**appended below.**

__Update 5-30-2020__----------------------------------

The Spacex website has changed from the last time I
retrieved data from it. In some ways it
is more informative than before, but in
most technical ways, it is less
informative. I had to use things found
only in Musk’s Boca Chica presentation (in front of a stainless steel Starship
prototype), plus stuff I found in
Wikipedia. I chose to re-use my
reverse-engineering estimates from last year for the Raptor engines. Those were posted 26 September 2019 as
“Reverse Engineered “Raptor” Engine Performance”.

The performance findings from my 2019 engine effort are
summarized in Figure 1 (1 lb = 4.4475 N,
for those who care to convert my thrust numbers). There are two design forms of the
engine, the sea level design with 40:1
nozzle expansion ratio, and the vacuum design
with 200:1 expansion via a nozzle extension fitted to otherwise the same
engine. There is also an experimental
test version of the vacuum design, with
only 150:1 expansion, so that open-air
nozzle tests can be performed without nozzle flow separation due to excessive
backpressure. That experimental test
version was not analyzed last year, or
included here.

Figure 1 – Engine Configurations and Performance Used For These Estimates

Note that the Superheavy (SH) booster uses only the sea
level (SL) form of the engine, just (as
currently envisioned) some 37 of them. I
averaged sea level and vacuum performance estimates for the SL engine as an
effective average value for the booster ascent to staging. For the reversal and entry burns, I used vacuum performance for the SL
engine. And for the landing touchdown
burn, I used sea level performance for
the SL engine.

The Starship (SS) second stage spacecraft uses 3 SL and 3
vacuum (vac) engines. Only the sea level
engines are gimballed up to 15 degrees for thrust vector control. The bigger-bell vac engines are
fixed-mounting. That means the SL
engines must be used for landing touchdowns,
not just on Earth, but anywhere
else, because thrust vector control is
required for attitude control during touchdown. I used vac engine performance for the SS
ascent, because it is essentially in
vacuum. I used the SL engine sea level
performance for touchdown.

Vehicle performance estimates require weight
statements, such as those given in
Figure 2. The Spacex website gives
payload and propellant figures for both SS and SH, but not the inert masses, or the all-up ignition masses. Note that the loaded SS is the payload for
SH. In Musk’s Boca Chica
presentation, there was a slide giving
the inert SS mass as 85 metric tons, but
Musk said this was wrong. He corrected
it to 120 metric tons for the “typical prototype”, with 100 tons for production vehicles a goal
he hoped to meet. That being said, in this analysis, I used the 120 ton figure. For SS,
a lowering of inert mass adds directly to LEO payload.

There is as yet no reported inert mass for SH that I can
find anywhere. Since they have yet to
build one, that is not surprising. However,
the Falcon-9 and Falcon-Heavy cores are about 5% inert mass, with the second stage and payload as the
payload for the first stage. At the 100 ton ultimate payload value, I used that 5% figure here to set a
“realistic” 250 metric ton guess for the inert mass of SH. I kept that inert mass as I changed ultimate payload, later in the effort.

The trajectory of interest is an eastward launch to low
Earth orbit (LEO). This could be out of
Cape Canaveral or out of Boca Chica. I
used surface Earth circular orbit velocity as a realistic value for LEO
circular orbit velocity. The way the
gravity-turn trajectory bends over,
essentially all the gravity and drag losses (assumed to be 5%
each), get charged against the first
stage. The staging velocity need not be
all that high, as long as the staging
altitude is out in essentially-vacuum,
and the trajectory angle is bent-over essentially-horizontal. From stagepoint, SS uses its vac engines to accelerate to
orbit speed.

Meanwhile, SH must
kill its forward staging velocity, and
add some more horizontal velocity Vx back toward launch point, plus some vertical velocity Vy to loft the
return for max ballistic range in what is essentially vacuum. Range in vacuum maximizes at 45
degrees, so that Vx tan(45

^{o}) = Vy. The vector sum of Vstg + Vx + Vy sets the delta-vee (dV) for the reversal burn. This is in vacuum and essentially horizontal, so the kinematic dV may be used unfactored as the mass ratio-effective dV1. Speed at the start and end of this return arc is the right-angle vector sum of Vx and Vy.
I presumed from staging altitude a fall to 20 km
altitude. This is just an assumption on
my part. Falling that far trades
potential for kinetic energy, so I calculated
the speed giving that kinetic energy,
and used it for the magnitude of the entry burn dV2. This is very likely not “right”, but it has to be “in the ballpark”. It gets us back to a speed identical to the
end-of-arc speed, just down at 20
km. I ignored both gravity and drag
losses for this dV2, and I treated it as
in-vacuo for rocket performance purposes.

From 20 km, the
vehicle picks up speed converting potential to kinetic energy, which change roughly adds to the end-of-arc
speed we had at the 20 km point. This
speed is what the touchdown burn must “kill” to zero. I did factor that speed up by factor
1.5, for the mass ratio-effective dV3 of
the touchdown burn. This burn is
essentially at sea level, so I used sea
level rocket performance for this burn. These
3 burns together conclude the return and recovery of SH. The three dV’s each have propellant
requirements, which must add to the
ascent propellant requirement, but within
a full propellant load.

Now, I ignored the
deorbit burn requirement for SS, which
is actually fairly modest. That might
not be “right”, but it is hardly a
“killer”, especially given the
uncertainties in some very fundamental data,
such as the inert masses for SH and SS.
SS “kills” most of its orbital velocity with hypersonic aerobraking
drag, coming out of that phase around 45
km altitude, at about 1 km/s
velocity. It pitches to 90 degree angle-of-attack
as the trajectory bends vertically downward,
as a sort of sideways “belly flop” to present maximum drag. Up high in the very thin air, this is supersonic terminal speed; down low in the dense air, it is very subsonic. One of the simulations on the Spacex website
suggested the terminal low-altitude “belly flop” speed was about 68 m/s, and I used that. The simulation seemed to suggest that the
vehicle is oriented tail first at something like 3 km altitude for the
touchdown burn. The velocity to be
“killed” is 0.068 km/s, which I factored
by 1.5 to create a mass ratio-effective dV value.

This touchdown burn could be done with 2 SL Raptor engines
operating at or just under full thrust,
but engine-out safety requires all 3 SL Raptors be used, operating somewhere in the vicinity of 40-60%
thrust. I did presume that the full
payload to LEO be carried all the way down to landing! If instead SS returns unladen, then both propellant and thrust requirements
are lower (not figured here). These
trajectory and related data are illustrated in Figure 3.

I did this analysis in a semi-automated format in an Excel
spreadsheet, pictured in two parts in
Figures 4 and 5 just below. There are a
number of user inputs, highlighted
yellow. Some selected outputs needed to
converge the analysis are highlighted in blue or green. There are two nested iterations
involved. The inner iteration converges
available and required (input) staging velocity for the booster. The return propellant allowance is affected
by stage velocity, in turn affecting
what stage velocity the vehicle can reach.
Obviously, payload (in this case
the loaded SS) also affects these numbers.

The outer iteration adjusts the tradeoff between ascent and
landing propellant, as a function of the
stage velocity set by the inner loop,
and the user input for payload to be carried by the SS. You
have to converge both loops acceptably close,
before you have a believable answer.
“Acceptably close” means 3 significant figures or better.

One thing mentioned by Musk in his Boca Chica presentation
was the liftoff thrust/weight ratio for SH.
He said they wanted something near 1.5 for this, which is higher than what was customary with
prior launcher technology. What I have is
“close” to that value, even with the
higher ultimate payload, as indicated in
Figure 4 just above.

What Spacex is currently saying on its website is that SS
will deliver “100+ metric tons” of payload to LEO. What I found in this analysis, under these assumptions, is that payload might be as high as 160
metric tons. That would be at 120 metric
tons of inert mass for SS. If the production
SS inert is actually only 100 tons, those
20 tons of difference could become an increase in payload to 180 tons. But,
even if the max payload is only 160 tons, it is still higher than any version of
SLS. The launch price is a wild guess at
about twice that of a Falcon-Heavy.

Prices are far more speculative. The latest public comments by Jim Bridenstine
of NASA indicates they are estimating about a $1.5B ($1500M) cost per
launch. That would be for the initial
Block 1 SLS. There’s no pricing
information for subsequent versions (Blocks 1B and 2B), but they have to be no less than Block
1, and probably higher. The NASA Users’ Guide for SLS lists LEO
payload as 70 metric tons for Block 1,
105 tons for Block 1B, and 130
tons for Block 2B.

What all that really means is that Spacex’s SS/SH will
probably send more payload to LEO than any version of SLS, and for a very substantially-lower
price. Those comparative data, crude though they are, are given in Figure 6.

Figure 6 – Price and Payload Comparisons (see update 5-30-2020)

**Final Remarks**

This analysis has been for LEO payload delivery only. I have not considered any tankers, and thus did not consider trips to the moon
or Mars. Anything outside LEO requires
refilling on orbit from tankers, and
essentially to the full propellant load of 1200 tons (I show about 9 tons
landing propellant). Those issues get
covered separately, elsewhere, at some future time.

One of the main differences between this analysis and my
prior efforts is the more detailed job I did getting to a realistic estimate of
staging velocity, and realistic
estimates for the three booster recovery burns.
This shows up in the lower staging velocity near 1.8 km/s, versus the 2.5-ish that I had in the previous
study. Recovery propellant turned out to
be a bigger percentage of the total first stage propellant load, than I had thought before.

This is out-of-line with results for expendable
boosters, whose stage velocity is nearer
3 km/s. But it is driven by the need to
recover the booster all the way back to the launch site, which has a far higher recovery propellant
requirement than just recovering somewhere downrange. Falcon-9 has closer to the 3 km/s staging
velocity, since its initial design heritage
really was as an expendable. It usually
recovers far downrange on a drone ship.

**Related Prior Studies**

26 September 2019 --
Reverse Engineered “Raptor” Engine Performance

24 September 2018 – Relevant Data for 2018 BFS Second Stage

17 April 2018 -- Reverse
Engineering the 2017 Version of the Spacex BFR

23 October 2017
-- Reverse-Engineering the ITS/Second Stage Of the Spacex BFR/ITS System

Figure A – Orbital Mechanics of the Deorbit Burn

Figure B – The Effects of Including Deorbit Burn on Expected
SS Performance and Payload

Figure C – Revised SS Spreadsheet, Part 1

Figure D – Revised SS Spreadsheet, Part 2

Figure E – Summary of Performance Estimates for “Tanker1”
Concept

Figure F – “Tanker1” Spreadsheet, Part 1

Figure I –

Figure II –

**Update 5-30-2020 SS/SH and “Tanker1” Estimates**

Two topics get covered in this update:

(1)
The performance estimates for Starship (SS) and
Superheavy (SH) get revised to include the effects of SS conducting a deorbit
burn before its entry and landing.

(2)
I look at a tanker concept suggested by a Musk
tweet, in which SS flies without payload
to reduce its ascent propellant burn,
with the leftover propellant available to deliver.

**Orbital Mechanics**

The first thing to cover is the size of the deorbit
burn, from a typical low Earth orbit
(LEO). I picked 400 km orbital altitude
as “typical”. The approach is shown in
Figure A: reduce speed (the deorbit burn),
so as to enter on an ellipse with apogee at LEO, and a perigee sufficiently deep in the
atmosphere to ensure re-entry.

I looked at perigee altitudes of 0, 50,
and 100 km; the deorbit burn delta-vees
were very little different. Since the
typical end-of-hypersonics altitude for Earth re-entry is around 50 km, I picked that altitude. The corresponding entry conditions are shown
in the figure. For Earth, entry interface altitude is generally taken
to be 140 km.

The resulting deorbit delta-vee is about 106 m/s, or 0.106 km/s. This is about the same as the factored-up
landing burn delta-vee, based on the
expected low-altitude terminal “belly-flop” speed for SS. Therefore,
it is a very significant effect upon the landing propellant allowance.

**Effects Upon SS / SH Design**

I figured this deorbit burn would require thrust-vector
control, therefore requiring gimballed
engines. That means it has to be done
with a sea level Raptor engine, those
being the ones with 15 degree gimbal capability. The vacuum Raptors are essentially
fixed-mounted.

As it turns out,
there was a small and easily-made addition to my spreadsheets to add
this burn to the SS landing delta-vee budget,
since the final landing burn must be made with the same sea level Raptor
engines.

What this does is to increase the landing propellant budget
at the expense of the ascent propellant budget in the second-stage SS. In order to meet a fixed final velocity, payload in SS must reduce somewhat to
compensate. There is very little effect
on the first stage and resulting stage point conditions. This is shown in Figure B. Payload carried to LEO reduces from the
prior 160 metric ton estimate to 149 metric tons. It still qualifies as “100+ tons”, per what is on the Spacex website for this
vehicle.

I include here as Figures C and D the two-part image of the
spreadsheet in which this was figured.
This is minimally-changed from the version originally used to calculate
SS / SH performance in the original article.
The two-level nested iteration still exists, driven by the need to achieve the same LEO
speed with the ascent propellant, given
that only payload is available as a variable.

Because changing payload affects the ignition mass of
SS, which is the payload of SH, there are also effects upon stage point
conditions, and the SH booster
flyback. However, because the change to SH “payload” is smaller
in proportion, these effects are
minimal. But we must have that inner
iteration loop on stagepoint velocity built-in to verify that outcome.

Therefore, this
update has the best estimates of performance available for the SS / SH
system, including all known
effects, and the best available data
about all the inputs.

**That is figured at 120 metric tons of inert SS mass, and 250 metric tons of inert SH mass, the two biggest remaining unknowns in this design.***Full propellant loads in both stages, and payload of no more than about 149 tons, is feasible for “typical” circular LEO insertion.***Tanker Concepts**

What I had been previously evaluating as a tanker design was
not what Musk had in mind. I had thought
to add extra tanks at the expense of cargo decks and bulkheads in the SS
design, so that the SS max payload (149
tons) could be delivered on-orbit to another SS. The ascent propellant is the refill
requirement, which is about 1182 metric
tons as listed in Figure D. With 149
tons of payload per Figure C, that would
require about 8 tanker flights to refill one SS on orbit, for a total of 9 launches.

__Musk’s tweets reveal he had a different concept in mind__. He said the initial tankers could just be cargo/passenger SS vehicles.

**. The lower ignition mass lowers the ascent propellant requirement (and the final deorbit and landing requirement), so that the leftover propellant is available to deliver on-orbit.**

*To make that work, you fly unmanned and utterly without payload*
I had never even considered this approach, and had never investigated how much leftover
propellant there would be to deliver.

*I was surprised (and pleased) to find that this was*__far better__than just carrying propellant-as-payload at full ignition mass.__Update 5-31-2020__: this result is in error. See below.

Indeed, Musk’s tweets
reveal that this was his initial tanker concept (denoted in my study as
“tanker1”), to be followed later by an
ill-defined dedicated tanker design.

**Tanker Performance Estimates**

In Figure E is summarized what I found when I added a second
modification to my spreadsheet aimed at tanker performance, in addition to the first that added deorbit
burn.

*I was astonished to find the ascent propellant greatly reduced, leaving a huge leftover available to deliver during the refilling process.***I found an error in my calculation of tanker-deliverable propellant. DO NOT USE that result!!! The revised calculation shows 9 flights required to fully refuel SS in LEO. If the other SS is rigged to carry propellant as its 149 metric tons of payload, that requires 8 flights to fully refuel the SS in LEO. See revised data in Figures I, II, and III below.**

__Update 5-31-2020__:**INCORRECT DELIVERED PROPELLANT !!! DO NOT USE!!! See instead Figure I below.**

According to these estimates, a single SS flown without any payload can
deliver over 600 tons of unused propellant to another SS on orbit! This is because the ascent propellant
requirement is reduced at the lower ignition mass.

**I can still hardly believe what I found!***What that makes feasible is*__only two tanker flights__necessary to fully-refill another SS on-orbit!
The change to the spreadsheet removes the outer iteration
loop, since the end velocity requirement
is fixed, and so is the payload. The only thing left to do is figure the
propellant actually used to make the ascent,
and subtract it and the landing budget from the initial propellant
load. That is the deliverable excess. This is seen in part 2 of the spreadsheet
images.

The numbers to support this are shown in the spreadsheet
images of Figures F and G.

**INCORRECT DELIVERED PROPELLANT !!! DO NOT USE!!! See instead Figure II below.**

Figure G – “Tanker1” Spreadsheet, Part 2

**INCORRECT DELIVERED PROPELLANT !!! DO NOT USE!!! See instead Figure III below.****Impact of These Results**

Why is this important?
Ultimately, it is about (1) reducing
the price of delivering tonnage to LEO.
And (2) reducing the number of tanker flights to send that tonnage
beyond LEO.

Consider: you launch
a SS / SH carrying 149 metric tons of payload to LEO. It arrives there with just enough propellant
left to deorbit and land, while still
carrying that same payload. That last
covers all the various abort possibilities.
Assuming (as in the original article) that such a launch prices at
$200M, the unit price of payload to LEO
is then $200M/149 metric tons = $1.34M/ton = $1342/kg = $609/pound. That is incredibly low; another factor of 10, and it starts looking like an airline ticket!

To go to the moon or to Mars, one must refill that SS on-orbit with only two more SS / SH flights in
the “tanker1” configuration.

**Assuming these also cost $200M each, the total launch price to send that 149 metric tons outside LEO is only about $600M! That computes as $4.03M/ton = $4027/kg = $1826/pound to the moon or Mars. That’s remarkable indeed for off-planet delivery, being about the same as orbital delivery today with our current launchers!**__Update 5-31-2020__: that figure is in error, do not use!!! See update 5-31-2020 below for corrected data.__And THAT is the effect of economy-of-scale and full reusability acting together__!**Final Remarks**

Spacex still has a very long way to go, before any of this becomes reality.

*But if they succeed, this will be a revolution in affordable spaceflight like nothing we have ever seen before!*
Among the many issues to resolve is rough field landing
capability for SS. So far, Spacex has only landed stages upon very
thick, steel-reinforced concrete pads
that are smooth and level, or hard steel
decks that are smooth and very-nearly level.
Both

__weight/pad area__and__center-of-gravity height-to-leg span ratio__are inadequate for rough-field operations, as the SS design currently exists.
This is important to resolve, even for LEO or suborbital point-to-point
operations on Earth. After all, there will always need to be capability for
an off-site abort landing, and there are
many places that offer only soft sand,
mud, or soft farmland for that.

---------------------------

__Update 5-31-2020__:**The nature of this error was incorrectly multiplying burnout mass by required mass ratio, to evaluate the**

*I found a serious error in my calculation of “tanker1” ascent propellant and propellant available to be delivered on-orbit.*__initial burn__of two burns. The correct procedure is to divide the ignition mass by the required mass ratio. Multiplying a burnout mass by mass ratio is only appropriate for the

__final burn__of a multi-burn sequence.

The corrected data that replace the affected Figures E, F, and
G are given in Figures I, II, and III here in this update, along with a comparison to the “tanker0”
concept, which is reconfiguring a SS to
carry its payload as deliverable propellant,
not in the ascent and landing tankage.

These data show that “tanker1” (flying with no payload and
delivering the unused ascent propellant) will require 9 tanker flights to
refill one payload-carrying SS to leave LEO,
for a total of 10 launches for the one departure. That departing SS carries 149.2 metric tons
of payload, per these calculations. At a guessed $200M per launch, that’s $2000M = $2B to depart LEO. The unit cost figures are $13.4M/metric ton =
$13,400/kg = $6090/pound to the moon or Mars.

The corresponding data for “tanker0” (reconfiguring to carry
the payload as deliverable propellant) requires 8 tanker flights to refill one
payload-carrying SS to leave LEO, for a
total of 9 launches for the one departure.
Again, the departing SS carries
149.2 metric tons of payload. At the
same guessed launch cost of $200M per launch,
that’s $1800M = $1.8B to depart
LEO. The unit cost figures are $12.1M/metric ton = $12,100/kg = $5470/pound to
the moon or Mars.

**Correcting the error shows it to be comparable to (and only**

*The “tanker1” idea is not the cost-effective breakthrough that I initially thought.*__slightly more expensive__than) a dedicated tanker design.

Either way, these
figures are comparable to what I had estimated before, comparing Starship to NASA’s SLS, and to Falcon-Heavy, Falcon-9,
Atlas-5, and Delta-4, as possibilities for sending payloads one-way
to Mars. The Starship is more than an
order of magnitude less expensive as a delivery vehicle for larger payloads to
Mars than SLS, and the payloads it can
deliver are far larger than SLS. If
refilled there, it is the

__only vehicle that can return__. Those data were posted almost 2 years ago on this site in this article:
2 September 2018,

**Payload and Cost-Effectiveness Comparisons to Mars**(part of a 5 article series, with the other four among the 8 references cited)**Revised**

**Figure E**– Summary of Performance Estimates for “Tanker1” Concept

**(replaces Figure E above)**

**Revised “Tanker1” Spreadsheet, Part 1**

**(replaces Figure F above)**

Figure III –

**Revised “Tanker1” Spreadsheet, Part 2 (replaces Figure G above)**