An SSTO as "God and Robert Heinlein intended".

[RGClark]

Much more simpler in a way: If the nozzle is operated at an ambient pressure, at which it is not designed for, the gas flow inside it can not follow the cross section of it properly.
If you for example have higher ambient pressure, the gas flow separates from the nozzle walls already before the nozzle exit, additionally producing shock waves that slow the exhaust down (over-expanded case). Or if you have lower ambient pressure, the exhaust is under-expanded and keeps on fanning out after the nozzle exit, so a part of the exhaust is only contributing partially to thrust.
But 3% is good enough for government work. The orbiter way is simply

[math]I_{sp} = \frac{I_{sp,vac} \cdot \left ( p_{sl} - p_a \right ) + I_{sp,sl} \cdot p_a}{p_{sl}}[/math]

Thanks for that explanation.
In that formula for the Isp you do still have to integrate it over the flight in accordance with how the altitude, and therefore the ambient pressure, changes over time.
BTW, on that page I cited that gives the altitude in 1 second intervals, it's given as an image file. This makes it so that you can't import it directly into Excel for example as a data file. You would have to type it in manually.
I have seen some web pages that give the altitude in wider intervals where it is written in text format. One I remember I believe was in 10 second intervals that might be adequate for the purpose.



Bob Clark

---------- Post added at 03:28 PM ---------- Previous post was at 01:08 PM ----------

I have seen some web pages that give the altitude in wider intervals where it is written in text format. One I remember I believe was in 10 second intervals that might be adequate for the purpose.

I found the links I was looking for. It was actually on Orbiter-Forum:

typical Shuttle / ISS Mission launch track.
http://www.orbiter-forum.com/showthread.php?p=33293&postcount=8

It is given in 2 second intervals for the first 20 seconds, then in 10 second intervals after that.
Since it gives the altitude all the way to when it reaches the ISS, we'll have to cut off the summation at the time of MECO during the flight.


Bob Clark

 

[RGClark]

Much more simpler in a way: If the nozzle is operated at an ambient pressure, at which it is not designed for, the gas flow inside it can not follow the cross section of it properly.

If you for example have higher ambient pressure, the gas flow separates from the nozzle walls already before the nozzle exit, additionally producing shock waves that slow the exhaust down (over-expanded case). Or if you have lower ambient pressure, the exhaust is under-expanded and keeps on fanning out after the nozzle exit, so a part of the exhaust is only contributing partially to thrust.

But 3% is good enough for government work. The orbiter way is simply

[math]I_{sp} = \frac{I_{sp,vac} \cdot \left ( p_{sl} - p_a \right ) + I_{sp,sl} \cdot p_a}{p_{sl}}[/math]

I believe your explanation is valid and this does have an effect on performance. However, I've been informed that the main source for the discrepancy in the calculation is that the cited value of the nozzle exit area is wrong. That wikipedia page gives it as 4.67 m^2:

http://en.wikipedia.org/wiki/Space_Shuttle_main_engine#Thrust_specifications

But on that same page is given the diameter of 90.7 in., about 2.304 m. This corresponds to an area of about 4.168 m^2. This value for the diameter comes from this Pratt & Whitney page:

Nozzle Design
by R.A. O'Leary and J. E. Beck, Spring 1992
http://www.pwrengineering.com/articles/nozzledesign.htm

so is probably reliable. Using this value for the exit area, the calculated value for the sea level thrust is quite close to the actual value.


Bob Clark

 

[RGClark]

I wouldn't call 69 Million USD per SSME low cost or even thinkable for commercial operations. Even the RD-0120, despite being much cheaper, would be anything attractive for commercial operations, if you want to reuse.

The advantages of a SSTO are best utilized as a reusable vehicle.
Then you would have to subtract from this estimated payload mass the
mass needed for reentry and landing systems.
However, the Ariane core stage SSTO could still be useful as an expendable vehicle. Then you could have up to a 9,000 kg payload without the reentry and landing systems. This is close to the 10,000 kg payload capacity of the Falcon 9.
I saw this article that had an estimate for the price of an expendable version of the SSME's:

PWR Offers Shuttle Engine Alternative.
Jul 15, 2009
By Joseph C. Anselmo
"The company also would manufacture additional engines using the
existing SSME design while beginning work on a modified design that
incorporates advances in the construction of nozzles and combustion
chambers. That would be ready to go into production within 3-4 years.
Maser estimates the modified SSME would cost two-thirds to four-fifths
of the original model - depending on the number ordered - and would be
'a little more expensive' than the company's RS-68 engine 'but in that
ballpark.'"
http://www.aviationweek.com/aw/gene...eadline=PWR Offers Shuttle Engine Alternative

Using a price of $40 million for the current SSME's this would
correspond to a price of from $26.7 to $32 million for the expendable
versions. Considering the fact the engines make up the bulk of the
cost of an expendable launcher, this expendable SSTO launcher very
well could be comparable in cost to the Falcon 9 at $50 million.


Bob Clark

 

[T.Neo]

Is there any major advantage to an expendable SSTO? Do the interstages and explosive bolts and seperation motors really cost that much?

Forgive me here, I have not really followed the conversation that well, but won't any properly-built rocket stage with efficient enough (read: not steam-powered) propulsion be able to lift at least some payload into orbit?

I remember the Aquarius concept... it was simple, pressure-fed and sea-launched, but hydrolox, and managed to get a 1 ton payload into orbit as an SSTO (the vehicle was rather large though). The premise was that Aquarius would ship replacable bulk goods to the station, such as food, clothing and water, which would mean that 30% of all flights failing would be acceptable, and warranted for the reduction in launch (and thus kg to orbit) costs.

 

[Sky Captain]

An SSTO, even expandable one would be advantegous where maximum reliability and safety is needed like manned launches and very expensive payloads.

 

[Urwumpe]

An SSTO, even expandable one would be advantegous where maximum reliability and safety is needed like manned launches and very expensive payloads.

That is pretty wrong. The relation between number of stages and reliability is currently even inversely to your claims.

Of course, a single stage sounds simpler, but it isn't. even a two stage rocket would be much simpler since it can do the same performance with less highly optimized engines or stage structures (if you use size instead of engine performance)

 

[RGClark]

Is there any major advantage to an expendable SSTO? Do the interstages and explosive bolts and seperation motors really cost that much?
Forgive me here, I have not really followed the conversation that well, but won't any properly-built rocket stage with efficient enough (read: not steam-powered) propulsion be able to lift at least some payload into orbit?
I remember the Aquarius concept... it was simple, pressure-fed and sea-launched, but hydrolox, and managed to get a 1 ton payload into orbit as an SSTO (the vehicle was rather large though). The premise was that Aquarius would ship replacable bulk goods to the station, such as food, clothing and water, which would mean that 30% of all flights failing would be acceptable, and warranted for the reduction in launch (and thus kg to orbit) costs.

I like the Aquarius concept. The only qualms I have about it is the plans for it were made too big. It required this huge infrastructure to launch quite a large number of rockets.
What should be done is just do a small scale test program. The most important effect of this would be to prove SSTO is possible even if at this small scale you don't see the savings in launch costs.
Once it is seen it is possible that would lead to investigating the possibility of reusable launchers that could cut the costs to orbit by 1 to 2 orders of magnitude.


Bob Clark

 

[Urwumpe]

I think that, until technology will have progressed far enough, two stage rockets are the optimal for low operating costs - a two stage rocket can already haul a lot of payload for its take-off weight, needs not much mass for separation systems and can also work well with less than optimal engines.

Also, it is much simpler to introduce reuse into two stage rockets...simpler in this case means: It is still pretty hard, but no longer a test of faith.

That one here was already pretty advanced, sadly it is now completely dead:

http://www.astronautix.com/lvs/kislerk1.htm

 

[T.Neo]

I am skeptical of a multi-stage reusable vehicle. I think that what you make up for in not needing absurd, paper-thin lightweight construction and high performance propulsion you lose in terms of logistics and complexity.

A flyback system already adds a lot of complexity and mass, I would dread to think about attempting to recover a second stage.

I have no idea how the Kistler upper stage was supposed to be reused, but my limited knowledge makes it seem that an upper stage isn't exactly an optimal shape for reentry...

 

[Urwumpe]

I have no idea how the Kistler upper stage was supposed to be reused, but my limited knowledge makes it seem that an upper stage isn't exactly an optimal shape for reentry...

It had actually (almost) the same shape as the Raduga capsules or exactly the same shape as the PARES reentry capsule options explored for the ATV.

http://en.wikipedia.org/wiki/VBK-Raduga

It is a blunt body at the nose, stabilized during ballistic reentry by a shuttlecock tail section.

The engineering is pretty sound, but not all technical problems had been solved until the money was used up.

 

[T.Neo]

Yes... I forgot Raduga and PARES, should have paid more attention to the shape of the vehicle. :facepalm:

I'll keep it in mind if I ever come across the subject in future.

Still, you need to have thermal protection... even if you minimise heating on most parts of the vehicle, it is still a large surface area to cover.

 

[Urwumpe]

Still, you need to have thermal protection... even if you minimise heating on most parts of the vehicle, it is still a large surface area to cover.

According to the vehicle state PDFs I have here on my HD (I also had a preliminary user manual of the K1 somewhere), it was meant to use ceramic tiles on the blunt nose, not different to modern capsule concepts.

The rest of the spacecraft doesn't need much protection. It is large and mostly empty tanks, which means the overall temperatures are very low. The energy per kg is constant for reentry, but the area at which this energy is turned into drag and aerodynamic heating is larger.

 

[RGClark]

I am skeptical of a multi-stage reusable vehicle. I think that what you make up for in not needing absurd, paper-thin lightweight construction and high performance propulsion you lose in terms of logistics and complexity.
A flyback system already adds a lot of complexity and mass, I would dread to think about attempting to recover a second stage...

There is no need to dread it. That's what the X-37B has accomplished.
In fact in another post I'll show the X-37B scaled up by about a factor of 2
could actually be SSTO.

Bob Clark

 

[T.Neo]

How has the X-37B accomplished that?

It is an orbital vehicle launched on Atlas, that only has orbital manuvering capability... or is there a critical research failure here on my part?

 

[Urwumpe]

It is an orbital vehicle launched on Atlas, that only has orbital manuvering capability... or is there a critical research failure here on my part?

I am also not sure how that could work.

Even if you are calculating in favor of many aspects there: Fuel mass could grow by x8, while structural mass grows by x4, so mass ratio changes by 4/12 = 1/3. By the little technical data that is known by the X-37B, like that it uses Hydrazine mono-propellant as fuel, but nothing about its fuel capacity, it means it could just get 1.09 times the exhaust velocity of a hydrazine thruster (1800 m/s) more. That is a lot, but not enough for SSTO.

 

[RGClark]

I like the Aquarius concept. The only qualms I have about it is the plans for it were made too big. It required this huge infrastructure to launch quite a large number of rockets.
What should be done is just do a small scale test program. The most important effect of this would be to prove SSTO is possible even if at this small scale you don't see the savings in launch costs.
Once it is seen it is possible that would lead to investigating the possibility of reusable launchers that could cut the costs to orbit by 1 to 2 orders of magnitude.

In doing some background web searches, I found that the upper stage of the Direct team's Jupiter-246 vehicle also would become SSTO when switched to a SSME engine. I guess I should not have been surprised by this. The thesis I have been arguing repeatedly via email with individuals in NASA and the industry and on space forums such as this one is that if you use BOTH the most weight optimized designs AND the highest efficiency engines available, then what you will wind up with will be SSTO capable whether you intend it to or not.
By highest efficiency engines I don't mean just an engine optimized to have a high vacuum Isp only. I mean an engine of highest efficiency over the entire flight range to orbit. For hydrogen engines that is the SSME, and the Russian analogue RD-0120. However, the point of the matter is that the same is true of kerosene-fueled vehicles, when using both highly weight optimized structures and highest efficiency engines, such as the NK-33 or RD-180.
That a SSME-powered Jupiter-246 upper stage would be SSTO capable is important since the Direct team is more amenable to thinking outside the box. So they would be more amenable to the idea you could have a SSTO vehicle. And in fact at least the expendable version for this SSTO would be no more difficult than their proposal for the upper stage on the Jupiter-246.
Attached below is a diagram showing the specifications of the Direct team's Jupiter-246.

It uses 6 RL-10B-2 engines, according to the specifications here these weigh about 300 kg each:

RL10B-2
Propulsion System
http://www.pratt-whitney.com/Static...er/Assets/1 Static Files/Docs/pwr_RL10B-2.pdf

So exchanging these for a SSME will add about 1,300 kg to the upper stage weight. The dry mass will be increased then to 13,150 kg, and the gross mass to 204,000 kg. However, by the Space Shuttle main engine thrust specifications, even at 109% thrust this comes to only 417,300 lbs, or 189,700 kgf. So we'll reduce the propellant load to be lifted by the SSME.
We'll take the liftoff thrust/weight ratio to be 1.2. This will bring the gross mass down to 170,000 kg. Then the propellant mass has to be reduced by 34,000 kg. This brings the propellant mass down to 156,850 kg. Note this results in a mass ratio close to 13, well sufficient for SSTO with a hydrogen-fueled engine.
This mass ratio for a hydrogen-fueled stage of 13 is high, but the original number for the Jupiter-246 upper stage is even higher at above 17. These high values for the Direct teams launcher led to some doubts about their calculations, but an analysis by Dr. Steven Pietrobon showed it was in keeping with historical trends for upper stages:

Analysis of Propellant Tank Masses.
http://www.nasa.gov/pdf/382034main_018 - 20090706.05.Analysis_of_Propellant_Tank_Masses.pdf

Then using Hudson's 425s average Isp for the SSME and the 9,200 m/s required delta-V value for orbit, this stage as an SSTO could loft 6,200 kg to orbit:

425*9.8ln(1 + 156,850/(13,150 + 6,200)) = 9,200 m/s.

Again, we might be able to loft 10% greater total mass to orbit with propellant densification by subcooling and also shave 10% off the structural mass of the stage with the recent weight saving research. This will bring the payload mass up to about 9,000 kg.
In this calculation I kept the same size tanks and only used them partially filled. This might be useful if for instance the Jupiter-246 upper stage was built to the original Direct teams specifications and you wanted to use the same size stage, though switched to a SSME engine, for the SSTO application to save on costs.
However, you could save additional weight off the stage if you used smaller propellant tanks for the SSTO application. I estimate about 900 kg could be saved with the smaller tanks that could go to additional payload.



Bob Clark

---------- Post added at 06:50 PM ---------- Previous post was at 06:41 PM ----------

I am also not sure how that could work.

Even if you are calculating in favor of many aspects there: Fuel mass could grow by x8, while structural mass grows by x4, so mass ratio changes by 4/12 = 1/3. By the little technical data that is known by the X-37B, like that it uses Hydrazine mono-propellant as fuel, but nothing about its fuel capacity, it means it could just get 1.09 times the exhaust velocity of a hydrazine thruster (1800 m/s) more. That is a lot, but not enough for SSTO.

I think of mass ratio in the other direction so would say it would change by a factor of 3. That's a big change.
I'll go into more detail later. But you would use the most high efficiency dense propellants and engines available. So the current engines would be switched out. And to get a SSTO every scrap of internal space has to be used for propellant so the payload bay would be removed to hold more propellant, with the payload instead carried in an external canister on top of the vehicle.


Bob Clark

 

[Urwumpe]

I think of mass ratio in the other direction so would say it would change by a factor of 3. That's a big change.

Not at all. Like said above, it only adds 1.09 x average exhaust velocity to the spacecraft.

[math]\ln{3} = 1.09[/math]
[math] -w \cdot \ln \left ( \frac{1}{3} \cdot r \right ) = -w \cdot \ln{\frac{1}{3}} -w \cdot \ln { r } [/math]
If it previously had 1200 m/s, which is roughly the maximum feasible of the current spacecraft, the larger one will just have 3000 m/s. Still about 6000 m/s short of a SSTO.

 

[T.Neo]

To be honest that sort of conversion doesn't make any sense to me; I would rather build an entirely new vehicle, it can be based (for example aerodynamics wise) on something like the X-37B, but it trying to shoehorn a totally different goal into the same airframe would probably be very inefficient.

 

[RGClark]

Not at all. Like said above, it only adds 1.09 x average exhaust velocity to the spacecraft.

[math]\ln{3} = 1.09[/math]
[math] -w \cdot \ln \left ( \frac{1}{3} \cdot r \right ) = -w \cdot \ln{\frac{1}{3}} -w \cdot \ln { r } [/math]
If it previously had 1200 m/s, which is roughly the maximum feasible of the current spacecraft, the larger one will just have 3000 m/s. Still about 6000 m/s short of a SSTO.

That is correct. I didn't give enough detail in what way it could become a SSTO.
Basically, what I'm saying is that a vehicle of about twice the scale of the X-37B and using kerolox propellant or other dense hydrocarbon could be SSTO.


Bob Clark

 

[Urwumpe]

That is correct. I didn't give enough detail in what way it could become a SSTO.
Basically, what I'm saying is that a vehicle of about twice the scale of the X-37B and using kerolox propellant or other dense hydrocarbon could be SSTO.

still not enough. You need something with about triple the energy density of Hydrazine. That is not just a higher specific impulse, but also a higher density of the fuel as hydrazine, and that is not kerolox. At the same density, you would need 5400 Ns/kg specific impulse, which is currently not possible. For getting into the range of kerolox, with 4300 Ns/kg at vacuum (using a high-pressure, high expansion engine), you would need 25% higher density of kerolox over hydrazine. and hydrazine has roughly the density of water.