Copyright 2012 Robert Clark
Credit: Gary Hudson
Preface
Arthur C. Clarke said:
Every revolutionary idea seems to evoke three stages of reaction. They may be summed up by the phrases:
1- It's completely impossible.
2- It's possible, but it's not worth doing.
3- I said it was a good idea all along.
SSTO's are at level 2 in Clarke's quote. Soon they will be at level 3.
Highlights
- Required high efficiency engines and lightweight stages for SSTO’s have existed since the 1970’s.
- The key figure of merit for a launch vehicle should not be payload to gross mass ratio, but payload to dry mass ratio.
- SSTO’s can have this payload to dry mass ratio greater than 1, better than any previous launcher.
- Reusable SSTO’s can be made the size of the very light (personal) jets, thus making routine manned spaceflight possible.
Abstract
___________________________________________________________________
Contrary to popular belief, SSTO's are actually easy - if done in the right way. The right way
can be summarized in one sentence:
If you use the most weight efficient stages and the most fuel efficient engines at the same time,
then the result will be SSTO capable whether you intend to or not.
___________________________________________________________________
Introduction
We all know that to get a good payload to space you want a high
efficiency engine. And we all know we want to use lightweight
structures so the weight savings can go to increased payload. So you
would think it would be obvious to use both these ideas to maximize
the payload to orbit, right?
And indeed both have been used together - for upper stages. Yet this
fundamentally obvious concept still has not been used for
first
stages. It is my thesis that if you do this, then what you wind up
with will automatically be SSTO capable. This is true for either
kerosene fueled or hydrogen fueled stages.
Part of the misinformation that has been promulgated is that the mass
ratio for SSTO's is some impossible number. This is false. We've had
rocket stages with the required mass ratio's since the 60's, nearly 50
years, both for kerosene and hydrogen fueled. Another part of the
misinformation is that it would require some unknown high energy fuel
and engine to accomplish. This is false. The required engines have
existed since the 70's, nearly 40 years, both for kerosene and
hydrogen fueled.
What has NOT been done is to marry the two concepts together for
first stages. All you need to do is swap out the low efficiency
engines that have been used for the high mass ratio stages and replace
them with the high efficiency engines. It really is that simple.
This makes possible small, low cost orbital vehicles that could
transport the same number of passengers as the space shuttle, about 7,
but would have a comparable cost to a mid-sized business jet, a few
tens of millions of dollars.
Then once you have the SSTO's they make your staged vehicles even
better because you can carry greater payload when they are used for
the individual stages of the multi-staged vehicle.
In disseminating the false dogma that SSTO's are not possible it is
sometimes said instead that they are not practical because the payload
fraction is so small. Even this is false. And indeed this is just as
damaging as making the false statement they are not possible because
the statements are often conflated into meaning the same thing. So
when those in the industry make the statement they are not
"practical", meaning actually they are doable but not economical, this
becomes interpreted among many space enthusiasts and even many in
the industry as meaning it would require some revolutionary advance to
make them possible.
The fact that you can carry significant payload to orbit using SSTO's
can be easily confirmed by anyone familiar with the rocket equation.
To get a SSTO with significant payload using efficient kerosene
engines you need a mass ratio of about 20 to 1. And to get a SSTO with
significant payload using efficient hydrogen engines you need a mass
ratio of about 10 to 1. Both of these the high mass ratio stages and
the high efficiency engines for both kerosene and hydrogen have
existed for decades now.
See this list of rocket stages:
Stages - Alphabetical Index.
http://www.friends-partners.org/partners/mwade/stages/staindex.htm
Among the kerosene-fueled stages you see that several among the Atlas
and Delta family have the required mass ratio. However, for the early
Atlas stages you have to be aware of the type of staging system they
used. They had drop-off booster engines and a main central engine,
called the sustainer that continued all the way to orbit. But even
when you take this into account you see these highly weight optimized
stages had surprisingly high mass ratios.
Atlas rocket derived SSTO
See for instance the Atlas Agena SLV-3:
SLV-3 Atlas / Agena B.
Family: Atlas. Country: USA. Status: Hardware. Department of
Defence Designation: SLV-3.
Standardized Atlas booster with Agena B upper stage.
Specifications
Payload: 600 kg. to a: 19,500 x 103,000 km orbit at 77.5 deg
inclination trajectory.
Stage Number: 0. 1 x Atlas MA-3 Gross Mass: 3,174 kg. Empty Mass:
3,174 kg. Thrust (vac): 167,740 kgf. Isp: 290 sec. Burn time: 120 sec.
Isp(sl): 256 sec. Diameter: 4.9 m. Span: 4.9 m. Length: 0.0 m.
Propellants: Lox/Kerosene No Engines: 2. LR-89-5
Stage Number: 1. 1 x Atlas Agena SLV-3 Gross Mass: 117,026 kg.
Empty Mass: 2,326 kg. Thrust (vac): 39,400 kgf. Isp: 316 sec. Burn
time: 265 sec. Isp(sl): 220 sec. Diameter: 3.1 m. Span: 4.9 m. Length:
20.7 m. Propellants: Lox/Kerosene No Engines: 1. LR-105-5
Stage Number: 2. 1 x Agena B Gross Mass: 7,167 kg. Empty Mass: 867
kg. Thrust (vac): 7,257 kgf. Isp: 285 sec. Burn time: 240 sec. Isp(sl): 0
sec. Diameter: 1.5 m. Span: 1.5 m. Length: 7.1 m. Propellants: Nitric
acid/UDMH No Engines: 1. Bell 8081
http://www.friends-partners.org/partners/mwade/lvs/slvgenab.htm
Looking at only the gross/empty mass of stage 1, you would think this
stage had a mass ratio close to 50 to 1. But that is only including the
sustainer engine. The more relevant ratio would be when you add in the
mass of the jettisonable booster engines to the dry mass since they are
required to lift the vehicle off the pad. These are contained within the
stage 0 mass at 3,174 kg. This makes the loaded mass now 117,026 +
3,174 = 120,200 and the dry mass 2,326 + 3,174 = 5,500 kg, for a mass
ratio of 21.85.
But this was using the low efficiency engines available in the early
60's. Let's swap these out for the high efficiency NK-33 [1]. The
sustainer engine used was the LR-105-5 [2] at 460 kg. At 1,220 kg the
NK-33 weighs 760 kg more. So removing both the sustainer and
booster engines to be replaced by the NK-33 our loaded mass becomes
117,786 kg and the dry mass 3,086 kg, and the mass ratio 38.2 (!)
How to calculate the delta-v the rocket can achieve
A problem with doing these payload to orbit estimates is the lack of a
simple method for getting the average Isp over the flight for an engine,
which inhibits people from doing the calculations to realize SSTO is
possible and really isn't that hard. To calculate the delta-V achievable
I'll follow the suggestion of Mitchell Burnside Clapp who spent many
years designing and working on SSTO projects including stints with the
DC-X and X-33 programs. He argues that instead of using the average
Isp you should use the vacuum Isp and just use 30,000 feet per second,
about 9,150 m/s, as the required delta-V to orbit for dense propellants.
The reason for this is that you can just regard the reduction in Isp at sea
level and low altitude as a loss and add onto the required delta-V for
orbit this particular loss just like you add on the loss for air drag and
gravity loss [3].
Using the vacuum Isp of 331 s and a 9,150 m/s delta-V
for a flight to orbit, we can lift 4,200 kg to orbit:
(1.) 331*9.81ln((117,786+4,200)/(3,086+4,200)) = 9,150 m/s.
This is a payload fraction of 3.4%, comparable to that of many multistage
rockets.
Note in fact that this has a very good value for a ratio that I
believe should be regarded as a better measure, i.e., figure of merit,
for the efficiency of a orbital vehicle. This is the ratio of the
payload to the total dry mass of the vehicle. The reason why this is a
good measure is because actually the cost of the propellant is a minor
component for the cost of an orbital rocket. The cost is more
accurately tracked by the dry mass and the vehicle complexity. Note
that SSTO's in not having the complexity of staging are also good on
the complexity scale.
For the ratio of the payload to dry mass you see this is greater than
1 for this SSTO. This is important because for every orbital vehicle I
looked at, and possibly for every one that has existed, this ratio is
going in the other direction: the vehicle dry mass is greater than the
payload carried. Often it is much greater. For instance, for the space
shuttle system, the vehicle dry mass is more than 12 times that of the
payload.
This good payload fraction and even better payload to dry mass ratio
was just by using the engine in its standard configuration, no
altitude compensation. However, for a SSTO you definitely would want
to use altitude compensation. Dr. Bruce Dunn in his report "Alternate
Propellants for SSTO Launchers" [4] estimates an ideal vacuum Isp of
375.9 s for high performance kerosene engines. Using altitude
compensation we may suppose our engine can achieve this while still
getting good performance at sea level. Modern engines can reach
efficiencies of 97% and above of their ideal Isp. Then I’ll take the Isp
as 365 s. Then we could lift 6,500 kg to orbit:
(2.) 365*9.81ln((117,786+6,500)/(3,086+6,500)) = 9,175 m/s.
Higher payload possible with more energetic hydrocarbon fuels
But kerosene is not the most energetic hydrocarbon fuel you could
use. Dunn in his report estimates an ideal vacuum Isp of 391.1 s for
methylacetyene. Dunn notes that Methyacetylene/LOX when densified
by subcooling gets a density slightly above that of kerolox, so I'll keep
the same propellant mass. Using altitude compensation and 97%
efficiency, I’ll take the vacuum Isp as 380 s. This would allow a
payload of 7,600 kg :
(3.) 380*9.81ln((117,786+7,600)/(3,086+7,600)) = 9,180 m/s.
Quite key for why reusable SSTO's will make manned space travel
routine is the small size and low cost they can be produced. A manned
SSTO can be produced using currently existing engines and
stages the size of the smallest of the very light, or personal, jets
[5], except it would use rocket engines instead of jet engines, and
the entire volume aft of the cockpit would be filled with propellant,
i.e., no passenger cabin. So it would have the appearance of a fighter jet.
Falcon 1 first stage based SSTO
We'll base it on the SpaceX Falcon 1 first stage. According to the
Falcon 1 Users Guide on p.8 [6], the first stage has a dry mass of
3,000 lbs, 1,360 kg, and a usable propellant mass of 47,380 lbs,
21,540 kg. We need to swap out the low efficiency Merlin engine for a
high efficiency engine. However, SpaceX has not released the mass for
the Merlin engine. We'll estimate it from the information here, [7].
From the given T/W ratio and thrust, I'll take the mass as 650 kg.
We'll replace it with the RD-0242-HC, [8]. This is a proposed
modification to kerosene fuel of an existing hypergolic engine. This
type of modification where an engine has been modified to run on a
different fuel has been done before so it should be doable [9], [10].
The engine mass is listed as 120 kg. We'll need two of them to loft
the vehicle. So the engine mass is reduced from that of the Merlin
engine mass by 410 kg, and the dry mass of the stage is reduced down
to 950 kg. Note that the mass ratio now becomes 23.7 to 1.
We need to get the Isp for this case. For a SSTO you want to use
altitude compensation. The vacuum Isp of the RD-0242-HC is listed as
312 s. However, this is for first stage use so it's not optimized for
vacuum use. Since the RD-0242-HC is a high performance, i.e., high
chamber pressure, engine with altitude compensation it should get
similar vacuum Isp as other high performance Russian engines such as
the RD-0124 [11] in the range of 360 s. As a point of comparison the
Merlin Vacuum is a version of the Merlin 1C optimized for vacuum use
with a longer nozzle. This increases its vacuum Isp from 304 s to 342 s
[12]. I've also been informed by email that engine performance
programs such as Propep [13] give the RD-0242-HC an ideal vacuum
Isp of 370 s. So a practical vacuum Isp of 360 s should be reachable
using altitude compensation.
Then with a 360 s vacuum Isp we get a delta-V of:
(4.) 360*9.81ln(1 + 21,540/950) = 11,160 m/s.
So we can add on payload mass:
(5.) 360*9.81ln(1+21,540/(950 + 790)) = 9,150 m/s,
allowing a payload of 790 kg.
To increase the payload we can use different propellant combinations
and use lightweight composites. For methylacetylene again, I’ll take the
vacuum Isp value as 380 s. Then the payload will be 1,070 kg:
(6.) 380*9.81ln(1 + 21,540/(950 + 1,070)) = 9,157 m/s.
We can get better payload by reducing the stage weight by using
lightweight composites. The stage weight aside from the engines is 710
kg. Using composites can reduce the weight of a stage by about 40%.
Then adding back on the engine mass this brings the dry mass to 670
kg. So our payload can be 1,350 kg:
(7.) 380*9.81ln(1 + 21,540/(670 + 1,350)) = 9,157 m/s.
Why payload to dry mass ratio is a better launcher figure of merit
Note this again has a very high value for what is now regarded as a
key figure of merit for the efficiency of a launch vehicle: the ratio of
the payload to the dry mass. The ratio of the payload to the gross mass
is now recognized as not being a good figure of merit for launch
vehicles. The reason is that payload mass is being compared then to
mostly what makes up only a minor proportion of the cost of a
launch vehicle, the cost of propellant. By comparing instead to the
dry mass you are comparing to the expensive components of the
vehicle, the parts that have to be constructed and tested [14].
This vehicle in fact has the payload to dry mass ratio over 2. Every
other launch vehicle I looked at, and possibly every other one that
has ever existed, has the ratio going in the other direction, i.e.,
the dry mass is greater than the payload mass. Often it is much
greater. For example for the space shuttle system the dry mass is over
12 times that of the payload mass, undoubtedly contributing to the
high cost for the payload delivered.
Because of this high value for this key figure of merit, this
vehicle would be useful even as a expendable launcher. However, a
SSTO is most useful as a reusable vehicle. This will be envisioned as a
vertical take-off vehicle. However, it could use either a winged
horizontal landing or a powered vertical landing. This page gives the
mass either for wings or propellant for landing as about 10% of the
dry, landed mass [15]. It also gives the reentry thermal protection
mass as 15% of the landed mass. The landing gear mass is given as 3%
of the landed mass here [16]. This gives a total of 28% of the landed
mass for reentry/landing systems. With lightweight modern materials
quite likely this could be reduced to half that.
If you use the vehicle just for a cargo launcher with cargo left in
orbit, then the reentry/landing system mass only has to cover the dry
vehicle mass so with lightweight materials perhaps less than 100 kg
out of the payload mass has to be taken up by the reentry/landing
systems. For a manned launcher with the crew cabin being returned, the
reentry/landing systems might amount to 300 kg, leaving 1,100 kg for
crew cabin and crew. As a mass estimate for the crew cabin, the single
man Mercury capsule only weighed 1,100 kg [17]. With modern
materials this probably can be reduced to half that.
Cost estimates comparable to a mid size business jet
For the cost, the full two stage Falcon 1 launcher is about $10
million. The engines make up the lion share of the cost for launchers.
So probably much less than $5 million just for the 1st stage sans
engine. Composites will make this more expensive but probably not
much more than twice as expensive. For the engine cost, Russian
engines are less expensive than American ones. The RD-180 at
1,000,000 lbs vacuum thrust costs about $10 million [18], and the NK-
43 at a 400,000 lbs vacuum thrust costs about $4 million [19]. This is in
the range of $10 per pound of vacuum thrust. On that basis we might
estimate the cost of the RD-0242-HC of about 30,000 lbs vacuum thrust
as $300,000. We would need two of them for $600,000.
I'm informed though this was based on ca. year 2000 prices and the
prices have approximately doubled since then, [20]. Even so the price
for two of these engines is likely to be less than $2 million.
So we can estimate the cost of the reusable version as significantly
less than $12,000,000 without the reentry/landing system costs. These
systems added on for reusability at a fraction of the dry mass of the
vehicle will likely also add on a fraction on to this cost. Keep in
mind also that the majority of the development cost for the two stage
Falcon 1 went to development of the engines so in actuality the cost
of just the first stage without the engine will be significantly less
than half the full $10 million cost of the Falcon 1 launcher. The cost
of a single man crew cabin is harder to estimate. It is possible it
could cost more than the entire launcher. But it's likely to be less
than a few 10's of millions of dollars.
Bob Clark
UPDATE, Sept. 26, 2013:
See
more accurate calculations using Dr. John Schillings Launch Performance Calculator here:
The Coming SSTO's: Page 2.
http://exoscientist.blogspot.com/2013/08/the-coming-sstos-page-2.html
REFERENCES.
1.)NK-33.
http://www.friends-partners.org/partners/mwade/engines/nk33.htm
2.)LR-105-5.
http://www.friends-partners.org/partners/mwade/engines/lr1055.htm
3.) Newsgroups: sci.space.policy
From: Mitchell Burnside Clapp <cla...@plk.af.mil>
Date: 1995/07/19
Subject: Propellant desity, scale, and lightweight structure.
http://groups.google.com/group/sci.space.policy/browse_frm/thread/3d981607d59684dc/
4.)Alternate Propellants for SSTO Launchers
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996
https://web.archive.org/web/20140215015634/http://www.dunnspace.com/alternate_ssto_propellants.htm
5.)List of very light jets.
http://en.wikipedia.org/wiki/List_of_very_light_jets
6.)Falcon 1 Users Guide.
http://www.spacex.com/Falcon1UsersGuide.pdf
7.)Merlin (rocket engine)
4. Merlin 1C Engine specifications
http://en.wikipedia.org/wiki/Merlin_%28rocket_engine%29#Merlin_1C_Engine_specifications
8.)RD-0242-HC.
http://www.astronautix.com/engines/rd0242hc.htm
9.)LR-87.
http://en.wikipedia.org/wiki/LR-87
10.)Pratt and Whitney Rocketdyne's RS-18 Engine Tested With Liquid Methane.
by Staff Writers
Canoga Park CA (SPX) Sep 03, 2008
http://www.space-travel.com/reports/Pratt_and_Whitney_Rocketdyne_RS_18_Engine_Tested_With_Liquid_Methane_999.html
11.)RD-0124.
http://www.astronautix.com/engines/rd0124.htm
12.)Merlin (rocket engine).
2.5 Merlin Vacuum
http://en.wikipedia.org/wiki/Merlin_(rocket_engine)#Merlin_Vacuum
13.)Propep
http://www.spl.ch/software/index.html
14.)A Comparative Analysis of Single-Stage-To-Orbit Rocket and Air-Breathing Vehicles.
p. 5, 52, and 67.
http://govwin.com/knowledge/comparative-analysis-singlestagetoorbit-rocket-and/15354
15.)Reusable Launch System.
http://en.wikipedia.org/wiki/Reusable_launch_system#Horizontal_landing
16.)Landing gear weight (Gary Hudson; George Herbert; Henry Spencer).
http://yarchive.net/space/launchers/landing_gear_weight.html
17.)Mercury Capsule.
http://www.astronautix.com/craft/merpsule.htm
18.)Wired 9.12: From Russia, With 1 Million Pounds of Thrust.
http://www.wired.com/wired/archive/9.12/rd-180.html
19.)A Study of Air Launch Methods for RLVs.
Marti Sarigul-Klijn, Ph.D. and Nesrin Sarigul-Klijn, Ph.D.
AIAA 2001-4619 , p.13
http://mae.ucdavis.edu/faculty/sarigul/aiaa2001-4619.pdf
20.)Personal communication, Gary Hudson.
