Update 7-2-2020: I found a mistake in my performance-estimating
spreadsheet. I used the unfactored
delta-vee requirements for figuring mass ratios, instead of the factored delta-vee
requirements. I corrected this in the spreadsheet, and used those revised images to correct the
spreadsheet results depicted here as Figures 5,
7, and 9. Then I corrected the results shown in Figure
10 by re-editing that figure. Where numbers changed in the text of the
article, I edited them with line-out and
red text.
-----------------------------
These results are based upon the earlier article posted here, titled “2020 Reverse-Engineering Estimates for Starship/Superheavy”, dated 25 May 2020, and also upon the earlier article titled “Interplanetary Trajectories and Requirements”, dated 21 November 2019.
The first examined the latest data available for the Starship/Superheavy
designs, and projected its performance
into low Earth orbit (LEO), complete
with a look at what kind of tanker flights might be required to leave LEO. That same set of weight statements and
engine performances is assumed here.
The second examined trajectories to Mars, including both Hohmann min-energy, and faster trajectories, and including direct entries, and entries into low Mars orbit, and to Phobos.
Of most interest here was the faster trajectory of an exactly 2-year period, which provides a 2-year abort path if the direct
landing on Mars cannot be made, for any
reason whatsoever.
This article also examines direct entry and landing upon
Mars, starting from LEO, via either Hohmann or the faster 2-year abort
trajectory. Further, it looks at stopping in low Mars orbit
(LMO), followed by deorbit and landing
on Mars. It does not examine going to Phobos, which would be broadly similar to stopping in
LMO, except a bit worse, energetically.
Returns are launched directly from the Martian surface, assuming a full refill using propellants made
locally on Mars. Whether one stops in
LMO or just escapes directly, the total departure
velocity requirement is the same, for
the same return trajectory. Stopping in
LMO relieves a tight launch window from the surface, replacing it with a fairly tight window for
trans-Earth injection from LMO, which is
actually an easier target to hit, in actual
practice.
A summary illustration (not to scale) of the two basic
transfer trajectories, with the LMO
option, is given in Figure 1. All figures are at the end of this article.
It must be understood at the outset that the kinematic
velocity requirements for this-or-that trajectory are not what you
design your vehicle with, using the
rocket equation! Those velocity
requirements must be factored-up appropriately to “mass
ratio-effective velocity requirements”,
in order to size a credible design,
or make credible performance calculations. That is because the rocket equation was mathematically
derived for zero-gravity, zero-drag
conditions. The real world often is not.
See Figure 2.
I have been to the Spacex website many times over the last
several years. Among the other things
posted there have been atmospheric entry simulations for their Starship
vehicle. There are two such: one for entry at Earth, and one for entry at Mars. These are rarely posted at the same
time, and are quite different, because the Martian atmosphere resembles the
Earthly atmosphere above 105,000 feet (about 33 km). See Figure 3.
The Earthly entry trajectory ends hypersonics at about Mach
3, above 40 km, followed by a bending downward while pitching
upward to dead-broadside descent angle-of-attack. This dead-broadside fall is termed the “belly-flop”
or “skydiver” maneuver. It is supersonic
up in the thin air, and very subsonic
down in the thick air near the surface. Spacex
lists this as 68 meters/second under about 5 km. There, they pitch to tail-first while
igniting the engines to land. That is a
very modest delta-vee on the order of 0.070 km/s, but it has to be factored-up significantly to
cover hover and divert allowances.
The Mars entry ends hypersonics at about Mach 3 very close
to the surface: about 5 km
altitude. Spacex’s simulation shows a
lifting pull-up to decrease speed while gaining altitude, to around Mach 2-ish at 10 km/s. Right after that is when they pitch to
tail-first and fire-up the engines to brake for landing, at something like 900 meters/sec = 0.9
km/s. Again, that needs a significant factoring-up to
cover hover and divert needs.
It may well prove to be, that Spacex will need to fire up the engines
earlier at Mars entry, in order to
augment lift with thrust to achieve the pull-up maneuver. If so,
the landing burn delta-vee is even higher, but I did not assume
that to be the case for this analysis!
The Hohmann min-energy trajectory is depicted in Figure
4. This is an ellipse with its
perihelion at Earth’s orbit about the sun,
and its aphelion at Mars’s orbit about the sun. Half of it covers the voyage to Mars, the other half covers the return voyage. For purposes of this analysis, I only looked at Earth and Mars at their average
distances from the sun. Those variations
do affect the results, Mars more than
Earth because of its more eccentric orbit.
But, the averages are close
enough to find out “what ballpark you are playing in”, which is the point here.
For the baseline outbound voyage, entry at Mars is direct from the
interplanetary trajectory. There is only
a course correction budget needed along the way. The three burns are LEO departure, course correction, and direct landing upon Mars. The value of the course correction budget (0.5
km/s) is nothing but a guess, but
it is a good ballpark guess, being about
2-3% of the typical velocity with respect to (wrt) the sun during the voyage. Note that in this baseline there is no
possibility of aborting the direct landing for reasons of adverse conditions at
Mars.
For the baseline return voyage, entry at Earth is direct from the
interplanetary trajectory. The same 0.5
km/s course correction budget is presumed for this leg. The three burns are Mars departure, course correction, and direct Earth landing. There is no possibility of aborting the
direct Earth landing. The difference
is Mars departure, which could be
broken-up into two burns: one to achieve
LMO, the other to escape onto the return
interplanetary trajectory. The total is
the same, either way.
What I got for this mission is the spreadsheet image shown
in Figure 5. The weight
statements, engine selections for each
burn, and engine performances, are all listed in the spreadsheet image. It covers both the voyage to Mars, and the return to Earth, as separate sections, with different weights (payload values) for
each leg. Payload both ways
exceeds what the “2020 Reverse-Engineering Estimates” article found to be the maximum
payload deliverable to LEO. The
payloads shown are the max values to the nearest metric ton, that gave positive fractional-ton remaining propellant,
after all burns were fully expended (the
spreadsheet really is iterative).
Therefore, to meet these
weight statements, not only must the
Starship’s propellant be refilled to 100% of capacity on LEO, but also some extra payload mass must be
brought up to LEO and loaded on board. Those means are not explored here. However,
284 220 metric tons of total payload (people plus cargo) is a generous
allotment that this design can deliver to Mars,
if an 8.62 month one-way voyage is acceptable.
The Hohmann return payload of 153 144 metric tons is less, because the net total delta-vee requirement
to return is higher. This mission
spends about 13 months at Mars waiting for the orbits to be “right” to come
home, so you have 13 months to make 1200
tons of propellant! The next
opportunity is 26 months after that. The min round trip total is about 30.2
months.
The faster transfer trajectory that I chose to analyze is
the 2-year abort return ellipse. Its
perihelion is at Earth’s orbit, but its
aphelion is far beyond Mars, nearly to
the main asteroid belt! Its
period is exactly two years, so that if
you follow it, the Earth will be at its
perihelion just as you arrive there. In
order to have Earth there when you are there,
the period of any such orbit must be an integer multiple of 1
year. It is simply not a free-return
abort orbit, if the Earth is not
there when you get there. See
Figure 6.
I used the same landing allowances and course correction
allowances for the faster transfer case.
The LEO departure and Mars surface departure velocities are significantly
higher, because the energy of this orbit
is also significantly higher. That
raises required mass ratio, and lowers
max payload. Again, the payloads I found were maximum to the
nearest ton, for a positive fractional-ton
remaining propellant, after all burns
were fully expended. What I
found is the spreadsheet image in Figure 7.
Max payload to Mars still
exceeds equals what can be delivered to
LEO without any separate freight deliveries!
Max payload returnable to the Earth is actually quite limited at only 39 34 tons! This mission has about 15-1/2 months
on Mars in which to manufacture the return propellant. It is 2 years long overall.
As for stopping in LMO instead of direct Mars entry, I only looked at the outbound voyage to Mars. I did look at both the Hohmann min-energy
transfer, and the faster transfer using
the 2-year abort orbit. This added more
burns to be made. Now, there are LEO departure and course correction
as before, plus an entry into LMO, plus a deorbit from LMO, and the same landing burn as before. The faster transfer has the higher LEO
departure and LMO entry requirements.
The final landing burn and the deorbit and course correction burns, are all the same. This is shown in Figure 8.
What I found for this, is the spreadsheet image given in Figure
9. I was quite surprised to find
that it is indeed possible for a Starship to enter LMO and still have the
propellant remaining to land. It can
only do this from the Hohmann min-energy transfer, and only with very drastically-reduced
payload (only 39 34 metric tons). This
is just not a possible landing abort mode,
unless you deliberately use Starship to transfer very small payloads to
Mars. From the faster transfer
trajectory, we are 21.5 33.6 tons short of the
min landing propellant needed to avoid a fatal crash, even at zero (!!!) payload. That is just not feasible.
I have summarized
all these results in Figure 10. Using the “2020 reverse-engineering”
numbers, payload transferable to Mars
looks to be more, or at least equal to, than what can be transferred to LEO, for both Hohmann min-energy transfer (284 220 metric tons for 8.62
months one-way), and for fast transfer on the 2-year
abort orbit (197 149 metric tons for 4.26 months one-way). The earlier article indicated a max of 149
tons could reach circular LEO, with full recovery
of both stages.
I looked at the LEO tanker issue in the “2020 Reverse
Engineering” article. Flying a cargo/passenger
Starship at zero payload results in 133 metric tons of deliverable and transferable
propellant, to LEO. That’s 9 flights to fully refill the one
vehicle going to Mars, assuming it
arrives in LEO with sufficient propellant remaining to deorbit and land. Flying a reconfigured Starship with extra tanks,
as a dedicated tanker design, can deliver the full 149 metric tons to
LEO. That’s 8 flights to fully refill
the one vehicle going to Mars. Sorry, 8 or 9,
not 4 to 6. The numbers do not
support the optimism!
None of
these tankers has the payload capacity to deliver what would increase the
payload of the vehicle going to Mars from the minimum 149 tons. Such increases would have to come from
separate “freighter” flights. There has
been no way identified yet, for transferring
cargo from one Starship to another while in LEO. No one has even mentioned this.
It is possible to stop in LMO before landing if you sharply
reduce your payload before you ever depart LEO, if you are on a Hohmann min-energy trajectory
(78 50 metric tons for 8.62 months one-way).
But it is impossible, even at
zero payload, to land without crashing, if you fly faster! The sharply restricted payload (78 50 versus 149
metric tons), makes this option very
undesirable, but discarding it also
eliminates a possible landing abort method, if landing conditions unexpectedly prove
adverse at Mars, such as a giant dust
storm with high winds.
Going to Phobos will not help this LMO-impracticality
picture. That slightly reduces
the delta-vee requirements to rendezvous with,
and then land on, the moon, but it significantly increases the delta-vee
requirements needed to reach the surface of Mars. This has already been thoroughly explored in
the article titled “Interplanetary Trajectories and Requirements“, dated 21 November 2019, on this site.
Other work I have done and not posted verifies that the
least-energy path from Phobos to Mars is a burn to escape from Phobos, a burn onto a transfer ellipse to LMO
altitude, a circularization burn at LMO
altitude, followed by a deorbit
burn, entry, and a landing burn.
There
are two critical items necessary to make this Starship/Superheavy design concept
more practical: (1) the ability to put
closer to 300 220 metric tons of payload in LEO while maintaining an abort deorbit
and landing capability, and (2) coming
up with a real tanker design. Those are
in addition to the rough-field landing capability problem, and the inert mass growth problem that
always occurs in experimental flight testing. You have to increase the size of
SuperHeavy to do that LEO payload increase,
so as to increase the staging velocity,
while still maintaining flyback capability for recovery.
Figure 1 – Types of Missions Considered
Figure 2 – Factors Applied to Kinematic Delta-Vees to Obtain
Mass Ratio-Effective Delta-Vees
Figure
3 – Trajectory Characteristics, Final
Speeds, and Factors for Entry, Descent,
and Landing
Figure 4 – Characteristics and Velocity Requirements for
Hohmann Min-Energy Transfer
Figure 5 – Spreadsheet Image of Results for Hohmann Min-Energy Transfer AS EDITED 7-2-20
Figure 6 – Characteristics and Velocity Requirements for
Fast Transfer with 2-Year Abort
Figure 8 – Hohmann and Fast Transfers to Mars Stopping in
Low Mars Orbit Before Landing
Figure 5 – Spreadsheet Image of Results for Hohmann Min-Energy Transfer AS EDITED 7-2-20
Figure 10 – Summary of Results for Transfers To and From
Mars
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