I decided to examine the historical record on this issue and
developed the table you see below. All the weights are in
thousands of pounds; the Ideal DV colum is in kft/sec. Prop wt
refers to the weight of propellants. The Isp numbers are
referenced as far as possible to vacuum Isp. The engine data are
from CPIA Revised Liquid Propellant Engine Manual (1972), and
Rocketdyne, SEP, Aerojet, and Pratt and Whitney product
information sheets. The vehicle weight data are from Isakowitz’
Space Launch Systems, 1st Ed. Ideal DV is calculated from the
rocket equation [DV = Isp * g * ln (gross/(gross-prop))]. The
column labeled PMSMF refers to the Propulsion-Free Structural
Mass Fraction, which refers to the weight of the stage after the
engine is removed, divided by the gross weight. This residual
weight includes the electronics, tankage, and so forth.
Here are the data:
Stage Prop Wt Gross Wt Engine Wt Isp PFSMF Ideal DV
Titan II Stg 1 260.0 269.0 3.258 287 2.13% 31.372
Black Arrow Stg 1 28.7 31.1 1.426 250 2.99% 20.755
Saturn V Stg 1 4584.0 4872.0 93.080 265 4.00% 24.114
Titan III Stg 1 294.0 310.0 3.343 283 4.08% 26.959
Titan IV Stg 1 340.0 359.0 3.343 283 4.36% 26.731
Delta 6925 Stg 1 211.3 223.8 2.528 295 4.46% 27.383
Atlas E 248.8 266.7 4.371 312 5.07% 27.073
Saturn V Stg 2 993.0 1071.0 17.400 425 5.66% 35.821
Zenit Stg 1 703.0 778.0 26.575 337 6.22% 25.364
Titan III Stg 2 77.2 83.6 1.144 312 6.29% 25.796
Saturn IB Stg 2 233.0 255.0 3.480 425 7.26% 33.504
Titan II Stg 2 59.0 65.0 1.102 308 7.54% 23.611
Saturn IB Stg 1 889.0 980.0 16.072 263 7.65% 20.111
Ariane 5 Stg 1 342.0 375.0 3.630 430 7.83% 33.624
Saturn 5 Stg 3 238.0 263.0 3.480 425 8.18% 32.179
Energia Core 1810.0 1995.0 21.000 452 8.22% 34.583
Zenit Stg 2 178.0 198.0 2.480 350 8.85% 25.816
Black Arrow Stg 2 6.5 7.8 .531 265 9.52% 15.450
Titan IV Stg 2 77.2 87.0 1.144 312 9.95% 21.919
Delta 6925 Stg 2 13.4 15.4 .207 267 11.82% 17.416
From this I conclude:
1. The effects of propellant density are for real. The Titan
stages used N2O4 and Aerozine 50, which has a bulk specific
gravity of about 1.04. Black Arrow used H2O2 (85%) and kerosene,
with a bulk specific gravity of 1.3. The LO2/RP-1 vehicles
(Saturn first stages, Atlas, and Delta Stage 1) are about
0.98 on the bulk specific gravity scale. The hydrogen vehicles
remaining are at a bulk specific gravity of about 0.42 for their
propellants. The top performers are the dense storable vehicles.
2. Scale matters. First stages do better than upper stages in
PFSMF, but less well in overall DV, partly because their engines
have to lift the whole stack. It takes a 5 million pound
behemoth like the Saturn V to get the PFMSF down to 4 percent
with LO2/RP-1, but storable vehicles do it handlily at much
smaller scales. Note that scale matters less than density. The
second best system in PFSMF is the second smallest in scale.
3. Note that the upper stages seldom have engines with thrust
greater than weight, or for that matter sea-level compatible
nozzles. Just a warning before someone proposes sending the
Saturn V stage II into the SSTO sweepstakes.
4. The Delta 6925 Stage II is pressure fed, but still has a
pretty good PFSMF.
5. Black Arrow Stage 1’s dry weight includes 154 pounds of
electronics, which would weigh 20 pounds these days, and the
engines have thrust to weight ratios of about 41. This is really
bad by modern standards. A Black Arrow Stage 1 with structure
made of something other than spot-welded aluminum, modern
electronics, and a decent engine T/W of about 75 (Acheived with
the AR-4, by the way -- another peroxide/kerosene engine) could
easily achieve orbit if the Isp were 290 or so.
6. Atlas doesn’t even rate structurally. Stages that need to
accomodate strapons also suffer (hence the reduced PFSMFs for
Titan III and IV). Titan II has the title at the moment, and
didn’t even need to use pressure-stabilized tanks.
7. There are several stages that have SSTO-class delta-V figures
(anything over 30000 fps). The Titan II first stage can itself
deliver 1400 pounds to low earth orbit as it sits, with no
modifications to engine or structure. That’s pretty impressive,
even if a load of propellant for it costs $2.5 miilion.
MITCHELL BURNSIDE CLAPP, Capt, USAF
Chief, Flight Operations, X-33
Thanks for the info, Mitch...I`ll have to add this to my ELV
database.
: Here are the data:
:
: Stage Prop Wt Gross Wt Engine Wt Isp PFSMF Ideal DV
: Titan II Stg 1 260.0 269.0 3.258 287 2.13% 31.372
: Black Arrow Stg 1 28.7 31.1 1.426 250 2.99% 20.755
: Saturn V Stg 1 4584.0 4872.0 93.080 265 4.00% 24.114
: Saturn V Stg 2 993.0 1071.0 17.400 425 5.66% 35.821
[snip]
: From this I conclude:
[snip]
It`s probably unwise to disagree with a "professional" like Mitch,
but doesn`t the table above suggest LOX/LH2 *is* easier after all...
for a medium size reusable VTOVL SSTO like DC-1, at least...? If you
play around with the rocket equation, it seems as if you need high Isp
more than the high bulk density of RP-1+LOX (or H2O2). Especially
since the the bulk density of a good LOX/LH2 system can get fairly
close if you start factoring some good design factors, and the
square/cube law on tank mass vs. volume. Traditionally, rocket
designers have tried to maximise thrust/weight and high bulk
density at launch when Isp less important. Once you reach higher
altitudes and velocities (a rocket spends little time [<20%] in the
dense parts of the atmosphere anyway), you want a high exhaust velocity
and LH2 yields a far higher Isp than kerosene or UDMH, so you switch
to a large LH2 "core" stage and jettison the empty boosters.
---
If we compare the Titan II 1st stage and Saturn V 2nd stages
(apples vs. oranges, I know, but these are the "best" structures
[LH2 & non-LH2 fuel-] that have flown) and upgrade the engines
to the highest vac. Isp currently available, we get the following
result:
Dry wt. (metric tons) Wet wt.(mt) Engine wt.(mt) Isp
S-II 35.4t 485.8t 7.9t 458s (SSME)
T-II 4t 122t 1.5t 327s (Proton)
Volume (cubic meters) vol./(dry-eng.wt)
S-II 1,400m3 50m3/mt
T-II 100m3 40m3/mt
dV(S-II)=11.78 km/s
dV(T-II)=10.93 km/s
: 3. Note that the upper stages seldom have engines with thrust
: greater than weight, or for that matter sea-level compatible
: nozzles. Just a warning before someone proposes sending the
: Saturn V stage II into the SSTO sweepstakes.
Yup, let`s add 3.9 metric tons worth of J-2 engines to the S-II,
to increase the vacuum thrust to 7,200 kilonewtons (vs. 1913kN for
the Titan II). Both rockets are now "on the same starting line", but
the S-II still wins at 11.3km/s vs. 10.9km/s.
---
If we add a payload to both vehicles to force down the delta-V to
10.5km/s (=the Delta Clipper`s theoretical capability to a 29.8deg
400km orbit and back to Earth again), the payload
fraction for the S-II becomes 1.8% and the mass ratio for the rocket
itself (with seven J-2s) is 0.08. For an RD-253:powered Titan II
we get a payload fraction of 0.5% and a mass ratio of 0.0327. This
means that a peroxide or hydrazine rocket will have to be much
heavier than a comparable LH2 SSTO, and carry more propellant
although the fuel tanks probably will be smaller.
---
Net-people with a fairly impressive track record such as Mitch
and Henry Spencer claim hydrocarbon fuels would be better, though.
Other "experts" with an equally impressive background have
told me LH2 is the only serious option for a reusable SSTO,
at least if we have to use 1990s materials technology and don`t
plan to make a Sea Dragon -size monster. Burning kerosene with
the hydrogen at liftoff does increase the performance, however.
Who is correct...?
: 7. There are several stages that have SSTO-class delta-V figures
: (anything over 30000 fps). The Titan II first stage can itself
: deliver 1400 pounds to low earth orbit as it sits, with no
: modifications to engine or structure. That’s pretty impressive,
: even if a load of propellant for it costs $2.5 miilion.
An interesting question: would it be cheaper (on a cost-per-pound
basis of course) to launch 635kg on a single-stage Titan II than
3,180kg (=the comparable TSTO capability) on a 2-stage T-II...?
Mitch says 118t of UDMH/N2O4 costs $2.5 million. The second stage
fuel load (26.7 metric tons)
would cost ~$570,000 so the total fuel cost goes up to $3 million
but the capability increases by 500%!!
---
If a dry first stage costs $20 million, the cost per kilogram
becomes $35,000 ($22.5 million divided by 635kg). For the two-
stage option to do worse than that, the _entire Titan rocket
would have to cost at least $113 million (=$35,000 * 3,180kg) or the
tiny second stage would cost 5.5 times as much as the first stage!
This, I believe, is why expendable SSTOs like the Atlas haven`t
become popular. The second stage increases performance far more
than overall costs.
:
:
: MITCHELL BURNSIDE CLAPP, Capt, USAF
: Chief, Flight Operations, X-33
:
--
MARCU$
---------------------------------------
Do you think you can tell,
A smile from a veil,
Do you think you can tell...?
Marcus Lindroos
PL 402 A
07880 Liljendal, FINLAND
Email:mlin...@aton.abo.fi
Fax:358-15-616667
WWW:http://www.abo.fi/~mlindroo
--------------------------------------
Boy, I hate to argue religion, but did you *have* to quote delta V in
units of kft/sec? AArgh!
____________________________________________
Geoffrey A. Landis,
Ohio Aerospace Institute at NASA Lewis Research Center
physicist and part-time science fiction writer
Well, I was educated where engineering was taught in SI units, too,
which is really nice until you have to go buy parts. Multiply by
0.3048 to get km/sec...it's not hard.
Mitchell
Depends on how sophisticated your approach is. The historical preference
for LH2 has been at least partly the result of naive analyses which made
incorrect assumptions. My own opinion is that a lot of the "wonder fuel"
reputation of LH2 dates from the 1950s, when its advantages were known,
but its disadvantages were unknown or inadequately appreciated. Even then,
if you look hard, you can find people saying "disregarding the theory, in
real systems the denser propellants seem to yield better performance",
but the hydrogen mythology has been amazingly tenacious.
>...the bulk density of a good LOX/LH2 system can get fairly
>close if you start factoring some good design factors, and the
>square/cube law on tank mass vs. volume...
Uh, Marcus, *what* square/cube law on tank mass vs. volume? That's not
the way rocket tanks work; their skin thickness does not remain constant
as they scale up. Typically they are primarily pressure vessels, and
pressure vessel mass scales with volume, not surface area.
Don't forget that hydrogen tank skins need insulation.
Even people who still buy into the hydrogen myth to some extent will
concede, nowadays, that the tank/contents mass ratio has one value for
hydrogen and another (better) value for everything else.
>...Once you reach higher
>altitudes and velocities ... you want a high exhaust velocity
>and LH2 yields a far higher Isp than kerosene or UDMH...
You also want a low engine mass, since engine mass counts directly against
payload mass (or, equivalently, is seriously bad for the mass ratio). LH2
loses badly here, which is something the "wonder fuel" advocates in the
1950s missed completely. Much of the engine scales like the tanks, with
volume flow rather than mass flow -- even exhaust nozzles have to function
as pressure vessels. (Note that Mitch's PMSMF numbers don't include the
engine mass.)
>If we compare the Titan II 1st stage and Saturn V 2nd stages
>(apples vs. oranges, I know, but these are the "best" structures
>[LH2 & non-LH2 fuel-] that have flown)...
I'm still somewhat unconvinced that T2 is the best non-LH2 stage.
Mitch's numbers for Atlas included the booster engines, i.e. they are
for the "first stage" of the Atlas. It's the "second stage" that has
the high mass ratio.
>: 3. Note that the upper stages seldom have engines with thrust
>: greater than weight, or for that matter sea-level compatible
>: nozzles. Just a warning before someone proposes sending the
>: Saturn V stage II into the SSTO sweepstakes.
>
>Yup, let`s add 3.9 metric tons worth of J-2 engines to the S-II,
>to increase the vacuum thrust to 7,200 kilonewtons (vs. 1913kN for
>the Titan II). Both rockets are now "on the same starting line"...
No, sorry, Marcus, they still aren't -- the J-2 is not a sea-level
engine, and the engine mass will go up (and performance down) when
that's allowed for.
Even disregarding that, note that by any reasonable measure, the
S-II was the beneficiary of far more radical weight-reduction efforts
than the T2. T2 was a much more relaxed design than the Atlas, since
it could use the two-stage configuration that was "ground ruled out"
for Atlas.
>...means that a peroxide or hydrazine rocket will have to be much
>heavier than a comparable LH2 SSTO, and carry more propellant
>although the fuel tanks probably will be smaller.
Everyone who has proposed non-LH2 SSTOs has immediately admitted
that their gross mass will be higher. The objective of the exercise
is lower *dry* mass and/or larger design margins. Gross mass and
propellant mass are almost irrelevant to cost. The *only* place
where gross mass is of real importance is for an upper stage (since
the lower stage has to lift the upper stage's gross mass), and this
has certainly encouraged the hydrogen myth.
>Other "experts" with an equally impressive background have
>told me LH2 is the only serious option for a reusable SSTO,
>at least if we have to use 1990s materials technology...
That is indeed the common wisdom; it happens that it doesn't hold up
on careful analysis, when the unspoken assumptions are hauled out into
the open and examined carefully.
>Mitch says 118t of UDMH/N2O4 costs $2.5 million. The second stage
>fuel load (26.7 metric tons)
>would cost ~$570,000 so the total fuel cost goes up to $3 million
>but the capability increases by 500%!!
Again, nobody has particularly disputed that, other things being equal,
two-stage vehicles lift heavier payloads. The point is that other
things *aren't* equal, especially for reusable vehicles.
--
The problem is, every time something goes wrong, | Henry Spencer
the paperwork is found in order... -Walker on NASA | he...@zoo.toronto.edu
Blair
p.s. The recent issue of Astronomy has an article on SSTOs as
well, but it is less technical-oriented.
> I'm still somewhat unconvinced that T2 is the best non-LH2 stage.
> Mitch's numbers for Atlas included the booster engines, i.e. they are
> for the "first stage" of the Atlas. It's the "second stage" that has
> the high mass ratio.
By the way, thanks for replying to Marcus' post. I was in Huntsville
all week and could not reply myself. But I would have said about what
Henry did (which is kinda creepy if you think about it).
When I calculated the PFSMF for the Atlas E,
I considered all the engines. The MA-5 ensemble was
included, booster and sustainer both, and the data were pulled
straight from a Rocketdyne information sheet I scooped up
at the Joint Propulsion Conference. Since both engines are
required to achieve takeoff, and are fed from the same tank, the
case is not analogous to strapons, which have separate propellant
sources. You will notice in the table that the Delta 6925 stage
one does a little better than Atlas, despite having the load paths
needed for the strapons. This is fair, since the tankage on
Delta 6925 stage 1 provides no propellant to the strapons.
But let's leave the booster segment off of both sides of the
equation and consider the sustainer as the sole propulsion source.
The booster engine alone weighs 3336 lb; the sustainer weighs
1035 lb. The gross weight of the booster-free stage becomes
263.4 klb, the empty weight of the stage becomes 14.564 klb, and
the empty weight less the engine is 14564-1035 = 13529 lbs. The
propulsion free structural mass fraction becomes (13.529)/(263.4)
= 5.14 percent. This is worse than the way I calculated it
originally, which means to me that the booster engines have better
thrust to weight ratios than the sustainer.
The ideal delta-V of the sustainer-only Atlas E is
ln(263.4/14.564) * 312 * 32.174, or 29,062 ft/sec. With an
aggressive takeoff T/W that might make orbit, but actually
the staging of the engines makes orbit possible
It is possible that the weights of the Atlas ICBM were less than the
Atlas E SLV. I don't have those data at hand. But with or without
the booster, Atlas E is third behind Titan and Delta for lightest US
SLV structure.
If you take the extra step of calculating the pounds of non-engine
mass per cubic foot of propellant, you find _slightly_ lower values
for the enormous Saturn S-II hydrogen stage. The number for the
S-II is 1.44 lb/ft^3, for the Titan II it's 1.58 lb/ft^3, and for the
Black Arrow stage 1 it's 2.46 lb/ft^3.
For comparison, if you take the NASA Langley Access to Space option
3 SSTO vehicle, and strip the engines and stuff specific to reusability
off, you get a value of 0.5 lb/ft^3, which sounds like structural
paint to me. :-)
Mitchell Burnside Clapp