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