**Propellant is sized to make the outbound and return voyages in one stage (no stage-off or jettisoning of anything along either way, just unload of the dead-head payload at destination). The journey baseline is low Earth orbit to low Mars orbit, and back.**

*It still assumes fairly large dead-head payloads, but only carried on the outbound voyage!*
How the ships or the payload get to low Earth orbit is
unaddressed. How the payload gets
delivered to Mars’s surface from low Mars orbit is unaddressed. How the ships are refueled and reloaded in
low Earth orbit is unaddressed. What is
addressed here, that is unlike the
earlier simpler study, are the separate
inert weights associated with the payload section, the propellant tankage section, and the
engine-with-its-associated-subsystems.
The minimum vehicle acceleration requirement is increased to 0.5
gee, except for one system deemed
adequate at 0.33 gee.

The previous closely-related article was “Colonization Ship
Study”, dated 9-9-19. It examined the simpler-to-analyze case of
carrying the dead-head payload both ways (outbound and return), so that there was one mass ratio and one
delta-vee (dV) to cover the round trip.
That scope was multiple fundamentally-different forms of
propulsion: nuclear explosion drive (or
“pulse propulsion”) as it was envisioned in the late 1950’s, nuclear thermal propulsion (as a version of
the solid core NERVA for which engine prototypes were tested), Hall effect ion propulsion based off of
plentiful, cheap, and solid-phase-but-sublimable iodine, LOX-LH2 chemical rockets, and storable-propellant rockets.

**but with the highly-variable tested or envisioned characteristics of six different design approaches. It is these six that are compared in terms of the ratio of initial ignition to dead-head payload weight, using the same maximum-attractive criterion of 5 as in the earlier study. These six approaches and their relative states of technological readiness are:**

*Scope here is only nuclear thermal rocket propulsion,*
(1) as-tested NERVA solid core,

(2) the best-anticipated solid-core NERVA derivatives that
never got built or tested,

(3) the particle bed solid core reactor engine (one version
of which was “Timberwind”, which got
some exploratory testing revealing unresolved problems, but never reached the engine prototype
stage),

(4) the so-called “nuclear light bulb” gas core concept
(some insufficient feasibility tests),

(5) the open-cycle gas core concept restricted to
regenerative cooling, meaning no
radiator required (some insufficient feasibility testing), and

(6) the open-cycle gas core concept with a large, heavy external waste heat radiator (some
insufficient feasibility testing).

To accomplish this investigation, I added an additional worksheet to the colony
ships.xlsx spreadsheet file that I used for the earlier study. Unlike the previous study, there are no closed-form ways to get from dead-head
payload to a vehicle weight statement.
The calculation uses iterative convergence of the propellant tank inert
weight, and iterative convergence of
engine thrust sizing in terms of the resulting vehicle acceleration gee
capability.

For this investigation,
the payload section is presumed to be some sort of enclosed hull, with adequate insulation, radiation shielding, and micrometeor protection for a crew built
into it, in some unspecified way.

**The dead-head payload size drives everything in the end, as all results are directly proportional to the dead-head payload input.***The ratio of dead-head payload mass (contained inside) to the loaded payload section mass is a fraction denoted as fpay.***Thus:***For this investigation, dead-head payload was arbitrarily set at 100 metric tons, and fpay = 0.8, the same for all six engine types.*
Loaded
payload section mass = dead-head payload mass/fpay

Payload
section inert mass = loaded payload section mass – dead-head payload mass

The propellant tank section contains the common propellant
for all nuclear thermal engine approaches:
liquid hydrogen (LH2). This is a
harsh cryogen, requiring solar heating
control, significant insulation, and some sort of cryocooler to control
evaporation. This is simply going to be
heavier than the lightest-possible single-wall bare tank.

*The ratio of propellant mass to loaded tank mass is the fraction ftank.***Thus:***The single value ftank = 0.95 was used for all six engine types.*
Loaded
tank section mass = propellant mass/ftank

Tank inert
mass = loaded tank mass – propellant mass

Propellant
mass must be the sum for two burns at differing dead-head payload

One
starts with a guess for tank inert, and
iteratively converges it to the result

The engine “section” is the nuclear thermal rocket engine
(or engines, for redundancy), complete with turbopumps and control
equipment, a radiation shadow shield for
the crew up forward, plus any waste heat
radiator that may be required (if regenerative cooling alone cannot do the
job).

*This radiator (if present) and the core-plus-engine hardware***, which is dimensionless under the definition that both thrust T and engine weight We (on Earth) are measured in force units. This ratio is different for each engine type, as is the resulting specific impulse. The values I used follow:***lead to a characteristic engine thrust/weight ratio T/We*__Type__

__Isp, s__

__T/We__

__development status__

NERVA 725 3.6 as-tested
in engine prototypes

derNERVA 1000 5 derivative-of-NERVA, estimated on paper

PBR 1000 7 particle-bed
reactor, based on “Timberwind”

Nuc.lt.blb 1300 10 “nuclear light bulb” gas core
concept, some feasibility

Open GCR 2500 20 open-cycle gas core concept
limited to regenerative cooling

GCR+rad 6000 0.5 open-cycle
GCR with heavy waste heat radiator,
concept

For this kind of data,
the main results used to size the vehicle are the exhaust velocity Vex
(km/s), and the engine system inert mass
(metric tons). These are:

Vex,
km/s = (Isp, s)*9.8067/1000

Engine
system inert mass, metric tons = thrust level, KN/(9.8067 * T/We)

For the remaining vehicle characteristics, all the concepts except “GCR+rad” were
required to size thrust level such that the vehicle acceleration at the initial
ignition mass was at or just above 0.5 gee.
This corresponds to about a 15 minute Earth departure burn, definitely short enough to qualify as
“impulse”, and not have the orbital dV be
factored-up for gravity loss to be mass ratio-effective.

With the data I used,
the GCR+rad system could not reach half a gee, but converged fairly well at 0.33 gee. This is less than a 30 minute burn, still short enough to consider as “impulsive”
for Earth departure.

Max gee at final burnout weight upon Earth return should be
under about 5, but this proved not to be
a problem.

It’s a two-level iteration:
first set a thrust level, then
converge your guess for propellant tank inert weight with the final result of
the calculation for tank inert weight. Then
check and adjust your thrust level for the right Earth departure gee
level. Then converge the tank inert
weight again. Repeat the process as
needed to get however-close a convergence you deem tolerable (0.1-0.01 ton
range).

**The values used are worst-cases that do not go together; the difference is a nice little “kitty” to cover midcourse corrections. Earth departure = Earth arrival = 3.84 km/s. Mars arrival = Mars departure = 1.83 km/s.**

*The orbital dV’s that are required are those for getting from low orbit onto a min-energy Hohmann transfer ellipse.*

*These sum to 5.67 km/s outbound in a heavier ship carrying payload, and 5.67 km/s return in a lighter ship with no payload and already having burned off some propellant on the outbound voyage.*
Factored for losses,
these dV figures become the mass ratio-effective dV’s for design
purposes. Those and the Vex for each
engine type give you the mass ratio MR for each engine type, one for outbound, the other for return.

MR =
exp(sum dV/Vex) with both velocities in
km/s, and the sum dV for outbound or
return

You start the calculation with the return voyage by summing
up the inerts (payload section inert + tank inert + engine inert), plus zero dead-head payload, as the burnout mass at Earth arrival.

**Apply the appropriate mass ratio to get Mars departure ignition mass. The difference in ignition vs burnout mass is the propellant expended for the two burns of the return voyage.***This starts with a best guess for inert tank mass, as well as for installed engine thrust level.*
The next step is the outbound voyage. The Mars departure ignition mass, plus the dead-head payload mass, is the Mars arrival burnout mass. Apply the appropriate mass ratio to get the Earth
departure ignition mass. The difference
in ignition vs burnout mass is the propellant expended for the two burns of the
outbound voyage to Mars.

The sum of the two propellant quantities is the total
propellant for the round trip. Divide
this total propellant by ftank to find the total loaded tank mass. The difference between loaded total tank mass
and total propellant mass is the inert tank mass.

*This resulting inert tank mass is what your guess for tank inert mass must converge to! The best next guess is close to the last result.*
Thrust divided by Earth weight is the vehicle acceleration
gee estimate. This is done at each of
the 4 vehicle masses: Earth departure
ignition, Mars arrival burnout, Mars departure ignition, and Earth arrival burnout. Two of these are of real interest: Earth departure ignition (min gees), and Earth arrival burnout (max gees). The other two conditions fall in-between. You
must adjust your installed thrust level to achieve min gees. Then iterate to convergence again on tank
inert mass.

Max gees at Earth arrival burnout did not prove to be a
problem, but should fall under 5 gees
for the most tolerable results. Be sure
you check for that outcome.

The last calculation sets up weight statements and estimated
dV performance for the six propulsion types,
using the data already calculated.
The initial part of the weight statement is the vehicle buildup from
payload and inert items to Earth departure ignition mass. Subtracting the total outbound propellant
gives the Mars arrival burnout mass. Their
ratio produces an outbound summed dV for both burns, to be calculated for each type (for
comparison to the initial summed requirement).

That Mars arrival burnout mass, less the dead-head payload, is the Mars departure ignition mass. Subtracting the return voyage propellant
produces the Earth arrival burnout mass.
Their ratio produces a return summed dV for the two burns, done for for each propulsion type (for
comparison to that summed requirement).

The deviations of these weight statement dV’s from the
required values reflect just how closely you converged your tank inert
weights. These should be only trivially
off (by under 0.001 km/s = 1 m/s).

__If you see bigger errors, you didn’t converge your tank inert masses closely enough.__The effect of being “off” on min gee (as set by installed thrust level) is small, when compared to the effect of being “off” on guessed tank inert mass.
At the very bottom of the weight statements are the vehicle
payload fractions, in both
definitions. One is the conventional
definition: dead-head payload mass /
Earth departure ignition mass. You
probably should not consider anything under 0.2 for a practical colonization
ship design. Its inverse is Earth
departure ignition mass / dead-head payload mass. In that definition, you probably should not consider anything over
5 for a practical colonization ship design.

**But, if dead-head payload mass is too small compared to Earth departure ignition mass, the resulting design will be inherently very expensive to build and to operate, just like with ocean-going transport when the cargo mass is small compared to the tonnage of the ship.**

*This limit (in either form) is inherently a very fuzzy judgement call.*
What I got for this study is given in Figures 1 and 2, a two-part image of the completed spreadsheet
worksheet page. Of the six propulsion
types, four look reasonably-to-very
attractive. These are the derivative of
NERVA, some form of PBR, and the two gas core concepts that do not
require a huge waste heat radiator. The
as-tested NERVA falls short because its engine thrust/weight is too low and the
resulting large engine inerts drive the vehicle inerts, constrained by the large thrust level to
achieve min acceleration gees. The gas
core with radiator falls short because of the gigantic, heavy radiator.

Figure 1 – Image of Nuclear Thermal Spreadsheet Analysis, Part 1

Figure 2 -- Image of Nuclear Thermal Spreadsheet
Analysis, Part 2

Near-term, the higher
Isp and engine thrust/weight of the derivative NERVA could be realized in a few
short years, to an engine prototype
ready for flight test. The PBR concept
would take a few more years than that,
since no prototype engines were ever ground tested, and some fundamental problems identified in
testing of “Timberwind” components remain unresolved. The gas core concepts would require
several-to-many years to reach a flight-testable prototype, since only very sparse lab-type feasibility
demonstrations were ever done;
plus, there is no guarantee of
eventual success, either.

My own recommendation would be to base an initial design
around the derivative NERVA as lowest-risk option of acceptable benefit, and plan on replacing it later with one of
the non-radiator gas core designs,
should that development prove successful.

Figure 3 sketches a ship design concept based on the
derivative of NERVA, figured at 100
metric tons of dead-head payload delivered to Mars. Volume of LH2 and a guess for tank L/D set
the tank dimensions. Everything else
scales one way or another from that, as
a first approximation. Everything about
the weight statement and thrust level sizing is proportional to dead-head
payload size. Dimensions would scale as
the cube root of mass, provided that L/D
ratios are preserved.

This vehicle rough-out delivers the same design dead-head
payload to Mars as the proposed Spacex “Starship” design. The differences are several: this vehicle never lands on Mars (delivery to
the surface is by

__unspecified other means__), this vehicle must make a full Mars arrival burn into low orbit (“Starship” only makes a final touchdown burn after an aerobraking direct entry), and this vehicle returns all the way to low Earth orbit for reuse, unrefueled.__It never needs to survive any sort of atmospheric entry__.
This design makes the round trip single-stage
unrefueled. The Spacex “Starship” is
entirely one-way only, unless and until it
can be refueled on the surface of Mars from local resources.

There is enough payload section volume to support a crew of up
to 15, at about 300 cubic meters per
person, in addition to the volume
occupied by the dead-head payload, at a
payload specific gravity averaging only 0.3.

Figure 3 – Sketch Layout of Derivative-NERVA Colonization
Ship, at the 100 Ton Payload Size

This result says a Mars colonization ship able to carry 100
metric tons of dead-head payload one-way to Mars, and return to Earth with no payload, all one-stage, is not that large an item. It is

__not__large enough to spin for artificial gravity like a rifle bullet, but it__is__large enough to spin end-over-end (like a baton) for artificial gravity. At about 3.24 rpm, there is about one full gee available in the payload section. That spin rate is tolerable to untrained, unacclimatized people, for long-term exposure.
The insulation and meteor shielding is about a meter thick
on the payload section, meaning it can
double as radiation protection. If those
layers of fabric average 0.20 effective bulk specific gravity, that is some 20 g/sq.cm shielding mass, adequate for solar flare events, and offering some reduction of galactic
cosmic radiation. The insulation and
tank shell thickness of the propellant tank section was assumed to be 0.1
m. Engine section length was just a
guess.

__Key to this design__as-sized is carriage of dead-head payload to Mars, but

__not from Mars__. The return dead-head payload must be zero! If not, the propellant tank section must be significantly larger, to the detriment of the payload fraction criteria. Any crew and their life support must come out of that dead-head payload allowance (meaning near-zero crew on the return voyage).

These results look more favorable than the
otherwise-comparable nuclear thermal option in the earlier study.

*That is precisely because dead-head payload is only carried one-way in this study, and it was carried both ways in the earlier study.*__That is one huge effect__. But the trend from the earlier study applies here as well: if we design for a farther destination than Mars, the design won’t look so attractive in terms of the payload fraction criteria.
The restriction of zero dead-head payload on the return
voyage is not as constraining as it first sounds, when one considers the goal is building a
colony with these payloads.

**Later, when an operating economy results in two-way trade, one will need***During that process there is little-or-nothing to ship home to Earth, except information, which is better sent electronically.*__commerce ships__,__not colonization ships__. But, by the time that need arises, significantly-better propulsion technology should have become available.**The best near-term option of the six nuclear thermal approaches, for a Mars colonization ship design, is the derivative-NERVA nuclear thermal propulsion approach (Isp ~ 1000 s and engine T/W ~ 5). For 100 metric tons dead head payload, the initial ignition mass is about 500 metric tons. That means for 1000 metric tons dead-head payload, the sized ship will initially mass about 5000 metric tons. For 2000 tons payload, the ship will be around 10,000 tons, etc. This is restricted to orbit-to-orbit operation,**

*Brief Result Summary:*__and to no dead-head payload on the return voyage__. Even the small 100-ton payload size is large enough to spin end-over-end for artificial gravity at near 1 gee and an easily-tolerated spin rate. The payload section insulated design (if a meter of fabric layers) also inherently provides a fair amount of radiation protection.

After Elon had his presentation, not sure if it was 16 or 17. Zubrin commented that the earth escape portion of the ship is too valuable. And would be better to boost back it into high eliptical orbit, so it comes back two weeks, ready for another payload.

ReplyDeleteThis would likely only make sense if both parts aerobraked.

More like LEO NTR booster for Starship.

But it would have to compete with Operational SpaceX rockets that deliver fuel to LEO at 6k$ per ton. Costs being aspirational from 2016 presentation.

I'm not at all sure of what you are talking about. Care to define better? -- GW

ReplyDeleteI was just reading this on Atomic Rockets, and your fuel tank is a cylinder. Considering this is a pure space application, one large sphere would be the best shape. I assume you are thinking the fuel tank would be build on earth and launched up empty?

ReplyDeleteThe tank serves more than one function. It must be longer than it is wide in order to get the spin radius for artificial gravity at a tolerable rpm.

DeleteDepending upon exactly which nuclear thermal engine gets used, you may be able to surface launch to orbit. That requires an average Isp exceeding about 1300-1500 sec. I did not explore that issue.

GW

For gravity, I strongly suspect you would be better off with a huge sphere tank and a scaffold of the distance you need. The only reason for a cylinder is if you are carrying the fuel tank alone up through the atmosphere.

DeleteIf you build the tank in orbit, and carry the engines up from earth that would be the best compromise, but space construction is definitely not near term tech, especially on that scale.

If I choose a cylindrical tank, its inert mass then serves two purposes. If I choose a spherical tank plus a truss structure, I have a bit less tank inert, but I have a lot more truss inert. That acts in the wrong direction to maximize mass ratio. -- GW

Delete