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.

Update 8-7-2022 These estimates were made using my evaluations of the sea level and vacuum Raptor-1 engines,  assuming they could be operated at the full intended chamber pressure of 4400 psia = 303 bar.  As it turned out,  they never operated that high,  and fell short on thrust and specific impulse.  I have since evaluated the revised designs for Raptor-2,  which indeed achieve the intended pressure levels.  Specific impulses are very close to what I assumed for these analyses because the pressure was achieved,  and thrusts are a bit higher because the throat diameter is slightly larger.  As a result,  these analysis results for payload capability on the various missions are still very close in the ballpark.  The other uncertainties and assumptions are likely larger effects than the specific impulse differences,  which are slight. 

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.