Multiple Updates planned (dates not defined), appended to bottom as completed (dates defined):
Update 10-23-19:
Change the Stagepoint
Update 10-24-19:
Going to Mars and the moon
Update 10-26-19:
Return from Mars
Update 10-28-19: To
the Moon from Elliptical Orbit
Update 10-29-19: Effects of Price Upon Elliptical Departure
Update 10-29-19: Effects of Price Upon Elliptical Departure
Update 10-30-19: Soil
Bearing Loads Estimates
Update 10-31-19:
Static Overturn Stability
Update 11-21-19: Choice of Landing Engines
Update 11-21-19: Choice of Landing Engines
*****************************
That being said, Musk
has recently revealed the most realistic design concept yet for this vehicle in
2019. It actually resembles in its
overall shape the test vehicles being constructed for flight tests out of Boca
Chica, Texas, and Cape Canaveral, Florida.
The entry heat protection isn’t included yet in the test vehicles. Presumably,
the inboard profiles of these test vehicles are reasonably
representative in terms of propellant tankage,
but likely very little else. Such
is the nature of experimental flight test.
The design is first and foremost a 100%-reusable two
stage system for launching payload to low Earth orbit (LEO). Instead of a disposable second stage and
separate payload shroud, the
innovation here is to make the entire second stage a reusable spacecraft named
“Starship” that is capable of re-entry and landing, and to contain the actual payload within it, much the same way as cargo is contained within
ships at sea, or inside air freighters. This vehicle uses engines that burn methane
and liquid oxygen.
The big first stage “Super Heavy” booster is a scale-up of
the Falcon booster core idea, refitted
with higher-performing engines that burn methane and liquid oxygen instead of
the kerosene and liquid oxygen that the Falcon stages used. These are in fact the same basic engines the
second stage uses, a design named
“Raptor”. This first stage booster conducts
a post-staging burn to reverse course, a
second burn to control supersonic entry into the atmosphere, and a third and final burn to land at the
site from which it was launched, exactly
like the smaller Falcon cores.
This concept has been through many fundamental design
changes. Initially, it was a 10 meter diameter system, but in the last couple of presentations, has converged upon a 9 meter diameter
system. Initially, its basic structure was supposed to be carbon
composite, but this last iteration has
settled upon stainless steel construction instead, which is a little heavier, but far more robust in terms of resisting a
multiplicity of cryogenic propellant effects,
as well as the high-temperature effects during re-entry. Although heavier, it resists heat far better than the aluminum
construction used in the Falcons, in
turn better than organic carbon composite at resisting heat, and by far.
A two-layer liquid-cooled heat protection scheme with this
stainless steel construction, has been
abandoned in favor of a simple single shell with an ablative heat shield on the
windward surfaces, and bare metal
radiative cooling on lee-side surfaces.
Landing pads at the tips of 3 or 4 fins have been abandoned in favor of
6 landing legs that extend right from the base of the vehicle, not from any fins or wings at all. Whether that is the “right” choice remains to
be seen.
The first stage now features 6 tip-mounted landing pads on
the tips of 6 small fins at the rear of the stage. It also features the same 4 grid fins at the
forward end of the stage, just
larger, that provided effective
aerodynamic control forces after entry,
with the Falcon stages.
Whether these landing leg and small size landing-pad
designs are truly appropriate remains to be seen. They are certainly appropriate for landing
upon a thick reinforced-concrete pad. Or
possibly upon a level, flat, thick,
solid slab of rock. It is
unlikely in the extreme that this kind of landing pad design is appropriate for
landing upon soft soils of various types. Such soft soils are inherent for off-site
launch abort landings on Earth, as well
as the great bulk of possible landing sites on the moon or Mars.
Data Sources
I got the latest data from two primary sources: (1) Spacex’s own website, which now for the very first time documents some
of the expected values for the “Starship”/”Super Heavy” design, and (2) Wikipedia articles for
“Starship”, “Super Heavy”, and the “Raptor” engines that are supposed to
power them.
Beyond this, I have
already used Spacex and Wikipedia data to reverse-engineer the expected
performance parameters for the methane-liquid oxygen “Raptor” engines. This includes both the sea level
version, and the vacuum-only version, which uses the same powerhead, just a larger expansion bell.
“Raptor” Engines
My engine performance reverse engineering is documented here
on my “exrocketman” site, as the article titled “Reverse-Engineered “Raptor”
Engine Performance” and dated “26
September 2019”. Readers should be aware that my reverse
engineering of the “Raptor” engine was done for lower values of r (the
oxidizer-to-fuel mass flow rate ratio) than Spacex currently claims.
What that means is that actual “Raptor” performance may be very
slightly different than what I estimated from my old 1969-vintage data. That being said, as near as I can tell, they (Spacex) have yet to demonstrate the
full claimed chamber pressure (of 4400 psia) in actual tests so far! So there are some very real
uncertainties remaining in “Raptor” performance numbers, as of this writing!
Nevertheless, my
estimated data pertain to engines that really do achieve the 4400 psia chamber
pressure. I actually got about a
second or two higher specific impulse than Spacex is claiming. Be aware that the data on the Spacex website
showing 330 sec Isp at sea level and 380 sec Isp in vacuum, is for two different versions of the
design: the sea level short bell, and the vacuum long bell. These share the same powerhead. All the pump drive gas eventually goes
through the nozzle. I assumed 5:1
throttle-down ratio on chamber pressure,
so that the min Pc = 880 psia. Be
also aware that Isp is reduced when throttled down (my reverse-engineering of
“Raptor” article gives those numbers).
Vehicle Weights and Loadings
What is shown on the Spacex website are payload masses and
propellant capacities, but not inert masses
or launch masses. Thrust values are
shown, but these are rounded to only two
significant figures. The Wikipedia
articles actually give data usable on weight statements, particularly the inert and launch
masses. Spacex now shows a 9 meter
diameter, with 50 meter length for the
“Starship” second stage, and 68 meter
length for the “Super Heavy” first stage booster.
The inert mass and propellant capacity of the Starship
second stage spacecraft have increased from the values publicized in 2018. Inert mass of a carbon composite structure was
widely said to be 85 metric tons. With
the switch to stainless steel hull construction, this is now unsurprisingly larger at 120
metric tons. Plus, propellant capacity has grown from 1100 metric
tons to 1200 metric tons. Payload is
quoted as “100+ metric tons”, with the
goal being 150 metric tons, or perhaps
even more. The ignition mass quoted on
Wikipedia is for reduced propellant and only 100 tons of payload.
Ignition mass (“Starship” alone) given as 1320 m.tons, which implies this weight statement:
The inert mass and propellant capacity of the “Super Heavy”
first stage is quoted as 230 metric tons and 3300 metric tons, respectively.
The ignition mass quoted on Wikipedia is for the stage alone, without the Starship upper stage. Thus the weight statement is different when
you include the upper stage.
These numbers were the startpoint for a spreadsheet-based
study of launch to LEO and return. In
that study, payload up was allowed to be
different from payload down.
Spreadsheet Study for LEO Operations
The basic assumptions and analysis conditions used in this
study are summarized in
Figure 1, with numerical values
shown. The most critical thing was
picking the actual staging point.
Nominally, most two stage
vehicles stage at roughly 3 km/s and about 50+ km altitude. Trajectory has largely bent over to not quite
horizontal at staging. For this
study, I used a staging velocity of 2.8
km/s, at “exoatmospheric altitude”, and 27 degrees up from horizontal, which sets the vertical and horizontal
velocity components at staging. All the
aerodynamic drag loss, and most but not
all of the gravity loss, is applied to
the first stage “Super Heavy”.
Figure 1 – Analysis Conditions and Values
Post-staging, the
“Super Heavy” booster immediately flips end-for-end and does the first return
burn dead-horizontal, which kills the
downrange velocity but not the vertical velocity. This burn actually reverses the direction of
flight to a modest horizontal return velocity.
From there the stage arcs high back toward its launch
point, requiring an entry burn to reduce
pathwise velocity to about 0.5 km/s as shown,
and extend the grid fins for stability and control.
For touchdown, the
assumed speed is just about Mach 1, to
be “killed” by the final landing burn. That burn delta-vee requirement has the
factor 1.5 applied to it, to cover
course and speed adjustments to make the pinpoint landing.
These return burns require a certain amount of
propellant, computed from dry tanks mass
without the upper stage payload, first. The ascent burn requires a large amount of
propellant, computed from ignition mass
with the second stage payload, second. For the trajectory (and assumptions)
shown, I was able to increase the
“Starship” ignition mass slightly (from its nominal 1320 metric tons to 1322.5
metric tons), and reconcile the amounts
of propellant with a full capacity propellant load. This is shown in the spreadsheet image of Figure 2. Inputs are highlighted yellow. Significant outputs are highlighted blue (or
green). Note that masses got converged
to within a few dozen kilograms, out of
hundreds of tons.
Figure 2 – “Super Heavy” Booster Operation Analysis
The “Starship” second stage cannot use all its propellant
just to reach orbit from the staging condition.
It must do a deorbit burn, and it
must do a retropropulsive landing burn.
The landing must kill a “belly-flop” velocity of about half a Mach
number, down at low altitude in the
denser air. I used factor 1.5 on this
delta-vee requirement to cover course and speed adjustments to make a pinpoint
landing.
The spreadsheet is set up to use different tonnage values
for descent and ascent payload, but for
this analysis, I made them the
same. I was able to increase the payload
figure significantly, while decreasing
the propellant load figure, and still
reconcile the propellant quantities. The
variation in payload and propellant amounts was made at the fixed ignition mass
determined from the “Super Heavy” analysis. You do the landing first, then the ascent.
These numbers are the spreadsheet image shown in Figure 3.
Figure 3 – “Starship” Operation Analysis
What this analysis shows is that there are limits on how
heavy “Starship” can be, and still
successfully reach orbit from the staging conditions that “Super Heavy” can
reach. Yet for LEO operations, “Starship” propellant load can be
reduced, for more-than-minimum cargo. The number I got was actually larger than the
“goal” value for payload.
Note in the spreadsheet images that I looked at the figures
for mass and thrust at some significant points in the flights of the two
vehicles. The resulting kinematic net
acceleration levels, along with
thrust/weight values, are shown in Figure 4.
The “Super Heavy” uses all 37 sea level “Raptor” engines
during its ascent, with max gees just
under 4 at staging. Takeoff thrust to
weight is a healthy 1.5 factor, for a
net upward kinematic acceleration of half a gee.
The “Starship” uses the 3 vacuum engines for its
ascent, and for its deorbit burn. The arrival on orbit is at just over 2
gees. It uses the 3 sea level “Raptor” engines
for its touchdown. Two could do the
job, but if three are running
throttled, loss of one can be compensated
most quickly by throttling up the remaining two. Throttle levels at thrust equal to weight are
in the 50% range, with 20% the presumed
min.
Figure 4 – Selected Summary Values from the LEO Analyses
Setup for Going Outside LEO
The propellant needed for “Starship” deorbit and touchdown
is about 29.89 metric tons. This would
be in the header tanks nested inside the main tanks. The possibility of abort-to-surface must be
considered for any “Starship” sent to LEO,
whether it says there or is refueled and sent elsewhere. That is why I made the descent payload equal
to the ascent payload in my spreadsheet analysis. So,
one still cannot use all the propellant just to reach LEO for a
“Starship” intended to be sent elsewhere.
It’s a flight safety thing.
The limitations of the “Super Heavy” dictate a
less-than-capacity propellant load for “Starship” in routine LEO
operations. This was identified in the
spreadsheet analysis. It might be
possible to relieve this limitation somewhat by lowering the staging
velocity. That is another analysis out-of-scope
here.
That limitation no longer applies, when refueling a “Starship” on-orbit for a
trip elsewhere. The full propellant load
can be used. That would be the full 1200
metric tons, less the about 30 tons of
return-and-land propellant, for about
1170 metric tons to be delivered by the tanker flights. From there,
destinations could be the moon or Mars.
Those analyses are extras to be added later, as updates.
********************************
Update 10-23-19:
Change the Stagepoint
I re-ran the LEO analysis with the intent to match
stagepoint vertical velocity with the return velocity such that a max-range 45
degree arc is obtained. This required
reducing both path angle at staging, and
staging velocity. Doing the trades
showed the result was very sensitive to path angle at staging, and less sensitive to staging velocity.
Therefore, I reduced
the path angle to “get in the ballpark” of a 0.5 km/s vertical velocity to
match the intended horizontal 0.5 km/s return velocity. Then I reduced staging velocity to get the
desired result. I iterated this procedure
about 3 times before settling on staging at 2.63 km/s at an 11 degree
path angle. This gives me a
booster returning 45 degrees upward,
for a max-range arc trajectory.
Looking at “Super Heavy” performance capability then uses
payload mass (ignition mass of the “Starship” upper stage) as my free variable
to balance out the propellant demand against the 3300 metric ton propellant capacity
from the Spacex website. What I saw
was an increase in the allowable max mass of “Starship, from 1322.5 metric tons, to some 1488 metric tons, favorable indeed! These results are shown in Figure 5, an image of the revised Super Heavy
spreadsheet analysis. It still lands
using 3 engines throttled back to no less than about 38% thrust.
Figure 5 – “Super Heavy” Results for Revised Stage Point
This increase in the “Starship” ignition mass is partly used
in the larger demanded delta-vee from stagepoint to orbit, but it also allows a larger payload, and a larger propellant load relative to the
Spacex-stated capacity. In the
spreadsheet, the balancing variable is
payload, with ignition mass set by the
“Super Heavy” result. This revised
stagepoint is quite beneficial, as can
be seen in the “Starship” results
of Figure 6.
In addition to carrying more payload (now slightly over
200 metric tons), the kinematic
acceleration levels just after staging are significantly better, being about 0.27 gee instead of the earlier
0.07 gee. That is the effect of
reducing trajectory path angle at staging! We still land on 3 sea level “Raptors”
throttled to about 50% thrust as a min value.
For the next update,
traveling outside LEO after refueling on-orbit, the analysis can be theoretically be simplified
considerably, by carrying the same
payload value both ways. That way, all the delta-vees are simply factored
appropriately and summed to a total mass ratio-effective delta-vee value. Reducing return payload is the way to try to
address shortfalls in available mass ratio.
A caveat here: these
numbers that get depend very fundamentally upon characteristics of the “Starship”
and the “Super Heavy” that simply are not yet known with certainty. I base this stuff on projections, not facts!
Small changes in things like inert mass have a huge effect. These things will NOT be known with certainly
until a lot of test flights and vehicle changes have been made!
*****************************
Update 10-24-19: Going to Mars and the moon
For Mars, the
trip is one-way, unless propellant can
be produced locally on Mars, in
quantities and at rates, that are
sufficient to support the return trip.
For the moon, the mission is
presumed to be two-way and unrefueled,
and only by direct landing on,
and departure from, the
moon.
This lunar scenario proved too limited to carry significant
payload to the moon, or to carry the
same payload two ways, which explains
why Musk’s recent presentations have referenced launching moon missions from an
elliptical orbit instead of a circular LEO.
The higher perigee velocity of the elliptical orbit reduces the
delta-vee onto the transfer orbit to the moon.
But this makes getting the “Starship” and its payload all the way to
orbit harder (reducing max feasible payload),
because the perigee velocity is a higher velocity to reach from the
stage point velocity.
For both cases reported here (Mars and the moon), the vehicle payload deliverable to LEO is based
on what the “Super Heavy” and “Starship” can successfully send to a circular
LEO, with the revised
stage-point data that increased allowable ignition masses for the “Starship”. Any elliptical orbit effects will have to be
the subject of a future update.
Mars
It turned out to be possible to send a very small payload to
low Mars orbit (LMO), with enough
propellant still onboard to deorbit, and
to make the landing on Mars. The
only feasible option for heavy payloads to Mars was the direct entry trajectory
straight off the interplanetary trajectory. This avoids the large burn otherwise
required to enter LMO. But it also
means you CANNOT abort the landing, no
matter what! And that includes the
surprise occurrence of giant planetary dust storms!
An image of the spreadsheet I used for Mars is given in Figure 7. A cartoon of what could be done is given in Figure 8. Scope includes both direct landing and
stopping in low Mars orbit before landing.
Bear in mind that this analysis is based upon a “Starship”
fully-refueled by tankers on-orbit to the full 1200 metric tons of
capacity. It is also based upon a spread
of payloads up to and including the max payload “Starship” can carry to a
circular LEO, as boosted by “Super
Heavy”, with the reduced stage point
velocity and path angle already investigated above.
I have not investigated what those tankers might
really be able to accomplish. That
would be the subject of another update.
Bear in mind that Spacex has published next-to-nothing about the
tankers! If the cargo/crew “Starship” is
used for a tanker at a nominal 200 metric tons of payload in extra tanks
instead of the regular cargo/cabin section,
then 6 such flights could deliver 1200 metric tons of propellant to a
circular LEO.
Note also that I have included a (wild guess !!!) course
correction payload allowance, as well as
factoring-up the landing delta-vee for pinpoint landing needs, up to and including brief hover. This was an
attempt to be as realistic as possible in these estimates.
What I got was all the payloads up to the max-orbited 203
metric tons are indeed feasible for direct landing on Mars, as long as the vehicle was filled to max propellant
capacity in LEO. Bear in mind that
my transfer trajectory was a minimum-energy Hohmann transfer orbit, not something faster! Depending upon where Earth and Mars are in
their orbits vs perihelion or aphelion,
the one-way flight times are never less than 8 months, and usually just short of 9 full months. The max is about 9.5 months.
The smaller payloads arrive with significant unburned
propellant (seen in the spreadsheet as unused delta-vee capability). This could be used for some degree of faster
transfer trajectory. The big payloads
really cannot be flown faster this way.
Too little is left over.
I was surprised to find that a fully-fueled “Starship” with
the smallest payload I considered (50 metric tons) actually had enough delta-vee
capability to make the burn to enter LMO,
and still have enough propellant to deorbit, and land.
Bear in mind this is ONLY for a min-energy Hohmann transfer to
Mars. I did not investigate whether this
could be done at 55 tons, because the
delta-vee margin was already quite low at 50 tons. This orbit entry would be the only way to
abort a landing in a dust storm, but the
payload capability available when doing this, is just not very attractive at all!
Once again, be
fully aware that going to Mars with “Starship” is a one-way trip, without adequate propellant production
capability on Mars. That is both
adequate produced quantities, and
production at appropriate rates, of
methane and oxygen, all in the required
ratio.
Bear in mind that the power and machinery requirements
for this have considerable scope.
Not only must there be methane production, but there must also be local water
electrolysis to produce the oxygen, and to
produce the hydrogen needed to make the methane. There must also be some way to compress
carbon dioxide from that near-vacuum-of-an-atmosphere, to make that methane.
Beyond that, there
must be the machinery to liquify the methane and the oxygen. Plus, there must be the machinery to sub-cool it to
the density required to put up to 1200 metric tons inside the tankage volume of
“Starship”. On Earth, that stuff is big and heavy. And very hungry for electric power!
And finally, there
must be some more machinery to keep such propellant cool enough not to boil
away, over very extended periods of
time. Approximately 2, to maybe 6 years, depending upon how often return flights are
to be made.
It's not “just a Sabatier reactor”!
The
Moon
Going to the moon is different, that being an unrefueled return
requirement. Again, be aware that I analyzed the case of
departing from a circular LEO. Spacex
has already said their “Starship” must use a more elliptical orbit about the
Earth in order to do the moon mission.
I could not use the same payload on the return voyage, as on the voyage to the moon. That proved infeasible. I investigated a list of payloads to the
moon, resetting vehicle mass statements
appropriately in response to an input return payload in the spreadsheet. I set that return payload to approximately 10
metric tons, corresponding to 10
persons, with a not-just-life support
allowance of 1 metric ton per person.
That would be the person, a
couple of space suits, and expendable
life support supplies for several days.
What I found was disappointing, as the spreadsheet image in Figure 9
shows.
From a circular LEO departure orbit, my numbers say that a fully-fueled “Starship”
cannot deliver more than about 27 metric tons of payload to the moon, starting from that circular LEO
departure. The 10 ton return payload is transporting
10 people home, all in the one
mission. The “eob-drytnk” results
highlighted blue in the figure are delta-vee-difference numbers in km/s units. Negative numbers are conclusively indicative
of an infeasible shortfall.
The cartoon in Figure 10 shows the highlights of these
results, including the trajectory
concept, which is NOT the figure-eight
trajectory Apollo used to reach lunar orbit!
Bear in mind that transfer orbit apogee velocity is less than the moon’s
orbital speed about the Earth. The moon literally
“runs over” the spacecraft from behind.
If your intent is lunar orbit, it will be retrograde. The Apollo “figure-eight” trajectory reflects
this, in the form of a computer-analyzed
3-body problem. If you are landing
direct, retrograde orbit is
irrelevant.
Figure 10 – Results for “Starship” Lunar Landings
Possible future updates would include both (1) the
elliptic orbit departure for lunar missions,
and (2) the return trip home from Mars to a direct entry and landing at
Earth. Elliptic orbit departure
implies a much higher apogee. If this
falls within the Van Allen belts, then
either no crew can be aboard, or else
there must be considerable radiation shielding available.
There is also the unaddressed issue of making
rough-field landings on the moon or Mars. This gets complicated by the far larger
weights on Mars of the fully-fueled vehicle ready to launch on the return. That issue is not a problem for the moon, since the vehicle is not refueled there. Even so,
it seems unlikely that sufficient attention has been paid to exerted
bearing pressures being within the allowable safe bearing pressures of soils
thought to be representative of the bulk of both Mars and the moon. Excess bearing pressures lead to landing pads
sink into the soil, which will happen
unevenly. That is a problem for takeoff
due to the extra friction holding the ship down. That is worthy of another update.
There is also the issue of static overturn stability
of a landed “Starship” on the moon or Mars. This presumes the landing pads do NOT sink
into the soil, which if it
happened, would happen unevenly. This is more of a
must-fall-within-the-footprint problem for the weight vector, something long-established in classical
freshman engineering mechanics. This is
also worthy of an update, addressing
both general land slope, and localized
roughness.
*****************************
Figure 11 – Spreadsheet Analysis for the Return Voyage, Part 1
Figure 12 -- Spreadsheet Analysis for the Return
Voyage, Part 2
For this analysis, I
assumed (1) full capacity propellant load of 1200 metric tons, (2) Hohmann min-energy trajectory home, (3) no prior constraint on return
payload, and (4) 3 sea level and 3
vacuum engines. The ascent from Mars is
a direct escape straight onto the transfer orbit, using the vacuum engines. I assumed a 0.5 km/s course correction delta-vee, same as for the trip to Mars. This is also done with the vacuum engines.
At Earth, entry is
direct from the interplanetary trajectory,
with aerobraking to about Mach 3 at about 45 km altitude. From there,
it belly-flops broadside to the relative wind, finally decelerating to about half a Mach
number at low altitude. Just prior to
the end, the vehicle turns tail-first for the
retro-propulsive touchdown. It must
use the sea level engines for this!
For the Mars ascent,
gravity losses are the Earthly 5% ratioed down by Mars’s surface gravity
(0.384 gee). Aerodynamic drag losses are
the Earthly 5% ratioed by the surface density ratio to Earthly standard
(0.007). The net ascent dV factor is
then just under 1.02. The touchdown
velocity requirement is factored up by 1.5,
as is my usual practice, to cover
pinpoint landing needs.
I split the spreadsheet image into two figures (see Figures 11 and 12), followed by a summary cartoon of the trip
home from Mars (see Figure
13). What I found was that under
these assumptions, the max payload
sendable home is 162.6 metric tons (assuming a full-capacity 1200 metric tons
of propellant at launch from Mars). This
also assumes course changes up to the full 0.5 km/s delta-vee get made.
Figure 13 – Illustration of the Salient Features of the
Return Voyage
For the feasible payload sizes, the 3 vacuum Raptors operated at full thrust
are adequate to launch the fully loaded and fueled “Starship” from the surface
of Mars (thrust/weight at or exceeding 1.2).
It is not possible to make the ascent with one vacuum engine “out” as
the thrust is less than the Mars ignition weight of the vehicle. One of the sea level engines must be
fired up to replace the lost vacuum engine. The sea level engine will operate in
vacuum, just at slightly reduced vacuum
thrust and Isp relative to the vacuum engine designs.
This way to handle an engine-out situation is included in
the Figure 11 data. The slightly-reduced
Isp does eat into the propellant margins (0.5 km/s worth of course
correction, and the factor 1.5 applied
to the touchdown burn). It would
be wise to reduce the max payload limit to compensate (but I did not determine
that here).
Figure 12 takes this through the aerobraking and
retro-propulsive landing on Earth. Here
the sea level engines must be used, with
no backup from the vacuum engines.
The reverse-engineering I did on the vacuum Raptor indicated
backpressure-induced flow separation in the nozzle, at about 20,000 feet altitude at full
thrust, and at about 55,000 feet
altitude at min thrust (20%).
However, at this point in the
voyage, the remaining propellant load is
small enough that even two sea level engines can do the landing, with three such running at 40-something
percent of thrust.
The illustration in Figure 13 summarizes these results, but without the details of the thrust/weight
and engine-out analyses. The max payload
listed corresponds to a min-energy (slow) trip,
a big course correction, and
landing with essentially-dry tanks on Earth.
It would be wiser to reduce this max payload figure to something
in the 150-160 metric ton range.
The remaining-propellant figures in Figure 12 at payloads
less than max are what could be used to support a faster trajectory home. These numbers are significant at 100 and
especially 50 metric ton payload values.
(A similar thing applies to the outbound voyage.)
Not analyzed here is the effect of not having a full 1200
metric tons of return propellant available.
That would be catastrophically-significant. The remaining-propellant figures correspond
roughly to how big the shortfall might be,
and still make the voyage. They are not large numbers, compared to the nominal capacity. This indicates just how crucial it is
to have a propellant production facility on Mars that exceeds requirements in
terms of quantities and rates.
*****************************
The idea behind this effort was to depart from an elliptic
orbit with perigee at the usual circular orbit altitude (about 400 km), and an apogee skirting the inner “edge” of
the Van Allen belts (at about 1400 km).
The higher perigee velocity relative to circular orbit velocity is a
delta that subtracts directly from the delta-vee required to depart Earth
orbit. The apogee restriction is to
eliminate the need for radiation protection during these flight operations.
This is a more difficult orbit for the “Super Heavy” /
“Starship” combination to reach from surface launch. For this analysis, I presumed the reduced staging velocity and
path angle already covered, which had given
the “Super Heavy” a larger throw weight.
For “Starship” to reach the higher perigee velocity of the elliptic
orbit, its payload must reduce at
constant “thrown weight”. What that
really means is that there is a tradeoff between the larger payload deliverable
to the moon, and the number of tanker
flights needed, since each can carry
somewhat less, flying to that
more-demanding elliptical orbit.
Basic orbital calculations gave me Figure 14,
from which the change in velocity at 400 km was at the very most 0.259
km/s, given a limited apogee at 1400
km, right at the inner “edge” of the Van
Allen belts. (That boundary is not a
sharp line.) From this, I picked a nominal increase of 0.25 km/s
perigee velocity for the vehicle rocket equation analyses. This variation of perigee velocity increase
over circular, versus the resulting
apogee altitude, is depicted in Figure 15.
The vehicle spreadsheets look exactly like those used for
the LEO operations and the moon mission from circular orbit. Only the detail numbers change. Those are not depicted here to save
space. The max payload delivered by
“Super Heavy” / ”Starship” to circular LEO was 203 metric tons, in a “Starship” limited to a 1488 metric ton
ignition mass and a less-than-capacity propellant load.
For this selected elliptic orbit, the ignition mass limit is the same 1488
metric tons, but the payload reduces to
179.8 metric tons, while the propellant
load increases closer to capacity at 1188.2 metric tons. (That capacity is 1200 metric tons.) Bear in mind that one cannot use 100%
of the “Starship” propellant to reach the desired orbit, no matter what. The deorbit and landing allowances must be
reserved, to cover the unplanned event
of an abort back to Earth, for any
reason at all.
For circular LEO, I
had estimated 6 tanker flights each able to carry a nominal 200 metric tons of
propellant as payload. Those 6 flights
could fully refuel the “Starship” for lunar departure, all the way to a capacity load of 1200 metric
tons. For the elliptic case, I figured 7 tanker flights at 171.4 metric
tons (falling within the 179.8 metric ton maximum) that could deliver the full
1200 metric tons to refuel the “Starship” for lunar departure.
The flight to the lunar landing has a departure delta-vee
reduced by the 0.25 km/s change to perigee velocity. Mid-course correction and lunar landing
requirements are the same as the circular orbit case. The return flight and Earth landing has
exactly the same characteristics as the circular-orbit case, right down to the reduced 10 ton return
payload. One must chase the required
mass ratios through the entire mission,
while “book-keeping” the remaining propellant all the way to final Earth
landing. Negative remaining propellant
is a conclusive indication of infeasibility.
For the circular orbit departure case, my earlier analysis indicated the max payload
deliverable to the moon was only 27 metric tons. Launching instead from the elliptic orbit, the payload increased to just about 52 metric
tons, although at the “cost” of 7 tanker
flights, not 6. See Figure 16 for the comparison of the two departure orbits and
their effects on payload and number of tanker flights.
Figure 16 – The Lunar Payload Tradeoff Results
I did not analyze still-higher apogee elliptic orbits
precisely because those apogees fall within the Van Allen belts, making the radiation exposure risk very real
indeed. Should that risk be
worth taking, the trend says that
lunar payload increases further, while
the number of tanker flights also increases,
raising cost per ton of payload delivered. The analysis responds sensitively to
this, since the available perigee
velocity change (up to 1 km/s at 6000 km apogee) is a fair fraction of the
original departure delta-vee from circular orbit (3.29 km/s). That would require venturing way into the
inner Van Allen belt, where radiation
levels get very high indeed.
As to whether that radiation risk is worth taking, that would depend upon there being adequate
radiation shielding built into the “Starship”.
This is something Mr. Musk claims will be available, but absolutely no details have been shown
publicly. I cannot yet analyze
for that issue.
But, assuming that
the refueling “Starship” in elliptic orbit needs to stay clear of the Van Allen
belts, then the payloads deliverable to
the moon (~50 tons) are rather disappointing compared to what might be
delivered to Mars (~200 tons). This is
because both the lunar mission is not refueled on the moon, and that unrefueled return adds to the
effects of the higher overall velocity requirement for a two-way lunar mission (8.475
mass ratio-effective km/s) versus a one-way direct-landing Mars mission (5.4
mass ratio-effective km/s).
In comparison, the
one-way Mars mission via LMO (with only 50 ton payload) has a mass
ratio-effective velocity requirement of
7.25 km/s. The mass ratio-effective
velocity requirement for a direct return from Mars is 6.075 km/s. All of these figures are for Hohmann
min-energy transfer orbits. Faster
trajectories have significantly higher velocity requirements! That
topic is not under study here.
*****************************
Update 10-29-19:
Effects of Price Upon Elliptical Departure
In response to a question posed by reader Rob Davidoff (see
comments below), I checked the numbers
as a function of assumed price per launch of “Starship” / “Super Heavy”. That launch price is a complete unknown at
this time. So I just tried a low guess
and a high guess. Note that the
number of tankers gets added to 1 ship carrying the lunar payload. While launch price affects price per
delivered ton greatly, I was surprised
to find that the ratio of price per delivered ton from elliptical orbit to the
price per delivered ton from circular orbit, seems to be quite independent of the launch
price for any one flight. See Figure 17.
Figure 17 – Launch Price Effects on Cost per Delivered Ton
to the Moon
I also briefly relaxed the constraint of not entering the
Van Allen belts, for a slightly taller
elliptical orbit that was 400 x 1900 km,
with the difference in perigee to circular velocity 0.383 vs 0.25
km/s. At the fixed stagepoint thrown
mass of 1488 metric tons, this
“Starship” requires a full propellant load of 1200 tons, with at most 170 tons max payload getting
there. Departing from there to the
moon fully fueled, the max deliverable
payload to the moon is 67 metric tons.
Note that the apogee associated with this departure orbit penetrates
about 400-500 km into the lower Van Allen belt,
presenting potentially a very significant radiation hazard to the crew.
Orbit payld,
m.ton
400 km circ.
27
400x1400 ellip. 52
400x1900 ellip. 67
*************************
Applied surface bearing loads depend upon the local weight
of the mass (1 gee Earth, 0.384 gee
Mars, 0.165 gee moon), and the total area of landing pad footprints actually
in contact with the surface. Force/area
means these get expressed as applied bearing pressures. The allowable bearing pressures depend upon
the nature of the surface: hard rock safely
supports more pressure than soft sand.
Exceed the maximum safe applied pressure, and the landing pads start to “dig in” like
tent stakes, regardless of what the
surface really is. And this will
happen very unevenly, from leg to leg!
That is just an ugly little fact of
life.
We have no local surface bearing strength test data from any
of the probes sent to Mars, or from the
probes and Apollo landings upon the moon.
What we have is only a sense of equivalent Earthly soil or surface
types, as seen by these probes
and landings.
Pretty much the entire surface of the moon resembles “fine
loose sand” on Earth. The presence of
various sizes of rocks scattered within the sand has little or nothing to do
with its bearing strength! It’s neither
cemented nor is it compacted, it
is just meteor-smashed dry regolith!
The vast bulk of the surface of Mars resembles the regolith
on the moon, meaning it is more-or-less
equivalent to Earthly “fine, loose dry
sand” in strength. The presence of rocks
of various sizes scattered within this regolith has no impact on its
safe bearing strength!
There are places on Mars where this is not true, but they are a minority of its surface! The main thing that comes to mind is ancient
alluvial deposits of sand and rocks (small rocks somewhat like coarse gravel)
on Mars, which in those ancient wet
times would have compacted and cemented like the natural beds of sand
and gravel here on Earth.
A very tiny minority indeed of Mars’s surface
would be exposed outcrops of “solid” rock. But,
there’s “solid rock”, and then
there is “solid rock”, in terms of just
how strong that rock really is! This
makes quite a difference here on Earth! Unfractured igneous rocks on Mars would be
much stronger than fractured sedimentary rocks,
same as here on Earth. The
variation in effective strength is enormous!
Yet all of these terrains would show about the same
density from remote sensing, simply
because most common minerals show specific gravities in the 2.5 to 3.5 range! Crystal density has nothing to do
with gross rock self-cohesion. Therefore, the remote sensing that we can do, is just not yet reliable at all for this safe
bearing load purpose! It does not
matter how inconvenient or unpopular that statement might be, it is still true.
I retrieved the safe bearing pressure capacities of various
Earthly surfaces from my old edition of Marks’ Mechanical Engineer’s
Handbook, and selected for each
type the minimum allowable safe bearing pressure. This minimum is the value you must
use for estimates regarding that apparent type, until and unless you have actual
soil bearing strength test data from the specific site you are considering!
We have no such test data yet for Mars, or the moon, but we understand the general range of values
for each type here on Earth. Soil types
on Mars and the moon seem equivalent to certain Earthly types. That apparent equivalency is currently
the best we can do right now.
I have already looked at the ranges of feasible landed
masses for “Starship” on Mars and the moon,
plus abort flights on Earth, in
the article and updates above. Each of
these has a local weight at local gravity.
I picked “typical” max local weight values for each of these scenarios.
Note that an abort-to-surface anytime during the
second stage ”Starship” ascent to LEO, will lead to a fatal crash with any “Starship”
fitted with 3 sea level and 3 vacuum engines. The same is true for a failure requiring “Starship”
to abort-to-surface during the “Super Heavy” booster burn. That is because the Earth weight of the
descending vehicle far exceeds the combined maximum thrust of the 3 sea level
engines.
The thrust available from the 3 vacuum engines is very
limited indeed, because full flow
separation in the vacuum bells starts around 20,000 feet altitude at max thrust. The sonic-only thrust coefficient is going to
be about 1.2 at the very most!
Plus, with separated flow, the vacuum engine bells may fail thermally-structurally, if operated in separated mode for any
appreciable length of time.
The moon landing as conducted from circular LEO has at most
27 metric tons of payload to the moon,
and features no more than 10 metric tons of return payload to
Earth. If instead conducted from an
elliptic orbit that still avoids penetrating the lower Van Allen belt, this payload increases to 52 metric
tons, with the same 10 ton return
payload. Moon missions are entirely unrefueled
on the moon. Excepting payload, there is
no other difference between lunar landing and lunar takeoff masses.
The Mars landing as conducted from circular LEO can carry at
most 203 metric tons of payload to Mars,
and at most 162 metric tons of payload back to Earth, all figured at min-energy Hohmann
transfer. Mars missions are
entirely one-way trips to Mars, unless
the full propellant load of some 1200 metric tons can really be manufactured on
Mars! Departure weights are far
higher than landing weights.
I figured the local weights for all these missions and
scenarios from the masses the missions required. These have been incorporated into a table of
applied and allowable bearing pressures that varies with Earthly surface
type. Those results are shown in Figure 18.
This is based upon the observation that for the 2019 version
of “Starship”, there are 6 landing legs
extending from the vehicle base (one each from each aft “wing” fillet, two others distributed across the ventral
surface, and the last two distributed
across the dorsal surface). Based
upon the visual characterization from published Spacex images, the landing pads of these short-extension
struts are “fractional-meter in dimension” at most. I have used an arbitrary 0.5 m diameter
as a sort of “default” value. It
is not right, but it is
“in the ballpark”.
There are NO published figures from Spacex regarding how big
these landing pads really are! Whatever
size they really are, the local
weight divided by the total pad area in contact with the surface, is the applied bearing pressure! This MUST be below the minimum credible
value of the surface’s safe bearing capacity!
No “ifs”, “ands”, or “buts”. For purposes of magnitude sizing, I consider 0.96 MPa the same number as 1
MPa. This is just roundoff error.
The first conclusion drawn from Figure 18 is that the moon
landing of a “Starship” is just NOT feasible,
given the current landing leg and landing pad design, by something like a factor of 4! If you consider the larger payload of an
elliptical-orbit launch, this
discrepancy increases to around factor 5!
The second conclusion from Figure 18 is that a one-way Mars
landing might be feasible with the 2019 “Starship” design, but only for a very tiny minority of
Mars’s surface: a “solid rock”
outcrop, that is also very smooth and
very level! Failing this
circumstance, something equivalent to a
thick, reinforced, concrete landing pad is simply required, even for just the landing! Much less the takeoff!
It gets worse by around a factor of 5 for a refueled takeoff
from Mars, even with a reduced return
payload. Mars takeoff at fully-fueled
launch mass requires something pretty close to 5 MPa bearing capacity, as seen in Figure 18. There simply are no surfaces on Mars
that are that known to be that strong!
Lava flows, even if
unfractured, are just not that flat
and level. This is reinforced-concrete-equivalent
landing pad stuff! No way around that!
Larger landing pad areas are just absolutely required! Figure 19 shows options for both square landing pads, and 2:1 ratio length:width pads. Thee are computed from the max local mission
weights as-rounded up to the nearest 100 KN,
at fine loose sand strengths of 0.1 MPa,
or a bit higher, as shown.
Figure 19 – Landing Pad Sizing Data
The worst case of all is not an abort landing upon an
Earthly soft sand beach (quite the common scenario otherwise), but fully-fueled takeoff from the vast bulk
of Mars, which is similar to soft, fine,
loose sand, regardless of any
rock content present! We need something
like 14-15 square meters of total landing pad area to make this happen
reliably! If the landing legs bury
themselves into the ground as we refuel on Mars, the resulting “tent stake” friction acts to prevent
liftoff! The ship may even
topple over (and explode) as it is being refueled.
These required pad areas are about 3.8 m x 3.8 m for 4 square
panels, deployed from the upper and
lower surfaces of the aft fixed-wing surfaces.
If 2:1 length:width, with length
chordwise along the fixed wing chord,
these are still four panels, each
about 4.06 m by 2.03 m in dimension.
Either way, such are
easily designed into the wings as panels folded out by hydraulics, much like landing gear bay doors on Earthly
aircraft. Bear in mind that “outrigger”
legs perpendicular to the body are still needed to get a big, stable “footprint” out of this.
There is not yet one single public word from Spacex
regarding this critical issue. I
doubt they will address this until an abort during a prototype test flight has
to land on soft ground, because it could
not reach the intended paved launch/landing pad. The resulting very serious problems will no
doubt spur action and changes to the design.
*****************************
Update 10-31-19:
Static Overturn Stability
We start with static stability of “Starship” as a flight
vehicle. Now, there is a shortfall of broadside projected
area of the nose, relative to the rest
of the cylindrical body, of the
”Starship” upper stage spacecraft. But
there is also a shortfall of broadside projected area of the forward steering
canards relative to the aft fixed wings.
These differences tend toward balancing each other.
Thus, the center of
aerodynamic pressure is somewhere very near the geometric center of the 50 m
long “Starship” upper stage. Call it 25
m from the base, of the 50 m long by 9 m
dimeter vehicle, per Spacex published
data.
For minimal “arrow stability” purposes, there is a need for the center of gravity of
an object to be about 75% of its body width,
ahead of its center of pressure.
For the 9 m diameter “Starship”,
this would be about 6.7 m ahead of the center of pressure, or about 31.7 m ahead of the base of the
vehicle.
The 2019 version of Spacex’s “Starship” has some 6 landing
legs that extend minimally and vertically from around the base of a 9 m
diameter vehicle (radius 4.5 m to the center of each pad). Assuming these are equally spaced around the periphery
in a hexagonal array, they correspond to
a 30-60-90-degree triangle with a hypotenuse of 4.5 m. The min distance from the vehicle centerline
to nearest edge of this footprint hexagon (halfway between two pads) is then
(4.5 m) (cos (30 degrees)) = 3.897 m. The
max is just the radius, 4.5 m.
Overturn stability on a flat, level surface then requires that the vehicle
weight vector always fall within the polygon representing the landing pad
footprint. The weight vector “hangs”
from the center of gravity, some 31.7 m
higher than the base of the vehicle. What
that really means is that tan(angle) = min distance/cg height, as landed.
For aft base-to-cg = 31.7 m, and
centerline-to-nearest-edge 3.897 m, that
angle is 7 degrees. (Figured at the radius
to a pad, it is 8 degrees, but you are interested in the smaller value
as your true limitation.) See Figure 20.
Figure 20 – The Geometry of Static Overturn Stability
What that really means is that for the 2019 “Starship”
design, any straight outcrop of
sufficiently-hard rock must NOT be sloped any more than 7 degrees off
horizontal, for a successful
landing to be made at all! Local
surface roughness variations make this requirement even more stringent!
For 7 degrees max tilt,
the local roughness variation of an otherwise absolutely-horizontal surface
may not exceed radius*tan(7 deg) = 0.55 m.
What that really means is that the max boulder size under any one
landing pad may not exceed 0.55 m,
without a topple-over risk, on otherwise flat and completely level
ground. This applies to roughness
in general, not just boulders. Landing with a couple of adjacent pads down
in a runoff channel has the same tilt-over effect, as illustrated in the figure.
If already sloped,
this limitation is far lower still! A wider landing pad base diameter than 9
meters would greatly improve this picture.
That gets back to landing pads deployed from the surfaces of multiple
fins-as-landing legs, for which the
effective polygon circumscribed diameter is larger than 9 m, as the first concept that would come to mind.
Figure 21 – An Idea for Higher Pad Area and Static Overturn
Stability Simultaneously
****************************
All of the above analyses notwithstanding, please bear in mind that these are design
analysis estimates for a design concept that has yet to “gel” into a real
design undergoing actual development.
There are now some initial flight test prototypes based on this design
concept (and not the earlier concepts),
but the fundamental nature of experimental flight test suggests that
major design changes are yet to come.
These changes will be uncovered by those flight tests.
I have pretty-well addressed the performance potential and
possible shortfalls of the “Starship” / “Super Heavy” design concept as it
currently exists, based on the sparse
data currently available. There would
seem to be little point to pushing this further, until the design concept evolves into a real
candidate design during flight test. So,
unless a reader has a question that I
might answer, I am pretty well done with
this particular article.
****************************
Update 11-21-19: Choice of Landing Engines
****************************
Update 11-21-19: Choice of Landing Engines
One should be aware that there are two variants of the Raptor engine to be installed on "Starship". These differ only in the size of the exit bell (expansion ratio), they share the same hot gas generation and throat area. Those are the smaller-bell "sea level" Raptor, and the larger-bell "vacuum Raptor". The vacuum Raptor has higher vacuum Isp precisely because the expansion ratio is larger. The sea level Raptor has good vacuum performance far higher than its sea level performance, but not as high a vacuum performance level as the vacuum Raptor.
My estimates for these engines indicated the vacuum Raptor could not be successfully operated in Earth's atmosphere below the stratosphere, due to backpressure-induced flow separation in the nozzle. But Mars's atmosphere is so thin as to permit operation of the vacuum Raptor at essentially its vacuum performance level. The vacuum designs have higher Isp. So in my analyses above, I used the sea level Raptors for landing on Earth, and the vacuum Raptors for landing on the moon or Mars.
I have since become aware of gimballing restrictions in the 2019 version of the Starship design. The vacuum Raptor engines cannot gimbal very much, if at all, due to a lack of room to swing the bells about. The sea level Raptor engines have plenty of room for significant gimballing, because there is plenty of room to swing those smaller bells about.
Now, significant gimballing is required in order to do retropropulsive landings, anywhere. What that really means is that the sea level Raptor engines must be used for touchdown on the moon and Mars, as well as Earth. The Isp during the touchdown burn is lower by nearly 20 seconds for this geometry-driven choice. The touchdown burn is not a large delta-vee item, but this does mean max payloads are a little lower than I estimated in the above analyses. (I did not re-run all those estimates.)
*****************************
