Discussion Elon Musk: the F9 first stage can reach orbit as an SSTO.

[Hlynkacg]

I did read 'em. a bit more carefully than you did it seems.

Your first suggestion, the nozzle extension, has no effect on Ve at sea-level and is questionable at altitude considering the that a vacuum-compensated Merlin is 2/3rds the diameter of a complete F9 stage, there is barely room for 1 of them never mind 9.

Your second suggestion, using turbine exhaust to produce idle thrust and burn off residual fuel, comes at the expense of Ve because you aren't extracting any energy from the combustion process beyond that which drives the pump and the combustion chamber never reaches operating pressure.

pertinent NASA technical report

Even if we assume for the sake of argument that the Merlin has the required plumbing, Tsiolkovsky's equation still applies. You've reduced your burnout weight, but you've more than doubled the amount of propellant required to complete your landing maneuver.

 

[Urwumpe]

Your second suggestion, using turbine exhaust to produce idle thrust and burn off residual fuel, comes at the expense of Ve because you aren't extracting any energy from the combustion process beyond that which drives the pump and the combustion chamber never reaches operating pressure.

Also, you can't use the turbine exhaust for that, without "ruining" the rest of the engine. The turbine has the purpose to drive the turbopump and have optimal pressure drop over turbine and "nozzle" to increase the mechanic power available for the pump.

Now, it is easy to think that since turbojet engines operate similar, that a turbopump is equally well capable of producing a high thrust. But that is wrong - you would need to find a very effective variable geometry turbine for such a conversion just for the start of the conversion:

A turbopump turbine has a maximal pressure drop from inlet to outlet to extract more energy from the exhaust to power the shaft. It is similar with turboshaft engines.

A turbojet instead only use a minimum pressure drop to preserve as much energy for the jet exhaust, while extracting the necessary work from the exhaust to keep the compressor running optimal.

Now, that is not the whole truth: A high bypass turbofan for example has a LP turbine that again extracts as much energy from the exhaust as needed to reach in sum (core thrust + bypass thrust) an optimum.

The F135 engine can for example provide 30,000 SHP to the LP shaft more (for driving the lift fan of the F-35). This is done by changing the hot nozzle area - the back pressure at the turbine drops, making it slightly more effective, but you loose a lot of thrust that way, the effectivity of the engine changes. But since the engine has two shafts, such a solution is possible (With one shaft, you would have a much stronger drop in effectivity, pushing the EGT quickly off-limits)

If you now try the same for rocket engines, you quickly find differences that make such a solution even MORE complex. First of all, you need a variable nozzle (possible), that is at least comparable in effectivity to the main nozzle (impossible). Then, you need a largely variable geometry pump ( with a lot of effort possible), that is as effective as a fixed geometry pump (impossible). If you have no variable geometry there, you would let the pump cavitate. One solution would for example be having an additional pump pair on the same shaft exclusively for the gas generator, with the main pumps simple being cut off from fuel flow and allowed to spin free in near-vacuum. But that means a lot of more mass and a small pump is much less effective as a large one during normal operations: Your specific impulse drops - not just during low thrust, but also doing full thrust operations as well. Still you have the problem of how to bypass the turbine in an effective way, so your gas generator can make as mass flow like during 100% thrust, even though just 2% of the power is needed, for example.

I don't know of any rocket design that did try that.

The LR-105 engine of the Atlas for example was using vernier engines that had been supplied by the same manifold that also supplied the gas generator of the engine. That the pump became much less effective at low mass flows was no issue for the mission, since the vernier-only flight was only consuming a few percent of the fuel. The exhaust of the turbine was still dumped overboard.

 

[RGClark]

I did read 'em. a bit more carefully than you did it seems.
Your first suggestion, the nozzle extension, has no effect on Ve at sea-level and is questionable at altitude considering the that a vacuum-compensated Merlin is 2/3rds the diameter of a complete F9 stage, there is barely room for 1 of them never mind 9.
Your second suggestion, using turbine exhaust to produce idle thrust and burn off residual fuel, comes at the expense of Ve because you aren't extracting any energy from the combustion process beyond that which drives the pump and the combustion chamber never reaches operating pressure.

pertinent NASA technical report

Even if we assume for the sake of argument that the Merlin has the required plumbing, Tsiolkovsky's equation still applies. You've reduced your burnout weight, but you've more than doubled the amount of propellant required to complete your landing maneuver.

For the altitude compensating attachments for all 9 engines, you could have them of varying shapes fitting together so the total shroud appears as a single large bell shaped nozzle from the outside. It might also work to simply have the extendable shroud only attached the exterior of the base of the stage with no portion attached to the individual nozzles, as long as it appears as a single large bell from the outside, i.e., as long as the ambient air encounters it as a single large nozzle.

This is for achieving the altitude compensation effect. For the hovering effect, you would in any case have an extendable shroud attached to the center engine that could also be extended with a restricted opening to reduce the thrust to allow hovering.

If all you wanted was to allow hovering you could simply have a extendable shroud attached to the center engine only that could restrict the thrust. That would not improve the payload. But the point is if you are going to apply extendable nozzle attachments why not apply them in a way that would also increase payload?

For the pressure-fed mode operation of the engines that are normally turbopump-fed, that is not discussed in that article you linked. This is known as "idle mode" and goes back to the Apollo days in research on the J-2 upper stage engine. Search on "idle mode" and "J-2s engine" for some reports on it from the time period.

In this mode the propellant goes through the turbopumps but they are simply not operating. The combustion takes place in the usual combustion chamber. It is not the turbine exhaust. The pressurization to enter the combustion chamber is coming from the pressurized tanks themselves.

Note that the high mass flow of propellant for turbopump engines at full thrust is coming from the high power provided by the turbopumps. Then if these turbopumps are not operating the mass flow rate is greatly reduced. This is okay for our application because we want the thrust to be reduced.

The nearly empty stage will be perhaps 4% to 5% of the fully loaded stage. And since the engines at lift-off have to loft both the fully loaded stage and second stage and exceed in thrust their weight to launch, the thrust needed for the hovering will be just a small fraction of the full thrust level.

It is true that the Isp of the turbopump mode is higher than in idle mode but it is wasteful of propellant to operate the engine in turbopump mode at landing because such a relatively small amount of thrust is needed then.

Moreover, any turbopump fed stage has a significant amount of propellant left over after "full" burn because they need a significant amount of pressure at the pump entrance to avoid cavitation. This residual propellant left in the tank can be from 0.5% to 1%. For the F9 first stage at a ca. 400 metric ton propellant load this can be from 2,000 to 4,000 kg left in the tank unused.

However, the idle mode can burn not only this residual liquid propellant but also left over gaseous propellant reducing the left over propellant and the burn-out mass.


Bob Clark

 

[Urwumpe]

For the pressure-fed mode operation of the engines that are normally turbopump-fed, that is not discussed in that article you linked. This is known as "idle mode" and goes back to the Apollo days in research on the J-2 upper stage engine. Search on "idle mode" and "J-2s engine" for some reports on it from the time period.

Wrong. It was planned but never implemented in the J-2S engine. It was not even tested.

The modern term for the same is "Tank head operation". Many smaller rocket engines up to the RL-10 support it, but you won't find it in big first stage engines. It was studied to be used with SSMEs in the Space Shuttle to replace the OMS, you can find a mentioning here:

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20130012517.pdf

The flown J-2 only supported a propulsive propellant dump, which was used together with the RCS for guiding the stage away from the spacecrafts.

Since chamber pressure in the rocket engine can NEVER exceed tank head pressure (hydrostatic pressure at the injector plate), you can easily calculate, how much thrust you can maximally get. It is pretty low in that calculation and it gets even lower if you remember that at such low thrust levels, the nozzle is extremely ineffective and very sensitive to ambient pressure. The gained thrust is really only a few percent higher than chamber pressure multiplied by throat area at sea level. It looks a bit better in vacuum.

PS: You are away that your "one nozzle extension fits all" approach means you have no longer thrust vector control?

 

[RGClark]

Wrong. It was planned but never implemented in the J-2S engine. It was not even tested.
The modern term for the same is "Tank head operation". Many smaller rocket engines up to the RL-10 support it, but you won't find it in big first stage engines. It was studied to be used with SSMEs in the Space Shuttle to replace the OMS, you can find a mentioning here:
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20130012517.pdf
The flown J-2 only supported a propulsive propellant dump, which was used together with the RCS for guiding the stage away from the spacecrafts.
Since chamber pressure in the rocket engine can NEVER exceed tank head pressure (hydrostatic pressure at the injector plate), you can easily calculate, how much thrust you can maximally get. It is pretty low in that calculation and it gets even lower if you remember that at such low thrust levels, the nozzle is extremely ineffective and very sensitive to ambient pressure. The gained thrust is really only a few percent higher than chamber pressure multiplied by throat area at sea level. It looks a bit better in vacuum.
PS: You are away that your "one nozzle extension fits all" approach means you have no longer thrust vector control?

Yes. I know it was not put into production on the Saturn V. But it was extensively tested on the ground and proven to work on the J-2S as you can confirm by a web search.
Also it was actually put into operational engines on the LE-5 of the Japanese space agency.
I'm aware the thrust is just a fraction of the full thrust under idle mode. Since the near empty weight is just a small fraction of the fully loaded weight, this will still be sufficient.
The extensible nozzle attachments can be made to gimbal if needed.

Bob Clark

 

[Urwumpe]

YAlso it was actually put into operational engines on the LE-5 of the Japanese space agency.

Can't confirm this. The LE-5 family is unrelated to the J-2 family. The LE-5 is noteworthy for using a very unique engine cycle, which only sounds similar to the tap-off cycle of the J-2S because its term is "expander/coolant tap-off cycle"

 

[Hlynkacg]

Can't confirm this. The LE-5 family is unrelated to the J-2 family. The LE-5 is noteworthy for using a very unique engine cycle, which only sounds similar to the tap-off cycle of the J-2S because its term is "expander/coolant tap-off cycle"

Robert's own source reports that the LE-5's Ve in idle thust mode is only 20% of that at full power.

 

[RGClark]

Robert's own source reports that the LE-5's Ve in idle thust mode is only 20% of that at full power.

Which source are you referring to? I saw several where the thrust is given as greatly reduced to the 3% to 5% range. But that may be due to the reduction in propellant flow rate instead of reduction in Isp.

Bob Clark

 

[Hlynkacg]

The LE-X development pamphlet that you linked to.

Ve, chamber pressure, and mass flow for a given engine + nozzle geometry tend to scale together for a given engine + nozzle geometry. Having one set of values for we can estimate the others. (See that paper I linked earlier) So given that the mass flow and chamber pressure for the LE-5 in idle mode is approximately 15-20% of that at operational power, and that thrust is 3-5% we can surmise that the Ve in idle mode is going to be between 16 and 25%. (hence "20%")

 

[Urwumpe]

The LE-X development pamphlet that you linked to.

Ve, chamber pressure, and mass flow for a given engine + nozzle geometry tend to scale together for a given engine + nozzle geometry. Having one set of values for we can estimate the others. (See that paper I linked earlier) So given that the mass flow and chamber pressure for the LE-5 in idle mode is approximately 15-20% of that at operational power, and that thrust is 3-5% we can surmise that the Ve in idle mode is going to be between 16 and 25%. (hence "20%")

Actually different - you have different regions, in which you can tell that some properties remain constant and others change in a simple way, ideally proportional.

The further you get to the extremes, like also the extreme low thrust, the more the simple approximations don't work. The throat is no longer choking the flow, it does not reach the speed of sound and does no longer accelerate in the nozzle. Also combustion gets more and more instable.

If you inject at tank pressure, you must have about 80% or less of that chamber pressure (or your injector fails to mix the propellants properly)

So, we are speaking about a maximum pressure of maybe 300 kPa and if you have a throat area of just 0.002 m² - you would get just 600 N thrust without any nozzle performance - and that nozzle performance will approach 1.0 at low chamber pressure.

 

[Hlynkacg]

@Urwumpe

At first glance that would seem to be even worse for Ve than my initial estimate.

 

[Urwumpe]

@Urwumpe

At first glance that would seem to be even worse for Ve than my initial estimate.

Of course, that is the problem with reality. Things generally won't work as good as before, if you use them under conditions they had never been designed for. For example the AC of German high speed trains does not cool the air any more if the ambient air temperature exceeds 32°C

 

[RGClark]

Yes, it is pretty academic. We know that we can already build one since 1960-something. We just have no reason to do so. It would be way more expensive than a much smaller TSTO at the same technology.
A reusable SSTO with reliable technology would be the turning point - if even launching a fully reusable TSTO (like Kistler K1) would be less economic over a full year of launches than a SSTO, that could require less ground infrastructure.

What do you calculate for the payload of the F9 FT first stage as an expendable SSTO using the newly released value by SpaceX of 22.8 metric tons for the TSTO?

http://www.spacex.com/about/capabilities

Bob Clark

 

[Urwumpe]

What do you calculate for the payload of the F9 FT first stage as an expendable SSTO using the newly released value by SpaceX of 22.8 metric tons for the TSTO?

http://www.spacex.com/about/capabilities

Bob Clark

While doing some initial checks about that, I discovered something strange, will need to check this again at home with my spaceflight books nearby (derived many special formulas by my head, so I could be wrong.

Is it even possible, assuming ZERO inert mass fraction, to construct a launcher that launches 22.8 tons into LEO and weights maximally 549,054.0 kg at lift-off and uses the engine performance data published by SpaceX?

I wondered why I failed to find coarse initial conditions here before noticing that the total inert mass ratio and the total payload mass ratio does not work out at the known lift-off mass.

---------- Post added at 11:10 PM ---------- Previous post was at 05:42 PM ----------

Results from the simplistic simulation (e.g. No fairing considered, simplified trajectory), setting the boundary conditions on the data of SpaceX, 500 generations with 10000 individuals in each generation before removing completely unsuitable candidates, the 10 best solutions in each generation had been used for the next generation:

# | Gen. | DeltaV1 | DeltaV2 | DT1 | DT2 | IMF1 | IMF2 | PMF | MTOW | S1 mass | S2 mass | PL mass | Fit. | RV1 | RV2
01.|100|3789.9 m/s|5410.1 m/s|148 s| 395 s| 3.8%| 3.7%| 4.0%|571.8 t|436.0 t|113.0 t|22.8 t| 5.03| +0.00 m/s| +0.00m/s
02.|262|3769.6 m/s|5430.4 m/s|148 s| 395 s| 4.0%| 3.6%| 4.0%|571.9 t|436.1 t|113.0 t|22.8 t| 4.84| +0.00 m/s| +0.00m/s
03.|189|3792.9 m/s|5407.1 m/s|148 s| 393 s| 3.9%| 3.6%| 4.0%|571.8 t|436.6 t|112.3 t|22.8 t| 4.72| +0.00 m/s| +0.00m/s
04.|143|3748.4 m/s|5451.6 m/s|147 s| 399 s| 4.1%| 3.6%| 4.0%|571.8 t|435.0 t|114.0 t|22.8 t| 4.55| +0.00 m/s| +0.00m/s
05.|286|3777.1 m/s|5422.9 m/s|148 s| 397 s| 3.8%| 3.7%| 4.0%|571.4 t|434.8 t|113.8 t|22.8 t| 4.53| +0.00 m/s| +0.00m/s
06.|024|3743.6 m/s|5456.4 m/s|147 s| 397 s| 4.2%| 3.5%| 4.0%|572.1 t|436.0 t|113.3 t|22.8 t| 4.47| +0.00 m/s| +0.00m/s
07.|295|3817.0 m/s|5383.0 m/s|149 s| 391 s| 3.8%| 3.8%| 4.0%|572.2 t|437.4 t|112.0 t|22.8 t| 4.43| -0.00 m/s| +0.00m/s
08.|080|3750.2 m/s|5449.8 m/s|147 s| 399 s| 4.0%| 3.6%| 4.0%|571.6 t|434.7 t|114.1 t|22.8 t| 4.40| +0.00 m/s| +0.00m/s
09.|272|3726.1 m/s|5473.9 m/s|147 s| 398 s| 4.3%| 3.4%| 4.0%|571.9 t|435.4 t|113.6 t|22.8 t| 4.35| +0.00 m/s| -0.00m/s
10.|405|3731.5 m/s|5468.5 m/s|147 s| 399 s| 4.2%| 3.5%| 4.0%|571.7 t|434.9 t|114.0 t|22.8 t| 4.26| +0.00 m/s| +0.00m/s

Gen. is the generation of the possible solution
DT1 and DT2 are the burn times (throttling to less than 100% and startup/shutdown are not taken in account)
IMF1 and IMF2 are the inertial mass fractions of the stages
PMF is payload mass fraction of the launcher
Fit. is the fitness value.
RV1 and RV2 are residual values for debugging.

Including a fairing would make the launcher even heavier.

Funny result: Stage 1 mass + stage 2 mass is approximately equal to the launcher mass stated by SpaceX. But excluding the payload mass from this boundary condition does not change the results much.


Result of a SSTO calculation on the final best solution:

Generation:|100
Propellant mass:|414.0 t
Inert mass:|21,9 t
Inert mass ratio:|3.83%
Payload mass:|2.4 t
Payload mass ratio:|0.56%

 

[RGClark]

Thanks for the calculation. A couple of questions. First, does your calculation take into account thrust/weight ratio? Judging from the thrust given in the specifications on the SpaceX Falcon 9 page, it's rather high with the upgraded Merlin 1D+, at about 1.8. A high T/W can reduce the gravity loss and increase payload.

Secondly, does the value you're using for the first stage dry mass include the interstage mass? To support the mass of a 110+ metric ton upper stage plus 20 metric ton payload I imagine this must be a significant mass, perhaps 2 metric tons. If this is included in the first stage dry mass, then it should be removed from the dry mass value of the first stage for the SSTO case, increasing the payload for this case by perhaps 2 metric tons.

Bob Clark

 

[Urwumpe]

Thanks for the calculation. A couple of questions. First, does your calculation take into account thrust/weight ratio? Judging from the thrust given in the specifications on the SpaceX Falcon 9 page, it's rather high with the upgraded Merlin 1D+, at about 1.8. A high T/W can reduce the gravity loss and increase payload.

No. Otherwise I would also need to include control losses, launch site and aerodynamics, which are all having stronger effects than the effect of T/W on the gravity loss.

Secondly, is the value you're using for the first stage dry mass include the interstage mass? To support the mass of a 110+ metric ton upper stage plus 20 metric ton payload I imagine this must be a significant mass, perhaps 2 metric tons. If this is included in the first stage dry mass, then it should be removed from the dry mass value of the first stage for the SSTO case, increasing the payload for this case by perhaps 2 metric tons.

Bob Clark

Also the first stage includes the interstage, I did not calculate any special effect there. The interstage would also not weight that much in comparison to the remaining inert mass.

 

[BrianJ]

Just for fun, I tried flying the 1st stage of my Falcon9R v1.2 add-on into orbit. No way to do a single burn insertion, so I used three burns - aprox.100s burn to put Apogee at 95km, short coast then burn at Apogee for 95km x 160km orbit, 88kg fuel left for burn at next Apogee for 124km x 160km orbit. So, it is possible(just) in my Orbiter world.
Specs
Max.Thrust(Vac) 825111N x 9 = 7425999N
Isp(SL) 2767Ns/kg
Isp(Vac) 3051Ns/kg
Empty Mass 22500kg (including 400kg RCS propellant and Interstage)
Fuel Mass 401500kg
Launched to 90deg azimuth from KSC.

Cheers,
Brian

 

[RGClark]

Just for fun, I tried flying the 1st stage of my Falcon9R v1.2 add-on into orbit. No way to do a single burn insertion, so I used three burns - aprox.100s burn to put Apogee at 95km, short coast then burn at Apogee for 95km x 160km orbit, 88kg fuel left for burn at next Apogee for 124km x 160km orbit. So, it is possible(just) in my Orbiter world.
Specs
Max.Thrust(Vac) 825111N x 9 = 7425999N
Isp(SL) 2767Ns/kg
Isp(Vac) 3051Ns/kg
Empty Mass 22500kg (including 400kg RCS propellant and Interstage)
Fuel Mass 401500kg
Launched to 90deg azimuth from KSC.

Cheers,
Brian

SSTO's get their best performance by using altitude compensation. Suppose then you were able to get the first stage engines to have the vacuum Isp of the Merlin Vacuum at 342 s, and with the proportional increase of the vacuum thrust. What would be the payload then?

Bob Clark

 

[Urwumpe]

SSTO's get their best performance by using altitude compensation. Suppose then you were able to get the first stage engines to have the vacuum Isp of the Merlin Vacuum at 342 s, and with the proportional increase of the vacuum thrust. What would be the payload then?

Bob Clark

Lets assume that the stage is not affected by gravity and completely frictionless, wouldn't this be much easier?

 

[RGClark]

Lets assume that the stage is not affected by gravity and completely frictionless, wouldn't this be much easier?

No, because how to do altitude compensation has been known since the 60's. All that has to be gotten rid of is the mental block that SSTO's can not carry significant payload.
For instance many people will carry out a mental exercise of a gravity free or friction-free launch but will refuse to do the calculation of an altitude compensation launch.


Bob Clark