Methalox Falcon 9 family

[Hyperion5]

Awhile back, I made a thread about the possibility of converting the Falcon 9 family to burn methane instead of kerosene.  Tragically, that thread died out long before we got the news about the Raptor's potent thrust and Isp.  I know we've had a Spacex member confirm that the Raptor engine family is very limited in scope.  However, it's very plausible that the MCT will need smaller engines to land on Mars.  For me the one logical secondary use for such possible engines is as replacements for the Merlin 1D.  They would, after all, be even more reusable.  The most important part is that they might be efficient enough that an identical size Falcon 9MR (Methalox-Reusable) would be able to match or exceed a Falcon 9R in payload capacity.  If you can do that, then this switch is a possibility, otherwise it shouldn't be considered. 

The key to accomplishing this, or so I thought, was whether or not the Raptor's impulse density (the amount of energy you can get from a constant unit of propellant volume), was the same as the Merlin 1D.  Not being the best at such math, I naturally asked NSF's Aussie guru of all things rocketry, Steven Pietrobon, to take a stab at the math.  Steven wound up providing a fantastic breakdown of the math involved.  (Warning: Rocket science following!)

Data below.

Merlin 1D
---------
Isp(vac) = 311 s
Exhaust Speed v_e = Isp*g = 3049.9 m/s
Mixture Ratio (MR) = 2.2
Oxidiser Density (LOX) d_o = 1.149 kg/L
Fuel Density (RP-1) d_f = 0.8 kg/L
Propellant Density d_p = (MR+1)/(MR/d_o+1/d_f)
                       = 3.2/(2.2/1.149 + 1/0.8 )
                       = 1.0112 kg/L
Impulse Density Id = v_e*d_p = 3084 Ns/L

Raptor
------
Isp(vac) = 363 s
v_e = 3559.8 m/s
MR = 3.6 (guess)
d_o = 1.149 kg/L (LOX)
d_f = 0.4239 kg/L (LCH4)
d_p = 0.8376 kg/L
I_d = 2982 Ns/L

So Merlin 1D has a 3.4% higher impulse density. For high delta-V though, this small difference would result in Raptor having a better volumetric efficiency than Merlin 1D.

Now at first glance I thought that the Merlin 1D having 3.4% greater impulse density than the Raptor would mean that the methalox Falcon 9 family could not be a physical possibility.  Steven however had other ideas.  Intrigued, I asked what he meant by the Raptor having better volumetric efficiency than the Merlin 1D. 

To understand why, you need to learn a little rocket science. We can express the rocket equation as

dv = ve*ln(1+mp/mf)

where

dv = change in velocity or delta-v
ve = g*Isp = effective exhaust speed
g = 9.80665 m/s² = international standard acceleration for one Earth gravity. Note that the actual value of gravity on Earth varies from 9.7639 m/s² to 9.8337 m/s2 depending on your location on the surface of Earth.
mp = propellant mass
mf = final mass

We can express the propellant mass as a function of propellant volume Vp (in litres or L) and propellant density dp (in kilograms per litre or kg/L) as

mp = dp*Vp

Thus, we have

dv = ve*ln(1+dp*Vp/mf)

It turns that mathematically, that if the ratio mp/mf is low, then we can approximate the rocket equation as

dv ~= ve*dp*Vp/mf = Id*Vp/mf

where Id = ve*dp is the impulse density, that is how many Newton seconds of impulse we have per unit litre of propellant (with unit Ns/L). ve is how many Newton seconds of impulse we have per unit kilogram of propellant (with unit Ns/kg which is the same m/s since 1 N = 1 kg m/s² from Newtons equation F = m*a). What this equation shows is that propellants that have high impulse density will have smaller size tanks, up to a point.

For two propellants if Id1 > Id2, but ve1 < ve2 there will be some delta-V or volume to final mass ratio value (Vp/mf) where the higher ve or Isp propellant will have a smaller volume. That is we require

f(V/mf) = ve1*ln(1+dp1*Vp/mf) - ve2*ln(1+dp2*Vp/mf) = 0

This is a non-linear equation which can only be solved iteratively, for example with Newton's method where

f(x) = ve1*ln(1+dp1*x) - ve2*ln(1+dp2*x)
f'(x) = ve1*dp1/(1+dp1*x) - ve2*dp2/(1+dp2*x)

x_n = x_{n-1} - f(x_{n-1})/f'(x_{n-1})

Using the attached program, the crossover point is Vp/mf = 0.549 L/kg and dv = 1345.9 m/s. That is for a delta-V below 1345.9 m/s, using Merlin 1D is better, but for a higher delta-V, Raptor is better.

So it’s likely some of your minds are still recovering from that explanation, so let me boil it down to this.  Impulse density only makes things more space-efficient up to a point.  Once you go past a certain amount of delta-v, an engine with higher Isp actually requires less propellant volume to move the same amount of payload.  In the case of the Raptor v. Merlin fight, the Merlin is only more space-efficient when the delta-v is below 1345.9 m/s.  Since the core stage alone would use more delta-v even when reused, this means a methalox Falcon 9 family is an actual engineering possibility!

Steven was also very sure that not only was a methalox Falcon 9 family an engineering possibility, but said that the math showed it would have even more performance. 

As long as staged combustion is used, performance would go up, as the first stage does more than 1345.9 m/s. However, a staged combustion kerolox engine would give even greater performance.

Of course the one catch with SC kerolox engines is the materials science involved.  The Raptor in contrast will have inferior volumetric performance but vastly better reusability.  Steven went on to volunteer his opinion as to whether or not swapping in small Raptor-like engines onto the Falcon 9 family would be worth it:

Yes, I think so. The increased Isp for the upper stage is where most of the performance will come from, but that might require a lengthening of the stage.

I just wanted to point out that the rocket’s length is likely to be roughly the same because the methalox Falcon 9’s greater volumetric efficiency would likely balance the added length of the SII. 

--

So in summary, a methalox Falcon 9 family built with small Raptor-like cousins can be the same size as the existing Falcon 9 family.  It will however be even more reusable, carry more to orbit, mass less, damage the pad with less thrust, and be burning an even cleaner propellant mix.  To me, this seems like it would be a worthy long-term upgrade to the Falcon 9 family.  To others I’m sure it is not, so please sound off below about the math posted above, what you think of a methalox Falcon 9, and whether you think it would be worth the change. 

[beancounter]

F9 v1.2.     I had similar thoughts but couldn't do the math - only intuitive which doesn't always work out.  Still nice to see someone confirm it as a possibility.  If I stay on this site any longer - guess I'm going to since I joined L2 as a lifer, think I'm going to have to go back to school.  Might even head off Altzeimer's a bit longer. 

[MP99]

The prop load looks to be ~17% less for the same tank volume. Could we expect a dry mass improvement from this? Of course, the methane tanks will require insulation, which will add some mass back.

Also, Elon recently discussed propellant densification / subcooling, which makes sense in light of the suggested 112% thrust version of M1D. How does the impulse density of methalox with both liquids densified compare with kerolox with only the oxygen densified?

Cheers, Martin

[MP99]

Yes, I think so. The increased Isp for the upper stage is where most of the performance will come from, but that might require a lengthening of the stage.

I just wanted to point out that the rocket’s length is likely to be roughly the same because the methalox Falcon 9’s greater volumetric efficiency would likely balance the added length of the SII.

The length of F9 V1.0 first stage was set to the max that could be transported without expensive convoying. The extra length of V1.1 must make that transport more hassle, and the even longer FH boosters even more so.

I would assume that the F9MR first stage doesn't want to be much / any longer for this reason. But, apart from efficiency of the launcher, a longer upper stage shouldn't have any practical difficulties.

But, there's also the question of what an optimised upper stage for FH would look like, and whether that could also fly on F9MR?

Cheers, Martin

[Ben the Space Brit]

For a while, I've thought that a "Merlin-1m" using LCH4 rather than RP1 might be a useful intermediate stage on the way to Raptor. It also occurs to me that LCH4 would give better vacuum Isp, which would improve the upper stage performance.

[Nomadd]

Yes, I think so. The increased Isp for the upper stage is where most of the performance will come from, but that might require a lengthening of the stage.

I just wanted to point out that the rocket’s length is likely to be roughly the same because the methalox Falcon 9’s greater volumetric efficiency would likely balance the added length of the SII.

The length of F9 V1.0 first stage was set to the max that could be transported without expensive convoying. The extra length of V1.1 must make that transport more hassle, and the even longer FH boosters even more so.

I would assume that the F9MR first stage doesn't want to be much / any longer for this reason. But, apart from efficiency of the launcher, a longer upper stage shouldn't have any practical difficulties.

But, there's also the question of what an optimised upper stage for FH would look like, and whether that could also fly on F9MR?

Cheers, Martin

I would assume the length of the F9 1.0 would be set by engine thrust.

[cuddihy]

The catch is that a FFSC engine might actually be harder to make at Merlin 1 sizes than a Raptor: it'd be a development on-par with the Raptor development, facing different issues. The thing is it would give immediate payoff for a higher energy upper stage for F9H, and without bringing in the market issues of a BFR, so maybe it would be worth it.

[go4mars]

Anyone care to link or merge the old thread here?

[R7]

Great stuff by Steven!

f(x) = ve1*ln(1+dp1*x) - ve2*ln(1+dp2*x)

And if one is interested in required ve change for given dps and x then:

ve2/ve1 = ln(1+dp1*x)/ln(1+dp2*x) = log_(1+dp2*x)(1+dp1*x)             

Did some BOTE calcs using numbers from Ed's page.

Second stage case, assuming:

propellant volume 93000L
stage dry mass 6000kg
payload 13000kg
plus Peter's prop densities

x= 93000L/19000kg = ~4.895 L/kg

with that ve2/ve1 is 1.095

If MVac Isp is 340s then "Merlin-RaptorVac" must do ~372s.


Assuming both stages convert to methane then first stage x is different for RP-1 and methane. Lighter second stage causes greater x.

first stage volume 385000L
first stage dry weight 19000kg
second stage full weight 99000kg/83000kg for RP-1/CH4
payload 13000kg

for RP-1:

x1 = 385000L/(19000kg + 99000kg + 13000kg) = ~2.939 L/kg

for CH4:

x1 = 385000L/(19000kg + 83000kg + 13000kg) = ~3.348 L/kg

for separate x1 and x2 the eq is

ve2/ve1 = ln(1+dp1*x1)/ln(1+dp2*x2) = ~1.03

Only 3% Isp increase needed. 11% if no second stage mass reduction assumed. Raptor vac Isp is almost 17% greater. If FFSC metholox Merlin could achieve the same then first stage dv increase would be substantial ( 4.76 km/s vs 4.21 km/s, 13% increase ).


At first Steven's results seemed to contradict now defunct Dunnspace paper but that's not the case. In Dunn's analysis methane was inferior because propellants had greater density difference but much lower Isp difference.

[Hyperion5]

Anyone care to link or merge the old thread here?

Here's a link to the old thread for you: http://forum.nasaspaceflight.com/index.php?topic=30473.0

The catch is that a FFSC engine might actually be harder to make at Merlin 1 sizes than a Raptor: it'd be a development on-par with the Raptor development, facing different issues. The thing is it would give immediate payoff for a higher energy upper stage for F9H, and without bringing in the market issues of a BFR, so maybe it would be worth it.

Well it might be harder to make, but I rather doubt it.  Staged combustion cycle engines like this can be built down to sizes as small as only a couple tonnes-force of thrust according to the Russians.  Something close to the Merlin in size should not be too much of a problem.  It's likely to be a much cheaper and smoother development as well, given it would be following the Raptor's development.  The higher energy upper stage alone would probably make it worth it to Spacex, so no disagreements there. 

The prop load looks to be ~17% less for the same tank volume. Could we expect a dry mass improvement from this? Of course, the methane tanks will require insulation, which will add some mass back.

So then, how much less thrust would we be looking at if such a change went through?  15% less?  13% less?  I can imagine that the lessened thrust would help the prospects of a methalox Falcon 9 family.  Less stress on the pads should make these things even easier to reuse, no? 

Also, Elon recently discussed propellant densification / subcooling, which makes sense in light of the suggested 112% thrust version of M1D. How does the impulse density of methalox with both liquids densified compare with kerolox with only the oxygen densified?

Cheers, Martin 

I was under the impression from several of Jim's posts that subcooling and densification of propellants wasn't worth it from a mass perspective.  Perhaps Elon's engineers have found otherwise in a few experiments. 

[JBF]

You might as well close this thread, no current plans for a smaller engine according to Ms. Shotwell's interview on the Space Show.

[hrissan]

Shotwell is clear enough: Falcon 9 flies, FH will fly soon, no point wasting money making them better, they are good enough.

All new efforts are towards enormous monster rocket with large and efficient engines using unorthodox fuel.

Sounds much more ambitious.

[DJPledger]

You might as well close this thread, no current plans for a smaller engine according to Ms. Shotwell's interview on the Space Show.

I agree in that given Ms. Shotwell's comments saying that SpaceX are not planning a smaller version of Raptor, it will be extremely unlikely that they will pursue methalox versions of F9 and FH. Converting F9 and FH to methane would divert funds away from their MCT system program dev. Although she did say that there could possibly be a methane US for F9 and FH in the future which may used a methalox version of MvacD.

[Llian Rhydderch]

You might as well close this thread, no current plans for a smaller engine according to Ms. Shotwell's interview on the Space Show.

I agree in that given Ms. Shotwell's comments saying that SpaceX are not planning a smaller version of Raptor, it will be extremely unlikely that they will pursue methalox versions of F9 and FH. Converting F9 and FH to methane would divert funds away from their MCT system program dev. Although she did say that there could possibly be a methane US for F9 and FH in the future which may used a methalox version of MvacD.

I concur; that is how I heard, and interpreted, Ms. Shotwell's comments on the matter.  Very clear that, no, they are not planning on a smaller Raptor-ish engine; just focusing hard on the one full Raptor size.

There are several posts covering this, from several folks, over on the Gwynne Shotwell/Space Show thread.

[Hyperion5]

You might as well close this thread, no current plans for a smaller engine according to Ms. Shotwell's interview on the Space Show.

No, we might as well not close this thread, because it's primarily about whether or not a methalox Falcon 9 family is feasible with Raptor engine technology.  It is not about current plans, JBF, which can obviously change.  We're simply investigating whether an engine that uses the basic technology of the Raptor engine could enable a methalox Falcon 9 family.  The answer to that is yes, thanks to the excellent work of Steven Pietrobon.  Whether or not it is worth making the engine required to make a methalox Falcon 9 is part of the debate meant to occur on this thread.  No one's going around saying a smaller engine is confirmed or any such nonsense like that.  Now are you going to weigh in on that debate or not? 

[Lobo]

From the thead on Shotwell's interview on the Space show:

http://forum.nasaspaceflight.com/index.php?topic=34268.msg1174825#msg1174825

Quick notes from Gwynne Shotwell's appearance on The Space Show, if anything here is wrong, feel free to correct:

LC-40 to be modded to allow FH launches, 39A will also launch F9 and FH

39A not big enough for SpaceX super HLV, would build new site

Raptor question, smaller methane engine than million lb thrust one? no smaller engine, some subscale components being made for testing, focus on full Raptor

Raptor super HLV not named yet

When will cargo Dragon make powered landings? powered landing is for Dragon V2 (crew), will retrofit powered landing to cargo version

Raptor methane engine is for super HLV, but wouldn't rule out methane upper stage for F9/FH

Dragon 2 unveiling later this year

what are markets for super HLV? F9/FH is for commercial sat launches, super HLV is for transport to Mars

what rockets Raptor will be used for, and specs? Raptor is for Mars launches, not releasing specs yet.

only doing a few secondary payloads, not a lot of money in secondary market

commercial crew (not SpaceX specifically) about a year behind where it would be if fully funded, Congress may consider more funding given Crimea

with increased launch rate, will SpX prep 2 launches at 2 pads at once? likely in 2015 (referring to next VAFB launch?)

biggest near term challenges for SpX? make rockets highly producible, increase production rate, no big issues meeting that, current TAKT time 1 core a month, should be 2 a month by end of year.

when will SpX Mars missions happen? Lots of work to do, Elon says 12-13 years, will shoot for that timeframe.

not focused on Phobos or Deimos, but doesn't mean we wouldn't look at them

concern on increasing regulation? not overly concerned, but keep close eye, pretty comfortable with where regs are now

SpX has over 3000 employees, will expand and where focus? yes, will expand at more "sane" pace than in past, in all our locations

almost recovered CASSIOPE 1st stage, what changes to successfully recover? optimize reentry/landing burn, get more stability on stage, add ACS, make iterative progress, hard problem but believe will solve it.

Interesting stuff here.  As some have pointed out, it would seem a Raptor based F9 booster is not in the projected plans for SpaceX.  But as Hyperion points out, this is a speculative thread about what "could be" not necessarily about "what is" or "what will be".  Besides, we know SpaceX folks read these forums, and as there's a lot of meaty calculations behind this with Steve Pietrobon's work, who knows?  Maybe someone will see there's some merit in looking into it?  If the performance is better, it makes for more easily reusable engines, and allows for propellant standardization over the SpaceX fleet, those are some "pros" that are hard to ignore.  Especially when you throw in the issue that Hyperion pointed out initially, that MCT will either need to land on a VERY deep throttling Raptor engine, or one a smaller engine that won't need as deep throttling.  If they can't get the full Raptor to throttle deep enough to hover and gently land on the 1/3g gravity of Mars, some other type of landing thruster will be required.  Logic would dictate that that landing thruster will be methalox to eliminate the need to have a whole separate propellant system for the landing thrusters.  Hypergolic landing thrusters, for example. 

And if there's a separate landing thruster needed, ironically it would probably be roughly M1D in side.  So it's not inconceivable there wouldn't be a move sometime later to cut SpaceX's cryo engine fleet from 3 engines to two, especially as two of those 3 engines would use different fuels but be of similar size.

As we probably won't see an MCT going to mars for over a decade, and SpaceX has -just- invested a lot of money into LC-40 and SLC-4 to launch kerolox Falcons, it could just be that such a mini-Raptor so far enough out that it's not even on the radar.  But not that it's not possible.
Especially because she DOES say that they might go methalox on the Falcon upper stage.  That's interesting into itself for a few reasons.
She says no smaller Raptor, but then says possible methalox upper stage for Falcon?  So perhaps a GG methalox version of Merlin?  That would go along with her words, but....a GG methalox engine will be a little more efficient than a GG kerolox, but not a lot.  It's the jump to stage combustion that really kicks up the ISP.  Obivously that's the most important factor in an upper stage.  So I think it's hard to see SpaceX going back to GG for a new engine, once they get the FFSC working.  Which would be a "mini-Raptor" obviously. 
But...maybe M1D-vac could be relatively easily converted to methalox using mostly the same parts, which is why she said that?  If it's a complete new engine, I just have a hard time seeing them go with a brand new methalox GG engine.  Seems like a big step backwards for not a lot of additional benefit.  Just stick with kerolox M1D.  So i think there could be a FFSC mini Raptor if there is even a move to methalox Falcon upper stage.  Maybe it would be called something other than "Raptor", so Shotwell's comments would hold true.  It wouldn't be a smaller Raptor.  It'd be something else.

As for not considering it for the booster, maybe they just don't think they'd get enough additional performance out of the modification to the booster to make it worth while?  Especially since if you want to reuse the booster and boost back to landing site, you can't have the booster moving too far or too fast down range.  A methalox Falcon booster with nine mini-Raptors might increase performance some, but will it be going to fast for RTLS with that greater ISP?  It might be just as well to stick with the denser and more powerful kerolox.
But, a full flow staged combustion methalox upper stage, maybe stretched with extra propellant, could quite significantly increase Falcon's payload capability.  It of course would be vacuum optimized, as would an MCT landing thruster in the near vacuum of Mars.  And of course it would be designed with a good throttle range to hover and land MCT on Mars.  Which...coincidentally, would open up the possibility of the Falcon reusable upper stage landing on mini-Raptor rather than on SuperDraco thrusters, necessitating a whole separate hypergolic propellant system.  That would greatly simplify a reusable Falcon upper stage I think.  So, several potential benefits possible there.

So not quite what Hyperion had in mind, not perhaps not far off either, using Shotwell's own comments.

The alternative would be GG methalox M1D with deep throttle range, with perhaps the overall benefit of being more reliable than a more complex FFSC engine.  And reliability is key to a landing thruster.  Failure to light properly during EDL and the crew is a smoking crater.  And the main Raptor is still used for the high dV TMI, TEI, and Mars ascent burns.  And when that'd developed, they modify Falcon's upper stage for it to get a little more performance, but still able to loose the hypergolic landing system on reusable Falcon upper stage, and land on the main engine.

[ArbitraryConstant]

Well it might be harder to make, but I rather doubt it.

Even if it's no harder it's a substantially new engine with much less utility. There's no existing payload FH can't launch.

[Lobo]

You might as well close this thread, no current plans for a smaller engine according to Ms. Shotwell's interview on the Space Show.

But she said a possible methalox upper stage for Falcon?

I'm no rocket scientist, but as I understand there's quite a bit more to that that just hooking up LCH4 to Merlin where RP-1 previously went in.  I think it'd be a quite considerable development to make Merlin run on LCH4.  And to what end, if M1D will still run on kerolox on the booster?  And a methalox version of Merlin on an upper stage will have a little better ISP due to the lighter fuel, but not a lot.  The staged combustion is what really gets that jump in ISP.

So, per Shotwell's own words, they might go with a methalox Falcon upper stage, and I think there's a pretty good chance the new engine for that would also be a staged combustion engine rather than just a GG methalox engine.  That would increase Falcon's performance notably, and possibly allow the upper stage to land on the main engine, depending on it's throttle range.  But most of the Russian staged combustion engines can throttle down to 30% I believe, so I don't think it's unrealistic to assume SpaceX's staged combustion engines won't do at least that as well.

So, no need to shut down this thread at all.
To the contrary, I think Shotwell's words give more weight to such a concept than they take away form it.  At least on the upper stage. 

[Lobo]

Converting F9 and FH to methane would divert funds away from their MCT system program dev. Although she did say that there could possibly be a methane US for F9 and FH in the future which may used a methalox version of MvacD.

It wouldn't divert funds away from MCT if MCT requires a smaller methalox engine of that class for Mars EDL.  Two birds with one stone.

Raptor is a 450mt-f engine. 
If you assume MCT + payload perhaps weighs 50mt dry, that's about 17mt(weight) in Mars's gravity.
But Mars gravity doesn't effect the force Raptor will put out.
So in order to hover a 50mt MCT, Raptor would need to throttle down to just under 4%!

if MCT is 100mt dry, if you take Meuller's statement literally and assume a big tri-core SBFR, that's still under 8% throttle point for Raptor to hover MCT!  The CECE version of RL-10 was getting about 10% throttle, and that was being developed specifically for use with a lander in Altair.
Even if MCT is 150mt dry, the largest possible mass that a big tri-core BFR could -possibly-get through TMI (that would assume over to 450mt LEO and 33% LEO mass through TEI), Raptor would need like an 11% throttle point to hover.

30% like RD-180 is pretty realistic I think, but 11% or below?  I don't know enough about rocket engines to know if that's even in the scope of feasibility.

However, if you have perhaps a 100klbs FFSC methalox engine (about 45mt-f), and a 150mt dry MCT would weigh about 50mt-f on Mars, so now you have a single engine running full out that might -just- hover MCT.
Or two engines on either side of the main Raptor nozzle running at about 50% throttle.
A 100mt MCT could hover on just one of these engines running at 74% throttle, or two of them on each side of a central Raptor nozzle running at 37% throttle.  Still within current SC engine throttle capability.
Etc.

And MCT with two Raptor engines could have a landing engine mounted centrally between them, which is why I refer to the possibility of just one landing thruster.  Obviously a lot depends on MCT's design.  About all we can say with any level of probability, is MCT will have at least one Raptor on it to do the TMI burn, Mars ascent, and the TEI burn. And if that can't be made with some crazy level of throttle ability, then 1 or more smaller methalox engines will need to be used to land.
 
So now we are getting into a range where an engine could land MCT.  Depending on a lot of variables, obviously.  But I have a hard time seeing any size of MCT landing on a single 1Mlbf Raptor.  And I'm pretty sure they won't use a landing engine that would use anything but the main methalox store, to reduce complexity and weight.  So the development cost of MCT's methalox landing engine could then give Falcon an upper stage methalox engine for "free", without diverting any funds.

:-)

[RocketmanUS]

The SpaceX Mars BFR could also be configured like the Saturn-INT 20/21 concept. If so that could eliminate the Falcon Heavy if BFR is reusable. That is the two stage version and not the tri-core concept that is being speculated.

Converting the F9 or FH US to LCH4/LOX could be used as a third stage for BLEO on the BFR launches. I don't see it being used on the F9/FH.

After F9/FH and Mars BFR I think they will come up will a new concept to replace F9/FH with lower cost, faster launch rate, and greater mass to LEO while being fully reusable.

So for this thread, compare mass to LEO and GTO. Compare payload mass to orbit for same size launcher with different fuels.

F9 v1.1 RP-1/LOX to LEO payload mass and GTO payload mass?
F9 LCH4/LOX to LEO payload mass and GTO payload mass?

So if there is not much differance then why convert?