Exoscientist

A SSTO research project.

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I’m actively seeking collaborators to calculate the payload possible by adding altitude compensating attachments to existing rockets:

https://www.researchgate.net/project/Single-stage-to-orbit-SSTO

 Elon Musk said the Falcon 9 booster could be SSTO, but with small payload. Altitude compensation can increase the payload, but by how much?

 

  Bob Clark

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This highly depends on the method used. Basically, what altitude compensation does is allow you to have a vac-optimized engine that is still capable of running at sea level. Rockets spend most of their flight time (and dV) at high altitudes, but a conventional nozzle optimized for those conditions suffers flow separation, which tends to wreck the engine. This, rather than the specifics of the Isp/pressure curve, is the primary design consideration.

Interestingly, according to equations from your own site, the Isp/altitude curve is a straight line. So while you can optimize for a given altitude, there's never a peak in Isp. Because of this, perhaps a simple extendable nozzle system would be all that's needed for altitude compensation. You can try to extrapolate it based on comparing the mass of an RL-10 with and without it, then calculate the rocket as a "pseudo-TSTO". Calculating an optimum point to extend the nozzle might be an interesting problem in itself.

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Posted (edited)
On 7/8/2019 at 9:57 AM, Exoscientist said:

I’m actively seeking collaborators to calculate the payload possible by adding altitude compensating attachments to existing rockets:

I'd need to rely on some pretty old brain cells, but this is up my ally. The difficulty of a problem like this really hinges on the assumptions we're willing to make. Ideal gas? Frozen Equilibrium? Isentropic Expansion? Constant Cp? There's a lot to it, so I think I'd need a bit of a better idea of what kind of end product you're going for. Would it be a simple equation that could get you in the ballpark, or a little program to get you a bit closer? Please let us know more specifically what you're interested in and I'll poke at it a bit to see what would be involved and whether I can give it a go. For the Isp calculations that is- the payload calculation would be a whole additional can of worms!

Edited by Cunjo Carl

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The reason the Space Shuttle engine was relatively insensitive to altitude was its extremely high chamber pressure.

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8 hours ago, mikegarrison said:

The reason the Space Shuttle engine was relatively insensitive to altitude was its extremely high chamber pressure.

It also had a "lip" designed to avoid separation at low pressure.  It could mostly ignore high atmospheric pressure inefficiency (but not any danger to the engine/nozzle due to separation) thanks to being carried by the SRBs for the first two minutes of flight (once they staged it was at nearly zero air pressure).

I have to doubt the premise of the thread.  Can you show that SSTO is viable with a constant Isp of 452s (SSME vacuum pressure)?  You don't get to use the RL-10's 510s unless you manage to get enough thrust out of an expander cycle to liftoff (perhaps a stratolaunch lift?).  You can expand that "zeroth order approximation" by assuming a T/W of 1.25 and an Isp that approximates 366s (SSME sea level) for the first minute (bv that time you hit 15,000 ft and your air pressure halves), 400s (roughly in between) for the next 30 seconds (at 35,000 ft pressure is halved again), and 450s for the rest.

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1 hour ago, wumpus said:

I have to doubt the premise of the thread.  Can you show that SSTO is viable with a constant Isp of 452s (SSME vacuum pressure)?  You don't get to use the RL-10's 510s unless you manage to get enough thrust out of an expander cycle to liftoff (perhaps a stratolaunch lift?).  You can expand that "zeroth order approximation" by assuming a T/W of 1.25 and an Isp that approximates 366s (SSME sea level) for the first minute (bv that time you hit 15,000 ft and your air pressure halves), 400s (roughly in between) for the next 30 seconds (at 35,000 ft pressure is halved again), and 450s for the rest.

This is the obvious issue, disposable an singe stage rocket might work for small satellites, its one company working on that. 
Here air dropped rockets works well as you say. 
However could you beat fully reusable two stages or something like new Shepard with an disposable upper stage? 

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2 hours ago, wumpus said:

It also had a "lip" designed to avoid separation at low pressure.  It could mostly ignore high atmospheric pressure inefficiency (but not any danger to the engine/nozzle due to separation) thanks to being carried by the SRBs for the first two minutes of flight (once they staged it was at nearly zero air pressure).

And to add to that even further its exhaust products were mostly water, which has a much better expansion efficiency (gamma) for a given pressure+nozzle than any currently fired alternatives. I think the space shuttle main engines were really amazing at what they were able to accomplish!

Not all amazing things are practical though, of course. :)

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I was guessing that the SLS would be a great candidate for this type of thing (not many rockets are going to have hydrolox engines, much less something like SSMEs designed for going from pad to orbit).  Unfortunately, the SLS "first stage" can't lift itself off the pad without the SRBs.  So I assumed that you would remove enough fuel to give a T/W ratio of 1.11 (weight 90% of thrust) and started running the numbers.  Assuming an Isp of 450s (total flight) you get a delta-v (no payload at all) of 9200m/s.  If you assume an Isp of 366s for the first minute (no altitude compensation will give you vacuum thrust, just maximum efficiency vs. backpressure) you get a delta-v of 8700m/s.  Don't forget that as a fully hydrolox rocket, it will have significantly higher aero losses than typical, and with the relatively low T/W ratio gravity losses will be higher.  I doubt 9200m/s will be enough (and you can't get that).

But I'd assume that with even puny single segment SRBs (such as what rings many delta rockets), the thing could lift off with a nearly full fuel tank and take at least some cargo to orbit.  Unfortunately, the whole thing is still going to come back down as the SSMEs can't reignite for orbital insertion.  You'd need a *tiny* second stage for insertion (see shuttle maneuvering engines), so your SSTO becomes three stages pretty quickly.  Then there is always the temptation to make all the stages roughly equal in delta-v...

If Falcon9's booster can basically get into orbit, I'd assume that Starship booster could too although I don't think that thing is ever intended for expendable use.  It should be designed for delivering more delta-v to the upper stage (than Falcon9 on a reusable flight), and could presumably burn the return fuel to get into orbit.  Why you would want to do this is beyond me, as you could easily get more cargo to orbit by using a much cheaper (even expendable) second stage and still reuse the booster. With the SLS there is no worries about reusing the "reusable" RS-25 engines, but it is still a wildly inefficient means of getting to orbit.

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1 hour ago, wumpus said:

Why you would want to do this is beyond me

This is my main objection to all discussions of SSTOs.

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2 hours ago, Nightside said:

@Exoscientist, does an SSTO need to have return capabilities also?

With current technology, an SSTO seems like a pretty pointless exercise unless you can return it.  If you're using a disposable rocket you may as well use a more efficient one that can launch more payload for your money.

 

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5 minutes ago, KSK said:

With current technology, an SSTO seems like a pretty pointless exercise unless you can return it.  If you're using a disposable rocket you may as well use a more efficient one that can launch more payload for your money.

 

Yeah, I was curious because the working Kerbal definition of SSTO seems to always include return, reentry and landing capability.

However that additional capability will  have a huge mass penalty. It would be helpful for the OP to define the parameters.

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On 7/8/2019 at 2:07 PM, Dragon01 said:

This highly depends on the method used. Basically, what altitude compensation does is allow you to have a vac-optimized engine that is still capable of running at sea level. Rockets spend most of their flight time (and dV) at high altitudes, but a conventional nozzle optimized for those conditions suffers flow separation, which tends to wreck the engine. This, rather than the specifics of the Isp/pressure curve, is the primary design consideration.

Interestingly, according to equations from your own site, the Isp/altitude curve is a straight line. So while you can optimize for a given altitude, there's never a peak in Isp. Because of this, perhaps a simple extendable nozzle system would be all that's needed for altitude compensation. You can try to extrapolate it based on comparing the mass of an RL-10 with and without it, then calculate the rocket as a "pseudo-TSTO". Calculating an optimum point to extend the nozzle might be an interesting problem in itself.

 

 Perhaps you can point me to the equation you mean. The equation that gives the exhaust velocity, which equals g*Isp, is quite complicated in its dependence on ambient pressure therefore altitude:

ef1daa8ee24795de2b8ab6cb7b657044846bf03f

 from, https://en.m.wikipedia.org/wiki/Rocket_engine_nozzle#One-dimensional_analysis_of_gas_flow_in_rocket_engine_nozzles

 

 Bob Clark

 

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19 minutes ago, Exoscientist said:

 

 Perhaps you can point me to the equation you mean. The equation that gives the exhaust velocity, which equals g*Isp, is quite complicated in its dependence on ambient pressure therefore altitude:

ef1daa8ee24795de2b8ab6cb7b657044846bf03f

 from, https://en.m.wikipedia.org/wiki/Rocket_engine_nozzle#One-dimensional_analysis_of_gas_flow_in_rocket_engine_nozzles

 

 Bob Clark

 

If the engineering solution is a parabolic nozzle, the "ideal nozzle" for vacuum is infinitely long.  Thus any real vacuum nozzle is a truncated parabola.  What you probably want is something that looks a lot like an additionally truncated parabola for atmospheric use and then clamp down the "only mildly truncated" rest of the nozzle for vacuum use.  This would certainly not be optimal for atmospheric use, but then again no nozzle is ideal for the whole range of the atmosphere anyway.

I expect my "quick, dirty, and expensive to implement" solution still isn't as efficient as the RS-25 nozzle (across all pressure levels), although maximizing vacuum Isp is absolutely critical for this type of thing.

While you Ve equation looks nasty, there aren't a whole lot of parameters that define a 3-d parabola: I think at most 2, not including absolute size (note that the RS-25 doesn't use a true parabola).

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Posted (edited)
On 7/8/2019 at 2:07 PM, Dragon01 said:

...

Interestingly, according to equations from your own site, the Isp/altitude curve is a straight line. So while you can optimize for a given altitude, there's never a peak in Isp. Because of this, perhaps a simple extendable nozzle system would be all that's needed for altitude compensation. You can try to extrapolate it based on comparing the mass of an RL-10 with and without it, then calculate the rocket as a "pseudo-TSTO". Calculating an optimum point to extend the nozzle might be an interesting problem in itself.

 

 

 I think I know which equation you mean. It’s the first one on this page:

http://www.braeunig.us/space/sup1.htm

  Here it is on that page::

 F = q × Ve + (Pe - Pa) × Ae

 

   where F = Thrust

         q = Propellant mass flow rate

         Ve = Velocity of exhaust gases

         Pe = Pressure at nozzle exit

         Pa = Ambient pressure

         Ae = Area of nozzle exit

  The problem is the Ve is quite complicated depending on ambient pressure.

 

 Bob Clark

Edited by Exoscientist

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22 hours ago, KSK said:

With current technology, an SSTO seems like a pretty pointless exercise unless you can return it.  If you're using a disposable rocket you may as well use a more efficient one that can launch more payload for your money.

 

This, its some who work on an disposable ssto for smalsats using just one engine and one separation has an benefit however rocket has to be far larger. Electron or using more solid fuel sound like an better idea. Here air launch also start to make sense as you can use an commercial jet or even an fighter jet, you start at low pressure and drag is also reduced. 

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Posted (edited)
On 7/10/2019 at 12:20 AM, Cunjo Carl said:

I'd need to rely on some pretty old brain cells, but this is up my ally. The difficulty of a problem like this really hinges on the assumptions we're willing to make. Ideal gas? Frozen Equilibrium? Isentropic Expansion? Constant Cp? There's a lot to it, so I think I'd need a bit of a better idea of what kind of end product you're going for. Would it be a simple equation that could get you in the ballpark, or a little program to get you a bit closer? Please let us know more specifically what you're interested in and I'll poke at it a bit to see what would be involved and whether I can give it a go. For the Isp calculations that is- the payload calculation would be a whole additional can of worms!

 

 You are quite right; there are a lot of variables. For simplicity sake, you can imagine the nozzle attachment is one that can be extended so the the exhaust gas pressure matches the ambient pressure. This was the idea behind an extensible nozzle investigated for the Apollo Saturn V rocket though not implemented:

J-2X_Airmat_DWG.png

https://www.alternatewars.com/BBOW/Space_Engines/Rocketdyne_Engines.htm

 For the Falcon 9 and Delta IV first stages this would result in a quite high increase in the vacuum Isp’s. From 312s to ca. 365s for the F9 first stage and from 412s to ca. 480s for the Delta IV first stage.

  Bob Clark

Edited by Exoscientist

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On 7/10/2019 at 12:32 AM, mikegarrison said:

The reason the Space Shuttle engine was relatively insensitive to altitude was its extremely high chamber pressure.

 

 Quite correct. But these were quite expensive engines. The point of this exercise is to match the best vacuum Isp for vacuum optimized upper stage engines, using the less expensive lower chamber pressure engines, while still being able to launch from sea level. The F9 first stage engine’s vacuum Isp would be extended from 312s to ca. 365s and the Delta IV’s from 412s to ca. 465s. Because of the exponential nature of the rocket equation this would result in significant increase in payload.

  Robert Clark

On 7/12/2019 at 10:54 AM, Nightside said:

@Exoscientist, does an SSTO need to have return capabilities also?

 Not necessarily. Just as a TSTO doesn’t necessarily have to have return capability. IF it is found with alt.comp it can offer significant payload then it can be determined if there is sufficient payload to add reusability systems.

 

  Bob Clark

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On 7/10/2019 at 9:32 AM, wumpus said:

It also had a "lip" designed to avoid separation at low pressure.  It could mostly ignore high atmospheric pressure inefficiency (but not any danger to the engine/nozzle due to separation) thanks to being carried by the SRBs for the first two minutes of flight (once they staged it was at nearly zero air pressure).

I have to doubt the premise of the thread.  Can you show that SSTO is viable with a constant Isp of 452s (SSME vacuum pressure)?  You don't get to use the RL-10's 510s unless you manage to get enough thrust out of an expander cycle to liftoff (perhaps a stratolaunch lift?).  You can expand that "zeroth order approximation" by assuming a T/W of 1.25 and an Isp that approximates 366s (SSME sea level) for the first minute (bv that time you hit 15,000 ft and your air pressure halves), 400s (roughly in between) for the next 30 seconds (at 35,000 ft pressure is halved again), and 450s for the rest.

 

 One of the few papers that calculated the flight averaged Isp for the standard bell nozzle version of an engine and one fitted with alt.comp was this paper by Dana Andrews et.al.:

Rocket-powered single-stage-to-orbit vehicles for safe economical access to low Earth orbit.
July 1992Acta Astronautica 26(8-10):633-642
DOI: 10.1016/0094-5765(92)90153-A
Dana G. Andrews E.E. Davis E.L. Bangsund
 
(This is behind a paywall but you can get a free copy through interlibrary loan from any university or public library.)
 
 I was surprised it showed the flight averaged Isp was 447s for the standard engine. The alt.comp version was a little higher at 460s. The flight averaged Isp is important since it allows you to make a rocket equation estimate of the payload using a single number for the Isp.
 
 Then you can get quite significant payload as an SSTO either for the standard version or the alt.comp version. However, it is known an SSTO is better realized using dense propellants. This is because their lower Isp is more than made up for by their higher density.
 
   Bob Clark
 
 

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Posted (edited)

 Dragon01 mentioned the equation for Isp was linear. It’s not really, but this reminded me of something I’m puzzled about. Fixed nozzles on a sea level engine are a compromise. They are overexpanded for sea level operation so they can get good Isp in vacuum.This should mean they get optimal Isp at some intermediate altitude, not at sea level and not in vacuum. But actually in graphics of engines they show the Isp either constant or increasing towards vacuum conditions. 

Performance-data-for-nozzle-of-Vulcain-1

  The graphic would be expected instead to look like this:

figS1-2.gif

 Taken from this page:

http://www.braeunig.us/space/sup1.htm

   But using the first image above we might be able to model approximately the Isp according to altitude by two straight lines, both for the fixed nozzle case and for the adaptive nozzle case.

 For the fixed nozzle case it would be an inclined straight-line to the altitude of 15,000m, then switching to a constant, i.e., flat-line thereafter at the vacuum Isp value.

 For the adaptive nozzle case, it would be two inclined straight lines. The first would be steeper than the second with the transition at around 15,000m to 20,000m.

  Bob Clark

 

Edited by Exoscientist

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On 7/12/2019 at 1:19 PM, mikegarrison said:

This is my main objection to all discussions of SSTOs.

Skylon is typing...

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18 minutes ago, Aperture Science said:

Skylon is typing...

I'm sure they have plenty of time to do that, because they are never going to be busy flying.

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Just now, mikegarrison said:

I'm sure they have plenty of time to do that, because they are never going to be busy flying.

I don't know about that one chief, the SABRE engine is expected to reach TRL 6 by 2020

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On 7/14/2019 at 3:11 PM, Exoscientist said:

 Dragon01 mentioned the equation for Isp was linear. It’s not really, but this reminded me of something I’m puzzled about.

The ideal is for the nozzle exit pressure to match the ambient pressure. This will never actually happen in vacuum, so all "vacuum nozzles" are always non-ideal. But they don't fall off in performance as the ambient pressure gets lower and lower. All that happens is that they increase performance until they have taken full advantage of the available nozzle. After that point it doesn't really matter how much lower the ambient pressure falls -- the nozzle is already extracting as much energy out of the flow as it can.

5 minutes ago, Aperture Science said:

I don't know about that one chief, the SABRE engine is expected to reach TRL 6 by 2020

Tell you what, come back here when Skylon reaches orbit and I'll send you $100 via PayPal.

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