Boldly Going: A History of an American Space Station

Inevitable that some sort of delay would appear, this is a NASA program after all but a schedule slip of only 18 months is really not bad. The bigger issue is that there already seems to be problems with the reuse element, just how dependent is the entire program on the quick and cheap turnaround of the OPAM and LRB engine pods?
 
Even with these cost reductions, it was unthinkable to watch hundreds of millions of dollars of precisely constructed engines fall into the ocean on every launch

Oh, I can think of some U.S. senators for whom it is *quite* thinkable.

maf_20200108_artemis_roll_out_dn-5673_0.jpg
 
Inevitable that some sort of delay would appear, this is a NASA program after all but a schedule slip of only 18 months is really not bad. The bigger issue is that there already seems to be problems with the reuse element, just how dependent is the entire program on the quick and cheap turnaround of the OPAM and LRB engine pods?

Given the engines, and the agency, we are talking about, I think we must be very generous with the terms "quick" and "cheap." This ain't SpaceX.
 
An 18 month slip isn't too bad. They can just change the promotional material. Instead of "moon by Apollo 11's 20th anniversary," just print up some monolith posters and send a landing to Tycho.
 
This will probably never happen in this timeline for some sort of technical or economic (or political) reasons, but I feel like the Space Island Group (from the early 2000s) is relevant to this, and their counterpart in this universe would be more motivated to promote their concept of "commercial wheel-shaped stations made out of Space Shuttle external tanks":
I think if there is hope to achieve the kind of sortie rates and launch price reductions this sort of grand vision requires, ironically tank disposal (on a routine basis anyway) would be eliminated, because the kind of "STS Mark 2 or 3" required would be to integrate a reusable tank with the SSME descended main engines, along with relatively low cost many times reusable LRBs, into a fully recoverable Launch Vehicle, which would carry, probably still sidesaddle, an Orbital Package to very low Earth orbit, say 100 km (in the full range of inclinations). The Orbital Package would surely have to boost to a higher orbit, but orbital maneuvers are relatively modest in delta-V unless we are talking about transfers to GSO or to deep space, Luna and beyond. I vaguely estimate it ought to be feasible to give TPS to a tank (perhaps a heavier tank made of steel), put some maneuvering flaps fore and aft (the big ones aft since the engines are there). The uncrewed Reused Launch Vehicle would have to boost the whole mass to the very low orbit, which decays rapidly, but not I think so rapidly the separated RLV can't make many orbits to phase to a reentry arriving at a launch site. Perhaps overoptimistically guessing the RLV masses about 100 tonnes dry, the payload to very LEO is about 40 tonnes, which seems respectable--some OPs are just deliveries of heavy cargo, one-way with disposed (or orbitally repurposed) shrouds and engine/propellant requirements cutting the payload delivery to say 25 tonnes, others are reusable crewed Orbital Shuttles, where we design a bare bones Space Truck with crew escape capsule being an alternative to an uncrewed version with maximal payload, and Lego in a minimal escape capsule for say 8 crew we can use as ongoing mission (for a short mission) habitation for say 3 flight crew, amounting to 15 tonnes leaving 10 tonnes orbital payload, with downmass of 10 tonnes. Or a larger crew uses some of the payload capacity for an Orbital Habitation extension with an airlock and docking tower, and only delivers a handful of tonnes or a modest module.

Both RLV and a basic space truck Orbital Shuttle reenter the way Starship is supposed to, controlled belly flop leading to terminal "skydiver" horizontal descent, unlike Starship they don't flip into nose-up for final retro-propulsion engine landing, but rely on sideways (down) thrusters for a horizontal landing.

I've been hung up on replying to several posts back regarding the choice of oxygen rather than hydrogen peroxide to burn ethanol in the Keplers.

My thinking on those lines leads me to suggest the landing thrusters for the proposed RLV would basically be the +Z (in horizontal aspect) reaction control thrusters but cranked up to far greater chamber pressures than required in vacuum orbital maneuvering. This requires hyper-rating just those (4) thrusters to really high pressures. The orbital maneuvering engines generally operate at fairly low pressure (OTL Shuttle OMS and RCS at about 8.6 atmospheres) and have a fairly high expansion ratio of 55; this works great in vacuum for modest thrusts, but to land 100 tonnes of RLV at terminal velocity as high as say 100 m/sec will require a lot of oomph and very high pressure to overcome the high expansion ratio at sea level. But in a thruster cluster of four (one fore or aft on the X axis, one outward on the Y axis, two on the Z axis up and down) only one each needs to endure the superpressures reusably; if we have four such thrusters in terminal descent we can finely throttle at high thrust, we should have a well controlled plop-down. So we'd need to super-rate the pressurizing tank for an ethanol-peroxide system, or a much smaller pressurizing tank for just the ethanol in an eth-lox system along with super-strength for the LOX tank, and of course reserve propellant mass for the final landing, including pressurizing gas. It is basically the same sort of thinking to SpaceX's SuperDraco for the Dragon capsule. Versus the full mass of the RLV I suspect the special requirements just for landing are a modest element in the mass budget. Horizontal landing strikes me as better for ground handling--if were possible to land the RLV precisely at the actual launching pad as planned for Starship it might be a different logic to be sure. But SSMEs are gross overkill for a tail landing I suspect.

OK with that sort of approach, we no longer are expending ETs; that's part of the major point of it. We get high launch sortie rates because of rapid and inexpensive "inspect, tweak, gas and go" reuse of LRBs and ET/engine integrated RLVs, and the higher the launch sortie rate the lower the per-launch costs of NASA launch site infrastructural support; we have trained specialized highly paid ground crew working continually instead of sporadically.

But to get there we know in this TL there shall be Shuttle C's that only recover the engines. It should remain possible to make custom non-return ETs, with custom sidesaddle integrated payloads, and for instance launch a replacement for Enterprise's station core custom made. These ET's are built prioritizing their future long term mission in orbit and somewhat compromising on the initial propellant tank mission.

Clearly to get the drawing you provided we need, let's see, what is that, 30 ETs? 24 in the double outer ring and 4 more in a radial cross, which appears to be offset from the 24 tank rim pair by a tank along the axis of the 4 radial tanks spinning like a jack with another one being the axis of the big 24 tank ring and inner torus , plus God knows how you get the inner lower G torus, plus who knows how many cargo packet missions for the trusses and solar panels etc.

Also, I don't see how the solar panels are going to work like that, we'd be swiveling the heck out of them with each revolution.

It looks like the radius of the circumference the tanks lie end to end to form the ring is about two tank lengths, plus some allowance for core radius and tank extensions. Standard ET length OTL is just shy of 47 meters, but I'd propose if possible adding a couple to widen the intertank space for easy passage. This means more dry mass and might raise VAB clearance issues, but let's hope not. The very bottom of each ring tank would thus be at 102.3, and each tank centerline at 98 meters radius, plus allowance for the core radius which I am going to declare to be 14 meters for reasons that might become apparent, thus 112 to the centerline and half tank diameter or 4.3 more to the very outermost points. Taking the centerline as basis for nominal 1 G, spin speed is a hair over 33 m/sec, thus we cover one radian every 3.38 seconds and a complete revolution every 21.23 sec--2.83 revolutions a minute! Now that doesn't seem all that severe, and recent space station studies indicate it is probably entirely bearable for humans aboard. Also of course your pictures say nothing about whether achieving a full G on the ring is desired or not. It could be a Lunar G, about 1/6 Terran, or Martian G, about 1/3. I suspect though that realistic space station designs for long term habitation will need to offer at least some full-G habitation and would be surprised if anything much less than half a G offer great long term benefits (bad news for Mars colonists if so; perhaps Martian 1/3 G is OK, if people don't expect to return to Earth anyway, or for moderately short stays like say half a year). I am assuming a full G throughout though, just FYI.

Now I couldn't resist starting a long discourse on how I'd build such a station, in sequence, deploy the solar panels and heat rejection radiators, what sorts of population it might support (all on an interim, generally not permanent, basis, for reasons involving radiation hazards long term, also I suspect children and pregnant women would be banned outright, until such time as a fancier station design cuts the cosmic ray hazard down to levels at least some Earth populations are born, live full lives and die of old age in).

Let me boil it down to this:
a) the sensible station orientation as I see it, and likely orbit to be chosen for reasonable access to orbit and also radiation safety, such as we can achieve, will be such that both the Sun and Earth (and Moon, and the rest of the planets) are in roughly the same plane as the rings are in. Thus such objects would be "down" half the time and behind the arc of the station from any window on the spinning rings all the time, or pretty near. We don't want windows that look at the Sun! (Maybe for specialized solar astronomy--otherwise it is just a hazard). Therefore no windows on the spun elements. Well, making the station out of ETs largely puts the kibosh on that anyway. I believe one sensible design is to mount solar panels on the "floor" of spun elements, with this orientation--it means each panel delivers only 1/6 the average power it could if aimed properly at the Sun, where a factor of two in there involves the whole station being on Earth's night side, and the rest relates to half of it being in shade even on Earth's day side and to the sunlit half spending a lot of time oblique to the Solar direction. The panels each hung endwise on separate moving arms shown in the picture make little sense to me. I figure the panels installed on the "floor" will shade both the ring units and any radial ones connecting them to the hub and the hub itself, and this might mean thermal radiation panels might be few because black body emission of the shaded modules might be more than enough to keep them cool enough, even with considerable power consumption in each tank unit.

Therefore if the structure is a space hotel, dedicated 100 percent to paying tourists from Earth, their motive to shell out to go up there is presumably not to lounge around in little cabins at full G. They are either going to want to take advantage of lower gravity, or take a look at open space--where a low Earth orbit puts them into sunlight half the time. If we have a dedicated viewing cupola for purposes of looking at Earth, such a thing would be spun on the station axis at a different rate than used for artificial gravity, and a cupola facing Earth would need sun-shading only briefly and intermittantly. One on the opposite side of such a separately spun unit would on the other hand be exposed to heavy sunlight half the time, only allowing a clear view in the 45-50 min the station is shaded on Earth's night side. Aside from the starscape, only the Moon would show a disk, and look about the same as from Earth at night anyway. Relatively few people would want this view--whereas I suppose most everyone would want to spend a lot of time looking at Earth, day and night. Perforce this is freefall time.

The other things to do all involve either effectively zero or lower gravity.

Therefore 24, or even just 12, ET tanks for tourists are just mainly for them to sleep in, maybe other forms of familiar-gravity rustication, private space to get dressed in, have intimate private conversations, and stow their luggage. I guessed at a rather Spartan volume ration of about 12 cubic meters per person in the private cabins (bearing in mind space tourists will be rich people not accustomed to privations). OTOH, if the major purpose of the spun station is to provide people who are working long term, on a time scale of half a year to several years, in space, the major reason for the full G rings would be to encourage them to spend as much time as feasible there, "heavy time" to compensate for free fall adaptation on the job. So personal (and communal) volume in full Earth G would be more at a premium for them.

Allowing for the idea that even cramming the tourists into compact sleeping quarters to encourage them to get out to other parts of the station is the philosophy for a space resort, one has to allow volume for access, and communal spaces in full G (dining lounges for those who find learning to eat and drink in free fall or even reduced G a challenge, for instance) suggest that perhaps a 2000 cubic meter tank might be expected to house 100 tourists, while the same volume might only serve 50 long term space residents.

On that theory, your 24 ring module picture suggests a facility for 2400 space tourists--or 1200 long term space workers.

At a guess, such a large facility seems likely to be divided between both categories, so we have say 800 paying space tourists, and 800 working crew--say 300 of these are catering to the groundhog tourists one way or another, 100 are visitors from other orbital facilities that can't provide Earth G and have been rotated over for "heavy time," while the other 400 either maintain the station itself or pursue scientific work in low to zero gravity.

Now even that latter number, reduced as it is, is 50 times the projected sustainable population of SSE. Those 400 alone thus merit 50 ET--even considering SSE as described hitherto is not using 3/4 the ET tank, still 400 space science crew merit say 6 ETs. With the layout I envision, with just one big ring and not two, and eight radial tanks, half that number meriting 3 would have about 1/4 of 21, or 5, they more or less have a piece of.

To be clear the layout I think is realistic involves--at least one tank with long axis on the central station axis, the near free fall spindle, which is counterspun to turn one face to the Sun, serve as a mast for sun-tracking solar panels, and for spaceship docking--we might add more endwise, and then perhaps surround these with tight clusters of more free fall tanks around this longer mast. Centered on the minimum single spindle, we have a single strong central truss ring surrounding the central spindle. This has four tanks mounted endwise, radially that is, and each of these has a second tank on the end of the upper one. This creates the room for each arm of two to have two circumferential tanks hanging from their tips, leaving room for four tanks, each of which we can regard as split 50/50 between the spokes completing the circle of 12. Thus two of the four radial pairs are various G level recreation towers and corridors to the core spindle and thus tourist free fall zones, including the Earth viewing lounge cupola. (For mere access to the zero G core and mast, working crew also travel up and down the tourist towers, making a businesslike transit efficiently; as accesses the other two radial towers are backup for emergencies only, being primarily work spaces for biological researchers).

I cannot figure what the inner torus in the picture is for or how it was supposed to be made, but the secondary cruciform need not spin at all. It could be a bunch of free fall labs and workshops, Whereas tourists could do with another such, or say a bundle of six tanks wrapped around another central access/core tank, providing free fall cubic. If there are 800 tourists and 12,000 cubic meters of free fall play space for them, each one has 15 cubic meters there...which does not sound like much, but supposing each tourist spends only a quarter of their time in free fall, and basically coming from all over Earth are on three shifts so usage is pretty evenly spread out around the 24 hour clock, at any given time each has more like 60. Also, such a facility as an Earth gazing cupola-lounge would have to be in addition to whatever we fit inside ETs.

We might need more intermediate gravity facilities for both tourists and scientists. If one purpose of this station is to be a jumping off point for Lunar expeditions we might want extra room at 1/6 G (hence radius under spin) to prepare crews headed there, or to ease crews returning from long Lunar visits before moving them into full Earth surface G facilities. If we are staging for Mars, we'd want more prep modules for outbound crews, and tourists might well want to spend time in reduced but non-zero G.

Therefore I question why this design has doubled up on the full G rings but seems a bit scanty on variable G or free fall volume.

Of course, the thing could be a staging base for a massive emigration push to Mars for instance, and all 24 of the ring tanks could be for acclimating prospective colonists to Mars G, giving a chance to scrub out any individuals who prove they cannot safely adapt before committing them to a ship headed that way.
 
How did SIG intend making that torroidal section that was not made of ET?

There was a paper in the December 1991 issue of the Journal of the British Interplanetary Society by Michael A Minovitch of Phaser Telepropulsion Inc proposing the building of rotating 2001 type stations 100 metres diameter for at least 150 crew by using automatic wrapping machines rotating round inflated Kevlar torus’ to wind thin layers of aluminium until the required thickness had been made.

The rotating toroidal living section would have a major and minor radii of 100m and 2m while the two central column cylinders with labs etc and constructed in the same way would each be 100m long x 10m diameter. The two column cylinders would connect into a pre-fabricated central hub into which three spokes 100m long x 4m diameter also constructed in the same way would be fitted to join the hub to the toroidal living section.

The station also served as the basis for a 'cycling' ship and would take about 10 HLLV (assuming 100 tons/launch) or 14 Shuttle-C launches and 1 STS flight with minimal EVA.

Costs were about $400 billion for an Earth orbit station, a Mars orbit station and a cycling ship

But if you are using this wrapping system then there is no need for external tanks.
 
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LH2 LRBs? Just how FAT are they?
I suppose the canon authors will answer before I can estimate. But here goes. Silverbird is useless for this; it swallows up the sea level portion of boosts in its approximations, while here that's exactly what we are looking at. Still, using SB I got a rough constant average (vacuum) thrust from the SRBs of about 11,100 KN thrust per booster and Isp of 277 sec, which led to inferring that between the SSMEs going all out (not quite true, since they throttle back near Max-Q to minimize aerodynamic stress, while of course the SRBs do not produce constant thrust even in vacuum--they start out high and ramp down, but I couldn't model these details in SB, I went for fixed figures that matched the payloads of its model of real Shuttles) and that led to the inference all the engines running on these nominal constant mass flows consumed 9622 kg per second--dividing total thrust by this mass flow gives average vacuum Isp of 305.15 sec and applying the mass ratio after 123 sec booster burn with that gives a vacuum/free fall delta V of 2576 m/sec.

Now in real life, we know the overall propellant consumption is a tad lower because of that Max-Q throttle-back, and that actual thrusts and Isp are varying as the vehicle ascends into thinner air, the SSMEs start out at considerably reduced Isp and thrust and throttling back when the air is still rather thick hurts Isp too--I suppose by the time this happens the air is pretty thin though, and perhaps the fact that the rocket is shoving through the air at supersonic speed significantly lowers the effective pressure at its tail too.

For what it is worth, my RPA model of the SSME gives 364 secs Isp at sea level and 452 in vacuum, and lowering the expansion ratio to 35 raises SL Isp to 394 while lowering vacuum performance to 438 sec. Since all these Isps apply to the same chamber and throat mass flow, they pretty much indicate thrust variations linearly too. Taking a simple average of the real SSME between SL and vacuum, that is 408 sec, while the modified one for the boosters averages 416, so each single engine would deliver about 2 percent more thrust during boost phase than any one SSME on Shuttle-C or Orbiter--these are holding at an expansion ratio of 69 aiming at better vacuum performance. At liftoff, the difference would be more dramatic of course, each individual booster modified engine delivers over 8 percent more thrust than any of the sustainer versions at SL. Also, we can expect a performance improvement if they modify the boost sequence to throttle back the 8 booster engines rather than the 3 sustainer engines--that lets the latter maintain higher Isp, and the former would throttle back a lower percentage of their full thrust, which also reduces the Isp hit on them.

Anyway, with 8 booster engines and 3 core sustainers each one of them drawing nominal 100 percent throttle 489.3 kg of propellant a second, eleven such engines are drawing a total of 5.3827 tonnes, whereas the average Isp as noted will be in the ballpark of 414, or about 92 percent the theoretical vacuum thrust (if all were 69 times expanded). 92 percent of 2576 m/sec is about 2360. With Isp 414, we get 2360 m/sec with overall mass ratio of 1.7885. Thus at burnout of the boosters, the stack should mass 56 percent its launch mass.

Now if this boost phase is 123 sec, we know how much the core of tank and Orbiter masses; the Orbiter is still about 125 as at launch, the ET is about 30 tonnes dry, and we started with 723 tonnes of propellant and used up about 1.468 tonnes per second:after 123 sec this amounts to 180 tonnes, so we should have 543 left in the main ET--all up, about 700 tonnes at this point. Plus of course the dry mass of the boosters! At a wild guess setting those at 80 (less than half the dry mass of the pair of SRBs for comparison) so we are at 780 altogether, we can infer we used another 435 tonnes of propellant beyond the 180 from the main tank. 8/3 of 180 is 480--that's what we'd expect 8 modified SSMEs with identical core mass flow to use up in the same time we burn 180 with the three sustainer higher-expansion Orbiter engines.

If the two boosters put together mass 137 tonnes dry (which still makes them lighter than the SRBs exhausted, though not by much!) these numbers all tally. Of course there is a lot of room for error in my delta-V target for instance, I imagine the boosters are lighter and perhaps the burn time to separation is less than 123 sec or the engines are derated not to run at full throttle or something. (I doubt that, with identical core sizing and tooling, it would hurt Isp to throttle back at sea level).

So with each booster 69 tonnes dry and holding 240 tonnes each of the same mix as in the main tank, massing all up 309 tonnes each on the pad and thus adding 618 to the core 752 tonnes in the tank group and 125 in the Orbiter, the whole thing stacks up to just under 1500 tonnes, which is a lot less than the almost 2100 tonnes of OTL STS, 5/7 as much. So we'd need 5/7 the thrust at boost for similar lift pattern and performance, so each of the 8 booster engines should deliver 1740 kN at sea level...whereas it seems to me it would actually deliver about 9 percent more, or about 1911. Note all this assumes a nominal 100 percent SSME throttle, not the 1.09 throttle Wikipedia uses to characterize the SSME.

Perhaps then we have a peppier liftoff, by some 7-8 percent faster acceleration--indeed, since the mass of propellant we burn up is a lot less than the thousand tonnes of it the SRBs do, we need to start out perkier to compensate for having less oomph at the end of the burn.

OK, I think I am vaguely in the approximate ballpark here. Each separate booster tank holds 240 tonnes, about 1/3 the ET volume each, and so if we tried to expand the ET to hold it all, we'd have to raise the volume by 5/3. Scaling linearly by volume, the booster tanks would mass about 10 tonnes dry--which in view of each booster having to mass 70 tonnes to match up the numbers above, means the recovered part is 60 tonnes each. Which is awfully hard to account for even granting we have 4 SSMEs instead of 3 (but each one is lighter due to shorter nozzle), thrust structure might account for another 20 tonnes or so, and we need atmospheric braking and soft landing and floatation gear, etc.

So if we kept the ET proportions, we'd scale each dimension down to 70 percent, and thus go from 8.4 meters diameter to 5.82. If we made each tank the same length, and scaled just the diameter down, we'd have diameter of 4.85 meters. I suspect the solution is to split the difference leaning toward slimmer and taller and have it 5 meters diameter or a bit and make the nose a bit like Ariane 5, or the Soviet R-9 boosters, with a tumblehome slant cap merging with the ogive nose cone. A little bit shorter, a little wider than it could be but a lot narrower than it would be in proportion?

This gives a decently wide platform for 4 modified pug-nozzle SSME variants I guess. I think maybe some of the gross overweight dry for the boosters I got goes away due to significantly higher air drag early in the boost.

I still think the LRBs should keep the tank and reuse it. After all it has to be strong enough to deliver all its thrust to the top ET tank hardpoint, doesn't it. This is natural on a solid rocket, which has to be strong to contain the bursting pressure of the grain combustion all along its entire length, but if STS had started with LRBs the temptation would be to arrange for thrust to come into the ET below, at the platform of the sidesaddle booster engines themselves, and let the tank for the booster ride along instead of using inherent strength to lift the tank and Orbiter from the shoulders as it were. Since the propellant tank must be strong enough to serve as a thrust beam, why not double down on their strength for many times reuse instead of multiplying Michoud's tank production by 5/3.

Going with hydrogen fuel underscores and emphasizes the value of making the LRBs fully reusable.
 
John Henry was a steel-driving man
Made to carry the sky
He laid steel all the way from Cape to Luna
Took five engines skyward, Lord, Lord!
Took five engines skyward.

Two he'd drop off part way
Three he'd bring down after
Leave a payload in orbit large as a house
Came back to swim in the sea, Lord, Lord!
Came back to swim in the sea.
 
To throw more complications at Shevak's wonderful analysis... How about introducing crossfeed? There's already plumbing in place to get fuel from the ET to the orbiter proper, so why not go a step further and A: get the stack a full ET at booster separation and B: allow fueling the full stack through the existing ET hookups.

Other thought, what kind of capability would these boosters have as a single stick first stage? I love the idea of NASA backing into modularity on par with Energia almost as much as I love the marketability that comes with the environmental aspects of an all hydrolox booster.
 
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A booster with 4 x SSME will burn about 2 tons of fuel and oxidizer per second at nominal thrust, so a 123 s burn time might use about 240 tons of fuel and oxidizer. A booster with that many engines will likely require a tank diameter of roughly 5 to 6 meters, so very similar to the Delta IV CCB. The CCB carries 200 tons of fuel and oxidizer and is 40 meters long, so a 5.1 meter stage with extended tanks could be 45 to 48 meters long, which is basically the same length as the 4-segment Shuttle SRBs.
 
Dug up some archival footage from the first Enterprise outfitting mission, somehow their camcorder had an incorrectly configured date but otherwise a cool still. (it's a heavily edited KSP screenshot)
 

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Is it wrong that I think those LRBs could make a decent basis for a launcher 1st stage themselves? Or am I completely crazy?
 
Is it wrong that I think those LRBs could make a decent basis for a launcher 1st stage themselves? Or am I completely crazy?
As was observed above, they bear some real similarity to the Delta IV core, and I've seen some work that suggests a core only SLS would offer about the capability of a Falcon 9, so no, the idea isn't crazy.
 
Is it wrong that I think those LRBs could make a decent basis for a launcher 1st stage themselves? Or am I completely crazy?
Mating the booster (4 x SSME, 9 MN thrust, 32 tons empty, 240 tons fuel) with a Centaur G Prime upper stage (2.7 tons dry, 20 tons fuel) in Silverbird comes up with 16.5 tons. The vehicle has a launch mass slightly over 300 tons, but liftoff thrust in excess of 750 tons, so it's an entirely impractical vehicle. The Delta IV Medium (single-stick) has a liftoff mass of 250 tons and thrust of 290 tons. A more reasonable vehicle would delete two of the SSMEs, reduce thrust to 375 tons, and double the first stage burn time.
 
Mating the booster (4 x SSME, 9 MN thrust, 32 tons empty, 240 tons fuel) with a Centaur G Prime upper stage (2.7 tons dry, 20 tons fuel) in Silverbird comes up with 16.5 tons. The vehicle has a launch mass slightly over 300 tons, but liftoff thrust in excess of 750 tons, so it's an entirely impractical vehicle. The Delta IV Medium (single-stick) has a liftoff mass of 250 tons and thrust of 290 tons. A more reasonable vehicle would delete two of the SSMEs, reduce thrust to 375 tons, and double the first stage burn time.

And would said two SSME rocket be any good for delivering stuff to orbit? Because it sounds decent.

Wait? These LRBs have 4 SSMEs? Each? Holy crap.. is that 11 engines igniting on the pad?
 
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Mating the booster (4 x SSME, 9 MN thrust, 32 tons empty, 240 tons fuel) with a Centaur G Prime upper stage (2.7 tons dry, 20 tons fuel) in Silverbird comes up with 16.5 tons. The vehicle has a launch mass slightly over 300 tons, but liftoff thrust in excess of 750 tons, so it's an entirely impractical vehicle. The Delta IV Medium (single-stick) has a liftoff mass of 250 tons and thrust of 290 tons. A more reasonable vehicle would delete two of the SSMEs, reduce thrust to 375 tons, and double the first stage burn time.
Then of course what happens is that the booster stage burning twice as long, we attain higher speed and altitude and downrange on that first stage burn--but while that's fine for a disposable stage, this stage is supposed to be semi-reusable. The engine packet will be coasting away from the launch site at something close to twice the speed, having reached something like 2 to 8 times the downrange distance at burnout and separation, and rising probably twice as high up--it experiences considerably harsher aerobraking heating and forces and splashes down, assuming we can design it to handle that tougher reentry, a much farther distance out from the launch site, at a more unpredictable location. This is OK I guess if the core unit can still be recovered at somewhat greater cost.

Now if we take the stage as is (with a different tank design, to be sure, but about the same length and exactly the same volume) with all four engines, we could instead reason this first stage has the job the old SRBs and new hydrogen booster have on the STS family stacks--provide about the same delta V in the same 123 second time frame at similar accelerations, and thus splash downrange about the same distance as SRBs used to. We would simply say, well, at burnout I estimated above 840 tonnes overall are left, of which 140 would be the dry booster mass.

(I am sure I went off track there somewhere and the LRBs mass nothing like that, though I think it shows they can mass in that range, meaning we can indeed give even such huge tanks a superstrong structure that easily handles the reentry heating and other stresses, and by being extra tough easily qualifies for reuse many many times, a dozen, a hundred--better engineering could tell us how many realistically. Until we get a canon author answer though, I think I had better stick to this probably gross overestimate which also kicks up the booster propellant requirement.)

So, with only 4 engines instead of 11, we would want the single-booster stick stack to be about 300 tonnes, or about 240 minus a 70 tonne dry weight for the booster, those 240 being the upper stage stack. Versus the 700 I estimated for the STS approach, that's a wee bit over 1/3. We can do a bit better too since counting 11 engines overestimates the worth of the central sustainers on an Orbiter or OPAM during boost. And I did some rounding down.

So I suspect with that much mass available for the upper stage stack, we could achieve quite a lot of payload with a variety of off the shelf engines and maybe some unmodified upper stage tanks. As a rough idea, the STS stacks proceeding with 700 tonnes on three SSMEs, now operating in near vacuum for highest thrust and efficiency (in vacuum, even when we throttle back, we don't lose much Isp) comes down to 155 tonnes (counting an Orbiter as 125 typically with OMS fuel and payload loaded in, the former is untouched until this point, plus 30 tonnes for the tank). Then we aren't quite in orbit yet, the OMS puts the Orbiter there with about 4 tonnes of propellant, this adds about 100 m/sec to finish the job, maybe more. So say we need a second stage engine burning more hydrogen and oxygen to achieve 6885 m/sec delta V, and we have an engine of identical Isp to an SSME (we can do better actually). 78.75 percent, nearly 4/5, must be propellant, which leaves 60 tonnes to reach orbit--maybe a bit more with higher Isp engines (like the old RL-10s, which is what Centaur uses). Of course some of that mass is the dry stage mass, but I think such a stage would not mass a great deal. Considering how low hydrogen density is and that that is some 240 tonnes of a hydrogen/oxygen mix, a great deal of the stage mass dry would be the tank actually, which would put it up above 10 tonnes. That still leaves some 50 tonnes of payload.

In fact, that idea I had for a fully reuseable integrated ET/OPAM? If I was not wrong in guesstimating its dry mass at around 100 tonnes, this smaller stack delivers the same mass to LEO--properly to LEO, not an extra low decaying orbit meant to buy the thing half a day to phase to a desirable landing location. Maybe a little less.

But if we can give the payload bus and also the second stage propellant tank decent TPS, a la Starship, we have basically (for purposes of orbital operations anyway) a 1/5 scale Starship right here. Well, maybe more like 1/8 scale in performance of delivery of cargo to orbit, around 25 versus 200. And unlike SS, because it uses hydrogen it would be challenging and costly in terms of more mass for auxiliary stuff like sun shades and recondensing boiled off hydrogen to use it like SS, that is ship up propellant loads and press on to Lunar or interplanetary destinations. Though if it can survive reentry from LEO, it can probably do something like aeroskip on Earth's atmosphere to brake most of the way back to LEO from a return from the Moon, and it has nearly 7000 m/sec delta-V, about what it takes to boost on TLI loaded down with one-way masses to the Moon, pull into LLO, and then boost back to Earth. It is a little small for an impressive Moon ship, but perhaps if we stretch it and aim for its orbited dry mass to be larger we can load it down with Lunar cargo later? For EOR/LOR operations. Meanwhile the more compact standard version can be a space truck delivering say 30 tonnes in variable form--the pure upmass cargo version delivering all of that, a minimal crewed truck (3 crew say, living entirely in a Kepler capsule on the nose tip, embedded in extra TPS on the reentry ventral side, this costs say 10 tonnes) delivering 20 with crewed supervision, a 5 tonne crew habitation extension back into the cargo volume allowing up to 8 crew and 15 tonnes upmass for a Spacelab type operation or delivery to SSE or later space stations. We have to watch how much downmass we propose to burden it with of course.

The rough estimate of 240 tonnes of propellant just happens to jibe closely with the size of the booster tank itself. Which suggests we could make both tanks nearly identical for a bit of mass production efficiency, though I am leaning very heavily on the idea we ought to reuse one--or both.

To fit within VAB height limits this vertical stack has to shorten the stages, which means widening them, but we have a lot of margin for that before we match or exceed the diameter of the ET at 8.4 meters!

I don't know whether you can match or beat 60 tonnes gross to LEO using a lighter thrust and longer booster burn. Certainly this approach has the advantage of sticking to the standard booster engine recovery unit suffering the same braking stresses and splashing down in the standard SRB recovery range. It does mean we have twice as many SSME-derived booster engines to refurbish of course. But only 4/11 as many as the notion of an integrated orbit/reentry back Recoverable Launch Vehicle I had, requiring as it would 2 boosters of some kind or other.
 
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