Update 4-8-2024:
Should any readers want to learn how to do what I do (estimating
performance of launch rockets or other space vehicles), be aware that I have created a series of
short courses in how to go about these analyses, complete with effective tools for actually
carrying it out. These course materials are
available for free from a drop box that can be accessed from the Mars Society’s
“New Mars” forums, located at http://newmars.com/forums/, in the “Acheron labs” section, “interplanetary transportation” topic, and conversation thread titled “orbital
mechanics class traditional”. You may
have scroll down past all the “sticky notes”.
The first posting in that thread has a list of the classes
available, and these go far beyond just the
two-body elementary orbital mechanics of ellipses. There are the empirical corrections for
losses to be covered, approaches to use
for estimating entry descent and landing on bodies with atmospheres, and spreadsheet-based tools for estimating
the performance of rocket engines and rocket vehicles. The same thread has links to all the materials
in the drop box.
The New Mars forums would also welcome your
participation. Send an email to newmarsmember@gmail.com to find out
how to join up.
A lot of the same information from those short courses is
available scattered among the postings here.
There is a sort of “technical catalog” article that I try to main
current. It is titled “Lists of Some
Articles by Topic Area”, posted 21
October 2021. There are categories for
ramjet and closely-related,
aerothermodynamics and heat transfer,
rocket ballistics and rocket vehicle performance articles (of
specific interest here), asteroid
defense articles, space suits and
atmospheres articles, radiation hazard
articles, pulsejet articles, articles about ethanol and ethanol blends in
vehicles, automotive care articles, articles related to cactus eradication, and articles related to towed decoys. All of these are things that I really
did.
To access quickly any article on this site, use the blog archive tool on the left. All you need is the posting date and the
title. Click on the year, then click on the month, then click on the title if need be (such as if
multiple articles were posted that month).
Visit the catalog article and just jot down those you want to go see.
Within any article,
you can see the figures enlarged, by the expedient of just clicking on a
figure. You can scroll through all the
figures at greatest resolution in an article that way, although the figure numbers and titles are
lacking. There is an “X-out” top right
that takes you right back to the article itself.
----------
I also want to keep this one fairly short. The ascent-averaged and vacuum specific impulses for the propulsion presumed here, came from earlier analyses of various engines contained in other articles posted on this site. What I did here was to first size an all-expendable two-stage to orbit (TSTO) vehicle as a baseline, then afterwards, look at two different ways to make the first stage recoverable and reusable. Then I compared those to previous single stage to orbit (SSTO) results.
The basic mission is surface launch to low Earth orbit (LEO)
at about 300 km altitude, eastward at
low inclination, as illustrated in
Figure 1. The surface circular
orbit speed 7.9 km/s is the “ideal speed” to reach, which covers the effects of both the kinetic
energy of the speed at that altitude,
and the potential energy of being at that altitude.
There is a staging point that is just barely
exo-atmospheric in terms of the rather modest ascent speeds reached at that
point (and which is not at all “exo-atmospheric” in terms of orbital speeds at
only around 50-60 km altitude). This
stage point for the expendable baseline was presumed to be at 2 km/s, and very nearly horizontal locally. I estimated 5.6% each, for gravity and drag
losses, at 0.45 km/s each, to be covered by adding to required delta-vee
(dV). That makes the min mass
ratio-effective dV to “barely reach LEO” 8.8 km/s. To which must be added a presumed rendezvous
dV budget of 0.6 km/s, and a deorbit dV
of 0.1 km/s, for a total expendable
mission dV = 9.5 km/s.
Figure 1 – The Basic Mission Parameters and Possible Design
Approaches
In the expendable baseline,
the first stage must accelerate from zero to the staging velocity
Vstg, and shoulder essentially 100% of
the drag loss, and a presumed 80% of the
gravity loss. It does this while carrying
the fully-loaded second stage as its payload,
complete with the payload shroud protecting the actual payload during
atmospheric ascent. Note that the second
stage shoulders a presumed 20% of the gravity loss, and none of the drag loss; not “right”,
but well in the ballpark.
In only the recoverable/reusable first stage scenarios, the first stage coasts downrange toward an
atmospheric entry at essentially the staging speed (approximately Mach 7). To be recovered as an exposed aluminum
structure item, this stage must
decelerate to an acceptable entry speed,
presumed to be 2.5 Mach, and
deploy grid fins to keep it below Mach 3 in the thin air, and a terminal speed of only about Mach 2.5
in the thicker air close to the surface.
To land retro-propulsively, it
must “kill” the 2.5 Mach terminal speed of about 0.75 km/s, factored up by 1.5 to cover any losses plus a
budget for hovering-and-diverting clear of obstacles.
There would seem to be two ways to “redesign” the expendable
baseline for first stage recovery and reuse.
First, one might
offload some payload from an otherwise fully-loaded second stage, which lightens the second stage and increases
its share of the mission dV, while
reducing the ascent dV requirement on the first stage, due to both the decrease in payload mass, and the decrease in staging velocity. Second stage recovery was not
considered, since it must be a real entry
vehicle.
Second,
one keeps the payload and second stage exactly the same as the
baseline, and just increases the size of
the first stage, so that it also has enough
propellant to land. Going into
this, my preconceived notion was the
larger first stage would be slightly more favorable in terms of overall payload
fraction, because I thought we would
have to offload around half the payload.
More details of exactly how I went about about the baseline
design, and the two re-designs for first
stage recovery, are shown in Figure 2. I used a fixed 10 metric tons of baseline delivered
payload.
Figure 2 – The Best Design Analysis Notions and Baseline
Data Going Into This Study
The baseline design was done using simple rocket equation
calculations in a spreadsheet, to
include kinematic acceleration requirements on both stages to determine overall
stage thrust requirements. Being only a
bounding calculation, I did not size
numbers of engines and their individual thrusts and turndown ratios. Modest propulsion technologies being
presumed, pressure turndown ratios might
be in the 2 to 2.5 class. Thrust
turndown ratios would be similar in vacuum,
and a bit more at sea level.
The baseline analysis used in both stages a presumed
inert/ignition mass fraction of 4% (0.04),
pretty much representative of bare aluminum alloy tankage exposed as the
stage airframes. The dV requirements and
effective exhaust velocities Vex determine mass ratio MR = exp(dV/Vex) for each
stage, from which the
propellant/ignition mass fraction can be computed as 1 – 1/MR.
The payload/ignition mass fraction is then 1 – inert
fraction – propellant fraction. Then the
payload mass and payload fraction determine the ignition mass, from which then everything else in the weight
statement scales. Vex scales from input
Isp as Vex = gc * Isp / 1000.
This calculation,
done for the two stages with the second stage as the payload for the
first, is quite simple as illustrated
in Figure 3. Note that the payload
shroud is jettisoned at staging. The
“overall payload fraction” is the actual delivered payload mass divided by the
complete launch vehicle ignition mass. Note also that gees estimated at stage burnout
masses are acceptable without throttling-down or shutting-down engines, being under 4 gees. This thing sized out near 138 metric tons at
launch, for a 10-ton payload
delivery, about half the size of a
Falcon-9. Under these analysis conditions, it shows just over 7% delivered payload, relative to launch mass.
Figure 3 – The Baseline Expendable Vehicle Results
The re-design calculations are a bit more complex, but are still done the same way with the
rocket equation and some kinematic acceleration constraints for the stages, that bound the thrust levels. For those,
the first thing to do was to copy the stage weight statements and thrust
results into new worksheets, and then
copy the dV items for a reanalysis of dV requirements, that includes those for stage 1
recovery. To this I added a revision
analysis for the lower stage inerts, to
account for adding grid fins and landing legs.
Values for these are simply presumed,
and added to the expendable stage inert mass value. Also,
one has to iterate the payload reduction to produce the same total
propellant mass in the first stage, but
with an increased stage inert mass.
There are also added kinematic requirements on the first
stage during its unladen descent. The
min thrust needs to be a bit less than the dry-tanks burnout weight, so that it can gently set down. That also enables hover at thrust equal to
weight. The max thrust relates to how
soon the landing burn begins. I simply
arbitrarily set it to 2 gees, for an effective
1 gee kinematic rate over gravity.
These worksheets include a revised dV analysis that includes
the descent dV for stage 1, located on
the right of the worksheet. For the
reduced-payload approach, I had to let
the staging velocity shift downwards,
responding to the greater dV capability of the second stage at reduced
payload. This reduced the first stage
ascent dV requirement, accomplished on
the laden weight statement. The descent
dV requirement has to be met unladen,
which determines the descent propellant requirement, that must be carried as if it were payload
during the ascent. See Figure 3. What
surprised me was how little payload I had to offload, which then had very little effect on the
overall payload fraction, still being
about 7%. The launch weight only
increased by about a ton.
Figure 4 – The Reduced-Payload Approach Results
For the larger-first-stage approach, the payload and second stage are entirely
unchanged, and the first stage need only
be large enough to accommodate both the ascent dV laden, and the descent dV unladen. See Figure 5. Again,
you do the first stage descent first to determine the descent propellant, in turn carried as if it were added payload
during the first stage ascent. I
actually did this larger first stage analysis first, developing the basic format. Then I copied it to the reduced-payload
worksheet and modified it into that analysis.
I was surprised to see the smaller overall payload fraction
nearer 6%, but in retrospect, the larger first stage increases the launch
mass significantly (nearer 164 tons compared to the original 138 tons), so the payload fraction reduction should not
have been such a surprise. There is no
iteration in this approach, we are
simply up-sizing the first stage to a larger propellant mass and inert mass.
Figure 5 – The Bigger First Stage Approach Results
Results and Recommendations
Because the overall propellant fraction fell more when upsizing
the first stage, than it did reducing
payload mass, I have to recommend
reducing payload mass as the better design approach to making an
expendable first stage recoverable and reusable! This is in fact exactly what SpaceX did with
their Falcons, when they made the first
stage cores recoverable and reusable,
although their recovery path proceeds back up-range, while what I analyzed here leads to recovery
far downrange. They have to offload
more payload to make that work, because
the first stage descent dV requirements are substantially higher when reversing
flight direction.
To Summarize:
If designing all-expendable vehicles, I can get up to about 5% payload fraction out
of a LOX-LH2 SSTO with modest engine technology and a good compromise-bell
conventional nozzle (based on the previous SSTO article). I can get about 7% payload fraction out of a
TSTO that uses LOX-LH2 modest technology vacuum engines in the second
stage, and LOX-RP1 modest technology
compromise-bell engines in the first stage.
The expendable TSTO and SSTO should be more-or-less competitive with
each other, but not with any renewable
technologies. The costs of thrown-away
hardware will be too high to compete.
Of the possibilities to make the first stage of the TSTO
recoverable and reusable, I can offload
just a tad of payload and recover the first stage far downrange for re-use. The payload fraction actually stays near 7%
doing that (it would drop if I recovered up-range)! It drops to about 6% if I up-size the first
stage instead (and would also drop further if recovering up-range). The expendable SSTO just cannot compete with
either one of those, having both a lower
payload fraction and much more hardware thrown away (first stages and SSTO’s
have many engines, second stages have
few).
As the previous SSTO article listed among the references
below indicates, there is no possibility
of a reusable SSTO that is chemically powered,
with more than about 1% payload,
if even that.
References
All of these listed below are earlier articles posted on
this site that relate to this topic in some way. Use the blog archive on the left side of this
page as a fast navigation tool to find them quickly. All you need is the article title and its
posting date. Click on the year, then on the month, then on the title if more than one article
was posted that month. The 2-4-23
article (bold italic) has a lot of the earlier propulsion work used here. The other 11-12-18 article (also bold italic)
was the first to explore free expansion designs as an alternative to
conventional bells. The bold italic
4-2-24 article at the top of the list, is the previous SSTO bounding study.
4-2-24 Bounding
Calculations for SSTO Concepts (compared to TSTO in this article)
3-3-24 Launch
to Low Earth Orbit: 1 or 2 Stages?
3-4-24 Launch
to Low Earth Orbit: Fixed Geometry Options
6-20-23 TSTO
Launch Fundamentals
2-4-23 Rocket
Nozzle Types (bells and aerospikes)
10-1-22 Rocket
Engine Calculations
2-9-21 Rocket
Vehicle Performance Spreadsheet
2-16-20 Solid
Rocket Analysis (solid ballistics and more)
11-12-18 How
Propulsion Nozzles Work
No comments:
Post a Comment