Propellant desity, scale, and lightweight structure
Mitchell Burnside Clapp
lightest aerospace structures ever built. The thing that keeps
it from being a single stage to orbit machine is its relatively
heavy and low performance engines.
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
Marcus Lindroos INF
: There has been some speculation about Atlas being one of the
: it from being a single stage to orbit machine is its relatively
: heavy and low performance engines.
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
--------------------------------------
Geoffrey A. Landis
cla...@plk.af.mil writes:
>...
> developed the table you see below. All the weights are in
> thousands of pounds; the Ideal DV colum is in kft/sec. Prop wt
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
Mitchell Burnside Clapp
>
> Boy, I hate to argue religion, but did you *have* to quote delta V in
> units of kft/sec? AArgh!
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
Henry Spencer
>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
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
bromley blair pat
articles relating to new engine designs, and propellant choices
(with special regards to propane) in the summer issues of
Aerospace America (June and July).
Blair
p.s. The recent issue of Astronomy has an article on SSTOs as
well, but it is less technical-oriented.
Mitchell Burnside Clapp
> 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
strap...@gmail.com
frank....@gmail.com
How would the availability of a functional aerospike engine effect this debate?
The aerospike enthusiasts insist that their dream child can achieve a 20 to 30 % improvement in fuel use over almost the entire ascent of a vehicle. 20% less fuel means 20% mass to lift, which, of cause, might be offset by the bulkier engines. Even a 10% reduction in overall vehicle mass does wonders for a vehicle's SSTO status.
Of cause aerospikes are the aerospace equivalent of vaporware, so we are debating theoretical hardware.
Take care all.
Regards
Frank Scrooby
Fred J. McCall
(PDT):
>
>How would the availability of a functional aerospike engine effect this debate?
>
>
>The aerospike enthusiasts insist that their dream child can achieve a 20 to 30 % improvement in fuel use over almost the entire ascent of a vehicle. 20% less fuel means 20% mass to lift, which, of cause, might be offset by the bulkier engines. Even a 10% reduction in overall vehicle mass does wonders for a vehicle's SSTO status.
>
may be conservative. Why do you think an aerospike needs to be
"bulkier"? The basic engine is the same. The only real difference is
replacing the fixed bell.
>
>Of cause aerospikes are the aerospace equivalent of vaporware, so we are debating theoretical hardware.
>
the way to ground test before the vehicles they were intended for were
cancelled for non-engine related reasons. Since an aerospike engine
provides the most advantage when used in an SSTO configuration, you
don't see a lot of development outside that application.
--
"The reasonable man adapts himself to the world; the unreasonable
man persists in trying to adapt the world to himself. Therefore,
all progress depends on the unreasonable man."
--George Bernard Shaw
Robert Clark
frank....@gmail.com
May 30
Wow, that's really a blast from the past. I was reading this on Google
Groups, and it pulled up the original thread from 1995:
sci.space.policy ›
Propellant desity, scale, and lightweight structure.
https://groups.google.com/forum/?hl=en#!topic/sci.space.policy/PZgWB9WWhNw
Quite key is that the rocket equation is exponential in nature. Ray Kurzweil
has noted people don't commonly think of how rapidly exponential functions
grow in scale, as people are more accustomed to linear change. But it is
notable that even a 10% increase in Isp, such as the F9 booster going from
its 310 s Isp to the 343 s Isp of the upper stage, can result in a 100%
increase in payload, at least for a SSTO.
The importance of altitude compensation, such as by the aerospike, extends
beyond the SSTO case however. I estimated using alt.comp. on a two-stage
vehicle could improve payload ca. 25%, not as dramatic as the SSTO case but
still significant. For instance the ESA was considering for a while spending
billions to upgrade the Ariane 5 to the Ariane ME to deliver that degree of
increase in payload. But it could be done for a fraction of that cost just
by using alt.comp.
Actually, the increase likely would be closer to 40% (!) for the Ariane 5
case. I had calculated that the parallel staged Falcon Heavy could get a 40%
increase in payload by using alt.comp. on the core stage and side boosters.
It's likely about the same increase would hold for alt.comp. applied to the
core stage and side boosters of the Ariane 5.
The problem though for alt.comp. via the aerospike is that it would be an
expensive change to convert existing engines with cylindrical combustion
chambers to toroidal ones for an aerospike nozzle. But the point of the
matter is it doesn't have to be by the aerospike. There are lots of ways of
getting alt.comp. by just adding an extension to the existing nozzle of a
conventional engine. Type in the search box on my blog
Exoscientist.blogspot.com for some possibilities how it could be done the
term: altitude compensation.
Bob Clark
------------------------------------------------------------------
Single-stage-to-orbit was already shown possible 50 years ago
with the Titan II first stage.
In fact, contrary to popular belief SSTO's are actually easy.
Just use the most efficient engines and stages at the same time,
and the result will automatically be SSTO.
Blog: Http://Exoscientist.blogspot.com
------------------------------------------------------------------
Lofty Goat
> ... a functional aerospike engine ... vaporware....
Perhaps someone can clear something up for me:
In a conventional rocket engine with bell-type nozzles the pressure of
expanding gas against the inside of the nozzle propels the rocket.
The greater the area of said nozzle, the more energy is recovered from
the expanding gas which explodes within, up to a point.
In an aerospike rocket engine, what does the pressure of the expanding
gas act against to propel the rocket?
BTW, I've read all sorts of very imaginative explanations of aerospikes,
yet none has shown a believable diagram of the forces at work.
(Yes, the air forms one surface of a "virtual bell". I see. Right.)
It'd be interesting.
--
Goat
Fred J. McCall
-0500:
>On Sun, 3 Jun 2018 03:58:11 -0400, "Robert Clark" wrote:
>
>> ... a functional aerospike engine ... vaporware....
>
>Perhaps someone can clear something up for me:
>
>In a conventional rocket engine with bell-type nozzles the pressure of
>expanding gas against the inside of the nozzle propels the rocket.
>
>
>The greater the area of said nozzle, the more energy is recovered from
>the expanding gas which explodes within, up to a point.
>
>
>In an aerospike rocket engine, what does the pressure of the expanding
>gas act against to propel the rocket?
>
reaction. Throw gas out back, rocket goes forward. No requirement to
'push against' anything.
>
>BTW, I've read all sorts of very imaginative explanations of aerospikes,
>yet none has shown a believable diagram of the forces at work.
>
forward. All the bell does is try to make more of the gas go directly
'aft' as it exits.
--
"Some people get lost in thought because it's such unfamiliar
territory."
--G. Behn
JF Mezei
> The same as any other rocket. Mass thrown after equals motion
> forward. All the bell does is try to make more of the gas go directly
> 'aft' as it exits.
by same amount force.
If this were just it, why need an engine bell since once the gase has
been accelerated as it leaves the combustion chamber it has done all its
pushing, right?
Sinxe, as the highly compressed gas leaves the combustion chamber and
wants to expand, doesn't the engine bell capture some of this energy as
expanding gas hits the engine bell and is diverted towards the back and
tush bell pushes rocket forward?
Fred J. McCall
22:17:47 -0400:
>On 2018-06-03 17:26, Fred J. McCall wrote:
>>
>> The same as any other rocket. Mass thrown after equals motion
>> forward. All the bell does is try to make more of the gas go directly
>> 'aft' as it exits.
>>
>
>I get the "acceletate 1gr of gas backwards and you get pushged forwards
>by same amount force.
>
there?
>
>If this were just it, why need an engine bell since once the gase has
>been accelerated as it leaves the combustion chamber it has done all its
>pushing, right?
>
opposite reaction' thing is about. Without something like an engine
bell, gas coming out the back is headed in all sorts of directions,
with only some small portion of the momentum aimed 'aft', so you get
much less reaction 'forward'.
>
>Sinxe, as the highly compressed gas leaves the combustion chamber and
>wants to expand, doesn't the engine bell capture some of this energy as
>expanding gas hits the engine bell and is diverted towards the back and
>tush bell pushes rocket forward?
>
You want the gas molecules headed 'aft' at essentially ambient
external pressure. This is why 'sea level' engines have relatively
small bells while vacuum engines have much larger bells (because the
lower pressure allows the exhaust to 'spread'). The bell doesn't
'push' anything. It's still about the momentum. This is why
aerospikes work, by the way. At low altitudes the air flow that makes
up the 'outside' of the virtual bell is at relatively high pressure,
which forces the exhaust to be 'directly aft' in a relatively short
distance. As you gain altitude, the lower pressure equates to a
'larger' bell where the gas has a longer path before it is headed
'aft'.
Jeff Findley
fjmc...@gmail.com says...
the particles in the exhaust go in the direction you want. Without some
sort of nozzle (bell or aerospike), all that high pressure exhaust
exiting the throat of a rocket engine is going to end up in a wide cone
shape, greatly reducing efficiency. You can show that with high school
physics and geometry if you examine an individual particle that's
shooting off at a 45 degree angle instead of straight "down".
Note that with ion engines, you don't typically see a large bell nozzle
on the thing. That's because an ion engine already shoots the ions out
in pretty much a single direction.
You could also make an engine out of a linear accelerator. Shoot mass
out the back and the spaceship goes forward. But to make this
efficient, you'd need a super high exit velocity and a super light
accelerator. Those two things are not very compatible with each other,
so the whole thing isn't very practical, but it's a good thought
experiment.
Jeff
--
All opinions posted by me on Usenet News are mine, and mine alone.
These posts do not reflect the opinions of my family, friends,
employer, or any organization that I am a member of.
Paul B. Andersen
(In the following I will assume that the rocket works in a vacuum)
If the rocket has a only a throat, but no nozzle,
then the speed of the exhaust is equal to the speed
of sound in the exhaust, let's use the symbol c*.
(The pressure in the combustion chamber can't
push the exhaust through the narrow restriction
faster than the speed of sound.)
The force exerted on the rocket measured in the inertial frame
where the rocket is momentarily at rest is then:
-------------------------
F = dp/dt = dm(t)/dt⋅c* (1)
--------------------------
where p is the momentum and m(t) is the mass of the rocket.
( dm/dt is the mass flow rate through the throat)
At the throat, all the exhaust gas is moving in the right
direction, so that isn't the problem.
However, the exhaust gas is high pressure, and it will
expand _after_ it has left the throat, and the energy
released in this expansion will be converted to kinetic
energy in the gas molecules, but will NOT do anything
to accelerate the rocket.
In the nozzle the exhaust is expanding and
accelerating to supersonic speed.
(The nozzle is shaped something like a paraboloid.)
Let's call the exhaust speed at the nozzle exit vₑ.
The speed of the exhaust in the throat is constant c*,
and the ratio vₑ/c* is only given by the geometry of
the nozzle, so pₑ⋅Aₑ, where Aₑ is the area of the
nozzle exit, will also be fairly constant.
Let's call the pressure at the nozzle exit pₑ.
The force the exhaust exert on the nozzle is
higher than pₑ⋅Aₑ. This is because the pressure
increases inwards in the nozzle.
So if we call the average of the longitudinal
component of the pressure on the nozzle wall pₐ,
we can write:
F = pₐ⋅Aₑ = (pₐ-pₑ)⋅Aₑ + pₑ⋅Aₑ
The last term is the force exerted by the exhaust
that has left the nozzle.
The first term is the force from the exhaust
inside the nozzle, and this force is:
(pₐ-pₑ)⋅Aₑ = dm/dt⋅Aₑ
Thus:
----------------------
F = dm/dt⋅vₑ + pₑ⋅Aₑ (2)
----------------------
Since vₑ is constant, the first term is
obviously proportional to the mass flow rate.
Since vₑ is constant, the density ρ of the exhaust
at the exit must be proportional to the mass flow rate.
The pressure at the exit is:
pₑ = 0.5⋅ρ⋅vₑ²
so the pressure must also be proportional
to the mass flow rate.
This means that the second term is also
proportional to the mass flow rate.
Thus can equation (2) be simplified to:
F = Cp⋅dm/dt
where
Cp⋅ = (vₑ + pₑ⋅Aₑ/(dm/dt)), a constant.
Since Cp has the dimension speed, it is customary to write
Cp = Cf⋅c*
where:
c* = the speed of sound constant at the throat
Cf = the thrust coefficient constant of the nozzle
(typically about 2)
And the thrust can be written as:
---------------------------------
F = Cf⋅dm/dt⋅c* (3)
---------------------------------
The nozzle will typically double the thrust.
--
Paul
https://paulba.no/
JF Mezei
> If the rocket has a only a throat, but no nozzle,
> then the speed of the exhaust is equal to the speed
> of sound in the exhaust, let's use the symbol c*.
> (The pressure in the combustion chamber can't
> push the exhaust through the narrow restriction
> faster than the speed of sound.)
as it exits nozzle to capture this motion and convert sideways momentum
into forward momemtum.
Right ?
Just before it exists the engine nozzle, would it be fair to state that
all particules travel almost parralel to each other and in the vector of
thrust?
Could one also state that the the postion of engine between combustion
chamnber and nozzle capture the thrust of the fuel/oxydizer being
accelereated, while the engine bell generates thrust from high pressure
gases expanding after they have left the nozzle?
In the case of SRBs, what enables the far more modest engine bells?
Does the hollow tube nature result in lower pressure so as they leave
the SRBs, the gases don't expand enough to warrant the weight of large
engine bells?
Lofty Goat
wrote:
posterity.
How the do you think the mass of gas being pushed backwards applies
force to the rocket which it is intended to push forward? It's gas
pressure against the nozzle inside of which it is exploding.
That's how the "throw gas out the back" part pushes the rocket towards
the front. That equal-and-opposite force gets applied to the rocket
somehow. With a bell nozzle, that's how it is applied.
Now, try again.
Or better still, just post a link to a free body diagram of the gas and
the nozzle, and a similar diagram of an aerospike, and I'll look at it
myself.
I'm not that choosy. But the ones I've seen of aerospikes are Popular
Mechanics-type diagrams, which are fanciful at best. "The air forms one
side of a virtual bell."
Really?
I don't doubt that they work, but every explanation I've seen of *how*
they work reeks ever so faintly.
--
Goat
Fred J. McCall
-0500:
>
>That's how the "throw gas out the back" part pushes the rocket towards
>the front. That equal-and-opposite force gets applied to the rocket
>somehow. With a bell nozzle, that's how it is applied.
>
>Now, try again.
>
useful way to do so. It's more useful to just think of it as total
momentum of the system.
>
>Or better still, just post a link to a free body diagram of the gas and
>the nozzle, and a similar diagram of an aerospike, and I'll look at it
>myself.
>
to think I work for you.
>
>I'm not that choosy. But the ones I've seen of aerospikes are Popular
>Mechanics-type diagrams, which are fanciful at best. "The air forms one
>side of a virtual bell."
>
>Really?
>
>
>I don't doubt that they work, but every explanation I've seen of *how*
>they work reeks ever so faintly.
>
If it helps you, think of the flow field as 'attached' to the
vehicle...
Lofty Goat
<snip>
I'll try again in simpler words.
When you throw something backward to push a vehicle forward, you have
somehow to exert force on the vehicle. The force being exerted against
whatever is doing the throwing backward has to be transmitted to the
vehicle itself.
That's true of me sitting on a skateboard throwing a sledgehammer, or of
a rocket throwing cesium ions, or a rocket throwing an exploding (yes,
it expands rapidly enough to be said to "explode") mixture of kerosene
and LOX.
You're a rocket scientist, no? You're supposed to know this.
In the case of throwing the sledgehammer or of throwing heavy ions it's
perfectly clear: whatever it is that's imparting momentum to the
propellant transmits force to the vehicle.
(BTW, in the reference frame of the launchpad the total momentum of the
system is zero. Propellant moves backward, rocket moves forward. Net
momentum is conserved, and is the same as when it was sitting still.)
In the case of kerosene and LOX rocket, it is the propellant providing
the momentum. Yet if you squirted the stuff out into the air and just
lit it without having a bell nozzle wrapped around it, it wouldn't exert
much force on the rocket.
It is the force of the expanding gas against the bell which pushes it.
Gas expands in all directions. The bell directs it backward. Force
against the bell is how that old-timey equal-and-opposite pushes the
rocket.
You're a rocket scientist, no? Good. This is high-school physics.
So we get to the aerospike: expanding gas, and about 10% of the nozzle
area of a bell-type engine, and the gas allowed to expand into the
surrounding space once it leaves the vicinity of the nozzle.
So I asked a perfectly simple question:
What causes the pressure against the vehicle, at the nozzles, which
apparently has to be something 10x as great to provide the same thrust,
to be great enough to make such an arrangement more efficient than a
bell-nozzle engine?
And no, "the air being one side of a virtual bell" does nothing to
explain how greater force is transmitted to the rocket, seeing as how
that air is not rigidly attached to the engine mount.
And don't fucking carp about your consulting fee. You *volunteered* a
non-answer. I'm surprised such conduct earns any sort of fee at all.
So... this newsgroup is populated by people who understand physics, and
that is a physics question. Instead of being a jackass you might have
just answered it, or kept your peace and let someone else do so.
I'm still curious. It's an interesting topic.
--
Goat / RLW
JF Mezei
> In the case of kerosene and LOX rocket, it is the propellant providing
> the momentum. Yet if you squirted the stuff out into the air and just
> lit it without having a bell nozzle wrapped around it, it wouldn't exert
> much force on the rocket.
>
> It is the force of the expanding gas against the bell which pushes it.
the rocket forward.
As the highly compressed hot gas leaves nozzle, it is allowed to expand
in all directions. The bell redirects sideways expansion to push rocket
even more.
BUT, your argument fails to quantify which of these 2 pushes are the
most significant. It could be that the primary acceleration comes from
accelerating fuel inside combustion chamber to nozzle and that the bell
adds only a small amount from expansion of gas. Or could be the other
way around. I don't know. But unless this is quantified, you can't
assume that most of the thrust is generated by the bell.
Jeff Findley
rlwa...@gmail.com says...
>
> What causes the pressure against the vehicle, at the nozzles, which
> apparently has to be something 10x as great to provide the same thrust,
> to be great enough to make such an arrangement more efficient than a
> bell-nozzle engine?
>
THE AEROSPIKE NOZZLE, FREQUENTLY ASKED QUESTIONS LIST
BY KEN DAVIDIAN
https://www.hq.nasa.gov/pao/History/x-33/aero_faq.htm
From above:
5. I CAN SEE HOW AN AEROPIKE TRAVELLING THROUGH THE AIR COULD
CONSTRAIN THE EXPANDING COMBUSTION GASES WITH THE AIRFLOW COMING
AROUND IT. BUT HOW DOES IT WORK AT A STAND-STILL? ALSO, HOW DOES
IT WORK IN A VACUUM, WHEN THERE IS NO AIR PRESSURE TO CONSTRAIN
THE EXHAUST?
The air flow around the aerospike nozzle exhaust is not what
constrains the plume but rather the ambient pressure. Therefore,
whether or not the nozzle is moving, the exhaust plume will be
more or less the same (shear layer effects between the nozzle
exhaust and the quiescent air being neglected, of course). In a
vacuum there is no ambient pressure to constrain the exhaust
plume and the turning angle of the plume will be
(approximately) determined by Prantl-Meyer expansion wave
theory.
A good reference for this material is Modern Compressible Flow
with Historical Perspective by Anderson. (Reference given by
David Garza, dga...@ccvf.cc.utexas.edu , December 3, 1997)
Sergio
much it adds.
afterburners on Jets use variable "bell" shapes to get a lot more thrust.
Fred J. McCall
-0500:
>On Tue, 05 Jun 2018 13:17:54 -0700, Fred J. McCall wrote:
>
><snip>
>
>I'll try again in simpler words.
>
to overlook you being an arrogant, ill-mannered little prick. I
can't. How's this for simple words? You can sit on your thumbs and
whistle for an answer, even though the answer is pretty obvious if
only you weren't such a thickie. My experience with people in the
sci.physics group is that most of them are ill-mannered little shits.
Or perhaps that's just those who crosspost over here. In any case,
you are no exception.
<snip asshattery>
>
>So we get to the aerospike: expanding gas, and about 10% of the nozzle
>area of a bell-type engine, and the gas allowed to expand into the
>surrounding space once it leaves the vicinity of the nozzle.
>
>So I asked a perfectly simple question:
>
can conceive.
>
>What causes the pressure against the vehicle, at the nozzles, which
>apparently has to be something 10x as great to provide the same thrust,
>to be great enough to make such an arrangement more efficient than a
>bell-nozzle engine?
>
>And no, "the air being one side of a virtual bell" does nothing to
>explain how greater force is transmitted to the rocket, seeing as how
>that air is not rigidly attached to the engine mount.
>
>
>And don't fucking carp about your consulting fee. You *volunteered* a
>non-answer. I'm surprised such conduct earns any sort of fee at all.
>
they must provide you with. And learn some manners. Beggars can't be
choosers and you're the beggar here. I choose to tell you to pound
sand.
>
>So... this newsgroup is populated by people who understand physics, and
>that is a physics question. Instead of being a jackass you might have
>just answered it, or kept your peace and let someone else do so.
>
Paranoid much? If I could do that, at this point I would purely
because of the size of the stick up your ass. But other people are
welcome to do what they want. As I said, the answer is obvious if
only you weren't quite such a thickie.
>
>I'm still curious. It's an interesting topic.
>
but thinks he can get them by being a rude little asshat.
--
You are
What you do
When it counts.
Lofty Goat
aerospike engine more effectively apply force to the rocket.
Eventually I'll grope my own way to a well-documented answer. Sometimes
it helps to ask people who know. Just knowing the right word can be
most helpful in library research, whether on paper or electronically.
Sometimes when one asks someone says something which makes sense. And
sometimes they'll start flaming like Fred.
As I said, the topic is an interesting one.
--
Goat
Lofty Goat
>Here is a cite from NASA that includes a primary source.
>
>THE AEROSPIKE NOZZLE, FREQUENTLY ASKED QUESTIONS LIST
>BY KEN DAVIDIAN
>https://www.hq.nasa.gov/pao/History/x-33/aero_faq.htm
--
Goat
Jeff Findley
rlwa...@gmail.com says...
>
> That is where I'm seeking guidance: how does the expanding gas in an
> aerospike engine more effectively apply force to the rocket.
>
> Eventually I'll grope my own way to a well-documented answer. Sometimes
> it helps to ask people who know. Just knowing the right word can be
> most helpful in library research, whether on paper or electronically.
>
> Sometimes when one asks someone says something which makes sense. And
> sometimes they'll start flaming like Fred.
>
> As I said, the topic is an interesting one.
looking for peer reviewed papers, not high level summaries like in the
cites given so far. I'd start with AIAA Publications.
https://www.aiaa.org/Publications/
Or look at NTRS (NASA Technical Reports Server).
https://ntrs.nasa.gov/
You'll find papers like this:
MULTIDISCIPLINARY APPROACH TO LINEAR AEROSPIKE NOZZLE OPTIMIZATION
J. J. Korte*, A.O. Salast, H.J. Dunn?, and N.M. AlexandrovP
NASA Langley Research Center, Hampton, Virginia 23681
and
W.W. Follett*, G. E. Orient*, and A.H. Hadid$
Rocketdyne Division of Boeing North American, Canoga Park, CA 91309
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20040105540.pdf