the "Starship" prototypes address none of these concerns adequately!

I covered much of this topic (the first two issues) in Ref. 11,  including some typical safe soil bearing pressure values,  and a guide to which soil in the list corresponds to the most common surfaces on the moon and Mars.  Refs. 14 and 15 also explore this topic. 

               Safe Bearing Pressures

The safe pressures in the Ref. 11 list are factored down from experimental soil failure values,  which factored-down allowable pressures prevent unintended penetration upon load application,  and also prevent settlement (compaction under the landing pad. 

Such compaction allows penetration downward) over long periods of time.  In the absence of actual test data,  you must use the low end of the range of values in the list as your landing leg design value.  You also need to factor-up the weight to be supported,  to represent the dynamic effects of touchdown,  and also the effects of coming down "crooked",  so that one leg hits first. 

The main lesson from the soil data is to use only 1 US ton/sq.ft = 0.1 MPa safe bearing pressure as a maximum tolerable value when sizing landing pad areas for the moon or Mars (or Earth,  for that matter).  That corresponds to loose fine sand or soft clay.  Even with the rocks dispersed (without adhesion) in the loose sand and dust of lunar and Martian regolith,  these regoliths would be very similar to loose fine sand on Earth,  because there is no adhesion between these sand and dust particles,  and no adhesion to the rocks

Further,  the soft tidal-flat muds adjacent to Spacex's landing pads at Boca Chica would be at most only that strong (0.1 MPa),  and very likely weaker still.  A prototype massing 120 metric tons,  and landing with 10-15 tons of propellant still aboard,  weighs about 1.3 MN here on Earth.  6 legs with "feet" 0.5 m x  0.5 m square would have about 1.5 sq.m total "pad" area.  The average static pressure upon the surface is then near 0.9 MPa (already 9 times too high),  and likely 2-to-3 times that (near 2 to near 3 MPa) during the dynamic transient of touchdown,  and for sure 6 times higher still (near 15 MPa) if one leg hits first. 

So,  a mudflat landing at less-than-0.1 MPa safe pressure (after missing the landing pad for any reason whatsoever) would clearly lead to disaster,  as the legs would penetrate deeply and unevenly,  leading to topple-over and explosion (see following)! 

               Static Stability

I also showed in Ref. 11 how the weight vector "hanging" from the vehicle center of gravity must fall within the footprint of the landing legs (as a polygon upon the ground),  even as the vehicle is tipped by sloping ground,  or leg penetration,  or boulders,  or contour roughness,  or anything at all.  That is the essence of static stability.  It is in all the elementary statics textbooks.

If the vehicle is statically unstable because its center of gravity height is too high relative to the stance (footprint polygon dimension),  the vehicle will (inevitably!!) topple over.  With topple-over of  a rocket,  an explosion is simply guaranteed. 

Note that the height to stance width ratio of all the successful landers on the moon and Mars has been in the vicinity of 1.  That ratio in the current Starship prototypes with 6 small legs mounted to the aft skirt is currently near 25/9 (not quite 3).  That is simply too high for rough field operation,  even for emergency landings on Earth.

Update 6-7-21:  Ref. 19 has the analysis results for a simple,  straightforward update to the Falcon-9 landing leg concept,  one that provides wide stance and large fold-out landing pads,  yet is hydraulically retractable.  Scope includes post-landing static bearing,  bearing of transient landing dynamics,  and pre-launch static bearing,  for each of 3 scenarios.  Those scenarios are Earth off-site abort,  lunar landings,  and Mars landings.  The basic forces and moments were determined with freebody diagram analysis.  

Update 6-15-21 Ref. 20 has an alternative version of the fold-out landing legs held by two link bars,  such that the leg itself is vertical.  This eliminates bending loads on the leg, reducing it to compression.  A revised fold-out pad is given that could be used with either concept.  It eliminates the large pad hinge moment,  and greatly reduces bending loads in the pads themselves. 

               Uneven Surfaces and "Crooked" Touchdowns

Hydraulically-telescoping landing legs are required to overcome three problems:  (1) the elastic bounce-back of spring forces-only acting upon the vehicle,  (2) the anticipated dimension of surface roughness features (boulders,  gullies,  and the like,  which would be typically around a meter or so),  and (3) having to come down "crooked" so that one leg hits first,  for any reason at all (such as leaning into a gust of wind on Earth). 

If the legs have sufficient telescoping stroke,  then both problems (2) and (3) can be solved,  without raising the forces on any one leg too high.  If you have sufficient stroke,  then the leg that hits first need not support the entire weight of the vehicle,  which has to be factored-up by 2 to 3 for dynamic effects.  It will support something only a little more than its share of the total,  and only for a short transient. 

It takes hydraulic dissipation to provide the damping necessary to prevent problem 1.  Otherwise,  you will bounce around like a rubber toy,  which means you are completely out of control,  during touchdown.

Engine Bay Fires

Fires inside the engine bay during ascent were seen on engine bay camera footage and from external views during the test flights of SN-8,  SN-9,  and SN-10,  and in engine bay footage only  during SN-11 (which was flown in fog,  obscuring the view from the ground).  The only failure officially attributed to fires destroying engine wiring was SN-11.  These fires are clearly methane leaks burning with air. 

No ascent fires were seen in the engine bay footage of SN-15's first flight (it may be re-flown).  That footage is incomplete,  but enough could be seen to rule out ascent fires.  SN-15 is said to be a revised design from that of SN-8 through SN-11. 

Lesson learned:  Spacex appears to have stopped the methane leaks and fires seen during ascent,  with its SN-15-on design revisions. 

Engine-Out During Flip Maneuver

Low thrust during the flip to vertical and final touchdown was seen during SN-8 (attributed to low fuel pressure) and SN-10 (attributable to helium pressurant ingestion?).  An engine-out (or two) was seen during SN-9,  SN-11,  and SN-15 (planned 3-engine relight for flip,  only two actually seen to light).  There was insufficient altitude available to decelerate SN-8 and SN-9 at all,  leading to fatal crashes. 

SN-10 was damaged in landing,  and then blew up a few minutes after the landing,  probably attributable to the post-landing methane-air fire that was seen.  SN-11 was destroyed by a midair explosion above the landing pad,  said to be caused by an engine "hard start" (which is just code for an engine explosion upon attempted ignition).  SN-15 landed successfully,  and survived the post-landing methane-air fire. 

Lesson learned:  start the flip and deceleration early,  because lowered thrust is likely,  due to multiple causes.  You can always throttle back or shut an engine down,  if you have more thrust than you need.  But insufficient altitude for lower-than-expected thrust to actually decelerate the vehicle,  will always lead to a fatal outcome.

Post-Landing Fires

SN-10 landed hard and crushed its legs unevenly,  so that it ended up leaning,  almost toppling.  It also reportedly crushed part of its skirt.  It definitely had a post-landing methane-air fire for a few minutes,  then blew up.  SN-15 landed more softly,  had a post-landing methane-air fire for a few minutes,  which was put out,  so that the vehicle survived.  Are these fires methane leaks associated with engine shutdowns?  Nobody has said,  yet.  But fire exposure endangers hardware,  and damaged hardware will leak propellant.  That is the nature of rocketry.

Lesson needing to be learned:  Spacex must stop the post landing fires,  because (1) any LOX venting into the fire for any reason at all will inevitably cause an explosion, and/or (2) the heat from fire exposure may damage tanks and plumbing,  causing a subsequent oxygen leak and explosion.

Cross Winds and Gusts at Touchdown

While SN-15 landed successfully in its first flight and survived the post-touchdown fire,  it did land near the edge of its landing pad,  with one leg about a meter from the soft tidal flat mud.  It supposedly was blown there by a last-second gust of wind.  I have seen photos of crumpling in the landing legs that supposedly reflect shear force damage being slid sideways during touchdown.  I am not so sure about that,  myself,  seeing more evidence of compressional crumpling than anything else in those photos. 

That being said,  being blown sideways at touchdown is a serious topple-over risk.  The lateral friction force (between pads and surface) is located pretty much perpendicular to a moment arm from there to the center of gravity.  For significant friction (comparable to weight) that is a big overturn moment,  which in turn is a really strong argument for a wide landing leg stance,  beyond the arguments already listed above.

While a flight control might compensate by leaning the vehicle into the crosswind,  the magnitude of the wind overturning moment once touched down is also quite large:  it is a force applied at the lateral center of pressure,  which is just a diameter or so down from the center of gravity.  The couple created by the wind force (which more-or-less equals the pad lateral friction) has a large moment arm,  almost as large as the center of gravity height.  That is a large overturn moment.  This is another argument for a wide stance.  It applies to Earthly landings where wind forces can be large. 

Beyond that effect,  leaning into the crosswind guarantees an uneven touchdown onto the landing legs.  One pad will always hit first because of the off-angle attitude.  The strength and stroke of that leg has to be high enough to absorb the entire weight load of the vehicle,  factored-up for dynamics,  during the touchdown transient!  It has to stroke,  in order to absorb those forces hydraulically;  spring forces-only will not do the job,  because of bounce-back risks!  All the legs must be designed that way,  because you simply cannot predict which one will hit first. 

Lessons to be learned:  landing leg designs must have

               (1) sufficiently wide stance (center-of-gravity height / stance dimension near 1), 

               (2) pad area on each leg must be large enough not to exceed safe soil bearing pressures,  for a vehicle weight factored-up for dynamic effects and for any uneven effects not mitigated with hydraulic leg stroke, 

               (3) legs must absorb dynamic loads with hydraulic stroking in order to have the damping necessary to prevent bounce-back,  and

               (4) the stroke length is set by the greater of (a) expected surface roughness dimension or (b) the off-angle effect of coming down "crooked". 

Heat Shield Robustness

This evaluation cannot be done until Spacex is flying its prototypes to orbit,  or at least to near-orbital speeds,  requiring hypersonic entry and aerobraking.  I would anticipate potential difficulties in 3 areas:  (1) loss of heat shield tile or tiles,  (2) vortex scrubbing of windows,  and (3) over-the-nose jet reattachment due to lateral vortices. 

               Tile Loss

Unlike the Space Shuttle,  any burn-through due to a lost tile will very likely be directly into a cryogenic propellant tank.  That is because a bit over half the vehicle length is propellant tankage,  of a single-wall design.  Such a burn-through not only causes loss of any remaining propellant in the tank,  it also causes depressurization of the tank to ambient,  which at entry altitudes is essentially vacuum.  If the vehicles depends in part on tank pressurization to maintain strength against the high-angle air loads,  then it will likely break up. The same would apply to any pressurized cargo spaces,  and to any pressurized crew habitation spaces.  If the tile retention scheme is redundant,  likelihood of any tile loss is significantly reduced.

               Vortex Scrubbing

There is a line of flow separation somewhere along each side of the vehicle when at significant angle of attack.  In the wake zone just downstream of the separation line,  there is a vortex along each side.  These vortices are much weaker at low angle of attack,  and very strong indeed at high angle of attack (where the flow is mostly crossflow). 

Where the vortex contacts the aft skin,  there is a scrubbing action at higher and higher velocities as the vortex grows stronger.  That scrubbing action enhances heat transfer rates to the skin,  despite the low pressures (and densities) in the wake zone.  If there are windows touched by this scrubbing,  they could very easily overheat and fail.  To a lesser extent,  the same risk is true of exposed metal skins. 

               Nose Jet Reattachment

The same lateral vortices,  if very strong,  can induce material from beyond the far side of the wake to relocate close to the aft surface between them.  In effect,  they can cause a jet of air coming over the nose not to separate,  but to stay attached.  This jet flows along the dorsal line.  There is very strong scrubbing associated with this jet contacting the surface.  And,  if it hits any projecting protuberance (such as a windscreen),  the jet shocks to high-pressure flow on the protuberance.  The combination of high scrubbing velocity and locally high shocked density can produce catastrophic heat transfer rates. 

Figure 2 -- Flow Field Effects

The Space shuttle suffered from this effect with its flight deck cabin roof structure and windscreen projecting into that reattached dorsal jet of high energy air.  This risk precluded operating the Shuttle at higher angles of attack than 40 degrees.  Below 20 degrees,  there was no lee-side separation,  and flow simply came around the nose and struck the windscreen.  The shockdown caused catastrophic heating.  Thus the Space Shuttle was strictly limited to angles of attack between 20 and 40 degrees during entry.

The cross section shapes and planform shapes of the Spacex Starship and the NASA Space Shuttle are different.  The Starship may,  or may not,  experience the same lateral separation lines with vortices;  and if it does,  the angle limits will likely be somewhat different.  However,  this same flow pattern effect was seen experimentally,  within pretty much the same limits,  for a variety of candidate nose shape details,  when the Shuttle was being designed.   Thus,  the Starship may well suffer similar risks to the windows and bare metal skin on its lee-side surfaces.

Lesson(s) to be learned are still TBD.

On-Orbit Refilling

This evaluation cannot be done until Spacex is flying multiple prototypes to orbit,  and attempting refilling operations on-orbit.  I can anticipate potential difficulties in two areas:  (1) required high attitude accuracy for tail-to-tail docking and automatic connection of propellant plumbing,  and (2) massive attitude thruster propellant usage during the main engine cryogenic propellant transfers,  at micro-acceleration levels (thus requiring a long time to accomplish). 

Lesson(s) to be learned are still TBD.

Radiation Risks

This will become a problem once Spacex attempts flights of its prototypes outside low Earth orbit.  I can anticipate problems in 3 areas:  (1) radiation-hardening of flight controls and propulsion controls,  (2) a place for any crew or passengers to shelter from solar storm events during flights to off-Earth destinations,  as well as sheltering from Van Allen radiation belt exposures,  while in high elliptic orbit for lunar departures,  and (3) co-locating crew control stations and at least some of the radiation sheltering,  so that critical maneuvers can be conducted by the crew during severe exposures.

Lesson(s) to be learned are still TBD.

Final Comments

I started this write-up in March,  intending to complete it and post it during April.  However,  my laptop died,  and took with it a lot of data,  including this write-up.  I was able to recover the data,  so that finishing this write-up became possible.

This article is intended as guide to previous reverse-engineering analyses,  which have evolved over time.  I have identified for the reader which articles have the latest and greatest data,  to which mission scenario they apply,  and exactly how to quickly and easily reach them.   

I am hoping that some of Spacex's engineers are aware of me and what I have done.  I might be able to shorten their learning process a little;  the "school of hard knocks" can be very expensive indeed.