SSTO - Mathematical Analysis Gravity vs Stages

tahanson43206 · 2024-05-11 06:34:47

SSTO Single Stage to Orbit

The purpose of this topic is to provide an opportunity for a mathematician (or several working together) to clarify the complex but important topic of Single Stage to Orbit rocket design.

From my perspective, there appears to be a direct relationship between the number of stages needed to reach orbit, and the strength of the gravitational field.

It appears that SSTO from the Moon or Mars is possible, but SSTO from a body with the mass of Jupiter would be impossible using chemical propulsion.

It appears that Earth gravity would permit SSTO, but just barely.

My hope is that this topic will provide an opportunity for mathematical Analysis of the relationship between gravity and stages needed to reach orbit.

There are several topics about SSTO, but none appear to be dedicated to the mathematics of the issue:

Search results
Topic Forum Replies Last post
Could the SuperHeavy booster be SSTO? by RGClark
Interplanetary transportation 16 2023-04-25 22:45:38 by Void
SSME based SSTO’s. by RGClark
Science, Technology, and Astronomy 9 2021-06-30 15:34:22 by kbd512
A SSTO research project. by RGClark [ 1 2 ]
Interplanetary transportation 42 2021-06-06 08:25:12 by Mars_B4_Moon
Reusable LOX/Kerosene SSTO with drop tanks by Antius [ 1 2 3 4 ]
Interplanetary transportation 92 2018-07-12 14:09:26 by GW Johnson
New high strength alloys for SSTO’s? by RGClark
Science, Technology, and Astronomy 0 2018-06-15 00:08:21 by RGClark
SpaceX BFR tanker as an SSTO. by RGClark
Interplanetary transportation 11 2017-10-28 23:46:22 by SpaceNut
Pages:1
Index» Search» Topics with posts containing 'ssto'

(th)

tahanson43206 · 2024-05-11 06:39:09

This post is reserved for an index to posts NewMars members may contribute over time.

Posts showing prior work in this field would be welcome.

It is entirely possible, and perhaps even likely, that deep study of the question of SSTO feasibility vs gravity has already been done and published.

Images of charts showing the data would be welcome.

Since this is a topic about mathematics, and since the forum software does not support rendering of equations, images of equations are a possible solution to allow readers to follow a discussion.

Update 2024/05/13 - The post by kbd512 at the link below provides reasons to pursue SSTO.

http://newmars.com/forums/viewtopic.php … 22#p223022

Update 2024/05/15 - The post by kbd512 provides a set of detailed numbers showing how an SSTO might be designed using Space Shuttle tank as a model.
http://newmars.com/forums/viewtopic.php … 56#p223056

(th)

GW Johnson · 2024-05-11 13:10:30

I posted a bounding calculation on my "exrocketman" blog site titled "bounding Calculations for SSTO Concepts", dated 2 April 2024. For comparison, there is also a bounding calculation study for TSTO on that site, titled "Bounding Analyses for TSTO", dated 3 April 2024. Both articles provide verbal instructions how to access the "orbits+" course materials from the forums. That site is (for the benefit of new readers): http://exrocketman.bogspot.com. Both studies would be germane here.

GW

tahanson43206 · 2024-05-11 13:41:11

For GW Johnson re #3

Thank you for pointing to your work in this topic!

I would be happy to help with display of specific charts or images that would help to illustrate the nature of the challenge.

It should be possible to show the general case for all gravitational fields, anywhere in the Universe. All rocket designers should be faced with the identical physics and chemistry. Human mission planners can expect to be able to launch SSTO from the Moon or Mars, or other smaller bodies, as you have shown.

There ** must ** a gravity field of sufficient strength to deny SSTO for any chemical propulsion method.

(th)

tahanson43206 · 2024-05-11 13:44:00

As a related focus for this topic ...

The efficiency of various launch staging designs might be of interest to readers....

Given a fixed amount of mass to launch, SSTO might be feasible, or TSTO might be more effective/efficient.

I'm hoping there might be analysis available to help a reader to understand the trades to be made.

(th)

kbd512 · 2024-05-12 00:09:26

tahanson43206,

There's one characteristic which would make SSTO, of whatever description, "more feasible":

1. Increase the mass-efficiency of the exhaust product from the rocket by using a higher specific impulse propellant, while retaining sufficient thrust to accelerate fast enough. As you increase your efficiency in generating thrust by increasing the velocity of the exhaust products, your mass flow rate goes down to the point that either extreme input power is required to produce more thrust, or the thrust becomes far too low to accelerate fast enough for your miserly fuel flow rate to mean anything in the context of achieving orbital velocity without consuming more propellant. Apart from a pure chemical reaction, doubling the exhaust velocity over what any chemical reaction can achieve requires doubling the input power to do that, which implies doubling the mass of the onboard equipment producing the input power. This rapidly becomes untenable.

There are only two known methods to achieve both high Isp and high thrust using combustion engine technology:

1. Consume some of the Oxygen / oxidizer from the atmosphere, thereby offsetting the total mass of onboard oxidizer, to propel the rocket to orbit. This typically involves running a turbofan, turbojet, ramjet, and/or scramjet engine, at much greater specific impulse than what a pure LOX/LH2 rocket can achieve, by virtue of greater overall cycle efficiency and reduction of onboard oxidizer mass.

For example, a high-bypass turbofan engine, sourcing its oxidizer from the Earth's atmosphere, can achieve around 3,600s of Isp. The very best LOX/LH2 rockets top out around 465s to 475s of specific impulse. That makes the mass-efficiency of said turbofan propulsion system about 7.5X higher than a rocket using one of the lightest / highest velocity combustion products available (and therefore mass-efficient at generating thrust, relative to lower-Isp bipropellant combinations such as LOX/RP1 or LOX/LCH4).

A major problem arises as you attempt to impart more velocity from your space plane, as well as operation outside an atmosphere that can provide an offboard oxidizer to consume. Turbofans operate most efficiently between about 450mph and Mach 1.6, IIRC, and then turbojets become more efficient, up to about Mach 3, and then ramjets are required to achieve Mach 4 to Mach 6, and finally, scramjets to travel between Mach 6 and Mach 10. Both turbofans and turbojets, aside from RamGen technology, are not designed to consume supersonic velocity inlet air, which means the air must be slowed down to subsonic velocity using inlet geometry and the shockwaves to produce air at high subsonic velocity at the compressor face / fan of the turbofan or turbojet. RamGen can accept inlet air between a dead stop and about Mach 3.5, and use the inlet ramp geometry that forms its "compressor face", to work with instead of mightily against that shockwave generated by the incoming air. It's much better than a turbofan or turbojet in that regard, albeit requiring a super computer to work out the precise ramp geometry, and is simpler and a more efficient compressor requiring far fewer stages. All well and good, but at inlet speeds faster than Mach 3.5, even that cannot process the incoming air fast enough, so then you need a ramjet (also requires subsonic air for combustion) or a scramjet (uses supersonic to hypersonic air for combustion).

Even if you can solve all of that using some air-breathing engine technology or combination of engine technologies, you still need to climb and accelerate out of the dense lower atmosphere as fast as you can, which requires lots of thrust to overcome the mass of the vehicle, which in turn requires more fuel (the "tyranny of the rocket equation"), using those higher-Isp engine technologies, because aerodynamic drag and heating, even in the upper atmosphere, is already a serious issue at Mach 3, which rapidly becomes an extreme issue by Mach 7, even above 100,000ft.

2. Decrease the mass of propellant using higher specific-impulse (more mass-efficient) propellant combinations.

This is a tough one. As chemical reactions go, water happens to be one of the lightest mass combustion products in existence, which means the exhaust velocity is highest, and therefore most mass-efficient. You can only "do better" using lighter combustion products, which means using exotic oxidizers such as Fluorine, or tri-propellant combinations involving Fluorine, LH2, and molten Lithium. There are a few tri-propellant combos with considerably higher-Isp than LOX/LH2, but all are horrifically toxic, as well as being dangerous and difficult to work with for other reasons, such as extreme temperature deltas in the case of molten Lithium and cryogenic LH2. Beyond initial laboratory investigation work, just to explore "the art of the possible", there are no engines which use Fluorine, and for good reason.

In a chemical rocket engine with a given fixed nozzle geometry, whilst ascending through the atmosphere to a place of reduced atmospheric density (low altitude to high altitude), the engine generates "more thrust", for a given mass of propellant pushed out the back, because there is less or even no back-pressure pushing against the expansion of the rocket engine's exhaust. There is no "increase in performance" in the way most people think about it. The engine doesn't magically become "more efficient" or "burn less fuel", it simply does not have atmospheric effects impeding the exit of the combustion products from the exhaust nozzle. This is how "increased Isp" is achieved at high altitude. If the engine's throttle is already shoved into the firewall, then the mass flow of propellant through the engine doesn't change at all. However, the "apparent effect", is that the mass efficiency has improved, and the reason is all because there is far less or even zero back pressure impeding the flow of exhaust.

If you have variable nozzle geometry, such as an in-flight extendable nozzle extension, you can actually get "more thrust" from that engine as you ascend to higher altitudes, by not under-expanding the now less-impeded (by back pressure from the atmosphere) exhaust flow.

If you have a nozzle geometry that uses back pressure from the atmosphere to control exhaust expansion, as would be the case for the much misunderstood "aerospike" nozzle designs, then while you are ascending through that much denser lower atmosphere, with its significant pressure gradient, you can or at least should theoretically achieve a higher Isp overall. When you're operating in a low or zero back pressure environment, an aerospike nozzle is almost always significantly less efficient than a traditional conical or "de Laval" nozzle design. The only reason for this apparent improvement in thrust generated, going back to the basic idea that mass flow through the engine is what produces a given thrust output, than with a conventional fixed nozzle design, is that if you attempted to extend that conventional bell shaped nozzle past the point where the exhaust flow velocity transitions from supersonic to subsonic, then you would get wild instability (vortex generation) inside your engine's nozzle, ultimately leading to destruction of the engine. Combustion instability associated with larger nozzles also generates a destructive vortex inside the nozzle. The "fence pattern" seen on the nozzle-facing side of the main injector plate prevents rotation in the big engines, thus solving combustion instability. Not extending the nozzle to the point that transonic flow separation occurs is how you prevent the instability associated with transonic exhaust flow. Eventually, someone got the bright idea that a nozzle that uses atmospheric pressure on one side can be, more or less, "optimally expanded", as the atmospheric pressure rapidly changes during ascent.

If someone was bound and determined to squeeze every last bit of thrust out of their engine throughout the atmospheric pressure range, thus improving Isp, then they could mount an ablative nozzle extension on a screw jack and gradually extend the nozzle as they ascend, optimizing exhaust expansion over the entire atmospheric back pressure range. Mostly, we don't do this, because it adds more weight and complexity to the engine, sometimes a lot more. That said, this is far simpler than an aerospike. When the engine in question mostly operates at very low atmospheric pressure as a function of the pure speed of ascent, they either stage-off the lower stage and then use vacuum optimized nozzles, or they accept the thrust performance penalty. Therefore, that performance penalty only applies to a brief period of time over which the booster stage engine(s) operate, relative to the total thrusting time of both stages of a TSTO, during which most of the thrusting time is allocated to a much smaller upper stage engine equipped with a vacuum optimized nozzle. This is seen as an acceptable compromise, since Isp / propulsive mass efficiency counts for a lot more with the upper stage than the booster. The booster is all about generating the raw power required to get out of the lower atmosphere and to get the upper stage moving downrange at low hypersonic velocity. Since 90% of the mass of the rocket has been staged off, that upper stage only has to push itself and a comparatively very small payload mass, relative to total vehicle mass at ignition / liftoff, all the way to orbital velocity. It turns out that this is a very worthwhile engineering compromise, even if it's technically more complex than a single stage. We have achieved near-complete mastery of two stage vehicles, with fully reusable boosters and recoverable payload fairings. The remaining question should be, "Can these new-ish air-breathing propulsion systems create a lower mass but cheaper and more practical reusable booster stage that lands on a runway like a conventional airliner?"

All of that also means the one and only time an aerospike nozzle could improve engine thrust performance is during the boost phase of flight- the shortest phase of flight for a two-stage orbital rocket, presuming operation in an atmosphere with a substantial pressure gradient, from bottom of atmosphere to top of atmosphere, as is the case for Earth's atmosphere, but not the Martian atmosphere. If the engine will spend most of its time operating in a vacuum or near-vacuum, then an aerospike nozzle design, regardless of geometry, only hurts and never helps performance, in actual practice, because the end result is either too large and heavy, or it's another compromise making it less performant than competing solutions.

That brings us right back to the mass of the combustion products thrown out the back, what velocity range the engine can operate over without exploding, and whether or not you can source some of your oxidizer from the atmosphere vs carrying all of it with you aboard your vehicle, thus subjecting your vehicle to the tyranny of the rocket equation, or more appropriately, the tyranny of low mass-efficiency propulsive methods and propellants.

Last night, I briefly entertained an idea for improving the overall mass-efficiency of an upper stage of a rocket by using arc flash to superheat LH2. Arc flash achieves temperatures of up to 19,000C. That is ridiculously hotter than any sort of combustion process. Dicyanoacetylene burns at up to 4,990C with LOX, or 5,730C with Ozone. Using chemicals we actually know how to make, that is the greatest amount of chemically-derived thermal energy that could be imparted to an expanding exhaust product. Electrical arc flash is about a factor of 4X beyond that. It's much hotter than the surface of the Sun. The "nuclear lightbulb", which was a closed cycle gas core nuclear thermal rocket, could theoretically achieve temperatures of up to 22,000C. Arc flash is therefore "right up there" with one of the most energetic nuclear thermal rocket concepts ever devised.

The problem I've run into is the tyranny of the mass efficiency of fuel cells or turbine-driven electric generators, in order to produce the arc flash energy input required to superheat LH2. The most mass-efficient electric motors or PEM fuel cells can both achieve about 20kW/kg- stuff that was literally invented within the past 2 years. The fuel cell supplies direct electrical power to produce the required arc, whilst an electric motor would be driven using a high pressure LOX/LH2 driven turbopump (100hp per pound of weight in the RS-25).

I figured out how much energy was required by using a NASA document on nuclear thermal rocket engines, which told me how much thermal power was being imparted into a given mass flow of LH2 through the core, to produce a particular Isp / thrust, what the total mass flow rate through the engine was, the temperatures involved, and the total Watt-hours of thermal energy imparted to the Hydrogen. Using that info, I could estimate LH2 mass flow through my theoretical "arc flash rocket engine" to achieve the same thrust as that nuclear thermal rocket engine. The NTR's total mass flow was 12.68kg/s, exit exhaust temperature was 2,794K, and thrust stated as 113.3kN. Arc flash produced an exit exhaust temperature of 19,273K, so only 1.8kg/s of LH2 required to produce that same 113.3kN of thrust. My problem was that the fuel cell stack would weigh 27,500kg. Thus, my theoretical SSTO's mass was so high that its acceleration rate was far too low to accelerate fast enough to attain orbital velocity, and still have any mass left over for useful payload. The total quantity of fuel consumed was worse than a Centaur upper stage, even though Isp was well north of 2,000s. That means this sort of "engine" could only be used in orbit, and only with an offboard power source, because 113.3kN of thrust is not enough for the total onboard propulsion system mass required. I needed to impart about 4km/s, and that required 2,648s / 44 minutes of thrusting. That pushed 4,766kg of LH2 out the back of the rocket, but producing 550MWe for 44 minutes consumed a lot more LOX and LH2.

The mass of the fuel cell and LH2 propellant alone, was approximately 1.4X greater than the Centaur upper stage. To that mass, I have to add the mass of LOX and LH2 for the PEM fuel cell to "burn" to produce 550MWe for 44 minutes. Did I actually "burn" any less fuel, while closing in on 2,500s Isp? Nope. Not even close. My generated thrust was far too low, and I end up consuming far more propellant to power that fuel cell for 44 minutes. Now I know why they used nuclear reactors, as well as researched off-board input power from microwaves and lasers. Even with a power-to-weight ratio higher than a jet engine and a propulsive mass efficiency approaching that of an ion engine, that fuel cell and electrical arc still cannot do what a fission reactor does. Centaur's propellant mass is 20,830kg. Dry mass alone prevents me from consuming less fuel than a 1960s vintage RL-10 engine, despite how superficially "efficient" my engine's mass flow rate appears.

The overall point is that both dry mass and sufficient thrust to accelerate quickly matter greatly to the overall performance of all types of rocket powered vehicles. Your Isp can be spectacular, as would be the case for my notional "arc flash rocket engine" that does what a closed cycle gas core nuclear thermal rocket engine does, but without the concerns over using nuclear power. Unfortunately, if your thrust is too low, as was the problem for my notional design, then you rapidly consume propellant trying to accelerate, to the point that no mass savings was possible. How it is that someone expects a very low-Isp chemical engine to attain orbital velocity is beyond my understanding. You simply cannot generate enough thrust to overpower the raw speed requirement (accelerate so fast that the mass inefficiency is overridden by your acceleration rate), in much the same way that extreme propellant mass flow efficiency (ion engine like efficiency) cannot overcome dry mass and a low acceleration rate (its own form of inefficiency).

SpaceNut · 2024-05-12 06:48:15

Here is the first attempt to create a SSTO.

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

Known issue was with the build design of the fuel tanks.

From what I remember of discussion here was that we could make this work with current technology.

X-33/VentureStar – What really happened

here are the topics discussed here.

SSTO to mars and back again.

VentureStar is it possible now

Spaceplane

RGClark · 2024-05-12 15:45:33

Former Air Force officer Mitchell Burnside Clapp, who did stints both with the DC-X and X-33 programs wrote an analysis discussing a NASA analysis that showed hydrolox SSTO is feasible. In this analysis he also showed that a dense propellant rocket more efficient for a SSTO:

A LO2/Kerosene SSTO Rocket Design Study.
https://erps.org/papers/LO2-KeroseneSSTO.html

Both versions use vertical launch. This has the advantage the wings only have to support the dry mass of the vehicle on return, so can be lighter.

Bob Clark

Last edited by RGClark (2024-05-12 16:53:55)

RGClark · 2024-05-12 16:52:26

Polaris Spaceplane is investigating a spaceplane:

FUTURE HEAVY SPACEPLANE.
https://www.polaris-raumflugzeuge.de/Te … Spaceplane

They want to use a horizontal take-off approach. This induces heavy wing weight since the wings have to support the fully-fueled weight of the vehicle. They note this makes SSTO problematical. They are first investigating the spaceplane only serving as the first stage reusable booster of a TSTO. They also mention a “semi-SSTO”. Perhaps they mean it will use sled launch.

Bob Clark

Calliban · 2024-05-13 06:18:26

Mark Goll's Rocket Science for Earthlings (late 90s vintage) is still fun to read, although it flies in the face of recent SpaceX design philosophy. Mark is a fan of MCD Big Dumb Booster rockets.
https://storage.googleapis.com/trctsi.net/rse0.htm

Now that Musk is close to perfecting fully reusable rockets, it appears questionable that expendables could actually be minimum cost design. But Goll's calculations do appear to show the benefits of frequent staging, with 3 stage to orbit having the benefit of allowing for higher structural mass, which is beneficial to reusability. From memory, about one third of total propellant mass burned during a shuttle launch was used accelerating to 1000mph. A very cheap, high dead weight but high thrust lower stage, could provide the initial boost needed to accelerate a rocket to 1000mph. Not quite SSTO, but more like 1.2STO.

Last edited by Calliban (2024-05-13 06:21:34)

tahanson43206 · 2024-05-13 06:50:01

For Calliban re #10

Thanks for your contribution to the topic, and to RGClark's discussion of SSTO...

Thanks in particular for your mention of the book by Mark Goff!

I don't know if this is of interest to you, but I set up this topic as a venue for mathematical analysis of the problem of staging with respect to gravity.

I'm hoping someone with the hard won gift of mathematics skill might be willing to create a chart that would show a plot of various staging designs against a background of a linear curve of gravity, running from lower left (Zero) to upper right (Jupiter).

At some point in that chart, SSTO would be infeasible. It appears to be just barely feasible with Eath's gravity.

It is clearly feasible from the Moon, since it has been done, and it is feasible from Mars per GW Johnson's calculations.

My guess is that SSTO will always remain a capability at the very edge of feasibility for Earth launches if traditional chemical propellants are used.

However, successful fusion reactors might produce enough energy to facilitate SSTO. Throwing water as the reaction mass would have the distinct advantage of not harming the Earth environment, which some residents might appreciate. On the other hand, it would be a good idea to avoid the area where a vehicle like that is lifting off. The exhaust would have a ** lot ** of energy.

If someone in the NewMars community is inspired to study that scenario, I (for one) would be most interested to see the results.

A scenario that might make sense (for a fusion powered space craft) is to ionize water so the atoms can be accelerated with electric/magnetic force.

The ions would then recombine to water after they bump around in Earth's atmosphere for a while.

In that scenario, the exhaust plume would be ionized for some time, in addition to being hot. A CFD analysis (Computational Fluid Dynamics) of that scenario would be interesting. It should be possible to predict the cooling and recombination of the water as the exhaust interacts with the Earth's atmosphere.

(th)

tahanson43206 · 2024-05-13 07:20:23

I asked Gemini to take a look at the problem. It's first response was limited to computing a chart showing escape velocity with respect to gravity for selected Solar System objects. Here is the Python code it used. I'll try to add the plot shortly.

import matplotlib.pyplot as plt
# Escape velocities (km/s)
escape_velocities = [11.2, 2.4, 5.0, 59.5] # Earth, Moon, Mars, Jupiter
# Planet names (corresponding to escape velocities)
planets = ["Earth", "Moon", "Mars", "Jupiter"]
# Gravitational multipliers (relative to Earth's gravity)
gravity_multipliers = [1, 0.166, 0.378, 2.54] # Earth, Moon, Mars, Jupiter
# Sort together by escape velocity
sorted_data = sorted(zip(escape_velocities, planets, gravity_multipliers))
escape_velocities, planets, gravity_multipliers = zip(*sorted_data)
# Plot
plt.plot(gravity_multipliers, escape_velocities, marker='o', linestyle='-')
plt.xlabel('Gravity (multiple of Earth\'s gravity)')
plt.ylabel('Escape Velocity (km/s)')
plt.title('Escape Velocity vs. Gravity (Chemical Rockets)')
# Add labels for each planet
for icount, planet in enumerate(planets):
plt.annotate(planet, (gravity_multipliers[icount], escape_velocities[icount]))
# Show the plot
plt.grid(True)
plt.tight_layout()
plt.show()

(th)

tahanson43206 · 2024-05-13 07:38:24

For all with mathematics skills AND an interest in rocket staging....

Post #12 shows a graph prepared by Gemini, plotting gravity vs Escape velocity for various Solar System objects.

I am hoping this topic will provide a place for someone to create a chart showing historical launches with respect to gravity, and including stage count.

As Calliban has just shown in Post #10. there is a case to be made for multiple stages (more than two). That case is greatly strengthened if all the stages are reusable.

SpaceX is working now on a reusable two stage solution. There might be a case to be made for a reusable three stage solution.

Apollo was a good example of an expendable three stage solution.

With modern technology and knowledge, Apollo might be recreated with all expendable equipment.

(th)

Calliban · 2024-05-13 10:15:37

Some kind of ground based launch assist could provide enough starting velocity to preserve a pure SSTO concept. It is very challenging if we require an SSTO vehicle to accelerate from zero velocity at sea level to orbital velocity on a single stage. The vehicle structural mass, heat shield and deorbit propellant wouldn't leave anything spare for payload.

In the past we have examined rocket sleds to accelerate rockets to speeds up 3km/s - enough to eliminate the need for a lower stage for Starship. But a launch assist would still be useful at more modest velocities. Every m/s boost that a launch assist provides allows mass ratio of an SSTO to decrease. At some point, mass ratio becomes achievable for a practical reusable craft, with an economically useful payload and achievable exhaust velocity. Exactly how much of a boost we would need to allow for a fully reusable SSTO achieving these goals would be an interesting design study.

There are a continuum of propulsion options for a launch assist. Electromagnetic launch is possible, but the power requirements are enormous. There are chemical bipropellants, compressed air, steam rockets, steam cannon, to name just a few. Much depends on how much dV the launch assist is expected to provide. Even a modest boost in starting velocity <Mach 1 could make a big difference to the required propellant mass to reach orbit, because at V = 0, the propulsive efficiency of rockets is poor. So a small boost can have an outsized effect.

See here:
https://en.m.wikipedia.org/wiki/Rocket_sled_launch

'Due to factors including the exponential nature of the rocket equation and higher propulsive efficiency than if a rocket takes off stationary, a NASA Maglifter study estimated that a 270 m/s (600 mph) launch of an ELV rocket from a 3000-meter altitude mountain peak could increase payload to low Earth orbit by 80% compared to the same rocket from a conventional launch pad.[5] Mountains of such height are available within the mainland U.S. for the easiest logistics, or nearer to the Equator for a little more gain from Earth's rotation. Among other possibilities, a larger single-stage-to-orbit (SSTO) could be reduced in liftoff mass by 35% with such launch assist, dropping to 4 instead of 6 engines in one case considered.[5]'

Without launch assist, mass ratio for an SSTO is about 10 using LOX/H2 propellant, i.e 90% propellant. A 35% reduction in takeoff weight implies a mass ratio of 6.5, i.e a 15.4% dry fraction instead of 10%. This moves the SSTO into the realms of technical achievability. Ideally, we want an SSTO that is fully reusable and burns CH4/LOX in raptor engines.

Last edited by Calliban (2024-05-13 10:56:40)

kbd512 · 2024-05-13 15:49:56

Dr Clark,

I think SSTO could work, but... What would we use it for?

Absent a lightweight and exceptionally high thrust-to-weight air-breathing propulsion that operates over brake-release to Mach 7, off-loading some of the vehicle's ascent oxidizer requirement, a TSTO's booster accelerates straight up, starts to point the nose downrange at Mach 5 to Mach 7, and then it detaches. This typically sheds 80% of the dry mass fraction of the entire vehicle during ascent. That mass advantage is impossible to overcome. I don't care how good your engines are, nor what materials your vehicle is made from. If we incorporate the same engines and structural materials into a TSTO, even a reusable TSTO, then it will either burn less propellant or out-perform a SSTO with the same liftoff mass, every single time. There's quite literally nothing that the SSTO can do to overcome deleting most of the inert mass of the vehicle.

We have to formulate a set of sensible arguments expressing how and why a SSTO can be superior to a TSTO. I think the best argument is that SSTO is potentially "safer" for human space flight than a TSTO, even though the TSTO can offer superior payload performance for delivery of cargo. If there's an option in the matter, and no compelling reason to use a more complex vehicle to deliver humans to space, then we can afford a marginal cost differential to use what should be a less complex and more reliable vehicle.

1. Whenever harriers lose power they fall out of the sky in a non-survivable way, for anyone not strapped to an ejection seat. For a reusable vehicle with wings providing aerodynamic lift, landing on a runway like an airliner will typically be less hazardous than an exceptionally fast "swan dive" vertical landing that is entirely dependent upon following a precise recovery trajectory and using jet thrust from the main engine(s) to arrest the descent at the last possible second. This would be especially true of a lower-wing loading glider than the Space Shuttle. As fast as the Space Shuttle landing was, swan dive vertical landings are supersonic until a very low altitude. If anything at all goes wrong, there is no time for recovery, which is why the entire landing sequence must be fully automated. In contrast, Space Shuttle landings were not significantly faster than modern airliner landings, and about on par with Concorde landings.

2. There is no staging event that takes place during ascent, thus no possibility of something untoward occurring during staging. Although issues with staging are quite rare amongst relatively modern and fully developed TSTOs (Atlas V, Delta IV Heavy, Falcon 9, Falcon Heavy), you are still relying upon ignition of secondary engine(s) during hypersonic flight. If this event was eliminated from ascent, then that which never occurs cannot "go wrong". A second complete set of man-rated redundant systems for the upper stage are not required for a SSTO. There are also no vehicle assembly steps required for a SSTO, whereas all TSTOs must be "stacked" in preparation for flight. This eliminates errors made during stacking being a possible cause for staging, specifically explosive bolts, misalignment of or asymmetric loading of interstages and stages preventing clean separation, connection of electrical umbilicals, etc. Basically, there's no pyro involved.

For a SSTO, the refurbished orbiter vehicle is transported to the pad from the orbiter processing facility, propellant is loaded, the crew and passengers are loaded, and then an onboard mission computer can autosequence startup. Modern computers, batteries, and fuel cells are efficient / light / compact enough that the complexity of an offboard autosequencer system is no longer required to facilitate launches. A modern wristwatch has so much computational power that it could run all of the Space Shuttle's avionics functions at an extreme multiple of the clock speed of the numerous racks of 1970s avionics electronic equipment that the historical Space Shuttle required.

The Space Shuttle contained ~120,400 wiring runs and 6,491 connectors. The 300+ miles of wiring weighed 4,600lbs and the connectors comprised the remainder of the 7,000lbs of total weight. Total avionics subsystem weight was 17,116lbs, spread amongst those 300+ "black boxes" and 300+ miles of wiring. The AP-101S GPCs weighed 64lbs, consumed 550 Watts of electrical power, and were capable of 1.2M floating point operations per second. Quoted MTBF was quite good for 1970s era computer tech, at 10,000hrs. The 1985 Cray-2 supercomputers were 1.9 gigaflop capable, but weighed 5,500lbs.

An Apple iPhone, for comparison purposes, weighs less than half a pound, features 50 hour battery life, is capable of 15.8 teraflops, and comes with 512GB to 1TB of storage capacity. In short, a single cell phone is ludicrously overly-capable of running all avionics functions of this notional SSTO. The Apple Watch is many times more powerful than the Cray-2 from 1985, yet fits on your wrist for your convenience. It's downright comical how absurdly powerful modern computers are, when compared to Space Shuttle technology. CNT wiring, now commonplace amongst military aircraft and satellites, reduces wiring weight by about 80%. If this SSTO still requires 300 miles of wiring, then it will weigh about 920lbs. That means all integral avionics / compute devices and wiring aboard might weigh in at 1,000lbs or so. The 16,000lbs saved goes straight to useful payload.

3. Modern materials and computing technology can readily do what 1970s or even 1990s simply could not. There is a literal night-and-day difference between the aerospace materials created within the past 10 years vs the past 50 years. AerMet 100, TorayCA T1100S, CNT wiring, and pocket-sized supercomputers simply were not available to the aerospace designers of decades past. There was an enormous chasm of hard-won knowledge to cross to get to where we are today, in the realm of materials science and computing technology. That said, we're here now. What was at the far edge of feasibility 10 or 20 years ago is now common cost-effective practice. We don't have to invoke any miraculous new materials or engine technology. The RS-25 was the "Ferrari" of rocket engines... in the 1970s. It cost as much as 72 Ferraris, and still does. A SpaceX Raptor engine costs the same or less than a single Ferrari- inflation is a bear these days, yet performs at the same level as the RS-25. It could be said that what we're doing is advancing "the art of the possible". RobertDyck stated as much in the thread about VentureStar.

What we really need to determine feasibility by way of an inert mass breakdown using an all-composite primary structure with high temperature resin and CNT or Graphene flakes to maximize fiber layer adhesion and minimize propellant diffusion, the latest and greatest heat shielding technology, multiple Raptor engine power heads feeding into a singular large ablatively cooled RCC / HfB2 coated nozzle with TVC provided by varying power head output feeding different sections of the main injector plate, redundant digital avionics provided by iPhone / iPad / iWatch hardware and software, CNT wiring, maraging steels to replace weaker Titanium or Aluminum alloys, and a clearly specified payload target tied to a design reference mission statement. We are taking away everything that does not absolutely need to be onboard the vehicle, in order to arrive at the lowest possible mass and simplest design. This vehicle must be a Master Class in composite multi-functional structures and simplified design, or it won't work.

I will arbitrarily set the tank volume to be the same as the historical Space Shuttle External Tank, and minimum acceptable payload to be 50t, with 75t to 100t being highly desirable. 50t was not selected at random, though. It's quite close to the LOX/LH2 powered "VTHL 45t" concept that Rockwell initially proposed to NASA as their SSTO design entry into the Space Shuttle program, way back when the entire Space Shuttle concept was still under active development.

Gross liftoff weight will fall somewhere between 2,000t and 2,100t, which happens to be remarkably similar to Space Shuttle's gross liftoff weight. The main "difference" is that all the propellant consumed averages out to about 353.5s, whereas 1,000t of the Space Shuttle's propellant was 242s, while the remaining 733.5t was about 409s. I think that means, given the involved mass fractions, that actual average Isp works out to be about 300s. To that starting disadvantage, you must then add up all the structural mass allocated to various different separate components of the vehicle. The SRBs provided 3,810MNs of total impulse, with 3,104MNs for the RS-25s, so 6,914MNs of total impulse for all stages. The problem was the 208.5t of additional inert mass for the booster casings and ET that the 78t dry mass orbiter vehicle was dragging with it. Well, I get 6,064MNs for 6X Raptors, but I don't have an additional 182t of mass for SRB casings, plus an additional 78t dry mass over the top of the external tank, for my orbiter vehicle.

The "Silverbird Astronautics" paylod calculator says that payload range should be achievable with high confidence in the estimate. I used what I thought would be a realistic inert mass for a minimalist vehicle with a composite primary structure, scaled-up Space Shuttle TPS weight, Raptor engines and thrust structure weight, Space Shuttle landing gear weight, plus the payload, by which I mean 100% of the payload can be safely landed, because the payload will only be passengers, rather than cargo.

The Design Reference Mission is safe delivery of 500 crew members to pilot a large colonization ship headed to the moon or Mars. This notional SSTO vehicle will ascend to orbit from a launch pad or launcher device (EMALS, rocket sled, runway- if that is a mission enabler), dock with a colonization ship orbiting in LEO, transfer its complement of passengers to their awaiting colonization ship, and land on a runway, similar to a regular airline service. If immediate docking and crew transfer cannot be accomplished, then the vehicle will return to Earth with all of its passengers and safely land on that same runway.

Anything not required for that very narrowly defined reference mission should not be included in the design. This SSTO will not have a cargo bay, only a passenger compartment suitable for seating 500 passengers in suspended fabric "sling seats" capable of orienting the passengers for high g-load mitigation, nor any scientific equipment. Elimination of all unnecessary subsystems, novel gadgets looking for a home, or "wouldn't it be cool, ifs...", might determine the difference between a practical real life implementation and the continuation of the pipe dream.

If the vehicle requires a slight scale-up to hit its payload target, that's fine, but if it becomes substantially heavier, meaning 3,000t vs 2,200t, then we've fallen into a mass trap and we need to admit that it's simply not practical, and that more performant TSTOs will continue to provide a lower cost alternative.

We already have small and medium lift launchers aplenty. We have three capsules and a mini shuttle for milk runs to ISS. We have Falcon Heavy and Vulcan-Centaur for heavy lift and probe missions to the planets. We will have Starship for super heavy lift of cargo and on-orbit refueling, plus the potential for fuel depots. A sleek winged SSTO, primarily intended as a reliable people mover, with the seating capacity of a 747 or A380, would truly be a feather in our cap, representative of a capability replicated nowhere else. As a "first of its kind", there will undoubtedly be many challenges, on par with those of the Space Shuttle's era. The "market for the product" will be created by the ability to colonize other worlds, which both NASA and their contractors are actively working on.

To the extent even possible, we will employ novel repurposing of available commercial materials and space flight hardware. We don't need a new Raptor class engine. We will need a novel new non-moving nozzle with TVC to reduce vehicle structural and engine nozzle weight, thus the use of RCC engine nozzles with UHTC ablative coatings, which NASA is actively working on to retire development risk. All the metal weight and complexity of the nozzle goes away if an ablative passive cooling system proves practical. Thus far, test results look remarkably good. RobertDyck identified ALON "glass" to reduce the weight and improve the temperature and impact resistance of the windscreen. If there are little bits of magic CNT or Graphene "pixie dust" that we can sprinkle into our composites to make them absurdly strong and resistant to cracking, then that's where the materials science innovations will come into play.

tahanson43206 · 2024-05-13 20:03:56

This topic has received contributions that advance understanding of the SSTO concept, and how it might apply to the Earth case.

I am still hoping to see actual mathematics applied to the problem. We have seen references to the rocket equation, and that is a good start, but what I would like to see in this topic is actual worked out computation showing that SSTO from the surface of the Earth to LEO is possible at all. To my knowledge it has never been done.

kbd512 has provided excellent support for the concept of an SSTO for delivery of passengers to LEO, in Post #15.

I would like to see actual equations and verifiable, repeatable numbers, showing that SSTO from the surface of the Earth is possible.

All I have seen to date is hand waving. This forum is good at hand waving. We have 20+ years experience at hand waving.

I am asking for something that should be easy for someone gifted with the ability to perform mathematical operations.

We have members who can help with visual presentation. Not every person gifted with mathematics skills is also gifted with presentation skills. GW Johnson is a rare example of someone who can do both.

We (members) include a few who might be willing to help, if a gifted mathematician would like to present results in visual form.

(th)

tahanson43206 · 2024-05-13 20:32:51

I decided to ask Gemini for an evaluation of the situation. Gemini seems to think there may be a mathematical solution to the SSTO probllem from the surface of the Earth. After a slight bobble, it corrected itself and agreed that a rocket did indeed achieve SSTO from the Lunar surface to Lunar orbit during the Apollo missions...

You're absolutely correct! I apologize for the misunderstanding. You're right, the Apollo Lunar Module ascent stage did indeed achieve a Single-Stage-To-Orbit (SSTO) flight, but from the lunar surface, not Earth.
This highlights the significant difference in the challenge of SSTO depending on the launch location. The Moon's much lower gravity (about 1/6th of Earth's) requires a much smaller Δv for lunar orbit insertion. This makes SSTO from the lunar surface much more feasible with current technology.

Here is the original response:

You're right! Here's the breakdown for your questions:
**(a) Mathematical Possibility of SSTO from Earth:**
Yes, there is a mathematical solution showing an SSTO from Earth is possible. The key factor is achieving enough **delta-v (Δv)**, which is the total change in velocity a spacecraft needs for its mission. Earth's orbit requires a very high Δv (around 7,400 m/s).
**(b) Existing SSTO Designs for Earth:**
No nation has achieved a true SSTO flight from Earth as of today (May 13, 2024). The main challenges are:
* **Balancing Fuel and Payload:** Chemical rockets need to carry a lot of oxidizer (like oxygen) along with fuel. This adds significant weight. For Earth's high Δv, it becomes difficult to have enough fuel left for a meaningful payload with current technology.
* **Aerodynamics and Propulsion:** Rockets need different engine types for optimal performance at different stages (atmosphere vs. space). An SSTO needs to function in both, making design complex.
**Examples to Consider:**
* The Apollo Lunar Module (LM) did descend on the Moon using its ascent engine, but it wasn't launched from Earth's surface. It docked with the command module in lunar orbit, which got it most of the way there.
* Designs like the Skylon spaceplane propose using scramjets (supersonic combustion ramjets) for air-breathing hypersonic flight, transitioning to rocket engines later. These are promising but remain unproven at scale.
So, while an SSTO for Earth is theoretically possible, the engineering hurdles are significant. It might require breakthroughs in propulsion technology or materials science to become a reality.

What I am looking for in this topic is a solid mathematical presentation that will stand up to the most intense scrutiny, that will show that SSTO from the surface of the Earth is possible.

(th)

tahanson43206 · 2024-05-14 10:13:53

GW Johnson wrote to confirm that he has published SSTO studies previously.... I will attempt to make the pdf and XLS files available as links from this post...

I've looked at the SSTO problem several times, and posted extensive results over at my "exrocketman" site. These were fairly realistic design sizing rough-out studies, done iteratively in a spreadsheet. None of these are simple single rocket equation calculations, though, as there is nearly always a payload shroud shed on the way up with an expendable vehicle. Two weight statements is ALWAYS two linked rocket equation calculations. There is no way around that, it's just the math. And that daunts a lot of people.
So, I looked at a slightly over-simplified scenario with no payload shroud, which means the payload rides "naked" on the tip of the stage. That gets you to a single weight statement and one rocket equation calculation. Which ought to be simple enough for anybody to understand. I looked at tankage inert derived from propellant mass, engine inert mass derived from necessary thrust, a fixed inert allowance to cover inter-tank shirts, guidance and control equipment, and a source of electricity, plus a required takeoff thrust/weight ratio of 1.5 to ensure adequate ascent kinematics for low gravity loss. The shape is a slender pointed cylinder of L/D = 6+ to minimize the ascent drag loss. The mass ratio-effective dV comes from eastward LEO at low inclination, plus gravity and drag losses, plus a small dV budget for rendezvous, plus a deorbit dV budget for disposal into the sea. The engines are modest SOTA, with nozzles compromise-designed for ascent, yet testable at sea level in the flight configuration.
There are two files attached: one is a one-page pdf text file that has two spreadsheet images on it, one for a LOX-LH2 design, the other for a LOX-LCH4 design. The other file is the Excel spreadsheet that I used for this. That one page pdf might be useful in two threads on the forums dealing with SSTO. And Bob Clark, Brian, or anybody else, is more than welcome to the spreadsheet.
Solution of the rocket equation for this simplified case is still inherently iterative: the mass ratio-effective dV with the propellant combination's Vex gets you the SSTO stage mass ratio, from which the propellant mass fraction is computed as 1 - 1/MR. That leaves a sum of the payload and inert fractions that you can have. You must then input a payload fraction, and compute a weight statement and liftoff thrust, to include an estimate of vehicle inert mass. The propellant mass from that weight statement sizes the tankage inert mass, and the liftoff thrust sizes the engine inert mass. You sum those with the fixed inert allowance, to produce an independent estimate of the vehicle inert mass. Then you compare that independent inert mass to the inert mass from the weight statement. Then you MUST ITERATIVELY adjust your payload fraction until the two converge. And that iteration is inherent, there is NO AVOIDING it! Which is why the spreadsheet is so nice!
What I found was that a LOX-LH2 all-expendable SSTO is entirely feasible and within the same payload fraction range as the all-expendable TSTO designs (which usually use LOX-RP1 in the first stage and LOX-LH2 in the second stage). But the low expendable vehicle inert fractions preclude entirely the possibility of making the SSTO reusable! The TSTO can be partly reusable at low inert fraction, with a slight reduction in payload fraction, since first stage flyback does not endure full re-entry heating! It is possible to come up with an expendable LOX-LCH4 SSTO, but the payload fraction is lower, because of the lower Isp, which fairly-dramatically drives up vehicle sizes and costs. That would be far less attractive than the LOX-LH2 SSTO design.
But, with the advent of partly-reusable TSTO's, and their already-seen dramatic reduction of launch costs with partial reusability, I see no point to anyone offering an expendable SSTO anymore. It can NEVER cost less than a partly-reusable TSTO!

Link to XLS goes here...
https://www.dropbox.com/scl/fi/7cne8ji5 … emd3x&dl=0

Link to PDF goes here...
https://www.dropbox.com/scl/fi/s41whkcb … v0ezr&dl=0

Correction: Error in the text of previous email: takeoff thrust/weight is 1.5, not the "5" in that text. <<== correction applied (th)

(th)

GW Johnson · 2024-05-14 10:30:30

I have been unable to post a response to the AI-generated plot in post 12 above. I will send it to Tom as a document. Maybe he can do his drop box thing here.

GW

edit update 5-14-2024: the links to the document and spreadsheet in Tom's post just above really work. I verified them.

Last edited by GW Johnson (2024-05-14 14:11:25)

SpaceNut · 2024-05-14 19:21:25

Bounding Calculations for SSTO Concepts

kbd512 · 2024-05-14 22:28:28

The Rocket Equation
Δv = standard gravity * specific impulse of propellant combination through the engine * ln(initial total mass / final total mass)
Δv = 9.81 * Isp * ln(mass_initial / mass_final)

LOX/LCH4, using avg (327s + 380s / 2) Raptor engine Isp of 353s
Δv = 9.81 * 353 * ln(2,125t / 125t)
Δv = 9.81 * 353 * ln(17)
Δv = 9.81 * 353 * 2.833213344056216
Δv = 9,811.22m/s

LOX/LH2, using avg (366s + 452s / 2) RS-25 engine Isp of 409s
Δv = 9.81 * 409 * ln(1,500t / 125t)
Δv = 9.81 * 409 * ln(12)
Δv = 9.81 * 409 * 2.484906649788
Δv = 9,970.17m/s

Since neither vehicle will spend much time thrusting anywhere near sea level, it would be more appropriate to increase the avg Isp for both vehicles accordingly.

LH2 is clearly the superior propellant if propellant weight and Isp are all that matters, but it's just not. Total vehicle volume also matters, because enclosing that volume requires materials to do so, and even the lightest materials capable of doing so still have significant mass associated with them, especially the thermal protection system materials required to keep the vehicle from burning up upon reentry, thus making the vehicle reusable.

The Space Shuttle's External Tank held 733,464kg of LOX (629,340kg / 553,358L) / LH2 (106,261kg / 1,497,440L) propellant.

That means I need to increase the size of the External Tank by 87.6% to hold enough LOX/LH2 propellant, and final mass still has to be 125t.

The Space Shuttle's External Tank will hold 1,825,210kg of densified LOX (698,338kg / 553,358L) / (655,879kg / 1,497,440L) LCH4 propellant.

That means I need to increase the size of the External Tank by 9.6% to hold enough LOX/LCH4 propellant, and final mass still has to be 125t.

You could densify the LOX held by a notional LOX/LH2 SSTO vehicle, and should to save structural mass, but doing so only saves 11% on your total propellant volume. You can't get rid of the heavy interstage between the oxidizer and fuel tanks when using LOX/LH2, because the oxidizer and fuel are at drastically different temperatures.

I'm not sure how much you could densify the LH2, without gelling it using LCH4, thereby reducing its Isp in the process and creating an additional complication- nobody uses gelled LH2, so there are no off-the-shelf engines capable of feeding it into their main combustion chamber. It could be done, obviously, but not without significant cost. The LOX/LCH4 vehicle is 625t heavier, obviously, but it's also 78% smaller for similar Δv capability, or 67% smaller with densified LOX, assuming you wish to retain LH2's Isp advantage over LCH4. It's really hard to increase the volume of a gigantic cryogen tank by 2/3rds without also increasing its weight, regardless of how light that material is in comparison to much weaker metals, because you still need 2/3rds more material to enclose the same volume of propellant.

Beyond that, there is the thorny problem of engine thrust-to-weight ratio (TWR).

RS-25 has a 73.1 TWR, so it weighs 3,177kg and produces 1.86MN (sl) to 2.279MN (vac) of thrust.
Raptor has a 143.8:1 TWR, so it weighs 1,600kg and produces 2.26MN (sl) to 2.53MN (vac) of thrust.

That means the propellant tanks for LOX/LH2 are 2/3rds heavier and the engines are almost twice as heavy. This does not bode well for a vehicle that needs sufficient thrust to get off the pad. I need 17 RS-25s to produce a 1.5:1 TWR at sea level. They will weigh 54,009kg, which is 43.2% of the weight of the entire 125t payload, just for the engines.

17 Raptors weigh 27,200kg, and they produce 3,910 tons of force at sea level, so TWR of that notional LOX/LCH4 SSTO is 1.84:1, and the engines represent 21.8% of the total payload. However, I only need 14 engines for a 1.5:1 TWR, so 22,400kg, which is 17.9% of the total payload weight.

So...

Besides propellant weight and the engine / propellant combination Specific Impulse to consider, there is engine weight, propellant tank weight, thermal protection system weight, and landing gear weight. Those other weights absolutely have to increase, if the volume of the propellant tank increases substantially, and the engines are significantly heavier relative to the thrust they provide.

The historical Space Shuttle Super-Light Weight Tank weighed 26,536kg. It was made from Al-2195 Aluminum alloy, which has a yield strength of about 87ksi. TorayCA T1100S fiber, when incorporated into a composite, has a yield strength of about 502ksi. That means we can enclose the same volume of propellant using less weight, even if we have to include a liner to prevent the propellants from permeating the composite. We must use that excess strength to make the propellant tank structures stronger for a given weight. We still have to enclose that much propellant volume, plus a bit more, to achieve orbit with a 125t vehicle, but the tanks will be significantly stronger.

The aero-structures of the Space Shuttle components were designed with a 1.2X strength margin, meaning they were 20% stronger than was strictly necessary for normal operation. I believe the ultimate strength factor of the materials selected was 2.4X. If the yield strength of the structure was increased by 5.77X, for a given weight, then that means it has a reserve of strength not present in the non-reusable metal flight articles. T1100S fiber is 1.79g/cm^3. Polyester resin should fall somewhere between 1.1g/cm^3 and 1.5g/cm^3. If there's a 60% fiber fill fraction, then the composite weight per cubic centimeter is about 1.674g/cm^3. The ET was 24,348kg or 9.017m^3 of Al-2195, plus 2,188kg of spray-on foam insulation. For the same mass, I get 14.545m^3 of T1100S composite. Volume is important, because increasing the thickness of a part increases its stiffness. If you double the thickness of the metal or composite part, it's not 2X as stiff, it's 8X as stiff, which means it can resist bending or deflecting under load much better. We will require stronger and stiffer structures for a reusable vehicle.

Edit: I was wrong about the ultimate safety factors in the Space Shuttle's design. It was 1.4X for limit loads and 1.25X, at end of life.

Last edited by kbd512 (2024-05-15 01:23:34)

tahanson43206 · 2024-05-15 11:25:50

This is a link to a pdf file reply to Post #12, showing a graph of gravity at various bodies vs escape velocity.

https://www.dropbox.com/scl/fi/jmteo71e … 15ntb&dl=0

Apparently there was something inside the pdf that caused AISE to choke.

I will attempt to paste a bit of the content here...

Nothing I attempted from the pdf was accepted...

(go to pdf to see equation and detailed discussion)

For GW Johnson ... thanks for bringing this acute case of AISE to our attention. I've never seen anything this severe.

However, this is a ** great ** opportunity to test the text against the new updated forum software, so I will do that shortly.

(th)

RGClark · 2024-05-15 15:27:44

tahanson43206 wrote:

…
What I am looking for in this topic is a solid mathematical presentation that will stand up to the most intense scrutiny, that will show that SSTO from the surface of the Earth is possible.
(th)

The analysis I linked to above by Air Force Capt.(Ret.) Mitchell Burnside Clapp I think is pretty firm because he cites a study by NASA itself showing a reusable hydrolox SSTO is doable. NASA assumed the propellant had to be hydrolox because of its high ISP. But later people in the industry realized dense propellants are preferred for a SSTO because of the hydrolox high tank mass:

A LO2/Kerosene SSTO Rocket Design Study
In February of 1997, Mitchell Burnside-Clapp posted a vehicle dsign study to the sci.space.policy Usenet Newsgroup. It was based on a NASA Access To Space study and looked at the same vehicle design but using higher density LO2/Kerosene propellants and engines rather than the LOX/Liuid Hydrogen propellant and engines of NASA's design. The results were quite interesting.
A LO2/Kerosene SSTO Rocket Design (long)
Mitchell Burnside Clapp
Pioneer Rocketplane
(view with a fixed pitch font such as courier or monaco)
Abstract
The NASA Access to Space LO2/hydrogen single stage to orbit rocket was examined, and the configuration reaccomplished
with LO2/kerosene as the propellants. Four major changes were made in assumptions. First, the aerodynamic
configuration was changed from a wing with winglets to a swept wing with vertical tail. The delta-V for ascent
was as a result recalculated, yielding a lower value due to different values for drag and gravity losses. The engines
were changed to LO2/kerosene burning NK-33 engines, which have a much lower Isp than SSME-type engines used in the
access to space study, but also have a much higher thrust-to-weight ratio. The orbital maneuvering system on
the Access to Space Vehicle was replaced with a pump-fed system based on the D-58 engine used for that purpose now
on Proton stage 4 and Buran. Finally, the wing of the vehicle was allowed to be wet with fuel, which is a
reasonable practice with kerosene but more controversial with oxygen or hydrogen. Additionally, in order to reduce
the technology development needed, the unit weights of the tankage were allowed to increase by 17 percent.
After the design was closed and all the weights recalculated, the empty weight of the LO2/kerosene vehicle
was 35.6% lighter than its hydrogen fuelled counterpart.
Introduction
NASA completed a study in 1993 called Access to Space, the purpose of which was to consider what sort of vehicle
should be operated to meet civil space needs in the future. The study had three teams to evaluate three different broad
categories of options. The Option 3 team eventually settled on a configuration called the SSTO/R. This vehicle was a
LO2/hydrogen vertical takeoff horizontal landing rocket. The mission of the Access to Space vehicle was to place a
25,000 pound payload in a 220 n.mi. orbit inclined at 51.6 degrees. The vehicle had a gross liftoff weight of about
2.35 million pounds. The thrust at liftoff was 2.95 million pounds, for a takeoff thrust to weight ratio of 1.2. The
empty weight of the vehicle was 222,582 pounds, and the propellant mass fraction (defined here as [GLOW-empty]/GLOW)
was 90.5%.
Main power for this vehicle was provided by seven SSME derivative engines, with the nozzle expansion ratio reduced
to 50. This resulted in an Isp reduction from 454 to 447.3 seconds. Each engine weighed 6,790 lbs, for an engine sea
level thrust to weight ratio of 62.
Aerodynamically the vehicle was fairly squat, with a fineness ratio (length:diameter) of 5. The overall length
of the vehicle was 173 feet and its diameter was 34.6 feet. It had a single main wing (dry of all propellants) of about
4,200 square feet total area, augmented by winglets for directional control at reentry. The landing wing loading
was about 60 lb/ft2. The oxygen tank was in the nose section. The payload was mounted transversely between the
oxygen and hydrogen tanks, and was 15 feet in diameter and 30 feet long.
This design exercise was among the most thorough ever conducted of a single stage to orbit LO2/LH2 VTHL rocket.
It was probably the single greatest factor in convincing the space agency that single stage to orbit flight was
feasible and practical, to borrow from the title of Ivan Bekey's paper of the same name.
A LO2/kerosene alternative
A number of people have been asserting for some time that higher propellant mass fractions available from dense
propellants may make single stage to orbit possible with those propellants also. The historical examples of the
extraordinary mass fractions of the Titan II first stage, the Atlas, and the Saturn first stage are all persuasive.
Further, denser propellants lead to higher engine thrust to weight ratios, for perfectly understandable hydraulic
reasons.
It has not usually been observed that higher density also leads to significant reductions in required delta-v.
There are two major reasons that this is so. First, the reduction in volume leads to a smaller frontal area and
lower drag losses. The second, and more significant, reason is that the gravity losses are also reduced. This is because
the mass of the vehicle declines more rapidly from its initial value. The gravity losses are proportional to the
mass of the vehicle at any given time, and hence the vehicle reaches its limit acceleration speed faster.
NASA itself has implicitly recognized this effect. When the Access to Space Option 3 team examined tripropellant
vehicles, the delta-v to orbit derived from their work was 29,127 ft/sec, for precisely the reasons described in the
previous paragraph. This compares to a delta-v of 30,146 ft/s for the hydrogen-only baseline, as reported in a
briefing by David Anderson of NASA MSFC dated 6 October 1993. To be clear, these delta-v numbers include the back
pressure losses, so that no "trajectory averaged Isp" number is used. They did not, however, report any results
for kerosene-only configurations.
To come to a more thorough understanding of the issues involved in SSTO design, I have used the same methodology
as the Access to Space team to develop compatible numbers for a LO2/kerosene SSTO. There are four major changes in
basic assumption between the two approaches, which I will identify and justify here:
1: The ascent delta-v for the LO2/kerosene vehicle is 29,100 ft/sec, rather than 29,970 ft/sec. The reason for
this is argued above, but I ran POST to verify this value, just to be sure. The target orbit is the same: 220 n.mi.
circular at 51.6 degrees inclination. The detailed weights I have for the NASA vehicle are based on a delta-v of
29,970 ft/sec rather than the 30,146 ft/sec reported in Anderson's work, but I prefer to use the values more
favourable to the hydrogen case to be conservative. The optimum value of thrust to weight ratio turns out to be
slightly less than the hydrogen vehicle: 1.15 instead of 1.20.
2: The aerodynamic configuration is that of Boeing's RASV. Without arguing whether this is optimal, the fineness ratio
of 8.27 and large wing lead to a much more airplane-like layout, better glide and crossrange performance, and
reduced risk. The single vertical tail is simpler and safer than winglets as well. Extensive analysis has justified the
reentry characterisitics of this aircraft. The wing is assumed to be wet with the kerosene fuel, as is common on
most aircraft. The fuel is also present in the wing carry-through box. The payload is carried over the wing
box, and the oxidizer tank is over the wing. This avoids the need for an intertank, which in the NASA Access to
Space design is nearly 6,600 pounds.
3. The main propulsion system is the NK-33. The engine has a sea level thrust of 339,416 lbs, a weight of 2,725 lbs
with gimbal, and a vacuum Isp of 331 seconds. Furthermore, it requires a kerosene inlet pressure of only 2 psi
absolute, which dramatically reduces the pressure required in the wing tank. It also operates with a LO2 pressure at
the inlet of only 32 psi. The comparable values for the SSME are about 50 psi for both propellants. This will have
a substantial effect on the pressurization system weight.
4. The OMS weight is based on the D-58 engine. This engine is used for the Buran OMS system and the Proton stage 4. As
heavy as it is the Isp is an impressive 354 seconds. NASA's vehicle used a pressure fed OMS, which is a sensible design
choice if you're stuck with hydrogen and you wish to minimize the number of fluids aboard the vehicle. But
because both oxygen and kerosene are space-storable, there is no reason to burden the design with a heavy pressure fed
system.
Using the same methodology for calculating masses, and accepting the subsystems masses as given in the Access to
Space vehicle, a redesign with oxygen and kerosene was accomplished. The results appear in Table 1.
Table 1: Access to Space vehicle and LO2/kerosene
alternative
Name O2/H2 LO2/RP
Wing 11,465 11,893 lb
Tail 1,577 1,636 lb
Body 64,748 33,741 lb
Fuel tank 30,668 - lb
Oxygen tank 13,273 17,271 lb
Basic Structure 14,610 10,274 lb
Secondary Structure 6,197 6,197 lb
Thermal Protection 31,098 21,238 lb
Undercarriage, aux. sys 7,548 5,097 lb
Propulsion, Main 63,634 36,426 lb
Propulsion, RCS 3,627 1,234 lb
Propulsion, OMS 2,280 823 lb
Prime Power 2,339 2,339 lb
Power conversion & dist. 5,830 5,830 lb
Control Surface Actuation 1,549 1,549 lb
Avionics 1,314 1,314 lb
Environmental Control 2,457 2,457 lb
Margin 23,116 16,105 lb
Empty Weight 222,582 141,682 lb
Payload 25,000 25,000 lb
Residual Fluids 2,264 1,911 lb
OMS and RCS 1,614 1,261 lb
Subsystems 650 650 lb
Reserves 7,215 8,895 lb
Ascent 5,699 7,587 lb
OMS 679 541 lb
RCS 837 767 lb
Inflight losses 13,254 17,445 lb
Ascent Residuals 10,984 15,175 lb
Fuel Cell Reactants 1,612 1,612 lb
Evaporator water supply 658 658 lb
Propellant, main 2,054,612 3,034,972 lb
Fuel 293,604 843,048 lb
Oxygen 1,761,008 2,191,924 lb
Propellant, RCS 2,814 2,556 lb
Orbital 2,051 1,756 lb
Entry 763 800 lb
Propellant, OMS 19,357 15,452 lb
GLOW 2,347,098 3,246,156 lb
Inserted Weight 292,486 211,185 lb
Pre-OMS weight 271,482 186,152 lb
Pre-entry Weight 252,125 170,700 lb
Landed Weight 251,362 169,900 lb
Empty weight 222,582 141,682 lb
Sea Level Thrust 2,816,518 3,733,080 lb
Percent margin 11.6% 12.8%
Assumed Isp(vac) 447.3 331.0 s
Ascent Delta-V 29,970 29,100 ft/s
OMS delta-V 1,065 987 ft/s
RCS delta-V 108 107 ft/s
Deorbit Delta-V 44 53 ft/s
Reserves 0.28% 0.25% lb/lb
Residuals 0.53% 0.50% lb/lb
Wing Parameter 4.56% 7.00% lb/lb
TPS parameter 12.37% 12.50% lb/lb
Undercarriage parameter 3.00% 3.00% lb/lb
Wing Reference Area 4,189 5,528 ft2
Density of fuel 4.4 50.5 lb/ft3
Density of oxygen 71.2 71.2 lb/ft3
Volume of fuel 66,276 16,694 ft3
Volume of oxygen 24,733 30,785 ft3
Fuel tank parameter 0.42 - lb/ft3
Oxygen tank parameter 0.48 0.56 lb/ft3

Some discussion of the results and justification is in order.
The wing is about 40 percent heavier as a percentage of landed weight than for the hydrogen fueled baseline. When
considered as a tank, it is about 60 percent heavier for the volume of fuel it encloses. Its weight per exposed area
is about the same and the wing loading is half at landing. No benefit is taken explicitly for the lack of a
requirement for kerosene tank cryogenic insulation.
The tail is assumed to have the same proportion of wing weight for both cases. This is conservative for the
kerosene wehicle because its single vertical tail is structurally more efficient.
The body of the kerosene vehicle has three components. The oxidizer tank has an increased unit weight of about 17
percent. This is done in order to avoid the need for aluminum-lithium, which was assumed in the Access to Space
vehicle. The basic structure group is unchanged, except that the intertank is deleted and the thrust structure is
increased in proportion to the change in thrust level. The secondary structure group is mostly payload support
related, and was not changed.
The thermal protection group is in both cases about 12.5% of the entry weight. This works out to 1.107 lbs/ft2 of
wetted area for the kerosene vehicle, which is common to many SSTO designs.
The undercarriage group is 3% of landed weight for both vehicles. There is no benefit taken for reductions in gear
loads for the kerosene vehicle due to lower landing speed and lower glide angle at landing.
The main propulsion group includes engines, base mounted heat shield, and pressurization/feed weights. The engines
are far lighter for their thrust than SSME derivatives. The pressurization weights are reduced in proportion to the
pressurized volume for the kerosene vehicle. No benefit is taken for reduced tank pressure.
Here is as good a place as any to point out the erroneous assertion that increased hydrostatic pressure is going to
lead to increased tankage weights. There is no requirement for a particular ullage pressure except for the need to
keep the propellants liquid. It is the pressure at the base of the fluid column rather than the top of the column that
is of engineering interest. The column of fluid exerts a hydrostatic load on the base of the tank, but this load
does not typically exceed the much more adverse requirement for engine inlet pressurization. For the kerosene vehicle,
the hydrostatic load at the base of the oxygen tank is 49 psi, which is compatible with the pressures normally seen
in oxygen tanks for rocket use. The load declines after launch because the weight goes down faster than the
acceleration goes up.
The bottom line here is that dense propellants may require you to alter a tank's pressurization schedule, but not to
overdesign the entire tank. Structures are sized by loads and tankage for rockets is sized principally by volume, and if
the vehicle is small, by minimum gauge considerations. This is not completely true for wet wings, however, as
discussed previously. In this particular example, there is no need for high pressure in the wing tank either, because
of the low inlet pressure required by the NK-33.
The OMS group is the only other major change, as discussed above. The reliable D-58 engine has been performing space
starts for decades and will serve well here. The acceleration available from the OMS is about 0.12 g, which
is standard.
All the other weights are pushed straight across for the most part. A brief inspection suggests that this is very
conservative. Control surface actuation requirements are certainly less, electrical power requirements less, much
better fuel cells available than the phosporic acid type assumed here, and reduced need for environmental control.
Nonetheless, rather than dispute any of these values it is easier simply to accept them.
The margin is applied to all weight items at 15% execpt for the engine group at 7.5%. The justification for this is that
the main and OMS engine weights are known to high accuracy.
The vehicle has an overall length of 1955 inches, and a diameter of 236.4 inches. The wing has a leading edge sweep
of 55.5 degrees and a trailing edge sweep of -4.5 degrees. Its reference area is 5,632 square feet, of which 3,992
square feet is exposed. The wing encloses 16,694 ft3 of fuel, with a further 5% ullage. The carry-through is also
wet with fuel. The wing span is 1293 inches, and the taper ratio is 0.13.
The payload bay has a maximum width and height of 15 feet. It sits on top of the wing carry through box. The thrust
structure from the engines passes through and around the payload bay to the forward LO2 tank. The payload bay is 30
feet in length. It has a pair of doors, the aft edge of which is just forward of the vertical tail leading edge.
The engine section encloses 11 NK-33 engines, with a 4 - 3 - 4 layout. The engines are each 12.5 feet long, and
additional structure and subsystems take up another 6.5 feet.
The oxygen tank comprises the forward fuselage, which encloses 30,785 ft3 of oxygen, with a further 5% ullage.
The length of the tank is about 100 feet. The ventral surface of the tank is moderately flattened as it moves
aft, to fair smoothly with the wing lower surface. This flattening reduces its length by about 5% with respect to a
strictly cylindrical layout. The aft edge of the oxygen tank is about even with the forward payload bay bulkhead. A
compartment of about 13.9 feet provides room for some subsystems and a potential cockpit in future versions.
Conclusion
The methods of the NASA Access to Space study were used to design a single stage to orbit vehicle using existing
LO2/kerosene engines. An inspection of the final results shows that the vehicle weighs about 36.5% less than its
hydrogen counterpart, with reductions in required technology level and off the shelf engines. The center of
mass of the vehicle is about 61% of body length rather than 68% for the Access to Space vehicle, which should improve
control during reentry. The landing safety is considerably improved by lower landing speed and better glide ratio.
Structural margins are greater overall. The vehicle designed here appears to be superior in every respect:
smaller, lighter, lower required technology, improved safety, and almost certainly lower development and
operations cost.

https://erps.org/papers/LO2-KeroseneSSTO.html

Bob Clark

Last edited by RGClark (2024-05-15 15:29:19)

SpaceNut · 2024-06-15 13:56:00

We are attempting to perform the profile of a 2 stage with just 1 complete to orbit ship.

Here is a place for numbers
https://exoscientist.blogspot.com/2012/ … first.html

The first stage propellant load is given as 553,000 lbs, 250,000 kg, and the dry weight as 30,000 lbs, 13,600 kg.
Characteristic    First stage    Second stage    Payload fairing
Mass (without propellant)    22,200 kg (48,900 lb) 4,000 kg (8,800 lb) 1,700 kg (3,700 lb)
Liquid oxygen tank capacity 287,400 kg (633,600 lb) 75,200 kg (165,800 lb)
Kerosene tank capacity    123,500 kg (272,300 lb) 32,300 kg (71,200 lb)

kbd512 wrote:

500 passenger vertical takeoff / horizontal landing SSTO will be posted here.
Gross Liftoff Mass: 2,100,000kg
Propellant Mass: 2,000,000kg
Dry Vehicle Mass: 60,000kg
Payload Mass: 40,000kg

GW Johnson · 2024-06-15 14:48:34

What about the need to rendezvous with whatever you are delivering the payload to?

What about the deorbit burn, necessary to properly dispose of the stage, even if not reusable?

GW

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