Some things to emphasize about the standard strap on liquid booster concept:
1) since they are meant to be developed to be reusable, on the assumption this leads to major cost saving despite retrieval and refurbishment costs, I want to be aggressive in their use. The balance between ker-lox lower stage and high-energy hydrogen-oxygen upper stage that would be optimal with a fully disposable or fully reusable system is upset in favor of the reusable lower stage. The name of the game at this point in development is to cheapen the overall launch cost in part by being stingy with upper stage propellant; smaller tankage there and less fuel mass makes fewer J series engines (I did look into RL-10 but they are so small they don't seem appropriate in this role, even for the smallest possible version of the system) more effective on the upper stack, lowering gravity losses in the early burn. To this point I've actually tried to maximize payload for a given engine set but I suspect that would evolve, with that volume option for the 2nd stage being a "max cargo" option, and I now intend to look for the mass combination where we get the most payload per kg of loaded tank--call that "economy" option. Then given that I expect a sort of parabolic-sinusoid sort of curve of payload plotted against full tank mass, going between these benchmarks would seem to be where the standard would lie--going 2/3 of the way down gives more payload without much lowering the payload/tank ratio, while going 1/3 back improves that ratio from the mediocre one of maximum load significantly while not lowering the total payload by much. This would require a lot of work with Silverbird and I am not sure I can trust it either, but could tune the economy of the system significantly. Also for small variations I think I can check Silverbird by estimating gravity loss due to larger fuel loads versus higher theoretical ideal delta-V.
2) On the other hand, tank mass (dry) estimates assume we get better volume/tank wall mass ratios with increasing volume. The tanks seem likely to scale as the 2/3 power of the mass/volume, that is with area rather than volume. To be sure at a given pressure, tanks that are sized solely as pressure vessels scale with mass, since increased diameter raises the force a cylindrical section's wall must restrain, so the volume of tank structural material hence mass scales with contained volume. But the pressure of an STS type tank is pretty low, 1.5 atmospheres absolute, so I believe the structure is not mainly a balloon but mainly a stress bearing structure moderately stabilized against buckling by modest pressure. However tanks were shipped across half a continent (well a third anyway) from Michoud to Cape Canaveral, very big tanks. And at 27 tons the ultra-lightweight latest model, containing 725 or so tons of propellant, massed just a bit under 4 percent of the propellant. Whereas in this ATL I assume, given the conservative nature of the program, that the starting design point for the 2nd stage is the Apollo program upper stage, which was 108 tons of propellant in 15 tons of stage all up. Figuring 2 tons for the engine and its primary thrust structure and articulation etc, and perhaps 1 for miscellaneous stuff, that is a fixed 3 tons for all single-engine sizes plus 12 of tankage. Note though that at 5.5/1 O/F ratio for J engines versus 6 for STS we can't directly compare STS tanks to Apollo ones, since the average propellant density is lower for the latter. LOX has density 1.14 times water or 8/7 and therefore takes 7/8 cubic meter per ton--though we practically have to allow for insulation--but then we also have that need for hydrogen so assume for the moment we can compare different mixes directly. LH2 requires 14 cubic meters per ton, 1/14 water density hence 1/16 LOX density. Thus for the 6:1 ratio used in STS we need 2.75 cubic meters/ton but for a 5.5:1 ratio we need 2.894, a 5 percent difference. Thus a tank the same size as the STS, with suitably rearranged internal volume ratios, would hold only 690 tons instead of 725, a difference equal to the mass of the dry tank!
A tank that holds 690 tons of the lighter mix and thus is the same size as the Shuttle tank, but extrapolated from the Apollo upper stage set, would mass 41.3 tons by the 2/3 law. At over 14 tons more than the same volume STS tank, 53 percent heavier, I figure it ought to be plenty strong to take the stress of compression by a payload on top while taking 22 percent more thrust than the three systems (asymmetrically!) of STS put on it from the sides. Except that come to think of it such a tank would be used for a much larger booster set than 6, since the system I propose has the 2nd stage lit aloft and thus burns a lot less propellant. So perhaps this procedure is a bit dubious but anyway it is less optimistic than extrapolating from OTL ultralight tank design. Perhaps it will be necessary to beef them up a bit more, but I think I am in the right ballpark here.
So anyway if it is legitimate to estimate tank masses by the 2/3 power method, and assume 2 tons for every J-2S engine installed and one miscellaneous overhead ton, we are going to tend to get better propellant/dry mass ratios with larger tanks, which tips the balance a bit toward larger tanks and thus payloads offsetting my desire to make the thrust of the recoverable units count for more.
3) If at a later date we go over to trying to recover elements of the 2nd stage, this will tip the balance of mass ratio of 2nd to first stage toward the former since now presumably, once we shake it down, net cost of each upper stage set is lower. But surely there will be significant, perhaps huge, mass penalties involved in deorbiting components and retrieving them in reusable form, so the payloads delivered for a given engine set will be reduced, perhaps dramatically. Thus despite larger upper stage sizes and perhaps significantly increased engine performance (SSME at ISP 453 versus J-2S at 436 sec; denser fuel mix allowing a tank that masses 41 tons to hold 30 more tons of propellant) we will need to realize really large cost reductions in both booster and upper stage burns to realize net economy in dollars/ton of payload.
Upper stage reusability may never happen therefore!
On the other hand, I estimated I needed only 3 J-2S to match the Shuttle's delivery capability to orbit, with 3 SSMEs of twice the thrust, and well over twice the mass! So to recover the engines alone might require much more modest systems. For instance if it would really require 45 tons to return the SSMEs from a standard Shuttle launch (with Orbiter eliminated in favor of separate return of the engines) here for the same payload I ought to only need half that, or under 23 tons. This only makes sense to do if the J series is evolved to become reusable, which would presumably raise their dry mass somewhat, so the scenario is not all that rosy after all. But with a core pressure of 30 atmospheres I can be optimistic that for half the thrust, they ought not weigh a lot more than half the mass of the SSME sets we'd need.
4) The idea is to be conservative with technology and thus get something useful on the shelf pretty quickly, then improve it gradually. Thus we can start with old-fashioned early 60s state of the art H-1 engines, then look up the studies done to sketch out the H-1b & -1c, aiming for the thrust of the latter which apparently called for a 20 percent chamber pressure increase that also raised the vacuum ISP from 289 to 296 (with sea level ISP of 262, and I assume thrust in proportion although impediment of the gas generator turbine might lower thrust further. I hope not as all my work up to now is based on vacuum thrust of 1131 kN per engine and thus sea level thrust of 1001--thus one set of 5 could lift 510 metric tons, which gives us the upper mass limit on the pad of each combination of boosters. (Lower for H-1 of course). At the same time we want the upgraded H engines, call them H-2 in the Mark 1 form (with H-1 being Mark 0, prototypes useful for real launches but with no intention of reusing the engines, rather to test out integration and the recovery mode) to be reusable as well as delivering the higher thrust and ISP.
5) Hitherto I have not been paying enough attention to keeping the G load low. My aversion to using more J engines than strictly necessary, since they are disposal items, tends to keep maximum G loads on the 2nd stage from being excessive, but I think we'll need some throttling on the boosters--though one way to get that is to simply shut down some of the 5. I have been figuring that the H engines can have simple gimbaling in one dimension, with each one veering tangential to stage circumference, so we have 3 axis control overall. We don't need roll control on the boosters affixed as side boosters, but I thought it would not save much weight to have one axle for 2 engines to gimbal on--physically it would be hard to do that anyway because the fifth engine is in the center. But this means we want to avoid shutting down more than the center engine since it would throw vectoring thrust off to shut down one of two for each dimension (yaw and pitch). This should be doable though, so shut down options are good for 20, 40 or 60 percent.
5) I am largely at a loss to explain how this "flies" politically, when there are so many interests to pull it another way--to go with F-1A instead, to reject liquid fueled engines completely and go for solids, to have pressure fed boosters with simple though large engines, to make a big integrated sexy fly-back stage (requiring more than a single F-1A worth of thrust due to having extra mass for flyback) that would have limited growth options and thus make making a single type extra large.
But perhaps the politics of having something useful before election day 1976 would appeal very much to Nixon; not knowing Watergate is looming on the horizon (though by the time of the Shuttle Decision it was already a thing) he thinks he'd be around then and the first iteration of the new system would be his baby politically. It is really Saturn based, but looks so different he can claim it for himself. This points in the direction of simple as damn possible; having avoided the Charybdis whirlpool of an ambitious high tech Great Leap Forward, we now have to elude the Scylla monster trying to pick off features such as liquid fuel (just make some simple solids, dude! Be done by this coming Christmas!) using H engines (hey lookit a single F-1A is better than 8 H-1!) water recovery (dude, we can make this fly back real simple...) and so on.
On another front, what if OMB is even more hardline than OTL? OTL at one point the proposal was made to scrap all work on anything like a Shuttle except for a small budged for researching very small spaceplanes to be launched from evolved expendable boosters. I've wondered if that path had been taken, with NASA really being cut back hard, something would evolve from it superior to OTL. But let us suppose NASA management (and we could steal a page from the ETS book and put in a different administrator) is so panicked and desperate that they beg for a two track project--namely develop an ultra-cheap and simple but somewhat reusable launcher system meant to serve all national needs by being modular and evolving, with a very short time frame for initial use of the first iterations, and that this saves so much money that they can justify insisting on a space station program to use it--which must involve a manned vehicle of some kind to be launched on the first iteration system. Can they negotiate a commitment that if they keep the first wave manned vehicle very simple in terms of research and development, by making a derivative of Apollo, they get to follow up with "upgrades" meant to make a space bus (for 5-8 space travelers at a time) with superior entry characteristic later?
Then you see, if all three elements are funded, NASA has a clear mission path for the next decade or so. Get Mark 0 of the national launcher system up and running, past initial testing, before 1976 is out; design space station modules (in the 20 ton range, later to stretch to 25-30) to be put up by the new launch system (and initially dock by remote control, so a pair is ready before any astronauts have to get up there to shepherd them together) followed by a manned mission to occupy the growing station; intersperse module upgrade launches and Apollo-derived missions to the station while at the same time touting the new rocket family as the cure-all for all launches, DoD, commercial, even seeking foreign customers and with proof of success, retire everything else meant to launch anything above 15 tons or so. By the beginning of the 1981 Presidential administration, have a more advanced reusable space "plane" of some kind--not necessarily a winged thing, but something with good hypersonic L/D for gentle and better controlled reentry and good landing characteristics and reusable with minor refurbishment--to carry people. Meanwhile, between '76 and '81, bigger versions of the modular system, with 3 or 4 boosters, would be first tested, then prototyped and then used, while the Mark 1 Standard booster module would come on line with the superior thrust and ISP of H-2, and its engines being reused many times while the basic tank frame is used many more times. After that, with the industry becoming accustomed to standardizing around that system's capabilities, further evolution would be incremental with the aim of achieving the same net impulse at the same accelerations but more cheaply and reliably--a 20 percent thrust upgrade can lower engine numbers from 5 to 4; ISP improvements can cut down on the propellant load, hence tankage, and free up more mass for more grandiose upper tank stages, or be used to further reduce the engine count to 3 perhaps; reliability improvements and durability allow the unit to be reused very promptly with minimal refurbishment cost thus cheapening launch prices. There is very little to improve in the upper stage unless one wants to explore reusable items from it. So the development budged goes from being mostly about the booster, but with a very minor increment on off the shelf stuff that just lasts a couple years, while the rest goes to an Apollo derivative--ETS suggests this might take half a decade or so, so available in first version by '78-9, 1980 at the latest. As the Mark 0 Booster goes into service, back burner development prepares H-2 engines that will be reusable and more powerful so that the Apollo derivative can count on a mass budget of 14 tons--6 tons for the capsule, 2 tons for propellant--twice as much as enough to get up to a 500 km altitude orbit, circularize there and deorbit, leaving 6 for structure and other supplies. That's a huge truncation of the Apollo SM of course, which all up for an Apollo Lunar mission was 24 tons.
I'm talking here about a launch on top of a single standard booster, with a bog standard Saturn V upper stage--108 tons of propellant, 15 tons dry mass. This can be done with 5 H-2 engines, so it has to wait for Mark 1 of the booster, and unusually we put the upper stage on top. What we have then is a basic replica of the Saturn 1B in capability, but with a smaller lower stage. We can't do it with old H-1 engines because these lack the sea level thrust needed to lift the whole stack.
With over 14 tons to the 100 NM standard low orbit, I think we can go ahead and modify the Apollo from Lunar Mark II to an orbital Mark III in this fashion:
Cut a hatch in the heat shield. Demonstrated to be safe with OTL STS since they have 3 landing gear hatches and a number of large fuel and other intakes all on the highly heated belly. It opens into a front section of the SM, lightly built, that is pressurized and with minimal clutter except for structural members carrying the pie-with-center disk cutout internal panel structure through, not as solid panels but as struts. This creates a "mission module" like extra habitable volume, and allows us to seat up to 5 crew members in the CM for launch and landing. Behind this is a toroidal service module zone proper, as with the larger CM of OTL containing much infrastructure for the CM and also mission propellant. But instead of a central single main engine the rim at the rear is flanked with 6 4-headed heavy maneuvering clusters, the forward pointing nozzles having been covered with light fairings during launch. These give roll control and translational thrust, supplemented by the maneuvering thrusters on the CM itself. In the center is a docking system and hatch; another hatch on the "bottom" of the habitable extension turns the narrow tunnel running to the rear hatch into an airlock. A light control set gives a pilot stationed at the rear port, which has a window, control of the ship for docking.
This is the standard vehicle for NASA human excursions in the late 1970s and early 1980s. With a 14 ton mass budget, something like HL-20 (a bit bigger than the OTL proposal) can replace it in the mid-80s if deemed desirable.
Launched on a heavier array, with a 30 ton budget to the standard orbit, a station mission can include a 16 ton actual mission module, which can also be a unit to be docked to the station permanently as a module, or could be a mere supply trailer to be deorbited along with the returning main vehicle to burn up trash in the atmosphere. A 30 ton robot cargo vehicle can arrive at a 500 km high station with 27 tons mass all up, over 15 of which would be actual cargo, perhaps all but 3 tons of it in fact. Or again a 30 ton launch can turn into a pure station module launch with a permanent 24 tons of structure added to the station. If we ever want bigger modules, we'd develop bigger combinations of standard boosters and upper stage tanks. But it would seem the orbital program can begin very handsomely with nothing but 2-booster and 1-booster versions authorized as man-rated.
Would we ever actually need the bigger versions then? Well, there might be military demands for something massive. An ambitious station might need large single piece structural units--and by the way, the upper stage tanks are all available for repurposing and gradual furbishment. Moving them up to a 500 km orbit might require 1.5-2 tons of hypergolic propellant.
And NASA, after some years of success with a LEO station, might be authorized to go farther again. To replicate Apollo, we'd want a 100+ ton launch capability although if we are clever we could also do it in a few smaller launches. To do more than replicate Apollo, we might want seven or eight booster vehicles that put up substantially more than 100 tons while massing more than Saturn V did and hitting the launch pad with a lot more thrust. This might allow the one-shot pre-placement of a Lunar surface lab. Or the assembly in a few steps of very large interplanetary vehicles, with heavy components such as nuclear engine cores and bells or massive solar arrays.
Probably the larger arrays will have to wait until some high priority project demands them, which would require the funding not only of the article itself but a couple predecessors for testing. I'd suggest a procedure whereby a hitherto untried combination first launches a "dummy" payload-given that we have an orbital infrastructure a launch of water ballast in a tank into orbit is not wasted if it has an OMS, or a tug is available, to take it up the station where it will serve many excellent purposes--perhaps even allow the development of an aquarium module, a pet idea of mine for appropriate space science (biology--and the fish can't escape to infest the rest of the station, the way any sorts of land animals could). The second test launch assuming the first goes well will be a cut-rate getaway special payload, advertised to all and sundry with high insurance coverage provided "free" by NASA (i.e. the US taxpayer). At bargain prices, people can put their payloads into orbit in one massive cluster. After that launch goes well, the urgent priority mission is cleared to use the new combination.
Or of course NASA could get authorization to take these steps years ahead of any particular demand, supplying water in truckload amounts to a going concern space station with one test and a bargain extravaganza launch opportunity, success not guaranteed but cargo insured, for the second. And thus put that combination on the shelf as ready to go when needed.
I'm not sure we'd get around to using the Saturn V scale options until the 1990s and then only if a Lunar mission were authorized, or perhaps a very large space station project. We might never need to exceed that scale ever.
