SSTO Engine Technology

kbd512 · 2024-05-25 20:42:08

For SSTO to work, we do require very high performance LOX/LCH4 or LOX/RP1 engines, so to kick off this topic I present the following:

Launcher's E-2 LOX/RP1 Oxidizer-Rich LOX-Cooled Staged Combustion Engine

1697159288514?e=2147483647&v=beta&t=DAgWi4bHAJ19KH3W6n4HIVllw1XrXmJgyEkFn7D9Kdo

Launcher-shows-off-its-3D-printed-rocket-doing-a-full-scale-burn.jpg

Rather than just watching a video of the engine, beautiful as that is, you get to see the performance data onscreen:
E-2 Test - Highest-performance kerosene rocket engine turbopump ever manufactured in the U.S.

My favorite video of the E-2 engine (brilliant blue flame, just like Methane and Hydrogen):
Who has ever seen a LOX/Kerosene liquid engine with a blue plume?

The characteristic sooty exhaust from most LOX/RP1 engines is replaced by a brilliant blue and orange flame, without a trace of soot, except for a very brief puff at startup and shutdown.

Thrust: 22,000lbf / 97,861N
O/F Ratio: 2.62:1
Isp: 365s (vac)
C* Efficiency: 98%+
Chamber Pressure: 100 bar

Turbopump Characteristics (you can see some of this data live during an engine test if you watch the first YouTube video link)
Pressure: 310 to 330 bar
Efficiency: 72%+
Power: 1.4MW
Pre-Burner Temperature 200°C
Inducer / Impeller rpm: 30,000
Impeller Material: 3D printed from Inconel 718
Combustion Chamber: 3D printed CuCrZr alloy using AMCM M 4K 3D metal printer
Co-Axial Injector: 3D printed using a Velo3D Sapphire 3D metal printer
Nozzle Diameter: 16 inches

Edit:
I forgot one other little tidbit about this engine- 99%+ combustion efficiency was ultimately achieved. It's a fine-tuned hypersonic speed machine. The exhaust plume makes it look just like a miniature Raptor.

Last edited by kbd512 (2024-05-25 20:52:53)

SpaceNut · 2024-05-26 08:05:14

With a heavy ship in the near approximate launch mass of a falcon Heavy 9 and this fuel type.

PROPELLANT LOX / RP-1

ENGINES MERLIN SEA LEVEL
Merlin is a family of rocket engines developed by SpaceX for use on its Falcon 1, Falcon 9 and Falcon Heavy launch vehicles. Merlin engines use RP-1 and liquid oxygen as rocket propellants in a gas-generator power cycle. The Merlin engine was originally designed for recovery and reuse.
THRUST 845 kN / 190,000 lbf
ENGINES MERLIN VACUUM
Merlin Vacuum features a larger exhaust section and a significantly larger expansion nozzle to maximize the engine’s efficiency in the vacuum of space. Its combustion chamber is regeneratively cooled, while the expansion nozzle is radiatively cooled. At full power, the Merlin Vacuum engine operates with the greatest efficiency ever for an American-made hydrocarbon rocket engine.
THRUST 981 kN / 220,500 lbf

SpaceNut · 2024-05-28 18:12:42

GW post on engines and equations

tahanson43206 wrote:

GW Johnson just posted a couple of studies on Single Stage to Orbit and Two Stage to Orbit ....
The spreadsheets can be provided if anyone is interested in seeing them.
Attached are copies in pdf format of two articles I wrote and just recently published on "exrocketman". They are bounding calculations on what can be done toward expendable and reusable vehicles to reach Earth orbit from the surface. One investigates and bounds what can be done SSTO. The other investigates and bounds TSTO. If you want to post these in the drop box thingie, go ahead.
<snip>
This is very simple rocket equation stuff, done in a couple of spreadsheets. The ascent-averaged Isp data come from other stuff I have recently published on "exrocketman", about estimating rocket engine performance. Some of that was done with a version of the bell nozzle rocket spreadsheet used in the orbits+ course. The free-expansion stuff came from a post on "exrocketman" dealing with aerospike nozzles. If anyone wants the spreadsheets, they can have them.
GW
The first file is to be linked from here (SSTO):
https://www.dropbox.com/scl/fi/hu5zc3qc … 3lptv&dl=0
The second file is to be linked from here (TSTO):
https://www.dropbox.com/scl/fi/4dnyyqjn … gsvmd&dl=0
Here is an update:
This is the one that supports the other two you just posted for me. I meant to post this on "exrocketman" some time ago, but never got around to it until today.
It shows vividly just how easy it is to use the "r noz alt" worksheet in the "liquid rockets.xls" spreadsheet file, plus the Paintbrush-made "engine sizing report.png" file to very rapidly size multiple engines and run trade studies. This is where I got my recommendations for how to size a fixed "compromise" bell nozzle to get really good ascent performance out of it.
That spreadsheet file is an update of the one that is part of the orbits+ course materials. I took that one, deleted the extraneous worksheets, added an altitude performance calculation block with automatic plots, and added a output data block that works perfectly with a "Paintbrush"-made engine sizing report. It becomes cut-and-paste with some minor edits to report a design.
The multiple engine designs I sized for the trade study also make a good data library. Pdf document file attached. It should go with the other two, which were "Bounding Calculations for SSTO Concepts" and "Bounding Calculations for TSTO" that you just posted for me.
Link to pdf goes here:
https://www.dropbox.com/scl/fi/s8v6c0zc … upmdo&dl=0
(th)

SpaceNut · 2024-06-01 14:40:16

I began to wonder if the Falcon first stage with modifications would be capable of a single stage to orbit.

https://en.wikipedia.org/wiki/Falcon_9_Full_Thrust

Mass (without propellant)[39] 22,200 kg (48,900 lb)
Mass (with propellant) 433,100 kg (954,800 lb)
Liquid oxygen tank capacity 287,400 kg (633,600 lb)
Kerosene tank capacity 123,500 kg (272,300 lb)
Payload fairing 1,700 kg (3,700 lb)

Thrust (stage total)[4] 7,607 kN (1,710,000 lbf) (sea level)
Specific impulse Sea level: 282 seconds[

RGClark · 2024-07-03 08:28:50

SpaceNut wrote:

I began to wonder if the Falcon first stage with modifications would be capable of a single stage to orbit.
https://en.wikipedia.org/wiki/Falcon_9_Full_Thrust
Mass (without propellant)[39] 22,200 kg (48,900 lb)
Mass (with propellant) 433,100 kg (954,800 lb)
Liquid oxygen tank capacity 287,400 kg (633,600 lb)
Kerosene tank capacity 123,500 kg (272,300 lb)
Payload fairing 1,700 kg (3,700 lb)
Thrust (stage total)[4] 7,607 kN (1,710,000 lbf) (sea level)
Specific impulse Sea level: 282 seconds[

We can estimate using the Silverbirdastronautics.com payload estimator. Some quirks of the program have to be noted though. First, always use the vacuum thrust and vacuum Isp, even for first stages. This is because the program already takes into account the diminution at sea level. Note in the images below the engine thrust and Isp fields have the vacuum values even though this is for the Falcon 9 first stage.
Secondly, input the “Inclination” for the launch as the latitude of the launch site. This is just a fact of orbital mechanics that the launch angle should match the sites latitude to maximize payload. So for a launch from Cape Canaveral I input 28.5 degrees.
Third, for the “Restartable upper stage?” Option, select “No”. Selecting “Yes” often reduces payload, perhaps because it keeps some propellant on reserve for a restart.

Then this is what the input and results screens look like:

About 3,400 kg to LEO for the Falcon 9 first stage as an expendable SSTO. About the expendable scenario, note I subtracted 2,000 kg from the dry mass input field taking the dry mass down from 22,000 kg to 20,000 kg since reportedly the landing legs add about 2,000 kg to the dry mass of the first stage.

The question arises then why subtract that off if you’re aiming for a reusable system? A few reasons. It is my opinion that the opposition to SSTO’s is so engrained that just doing a launch carrying a payload would be an important thing to do. So first accomplish the expendable case then proceed to the reusable case.

[Sidebar: this is one of the reasons why I disagree with the approach SpaceX is taking with the Starship. SpaceX was spectacularly successful by first getting the expendable Falcon 9 then proceeding to reusability. If they had taken that approach to the Starship, they would already be flying expendable rockets to orbit at a profit. Moreover, they would already have rockets capable of single flight missions now to the Moon or Mars. No refueling flights nor SLS required. I mean they could do that literally like tomorrow.]

Secondly, the margins for a SSTO are slim, so you want to maximize the payload. So for the operational SSTO you want to use the known technology of altitude compensation. Using this instead of the vacuum Isp for the Merlin being 311s you could get the highest known possible vacuum for a kerolox engine, ca. 360s, while still having an engine able to fire at sea level.

This will greatly increase the payload possible, at least to 10,000 kg possibly higher, simply by having a variable nozzle. Now, when you have that higher payload then you can add on reusability systems.

Bob Clark

Last edited by RGClark (2024-07-03 09:00:22)

RGClark · 2024-07-03 08:57:08

In addition to using a Falcon 9 first stage, I would like to see smaller versions tried, specifically using the F9 2nd stage. The Merlin Vacuum on the 2nd stage can’t operate at sea level because of its high expansion. And the sea level Merlin would not have enough thrust to loft the stage from the ground.
So I’ll reduce the propellant load by 1/2. A single sea level Merlin could then launch it. I’ll estimate this half-size 2nd stage’s dry mass by first subtracting off the engine mass from the dry mass, taking half the remaining mass, then adding back on the mass of the engine. The reason is you still need the full engine size and mass to lift off, not a half-size engine.

The results are as below:

So about 670 kg to orbit as an expendable. Again for an operational SSTO you really want to use altitude compensation. I estimate using it you could raise it the payload to ca. 1,600 kg or possibly higher.

Another nice thing about this is you could get 10 of the these small SSTO’s from one Falcon 9, since there are 10 Merlins on the Falcon 9, and the total propellant size on the Falcon 9 of 500 tons amounts to 10 of the small size SSTO’s.

So you could buy a single reused Falcon 9 at $40 million, and break it down to 10 of the small SSTO’s at $4 million each.

Bob Clark

Last edited by RGClark (2024-07-03 08:57:45)

SpaceNut · 2024-07-03 14:53:14

Thanks for the working of the reuse with https://silverbirdastronautics.com/

RGClark · 2025-05-09 23:17:37

I started a group on LinkedIn on developing SSTO’s:

SSTO - Single Stage to Orbit.
https://www.linkedin.com/groups/13205030

My first post in that group was on developing an expendable SSTO. The reason is the opinion against a SSTO being feasible is so strong it’s important to break that mindset by just getting an expendable one with significant payload.

The point of the matter is getting an expendable SSTO is easy with minor modification to existing engines: add an extensible nozzle to get high vacuum ISP at vacuum, but which can be retracted at sea level. Such extensible nozzles have been in use since the 90’s with the RL10 upper stage engine. The problem is they haven’t been used on first stage engines.

The surprising conclusion you get is any existing (liquid fueled) stage can be made SSTO by addition of an extensible nozzle, though for an upper stage you would have to cut fuel load or add additional engines since commonly they don’t have enough thrust for liftoff from ground since they don’t need it.

But there is a problem here as far as estimating payload capability. Commonly with fixed nozzle stages you use a fixed value for the ISP to estimate the delta-v possible. This is convenient since it is only a single line calculation using the rocket equation. But that probably is not accurate for a variable nozzle since you are changing the characteristics of the nozzle through out the flight. You could you use, say, the vacuum isp for this case but that would probably over estimate it.

What really needs to be done is accurate trajectory simulations of the type NASA uses. Then you could see how the variable nozzle deviates from what a fixed nozzle would do. I’ve only seen one paper actually do that. I’ll see if I can find it.

Bob Clark

tahanson43206 · 2025-05-10 13:57:58

For RGClark re Post #8

Thanks for the good news of your new LinkedIn group, and for your contribution to this topic.

GW Johnson wrote a short email reminder to think about cooling for your variable geometry nozzle.

With that as a hint, I asked Google's Gemini about variable geometry nozzle design and related research, and followed up with a question about cooling. It appears that different cooling methods are needed at different phases of flight, so your solution will need to include more than one cooling method.

Conversation with Gemini
Variable Geometry Rocket Expansion Bell - Hello Again
***
Hello again! It sounds like you're interested in learning about Variable Geometry Rocket Expansion Bells. This is a fascinating and advanced concept in rocket propulsion.
Here's a breakdown of what this technology entails:
Understanding the Basics: Rocket Nozzles and Expansion Bells
Purpose of a Rocket Nozzle: A rocket nozzle is a critical component that accelerates the hot gases produced in the combustion chamber to supersonic speeds. This acceleration generates the thrust that propels the rocket.
The Expansion Bell: The "bell" shape (like in a traditional de Laval nozzle) is the diverging section of the nozzle, downstream of the narrowest point called the throat. Its function is to expand the exhaust gases, converting their thermal energy and high pressure into kinetic energy (velocity).
Optimal Expansion: For maximum efficiency, the pressure of the exhaust gases at the nozzle exit should ideally match the ambient (surrounding atmospheric) pressure.
Under-expansion: If the exit pressure is higher than the ambient pressure (e.g., a nozzle designed for vacuum operating at sea level), the nozzle isn't extracting all possible thrust.
Over-expansion: If the exit pressure is lower than the ambient pressure (e.g., a large vacuum nozzle operating at sea level), the exhaust plume can become unstable, and performance can be lost. Flow separation can occur inside the nozzle, leading to instability and reduced thrust.
The Challenge: Changing Ambient Pressure
A rocket's operating environment changes dramatically during its ascent:
At Sea Level: Ambient pressure is high. A nozzle with a smaller expansion ratio (the ratio of the exit area to the throat area) is more efficient.
In Vacuum (Space): Ambient pressure is virtually zero. A much larger expansion ratio is needed to continue expanding the gases and extract maximum thrust.
A fixed-geometry nozzle is therefore a compromise, optimized for a specific altitude or range of altitudes, leading to reduced efficiency at other points in the trajectory.
Enter Variable Geometry Expansion Bells
A variable geometry rocket expansion bell aims to solve this problem by allowing the nozzle's expansion ratio to change during flight. This means the shape or length of the bell can be adjusted to optimize performance across different altitudes and ambient pressures.
How it Might Work (Conceptual Designs and Research Areas):
While not widely implemented in operational rockets due to complexity, several concepts have been explored:
Extendable/Retractable Nozzle Sections: Parts of the nozzle bell could extend outwards as the rocket ascends into lower pressure environments. This is perhaps the most intuitive approach.
Dual-Bell Nozzles: These nozzles have two different bell contours. At low altitudes, the exhaust flow separates at the point where the first, smaller bell ends. As ambient pressure decreases with altitude, the flow remains attached longer, utilizing the second, larger bell contour, effectively increasing the expansion ratio. While not continuously variable, it offers a step-change in geometry.
Aerospike Nozzles (a related concept): While not a "bell" in the traditional sense, aerospike nozzles are inherently altitude-compensating. The exhaust flows along the outside of a central spike, and the ambient pressure forms the outer boundary of the "nozzle." This allows the exhaust to expand optimally across a wide range of altitudes without moving parts in the nozzle itself.
Advanced Flow Control: Research also looks into methods of forcing flow separation or attachment at desired points within a nozzle to mimic changes in geometry without large mechanical movements.
Advantages of Variable Geometry Rocket Expansion Bells:
Improved Performance: Higher average thrust and specific impulse (a measure of engine efficiency) over the entire flight trajectory.
Increased Payload Capacity: Better performance can translate to the ability to carry heavier payloads or achieve higher orbits.
Single-Stage-to-Orbit (SSTO) Enabler: For ambitious concepts like SSTO vehicles, which need to operate efficiently from sea level to orbit with a single engine system, variable geometry nozzles are highly desirable.
Disadvantages and Challenges:
Increased Complexity: Moving parts in the harsh environment of a rocket exhaust (extreme temperatures, pressures, and vibrations) present significant engineering challenges.
Increased Weight: The mechanisms required to adjust the nozzle geometry add mass to the engine, which can offset some of the performance gains.
Reliability: Ensuring the mechanisms work flawlessly during flight is critical.
Cost: Development and manufacturing costs are higher compared to fixed-geometry nozzles.
Current Status and Research:
While fully variable expansion bells are not standard in most operational launch vehicles (which often use fixed nozzles optimized for a portion of the flight or different engines for different stages), research and development continue.
Concepts like dual-bell nozzles have seen more practical investigation and testing.
There's ongoing research into advanced nozzle concepts, including those that adapt to ambient pressure, as the space industry seeks more efficient and versatile propulsion systems. This includes work on controlling solid rocket motors by modifying nozzle throat geometry, which is a related application of variable geometry.
In summary, variable geometry rocket expansion bells represent a sophisticated approach to optimizing rocket engine performance across varying altitudes. While facing significant engineering hurdles, the potential benefits, especially for future launch systems and ambitious mission profiles, keep it an active area of interest and research.
***
Thank you for this very ** nice ** overview of what I understand is a complex subject. Cooling appears to be necessary to preserve the integrity of a rocket nozzle. How does the need for cooling factor into the design?
***
You're absolutely right to bring up cooling! It's a massive challenge in rocket engine design, and it becomes even more complex when you start talking about variable geometry nozzles. The temperatures inside a rocket combustion chamber and nozzle can reach thousands of degrees Celsius, hot enough to melt most materials.
Here's how the critical need for cooling factors into rocket nozzle design, especially in the context of variable geometry:
Why Cooling is Paramount
Material Integrity: Without effective cooling, the nozzle materials would rapidly overheat, lose structural strength, and fail catastrophically.
Maintaining Nozzle Shape: The precise contour of the nozzle is crucial for performance. Overheating can cause warping or erosion, degrading thrust and efficiency.
Preventing Burn-Through: Hot gases can literally burn through the nozzle walls if not adequately cooled.
Common Cooling Methods in Rocket Nozzles
Several techniques are used, sometimes in combination:
Regenerative Cooling:
How it works: This is the most common method for liquid-propellant rocket engines. The fuel (or sometimes the oxidizer) is circulated through channels built into the walls of the combustion chamber and nozzle before it's injected into the chamber for combustion. As it flows, it absorbs heat from the walls, cooling them down while also preheating the propellant, which can slightly improve combustion efficiency.
Design Impact: Requires a double-walled nozzle with intricate internal channels. The material must be conducive to heat transfer and able to withstand the pressure of the coolant.
Ablative Cooling:
How it works: Used primarily in solid rocket motors and sometimes for simpler liquid engines or specific nozzle sections. The inner surface of the nozzle is lined with a material (often a reinforced phenolic or carbon-carbon composite) that slowly burns away and vaporizes in a controlled manner. The process of phase change (solid to gas) absorbs a significant amount of heat, and the vaporized material creates a protective layer of cooler gas along the nozzle wall.
Design Impact: The nozzle wall thickness must account for the material that will be consumed. The choice of ablative material depends on burn time and heat flux. Performance can change slightly as the material ablates and the nozzle contour subtly changes.
Film Cooling/Curtain Cooling:
How it works: A thin film of relatively cool gas or liquid (often unburnt fuel) is injected along the inner surface of the nozzle wall. This film acts as a barrier between the hot combustion gases and the wall.
Design Impact: Requires small injection ports or slots at strategic locations within the nozzle. The distribution of the coolant film is critical.
Radiation Cooling:
How it works: For nozzles (or parts of nozzles) that operate primarily in the vacuum of space, some heat can be radiated away to the surroundings. This is often used for nozzle extensions made of high-temperature materials like refractory metals (e.g., niobium, molybdenum) or ceramic matrix composites.
Design Impact: Requires materials with high emissivity and the ability to maintain strength at very high temperatures. The nozzle extension is typically uncooled by fluids.
How Variable Geometry Complicates Cooling
Introducing moving parts into this extremely hot and high-pressure environment dramatically increases the cooling challenge:
Regenerative Cooling with Moving Parts:
Seals: Maintaining effective seals for coolant passages between segments of a nozzle that move relative to each other is incredibly difficult. Any leakage of hot gas into coolant channels or coolant into the exhaust stream would be detrimental.
Flexible Coolant Lines: If parts of the nozzle extend or articulate, flexible high-pressure lines capable of withstanding extreme temperature gradients might be needed. These add complexity and potential failure points.
Consistent Coverage: Ensuring that all parts of the changing nozzle surface are adequately and evenly cooled as the geometry shifts is a major design hurdle. Hot spots could develop at interfaces or in areas where coolant flow is disrupted.
Structural Integrity: The coolant channels themselves contribute to the nozzle's structure. Designing these to accommodate movement while maintaining strength is complex.
Ablative Cooling with Moving Parts:
Interface Issues: If an ablative nozzle has moving sections, the interface between these sections could experience uneven erosion or stress concentrations.
Structural Support: Ensuring the ablative liner stays bonded and intact as the underlying structure moves is a challenge.
Predictability: The ablation rate might be harder to predict accurately with changing flow conditions due to variable geometry.
Film Cooling with Moving Parts:
Consistent Film: Maintaining an even and effective coolant film over a surface that is changing its shape or length is very difficult. Injection points might become misaligned or less effective as the geometry shifts.
Flow Dynamics: Changes in nozzle contour can alter the flow dynamics near the walls, potentially disrupting the protective film.
Material Constraints:
Materials used in variable geometry mechanisms must not only withstand high temperatures (even with cooling) but also the mechanical stresses of movement, vibration, and thermal cycling. Finding materials that satisfy all these requirements is tough.
Increased Complexity and Weight:
Any cooling system for a variable geometry nozzle will inevitably be more complex and likely heavier than for a fixed nozzle. This added mass can offset some of the performance gains the variable geometry is intended to provide.
In summary:
The need for cooling is a fundamental driver in rocket nozzle design. For fixed nozzles, it's already a significant engineering challenge. When you add the mechanical complexity of variable geometry, ensuring reliable and effective cooling across all operating configurations and moving interfaces becomes exceptionally difficult. This is one of the primary reasons why variable geometry nozzles, despite their theoretical performance benefits, are not yet commonplace in operational rockets. The trade-off between the performance gain from variable geometry and the added weight, complexity, and potential failure modes of the cooling system (and the mechanism itself) must be carefully evaluated.

Sources and related content
Topic 5: Engine Cooling Design - MIT Rocket Team
wikis.mit.edu
Breakthrough in topology-optimized rocket engine cooling cuts maximum temperature by 63ºC - ToffeeX
toffeex.com
Research of material for uncooled nozzle extensions of liquid rocket engines
www.researchgate.net
***
Thank you for the helpful overview of both the opening question, and the cooling follow up! While I am away, best wishes for success as you attempt to help all your other customers!
Thank you very much! I appreciate your kind words and well wishes. I'm here to help whenever you have more questions in the future.
Best wishes to you as well!

For RGClark ... please continue investigating this interesting and potentially rewarding topic.

(th)

kbd512 · 2025-05-10 15:46:08

Dr Clark,

Tim Chen (Chief Engineer for Boeing Satellite Systems) seems to think SSTO with LOX/RP1 is impossible and SSTO with LOX/LH2 is possible but very difficult. I want to understand why that is, because there seems to be an absolute fixation on the marginal Isp differences between RP1 and LH2. The combination of Total Impulse (Total Force) generated to accelerate a vehicle with a constrained mass is what dictates whether or not that vehicle attains orbital velocity, or doesn't. You get marginally better Isp with LOX/LH2 at the expense of much larger propellant tank structures that add to SMF and detract from PMF. Materials don't get any stronger as vehicle volume increases. On top of that problem, LH2-fueled engines produce less than half as much thrust per unit engine mass, as compared to LCH4/RP1-fueled engines. Modern hydrocarbon fueled rocket engines (Merlin-1D, Raptor-3; 185:1 to 190:1 TWR), about 2.5X as much thrust per unit engine mass as LH2-fueled engines (RS-25D, J-2X, RS-68A; 47:1 to 75:1 TWR).

I can see why they think this is impossible. They act as if a LH2-fueled vehicle with more than double the internal volume of an equivalent RP1 fueled vehicle will somehow generate meaningfully more total force for a given propellant mass, but the actual mass differential due to poor vehicle acceleration (fighting gravity) and added drag makes the vehicle's mass (and thus Isp) differential trivial by the time we scale-up the PMF to a Space Shuttle mass equivalent.

My operating assumptions are that for practical SSTOs, we require structural fibers with the strength of T1200 and engines with 200:1 thrust-to-weight ratios, so as to keep SMF low and TWR high enough for the vehicle to deliver useful PMF.

Please tell me if you find any serious flaws in the figures I've presented below:

Using 90% of vacuum Isp, you get 304.2s for RP-1 (RD-180), 324.9s for LCH4 (Raptor 3; sea level model), and 382.5s for LH2 (RS-25). LH2 is clearly better than RP1 on Isp, but that figure of merit is highly misleading without understanding just how much Density Impulse affects Total Impulse for a given vehicle / structural mass fraction (SMF), by way of its propellant tank structure, and how high engine TWR is required for any SSTO concept to succeed.

Oxidizer: 2,339.2kg (1.746m^3 of LOX at 1,340kg/m^3)
Fuel: 860kg (1m^3 of RP1)
Total Propellant Volume: 2.746m^3
Engine: RD-180
Mixture Ratio: 2.72:1
Mass Flow Rate: 1,250kg/s
Thrust: 3,723,161N / 379,657kg-f (90% of vacuum thrust)
Firing Time: 2.55936s
Total Impulse from 1m^3 of fuel: 9,528,909N-s
Propellant Mass for 510s of Firing Time: 637,500kg; 1,899MN-s Total Impulse
LOX/RP1 Propellant Mixture Ratio and Total Propellant Mass and Volume for 510s of Firing Time:
1,250kg/s * (2.72/3.72) = 913.978494623655914kg/s LOX; 1,250kg/s * (1/3.72) = 336.021505376344086 RP1
466,129kg / 347.857m^3 LOX; 171,371kg / 199.269m^3 RP1; 547.126m^3 ttl propellant vol

Oxidizer: 1,606.64kg (1.2m^3 of LOX at 1,340kg/m^3)
Fuel: 422.8kg (1m^3 of LCH4)
Total Propellant Volume: 2.2m^3
Engine: Raptor 3
Mixture Ratio: 3.8:1
Mass Flow Rate: 1,160kg/s
Thrust: 2,471,276N / kg-f of thrust (90% of vacuum thrust for sea level nozzle)
Firing Time: 1.74952s
Total Impulse from 1m^3 of fuel: 4,323,540N-s
Tank Volume for RP1 Equivalent Total Impulse: 4.849m^3 (77% increase over RP1)
Propellant Mass for 510s of Firing Time: 591,600kg (92.8% of RP1); 1,260MN-s Total Impulse (66.4% of RP1)
LOX/LCH4 Propellant Mixture Ratio and Total Propellant Mass and Volume for 510s of Firing Time:
1,160kg/s * (3.8/4.8) = 918.333333333333333kg/s LOX; 1,160kg/s * (1/4.8) = 241.666666666666667kg/s LCH4
468,350kg / 349.515m^3 LOX; 123,250kg / 291.509m^3 LCH4; 641.024m^3 ttl propellant vol; 17.2% vol increase over RP1)

Oxidizer: 425.4kg (0.317m^3 LOX at 1,340kg/m^3)
Fuel: 70.9kg (1m^3 of LH2)
Total Propellant Volume: 1.317m^3
Engine: RS-25
Mixture Ratio: 6:1
Mass Flow Rate: 514.49kg/s
Thrust: 2,050,942N / 209,138kg-f of thrust (90% of vacuum thrust)
Firing Time: 0.96464s of firing time
Total Impulse from 1m^3 of fuel: 1,978,421N-s
Tank Volume for RP1 Equivalent Total Impulse: 4.816m^3 (75% increase)
Propellant Mass for 510 Seconds Firing Time: 262,390kg (41.2% of RP1); 1,046MN-s Total Impulse (55.1% of RP1)
LOX/LH2 Propellant Mixture Ratio and Total Propellant Mass and Volume for 510s of Firing Time:
514.49kg/s * (6/7) = 440.991428571428571kg/s LOX; 514.49kg/s * (1/7) = 73.498571428571429kg/s LH2
224,906kg / 167.840m^3 LOX; 37,484kg / 528.692m^3 LH2; 696.532m^3 ttl propellant vol; 27.3% vol increase over RP1)

Implications:
To deliver the same 1,898,812,110N-s (1,899MN-s) Total Impulse that LOX/RP1 delivers by firing for 510s:
Raptor 3 has to fire for 768s, which implies 705,280kg (526.328m^3) of LOX, 185,600kg (438.978m^3) of LCH4, 891,289kg (965.306m^3) in total
RS-25 has to fire for 926s, which implies 338,681kg (242.747m^3) of LOX, 56,447kg (796.148m^3) of LH2, 476,327kg (1,038.895m^3) in total

The typical response, "I'll just add more engines" doesn't work here. You increase the vehicle's SMF the moment you do that. The only valid response would be to double the TWR of the LH2-fueled engine, which we cannot seem to do. IF you could actually do that, then what's stopping you from proportionally increasing the TWR of RP1-fueled engines? The only methods we have for doing that at this point (reducing engine weight by using advanced materials and design simplification), are broadly applicable to any chemical rocket engine. For a SSTO vehicle, you cannot overcome a force-generating deficiency merely by adding more engine weight. At some point, you must improve TWR. The TWR for the RP1 and LCH4 engines is already sufficient. LH2 engines need dramatic TWR improvements.

You may or may not need to deliver 1,899MN-s to push any particular payload into orbit using lighter / higher-Isp propellants, but if that's how much force you require to deliver a heavy payload to orbit, then your propellant volume increases for equivalent total force generated, by 76.4% for LCH4 or 89.9% for LH2.

Space Shuttle Main Engines typically fired for about 520s. I used 510s, which is close enough to what I could recall from memory. Using 90% of vacuum Isp, Total Impulse equates to 1,066,489,840N-s over 520 seconds, so 3 RS-25 engines would deliver 3,199,469,520N-s. The pair of Solid Rocket Boosters delivered about 3,309,476,870N-s. All together, 6,508,946,390N-s of thrust was required to deliver a 116,120kg Space Shuttle Orbiter to LEO. Space Shuttle consumed approximately 997,904kg of APCP plus 735,601kg of LOX/LH2 to achieve orbit, 1,733,505kg in total, which is pretty darn close to LOX/RP1.

How much of each liquid bi-propellant combination do I need to generate 6,508,946,390N-s of thrust using real world engine designs?

LOX/RP1: 1,597,846kg (1,192.422m^3) of LOX; 587,443kg (683.074m^3) of RP1; 2,185,289kg (1,875.496m^3)
LOX/LCH4: 2,418,744kg (1,805.032m^3) of LOX; 636,511kg (1,505.467m^3) of LCH4; 3,055,255kg (3,310.499m^3; 177% of LOX/RP1)
LOX/LH2: 1,399,547kg (1,044.438m^3) of LOX; 233,258kg (3,289.956m^3) of LH2; 1,632,805kg (4,334.394m^3; 231% of LOX/RP1)

The propellant mass differential between LOX/RP1 and LOX/LH2 is only 552,484kg in favor of LOX/LH2 for equivalent Total Impulse, so a 33% propellant mass increase crammed into 2.3X LESS volume. The LOX tank for a RP1 fueled vehicle is 14% larger while its fuel tank is 4.8X smaller than an equivalent LH2 tank. A 43% propellant volume reduction is likely to have an outsized effect on SMF, as we're about to see.

Will that 552t of additional propellant mass for LOX/RP1 over LOX/LH2 make an actual difference to payload mass for a SSTO?

For a SSTO, the driving forces behind vehicle SMF / dry mass fraction are engine TWR and propellant tank volume and hoop stress from internal pressurization, not aero loads or acceleration loads. NASA's Composite Cryo-Tank Demonstrator Program already proved that the internal pressurization load required by the LH2 tank drove the minimum structural mass requirement, rather than the much higher mass of the LOX in the associated LOX tank, so long as vehicle acceleration was limited to 3g, as it was for the Space Shuttle. LH2 propellant tanks require the highest internal pressurization levels and are physically the largest in size across all common fuels, so this internal load problem is worse than it superficially appears to be, but let's hand-wave that for now.

We have a constrained mass-to-orbit to work with, of 116,120kg, which is equal to the Space Shuttle's max liftoff mass. This is where the pitiful TWR of the RS-25 absolutely kills our LH2-fueled SSTO concept, especially for full reusability. We need 14X RS-25s for a 1.5:1 liftoff TWR, which adds 44,478kg of engine mass to our vehicle. Unfortunately, our total mass-to-orbit won't change to accomodate that low TWR. 38% of our total mass-to-orbit cannot be the engines! We get 17,261kg as the equivalent engine mass for 200:1 TWR LOX/RP1 engines, for the same 1.5X liftoff TWR. We get 20,658kg as the propellant tank mass for LOX/LH2. That takes our SMF, for engines and propellant tanks only, up to 56% of our total PMF, for the LH2 SSTO concept. Stick a fork in that LH2 SSTO concept, because it's done! We only have 50,984kg remaining for the LH2 SSTO's heat shield, life support systems, and useful payload. We still have 72,767kg to work with after accounting for the propellant tanks, engines, and heat shielding for the RP1 SSTO concept.

The remaining PMF for a RP1 SSTO, after engine and propellant tank mass are accounted for (89,916kg / 2,185,289kg = 0.039), is 1% higher than the LH2 SSTO payload mass (50,984kg / 1,748,925kg = 0.029). Fixating on Isp, when we're discussing a practical SSTO that will be powered by RP1 or LCH4 or LH2, is an utter waste of time. Total mass to orbit is the same 116,120kg. The higher propellant mass of the RP1 SSTO gets converted into additional thrust, with the end result that usable PMF is slightly better than it is for LH2 fueled design.

The Space Shuttle Orbiter's internal volume, excluding engines and control surfaces, was about 965m^3 and total surface area was about 1,105m^2. Therefore, a SSTO Space Shuttle's internal volume for propellant is about 1.95X that of the historical Space Shuttle Orbiter when powered by LOX/RP1, 3.43X larger in terms of internal volume when powered by LOX/LCH4, or 4.49X larger when powered by LOX/LH2.

Rockwell's VTHL SSTO concept was to be powered by LOX/LH2 only, have roughly the same payload as the ultimate Space Shuttle design, so it was substantially larger than the historical Space Shuttle Orbiter as a result. They were overly-optimistic about dramatic LH2 engine TWR improvements that never materialized. The only major differences between the various Space Shuttle vehicle designs relate to how large the vehicle volume becomes and its GLOW. At this scale, a 1,000t increase in GLOW is far less concerning than a doubling of internal vehicle volume and/or surface area. My basic assertion is that the vehicle has to remain as small as possible because materials don't get any stronger or lighter or more heat-resistant as you scale-up the total internal volume and surface area. The historical Space Shuttle's GLOW was 2,029,633kg. The GLOW for my RP1 SSTO Space Shuttle concept is only 271,776kg greater.

200:1 TWR RP1 fueled engines, for a 2,301,409kg GLOW and 1.5:1 liftoff TWR, would weigh 17,261kg
185:1 TWR LCH4 fueled engines, for a 3,171,375kg GLOW and 1.5:1 liftoff TWR, would weigh 25,714kg
75:1 TWR LH2 fueled engines, for a 1,748,925 GLOW and 1.5:1 liftoff TWR, would weigh 34,979kg

Lockheed-Martin's externally box-stiffened 10m diameter composite cryogenic tank demonstrator had an internal volume of 634.297m^3 and a weight of 2,981kg, so 3 of them, sufficient to hold 1,875.496m^3 of LOX/RP1 propellant, would weigh 8,943kg. It was made with IM7 fiber (820ksi tensile strength) vs Toray T1200 fiber (1,160ksi tensile strength), a 41.5% strength improvement. I specify a stronger fiber for even more strength, not less weight.

116,120kg - 8,943kg (propellant tanks)- 17,261kg (engines) - 17,149kg (heat shield) = 72,767kg remaining (for the landing gear, pressurized cabin, payload- passengers or cargo)

The 17,149kg heat shield mass figure represents the historical Space Shuttle Orbiter's heat shield weight multiplied by 2. I presume lighter and more protective modern heat shielding materials will allow us to constrain the heat shielding mass to this value.

If we remain fixated on using LH2, then most of the mass that we actually deliver to orbit is engines, propellant tanks, and heat shields.

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