An Ex Rocket Man's Take On It: Launch to Low Orbit Study

This study explores launch to low circular Earth orbit at low inclination. It encompasses two different propellant combinations, and 1-shot throwaway designs versus recoverable and reusable designs. It considers both single-stage-to-orbit (SSTO) and two-stage-to-orbit (TSTO) configurations. It includes a mixed-propellant TSTO as 1-shot and reusable. This study used the new worksheet “both” added to the “stage studies.xlsx” spreadsheet. See “Launch Vehicle Rough-Out”, 5-18-2026 on this site, for spreadsheet descriptions.

The two propellant combinations are oxygen-hydrogen (LOX-LH2) and oxygen-methane (LOX-LCH4). These bound the performance problem, be it SSTO or TSTO, and regardless of whether 1-shot or reusable. The mixed-propellant option looks at a LOX-LCH4 first stage, and a LOX-LH2 second stage, in the TSTO, for both 1-shot and reusable designs.

This study is based on the performance levels of modest-technology engine designs, be they sea level/ascent-capable, or vacuum-capable. They have lower max chamber pressures Pc, lower pressure turndown ratios P-TDR, and a cycle resulting in some turbo-pump bleed drive gas dumped overboard. One can always do a little better with higher-technology versions of these same engines, especially with full-flow cycles.

The difference between 1-shot and reusable designs is two-fold: (1) slightly-different design delta-vee (dV) requirements for reusable versus 1-shot, and (2) significantly different stage inert fractions for reusable versus 1-shot.

See Figure 1 for the basic mission concepts, and Figure 2 for the orbital mechanics data. All figures are at the end of this article.

The engine performance analysis results for the four baseline engine types are included as Appendix A below. These are easily re-scaleable to other sizes and thrust levels. The thrust level used was 220,500 lb = 100 metric ton-force. Areas and flow rates are proportional to thrust. Dimensions are proportional to the square root of thrust.

The numbers used are summarized in Figure 3 below. It covers both the SSTO and TSTO configurations. The specific impulse (Isp) values came from the engine sizing analyses in the appendix. They were reported to the nearest-second of Isp, but without any rounding-up. The inert fractions were simply presumed, with modern 1-shot stages typically near 0.05 (5%). The reusable stages must have higher inert fractions, reflecting the inert additions for entry and descent aerodynamic control, minimal landing legs or fittings, and in the case of SSTO or TSTO 2^nd stages, heat shielding to survive full-speed entries. These were simply presumed as educated guesses for this study.

There is one fundamental governing equation here, regarding mass numbers: the sum of the payload fraction, inert fraction, and propellant fraction, must be 1.000! The dV values for the reusables are larger by the presumed landing budgets. All the other components of dV are shared by both 1-shot and reusable designs. For this study, all the gravity and drag losses are borne by the SSTO, and by the TSTO 1^st stage. These were each presumed as 5% of perigee speed for the transfer ellipse as a measure of the orbital mechanical energy.

The basic bounding study results are given in Figure 4 below. They comprise a data table for the SSTO configurations, and plots for the TSTO configurations. The SSTO table includes both 1-shot and reusable configurations, and LOX-LH2 and LOX-LCH4 propellant combinations. Mass ratio MR = exp(dV/Vex), where Vex = 9.80667*Isp/1000.

The SSTO using LH2 as a 1-shot, looks rather competitive in terms of payload fraction. The SSTO using LCH4 as a 1-shot is technically feasible, but has a very unattractive, tiny payload fraction. Neither of the SSTO reusables is technically feasible at all, whether H2 or CH4, with their negative payload fractions.

The all-H2 TSTO looks very attractive in terms of payload fraction as a 1-shot, and is still quite competitive as a reusable. The all-CH4 TSTO as a 1-shot, is also feasible, and more-or-less comparable in terms of payload fraction with the all-H2 reusable. The all-CH4 reusable TSTO is mostly technically feasible except at the lowest staging velocities, but it is not very competitive in terms of payload fraction.

Those TSTO results as bounds bring up the question of using H2 in one stage and CH4 in the other. Only H2 in the 2^nd stage and CH4 in the 1st stage makes any sense, since the 1^st stage Isp is lower, but that 1^st stage also shoulders a lower dV requirement. That combination was run as both a 1-shot and a reusable, with results given in Figure 5 below.

6% mixed vs 8% all-H2 payload fraction is pretty comparable for the 1-shot TSTO, and 3.5% mixed vs 5% all-H2 is pretty comparable for the reusable TSTO. The mixed results are closer to the upper-bound all-H2 results than the lower-bound all-CH4 results, whether you look at 1-shot or reusable. What you “buy” with that slight drop with mixed, is a smaller 1^st stage-as-LCH4 volume, sitting on the launch pad. The 2^nd stage is the same H2 configuration, either way. The mixed-propellant reusable TSTO payload fraction is not as sensitive to staging V, compared to all the other configurations here. 2 km/s is “typical”.

Conclusions and Caveats

The highest payload fractions are 1-shot (not surprisingly). The “best” TSTO 1-shot payload fractions are all-H2 at 8+%, with mixed 1-shot not very far behind at ~6.5%. The all-CH4 TSTO 1-shot falls significantly short of these at about 4%. The 1-shot H2 SSTO is also comparable at ~5.7%, but the reusable H2 SSTO has essentially zero payload fraction. Neither of the CH4 SSTO’s was even technically feasible at all.

The mixed reusable TSTO is almost as good in terms of payload fraction at ~3.5% as the reusable all-H2 TSTO at ~5%, with reusables having much lower operating costs!

The mixed reusable TSTO is less sensitive to staging V than the rest, and it would have the lowest stage 1 volume sitting on the launch pad.

Caveat: inert fractions were presumed as educated-guess values, and no inert buildup analyses were done to verify those numbers!

Caveat: no thrust requirements were determined for any of these stages, no numbers of engines and their thrust levels were determined, so there was no determination of dimensions, and no determination of whether the engines would fit behind the stages!

Additional Related Information

The author cross-plotted his results for the TSTO, separated into two plots, one for 1-shot designs and the other for all-reusable designs. This was to determine the sensitivities to propellant selection, but bear in mind that we are examining effects that are “down in the weeds” compared to engine Isp and stage inert fraction effects.

The author ran one more design that was mixed-propellant with a methane stage 1 and a hydrogen stage 2. The 1^st stage was calculated as reusable, with those dV, Isp, and inert fraction values, while the 2^nd stage was calculated as 1-shot, with those dV, Isp, and inert fraction values.

Like the both-stages-reusable case with mixed propellants, overall payload fraction is well below the both-stages-1-shot values, and very near the both-stages-reusable values. However, it exceeds the both-reusable only at rather high staging speeds, and in any event would be more expensive to operate, with its 1-shot 2^nd stage. Again, this is “down in the weeds” compared to engine Isp and inert fraction effects. See Appendix B below.

About the Author

The author had two 20-year careers, the first in aerospace/defense new product development work, and the second in mostly teaching, with some civil engineering and aviation work thrown in. The change was necessitated by the huge aerospace/defense workforce drawdown that took place shortly after the fall of the Soviet Union. For most of these careers, he had BS and MS degrees in aerospace engineering. He obtained a PhD in general engineering late in life. He is now long-retired, only doing some consulting now and then. Contact him by email at gwj5886@gmail.com.

Figure 1 – Basic Mission Concepts

Figure 2 – Orbital Mechanics Defines Most of the dV Requirements

Figure 3 -- The Numbers As-Used In This Study

Figure 4 – The Bounding Results for Both SSTO and TSTO/Both Stages Same Propellants

Figure 5 – Results for TSTO with LOX-H2 Stage 2, and LOX-LCH4 Stage 1

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Appendix A -- Rough-Sized Baseline Engines

These were two LOX-LH2 engines sized for ascent and for vacuum, and two LOX-LCH4 engines sized for ascent and for vacuum. These were sized from propellant combination c*, using a specific heat ratio of 1.20, and the appropriate nozzle throat to deliver a required thrust. We are only interested in the specific impulse (Isp), for this study. Figures A-1 through A-4 below are the reported results for these sizing calculations.

The ascent nozzles were sized to be on the verge of flow separation in the exit bell, when operating at 80% of max Pc, while testing at sea level. That corresponds to an exit area ratio of 35.88:1, when max Pc is the rather modest 2000 psia.

The vacuum nozzles were sized to an arbitrary exit area ratio of 150:1.

An 18-8-degree curved bell was presumed, with throat discharge coefficient of 0.995.

The engine cycle need not figure into any of this, except as its dumped bleed fraction. 5% (0.05) was presumed for that. The value of “Pc” here is that taken just before the contraction from chamber to throat.

Nozzle separation: Psep/Pc = (1.5 * Pe/Pc)^0.8333, where Pa > Psep is separated.