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The equation is expressed as: Δv = Ve * ln (Mi/Mf)

Where:
Δv = velocity change of the rocket
Ve = exhaust velocity of the propellant
Mi = initial mass of the rocket (including propellant)
Mf = final mass of the rocket (after propellant is expelled)

I'm old and obsolete,  but in my days there were no materials that even came close to 572 ksi tensile strength,  and there were no organic matrix composites that could withstand steady service temperatures above 300 F. The highest strength steels back then were in the 280 ksi class,  and all the then-known composites no better than mild steel. The best organic bound material we had available was asbestos-epoxy,  and it became junk at 290 F.  You had to trowel it on thick,  to meet burn time (2-10 sec) as a protectant inside rocket motors. 

Let's just say I am an open-minded skeptic about such material claims,  especially given the way corporations out-and-out lie in their advertising hype.  They will say literally anything to make sales,  especially to the government.  I saw that happen for decades in the defense industry.

The point of my bounding calculations was to show that getting 9.3 km/s out of a single stage was possible with Isp in the low to mid 400 sec range,  but not possible in the low-to-mid 300 sec range.  It is possible in the high 300-sec range,  but you have very little inert+payload allowance left over.  Too low to be in the least credible.  Not when the indicated propellant mass fraction is 88+ %,  and above 90% as the Isp drops.  100 minus that propellant percentage is all the allowance you have!  Your inert and payload fractions have to fit within that.  And bear in mind that something surviving one entry is still a hell of a long way from providing a long useful service life!

Entry isn't a single temperature at this-or-that location.  It is literally a heat balance among some 5 items,  not all of which are present in any given scenario.  Consider this:  at around Mach 10-to-12 around 50 km up,  most shallow-angle entry vehicles are close to,  or in,  max heating.  Depending upon shape and ballistic coefficient,  that convective heating rate can be anywhere in the range of 300-3000 W/sq.cm. 

It's a short pulse,  only several seconds long,  but it is several seconds long!  It will not be equilibrium,  but an equilibrium model is a decent guide to what you have to fight.  And a rough guide to the effective driving temperature of the plasma in the sheath about that vehicle is in the range of 3300-4000 K. 

If that balance is not achieved,  the material is going to soak out locally to that driving temperature,  much faster than conduction or convection inward to a heat sink can possibly occur.  Your only real,  demonstrated,  cooling options are high-temperature re-radiation or fast ablation,  right from the heated surface.  Transpiration cooling analyzes as possibly a good third candidate,  but has never actually yet been flown to verify that claim.

I'm not saying that an SSTO few-people-only mover to LEO is impossible.  I'm just saying it won't be very attractive,  and the design space is very limited indeed. You'd be better off with a TSTO and a few people in a simple capsule.  Something we already know works.  With a wide range of design options available.

GW

GW,

At no point in time has any claim been made that SSTO will beat TSTO on payload performance.  That never was and will never be in the cards for SSTO.  Basic physics says TSTO is superior for orbital launch.  However, that is not the point behind SSTO.  The point is to use a singular vehicle to send humans, and only humans, into orbit.  For any kind of cargo, we will use TSTO or launch assist technologies (for low value materials such as water, gases, and metals).  Human transport is the only plausible use case for spending more money, in order to reduce operational cost and complexity- not the complexity of designing or building a SSTO, but the actual operation of one high-performance rocket powered vehicle vs two, for the express purpose of creating an orbital passenger transport that operates similarly to an airline service.

Falcon 9 is a reusable booster with a 6.06% structural mass fraction for the booster stage.  It's primarily Al-2195 alloy, which has a yield of 87ksi.  T1200 fiber composite has a tensile / yield strength (basically the same thing) for CFRP, of 572ksi.  To that, we're going to add SWCNT to the resin matrix.  That bumps up yield / shear / buckling strength by about 75% for a given weight, because the CNT literally locks plies of fibers together by wrapping around them, like almost like a double-ended fish hook (what it looks like under a microscope), to the point that a high pressure CFRP PET-lined O2 tank for a firefighter that previously weighed 57lbs then became 6.1lbs for the same CFRP and PET liner, with the SWCNT resin matrix additive, for equivalent strength.  The tank holds back the same pressure as a much thicker ordinary CFRP O2 tank, but it's drastically lighter because it's drastically stronger in every dimension.

If we built the Falcon 9's propellant tanks from T1200 composite, there is no reason I can think of as to why it absolutely must remain at or near the same weight as the Al-2195 propellant tanks.  It will be both stiffer and stronger, by quite a lot, as compared to its metal-based counterpart.  Al-2195 has 15% of the strength of a T1200 fiber composite, or 17.33% the strength of T1100 fiber composite (current technology for high-strength aerospace parts which are mass produced).  T1100 fiber composite (the composite, not the fiber itself, which is 2X stronger than the composite) is both stronger and lighter than any metal alloy that is not more brittle than glass.  Weaker but cheaper fibers such as T700, T800, and IM7 have been used by NASA and our primes for reducing weight and total fabrication cost, as compared to Al-2195.  PROOF 900HT resin has a maximum wet service temperature of 288C, and is CTE-matched to the fiber, which is far more heat than Al-2195 can tolerate without becoming silly putty, with very little loss of tensile strength up to that temperature (somewhere between 10% and 20% loss of strength, but that only happens during reentry when the vehicle is much lighter, because the TPS provides quite a bit of thermal insulation during ascent).  It cures at a much higher temperature than that (454C, IIRC), which is how and why I know that resin won't "go soft" (because you have to get it much hotter to cure it).  This has been exhaustively tested by the US military for composite parts in close proximity to very hot jet engines.  That is how and why we know that it works.  It's been tested- a lot.

UltraMet makes 4.4lb/ft^3 toughened aerogel "Space Shuttle tiles", flown in space aboard the X-37 as part of its TPS package.  A 243s exposure to 3,500F / 1,927C for a 1inch thick tile (0.367lbs/ft^2 / 3.3lbs/yd^2), resulted in a backside tile temperature of 350F / 177C at the end of the test.  177C is well below 288C (wet service limit for 900HT) or 350C (dry service limit for 900HT resin).  Maximum Space Shuttle reentry temperature was 1,477C.  Despite that fact, my mass estimate for TPS included RCC for the leading edges and UltraMet tiles everywhere else, even though lighter flexible fabric reusable surface insulation would suffice.  NASA is actively developing BNNT and aerogel fabrics which are absurdly lighter than the flexible reusable fabric insulation used aboard the Space Shuttle.

When the composite strength is 572ksi, you're nowhere near the limit of its strength, your stiffness is more than double that of Al-2195, and the thickness of the composite (5.08mm) is more than double that of Aluminum, which means it's 16X as stiff, as compared to 2195.  If Falcon 9's metals-based propellant tank structure doesn't provide that kind of strength, yet it's reusable, then how is a much stronger composite going to fail when its subjected to the same forces during ascent (when the vehicle is heaviest)?  What I'm working on is, in point of fact, and despite greatly reduced weight, still far stronger than any equivalent metals-based structure.  I've allocated more volume of material that is both stiffer and stronger.  How is a Falcon 9 booster reusable when it cannot come anywhere near the strength and stiffness of a composite for equivalent weight?  What mechanical properties does Al-2195 imbue the structure with?

My Delta-V with 2,000t of LOX/RP1 propellant, at 316s Isp, is 9,746m/s.  The Isp of Oxygen-Rich Staged Combustion RP1 fueled engines, without vacuum nozzles, ranges between 311s and 338s, so I chose an Isp value modestly above sea level, since the vehicle won't remain at sea level for more than a handful of seconds.  The majority of its ascent time will be spent substantially above sea level, where the engines produce more thrust per unit mass of propellant expended.  I need RP1 engines with demonstrated Isp and a 200:1 thrust-to-weight ratio.  That's already been achieved, plus a little extra.  I'm not invoking any engine technology which hasn't already existed for quite some time now.

Everything that is not "engine" on the Falcon 9 booster weighs 21,370kg.  The landing gear weigh about 2,000kg.  By definition, the rest of that 19,370kg has to be propellant tank or thrust structure.  It's 7.174 cubic meters of metal if it's primarily Al-2195.  If it was made from HexCel IM7 fiber composite, then 7,361kg is a good guess as to how much it would weigh.  If it was made from T1200 composite, then 2,906kg (no CNT resin additive) is a good guess as to how much it would weigh for equal strength.

25,600kg dry mass / (25,600kg + 395,700kg) = 6.08% dry mass fraction (as-built by SpaceX)
4,230kg + 7,361kg + 2,000kg = 13,591kg (new dry mass fraction with IM7 composite (as-built by Boeing / NASA)
13,591kg / (13,591kg + 395,700kg) = 3.32% dry mass fraction (IM7 / CYCOM 5320-1 resin)
4,230 + 2,906kg + 2,000kg = 9,136kg (new dry mass fraction with T1200 composite (no CNT additives)
9,136kg / (9,136kg + 395,700kg) = 2.26% dry mass fraction (T1200 composite)

FYI, the IM7 composite, rather than bursting at 1.5X the pressurization load of the Al-2195 tank, burst at 277psi, which means it was absurdly over-built, but was absolutely guaranteed to pass all load tests.  Every single one of these composite substitutes for Al-2195 has been overbuilt to the nth degree.  Instead of asking why we're over-building composites 2X to 3X stronger than Aluminum (the reason they're not even cheaper), why isn't anybody asking what the logic is behind making the composites ridiculously stronger than any of the metal structures we routinely accept into service?

Boeing used a whole lot of fiber to avoid putting that tank into an autoclave.  It could've been much thinner and lighter than it was, using the same IM7 fiber, with improved H2 permeability rates, had they used their giant autoclaves.  Yes, it would take longer, no it probably would not be much cheaper than Al-2195 at that point, but performance is what makes the SLS useful, not saving a trivial amount of money relative to the entire project cost.

Anyway...

Would the landing gear still need to weigh 2t for a rocket stage with less than 1/2 of its original dry mass?

The kinetic energy absorbed by the landing gear is the product of mass and acceleration- ye olde F=ma.  If the mass is half but vertical acceleration rate is the same, then you have half the kinetic energy.  The vehicle is also dramatically "butt heavier", thanks to the engines and thrust structure now comprising almost 46% of the entire dry vehicle weight, so track width can be narrower for equivalent stability, which further reduces weight.  We'll ignore that optimization and focus solely on weight added to make the gear strong enough.

8,136kg (gear now half as heavy, absorbing half as much energy on landing) / (8,136kg + 395,700kg) = 2.01% dry mass fraction

Would we be modestly "heavier than that" after accounting for our engine thrust structure and grid fins?

Yes, but not by a lot.  That means a 2.75% dry mass fraction is achievable using 1,000ksi+ composites (T1200 fiber plus SWCNT resin matrix additive) and 200:1 thrust-to-weight ratio RP1 engines with a non-regeneratively cooled RCC nozzles plasma sprayed or CVD coated with UHTC, to prevent oxidation, as already proven to work and reduce weight and engine complexity by NASA engine testing with these nozzles.

The notional SSTO I have in mind is 4.31% payload and dry mass fraction.  The 2,000t of propellant provides 9,746m/s of ΔV at 316s fixed Isp (reality is that Isp improves by a little bit more during ascent, up to 338s, 100bar chamber pressure).  No aerospike, no nozzle extensions, etc.  That should be enough to make up for drag and gravity losses.

To reiterate, I have completely conceded the point that a TSTO will outperform a SSTO, every single time.  That is not "the why" behind building a SSTO.  There are other factors at play beyond simple fuel cost and payload performance.

Can we also apply our same SSTO composite tech to TSTOs?

We obviously can, and we already have companies like Rocket Labs doing that with their LOX/RP1 TSTOs.  We'd be foolish not to, assuming performance matters so much that we're de-justifying SSTOs on the basis of payload performance per unit of dry vehicle mass.  It can't possibly be the cost of the composite tech, because we're using that more and more over time, regardless of SSTO vs TSTO.  For me, this is more about advancing rocket tech than whether or not a SSTO can deliver more payload than a TSTO.  The answer to that question is beyond obvious.

I want to roll our best composite tech, best engine tech, best thermal protection system tech, and best avionics / life support / power / thermal management tech into a single vehicle, to show the entire world what "the best" actually looks like and how astonishing the end result is- something previously thought impossible actually is possible with modern materials.  Whether or not it's practical is a different question.

For all ... this post is about rocket sizing ... GW Johnson provides a spreadsheet and user manual

I'll put the text after the links...

Here is the spreadsheet:
https://www.dropbox.com/scl/fi/600qk03p … yqmag&dl=0

Here is the user manual:
https://www.dropbox.com/scl/fi/cuvcuddj … iijai&dl=0

Here is an addendum to the user manual:
https://www.dropbox.com/scl/fi/btl8weqm … 0xh7t&dl=0

And here is a pdf comparing SSTO and TSTO designs ...
https://www.dropbox.com/scl/fi/rjv90o1o … pg5ak&dl=0

And here is the text about the links:

(for NewMars members):

As you know,  I did a little simplified vehicle sizing spreadsheet “launch sizing.xlsx”,  responding to the latest round of SSTO talk on the forums.  These were simplified to one weight statement per stage,  no linked burn calculations.  That rules out complicated missions and reusability. But it works for simple all-expendables on a simple mission:  LEO.

I wrote up a user’s manual for it.  At that time,  there were only worksheets for SSTO and TSTO expendables.  The default examples in those worksheets were just approximate guesses.  I went back and adjusted those data by running the “r noz alt.xlsx” spreadsheet to get better Isp data,  and I revised the TSTO second stage acceleration requirement at its ignition.

Those data got written up in a document titled “Effects of Better SSTO and TSTO Modeling Data”.  It covers both LOX-LH2 and LOX-LCH4 SSTO’s,  and a LOX-LH2/LOX-RP! TSTO.  I was surprised to find the hydrogen SSTO had about the same payload fraction as the TSTO,  close enough to be a serious competitor in the expendable launcher market.  I was unsurprised that the methane SSTO turned out as poorly as it did.  We have known since before WW2 that low Isp requires more stages,  and that is exactly the dilemma where the methane SSTO falls.

I then added a third worksheet “tank volumes” to “launch sizing.xlsx” that estimates the tank volumes and stage dimensions for designs created in the “SSTO exp” and “TSTO exp” worksheets.  This is designed to work with engine data from “r noz alt.xlsx”,  beyond just Isp.  The engine configuration is thrust-rescaled to fit the required thrusts coming from the “SSTO exp” and “TSTO exp” worksheets.  And the r-value is used to split propellant into oxidizer and fuel masses.

This third worksheet is documented in an addendum document for the user’s manual for the “launch sizing.xlsx” spreadsheet.   Attached hereto are 4 of the 5 listed items (there is no need to transmit the original spreadsheet without the tank sizing worksheet):

1.        Excel spreadsheet “launch sizing.xlsx”  (original:  only worksheets “SSTO exp” and “TSTO exp”,  not attached hereto)

2.        User’s manual:  “User’s Manual Launch Sizing.pdf”  (cruder examples for “how-to”)

3.        Refined models by “r noz alt.xlsx”:  “Effects of Better SSTO and TSTO Modeling Data.pdf” (these are still only weight statement results,  no tank volumes or stage dimensions)

4.        Added tank sizing to “launch sizing.xlsx”:  “Addendum to User’s Manual.pdf”,  refined examples complete with tank volumes and stage dimensions (this version attached)

5.        Revised spreadsheet file “launch sizing.xlsx”:  added worksheet “tank sizing”

I suspect you will want to put these things in that dropbox thingie,  with links in a posting somewhere on the forums.  The text of this letter could go in that posting with those links.

What I found with these simple tools:

When I tried tank sizing for the methane SSTO,  I found I needed an engine cluster that simply would not fit behind a stage that met the “aerodynamically-clean” criterion of stage L/D = 6.  The much larger takeoff mass (and required thrust) prevents that.  It’s not just unattractive from a payload fraction standpoint,  it’s actually geometrically infeasible!   It would have to be shorter and fatter for the engines to fit,  and that is more drag,  more drag loss,  and a higher required mass ratio-effective dV,  which drives payload fraction even closer to zero.

With the advent of TSTO launchers that have partial reusability (SpaceX’s Falcons),  which demonstrably impacts cost even more than payload fraction,  I see no point to offering SSTO expendable launchers anymore.  They are feasible,  and competitive in terms of payload fraction with all-expendable TSTO’s,  but they cannot offer any reusability,  while the TSTO can (flyback first stages),  at the “cost” of somewhat-reduced payload fraction.  The expendable market will vanish!

And,  by the way,  when I do the engine ballistics thing versus altitude,  I can get a higher ascent-averaged Isp out of an “ascent compromise” fixed bell,  than from any conceivable free-expansion nozzle.  Meanwhile,  bell extensions,  which do work,  reduce engine thrust/weight considerably.  That adds extra inert mass,  costing payload fraction out of otherwise the same design.  Plus,  they add failure modes the fixed bell simply does not have.

GW

(th)

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