Reverse-Engineering the ITS/Second Stage of the Spacex BFR/ITS System

Update 4-17-18:  since writing this article,  I have gone to the Spacex website,  where the 2017 presentation materials and more are posted about this design.  I have re-visited my reverse-engineering of the capabilities of this vehicle in greater detail with greater fidelity to reality,  in all its complexity.  I have posted that new,  improved analysis as "Reverse-Engineering the 2017 Version of the Spacex BFR", dated 4-17-2018. I do recommend that readers use that newer analysis article, rather than this one.

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The “giant Mars rocket” proposed by Spacex has reduced in size somewhat since its first reveal at the Guadalajara meeting.  The term “BFR” is now beginning to refer to the first stage of the two-stage system,  which flies back and lands for reuse.  The term “ITS” more properly applies to the reusable second stage,  which apparently has two forms.  Those are the cargo/passenger craft that goes to destination after refilling on-orbit,  and a flyback tanker that provides the refill propellants on-orbit. 

Data published by Spacex at the latest meeting indicate a cargo/passenger vehicle that summarizes as given in Figure 1.  Grossly,  this is a 9 m diameter vehicle about 48 m long,  with a dry mass of about 85 metric tons,  and propellant tankage that holds about 240 metric tons of liquid methane and 860 metric tons of liquid oxygen.  Stated payload weights are 150 metric tons on ascent (and presumably to destination), and “typically” 50 metric tons on return.  Characteristics of the tanker form are less clear,  but it seemingly has a lighter dry weight of about 50 metric tons.

Figure 1 --  Estimated Characteristics of ITS Per 2017 Revelations

These two versions presumably share the same ascent propellant tankage and engine cluster.  Those engines include both sea level and vacuum expansion forms of the same Raptor engine,  with a nominal chamber pressure of 250 bar,  and deeply-throttleable to 20% thrust.  The cluster has 4 vacuum engines of 1900 kN thrust each at 375 sec vacuum specific impulse,  and two sea level engines of 1700 kN thrust each,  and specific impulses of 356 sec in vacuum and 330 sec at sea level.  Exit diameters are 1.3 m and 2.4 m for the sea level and vacuum forms,  respectively.  (I did not correct sea level thrust to vacuum.)

I am presuming here that second stage operation during launches to Earth orbit takes place in vacuum,  so I use the vacuum thrust data for both versions of the engine.  Each type’s thrust is therefore associated with a propellant flow rate via its specific impulse.  Summing these gets a total full thrust and a total propellant flow,  and thus an effective “average” vacuum specific impulse with all six engines running,  for an effective exhaust velocity of about 3.5762 km/sec.  That calculation summarizes as follows,  where effective cluster specific impulse is total thrust divided by total flow rate (Figure 2).

Now,  on the assumption that both forms of the vehicle have the same ascent propellant tanks and quantities (totaling 1100 metric tons of propellants),  the following weight statement and delta-vee table applies (Figure 3).  For the tanker,  the first-listed payload of 150 tons is assumed from the cargo passenger version.  The second is back-calculated from holding tanker delta-vee capability to be the same as the heavier ascent form of the cargo/passenger vehicle.   

To do that,  one finds the required mass ratio from the delta-vee,  then solves the mass ratio build-up for the unknown payload:

                Wpay = [Wp – (MR – 1)Wdry] / (MR – 1)

What I find very interesting here is that Spacex seems to have said it takes 6 tankers to fully refill an ITS on orbit for its voyage to destination.  If you look at the heavier tanker that gets the same 6.2 km/sec delta-vee as the fully-loaded cargo/passenger form,  then 1100 metric tons of propellant divided by an estimated 184.7 metric tons per tanker equals 5.956 (almost exactly 6) tankers required.  So the tanker at 50 tons dry weight seems to hold 1100 tons of ascent propellant,  and just about 185 more tons of propellant-as-payload with which to refill a cargo/passenger ITS on orbit.  It would appear this estimate is then just about right.  It does presume all 6 engines running all of the time.

Using BFR/ITR at Mars

For a trip to Mars from low Earth orbit,  the departure delta-vee for a Hohmann minimum-energy orbit to Mars is around 3.71 km/sec at average orbital conditions.  For a direct entry without stopping in Mars orbit,  you let the planet hit you from behind,  as the planet’s orbital velocity is faster than the transfer orbit’s aphelion speed.  Velocity at entry interface will fall in the 6 km/sec range,  and aerodynamic drag kills most of that to about 0.7 km/s coming out of hypersonics fairly deep in the Martian atmosphere.  Double or triple that for the landing burn:  about 1.5-to-2 km/sec delta-vee requirement. 

That’s crudely 5.21 to 5.71 km/sec delta-vee required to make a direct landing on Mars,  with just almost 6.2 km/sec available.  The difference can be used to fly a somewhat higher-energy transfer orbit,  for a shorter flight time than 8 months.  Faster is possible if payload is reduced.

To return,  the ITS is refilled with in-situ propellant production on Mars.  It will need around 6 km/sec delta-vee capability to launch and escape directly,  with enough energy to achieve the return transfer orbit.  We assume a direct entry at Earth,  which means in turn we run into the planet from behind,  since vehicle perihelion velocity is higher than Earth’s orbital velocity. 

It will be a very demanding entry interface speed (well above 11 km/sec):  this is what stresses the heat shield,  not entry at Mars.  But,  the vehicle will come out of hypersonics at about the same 0.7 km/sec moderately high in the atmosphere.  It will need at least 3 times that as the landing burn delta vee requirement,  because the altitude is higher,  and the gravity is stronger.  Call it 2 km/sec as a “nice round number” to assume.

The total delta-vee requirement to ascend from Mar’s surface and achieve a direct transfer orbit and a powered landing on Earth is therefore in the neighborhood of 8 km/sec.  That is just about what the ITS cargo/passenger version seems capable of,  if restricted to about 50 metric tons return payload.  Again,  that particular payload correspondence lends confidence to these otherwise-guessed numbers. 

It also points out how critical in-situ propellant production will be for using this vehicle on Mars.  Unless this vehicle is refilled locally with the full 1100 metric ton propellant load,  it is stranded there!  Each launch from Mars requires 240 metric tons of locally-produced liquid methane,  and 860 metric tons of locally-produced liquid oxygen.  Launch opportunities are 26 months apart.  Required production rates are thus 9.23 tons/month methane,  and 33.08 tons/month oxygen,  at a bare minimum,  per launch.

BFR/ITS For the Moon

Some have pointed out that this vehicle could also visit the moon.  To leave Earth orbit for the moon,  the delta-vee requirement about 3.29 km/sec.  The delta-vee to arrive into low lunar orbit is just about 0.8 km/sec,  or to land direct,  about 2.5 km/sec.  Those one-way totals are 4.09 km/sec to lunar orbit,  and 5.79 km/sec to land direct (remarkably close to the Mars value at min energy transfer). 

To return by a direct departure from the lunar surface requires about 2.5 km/s,  or from orbit about 0.8 km/sec.  Landing at Earth is largely by aerodynamic braking,  but requires about a 2 km/sec landing burn.  Therefore,  total delta-vee requirements to return are 4.5 km/sec from the surface,  or 2.8 km/sec from lunar orbit.

One could conclude that the ITS could ferry cargo to lunar orbit and return entirely unrefilled,  a trip requiring total 6.89 km/sec delta-vee capability.  This is not available at 150 metric tons of payload,  but it is available at something a little larger than 50 tons.  I get about 102 metric tons of payload. 

The requirements to land and return entirely unrefilled would be 10.29 km/sec,  which is out-of-reach even at only 50 tons payload.  To use the ITS on the lunar surface will require propellant production on the moon,  although likely at somewhat lower rates and quantities than at Mars.

Guessing Reusable Performance of BFR

A related point:  if we presume the fully-loaded ITS uses essentially all of its 1100 tons of propellant achieving low Earth orbit,  we can back-estimate the delta-vee that is actually available from its BFR first stage,  even allowing for flyback.  Earth orbit velocity is just about 8.0 km/sec.  Allowing 5-10% gravity and drag losses for a vertical ballistic trajectory,  the min total delta vee is about 8.4-8.8 km/sec.  About 6.1 of that is from the ITS second stage.  The first stage need only supply 2.3-2.7 km/sec,  which means the staging velocity is just exoatmospheric at around 2.5 km/sec.  It should easily be capable of ~5 km/sec,  so the difference is for flyback all the way to launch site,  and propulsive landing.

Suborbital Intercontinental Travel

Finally,  there has been some excited talk about using the BFR/ITS for suborbital high speed transportation across intercontinental ranges here on Earth.  That is a ballistic requirement similar to that of an ICBM.  The burnout velocity of the typical ICBM is around 6.7 km/s.  Allowing 5-10% margin for gravity and drag losses,  the delta-vee necessary to fly intercontinentally is 7 to 7.3 km/sec,  plus for the ITS,  about 2 km/sec for the landing burn.  Total is thus 9 to 9.3 km/sec delta-vee. 

This is way beyond the delta-vee capability of the ITS stage alone,  notwithstanding the fact that 4 of its 6 engines will not operate at sea level,  and even if they did,  total 6-engine thrust of the ITS stage (1100 kN) is less than its weight (1300 kN or more).  But this delta-vee is within reach of the two-stage BFR/ITS combination (6.2 to 7.9 km/sec ITS and ~2.5 km/sec BFR for 8.7 to 10.4 km/sec),  and likely with a little less payload than the 150 tons typical to Mars.  Maybe something in the vicinity of 100 tons. 

Final Remarks

These estimates are rough.  I did not correct sea level thrust to vacuum for one thing,  my delta vee requirements are approximate for another,  and I did not explore the effects of using only the vacuum engines for higher specific impulse out in space.  

Even so,  these results are very intriguing.  These calculations were made pencil-and-paper with a calculator.  Nothing sophisticated.  

ASUS Hardware, Windows Software? Never Again!

My ASUS X553M laptop with factory Windows 10 operating system is a low-quality,  unreliable piece of crap!  So is its operating system!  (Its predecessor was a Toshiba laptop running Windows 8/8.1.  The hardware failed at age 2:  the display hinges broke.  I hated Windows 8 from the moment I saw it.)

This ASUS machine/Windows software combination has several very serious issues that Best Buy’s Geek Squad cannot,  or will not,  help me with.  All these major issues are fatal,  as far as my estimate of quality is concerned.  That list follows below.

I would appreciate comments from readers as to what machines or operating systems might possibly be acceptable (since this machine and operating system are so very clearly not). 

I need to do word processing,  powerpoint-type slides,  spreadsheet work with plotting,  and a shell within which to run old-time DOS software.  I need something that can use wi-fi to access the internet and email.  I want a battery pack that I can pull,  to force a restart,  when all else fails.

ASUS X553M / Windows 10 Fatal Issues List:

#1. The screen dims and flashes or flickers,  when not plugged into the AC power supply.  This renders the machine unusable,  in spite of the battery being charged.  When the issue first started,  it did this with about 50% battery charge remaining,  as indicated on the display.  This rapidly got worse over a period of only months,  accelerated to starting the flicker at 90% battery indicated.  Now it will not run without flashing even at 100% indicated charge state.  Nothing in the Windows settings affects this. 

#2. The machine turns off its wi-fi device spontaneously,  without warning,  and for no perceptible reason.  This happens erratically and unpredictably.  The frequency with which it occurs is increasing as time goes by.  More of the time,  It still sees the wi-fi network,  and will reconnect if you command it.  But for a significant portion of the time,  it does not see the wi-fi network,  and so cannot be commanded to reconnect.  The only recourse in that case is reboot. 

#3. This machine on occasion locks up without warning,  rendering the keyboard and the mouse totally inoperative.  The only way to deal with this is a reboot.  It always loses all data up to the last save.

#4.  I cannot trust the reboot to be effective,  unless I unplug the AC power,  and either select full shutdown (not restart),  or else use the power switch.  I have noticed that the tiny indicator lights do not go out,  and that the issues the reboot was supposed to correct do not reliably get corrected,  unless I go for the complete shutdown with no AC connected.  There is no battery pack to pull,  as the battery is all-internal.  

#5.  The machine erratically and unpredictably ignores clicks of the mouse.  This problem comes and goes erratically. 

#6.  The keyboard has unreliable keys,  and a slow response to keystrokes.  You can type fast,  and it will miss a lot of letters.  Some are worse than others.  Those will often ignore slow repeated keystrokes,  even ignore continuous hold-down of the offending key.  Plus,  the symbols wore off the keys in only a year.

#7.  I haven’t seen a stable operating system out of Microsoft since DOS,  which would fit on a 1 megabyte floppy disk.  The entire fundamental Windows concept is flawed,  forcing people to learn a second language (icons),  which was (and still is) unnecessary.  The last DOS machine I had also had a little shell program (from a German company) that did a text-based point-and-click mouse controlled interface.  This interface did everything for file navigation that Windows ever did,  but would fit on another 1 megabyte floppy disk without even filling it. 

#8. Windows 8/8.1/10 are all useless pieces of crap totally bogged down with useless touch-screen crap that is totally inappropriate to an ordinary laptop.  That kind of marketing arrogance totally negates any possible past reputation Microsoft ever had for quality or for customer service. 

#9. All of the Windows operating systems are very hard-to-remove (you must wipe the hard drive),  behaving exactly like a virus or malware,  ever since Windows 95.  The last semi-stable version I had was Windows 3.1,  but it was nowhere near as stable as DOS 2 or DOS 6,  which never corrupted themselves or required reboots.

#10.  The Windows operating systems are all self-corrupting,  and they do not clean up the messes they make,  which clog up your hard drive memory,  and bog down your machine’s operating speed.  DOS did not do that.

Machine Guns in Las Vegas?

Update 10-3-17:  in red text below.

Update 10-4-17:  in blue text below.

Update 10-6-17:  in purple text below.

Under federal law,  a “machine gun” is a firearm that shoots more than one bullet per trigger pull.  The synonym for this is “fully-automatic”.  A “semi-automatic” weapon is one that sends one bullet per trigger pull,  loading the next round automatically.  If it doesn’t load the next round automatically,  that means the user must operate some sort of manual bolt or other mechanism to load the next round.  Bolt-action rifles,  pump or breakdown shotguns,  and ordinary revolver handguns fall into that last category. 

The M-16 used by US armed forces is indeed a machine gun,  a fully-automatic weapon,  although it can be operated as a semi-automatic single-shot weapon as well.  The same is true of the Russian-developed Kalashnikov AK-47.  These are true “assault weapons” for military use precisely because they really can be machine guns.  A military unit not so armed is at a lethally-distinct firepower disadvantage when confronted by such weapons. 

The AR-15 (and most modern hunting and sport guns) is a semi-automatic weapon,  not a machine gun / fully-automatic weapon.  The fact that an AR-15 looks exactly like an M-16,  has absolutely nothing to do with its rate of fire.   Calling it an “assault weapon” is wrong,  because no military unit today would ever go into combat with the AR-15.  They would be totally outgunned by any group with fully-automatic weapons.  It’s not about what the gun looks like,  it is entirely about what the gun can actually do.  Simple common sense.

Civilians in this country currently can indeed own or possess machine guns,  but what devices they can own,  and what they can do with them,  is very,  very,  very severely restricted.  This began with the National Firearms Act (NFA) of 1934.  That law came about because the mafia was causing mass death in the streets with the venerable old “Tommy gun”,  which really was a machine gun.  It severely restricted civilian ownership of fully automatic weapons,  short-barrel rifles and shotguns,  and certain explosives.  It was amended in 1968 and again in 1986.

The 1986 amendment restricted civilian ownership of fully automatic weapons to only those made before 1986,  only with payment of a $200 tax along with an enormous and very invasive application,  and only with a very,  very thorough ATF background investigation,  plus requirements for notification of the ATF any time the owner traveled with any of those devices. 

Such devices could not be updated or repaired with modern parts.  Parts for such devices are largely out-of-reach of all but the richest today.  There are no exceptions to allow for the ownership of anything newer than 1986.  There are no exceptions to any of the other requirements.

This status was superseded for a while in 1994 to disallow entirely the civilian ownership of those pre-1986 machine guns,  short-barrel guns,  and devices,  but that restriction expired in 2004.  So,  we are still under the 1986 version of the law today.

In all 50 states,  it may indeed be legal to own machine guns,  but only in accordance with the federal law!  If the possession or use is not in accord with federal law,  then such possession or use is presumed illegal under state law,  period!  Some states impose further restrictions,  some do not.  And that federal law is exactly the 1986 update of the 1934 NFA law.  Period.  No exceptions.

Modifying a semi-automatic weapon into a full-automatic weapon is indeed possible,  but it is generally not very easy to do.  It requires appropriate tools and knowledge and experience.  It also requires testing.  This is already illegal under any circumstances,  no exceptions. 

Update 10-4-17:  Two new technologies for increasing firing rate have come to light.  These are the "bump stock" and the "gat-crank".  These act to increase the firing rate of a semi-automatic weapon to that of a fully-automatic weapon,  without modifying the loading mechanism inside the weapon.  These are therefore technically legal,  but they definitely do violate the intent of the 1986 prohibition on all but grandfathered machine guns.  In my opinion,  this is cheating,  and should not be allowed.  

What the shooter in Las Vegas did,  and what motivated him,  are still the subjects of investigation.  Nothing is yet known with any certainty,  and such certainty is unlikely for quite a while yet. Update 10-6-17:  information in news reports keeps surfacing that point to mental illness of some kind in this shooter.  He got his guns legally,  because no judge ever had him committed.  If you look at the earlier article cited below,  that "leak" of guns into the hands of crazies is the most common cause of these mass shooting incidents!  

The best speculations are (1) he sneaked some 10 (weapon count has been climbing in subsequent reports,  both in the hotel and at his home) long-barrel weapons into his hotel room overlooking the outdoor concert venue,  (2) at least some of those weapons were machine guns based on the high rates of fire evident from the audio recordings of the event,  and (3) he fired into a dense crowd that could not move quickly,  so that without aiming,  he was certain to hit lots of people. 

Item 3 means that fully-automatic weapons are not required to exact a huge death toll,  but they do considerably raise it.  Not even semi-automatic weapons are needed.  A considerable death toll could still be expected with just single-shot,  bolt-action rifles.  So,  it’s not really about the gun,  it’s much more about the situation:  a densely-packed,  immobile crowd as the target from a nearby high place. 

Every time there is such a mass shooting event,  there is an immediate knee-jerk reaction:  a call for tighter gun control.  Always the same things are proposed,  and almost none of them would have prevented any of these events,  including this one!  The exceptions are (1) selling weapons too easily to crazy folks,  and (2) loopholes to the required background checks we already have. 

The problem here really isn’t so much the guns,  it is what motivates people to want to kill their neighbors.  What causes that?  I have never heard a good answer to that question.  Maybe it is past time to go find out. 

Update 10-3-17:  To find out what the gun violence is really trying to tell us,  go see my analysis of excerpts from the Mother Jones gun violence database.  It is not what you think!  This analysis is in the article titled "What the Gun Violence Data Really Say" dated 6-21-2016 on this website.  It has a list of titles and dates for other articles I have also written on this subject.  The navigation tool on the left gets you there most easily.  Click on the year,  then on the month,  then on the title. 

For those unwilling to go to the cited article and examine the data for themselves,  here is the short form of the message:  (1) we have a major "leak" of guns legally sold to people who are mentally ill,  but have never been so ruled by a court,  (2) we have a major problem with inadequately-defended (or entirely-undefended) gun-free zones,  which also invite terrorist attack,  and (3) the "usual" gun control proposals of "assault" weapons bans,  clip size limits,  and the like,  have already been tried and were already found to be ineffective.  

It's both that simple and that ugly.  Fix those two items properly,  and it looks to me like most of this problem goes away.  Item 3 tells you what not to do.  Update 10-4-17:  I also recommend outlawing "bump stocks" and "gat-cranks".  That won't prevent the incidents,  but it will reduce the death tolls.