“Rocket science really isn’t science, it’s only about 40% science. It’s about 50% art, and 10% blind dumb luck” – unknown author
The old saying about rocket science actually applies to all
of engineering. The numbers shift a bit
depending upon what exactly you are attempting to accomplish. Other than that, the illustration needs no comment. -- GW
PS – I drew the illustration myself in Windows 2-D “Paint”.
Up front comments:
This article is an earlier,
smaller effort, aimed at
identifying and characterizing the 3-phase process required to plant colonies
off-Earth. It examines the effects of
the process upon mission plans and the requirements upon the appropriate
vehicle designs. I plan to supersede it
with a longer article or articles, which
will include some vehicle rough-sizing results.
There is a corresponding slide show to this shorter
article, that could be given in a 30-45
minute window. It and myself are
available to speak on this topic at meetings,
preferably (but not exclusively) local to me here in central Texas.
--------
This article is about a reliable process for getting from
initial explorations on Mars, to
actually being able to reliably plant a permanent settlement there, without killing a lot of people. That process is defined by the experiences of
the cross-ocean voyages from Europe,
starting about 500 years ago, but
with due consideration for what they did wrong back then.
The
Lesson of History
Based on what Europeans did, establishing colonies in the New World and the
far Pacific, there are definitely 3
phases. They didn’t get it “right” much
of the time: the Roanoke colony in North
America disappeared entirely in rather short order. The Jamestown colony almost disappeared but
for knowledge obtained from the hostile local Indians. The Plymouth Rock colony would have failed, but for direct aid (plus useful knowledge
obtained) from friendly local Indians.
But when they did do it “right”, it worked rather well, such as in Indonesia, and with the later colonies in North America
after it had become widely known how to “live off the land” there. The proper process is illustrated in Figure
1, complete with the necessary
phases, and with the objectives, characteristics, and who usually does the funding, listed for each phase.
Figure 1 – The Lesson of History: 3 Phases Ending in a Settlement
Phases
Set the Missions
The same 3 phases apply to colonizing Mars (or anywhere
else, but Mars is the example
here). Different needs in the different
phases result in different missions being necessary during each of the 3
phases. Note that the Mars analog to
multiple sites explored in the first mission requires basing out of low Mars
orbit to visit multiple sites in the one mission to Mars! There is no way around that, precisely because there will be no long-range
surface transport on Mars during that first exploratory mission!
Other sites cannot be visited from a direct surface landing at one
site!
It’s
either visit multiple sites in the one mission,
or else mount a mission to each and every site of possible interest, or else bet lives on remote sensing results
(which you should never do)!
But done “right” by visiting multiple sites in the one mission, there will only be the one exploratory
mission! This is actually a good
outcome, considering the high costs of
mounting any sorts of missions to Mars.
See Figure 2.
Figure 2 – The Phases Set Different Mission During the
Process at Mars
Different
Mission Requirements and Vehicles
The different phases have different mission
requirements, and they in turn require
different vehicles. There may be significant
vehicle overlap between the first 2 phases,
but not very much at all with the third.
Note in Figure 3 that one required outcome of the experimental
base phase is hard-surfaced,
large-and-level landing pads, and
another is in-situ propellant manufacture at full scale. Those enable completely different vehicles to
serve more efficiently later in the phase.
Therefore, the mix of
vehicles used in the experimental base phase is going to change as that phase
proceeds.
Bear in mind that these mission approaches and vehicle
concepts are all “clean sheet of paper” designs! This is what could be done, if we could get away from a space program
micromanaged by Congress to only maximize the political return from pork-barrel
and corporate-welfare projects in powerful Senator’s districts. Privatization may help some with that, but it also brings other resource allocation
problems associated with an oligarchy of the rich and powerful.
Figure 3 – Different Vehicles Are Appropriate in the
Different Phases, at Mars
Typical
Transfer Velocity Requirements
These numbers reported in Figure 4 for the
interplanetary transfers are rough, but “well
inside the ballpark”, good enough to get
started. One should obtain better
estimates before actually sizing vehicles,
because of the exponential nature of the rocket equation. One should also use actual engine ballistics estimates, not handbook specific impulse values, to size appropriate specific impulses for use
in the rocket equation. The remaining
uncertainties will lie in the inert mass fractions for the weight statements of
the vehicles, and the resulting mass
ratios.
The Hohmann min-energy transfer is for “average planetary
distances from the sun”. There’s not
much effect of the Earth’s low eccentricity on this, but there is,
for Mars’s more-eccentric orbit.
However, these average values are
quite representative values for initial sizing purposes.
The same is true of the “fast trajectory” shown. This is an ellipse with an exactly-2-year-period, so that it could also serve as an abort
orbit. That way, Earth is there at perihelion, when the craft arrives at perihelion after a
single two-year circuit about the ellipse.
Slightly-different velocity requirements obtain, for more extremized planetary distances about
the sun. But that is a smaller
effect, so these are good “ballpark”
numbers for getting started.
Be aware that the near-field encounter velocities shown are
corrected from the 2-body solar orbit values, by the third-body gravitational attraction of
Mars (or Earth), as the distance closes
between Mars and the spacecraft, or
opens between Earth and spacecraft. The
far-field “encounter” velocities computed from simple 2-body equation models of
orbits about the sun are lower, but
unrealistic! Budgets for two course
corrections are also estimated in the figure.
One of these is to be done about mid-way, the other takes place as the craft approaches
Mars close-up.
Figure 4 – Rough Figures for Transfer Trajectory Velocity
Requirements
Typical
Local Mission Velocity Requirements at Mars
The numbers indicated in Figure 5 are fairly
reasonable, but that ignores thrust and
acceleration-level issues, which affect
engine inert weights, as well as the numbers
of engines vs thrust turndown ratios needed.
One must actually do the Mars entry ballistics and the final descent and
landing estimates, in order to firm up lander
vehicle thrust/weight requirements!
Entry, descent, and landing on Mars is both similar and
dissimilar to that same process on Earth.
The Mars atmosphere is thick enough to use entry aerobraking to “kill”
most of the close approach velocity, but
it is also so thin that the end-of-entry-hypersonics altitudes are very
much lower, and also much more scattered
with varying vehicle masses.
Almost regardless of size,
at Earth the end-of-hypersonics altitudes are above 40 km, and the atmosphere below that is thick enough
to enable the effective use of parachutes or wings to conduct landings without
any rocket braking. Mars is quite
different: even at smaller
sizes, vehicles come out of the entry
hypersonics at rather low altitudes, and
even lower still at higher vehicle mass and higher entry speeds. Impacting the surface still-hypersonic is a very
real risk!
Terminal velocities on parachutes at Mars are just barely
subsonic, so that terminal rocket
braking is absolutely required, even at
only 1-ton-or-smaller vehicle masses. At
higher masses, there is just not time to
deploy such a chute at all, before
surface impact, much less have it
decelerate you from high supersonic. Either
way, that Mars landing scenario requires
significant, even major, amounts of terminal rocket braking, in order to achieve a survivable touchdown at
all!
And while the velocity to “kill” is not all that large at only
0.7 km/s, you have a rough-field
obstacle problem to design for. You must
essentially hover and divert to avoid fatal obstacles or hazards on the
surface. That dominates over gravity and
drag loss effects, so that you need to
use a factor of somewhere between 1.5 and 2.0,
applied to the 0.7 km/s velocity-to-kill, for estimating the lander braking-rocket
velocity requirement, as near 1.0 to 1.5
km/s.
Beyond that, there is
also the wildly-varying thrust-to-local-weight deceleration requirement: near 4+ gees for braking-to-zero before
impact, versus only about 0.382 gees for
hover-and-divert. These are NOT easy
design requirements to satisfy, but
they must be satisfied, for all
lander designs at Mars! Rocket
engines, even today, do NOT have that kind of turndown ratio (near
11).
Figure 5 – Local Entry,
Descent, and Landing Velocity
Requirements at Mars
Rough/soft
field requirements drive exploration and experimental-base designs
The rough/soft field issues will drive vehicle designs in
both of the first two phases, because
hard, level, smooth landing pads do not yet exist! Some design criteria shown are shown in Figure
6.
There are fundamentally 3 problems to address: (1) static stability vs overturn on rough
ground, (2) sinking into the surface at
too high a dynamic or static bearing pressure upon soft ground, and (3) touching down at non-zero horizontal
speed, causing the leading-side landing
pads to “dig in” and “trip” the vehicle dynamically.
There is a rule of thumb used successfully for many decades
for landers on the moon, Mars, and elsewhere. There is a minimum lander pad footprint
dimension, as indicated in Figure 6. That dimension needs to exceed the height of
the vehicle center of gravity above the surface. This criterion simply rules out the safe
touchdown of tall, narrow vehicles on
rough ground! It is based on high
school physics: when the weight vector
points outside the landing pad footprint at its minimum dimension, the vehicle WILL topple over!
Sinking into the regolith happens when the landing pad
bearing pressure exceeds the ultimate failure pressure of the soil. Murphy’s Law says this will always occur
unevenly, leading to the craft being at
an angle, even on level ground. Too much, and it topples over! Even if it does not topple, pads buried in the regolith accumulate loads
of soil that must be removed before a takeoff can be attempted. One must design for landing pads large enough
to reduce the soil bearing pressure below that ultimate failure pressure! That is true dynamically at landing, and statically at takeoff.
99% of Mars’s surface corresponds to Earthly “soft, dry,
fine sand”, whether in dunes or
in plains with a loose rock content.
Such loose rocks cannot add strength until their spacing is essentially
zero, which is rare on Mars. The civil engineering handbooks have values
for the “safe” or “allowable” soil bearing pressures for a variety of
soils, up to and including “hard rock
ledge”. These allowable values are lower
than ultimate, to prevent soil settling
in the long-term foundation design problem.
The ratio of ultimate to allowable is usually about 2, sometimes 2.5.
As for the residual horizontal velocity problem, there is a mechanical energy criterion for
that. There is a radius from the center
of gravity to the pad or pads that dig in.
Dug in, the craft rotates about
that dig-in point, raising its center of
gravity. If the kinetic energy of the
horizontal velocity exceeds the potential energy change of the
center-of-gravity rise, then the vehicle
WILL topple over! This criterion also
pretty much eliminates landing tall,
narrow vehicles on rough ground.
Figure 6 – Rough/Soft Field Lander Design Requirements
There are 3 different vehicles required at Mars during this
phase, as listed in Figure 7. The direct 1-way cargo shots can be sent
prior to the manned mission. It is
presumed that a few of these need to arrive fairly quickly, although Hohmann min energy transfer should
be adequate for most. The manned
orbit-to-orbit transport will need to cross the Van Allen belts quickly both
outbound and on return for re-use. The
landers and their propellant supplies (plus propellants for the manned transport
return) can be sent ahead unmanned, and slowly, by electric propulsion. The space tug assist concept can be used to
reduce departure velocity requirements from Earth orbit.
Figure 7 – Recommended Vehicle Concepts for Exploration
Phase
Experimental
Base Phase Vehicles
Although they don’t have to be, the same mix of 3 vehicles can be used to
support much of the experimental base phase.
Note the additional requirement to have nothing jettisoned
before, during, or after Mars entry for the 1-way direct
cargo vehicles. This is to avoid
falling debris hazards to people and things already on the surface. All of this is listed in Figure 8.
The right time to apply the debris requirement is during the
exploration phase, so that no design
changes are needed when the phase changes to experimental base. Bear in mind that during this phase, the mission is still entirely supplied by
Earth, until and unless there is full success
in living off the land. The 1-way cargo
flight rate only decreases when success obtains in living off the land.
Again, the space tug
concept can be used to reduce departure velocity requirements from Earth.
Figure 8 – Recommended Vehicle Concepts for Experimental
Base Phase
Permanent
Settlement Phase Vehicles
This phase can only happen once all the “living off the
land” experiments succeed reliably in the experimental base phase, otherwise lots of people will die! That includes both in-situ sustainable life
support and in-situ propellant production, plus the construction of large, flat,
level, hard-surfaced landing
pads. The infrastructure for in-situ
production of large amounts of electricity is implied. See Figure 9.
The mix of vehicles is quite different: there can be both orbit-to-orbit and
direct-landing transports, and there need
be no further 1-way direct cargo flights,
alleviating that hazard to people and things on the ground at the
selected site. The “lighter” is a much
larger 2-way 1-stage surface-to-LMO-to-surface vehicle, with a larger payload fraction, based on the surface, and using higher-energy in-situ propellants
and the appropriate engines. It
functions to load and unload orbit-to-orbit transports, of both cargo and people.
And as with the other two phases, Earth departure velocity requirements can be
reduced by using the tug-assisted departure concept.
Figure 9 – Recommended Vehicle Concepts for Permanent
Settlement Phase
Conclusions
There is overlap among vehicle designs for phases 1 and
2, but not much with phase 3, as indicated in Figure 10. Rough/soft field landing is the driving
vehicle design requirement for both phase 1 and the first part of phase 2. Having such a rough field capability as an
abort capability would be wise even in later phase 2, and in phase 3. Each vehicle design is worthy of its own
vehicle design study. Such studies are
not included here!
The manned vehicle designs are the most demanding, because of the needs to provide not only life
support over months-to-years in space,
but also radiation protection,
and protection against microgravity diseases. Those are all worthy topics in and of
themselves, not covered here!
Figure 10 – Overall Conclusions
Final
Comments
Perhaps
the most important finding here is also quite divergent from most other mission
concepts for Mars! That is the need to visit multiple
sites in the one exploration mission,
driven by two things.
First,
the huge difficulty and expense of mounting any sort of mission to Mas
at this time in history. Second, the need to definitively-determine real ground
truth (including deep underground) at each candidate site, in order to reliably select the “best one”.
This
drives one to orbit-to-orbit manned transports with landers, instead of direct manned landings!
That is
true precisely because it is not just unwise to bet lives on possibly-wrong remote-sensing
results, it is actually immoral and
unethical to do so off Earth! Why? Because even today, there are still (more often than not) small
but significant disparities between remote sensing results and real ground
truth. Such is likely lethal, in a hostile lethal environment!
Most people still don't believe me when I say that massive government dysfunction IS the plan! Once dysfunctional enough, the MAGA crowd (about half the voting population, as we just saw), can be induced to rise up and replace it, imposing their alternative upon the rest of us, in a surprise fait accompli. With Trump as dictator/king/”whatever”, that's their alternative.
That is EXACTLY how Adolf Hitler went from being appointed Chancellor in a democratic government, to being absolute Fuehrer, in 1934 Germany. It just takes a triggering event to set the uprising off: an analog to the Reichstag fire (that the Nazis set, by the way).
This was already prematurely attempted Jan 6, 2021, as a last-ditch resort by Trump to stay in power past the end of his term. It might have even succeeded if he had been able to get to the Capitol to lead it the rest of the way. But his secret service agents refused, and took him back to the White House, where he fussed and fumed for about 3 hours watching the coup attempt fizzle out on TV. It fizzled out because he wasn’t there to inspire it into even more violence, actually killing all they could find who opposed him. That level of violence would have justified a martial law declaration, and thus kept him in power past the Jan. 20 handover.
Nobody wants to believe me when I tell them that the MAGA crowd’s “deep state" that they want to overthrow, is not what they were told (which is basically all the non-MAGA people and institutions), but actually really is Trump and his billionaire cronies and giant corporate allies. There were photos of most of them all together just the other day, about the same time as Biden so belatedly warned us about "the encroaching oligopoly". That WAS the oligopoly in the photos! “Oligopoly”, “deep state”, those are just different words for exactly the same thing. The photo here is of only some of them:
Doing what you accuse
others of, is EXACTLY out of the playbook Adolf Hitler (and so many
others) have used. The accusations about a deep state specific to MAGA
Republicanism/Q-Anon conspiracy theory actually started in 2015,
when Trump first began to run for president and the Q-Anon crowd embraced him.
I knew what he was then: he did not want to be president, he wanted
to be king/dictator/”whatever”. I tried to tell that to everyone around me
back then, but nobody wanted to believe me.
Nobody wants to believe me now, when I tell them that the Department of Justice (DOJ) was not weaponized, until Trump weaponized it in the last few days, with his Attorney General pick and his executive orders for the firing of so many DOJ employees. (That's part of what most of the rest of the incompetent cabinet picks are for, too: both weaponization and massive government dysfunction.) And when he was president the first time, he already did it to the Supreme Court (and several federal judgeships) with McConnell's bumbling partisan support.
Once Trump consolidates his power as the dictator of the US, he will damage our NATO alliance and hand Ukraine “on a platter” to Putin. China will make its move on Taiwan when it sees Putin successful in Ukraine. That will slowly start World War 3 with both Russia and China. That war will go nuclear, so “you ain’t seen nothing yet”, as far as chaos goes!
However, the roots of this disaster date back much earlier, to the aftermath of Bill Clinton's first election in 1992, when 4 Republican leaders were in a bar crying in their drinks, and hatched the plot to turn the Republican party into the "party of no", meaning opposition above all, even if it damages the public good. They were Newt Gingrich, Paul Ryan, and 2 others whose names I can no longer recall. Then-brand-new Fox News picked up on this and joined in, as a far-right-wing propaganda organ. And a sarcastic “thank you very much Rupert Murdoch”, for bringing infamous British tabloid “journalism” to America, to masquerade as real news!
The name used then was the "Republican contract with America", which turned out to be a fraud, just as Bernie Sanders claimed, but few believed him back then either. The name "party of no" actually came into wide usage some years later, after the election of Barack Obama. But make no mistake, the "contract with America" was just a cover for (1) gaining power by fraud, and (2) by being the "party of no" whenever and wherever they were not in power.
Republican politicians go along with this travesty, because that is what their voters have been brainwashed to want. And THAT is really why Congress has been so dysfunctional, for so many decades now! And we have seen that pattern continue, until Trump came down that escalator in 2015 and turned it into an overt dictatorship movement, hiding right in plain sight!
If you listen to what politicians say, you will never see the pattern, which is why most of you did not, and still do not, believe me.
You must only pay attention to what politicians actually do, which is how I slowly came to see this pattern for what it really is, more than a decade ago.
-----
If you want to
see the predictions I made for Trump’s second term, which are actually starting to come
true, then either scroll down or use the
archive tool on the left to find “Trump Again?”, posted 11 November 2024. The MAGA/Q-Anon movement about Trump is
actually a dangerous fearless leader cult.
Political, religious, or some of both, those cults are always very bad. If you want to understand such cults, and understand why I think there is one around
Trump, see “Trump Cult Warning”, posted 23 January 2024.
All you
need, in order to use the archive
tool, is the article’s posting date and
its title. Click on the year, then on the month, finally on the title if need be (such as
multiple postings that month).
Previous studies (References 1 and 2) explored the use of reusable space tug-assist for interplanetary departures and arrivals. For this purpose, an extended elliptic orbit was used for its high perigee speed very near escape speed. The tug provides the big speed increase to just below escape, staying in the ellipse for recovery back to low orbit. The interplanetary craft only has to supply that smaller speed increase from just below escape to above, for hyperbolic departure.
Lunar trajectories are different, there being no hyperbolic-escape departure
(or arrival). An extended ellipse will
take a craft to the moon’s vicinity,
where the 3-body effects of Earth,
moon and craft, will warp the
trajectory into a figure-8 low-altitude flyby of the moon, and automatic return to Earth’s
vicinity. This was the lunar transfer
trajectory used for the Apollo moon missions.
There is only a modest speed change required, behind the moon (as viewed from Earth), to enter a retrograde low lunar orbit, or to leave it for return to Earth. Something representative of the velocity
requirements analysis, for such a lunar
mission, is given in Figure 1 below. (All figures are located at the end of this
article.) Values were obtained using the
2-body analysis of my “orbit basics.xlsx” spreadsheet tool, which simply automates the standard textbook
equations in a convenient way.
The question explored in this article
is whether a reusable space tug with chemical propulsion could transport
dead-head “payload” items from low circular Earth orbit (LEO) to low circular
lunar orbit (LLO), and then return
unladen to LEO, without refueling. This question was explored with
modest-technology storable propellants,
modest-technology oxygen-methane (LOX-LCH4), and modest-technology oxygen-hydrogen
(LOX-LH2), plus some crude but
representative assumptions for inert fractions. The storables examined were specifically nitrogen
tetroxide (NTO) and monomethyl hydrazine (MMH).
A Tug Using Storables is Probably Feasible, But Not Very Attractive
We would like to use storables to avoid the evaporation
losses and evaporation mitigations that are inherent with cryogenics. Only a thin insulation with a reflective foil
outer layer is required to avoid solar heating,
plus small in-tank heaters to prevent freezing, when shaded in space.
The engine needs to be turbopumped, to achieve significant final chamber pressure
without needing high-pressure tankage.
This would be more like the old liquid-propellant Titan missiles than
any modern pressure-fed thruster systems.
I picked a nominal chamber pressure of 2000 psia (136.1 std atm, 137.9 bar),
with a nozzle expansion sized to an arbitrary 50:1 mild vacuum area
ratio, on a nominal 18-8 degree curved
bell shape. The nozzle kinetic energy
efficiency and throat discharge coefficients that I used are pretty
standard. Engine thrust/(Earth) weight
ratio was simply presumed to be about 70.
The turbopump drive cycle is unspecified, but is presumed to involve a dumped massflow
fraction of 5% of the propellants drawn from tankage. Nominal as-sized vacuum thrust for the
reference engine was 22,050 lb (10 metric tons-force) on an exit area of 293.4
square inches (0.1893 square meters),
which can be rescaled to a more appropriate thrust level, as needed.
Vacuum specific impulse at full thrust was near 322 sec, as indicated in Figure 2 below. Values were computed from standard
compressible flow analysis, and models
for characteristic velocity (c*) and oxidizer/fuel mass ratio (r), using my “liquid rockets.xlsx” spreadsheet
worksheet “r noz alt”, that automates
the standard textbook equations in a very convenient way. The propellant data I used for c* and r came
from Reference 3.
A tug vehicle was rough-sized using the estimated engine
performance, these velocity
requirements, and a presumed
as-built-and-loaded inert mass fraction of 5%,
typical of many upper stages today.
The calculation was a rough size-out followed by two linked rocket
equation analyses: all the laden burns
combined in the first one, followed by
all the unladen burns combined in the second one. The user sets the as-built propellant mass
fraction iteratively, until he can just
barely accomplish the mission, with a
positive value of “propellant remaining” that is close to zero. This was done
in a convenient spreadsheet file “space tug stuff.xlsx”, specifically the worksheet “scrtch
size”.
These rocket equation calculations lead to start and stop
vehicle masses for each set of burns, to
which input min and max vehicle acceleration limits can be applied to determine
min and max limits on thrust values. The
user has to look at those, and decide
how many engines of what actual design thrust level are needed, and how many engines to actively burn
laden, and unladen. That sets the actual applied thrusts, and the actual resulting vehicle gees. The worksheet rescales from the input value
of reference thrust to this design thrust per engine that is needed.
There are inputs for the masses of the guidance and control
unit, and the electric power source for
it, as part of an inert mass buildup
calculation (the tug is unmanned). The
final propellant mass determines a mass estimate of the empty tank inert mass, using an R-ratio input representing
propellant mass divided by filled tank mass. The final design thrust level per engine, and number of engines, determines the total engine inert mass by
means of the thrust/weight ratio input.
The sum of these inert masses is an estimate of the vehicle inert
mass, to be compared with the inert mass
figured from the 5% assumption in the rocket equation calculations. Inert mass is not automatically converged, however!
Even so, if the two estimates are close,
that is “good enough”.
The results obtained for the storable-propellant tug sizing
are given in Figure 3 below.
While such a design is possible,
the payload mass fraction is quite low,
at somewhere near only 2%. That
means a very large tug vehicle, to be
kept supplied on-orbit with very large quantities of the NTO-MMH
propellants, must be used to transport
even modest payloads to LLO this way. The
full-load propellant/payload mass ratio is over 42:1!
That outcome is quite unattractive, because of the bad logistics the
propellant/payload ratio implies.
Anything we could do to push the state of the art of the engines would
help, but not by all that much, because we are inherently playing in the
wrong ballpark: our effective exhaust
velocity relative to the magnitude of the velocity requirements, is simply far too low.
A Tug Using LOX-LCH4 is Quite Feasible, But Still Less Than Attractive
A similar engine-sizing analysis was performed with the same
engine sizing spreadsheet, just using
propellant data for LOX-LCH4. This was
also for a modest-technology design, not
one pushing the state-of-the-art so hard as the SpaceX Raptor engines do! This is a 3000 psia (204.1 std atm, 206.8 bar) chamber pressure, with a presumed 5% bleed fraction
representing its cycle. Its nozzle
expansion was sized to permit test-firing in the open air at sea level, operating at full thrust, but on the verge of separating in the
nozzle. That produced an area ratio of
about 65 in its 18-8 degree curved bell.
The re-scalable reference engine sized vacuum thrust was 22,050 lb (10
metric tons-force), at an exit area of
252.0 square inches (0.1626 square meters),
operating at a vacuum specific impulse of about 349 sec. This is illustrated in Figure 4 below.
I should have revised the tank R ratio downward a little, to reflect the need for extra insulation and
header tank construction approaches because of the cryogenics, but I did not. As-sized at an as-built 5% inert, the LOX-LCH4 tug vehicle sized with a
substantially-higher payload fraction of about 7%, as shown in Figure 5 below. This is a marked improvement over the
storables tug, but is still only a
single-digit payload percentage. This is
definitely technically feasible to do,
but the logistics of propellant supply are still rather
unattractive, when considering any
significant payload mass. The
propellant/payload mass ratio is still rather high at just over 12:1!
A Tug Using LOX-LH2 is Quite Feasible, But Also Becoming Much More Attractive
I did not do an arbitrary spreadsheet engine sizing for the
LOX-LH2 case. Instead I used the actual
data for the RL-10C-1-1 engine as “representative” of a modest-technology
design, as this basic engine series has
a history going back over 60 years now.
It is an expander cycle with no dumped bleed, and a 57:1 thrust/weight ratio. Vacuum Isp is 453 sec. I got this data from Reference 4.
I took this data and went straight to the tug vehicle sizing
spreadsheet, shown in Figure 6 below. Instead of the arbitrary 1-ton payload
resize, I resized the payload to 12
metric tons, so that the listed vacuum
thrust of the RL-10 engines, at 3
engines total, 3 active laden, 1 active unladen, would provide the desired gees within the
kinematic limits for both sets of burns.
The results proved to be very-significantly
better, with a payload fraction of over
21%, and a propellant/payload mass ratio
of only about 3.4! With numbers
in this range, the on-orbit propellant
supply logistics for the tug vehicle become much more attractive. There are more high-technology engines
available (such as the RS-25 series),
which would improve things somewhat further still.
For massive improvement,
there might be nuclear thermal,
using hydrogen only, but also
with the risks involved in routinely using reactors in LEO and near-Earth
space. The inherently higher inert
fractions associated with low engine thrust/weight, will offset some of the higher Isp advantage
of nuclear thermal, though.
Discussion of Results and Conclusions
Despite the crudity of this study, the clear winner (by far) is LOX-LH2. See Figure 7 below.
But with those cryogenics,
there are some severe design constraints not modeled in this
study! Those include thicker insulation
on the tank exteriors, and a header-tank
design approach. With LOX-LCH4, SpaceX has shown that a simple
single-membrane inter-tank bulkhead can be used between the main hydrogen and
oxygen tanks. This is because the LOX
and LCH4 temperatures are just not that far apart.
However, the
experiences with the Centaur stage and LOX-LH2 show that only hours of stage
life can be obtained, even with a
common bulkhead composed of a double membrane with insulation between
them. The “hotter” LOX just bleeds too
much heat into the very much colder LH2!
The tug missions are multiple days long,
not hours, so a common
bulkhead is just not very feasible.
The external insulation can still be fairly modest, if internal header-tank construction is
used, enabled by the fact that the first
set of burns occurs laden, and uses the
largest propellant mass. If the header
is inside the main tank, it can use the
empty main tank as part of its insulation scheme! That is the way to get the mission-required
days of stage life, without resorting to
active cooling!
References:
#1. G. W. Johnson,
“Tug-Assisted Arrivals and Departures”,
posted 12-1-2024, to the
“exrocketman” blog site http://exrocketman.blogspot.com.
#2. G. W. Johnson,
“Elliptic Capture”, posted
10-1-2024, to the “exrocketman” blog
site http://exrocketman.blogspot.com.
#3. Pratt & Whitney Aircraft, “Aeronautical Vest-Pocket Handbook, 12th Edition, 21st printing, December 1969.
#4. Wikipedia article
“RL10”, last updated 24 November
2024, article retrieved 4 December 2024.
Figures:
Figure 1 – Velocity Requirements Analysis for Tug Missions
LEO to LLO
Figure 2 – Arbitrary Modest-Technology Storables Engine
Figure 3 – Initial Scaleable Rough Size: Storables Tug
Figure 4 -- Arbitrary Modest-Technology LOX-Methane Engine
Figure 5 -- Initial Scaleable Rough Size: LOX-Methane Tug
Figure 6 – Initial Scaleable Rough Size: LOX-Hydrogen Tug Based on RL-10C-1-1
Figure 7 – Overall Comparison, With Rescaling to a Common Payload Mass
Update 1-27-2025:
For completeness, I looked up
some Wikipedia data about the old NERVA nuclear thermal engine that used liquid
hydrogen, and made a judgement about
what characteristics the flight-adapted form of the test article might
have. The test article itself was very heavy at
about 40,000 lb; a flight design should
be much lighter, maybe near
thrust/weight 4.
I chose an arbitrary payload mass of 50 metric tons, so that 3 NERVA engines would serve, with 3 active laden, and 1 active unladen, and meet the kinematic gee requirements, at the estimated per-engine thrust of about
25 metric tons-force per engine for the NERVA design.
I reset the stage inert fraction input to make the inert
mass from the buildup calculation about equal to the inert mass estimated with
the input fraction. That happened at
about 15% loaded stage inert, reflecting
the low expected thrust/weight ratio for these engines. I also lowered the tank R value a bit, to 0.95,
to better reflect the necessary constructions.
This resulted in a stage payload fraction of about
31-32%, and a propellant/payload ratio
of about 1.6 to 1.7. The image of the
“scrtch size” worksheet is given in Figure 8. The logistics of supplying this vehicle would
be about twice as attractive as the LOX-LH2 chemical tug, if the technical and political risks of operating
active reactors near Earth can be adequately addressed.
The tankage would need external insulation plus the internal
header tank approach for several days of stage life. A real design would do the rendezvous burns
with an added chemical engine and tank system,
not the nuclear engines. But the
point here was not complete design accuracy,
but just exploring feasibility and relative merit in a realistic way. Garbage-in,
garbage-out applies here!
Figure 8 – Results For a NERVA-powered Lunar Tug
This article examines the potential capability of “Starship” to be a space tug for the elliptic orbit departure and arrival processes. It is merely a first ballpark look, I would need more precise data for the orbital mechanics, and for the vehicle weight statement and engine performances, to obtain more reliable detail. But these results are “good enough” to show considerable promise!
The notion of space tug assist to reduce the delta-vee (dV)
requirements on interplanetary craft for hyperbolic departure from, and arrival to, Earth have been discussed in more detail in references
1 and 2. Some educated guesses for the
“Starship” weight statement and engine performances are given in references
3 and 4.
Presumed Input Data Values
For purposes of this preliminary look, it is the tug, not the unspecified interplanetary
craft, that is the focus. The following data were assumed about the
trajectories: a very extended elliptic
departure and arrival orbit, with
perigee altitude same as low circular orbit at about 300 km, a periapsis speed of about 10.9 km/s, which is very near Earth escape at that
altitude, and roughly a 9-day
period. Circular orbit is presumed to be
7.8 km/s at 300 km, with a 90 minute
period. That makes the dV requirement
from one orbit to the other just about 3.1 km/s, and I simply “budgeted” 0.2 km/s dV for any
rendezvous and docking requirements.
This is what I assumed about “Starship” for the purposes of
this study: inert (dry) mass 120 metric
tons, maximum-capacity propellant load
1200 metric tons, and the flaps and heat
shield left in place, pretty much as
with the prototypes that are test-flying now.
It flies with 6 Raptor-2 engines,
3 the sea level form, and 3 the vacuum
form. For the sea level engines in
vacuum, I presumed 230 metric tons-force
thrust and 355 sec Isp. For the vacuum
engines, I presumed 250 metric
tons-force thrust and 379 sec Isp. I
presumed a max turndown ratio of 4 for both variants.
Departure and Arrival Missions
The departure mission differs from the arrival mission, both in dV requirements and in the events
sequence. It is presumed that both vehicle
assembly and refueling take place at an unspecified facility located in low
Earth orbit (LEO), to which the tug
returns after assisting departures, and
with the interplanetary craft after assisting arrivals. Reaching such a facility from the Earth’s
surface is easiest, if it is located in
LEO at low inclination launching eastward.
At departure, the tug
is already coupled to the interplanetary craft,
so there is only the dV onto the ellipse, followed immediately by undocking and the
interplanetary craft firing its engines to reach hyperbolic speed. The unladen tug must then coast once about
the extended ellipse, and then finally supply
the dV’s for return to circular at the proper time-of-perigee, and for rendezvous
and docking with the unspecified facility there.
For arrivals, the
unladen tug must supply the dV’s for entry onto the ellipse at the proper ellipse
perigee time, plus a rendezvous and
docking budget for coupling to the interplanetary craft, which had already supplied the dV to enter
that ellipse from its hyperbolic approach.
The docked pair coast about the ellipse.
Then the laden tug must supply the dV’s for getting from the ellipse back
to circular, plus a rendezvous and
docking budget for returning to the unspecified facility.
Methods of Computation
I did this with a spreadsheet, embodying both rocket equation calculations
and a look at vehicle thrust/weight ratio for in-space accelerations. I simply presumed vehicle accelerations
outside the range of 0.2 to 4 gees as “unacceptable”. These are nothing but by-hand
pencil-and-paper-type calculations, just
automated for easy iteration with the spreadsheet.
The “first cut” single rocket equation calculation provided
performance data and a plot showing gross dV capability and accelerations for
variable “payload masses” representing the unspecified interplanetary
craft, and various selections of which
engines are operating. Those results are
given in Figure 1 below.
This is very unrealistic as a tug estimate, because the tug’s weight statements are
vastly different laden versus unladen,
but it does help to determine how many engines to use for acceptable accelerations, for various “payload” masses, including none.
When the weight statement does not change between burns, one may sum dV’s to a single overall dV
requirement (or not, as desired). When the weight statement does change, there must be a separate rocket equation
calculation for each weight statement,
and these calculations are linked by those weight statements, with the linkages consistent with the order
in which burns are made. I chose to
represent every tug burn, 3 for the
departure mission, and 4 for the arrival
mission.
The missions portion of the spreadsheet was set up for
arbitrary payload mass inputs, different
for each mission, with the option to
reduce propellant mass if excess dV resulted.
I used this to find the max payload masses for each mission, flown at full propellant load. Reduce the “payload” mass, and you may reduce the propellant load. However,
I did not explore that issue,
having no information at all about the unspecified interplanetary craft
that is the “payload” here.
Bear in mind that this is the first time I set up a tug
mission spreadsheet. It may get revised
as it gets used. But it is general
enough to investigate other possible tug designs, just using different inputs for vehicle
characteristics. An image of this
initial spreadsheet is given as Figure 2 below.
Discussion of Differing Mission Results
First, I used
the vehicle characteristics more-or-less representing the “Starship” prototypes
being test flown as of this writing.
Those masses include the heat shield and the aerodynamic control
flaps. This allows the vehicle to return
for repair and refurbishment, after
“something” wears out from repeated use,
presumably engines.
Second, the
mass of the unspecified interplanetary craft is much larger at departure than
at arrival. This is not as adverse a
result as it might seem. Any
interplanetary craft departing Earth will have a full load of propellants and
any other items for its mission, and
this will inherently be heavier. On
arrival back at Earth, it will be
essentially depleted of propellants and presumably unloaded of some
mission-related things, and so will
inherently be much lighter. That more-or-less
matches tug capability.
Third, for
departure tug missions, the docked pair
departs at fully-loaded mass, and the
larger mass ratio associated with the dV = 3.1 km/s burn onto the ellipse then reduces
that larger mass considerably. There is
no rendezvous and docking to worry about in this phase of the mission. The tug undocks from the interplanetary
craft, and then coasts around the
extended ellipse once, firing unladen
for a dV = 3.3 km/s to cover both getting back to circular and
rendezvous and docking with the unspecified orbital facility. That mass ratio applies to a much smaller
unladen mass, which is why the
propellant quantities are so small. And
THAT “laden-then-unladen” burn sequence is also the “magic” of booster flyback
recoveries for the Falcon and Starship systems! It does NOT work that
advantageously, for the “unladen-then-laden”
burn sequence.
Fourth, for
arrival tug missions, the tug departs
unladen from the unspecified orbital facility,
and must burn for a dV = 3.3 km/s to cover getting onto the ellipse and
rendezvous and docking with the unspecified interplanetary craft. That mass ratio applies to a smaller but
still-large mass at ignition, using a
lot of propellant. Then it gains
considerable “payload” mass after docking,
and must still supply dV = 3.3 km/s to cover getting back to
circular, plus rendezvous and docking
with the unspecified orbital facility,
while laden. That is another
large mass ratio reducing the burnout mass,
which is now required to be much larger,
being laden. And THAT unfavorable
reverse of the booster flyback “magic” is what limits the size of the arrival
payload mass!
Conclusions
First, “Starship”
as currently flown is a very large vehicle,
and so has a very large “payload” capacity if used as a departure
scenario tug assisting any unspecified departing interplanetary craft. These preliminary numbers as reported in the
first figure say the size of that “payload” is almost but not quite 500 metric
tons! The arrival “payload” capability
is much smaller at 175 metric tons, but
still quite considerable.
Second, crudely
speaking, this scales up or down with
the tug stage-only mass at its ignition:
that being the inert mass plus the propellant mass. We are presuming all the “payload” mass is
the unspecified interplanetary craft,
and none is inside the “Starship” cargo bay itself. Other stages or vehicles, fitted with the right controls and some sort
of on-orbit refueling plumbing, could
also serve this tug function, and still
be recovered for refueling and reuse. Such
might include the second stages of the Falcons,
the SLS upper stage, the Vulcan
second stage which is an upgraded Centaur,
and so on. There many
possibilities.
Third, that
being the case, it should not be very
difficult to develop multiple space tug designs out of these various upper
stages. The hardest part will be setting
up a space station facility in LEO that functions as both an assembly
facility, and a propellant refill
depot facility! And THAT is the most important result
here! We will need that LEO-based
facility to support any space tug-assist for any interplanetary craft. That is the real gateway to less-expensive
interplanetary travel, not some
hard-to-reach space station around the moon!
References 1 and 2 prove this conclusively.
Fourth, such
would also support lunar missions, as
well, since the extended ellipse could
apogee right near the moon’s orbit about the Earth. It is the 3-body effects when the moon is
there at craft apogee, that then turn
this into a figure-8 lunar transfer trajectory.
References
#1. G. W. Johnson, “Tug-Assisted
Arrivals and Departures”, posted to
“exrocketman” 12-1-2024.
#2. G. W. Johnson,
“Elliptic Capture”, posted to
“exrocketman” 10-1-2024.
#3. G. W. Johnson, “Rocket
Engine Calculations”, posted to
“exrocketman” 10-1-2022.
#4. G. W. Johnson,
“Reverse-Engineering Starship/Superheavy 2021”, posted to “exrocketman” 3-9-2021.
Use the archive tool on the left side of this “exrocketman”
page to quickly reach any of these references (or any other article posted
here). All you need is the date of
posting and the title. Click on the
year, then the month, and then the title if more than one article
was posted that month. This is far
easier than scrolling down.
Figures
Update 1-4-2025: added plot axis titles to the Figure 3 data plot made for Centaur-V as a tug. You may click on any figure to see them all enlarged. There is an X-out tab top right of that view, which takes you right back to this article.
Figure 1 – Spreadsheet Results For Both Gross-Overall
And Specific Mission Capabilities
Figure 2 – Image of the Initial Form of the Tug Spreadsheet
Set Up for “Starship”
Update (also) 1-2-2025:
I have started looking at other stages for possible tug
use, notably the Centaur, which uses higher-energy LOX-LH2
propellants. The Common Centaur stage
design uses a common bulkhead between the LOX and LH2 tanks, and single-wall thin stainless steel tank
walls that gain their strength from internal pressure by the “balloon effect”. The inter-tank bulkhead is two
stainless-steel membranes separated by some fiberglass hex as insulation, to keep the warmer LOX from heating the
colder LH2 too rapidly. Even so, the useful stage lifetime is only “hours
long”, limited by heating of the
hydrogen by the warmer oxygen, leading
to tank overpressure failure.
Centaur-III is the 3.05 m diameter form used on
Atlas-V, which only uses two RL-10
engines when lofting the Boeing CST-100 “Starliner”. The other applications are all one-engine, presumably underlying the data I found. The tank wall is 300-series stainless steel
0.020 inches (0.51 mm) thick.
Centaur-V has a larger hydrogen tank diameter, and comes in only the two-engine form, for use on the new Vulcan launcher. Centaur-V initially has only about 40% longer
stage lifetime, but it is said that it
will eventually have a few hundred percent longer lifetime, for much longer missions.
Centaur-III/Common Centaur simply does not have the
stage lifetime needed to serve as a tug on ellipses with multi-day periods! Eventually,
if the expected longer stage lifetimes turn out to be true, Centaur-V could serve as a tug! Tug duty could involve stage lifetimes in the
range of 10-days to 2 weeks, before
intervention is required to address hydrogen boiloff and overpressure risks.
I can only estimate, based on the “balloon pressure”
approximation, that total applied thrust
equals the “PA-kick load” associated with the tank pressure. Thus, the minimum operating tank pressure for the
1-engine Common Centaur stage would be P = Ftot/Atank = 22,300 lb/11,310 in2
= 2 psia min. For the 2-engine
form, that would be 4 psia min. The ideal tank failure hoop stress would the
ultimate tensile strength of 300-series stainless steel per Mil Handbook
5, which is about 95 ksi. The corresponding failure tank pressure is P
= 2 s t/D = 31-32 psi. However, it is rendered unusable by yielding, before reaching that value. This would actually be a bit lower for the
larger-diameter Centaur-V, nearer 20
psia.
Without an accurate empty mass for Centaur-V, I cannot run reliable tug performance
estimates for it! A “wild educated
guess” for the Centaur-V empty mass might be near 3200-3300 kg, based on a guess for the change in tank mass,
based on propellant masses, using “97% propellant”.
I ran these numbers as a rough cut for what a “long stage
life” Centaur-V might be able to do as a space tug for these elliptic arrival
and departure missions, using an
educated guess of 3.25 metric tons for the empty stage mass. The results are depicted in Figure 3, using the same spreadsheet as was used to
investigate “Starship” as a tug. I just
copied the “Starship” worksheet to another worksheet, and then changed all the input numbers, and finally re-iterated for max payload.
Unladen burns used only one of the two RL-10 engines on the
Centaur-V stage to limit vehicle gees. The results look good, except that the unladen burns for the
departure mission were around 6 gees. It
would probably be required to reduce from full thrust for that mission. That may reduce specific impulse a
little, which would in turn reduce max
payload a little.
Errors in the assumed stage empty mass subtract directly
from max payload capability on the tug missions.
Figure 3 – Results for Centaur-V As a Possible Tug (updated with axis titles 1-4-25)
Conclusion to this Update:
It would be fairly easy to install those changes needed to
use Centaur-V as a tug to assist interplanetary departures and arrivals, based from the unspecified facility in
LEO. The hardest part would be achieving
the necessary 2-week “stage life” to support extended ellipses to a 10 day
period. The biggest uncertainty
is the longer service life necessary for doing these missions routinely. The RL-10 engines were not intended to be “permanently”
re-startable.
