Single Stage Launch Trade Studies

Several friends and on-line correspondents (all of whom are also interested in space flight) have been discussing how to launch single stage to Earth orbit (SSTO),  with an eye toward reusability.  Both traditional launch rockets and winged launchers that are effectively spaceplanes are investigated here. 

All items considered here are vertically-launched.  The depressed trajectories flown by horizontally-launched designs are completely different,  and cannot be analyzed in this way at all.  See Figure 1 (all figures at end) for the assumed trajectory shape,  and associated bounding analysis assumptions.

I personally think reusability will “cost” the extra weight to make the structure robust enough to fly multiple times.  Otherwise,  from a rocket propulsion standpoint,  the typical rocket performance levels available to us are:

LOX-RP1……………………305-310 sec Isp

LOX-liquid-CH4…………near 350 sec Isp

LOX-LH2……………………near 460 sec Isp

1972-vintage NERVA…near 900 sec Isp

Note that NERVA is a solid core nuclear device.

I did this as a parametric bounding analysis,  based on the simple rocket equation and some convenient simplifications to support it.  The supporting calculations are summarized in Figure 2.  I looked at inert structural fractions from 5% to 40% (in increments of 5%) as the independent variable,  with required Isp as the dependent variable.  The parameter was payload fractions from 2 to 10%,  in increments of 4%. 

I did not look at ramjet-assist or any other type of airbreather-assisted vertical launch.  The analysis required to support usable trade studies with airbreathers goes well beyond this kind of rocket equation-based bounding analysis. 

The basic results are presented in Figure 3 as parametric curves.  Required Isp (as the ordinate) to accomplish a launch mission that effectively requires 8.56 km/s delta-vee,  is plotted versus inert structural fraction as the abscissa.  The parameter is imposed dead-head “payload” fraction from 2% to 10% by 4% increments. 

Linear interpolation between payload fractions is clearly permissible.  Horizontal lines have been added to represent the available Isp levels,  as described above for the four “realistic” types of rocket propulsion listed above. 

“Dead head” payload includes the real delivered payload,  plus any shroud or capsule weight,  as appropriate.  The structural inert weight includes basic tankage or airframe structures,  plus engines,  plus any recovery equipment or propellants that might be required. 

One-Shot One-Stage Rockets

For one-shot single-stage rocket boosters,  the inert structural fractions can resemble those of currently-flying vehicles,  two-stage or otherwise.  Those range from 5 to 10%,  and are probably closer to 5% in new designs today,  at least with dense propellants that are not “extreme” cryogenics.  With that range of inerts “spotted” on the graph,  Figure 4 gives the trade study results. 

The LOX-LH2 propellant choice gives the “best” results throughout the 5-10% inerts range,  provided that the propellant volumes can be reconciled with a 5% drag loss.  One might “guess” about a 7% dead-head payload allowance,  that might reconcile fairly well with perhaps 7% inerts (very voluminous LH2 tankage with extra insulation). 

Vehicles like that can carry large payload masses inside a fairly-lightweight shroud (say near 1% of launch weight,  leaving the remainder of the “dead head payload” fraction as real payload delivered to orbit).  Or,  they might carry smaller payloads inside one-way or returnable capsules,  such as Orbital’s Cygnus or Spacex’s Dragon,  respectively.  For the sake of argument,  assume 80% of a one-way capsule’s weight might be real payload,  and 60% of a returnable capsule’s weight might be real payload. 

For that 7% deadhead payload LOX-LH2 sizeout,  if shrouded,  then about 6% of the launch weight might be real delivered payload.  If instead a one-way capsule,  then again about 5.6% of the launch weight might be real delivered payload.  If instead a returnable capsule,  then about 4.2% of the launch weight might be real delivered payload. 

LOX-RP1 is just barely infeasible as shown in Figure 4,  but 5% inerts and 4% dead-head payload is feasible with LOX-CH4.  If shrouded,  then perhaps 3% of the launch weight might be real deliverable payload.  If a one-way capsule,  then about 3.2% of the launch weight might be real deliverable payload.  If a returnable capsule,  then about 2.4% of the launch weight might be real deliverable payload. 

For something comparable to a Falcon-9,  the launch weight would be in the neighborhood of 500 metric tons.  The launch price would be near $56.5M.  (Falcon-9 lists as $4300/delivered kg.)  Using these values and the percentages in the preceding paragraphs,  I get:

Propellant…………….inerts%............deadhead%

LOX-LH2……………….7…………………….7

Type…………………….deliv%...............$/del.kg

Shroud…………………6……………………..1880

1-way capsule………5.6………………….2020

Returnable cap…….4.2………………….2690

 

Propellant…………….inerts%.............deadhead%

LOX-CH4……………….5…………………….4

Type……………………..deliv%..............$/del.kg

Shroud………………….4…………………….3770

1-way capsule……….3.2…………………3530

Returnable cap……..2.4………………….4710

Any of the LOX-LH2 configurations would then seem to offer slight cost advantages per unit delivered payload,  over the LOX-RP1 two-stage-to-orbit (TSTO) baseline Falcon-9.  (This baseline is based on Spacex website data as of 9-24-13.)  The LOX-CH4 data are less advantageous than LOX-LH2,  because of the lower Isp performance.  The shroud and 1-way capsule versions seem to offer very slight advantages over the Falcon-9 baseline,  but the returnable capsule seems to be a little less cost-effective. 

Really,  at this level of analysis,  all the LOX-CH4 data are effectively the same unit price as baseline,  and the LOX-LH2 only very slightly better than baseline.  This looks attractive only for a clean-sheet-of-paper LOX-LH2 design.  Otherwise,  the LOX-RP1 TSTO baseline that we have is better. 

Re-Usable One-Stage Rockets

This is a “screwy” case.  It all boils down to what one believes that the realistic effective inert weight fractions might be.  The trade study results are given in Figure 5,  on which I have spotted the roughly 10% inert fraction of Space Shuttle SRB’s,  which are 900-psi pressure vessels,  being solid motor cases,  yet of limited demonstrated reusability. 

My own guess for the inert fractions of fully-reusable liquid stages is closer to the 15-25% range also spotted on the figure.  This “budget” includes not just the tankage and engines,  but also all the necessary recovery equipment (such as chutes and landing legs),  plus a considerable amount of retro-thrust propellants (if a powered descent is the approach taken,  as in Spacex’s “Grasshopper”).  

This might actually be a “low-ball” estimate,  since entry is so demanding an environment.  But it doesn’t really matter.  The curves show basic infeasibility for all three chemical rocket choices,  with the possible exception of LOX-LH2 at only 1% “dead-head” payload.  Such a payload would have to ride the booster “naked”,  as there is no allowance available for a shroud.  No capsule options seem feasible. 

That leaves you only with the nuclear rocket option “NERVA”,  which at 20% inerts could probably carry 13-14% dead-head” payload.  Actually,  considering the relatively low engine thrust/weight for NERVA-type engines,  we’d be lucky to obtain 35% inerts at 2% dead-head” payload.  That would be about a 1% real delivered payload fraction,  inside a shroud,  as the only feasible option.  That’s 5 metric tons delivered,  at the “same $56.5M” price,  for about $11,000/delivered kg.  That’s not very attractive. 

But,  in any event,  to be re-usable means you are flying back to Earth an already-fired nuclear reactor engine,  and you are doing this multiple times.   There are some very serious safety concerns with such an approach.  I really don’t recommend this for Earth surface launch. 

The bottom line is that a re-usable SSTO booster is technically attainable with nuclear rocket propulsion,  but nobody will like the safety risks.  I did not look at re-usable first stages for a chemical TSTO system.  That is what Spacex is really looking at. 

Re-Usable One-Stage Rocket Spaceplanes

Winged rocket spaceplanes that launch by vertical takeoff (VTO) as SSTO,  but return to horizontal landing (HL) have been a longstanding dream.  Again,  the driving assumption is what you believe a realistic inert weight fraction might be. 

Being a winged airframe,  this is the vehicle that most closely resembles an airplane as we have known them for over a century.  Most modern transports and bombers fall in the 40-50% inert weight fraction range,  with carrier-capable Navy “birds” pushing 60% inerts.  That would be for traditional metal construction.  Airframes like that are usually designed for 40,000+ landings and takeoffs. 

You cannot replace all of the metal structures with composite materials.  These are very intolerant of heat.  Not only orbital descent,  but also ascent,  are rather vicious aeroheating environments.  But,  the number of landings and takeoffs might be in the 100-1000 range,  which eases somewhat the robustness (and inert weight) required of the design. 

A “reasonable guess” might be half composites and half metallic,  for a minimum-credible reusable inert weight fraction in the range of 25 to 30%.  Accordingly,  I showed inert fractions from 25 to 40% on the trade study results given in Figure 6. 

All the chemical options are quite clearly infeasible.  Only a nuclear spaceplane powered by some version of a NERVA (or better) would be feasible.  This brings up (again) all the safety concerns of flying back to Earth with a fired nuclear reactor core,  as discussed above for reusable rocket stage boosters. 

Allowing for the low engine thrust/weight ratio of NERVA,  we might achieve 35% inerts at 2% payload fraction.  No shroud or capsule is required,  so the delivered payload is 2%.  That’s 10 metric tons for a 500 ton launch weight.  Again,  assume the same launch cost of $56.5M for the 500 ton nuke,  and you get around $5700/delivered kg.  It does not seem to offer any cost advantage over what we are doing right now:  the Falcon-9 one-shot TSTO calculates as $4300/delivered kg. 

Options Not Considered Here

I have not looked at airbreather-assist for VTO SSTO,  or any depressed-trajectory SSTO and TSTO systems (whether airbreather-assisted or not).  (I have actually looked at the latter,  but not in a way that I trust yet.)  The airbreathers,  particularly ramjet,  require substantially-more sophisticated performance-estimation methods than the simple rocket-equation stuff presented here.  Those are destined for a future article.

Final Comments

One-shot VTO SSTO rocket-stage systems seem to be marginally attractive (relative to a one-shot LOX-RP1 VTO TSTO baseline) from a delivered payload unit cost standpoint,  but only if a LOX-LH2 system is considered in a clean-sheet-of-paper design.  LOX-CH4 seems to offer no real improvement,  and one-shot LOX-RP1 VTO SSTO seems to be essentially technologically infeasible.

Re-usable VTO SSTO rocket-stage systems appear to be completely infeasible for all known chemical propulsion choices,  relative to the one-shot LOX-RP1 VTO TSTO baseline.  A NERVA-type nuclear approach appears to be technically feasible,  but at lower payload fraction due to the low engine thrust/weight inherent with solid core nuclear engines.  Assuming the same basic launch cost for the same launch weight class,  the unit price for delivered payload appears to be more expensive,  relative to the one-shot VTO TSTO LOX-RP1 baseline. 

 

For VTO SSTO rocket spaceplanes,  only the NERVA (or better) option looks to be technically feasible.  Under the same price/launch weight assumptions,  the unit price for delivered payload looks at-best more-or-less comparable to the one-shot LOX-RP1 VTO TSTO baseline,  probably more expensive.

 

Figure 1 – Basic Trajectory and Assumptions

Figure 2 – Basic Calculations and Related Conditions

 

 

Figure 3 – Basic Parametric Rocket Equation Results

Figure 4 – Basic Results for One-Shot One-Stage Rocket Launchers

 

Figure 5 --  Basic Results Revisited for Re-Usable One-Stage Rocket Boosters

 

Figure 6 – Basic Results Revisited for Re-Usable One-Stage Rocket Spaceplanes

Update 9-29-13:

For those not so familiar with rocket work,  these plots can be a little confusing or misleading.  First:  these are for single-stage operations only.  You cannot use these directly for staged vehicles.  Nor can you do anything useful with these plots toward airbreathing-assist,  it's just too coarse for that,  although concepts can be illustrated. 

For airbreathing-assist,  you have to "account" for highly-variable airbreather Isp effects,  how much of the thrust is airbreather,  and what fraction of the whole trajectory is actually assisted by the airbreather.  You also have to worry about having enough thrust to take off,  and that these charts embody only vertical takeoff on a fast ascent trajectory. 

Second,  the slanted curves are just physics as embodied by the classic rocket equation.  There's only 3 categories of vehicle mass considered here:  inerts,  propellant,  and dead-head payload.  The curves show the interplay among the three,  with two explicitly shown,  calculated to a fixed velocity-change requirement.  None of those curves would ever change,  given the same velocity requirement.

The horizontal lines represent the performance levels of typical rocket propulsion technologies.  In essence,  this is the influence of that portion of the mass budget that is propellant.  I showed 3 chemical and one old nuclear system as a guide. 

Technologies can improve,  shifting these horizontal lines slightly,  but chemistry has been "stalled" for decades,  pretty much where it is depicted.  The nuclear technology offers the most hope of improvement,  but has not been seriously worked-on in 4 decades.    What I show is what was cancelled right before it could be flight-tested,  the variant that was most mature back then. 

The vertical lines represent the effects of materials and construction techniques upon the inert weight.  This has seen the most change in recent decades.  The modern 5-10% inert range is now pretty typical of commercial launcher stages.  Rolled textured aluminum alloy panels are what make this possible,  in concert with higher-tech versions of the engines that have lower engine weight for the same thrust.  Long ago,  that was closer to 20% with things more like frame-and-stringer type construction. 

I have to caution readers and users of these graphs that these 5-10% inert weight percentages are typical of one-shot (throwaway) stages,  not anything that might be reusable.  One-shot designs contend with ascent loads and ascent heating only.  Descent loads and descent heating are not only worse,  they are totally different in character.  You have to deliberately design for them from the outset in a reusable design.  You also have to have a service lifetime in mind for a reusable design,  something totally different than "just-surviving-the-mission" with a one-shot design. 

The early history of aircraft design is the most recent example of a technology arena where we have learned a very fundamental lesson the hard way (with many lives lost):  the robustness of a long service life is simply heavier,  because more materials are required to withstand the forces.   There is no escaping that fact-of-life,  and that is why I spotted recent modern aircraft values on the figure 6.  These are basically dry weight divided by max gross weight.  The difference is really both payload and fuel together.  (Airplanes are different from rockets,  after all.)

The 50% I show as "typical" of a long-life transport or bomber aircraft might not be representative of a reusable winged space launcher,  but the 40% of the all-metal X-15 rocket airplane is a good startpoint for guessing what might be suitable for a reusable winged craft.  Those are fundamentally different from "not-winged" vertical launch stages,  reusable or not.   

Composites typically have at least twice the strength to weight of aluminum,  but are even more vulnerable to overheating.  You cannot replace all the metal with all-composites,  except in minimum-velocity suborbital flight,  and even that is on a heat-sink transient. 

I hope these comments help provide additional guidance for those wishing to use my results.  I really do appreciate the comments,  Google +1's,  and other feedback.  Thanks,  and have some fun playing with this stuff.  I certainly did. 

--GW

More Gun Control? No Way!

I have a real problem with the disrespect for our constitution evident in the guest column written by Rosa Brooks (1),  that appeared Friday 9-20-13 in the Waco “Trib”.  On the other hand,  the guest column by Charles Krauthammer (2) that appeared the same day,  is something I very much agree with,  which is actually unusual for me,  as we have very different approaches to politics. 

Krauthammer’s article makes very good sense:  the mass shootings of late mostly seem to have been committed by deranged folks who “dropped through the cracks”,  either in the medical care system,  or in the gun background check process.  The scandal is not the violence they commit,  or that they use guns to commit it,  the scandal is that they drop through the cracks,  which tells us what really needs to be fixed. 

The Second Amendment

As for understanding the intent of the second amendment that Brooks so derides along with the entire constitution in her article,  I don’t need some court to tell me what it means. 

All I need is junior high grammar skills,  and a little junior high-level history for its context.  Here is the text,  as downloaded from Wikipedia (3).  It is a very short and straightforward item:

A well regulated militia being necessary to the security of a free state, the right of the people to keep and bear arms shall not be infringed.

There are only two phrases separated by a comma,  which version is what the states ratified when they ratified the constitution.  This was verified by its author,  Thomas Jefferson.  Other versions with extra commas and capitalizations are not what was ratified,  which means ascribing intent to the extra commas and capitalizations is bogus.  Period.  (Congress did that when they put it in the records.  Surprise,  surprise!)

The first phrase is a justification,  not a modifier.  Interpreting it any other way violates the basic rules of English grammar,  which have not really changed since the amendment was written.  The second phrase is a statement of what is to be done,  plain and simple.  The only “modifier” is not in the amendment,  it is in the context of the times (more about that below).

That first phrase calls forth the concept of a militia (as opposed to the “mob” that carried out the French revolution).  A militia was then,  and still is,  “citizen soldiers” that grab their weapons and come forth from home to fight on the battlefield in an emergency.  This was then,  and still is,  a different concept from the standing regular army (by extension today’s armed services).  

Historical Context

Back then,  the militia was the “Minute Men”.  Today’s real militia is the national guard,  and the inactive reserves that could be called back to duty.  In a really serious “nightmare-scenario” emergency,  the old “Minute Men” precedent still stands:  armed civilians could “spontaneously” join the ranks of the militia,  bringing their personal weapons with them.   Simple enough.

Also back then,  there was the concept of the armed population making the threat of armed revolution credible.  That was intended to make government behave itself,  instead of turning to dictatorship,  as so many others did before.  That risk,  and that need,  are still with us,  and in my opinion not enough “revolutionary threat” has been made in recent times:  government has been misbehaving!  (I think most might agree with that last assessment.) 

Also in historical context,  there was never any question that cannons and their ammunition would be kept in any other place than an arsenal.  That’s still true today,  and extends to missiles and a lot of other heavy-weapon stuff. 

Applying the Concepts

My point here is that both the regular army and the militia have to have the same kinds of weapons,  which back then were also exactly the same as civilian hunting weapons.  Our national guard uses pretty much the same weapons as the regular army,  although maybe not the “latest-and-greatest” versions. 

The only thing that has really changed is firearm technology:  there are repeating rifles,  machine guns,  and repeating handguns available today that were undreamed-of in Jefferson’s time.  The battlefield demands full-automatic weapons (machine guns) that in some cases (real assault rifles) can be operated as semi-automatic (one shot at a time without manual reload). 

If the “Minute Men” concept must ever be employed (and none of us wants that,  but prudence demands that we be prepared),  then the weapons brought from home need to be at least marginally useful on a battlefield with today’s machine guns.  That’s semi-automatic rifles and handguns that could (in an emergency) be quickly modified to operate as full-automatic weapons. 

There’s no way around that technical requirement.  You cannot ban semi-automatic weapons like the AR-15 (which is not a real assault rifle,  because it cannot operate as a machine gun),  and still have civilian citizen-soldiers credible for that last-ditch,  maximum-emergency battlefield scenario. 

What you do instead is ban that full-auto modification,  and then de-facto suspend it for that nightmare scenario.  We already did that,  with the 1934 firearms law that outlawed civilian possession of fully-automatic weapons.  It made sense then,  with the organized crime violence,  and still does today. 

What About Magazine Size?

As for the politically-popular idea of limiting magazine size,  it is easy to show by elementary calculation that switching-out large versus small magazines does not really affect firing rates very much,  averaged over multiple magazines.  So,  there’s not much to gained in mass-shooting scenarios by doing this. 

But,  if the citizen soldier’s magazines are interchangeable with the military’s,  then he is more effective in that last-ditch nightmare scenario because of vastly-improved logistics.  So,  limiting magazine size is a bad idea:  it doesn’t solve the civil violence problem,  but it does degrade our maximum militia capability.  Simple,  clear,  and compelling.

So,  What Do We Do?

If you want to reduce gun violence in America,  then do something about all the untreated mental illness all around us.  First on the list.

The main “leak” in the gun background check process is:  nothing may be done to prevent sales to the mentally ill until they have been judged mentally ill by a court. 

We have had a lot of mentally-ill mass shooters recently,  and none of them were so-judged by any court.  Fix THAT.  Make it a staged process,  instead of an either-or choice that only lawyers and judges control. 

Do those two things,  and you won’t need any of the other “gun control” ideas. 

Then you won’t have to degrade that maximum-defense capability that the civilian volunteer provides for that nightmare scenario,  or the citizen revolution capability that makes government behave itself.    

It ain’t rocket science,  as Brooks said in her article (the one thing I did agree with).  Nor do any of you have to be one,  in order to understand this issue,  or what to do about it. 

References:

(1) Rosa Brooks, "Over and Over and Over Again",  opinion-page article in Waco Tribune-Herald newspaper,  appearing Friday 9-20-13.

(2) Charles Krauthammer,  "Our Society Abandons Mentally Ill,  At Huge Price",  opinion-page article in Waco Tribune-Herald newspaper,  appearing Friday 9-20-13.

(3) results of google search for "second amendment,  being the article on Wikipedia,  as it appeared Friday,  9-20-13.  (This wording of the amendment matches that in my history books.)

Related Articles

I have written about this topic before,  with pretty much the same message,  just different details being addressed.  The other articles are listed here by date and title,  all on this site.  I added the search keyword "guns" to all 6 articles. 

2-5-13:  Real Problems with the Proposed Gun Control Legislation Items
12-20-12:  On the Tragedy in Connecticut
12-14-12:  School Shooting in Connecticut
8-9-12:  Mass Murder Shooters and Gun Control
1-13-11:  On the Shooting Rampage in Tucson

Update 9-22-13:

Since posting this article (or any of the older ones),  I have seen nothing in the news (or anywhere else) to induce me to revise these opinions.  Not even Wayne LaPierre's recent inflammatory remarks alter my views.  He was actually fundamentally correct,  in that there surely seemed to be a dearth of armed guards defending the otherwise gun-free zone that was a navy base facility. 

Update 12-15-13:

I have seen nothing to change any of my conclusions or recommendations in this,  or any of the referenced articles,  not even with the latest shooting incident at Arapahoe High School in Colorado.  In point of fact,  the Arapahoe HS incident confirms what I have been saying. 

The news reports indicate that the Arapahoe HS shooter killed himself only 80 seconds into the incident,  because he knew the on-site deputy was “on the way”.   This quite apparently stopped him from shooting more kids and/or teachers. 

My contention is that we should be defending our gun-free zones on a 60-second time scale,  just as what worked very well in the old west.  At Arapahoe HS,  unlike Newtown elementary in CT,  there was a deputy on site.  That so very obviously made a huge difference to the outcome. 

What is unclear about Arapahoe HS in CO is whether getting down from 80 sec to 60 sec might have saved the 17 year old Ms. Davis from her shotgun head wound.  But,  what is clear,  is that more did not die,  as was the shooter’s intent. 

Properly-defending declared gun-free zones really does work,  just like it did a century (and more) ago. 

We already know this works.  So,  just get on with it!

Update 5-28-14:

The latest incident with Elliot Rodger in California is simply another crazy never institutionalized,  and so still able to legally buy guns without any impediments at all.  That gets right back to the text highlighted in yellow in the main article above,  under "So What Do We Do?"

This is "lawyer/judge nonsense" at its very worst!  Until that loophole is closed with a policy that makes good common sense,  these horrific incidents will continue,  mark my words!  Nothing else is going to fix that very fundamental lack.