A Kerosene-Fueled X-33 as a Single Stage to Orbit Vehicle.

[EarthlingX]

This might interest you, they use ethanol fuelled aerospike engine :

home : Garvey Spacecraft Corporation

They are also mentioned here :

Wiki : Aerospike engine

and here (page 22) :

www.faa.gov : 2010 U.S. Commercial Space Transportation Developments and Concepts: Vehicles, Technologies, and Spaceports

A bit more about the Prospector rocket :

www.csulb.edu : CALVEIN - California Launch Vehicle Education Initiative

[youtube]http://www.youtube.com/watch?v=dbVEBaQApXM[/youtube]

[youtube]http://www.youtube.com/watch?v=4sK1519KJBs[/youtube]

[youtube]http://www.youtube.com/watch?v=ndgvIbtZ5hU[/youtube]

 

[exoscientist]

Thanks for those, Earth. In that last video what was that transparent tube ahead of the aerospike?
A combustion chamber?

Bob Clark

 

[exoscientist]

... the SSTO can actually help if you wanted to get a TSTO to loft
larger payloads. For instance I argued that the X-33, when kerosene fueled,
could become orbital, though with small payloads, and the full-sized
VentureStar could loft large payloads when kerosene fueled. However, the
full-sized VentureStar would be quite expensive, in the billions of dollars
range, while the X-33 would be about $360 million to build a new one. So the
smaller X-33 could launch smaller payloads at an smaller initial investment.
But quite key also is that using two of them as the first and second stages,
they could now serve as a heavy launch system, and this would be at a much
smaller investment than building the full-size VentureStar...

We'll estimate the payload we can loft to orbit with two X-33's mated in bimese fashion, where two similar vehicles serve as the first and second stages. See for instance the attached image from this report:

Simulation and Analyses of Staging Maneuvers of Next Generation Reusable
Launch Vehicles.
Bandu N. Pamadi1, Thomas A. Neirynck2, Peter F. Covell3
NASA Langley Research Center, Hampton, VA
Nathaniel Hotchko4, David Bose5
Analytical Mechanics Associates, Inc., Hampton, VA
http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf

Using two similar reusable vehicles for both stages has been estimated to save on development costs.
The reconfigured X-33 with three NK-33 engines we calculated to have a dry weight of 21,700 kg, and carry 307,000 kg of kero/LOX propellant. However, to maximize performance we'll use aerospike nozzles on the engines. The NK-33 had a 331 s vacuum Isp. But this is because the engine had a nozzle that was a compromise between optimal sea level and vacuum performance. With an aerospike nozzle it could get the ca. 360 s vacuum Isp of other Russian high performance kerosene engines. We'll also take its sea level Isp as the ca. 331 s of some first stage optimized Russian engines.
Since the vehicles will be mated symmetrically instead of one standing vertically atop another, what I'll call the first stage or booster is the one that stops firing first, separates from the second one, does not go to orbit, and returns to the launch site. The second or upper stage, or orbiter, will be the one that goes on to orbit.
We'll have all 6 engines firing from both X-33's for the first part of the trip. However, we want to have the upper stage X-33 to be fully fueled for the second stage firing, so we'll use cross-feed fueling to have fuel from the first stage provide the fuel for the upper stage also for the first portion of the trip where they are still connected.
Let's calculate the payload that could be carried, taking again the required delta-V as 8,500 m/s. Take as an estimate 35,000 kg for the payload. The gross liftoff mass will then be 2x21,700 + 2x307,000 + 35,000 kg = 692,400 kg. The amount of fuel we'll be using for this first portion of the trip will be the amount stored in the booster, 307,000 kg, then this stage will separate and return to the launch site. The total mass at the end of this first portion will be 385,400 kg. For this first portion of the trip I'll take the Isp as the midpoint of the sea level and vacuum values so 345 s. Then the delta-V we can reach for this first portion will be 345*9.8ln(1 + 307,000/385,400)=1,981 m/s.
For the second portion of the trip with just the upper stage remaining, the propellant mass will again be 307,000 and the mass at the end of this final burn will be 21,700 + 35,000 kg = 56,700 kg. So the delta-V reached here will be 360*9.8ln(1+307,000/56,700) = 6,557 m/s, for a total delta-V of 8,538 m/s.
This is for using kero/LOX as propellant. But this is not the most efficient dense propellant combination to use. Others can result in even greater payload to orbit. For instance as described here some hydrocarbon fuels when also densified by subcooling could result in 50% greater payload than kero/LOX:

Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix, Arizona
April 25 – 27, 1996
http://www.dunnspace.com/alternate_ssto_propellants.htm

So possibly we could get 52,000 kg payload to orbit. What would be the launch costs? I estimated before a single reconfigured X-33 might cost $4,500,000 per launch:

viewtopic.php?f=15&t=21008&start=60#p438221

So lets say the bimese launcher would cost twice this to $9,000.000 per launch. Then at a 52,000 kg payload, this would amount to a $9,000,000/52,000kg = $173/kilo cost to orbit, or only $80/lb, a major reduction in launch costs.


Bob Clark

 

[EarthlingX]

Thanks for those, Earth. In that last video what was that transparent tube ahead of the aerospike?
A combustion chamber?

Bob Clark

I'm not sure exactly how it works, without looking at some plans, but it does look like some sort of a staged combustion, at least, unless propane (propylene ?) and oxygen are ionized to cause that light, which i doubt.
Temperature damage gives some clues, but not enough for me. Video title says 'nozzle test', so that's probably what it is, not the whole engine.

I wish them good luck, and i hope we will see. Some can be seen at that flight video, where engine works fine, if it is aerospike, they just seem to have some other problems.

edit. :
I checked their site, and they are busy.

Prospector 13A Flight Test of a LOX/Propylene Rocket Engine (with videos, and images)

21 February 2009

FAR Test Site, CA

The GSC/CSULB team developed and flew the Prospector 13A (P-13A) as a joint, internally sponsored propulsion R&D project (VIDEO). The primary objective was to demonstrate the use of LOX and propylene for the first time in flight vehicle. This is the same propellant combination that has been baselined for both stages of the NLV. Propylene is of interest as an alternative hydrocarbon fuel because of its potential to provide greater specific impulse than RP-1, while achieving higher densities than methane.

 

[exoscientist]

... the SSTO can actually help if you wanted to get a TSTO to loft
larger payloads. For instance I argued that the X-33, when kerosene fueled,
could become orbital, though with small payloads, and the full-sized
VentureStar could loft large payloads when kerosene fueled. However, the
full-sized VentureStar would be quite expensive, in the billions of dollars
range, while the X-33 would be about $360 million to build a new one. So the
smaller X-33 could launch smaller payloads at an smaller initial investment.
But quite key also is that using two of them as the first and second stages,
they could now serve as a heavy launch system, and this would be at a much
smaller investment than building the full-size VentureStar.
Note also the comparison to a two-stage expendable system: the two stages in
such a case would be expendable because they don't have sufficient mass ratio
to singly get to orbit. That is they aren't weight optimized. But suppose you
were able to make each stage be so optimized that each separately could reach
orbit at the same size vehicles. Then now note this means these weight
optimized versions could therefore loft *more* payload because the weight
savings could go to extra payload AND would be less costly per launch in being
reusable...

This is a general feature of using SSTO vehicles to serve as your stages for multistaged rockets. It shows there really is no valid objection to developing SSTO's. For even if true that you could lift more payload by using multistage rockets you could lift *even* more if you made those stages be separately SSTO's.
This works even if the SSTO's are expendable, not reusable. You may not want to develop a reusable version because of the cost, but just using an expendable vehicle so weight optimized that it is separately SSTO capable means you can loft more payload on that expendable rocket.
Here's an example of this for the Falcon 1 first stage SSTO discussed here:

viewtopic.php?f=15&t=21008&start=60#p438225

I'll use the single engine version discussed there to make a better comparison to the actual Falcon 1 two-stage rocket. For the single engine SSTO version I used 25% less propellant to be able to be lofted by a single RD-0124 engine. Using just one of the RD-0124's brings the dry mass down to 1,271 kg. But the tank weight is reduced too. Using the common 100 to 1 estimate of propellant mass to tank mass ratio for kero/LOX, I'll reduce the tank weight 71 kg to bring the dry mass to 1,200 kg.
The propellant mass being reduced 25% is now 20,325 kg. So using an average Isp of 345 s for the RD-0124 we would be able to loft about 580 kg to orbit since 345*9.8ln(1 + 20325/(1,200 + 580)) = 8,517 m/s. This is still more than the current two-stage version of the Falcon 1, and would be cheaper in being single staged and using only one engine, and by using a cheaper Russian engine as well.
Now suppose we used two of these Falcon 1 derived SSTO's mated bimese fashion to loft higher payloads. I estimate we could loft a 2,600 kg payload: the first stage portion of the trip would have a delta-V of 345*9.8ln(1 + 20,325/(2*1,200 + 20,325 + 2,600)) = 1,992 m/s. The second stage portion would have a delta-V of 360*9.8ln(1 + 20,325/(1,200 + 2,600)) = 6,521 m/s, for a total delta-v of 8,513 m/s.
Note a 2,600 kg payload is more than 5 times the payload of the current Falcon 1 two-stage rocket. So by weight optimizing our stages and using high performance engines, to the extent the stages are separately SSTO capable, we can increase our payload multiple times.


Bob Clark

 

[nux]

We can increase our payload multiple times.

Thank you, Bob, for the argument and math. The first is convincing, and the second has not been overturned in this thread by other knowledgeable posters.

Single-Stage to Orbit briefly and back using hydrocarbon fuel brings to three the number of recently discussed reusable craft that would be worth mass-using or mass-producing. The other two craft are the space elevator, which is still theoretical, and the air-lifter plus rocket, which is gentle enough for humans. It uses air to lift a second craft (maybe kerosene-powered in small slosh-proof tanks) as high as possible, at which point it detaches, forges its way to orbit, and stays for a suitably long time.

So, that's the air-lifter as a people-carrier; the elevator for transporting sea-water, ore, goods, stuff, and maybe people to and from space; and the kerosene single for quick-response and quick turnaround, general-purpose, near equator mass-usage.

An extreme heavy-lifter may or may not be required. If so, it probably has to be nuclear-powered. (I mean the one which drops nuclear bombs through or below its under-shield.) And a fifth craft (hydrogen-powered, solid-fueled, liquid, hydrocarbon sea-water mixture, I don't know) may or may not be required for robot transfer.

Five craft in total; Five craft that do not overlap each other's territory or niche; Five craft that will serve our needs while still in this grav-well.

David C, fan of SDC posters

 

[exoscientist]

I wanted to get some info on minimal trajectories to orbit. I found this page after a web search:

Atmospheric Flight of a Launch Vehicle.
http://astro.u-strasbg.fr/~koppen/launc ... ncher.html

It has a JAVA applet for calculating the ascent to orbit for some known rockets. It requires you to tweak the ascent angles, but fills in much of the information for you.
Problem is I haven't been able to get it to work right. For the given rockets, we know they were able to achieve orbit but every time I try it I get that the orbit was not achieved. Perhaps someone here can figure out how to work it.


Bob Clark

 

[EarthlingX]

My guess is, wrong thrust vector, and applet complains about not being able to calculate dynamic pressure, or something.

Error message is in French, so it's a guess.

I tried Ariane V, with default settings, no orbit. Seams there's still a bit of science in rocket science

Perhaps check vehicle stats, thrust, mass ?

 

[exoscientist]

It is known that you can reduce the fuel requirements to orbit by using a lifting trajectory. For instance it was explored for use on a reusable orbital craft in the 80's:

Fire in the sky: the Air Launched Sortie Vehicle of the early 1980s (part 1)
by Dwayne Day
Monday, February 22, 2010
http://www.thespacereview.com/article/1569/1

In the first post in this thread I suggested this fact be used for a lifting-body SSTO. Here is the argument I made:

...
Then the gravity losses could be further reduced by flying a lifting
trajectory, which would also increase the payload capability by a small
percentage.
The trajectory I'll use to illustrate this will first be straight-line at an
angle up to some high altitude that still allows aerodynamic lift to operate.
At the end of this portion the vehicle will have some horizontal and vertical
component to its velocity. We'll have the vertical component be sufficient to
allow the vehicle to reach 100 km, altitude. The usual way to estimate this
vertical velocity is by using the relation between kinetic energy and
potential energy. It gives the speed of v = sqrt(2gh) to reach an altitude of
h meters. At 100,000 m, v is 1,400 m/s.
Now to have orbital velocity you need 7,800 m/s tangential, i.e., horizontal
velocity. If you were able to fly at a straight-line at a constant angle to
reach 7,800 m/s horizontal velocity and 1,400 m/s vertical velocity and such
that the air drag was kept at the usual low 100 to 150 m/s then you would only
need sqrt(7800^2 + 1400^2) = 7,925 m/s additional delta-v to reach orbit. Then
the total delta-v to orbit might only be in 8,100 m/s range. Note this is
significantly less than the 9,200 m/s delta-v typically needed for orbit,
including gravity and air drag.
The problem is with usual rocket propulsion to orbit not using lift the thrust
vector has to be more or less along the center-line of the rocket otherwise
the rocket would tumble. You can gimbal the engines only for a short time to
change the rocket's attitude but the engines have to be then re-directed along
the center line. However, the center line has to be more or less pointing into
the airstream, i.e., pointing in the same direction as the velocity vector, to
reduce aerodynamic stress and drag on the vehicle. But the rocket thrust
having to counter act gravity means a large portion of the thrust has to be in
the vertical component which means the thrust vector has to be nearly vertical
at least for the early part of the trip when the gross mass is high. Then the
thrust vector couldn't be along the center line of a nearly horizontally
traveling rocket at least during the early part of the trip.
However, using lift you are able to get this large upwards vertical component
for the force on the rocket to allow it to travel along this straight-line. A
problem now though is that at an altitude short of that of space, the air
density will not be enough for aerodynamic lift. Therefore we will use lift
for the first portion of the trajectory, traveling in a straight-line at an
angle. Then after that, with sufficient vertical velocity component attained
to coast to 100 km altitude, we will supply only horizontal thrust during the
second portion to reach the 7,800 m/s horizontal velocity component required
for orbital velocity...

The key fact I want to focus on is that sqrt(7800^2 + 1400^2) = 7,925 m/s number. Actually if you add on the ca. 460 m/s velocity you get for free from the Earth's rotation you might be able to reduce this to sqrt(7400^2 + 1400^2) = 7,531 m/s. So I what I want to investigate is if it is possible for a rocket that does not have wings or lifting surfaces to travel at such a straight-line trajectory at an angle from lift-off so that the achieved velocity will be in this range (but keeping in mind this might not be the same as the equivalent "delta-V" that actually has to be put out by the engines.)
But I have question: if you angle the rocket launch from the start with the thrust vector along the center line with the trajectory angle such that the vertical component of the thrust equals the rocket weight could you have the rocket travel at a straight-line all the way to orbit? I'm inclined to say no because the gravity is operating at the center of gravity of the rocket not at the tail where the thrust is operating. This would certainly work if you had a point particle, but I'm not sure if it would work when your body has some linear extent.
This method for traveling at a straight-line at an angle for some or all of the trip would make my calculation easier. However, I'll show in a following post there is another way to do it even if this first method doesn't work.
The second method though would require some modification to the usual design of rockets and is more computationally complicated.


Bob Clark

 

[exoscientist]

...what I want to investigate is if it is possible for a rocket that does not have wings or lifting surfaces to travel at such a straight-line trajectory at an angle from lift-off so that the achieved velocity will be in this range (but keeping in mind this might not be the same as the equivalent "delta-V" that actually has to be put out by the engines.)
But I have question: if you angle the rocket launch from the start with the thrust vector along the center line with the trajectory angle such that the vertical component of the thrust equals the rocket weight could you have the rocket travel at a straight-line all the way to orbit? I'm inclined to say no because the gravity is operating at the center of gravity of the rocket not at the tail where the thrust is operating. This would certainly work if you had a point particle, but I'm not sure if it would work when your body has some linear extent.
This method for traveling at a straight-line at an angle for some or all of the trip would make my calculation easier. However, I'll show in a following post there is another way to do it even if this first method doesn't work.
The second method though would require some modification to the usual design of rockets and is more computationally complicated.

The question can be boiled down to this: imagine you have a long cylindrical object, could be a pencil, could be a broom stick. You can give it an initial thrust at the bottom and push it away at an angle. It will then follow a parabolic trajectory with its center of mass following a parabolic arc, disregarding air drag.
What I'm asking is will it work to supply a continual push at the bottom with the force maintained at the bottom at a fixed angle to the horizontal such that the vertical component of this force is the cylindrical body's weight?
Will the body maintain a continual straight-line trajectory at this set fixed angle?


Bob Clark

 

[EarthlingX]

Did you take into account planet rotation ?

 

[exoscientist]

Did you take into account planet rotation ?

Yes. Here:

The key fact I want to focus on is that sqrt(7800^2 + 1400^2) = 7,925 m/s number. Actually if you add on the ca. 460 m/s velocity you get for free from the Earth's rotation you might be able to reduce this to sqrt(7400^2 + 1400^2) = 7,531 m/s.

What I'm asking is really just a question in continuum mechanics, sometimes
called solid mechanics. In physics, we often idealize a body
subject to forces as a point particle. Idealized this way, the thrust
force applied to the rocket would add as a vector to the force of
gravity so it would cancel gravity no matter what the angle of the
trajectory.
But in continuum mechanics you have to consider the physical extent
of the body and where on the body the forces are applied. I imagine
this is a common type of problem addressed in mechanical engineering
and civil engineering.
A force applied at one position on the body won't have the same
effect as when it is applied to another point for instance in regards
to the torque produced. Torque is measuring the turning "force" on the
body. But it's defined as the cross product of the force vector times
the radial vector to the center of rotation.
Intuitively, what we have to worry about is rotation of the rocket
with the thrust applied only at the tail. But if the rocket were to
rotate it would be about the center of gravity. However, if we make it
so the thrust is always along the center line, the radial vector to
the cg and the force vector are parallel, resulting in a 0 torque
vector. That would mean there would be no rotation around the center
of gravity so we should be able to maintain our straight-line
trajectory.
This would be valid if the center of gravity were fixed. But the cg
is accelerating as the thrust is applied. So I'm not sure if this
argument applies in that case.

Bob Clark

 

[vulture4]

>>What I'm asking is will it work to supply a continual push at the bottom with the force maintained at the bottom at a fixed angle to the horizontal such that the vertical component of this force is the cylindrical body's weight?
Will the body maintain a continual straight-line trajectory at this set fixed angle?

Yes, and the use of a separate lift thruster system was proposed for a lunar landing craft where the typical in-line arrangement made it overly tall when on the lunar surface. But on earth accelerating horizontally to any significant fraction of orbital velocity below 50-100km altitude imposes excessive air drag, so the first part of the trajectory has to be vertical. After that one is clear of air drag and the thrust vector can be chosen arbitrarily, though often a lofted trajectory (climb to well above orbital altitude before geting much horizontal velocity) is often applied.

 

[EarthlingX]

Example of launch trajectory :

http://www.space.com/common/forums/viewtopic.php?p=459109#p459109

Ballistic data has been published: http://translate.google.com/translate?j ... l=ru&tl=en
(without Google translation: http://www.mcc.rsa.ru/sojuztma19/start.htm)

Just the first one i stumbled upon, there are better examples in Missions and Launches

 

[exoscientist]

The point I have been arguing in this thread is that not only is SSTO technically doable, it is in fact *easy* if you use DENSE propellants. This point is made in this article:

Single-stage-to-orbit.
"The early Atlas rocket is an expendable SSTO by some definitions. It is a "stage-and-a-half" rocket, jettisoning two of its three engines during ascent but retaining its fuel tanks and other structural elements. However, by modern standards the engines ran at low pressure and thus not particularly high specific impulse and were not especially lightweight; using engines operating with a higher specific impulse would have eliminated the need to drop engines in the first place.
The first stage of the Titan II had the mass ratio required for single-stage-to-orbit capability with a small payload. A rocket stage is not a complete launch vehicle, but this demonstrates that an expendable SSTO was probably achievable with 1962 technology."
http://en.wikipedia.org/wiki/Single-sta ... t#Examples

The Titan II first stage did have SSTO capability using dense propellants. And I'll show here the kerosene-fueled Atlas III does have SSTO capability if switched to using the lighter NK-33.
The original Atlas from the 1960's was close to being SSTO capable. It was able to be highly weight-optimized because it used what is called pressure-stabilized or "balloon tanks". These were tanks of thinner wall thickness than normal and were able to maintain their structure in being pressurized. The wall thickness was so thin that they could not stand alone when not filled with fuel. To be stored the tanks had to be filled with an inert gas such as nitrogen, otherwise they would collapse under their own weight.
The Atlas III first stage also uses balloon tanks and a common bulkhead design, used effectively by the SpaceX Falcon launchers to minimize weight. The Falcons probably are able to get the good weight optimization comparable to that of the Atlas launchers without using balloon tanks because their tanks are made of aluminum instead of the steel used with the Atlas tanks. The Atlas launchers might be able to weight-optimize their tanks even further by using aluminum for their balloon tanks, but there may be structural reasons that for balloon tanks steel has been preferred.
The specifications for the Atlas III first stage are given on this Astronautix.com page:

Atlas IIIA
http://www.astronautix.com/stages/atlsiiia.htm

The gross mass is given as 195,628 kg and the empty mass is given as 13,725 kg, resulting in a propellant mass of 181,903 kg. The Atlas III uses an RD-180 engine:

RD-180
http://www.astronautix.com/engines/rd180.htm

The Atlas III first stage is actually somewhat overpowered with the RD-180, as evidenced by the fact that Atlas V first stage carrying 50% more propellant is still able to use the RD-180. For an SSTO the weight of the engines is a major factor that has to be tailored to the size of the vehicle. A engine of greater power may be unsuitable for the SSTO purpose simply because the larger than needed engine weight may prevent the required mass ratio to be SSTO.
So again I'll use NK-33's two this time for the engines:

NK-33.
http://www.astronautix.com/engines/nk33.htm

Then the engine weight is reduced from 5,393 kg to 2,444 kg. This brings the dry mass to 10,776 kg, and the gross mass is now 192,679 kg. So the mass ratio is 17.9.
Using aerospike nozzles or other altitude compensation methods on the NK-33 we might be able to get the vacuum Isp to increase to the 360 s reached by other vacuum optimized high performance Russian engines. For the average Isp over the flight we'll use the value 338.3 s estimated for high performance kerolox engines using altitude compensation given in table 2 of this report:

Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996
http://www.dunnspace.com/alternate_ssto_propellants.htm

For the delta-V to orbit use 8,900 m/s, approx. 300 m/s less than that required for hydrogen fueled rockets due to the reduction in gravity loss using dense propellants:

Single-stage-to-orbit.
4 Dense versus hydrogen fuels.
http://en.wikipedia.org/wiki/Single-sta ... ogen_fuels

Then this would allow a payload of 2,500 kg:

338.3*9.8ln(1 + 181,903/(10,776 + 2500)) = 8,911 m/s.

Now let's calculate the payload for these two Atlas III's mated bimese fashion and using cross-feed fueling:
with a payload of 19,000 kg, we get a first stage delta-V of 338.3*9.8ln(1 + 181,903/(2*10,776 + 181,903 + 19,000)) = 1,981 m/s, and a second stage delta-V of 360*9.8ln(1 + 181,903/(10,776 + 19,000)) = 6,919 m/s for a total delta-V of 8,900 m/s.

But there are other hydrocarbon fuels that would give even better performance, for instance, methylacetylene. Table 2 in Dunn's report gives its average Isp as 352 s with altitude compensation. The max theoretical vacuum Isp is given as 391.1 s. High performance engines can get upwards of 97% of the theoretical value. So we'll take the vacuum Isp with the methylacetylene fuel as 380 s.
For the SSTO version we would get a payload of 4,000 kg:
352*9.8ln(1 + 181903/(10,776 + 4,000)) = 8,929 m/s.
For the bimese, cross-feed fueled version, estimate the payload as 23,000 kg:

352*9.8ln(1+181,903/(2*10,776 + 1*181,903 + 23,000)) = 2,033 m/s for the first stage delta-V and 380*9.8ln(1 + 181,903/(10,776 + 23,000)) = 6,904 m/s for the second stage, for a total of 8,937 m/s.
The "Atlas IIIA" page on Astronautix.com gives the cost for the Atlas III first stage as $50,000,000. Two NK-33's are actually slightly cheaper than one RD-180 used. So keep the price of the NK-33 powered version the same and take the price of the bimese version as twice as high. Then the cost to orbit per kilo would be $100,000,000/23,000 = $4,350/kg, about half-current launch rates.


Bob Clark

 

[exoscientist]

So we saw the Atlas III switched to a pair of lighter but still high
performance NK-33 engines becomes SSTO with significant payload.
This is the import of the report of Dr. John C. Whitehead:

Single Stage To Orbit Mass Budgets Derived From Propellant Density and
Specific Impulse.
John C. Whitehead
32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference
Lake Buena Vista, FL July 1-3, 1996
http://www.osti.gov/bridge/servlets/pur ... 379977.pdf

that it is easier to produce a SSTO with dense propellants rather than
using hydrogen fuel.
Indeed, this is a common state of affairs: if you use highly weight
optimized stages, such as with the Atlas's "balloon tanks", AND you
also use high performance kerosene engines, then what you will wind up
with will be a SSTO.
Further examples are provided by earlier, smaller Atlas versions. Use
for instance the Atlas I first stage, also called the "sustainer"
stage:

Atlas-I, Design
http://www.b14643.de/Spacerockets_2/Uni ... lasG_I.htm

The first stage gross mass is given as 143,200 kg, and the propellant
mass as 137,530 kg, giving a dry mass of 5,670 kg. It would appear
this Atlas first stage had a mass ratio of over 25 to 1(!) However,
the design of these early Atlas versions was for most of the lift-off
thrust to be provided by the drop off booster engines. The engine
that came with the first stage was smaller and did not have sufficient
thrust to lift the first stage on its own.
So we'll replace it with one NK-33 engine, with a mass of 1,222 kg:

NK-33.
http://www.astronautix.com/engines/nk33.htm

The mass of the engine that came with the Atlas I first stage was 460
kg:

LR-105-7.
http://www.friends-partners.org/partner ... lr1057.htm

So replacing it with the NK-33 adds 762 kg to the dry mass to bring
it to 6,432 kg kg, and the gross mass becomes 143,962 kg. This is
still within the lift capacity of a single NK-33, and the mass ratio
is still a very good 22.4.
To estimate payload, again use the Isp values given in Table 2 in
Dunn's report. The average Isp for kerolox with altitude compensation
is given as 338.3 s, and for high energy density methylacetelyne it's
352 s. Then for kerolox we could get a payload of 3,600 kg:
338.3*9.8ln(1 + 137,530/( 6,432 + 3,600)) = 8,900 m/s, and for
methylacetelyne it's 4800 kg: 352*9.8ln(1 + 137,530/( 6,432 + 4,800)) =
8,910 m/s.

The John Whitehead article showed the mathematics for why SSTO's with
dense propellants are achievable. And real world examples bear this
out if you use both weight optimized vehicles and high performance
kerosene engines at the same time.


Bob Clark

 

[kk434]

The greatest problem with SSTO is the reentry, the titan stage with modern tech can easly get to orbit but to bring it back in one piece??????? Not even the firsth stage of falcon9 can be reused and it travels at a relatively slow speed. I think that with current tech reusable SSTO is impossible, however a fly back firsth stage would save a lot of money and be reusable. Fishing up a firsth stage from the ocean like Musk wants is to hard.

 

[exoscientist]

The greatest problem with SSTO is the reentry, the titan stage with modern tech can easily get to orbit but to bring it back in one piece??????? Not even the first stage of falcon9 can be reused and it travels at a relatively slow speed. I think that with current tech reusable SSTO is impossible, however a fly back first stage would save a lot of money and be reusable. Fishing up a firsth stage from the ocean like Musk wants is to hard.

True. But remember way back at the beginning of this thread my argument was that if instead of using hydrogen for its reusable launch vehicle proposals NASA had used dense propellants then we would already would have RLV's 10 years ago, cutting the costs to space by an order of magnitude and possibly by two orders of magnitude.
Just as with the Lockheed lifting body X-33/VentureStar I was discussing before, the other NASA RLV proposals based on either the vertical landing DC-X design or the winged space shuttle design, would be able to lift multiple times greater payload at the same size vehicle when switched to kerosene-fueled, and quite likely at lower cost to boot since kerosene fueled vehicles are generally cheaper than hydrogen fueled ones.
I'll show in a following post that using the DC-X vertical landing mode and an Atlas balloon tank structure or the Falcon 9's 20-to-1 mass ratio structure, you can get a reusable launch vehicle that is still able to carry significant payload.


Bob Clark

 

[exoscientist]

The import of the Dr. John C. Whitehead article "Single Stage To Orbit
Mass Budgets Derived From Propellant Density and Specific Impulse" is
that it shows that for a rocket SSTO even though hydrogen has a higher
Isp than kerosene its low density means that it's actually easier to
make a rocket SSTO using dense fuels such as kerosene:

Single Stage To Orbit Mass Budgets Derived From Propellant Density and
Specific Impulse.
John C. Whitehead
32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference
Lake Buena Vista, FL July 1-3, 1996
http://www.osti.gov/bridge/servlets/pur ... 379977.pdf

This result very well may also apply to a partial airbreathing system
such as the Skylon spaceplane that uses air breathing propulsion in
the first part of the trip, switching to rockets in the later part.
The key reasons why dense hydrocarbon-fueled rockets can supply
multiple times greater payload in the same size vehicle than a
hydrogen-fueled one is that their engine T/W ratio is twice as good
and their propellant weight to tank weight ratios are 3 times as good
as hydrogen, resulting in major reductions in vehicle dry mass.
These factors should also apply to a partially airbreathing system,
and an example from the past strongly implies this is the case. Back
in the fifties the Air Force wanted a long range reconnaissance craft.
Based on the fact that hydrogen has a higher Isp the belief was the
vehicle should be hydrogen fueled. The vehicle proposed by Lockheed
under this top secret "Suntan" program was the CL-400:

LIQUID HYDROGEN AS A PROPULSION FUEL,1945-1959.
Part II : 1950-1957
8. Suntan
Lockheed CL-400.

http://history.nasa.gov/SP-4404/ch8-3.htm

Notice the similarity to the Skylon with the long thin fuselage and
the engines on the ends of the wings. The main difference would be the
lack of a tail section on the Skylon, probably because the engines
need to gimbal for the flight to space which can also be used for
vehicle control in the air.
However, note that the range given on this page is only 4,000 km, for
a mission radius of 2,000 km for missions returning to the starting
point. This is for a vehicle 160 feet long. But the smaller kerosene-
fueled SR-71 at only 100 feet long has a range of 4,800 km:

Lockheed
SR-71 Blackbird
Strategic Reconnaissance.
http://www.aerospaceweb.org/aircraft/recon/sr71/

Indeed the legendary Kelly Johnson soured on the Suntan program when
he found despite hydrogen's higher energy content that its use would
result in such short range:

LIQUID HYDROGEN AS A PROPULSION FUEL,1945-1959
Part II : 1950-1957
8. Suntan
Suntan Fades.
http://history.nasa.gov/SP-4404/ch8-12.htm

Another key advantage of a kerosene-fueled version is that fuel can be
carried in the wings, as with the SR-71, but not in a hydrogen-fueled
version:

Suntan fades.
"Ordinarily, range can be extended by adding more fuel or improving
the fuel consumption of the propulsion system for a given thrust.
Johnson could see a range growth of only a paltry 3 percent or so from
adding more fuel. ". . . we have crammed the maximum amount of
hydrogen in the fuselage that it can hold. You do not carry hydrogen
in the flat surfaces of the wing," he explained.42 Johnson turned to
Perry Pratt for estimated improvements in the 304 engine and his
answer was equally pessimistic: no more than 5 or 6 percent
improvement in specific fuel consumption could be expected over a five-
year period. The very low growth estimates were compounded by
operational logistics problems of liquid hydrogen. As Ben Rich asked:
'How do you justify hauling enough LH2 around the world to exploit a
shortrange airplane?'"
http://history.nasa.gov/SP-4404/ch8-12.htm

So both for the rocket propulsion and the airbreathing propulsion
components dense propellants provide better performance despite
hydrogen's greater Isp. For this reason I suggest Reaction Engines do
a trade study on replacing the hydrogen with kerosene or other
hydrocarbon.
Hydrogen does have advantages for the Skylon system in that it has
greater cooling capacity for the heat exchangers and it is lighter so
requires lower wing weight. Still, careful trades would be required to
see if these advantages are enough to counteract the advantages of
dense propellants for a SSTO.


Bob Clark

 

[annodomini2]

This result very well may also apply to a partial airbreathing system
such as the Skylon spaceplane that uses air breathing propulsion in
the first part of the trip, switching to rockets in the later part.
The key reasons why dense hydrocarbon-fueled rockets can supply
multiple times greater payload in the same size vehicle than a
hydrogen-fueled one is that their engine T/W ratio is twice as good
and their propellant weight to tank weight ratios are 3 times as good
as hydrogen, resulting in major reductions in vehicle dry mass.
These factors should also apply to a partially airbreathing system,
and an example from the past strongly implies this is the case. Back
in the fifties the Air Force wanted a long range reconnaissance craft.
Based on the fact that hydrogen has a higher Isp the belief was the
vehicle should be hydrogen fueled. The vehicle proposed by Lockheed
under this top secret "Suntan" program was the CL-400:

Bob Clark

I'm not arguing that the studies were accurate or inaccurate, however using kerosene is not feasable for the Skylon.

The liquid hydrogen is used as a part of the inlet heat exchanger to cool the incoming air, as a result the liquid /air oxygen has to be used to cool the rocket motor.

Carrying kerosene and limited oxydiser would remove the capability for the engine to operate.

 

[exoscientist]

The greatest problem with SSTO is the reentry, the titan stage with modern tech can easily get to orbit but to bring it back in one piece??????? Not even the first stage of falcon9 can be reused and it travels at a relatively slow speed. I think that with current tech reusable SSTO is impossible, however a fly back first stage would save a lot of money and be reusable. Fishing up a firsth stage from the ocean like Musk wants is to hard.

True. But remember way back at the beginning of this thread my argument was that if instead of using hydrogen for its reusable launch vehicle proposals NASA had used dense propellants then we would already would have RLV's 10 years ago, cutting the costs to space by an order of magnitude and possibly by two orders of magnitude.
Just as with the Lockheed lifting body X-33/VentureStar I was discussing before, the other NASA RLV proposals based on either the vertical landing DC-X design or the winged space shuttle design, would be able to lift multiple times greater payload at the same size vehicle when switched to kerosene-fueled, and quite likely at lower cost to boot since kerosene fueled vehicles are generally cheaper than hydrogen fueled ones.
I'll show in a following post that using the DC-X vertical landing mode and an Atlas balloon tank structure or the Falcon 9's 20-to-1 mass ratio structure, you can get a reusable launch vehicle that is still able to carry significant payload.

At the beginning of this thread I showed the X-33 would become a fully orbital SSTO, rather than just suborbital, if switched to using dense fuels from using hydrogen. A key fact is that this is true for the other RLV proposals made to NASA in the 90's, the DC-X modeled version by McDonnell-Douglas and the space shuttle modeled version by Rockwell. For these two cases as well their half-scale demonstrators could only be suborbital when hydrogen fueled. However, switched to hydrocarbon-fueled the half-scale demonstrators now become fully orbital craft. This is an important fact because rather than just being expensive suborbital test vehicles they are now orbital, reusable launch vehicles that can profitably launch payloads at a lower cost than comparably sized expendable systems.
These would have an advantage over the Lockheed version of the X-33 because they wouldn't have the problem of the conformally-shaped tanks getting a poor propellant mass to tank mass ratio which led to the X-33 downfall. As described here the circular cross-section tanks for these versions could get the high tankage ratios as for usual cylindrical rockets:

Space Access Update #91 2/7/00.
The Last Five Years: NASA Gets Handed The Ball, And Drops It.
"...part of L-M X-33's weight growth was the "multi-
lobed" propellant tanks growing considerably heavier than promised.
Neither Rockwell nor McDonnell-Douglas bid these; both used proven
circular-section tanks. X-33's graphite-epoxy "multi-lobed" liquid
hydrogen tanks have ended up over twice as heavy relative to the
weight of propellant carried as the Shuttle's 70's vintage aluminum
circular-section tanks - yet an X-33 tank still split open in test
last fall. Going over to aluminum will make the problem worse; X-
33's aluminum multi-lobed liquid oxygen tank is nearly four times as
heavy relative to the weight of propellant carried as Shuttle's
aluminum circular-section equivalent."
http://www.space-access.org/updates/sau91.html

I'll show a DC-X modeled version of similar size to the Lockheed X-33 would also be SSTO when hydrocarbon-fueled. Key fact: the Falcon 9 first stage has demonstrated a 20 to 1 mass ratio:

SPACEX ACHIEVES ORBITAL BULLSEYE WITH INAUGURAL FLIGHT OF FALCON 9 ROCKET.
Cape Canaveral, Florida – June 7, 2010
"The Merlin engine is one of only two orbit class rocket engines developed in
the United States in the last decade (SpaceX’s Kestrel is the other), and is
the highest efficiency American hydrocarbon engine ever built. The Falcon 9
first stage, with a fully fueled to dry weight ratio of over 20, has the
world's best structural efficiency, despite being designed to higher human
rated factors of safety."
http://www.spacex.com/press.php?page=20100607

I estimated the Falcon 9 first stage fuel load as 285,000 kg and dry weight as 15,000 kg. When switched to using the more high performance NK-33 engines rather than the Merlins, I estimated the dry mass as 12,726 kg:

viewtopic.php?f=15&t=25096#p466150

We'll keep the same propellant load but use a DC-X conical shape for the vehicle. The DC-X had about a 3 to 1 length to base diameter ratio. The bulk density of kerosene/LOX propellant is about 1,000 kg/m^3; so a 285,000 kg propellant load is about 285 cubic meters. The formula for the volume of a cone is (1/3)*Pi*r^2*h. This gives a base diameter of 7.1 m and a height of 21.3 m.
Now we need to add landing and thermal protection systems. The landing gear for an aerial vehicle is commonly taken as 3% of the landed weight:

Landing gear weight.
http://yarchive.net/space/launchers/lan ... eight.html

So 382 kg.
To make a powered vertical landing the common estimate is 10% of the vehicle landed weight has to be used in propellant:

Reusable launch system.
Vertical landing.
http://en.wikipedia.org/wiki/Reusable_l ... al_landing

So 1,273 kg.
For thermal protection, we'll assume it'll make a ballistic reentry, base first. For this vehicle the base will only be 7.1 meters wide, for an area of 38.5 m^2. We'll assume this will be covered on return by high temperature resistant material, the RCC material used on the space shuttle wing leading edges being one such material:

Space Shuttle thermal protection system.
http://en.wikipedia.org/wiki/Thermal_Protection_System

The areal density of this is 44.7 kg/m^2. We'll assume that as with ballistic reentry with a blunt base such as with the Apollo capsule return, only the base will be directly exposed to the bow shock wave, and only the base has to be covered by the high temperature material. This will then require 1,721 kg.
Then the total mass for landing and thermal protection is 3,376 kg, and the total mass that has to be lofted to orbit would be 12,726 + 3,376 = 16,102 kg. For the delta-V to orbit, I'll take it conservatively as 8,900 m/s. Note this is about 300 m/s less than for a hydrogen fueled vehicle since dense fueled vehicles incur less gravity loss.
First estimate the payload using standard nozzles for the engines, not using altitude compensation methods such as an aerospike. Then the average Isp over the trajectory will be in the range of 329 s, and the payload to orbit will be 3,000 kg:
delta-V = 329*9.8ln(1 + 285,000/(16,102 + 3,000)) = 8,923 m/s, sufficient for orbit.
However, for a SSTO you definitely would want to use altitude compensation for the engines such as aerospike nozzles, which have been well tested for decades now. According to this report by Dr. Bruce Dunn given in Table 1, you might get an average Isp with altitude compensation of 338.3 s for high performance kerolox engines:

Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix, Arizona
April 25 – 27, 1996
http://www.dunnspace.com/alternate_ssto_propellants.htm

Then with this average Isp we could loft 4,750 kg to orbit:
delta-V = 338.3*ln(1 + 285,000/(16,102 + 4,750)) = 8,904 m/s.
Kerosene is not the highest energy density hydrocarbon fuel you could use though. Dunn gives in his report others that would result in higher payload to orbit than kerosene, such as methylacetylene. In Table 2 of his report Dunn gives its average Isp using altitude compensation as 352 s. The overall propellant density with LOX oxidizer when the methylacetylene is chilled down to close to its freezing point is slightly above that of kerolox. So I'll take the propellant load now as 290,000 kg. Then the payload that could be lofted to orbit would be 7,600 kg:
delta-V = 352*9.8ln(1 + 290,000/(16,102 + 7,600)) = 8,910 m/s
Note that the payload fraction here is 2.4% of the gross mass, which is quite good even for expendable rockets.


Bob Clark

 

[exoscientist]

Just saw this:

RPA – Tool for Liquid Propellant Rocket Engine Analysis.
http://software.lpre.de/index.htm

According to the description, it is a freeware program for calculating the performance of engines given the propellants used, and on properties such as chamber pressure, nozzle size, etc.
It can also determine the variation with altitude.


Bob Clark

 

[exoscientist]

SpaceX has noted that its Falcon 9 first stage has reached a milestone in achieving a better than 20 to 1 mass ratio:

SPACEX ACHIEVES ORBITAL BULLSEYE WITH INAUGURAL FLIGHT OF FALCON 9 ROCKET.
Cape Canaveral, Florida – June 7, 2010
"The Merlin engine is one of only two orbit class rocket engines developed in
the United States in the last decade (SpaceX’s Kestrel is the other), and is
the highest efficiency American hydrocarbon engine ever built. The Falcon 9
first stage, with a fully fueled to dry weight ratio of over 20, has the
world's best structural efficiency, despite being designed to higher human
rated factors of safety."
http://www.spacex.com/press.php?page=20100607

The early versions of the Atlas rocket also reached comparably high mass ratios using both "balloon" tank and common bulkhead design, though the latest version, the Atlas 5 first stage, has a poorer mass ratio in not using either of these methods.
As described in SpaceX news releases, the Falcon launchers are able to get their high mass ratios because they use both common bulkheads and lightweight aluminum-lithium alloys, instead of the balloon tanks of the earlier Atlas versions.
But then I was startled to see that some early Delta rocket first stages, which were kerosene fueled, also had better than 20 to 1 mass ratios, particularly ones using an extra long first stage tank, known as the Delta Thor ELT:

Delta 1914.
http://www.friends-partners.org/partner ... la1914.htm

Astronautix is sometimes inaccurate but this is probably about right since on this page as well the early Delta versions using the first stage long tank has a first stage mass ratio of over 20 to 1:

Delta vehicle designs
http://www.b14643.de/Spacerockets_2/Uni ... elta_5.htm

This is notable because these Delta rocket first stages were able to achieve these high mass ratios without using balloon tanks or common bulkheads. Note that the Atlas 5 first stage remember in not using common bulkheads or balloon tanks results a much poorer first stage mass ratio.
We'll show the Delta Thor ELT can become a reusable SSTO with a vertical DC-X landing mode by replacing its RS-27 engine with the higher performance NK-33 engine and adding thermal protection and landing systems. The use of the NK-33 will add only 200 kg to the dry mass even though it has nearly twice the thrust. Interestingly the Delta Thor ELT can be made into a SSTO while keeping the vehicle close to the same size of the original DC-X.
The original DC-X created quite a stir when it was first flown because it was produced in such a short period, in less than two years, at relatively low cost, less than $60 million, and most importantly it demonstrated quick turnaround with a small ground crew.
The DC-X though was only able to make vertical takeoffs to a few thousand feet altitude and vertical landings using hydrogen fuel. To make an orbital version capable of 10,000 kg payload would require a much larger version at over a billion dollar cost, the DC-Y. Even the 1/2-scale version, the DC-X2, would cost $450 million and would only be suborbital using hydrogen fuel even though this 1/2-scale vehicle was twice the size of the DC-X. It is important then that by switching to hydrocarbon fuel that you can get a fully orbital vehicle of close to the size as the DC-X.
The Delta Thor ELT had a gross mass of 84,067 kg and an empty mass of 4,059 kg, for a propellant mass of 80,008 kg. The density of kerolox propellant is about 1,000 kg/m^3, so this corresponds to a propellant volume of about 80 m^3. The DC-X had a conical shape with a base about 4.1 m wide and length about 12 m, for a 3 to 1 ratio of length to base. A propellant tank of volume of that of the Delta 1914 first stage, but conically shaped at the same proportions as the DC-X, gives a base of 4.67 and a length of 14 m.
According to this, circular-cross section tanks, such as a cone, can get the same propellant mass to tank mass ratio of cylindrical tanks:

Space Access Update #91 2/7/00.
The Last Five Years: NASA Gets Handed The Ball, And Drops It.
"...part of L-M X-33's weight growth was the "multi-
lobed" propellant tanks growing considerably heavier than promised.
Neither Rockwell nor McDonnell-Douglas bid these; both used proven
circular-section tanks. X-33's graphite-epoxy "multi-lobed" liquid
hydrogen tanks have ended up over twice as heavy relative to the
weight of propellant carried as the Shuttle's 70's vintage aluminum
circular-section tanks - yet an X-33 tank still split open in test
last fall. Going over to aluminum will make the problem worse; X-
33's aluminum multi-lobed liquid oxygen tank is nearly four times as
heavy relative to the weight of propellant carried as Shuttle's
aluminum circular-section equivalent."
http://www.space-access.org/updates/sau91.html

Now we have to mass the thermal protection and landing systems. For thermal protection, we'll assume it'll make a ballistic reentry, base first. The base will only be 4.67 meters wide, giving an area of 17 m^2. Using base first reentry we'll have to cover primarily the base only:

Blue Origin New Shepard.
"A passenger and cargo spacecraft has considerably less need for cross-range."
...
"As a result, the craft is much "rounder" than the DC-X, optimized for tankage and structural benefits rather than re-entry aerodynamics. It has not been stated if the vehicle is intended to re-enter base-first or nose first, but the former is most likely for a variety of reasons. For one, it reduces heat shield area, and thus weight, covering only the smaller bottom surface rather than the much larger upper portions. The area around the engines would likely require some sort of heat protection anyway, so by using the base as the heat shield the two can be combined. This re-entry attitude also has the advantage of allowing the spacecraft to descend all the way from orbit to touchdown in a base-first orientation, which would seem to offer some safety benefits as well as reducing aero-loading issues."
http://en.wikipedia.org/wiki/Blue_Origin_New_Shepard

We'll use the high temperature resistant but low maintenance metallic shingles developed for the X-33:

REUSABLE METALLIC THERMAL PROTECTION SYSTEMS DEVELOPMENT.
http://reference.kfupm.edu.sa/content/r ... 117853.pdf

These have an areal density of 15 kg/m^2. This will require 255 kg to cover the base only. This plus the 200 kg extra mass for the more powerful NK-33 engine brings the dry mass to 4514 kg.
The landing gear for an aerial vehicle is commonly taken as 3% of the landed weight:

Landing gear weight.
http://yarchive.net/space/launchers/lan ... eight.html

So 4,650 kg dry mass with the landing gear.

To make a powered vertical landing the common estimate is 10% of the vehicle landed weight has to be used in propellant:

Reusable launch system.
Vertical landing.
http://en.wikipedia.org/wiki/Reusable_l ... al_landing

So 5,115 kg has to be lofted to orbit.

For the average Isp over the flight we'll use the value 338.3 s estimated for high performance kerolox engines using altitude compensation given in table 2 of this report:

Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996
http://www.dunnspace.com/alternate_ssto_propellants.htm

For the delta-V to orbit use 8,900 m/s, approx. 300 m/s less than that required for hydrogen fueled rockets due to the reduction in gravity loss using dense propellants:

Single-stage-to-orbit.
4 Dense versus hydrogen fuels.
http://en.wikipedia.org/wiki/Single-sta ... ogen_fuels

Then this will allow about 750 kg to orbit:

338.3*9.8ln(1 + 80,008/(5,115 + 750)) = 8,898 m/s.

More energetic fuels than kerosene are also discussed in Dunn's report. Methylacetene for example with altitude compensation gets an average Isp of 352 s. This will allow about 1,450 kg to orbit:

352*9.8ln(1 + 80,008/(5,115 + 1,450)) = 8,897 m/s.

The cost? The original DC-X cost $60 million. Since this reusable kerosene-fueled version is of similar size it might be estimated to be of approx. the same cost. However, there is this surprising cost for the Delta Thor ELT:

Delta Thor ELT.
"Lox/Kerosene propellant rocket stage. Loaded/empty mass 84,067/4,059 kg. Thrust 1,030.21 kN. Vacuum specific impulse 296 seconds.
Cost $ : 11.600 million."
http://www.astronautix.com/stages/delorelt.htm

Astronautix though is sometimes inaccurate, but I haven't found any other source estimate for the cost of this stage.
Typically the cost of the engine is the largest portion of the cost of a rocket stage, so more than half of the $11.6 million would be for the original RS-27 engine. But this would be for more than the price of the more powerful NK-33 currently at $4 million. The metallic shingle TPS though would also be an additional add on to the cost.
Still, it is possible the cost could be in the $10 million to $20 million range. Considering we have a reusable launcher with engines that could get perhaps 10 flights and with possibly a 1,450 kg payload capacity, the price per kilo might be as low as $700/kg, or $350/lbs.


Bob Clark