Arianespace launch thread

[Exoscientist]

Towards a revolutionary advance in spaceflight: an all-liquid Ariane 6.
http://exoscientist.blogspot.com/2023/06/towards-revolutionary-advance-in.html

Most rockets have payload fractions in the range of 3% to 4%. The Ariane 6 using 2 and 4 SRB’s, because of the large size of the SRB’s and because solids are so inefficient on both mass ratio and ISP, the two key components of the rocket equation, it will count among the worst rockets in history at a payload fraction of only 2%.

In contrast a two Vulcain Ariane 6 could have a payload fraction of 7% and a three Vulcain Ariane 6 could have a payload fraction of 7.5%. This is well-above what any other rocket has ever achieved in the history of space flight.

 To put this advance in perspective, it would be like SpaceX using the very same Merlin engine and the very same propellant tanks, and the very same size Falcon 9, suddenly being able to change the Falcon 9 payload from 22 tons to 40 tons.

 It will be a paradigm shift in what payloads rockets should be able to deliver to orbit. 

  Robert Clark

 

[darthgently]

39 minutes ago, Exoscientist said:

Towards a revolutionary advance in spaceflight: an all-liquid Ariane 6.
http://exoscientist.blogspot.com/2023/06/towards-revolutionary-advance-in.html

Most rockets have payload fractions in the range of 3% to 4%. The Ariane 6 using 2 and 4 SRB’s, because of the large size of the SRB’s and because solids are so inefficient on both mass ratio and ISP, the two key components of the rocket equation, it will count among the worst rockets in history at a payload fraction of only 2%.

In contrast a two Vulcain Ariane 6 could have a payload fraction of 7% and a three Vulcain Ariane 6 could have a payload fraction of 7.5%. This is well-above what any other rocket has ever achieved in the history of space flight.

 To put this advance in perspective, it would be like SpaceX using the very same Merlin engine and the very same propellant tanks, and the very same size Falcon 9, suddenly being able to change the Falcon 9 payload from 22 tons to 40 tons.

 It will be a paradigm shift in what payloads rockets should be able to deliver to orbit. 

  Robert Clark

 

I could be missing something (probably) but when recovering the boost stages you don't want them to make it too far and too fast such that recovery becomes problematic.  For expendable rockets the idea you posted is interesting, but the huge economic efficiencies of booster recovery aren't theoretical any longer having been proven many times in the real world.

The idea of Ariane 6 replacing the SRBs with recoverable liquid fuel boosters comes to mind.  Even if they come down by parachute (not sure that is realistic, but I've done similar in KSP, lol)

[Exoscientist]

 I added the following abstract to the blog post:

 

Towards a revolutionary advance in spaceflight: an all-liquid Ariane 6.

ABSTRACT 

 Most orbital rockets have payload fractions in the range of 3% to 4%. The Ariane 6 using 2 and 4 SRB’s, because of the large size of the SRB’s and because solids are so inefficient on both mass ratio and ISP, the two key components of the rocket equation, it will count among the worst rockets in history at a payload fraction of only 2%.  

In contrast a two Vulcain Ariane 6 could have a payload fraction of 7% and a three Vulcain Ariane 6 could have a payload fraction of 7.5%. This is well-above what any other rocket has ever achieved in the history of space flight.  

 So how is an all-liquid Ariane 6 able to accomplish this? First, this version is based on the Ariane 5 core. The mass ratio for the Ariane 5 it turns out is quite extraordinary for a hydrogen+liquid oxygen(called “hydrolox”) stage at 16.3 to 1. This is in the range commonly seen by dense propellants. To use a colorful analogy, it’s like the ArianeSpace engineers in designing the Ariane 5 core found a way to make liquid hydrogen as dense as kerosene!

 Obviously, this is not what happened. But they must have found a way to achieve extreme lightweighting of a hydrolox stage. To put this in perspective, the mass ratio of the famous Centaur hydrolox upper stage is at 10 to 1, which was achieved back in the 1960’s. And the Delta IV hydrolox core is at a quite ordinary 8.7 to 1 mass ratio. So the Ariane 5 core is about twice as good as the Delta IV core on this key mass ratio scale.

 Because the Ariane 5 core has the high Isp of a hydrolox stage while achieving (somehow!) the high mass ratio of a dense propellant stage, it calculates out to have the highest delta-v of any rocket stage in the history of spaceflight.

 Since delta-v is the single most important parameter for orbital rockets, you can legitimately say the Ariane 5 core is the greatest rocket stage ever produced in the history of spaceflight.

 The high 7.5% payload fraction of the all-liquid Ariane 6 would mean SpaceX would have to be chasing ArianeSpace rather than the other way around.

   To put this advance in perspective, it would be like SpaceX using the very same Merlin engines and the very same propellant tanks, and the very same size Falcon 9, suddenly being able to change the Falcon 9 payload from 22 tons to 40 tons.

 It will represent a paradigm shift in terms of the payloads that rockets will be expected to deliver to orbit.

 Usually, when we think of a radical shift in rocket capability we imagine some great advance in engines such as nuclear, or some great advance in materials to greatly reduce tank weight. 

 Quite extraordinary is the the fact this radical increase in rocket capability can come from using currently existing engines and tanks.
https://exoscientist.blogspot.com/2023/06/towards-revolutionary-advance-in.html

  Robert Clark
 

[Kermann Nolandung]

If I am not wrong on Ariane 5, the boosters apply the thrust to the upper part of the core stage.
I guess, it permits a lighter structure and would explain the large payload fraction.

If you remove the booster, I think you have to use about the same mass ratio as Delta IV. 

[Exoscientist]

On 6/27/2023 at 10:32 PM, Kermann Nolandung said:

If I am not wrong on Ariane 5, the boosters apply the thrust to the upper part of the core stage.
I guess, it permits a lighter structure and would explain the large payload fraction.

If you remove the booster, I think you have to use about the same mass ratio as Delta IV. 

 

 I’m not so sure about that for two reasons. First, the core has to withstand the full thrust of the engine even without the SRB’s when they are jettisoned. Second, the core has a structure called the JAVE("Jupe AVant Equipée")  that transmits the forces of the two side boosters to the core. That structure weighed 1,700 kg. So that structure would be unneeded without the SRB’s so the core could be made even lighter. That lighter weight without the JAVE is what I used in my calculation.

 By the way, I’ve been informed by someone familiar with the Ariane 5 construction that the core tank weighed ca. 4,400 kg. But it was made of aluminum. But you can save about 50% off tank weight over aluminum using carbon fiber or the specialty high strength stainless steels SpaceX is using on the Starship. So you could subtract an additional 2,200 kg from the core stage mass by using these lightweight materials for the tank. That would bring the dry mass down to 8.1 tons. But that would mean the mass ratio of the core would be over 20 to 1.

  Robert Clark

Edited June 30, 2023 by Exoscientist

[tater]

 

[tater]

So after tomorrow Arianespace has no launches until next year given the issues with Vega I guess.

[tater]

 

[tater]

 

[sevenperforce]

On 6/22/2023 at 4:52 PM, Exoscientist said:

In contrast a two Vulcain Ariane 6 could have a payload fraction of 7% and a three Vulcain Ariane 6 could have a payload fraction of 7.5%.

Do you mean two (or three) Vulcain engines on a single core stage, or do you mean multiple cores?

I'm going to assume that what you're imagining here is a frankenrocket with the Vinci-based ULPM upper stage on top of a Ariane 5 lower stage and some sort of cluster of Vulcain engines on the lower stage.

If you're adding engines, how is the payload fraction going up?

On 6/22/2023 at 4:52 PM, Exoscientist said:

The mass ratio for the Ariane 5 it turns out is quite extraordinary for a hydrogen+liquid oxygen(called “hydrolox”) stage at 16.3 to 1. This is in the range commonly seen by dense propellants.

Where are you getting that number? According to the ArianeSpace website, the core stage carries 158.11 metric tonnes of propellant with a dry mass of 12.2 metric tonnes, which less the 1.3 tonnes of engine comes to a mass ratio of 14.5:1. That's impressive, but it's not particularly out of the ordinary; the Saturn V's S-II second stage had a dry mass of 27.26 tonnes and carried 443 tonnes of props, for a mass ratio of 16.3:1.

One of the reasons the Ariane 5 achieves this mass ratio is by "hanging" the fluffy, lightweight hydrogen tank off of the bottom of the smaller, beefier LOX tank. The side boosters, too, transfer their force directly into the LOX tank and upward, reducing the structural load that the hydrogen tank has to carry. By the time the boosters burn out, 21% of the core's propellant has been burned, significantly reducing the loads involved.

An all-liquid Ariane frankenrocket would need to have the core strengthened dramatically to be able to lift its own weight safely, which in turn would make it much heavier.

On 6/22/2023 at 4:52 PM, Exoscientist said:

To put this in perspective, the mass ratio of the famous Centaur hydrolox upper stage is at 10 to 1, which was achieved back in the 1960’s.

Comparing upper and lower stages with orders of magnitude differences in capacity is never a good idea. Remember the square-cube law.

On 6/22/2023 at 4:52 PM, Exoscientist said:

And the Delta IV hydrolox core is at a quite ordinary 8.7 to 1 mass ratio.

The Delta IV common booster core stage has a mass ratio of 9.97:1 which is relatively poor, even for hydrolox.  The currently-operating Long March 5 hydrolox core stage has a dry mass of 16.2 tonnes and carries 165.3 tonnes of propellant, which comes to 10.2:1...I would call that "quite ordinary".

On 6/22/2023 at 4:52 PM, Exoscientist said:

Since delta-v is the single most important parameter for orbital rockets, you can legitimately say the Ariane 5 core is the greatest rocket stage ever produced in the history of spaceflight.

I mean you can say whatever you like but there are many rocket stages with much much higher Δv.

On 6/22/2023 at 4:52 PM, Exoscientist said:

 The high 7.5% payload fraction of the all-liquid Ariane 6...

...still unsure how this gets off the ground under its own weight...

On 6/22/2023 at 4:52 PM, Exoscientist said:

...would mean SpaceX would have to be chasing ArianeSpace rather than the other way around.

I don't think SpaceX is prioritizing payload mass fraction. They're prioritizing dollars per launch. So SpaceX has no reason to chase ArianeSpace.

On 6/29/2023 at 4:50 AM, Exoscientist said:

On 6/27/2023 at 10:32 PM, Kermann Nolandung said:

If I am not wrong on Ariane 5, the boosters apply the thrust to the upper part of the core stage.
I guess, it permits a lighter structure and would explain the large payload fraction.

First, the core has to withstand the full thrust of the engine even without the SRB’s when they are jettisoned.

It's not a very powerful engine -- which again, is why it can't lift its own weight off the ground. If you added a cluster of engines, you'd need to make the core stronger.

On 6/29/2023 at 4:50 AM, Exoscientist said:

Second, the core has a structure called the JAVE("Jupe AVant Equipée")  that transmits the forces of the two side boosters to the core. That structure weighed 1,700 kg. So that structure would be unneeded without the SRB’s so the core could be made even lighter.

No, removing the thing that makes the core strong enough to handle launch loads will not enable you to make the core lighter. The core will need to get heavier overall.

On 6/29/2023 at 4:50 AM, Exoscientist said:

I’ve been informed by someone familiar with the Ariane 5 construction that the core tank weighed ca. 4,400 kg. But it was made of aluminum. But you can save about 50% off tank weight over aluminum

This is a made up number.

On 6/29/2023 at 4:50 AM, Exoscientist said:

using carbon fiber

Aluminum has a LOWER density than carbon fiber, and a HIGHER tensile strength. Carbon fiber does have a higher compressive strength, but you need all three. Plus, the cost of carbon fiber is prohibitive, particularly for a disposable vehicle.

On 6/29/2023 at 4:50 AM, Exoscientist said:

or the specialty high strength stainless steels SpaceX is using on the Starship.

SpaceX is using stainless steel because it handles both extreme heat and extreme cold better than aluminum. Aluminum is much lighter and stronger for its weight than stainless.

So no, replacing aluminum with carbon fiber or stainless steel wouldn't "save about 50% off tank weight" for Ariane 5; it would INCREASE tank weight.

And even then, you're talking about a completely new vehicle, so why would the allegedly magical dry mass ratio of Ariane 5's core still be expected to apply?

[tater]

~4 minutes until... (for @kerbiloid):

Spoiler

 

 

[kerbiloid]

https://space.skyrocket.de/doc_sdat/heinrich-hertz.htm

Quote

Besides the scientific and technological part of the mission on behlf of the German Federal Ministry of Economics and Technology (BMWi), there is also a cooperation with the German Federal Ministry of Defence (BMVg) to provide additional and independent communications for the German armed forces (Bundeswehr).

So, yes, the antisat lasertech is very actual.

[Exoscientist]

10 hours ago, sevenperforce said:

Do you mean two (or three) Vulcain engines on a single core stage, or do you mean multiple cores?

I'm going to assume that what you're imagining here is a frankenrocket with the Vinci-based ULPM upper stage on top of a Ariane 5 lower stage and some sort of cluster of Vulcain engines on the lower stage.

If you're adding engines, how is the payload fraction going up?

Where are you getting that number? According to the ArianeSpace website, the core stage carries 158.11 metric tonnes of propellant with a dry mass of 12.2 metric tonnes, which less the 1.3 tonnes of engine comes to a mass ratio of 14.5:1. That's impressive, but it's not particularly out of the ordinary; the Saturn V's S-II second stage had a dry mass of 27.26 tonnes and carried 443 tonnes of props, for a mass ratio of 16.3:1.

One of the reasons the Ariane 5 achieves this mass ratio is by "hanging" the fluffy, lightweight hydrogen tank off of the bottom of the smaller, beefier LOX tank. The side boosters, too, transfer their force directly into the LOX tank and upward, reducing the structural load that the hydrogen tank has to carry. By the time the boosters burn out, 21% of the core's propellant has been burned, significantly reducing the loads involved.

An all-liquid Ariane frankenrocket would need to have the core strengthened dramatically to be able to lift its own weight safely, which in turn would make it much heavier.

Comparing upper and lower stages with orders of magnitude differences in capacity is never a good idea. Remember the square-cube law.

The Delta IV common booster core stage has a mass ratio of 9.97:1 which is relatively poor, even for hydrolox.  The currently-operating Long March 5 hydrolox core stage has a dry mass of 16.2 tonnes and carries 165.3 tonnes of propellant, which comes to 10.2:1...I would call that "quite ordinary".

I mean you can say whatever you like but there are many rocket stages with much much higher Δv.

...still unsure how this gets off the ground under its own weight...

I don't think SpaceX is prioritizing payload mass fraction. They're prioritizing dollars per launch. So SpaceX has no reason to chase ArianeSpace.

It's not a very powerful engine -- which again, is why it can't lift its own weight off the ground. If you added a cluster of engines, you'd need to make the core stronger.

No, removing the thing that makes the core strong enough to handle launch loads will not enable you to make the core lighter. The core will need to get heavier overall.

This is a made up number.

Aluminum has a LOWER density than carbon fiber, and a HIGHER tensile strength. Carbon fiber does have a higher compressive strength, but you need all three. Plus, the cost of carbon fiber is prohibitive, particularly for a disposable vehicle.

SpaceX is using stainless steel because it handles both extreme heat and extreme cold better than aluminum. Aluminum is much lighter and stronger for its weight than stainless.

So no, replacing aluminum with carbon fiber or stainless steel wouldn't "save about 50% off tank weight" for Ariane 5; it would INCREASE tank weight.

And even then, you're talking about a completely new vehicle, so why would the allegedly magical dry mass ratio of Ariane 5's core still be expected to apply?

 

 As I mentioned in the blog post, on the Ariane 5 core the JAVE on the forward skirt of the Ariane 5 core is specifically to transmit the high thrust of the two side boosters:

https://www.esa.int/Enabling_Support/Space_Transportation/Launch_vehicles/Cryogenic_main_stage_EPC

This is unnecessary without the two side boosters. Removing this 1,700 kg is how I get the 16.3 to 1 mass ratio.

I encourage you to do the ideal delta-v calculation of this Ariane 5 core with a 434s vacuum Isp and 16.3 mass ratio. It is higher than any other stage ever existing including the Saturn V upper stages and including either stage of the Falcon 9.  

 Using this high mass ratio Ariane 5 core, calculate the estimated payload to LEO by the rocket eq. of a two Vulcain, no-SRB version of the Ariane 6 using the lighter Ariane 4 H10 upper stage at ~10 ton prop. load to enable lift-off with the lower thrust without SRB’s.

 Then for a three Vulcain, no-SRB version, use a larger Centaur V like upper stage enabled by the higher take-off thrust and estimate the payload by the rocket eq. in that case.

 The payload fraction is worsened with the SRB’s because their mass is so high you get a high number in the denominator, reducing the fraction even if the payloads are similar. 

The low mass of the hydrolox stages in contrast puts a smaller number in the denominator, so increases the fraction size.

   Robert Clark

Edited July 6, 2023 by Exoscientist

[sevenperforce]

12 hours ago, Exoscientist said:

on the Ariane 5 core the JAVE on the forward skirt of the Ariane 5 core is specifically to transmit the high thrust of the two side boosters

From the link you provided:

"This element . . . transmits thrust from the two solid boosters to the launcher in order to lift the fully loaded EPC."

Let's do some math, shall we? The core stage (including for the moment the JAVE element) had a dry mass of 12.2 tonnes and carried 158.1 tonnes of propellant (21.9 tonnes of fuel and 136.1 tonnes of LOX). The dry mass of the core stage itself can be roughly separated into the JAVE element (1.7 tonnes), the Vulcain engine (0.63 tonnes), and the two tanks:

Spoiler

The LOX tank uses 4.7mm aluminum while the LH₂ tank uses 1.3mm aluminum; the LH₂ tank (390 m³) has 325% the volume of the LOX tank (120 m³). The system uses a common bulkhead with the lightweight LH₂ tank hung on the bottom of the heavier LOX tank. Assuming hemispheric caps for simplicity (they aren't, but it won't make much of a difference here), the volume of the hemispheric sections of the LOX tank is 82.45 m³, meaning that the cylindrical section of the LOX tank needs to have a volume of 37.55 m³, requiring a height of 1.64 m. This allows us to calculate the surface area of the LOX tank at 119.43 m². The lower hemispheric portion of the LH₂ tank has the exact same volume as that portion occluded by the lower hemispheric portion of the LOX tank, so its total volume is equal to the volume of a regular cylinder with the same height as its full cylindrical portion; this allows us to find that height as 17 meters. We can therefore calculate the surface area of the LH₂ tank at 334.7 m². Given that the LOX tank skin is 3.62 times thicker than that of the LH₂ tank but the LH₂ tank has 2.8 times as much surface as the LOX tank, this means that the LOX tank has a mass 1.3 times greater than the mass of the LH₂ tank. The remaining 9.87 tonnes of core stage mass are allocated at 43.5% for the LH₂ tank and 56.5% for the LOX tank.

Note that the actual density of aluminum would suggest a lower total mass, but that's not accounting for things like downcomers, stringers, and the like.

The LOX tank has a mass of about 5.6 tonnes and the LH2 tank has a mass of about 4.3 tonnes.

The Vulcain 1 engine developed sea level thrust of 773.2 kN. At liftoff, the mass of everything below the JAVE element -- engine, LH2 tank, and fuel -- came to 26.8 tonnes. The gross mass of the LOX tank was 141.7 tonnes, plus the 1.7 tonnes of the JAVE element.  The original EPS L9.7 second stage had a gross mass of 10.9 tonnes and could send 6.95 tonnes to GTO. Add on the 2.4 tonne fairing, and the mass of the LOX tank and everything above it came to 163.7 tonnes.

Meanwhile, each of the boosters had a dry mass of 39.8 tonnes and was loaded with just under 238 tonnes of propellant for a gross mass of 277.5 tonnes each. Each one produced 6,470 kN in vacuum and 5,881 kN at sea level.

Ariane 5 leapt off the pad with an impressive liftoff T/W ratio of around 1.8:1. This meant that the Vulcain engine was spending 473.2 of its 773.2 kN just lifting itself and the LH₂ tank, and only transferring 300 kN into the LOX tank through compressive loading of the LH₂ tank. Meanwhile the boosters were each spending 4,900 of their 5,881 kN lifting themselves and were collectively transferring 1,962 kN into the LOX tank through the JAVE element.

But the full LOX tank has a mass of 141.7 tonnes, meaning that the excess 300 kN contributed by the Vulcain engine isn't even enough to lift it. Hence the bolded element above: the JAVE element is necessary for the boosters to lift the fully-loaded core.

12 hours ago, Exoscientist said:

This is unnecessary without the two side boosters. Removing this 1,700 kg is how I get the 16.3 to 1 mass ratio.

Without the two side boosters providing 87% of the forces acting on the LOX core and upper stage, the LH₂ tank would need to be dramatically stronger and therefore dramatically heavier. It's likely that the stage would simply need to have that 4.7 mm skin everywhere, which per my calculations above would add 11.2 tonnes of dry mass. You would also need to add at least one additional Vulcain engine at 0.63 tonnes. Adding 11.8 tonnes to get rid of 1.7 tonnes doesn't seem like a great exchange.

The Ariane 5 core achieves an extremely good mass fraction because it is able to use (partial) balloon tanks on a first stage, something that hasn't really been done since the Atlas B. The Atlas B sustainer stage achieved a whopping 26:1 propellant fraction using balloon tanks. But just like the Atlas B sustainer stage couldn't have gotten off the ground without its dual-engine skirt, the Ariane 5 core couldn't get off the ground without its boosters, and its balloon hydrogen tank would crumple under the weight of the LOX tank and upper stage.

12 hours ago, Exoscientist said:

I encourage you to do the ideal delta-v calculation of this Ariane 5 core with a 434s vacuum Isp and 16.3 mass ratio. It is higher than any other stage ever existing including the Saturn V upper stages and including either stage of the Falcon 9.

The ideal delta-v of a stage can be arbitrarily high if you give it arbitrarily large balloon tanks and an arbitrarily wimpy engine and magic it into orbit where it doesn't have to worry about gravity drag or sea level specific impulse. Hell, they don't even have to be balloon tanks. If you attached a single RD-0146 engine to the butt end of a Space Shuttle SLWT and magicked it into space you'd get an "ideal delta-v" of 15.43 km/s thanks to the SLWT's 27.7:1 hydrolox propellant fraction and the RD-0146's stupidly high specific impulse. Doing something useful with it is a different matter.

12 hours ago, Exoscientist said:

 Using this high mass ratio Ariane 5 core, calculate the estimated payload to LEO by the rocket eq. of a two Vulcain, no-SRB version of the Ariane 6 using the lighter Ariane 4 H10 upper stage at ~10 ton prop. load to enable lift-off with the lower thrust without SRB’s.

Vulcain 1 is no longer in use, so I'll use Vulcain 2 instead. It has a sea level specific impulse of 318 seconds and a dry mass of 811 kg, and it develops 939.5 kN of thrust at sea level. Using two of those would give a liftoff thrust of 1,879 kN. Building a frankenrocket with two of those on a JAVE-less Ariane 5 core stage the Ariane 4 H10 upper stage would give a liftoff mass of 181.6 tonnes, for a painfully anemic liftoff T/W ratio of 1.05:1. That's woefully insufficient, and we haven't even added payload or strengthened the LH₂ tank enough to get off the ground. Decreasing the propellant (on either stage) would only make your mass fractions worse and decrease your total Δv.

Add a third Vulcain 2 and we might be getting somewhere. Now our liftoff mass is 182.4 tonnes and our liftoff thrust is 2,818 kN, giving us a respectable T/W ratio of 1.58:1. Let's target 1.4:1 after we account for payload and strengthening the core stage (a lower liftoff T/W ratio will help reduce the amount of core stage strengthening we need to do anyway). At 1.4 gees, those three Vulcain 2s are using 393.2 of their 2,818 kN to lift themselves, the hydrogen tank, and its contents, leaving  2,424.8 kN of force to be transferred through the hydrogen tank into the LOX tank.

That's a whopping eight times greater than the amount of force that the Ariane 5 LH₂ tank transferred to the LOX tank and JAVE element at liftoff. Fortunately, physics allows us to take the square root here, in order to account for the circumferential change in skin thickness. We'll need to bulk up the hydrogen tank from 1.3 mm to 3.68 mm, raising its dry mass to 12.2 tonnes. Add three Vulcain 2 engines and the LOX tank and the dry mass of our first stage now comes to 20.3 tonnes, giving us a propellant fraction of 7.8:1. That's about the same as the propellant fraction of a Delta IV common booster core stage.

Hydrogen can be useful in a sustainer stage architecture but it simply is not very good for a single-stick first stage. The engine needs to be overweight in order to get you off the ground quickly and the tank is going to be overweight because it must be both bulky (due to hydrogen's low density) and strong (to transmit loads).

12 hours ago, Exoscientist said:

calculate the estimated payload to LEO

Assuming a small 800 kg fairing, Silverbird gives an estimated 7.3 tonnes to LEO from the French Guiana launch site, but that's probably an overestimate because Silverbird isn't using a large enough sea level thrust penalty.

So we've built a completely new hydrogen tank, dusted off a retired upper stage, and bought three times as much engine per launch, all to get less than ten tonnes to LEO? Just for the sake of avoiding SRBs?

12 hours ago, Exoscientist said:

 The payload fraction is worsened with the SRB’s

Payload fraction doesn't matter. Price matters. If you need to send 5 tonnes to GTO, and you can do the job with a 250 tonne rocket for $40 million or a 120 tonne rocket for $90 million, you'll pick the 250 tonne rocket every time, even though the 120 tonne rocket has twice the payload fraction.

But for the record, the LEO payload fraction of our all-liquid Ariane 6-5-4 frankenrocket is 4%, which is only 1.3% better than the 2.7% payload fraction of the Ariane 5 ES. And, again, customers aren't chasing payload fractions; they're chasing price.

Edited July 6, 2023 by sevenperforce

[Exoscientist]

8 hours ago, sevenperforce said:

From the link you provided:

"This element . . . transmits thrust from the two solid boosters to the launcher in order to lift the fully loaded EPC."

Let's do some math, shall we? The core stage (including for the moment the JAVE element) had a dry mass of 12.2 tonnes and carried 158.1 tonnes of propellant (21.9 tonnes of fuel and 136.1 tonnes of LOX). The dry mass of the core stage itself can be roughly separated into the JAVE element (1.7 tonnes), the Vulcain engine (0.63 tonnes), and the two tanks:

  Reveal hidden contents

The LOX tank uses 4.7mm aluminum while the LH₂ tank uses 1.3mm aluminum; the LH₂ tank (390 m³) has 325% the volume of the LOX tank (120 m³). The system uses a common bulkhead with the lightweight LH₂ tank hung on the bottom of the heavier LOX tank. Assuming hemispheric caps for simplicity (they aren't, but it won't make much of a difference here), the volume of the hemispheric sections of the LOX tank is 82.45 m³, meaning that the cylindrical section of the LOX tank needs to have a volume of 37.55 m³, requiring a height of 1.64 m. This allows us to calculate the surface area of the LOX tank at 119.43 m². The lower hemispheric portion of the LH₂ tank has the exact same volume as that portion occluded by the lower hemispheric portion of the LOX tank, so its total volume is equal to the volume of a regular cylinder with the same height as its full cylindrical portion; this allows us to find that height as 17 meters. We can therefore calculate the surface area of the LH₂ tank at 334.7 m². Given that the LOX tank skin is 3.62 times thicker than that of the LH₂ tank but the LH₂ tank has 2.8 times as much surface as the LOX tank, this means that the LOX tank has a mass 1.3 times greater than the mass of the LH₂ tank. The remaining 9.87 tonnes of core stage mass are allocated at 43.5% for the LH₂ tank and 56.5% for the LOX tank.

Note that the actual density of aluminum would suggest a lower total mass, but that's not accounting for things like downcomers, stringers, and the like.

The LOX tank has a mass of about 5.6 tonnes and the LH2 tank has a mass of about 4.3 tonnes.

The Vulcain 1 engine developed sea level thrust of 773.2 kN. At liftoff, the mass of everything below the JAVE element -- engine, LH2 tank, and fuel -- came to 26.8 tonnes. The gross mass of the LOX tank was 141.7 tonnes, plus the 1.7 tonnes of the JAVE element.  The original EPS L9.7 second stage had a gross mass of 10.9 tonnes and could send 6.95 tonnes to GTO. Add on the 2.4 tonne fairing, and the mass of the LOX tank and everything above it came to 163.7 tonnes.

Meanwhile, each of the boosters had a dry mass of 39.8 tonnes and was loaded with just under 238 tonnes of propellant for a gross mass of 277.5 tonnes each. Each one produced 6,470 kN in vacuum and 5,881 kN at sea level.

Ariane 5 leapt off the pad with an impressive liftoff T/W ratio of around 1.8:1. This meant that the Vulcain engine was spending 473.2 of its 773.2 kN just lifting itself and the LH₂ tank, and only transferring 300 kN into the LOX tank through compressive loading of the LH₂ tank. Meanwhile the boosters were each spending 4,900 of their 5,881 kN lifting themselves and were collectively transferring 1,962 kN into the LOX tank through the JAVE element.

But the full LOX tank has a mass of 141.7 tonnes, meaning that the excess 300 kN contributed by the Vulcain engine isn't even enough to lift it. Hence the bolded element above: the JAVE element is necessary for the boosters to lift the fully-loaded core.

Without the two side boosters providing 87% of the forces acting on the LOX core and upper stage, the LH₂ tank would need to be dramatically stronger and therefore dramatically heavier. It's likely that the stage would simply need to have that 4.7 mm skin everywhere, which per my calculations above would add 11.2 tonnes of dry mass. You would also need to add at least one additional Vulcain engine at 0.63 tonnes. Adding 11.8 tonnes to get rid of 1.7 tonnes doesn't seem like a great exchange.

The Ariane 5 core achieves an extremely good mass fraction because it is able to use (partial) balloon tanks on a first stage, something that hasn't really been done since the Atlas B. The Atlas B sustainer stage achieved a whopping 26:1 propellant fraction using balloon tanks. But just like the Atlas B sustainer stage couldn't have gotten off the ground without its dual-engine skirt, the Ariane 5 core couldn't get off the ground without its boosters, and its balloon hydrogen tank would crumple under the weight of the LOX tank and upper stage.

The ideal delta-v of a stage can be arbitrarily high if you give it arbitrarily large balloon tanks and an arbitrarily wimpy engine and magic it into orbit where it doesn't have to worry about gravity drag or sea level specific impulse. Hell, they don't even have to be balloon tanks. If you attached a single RD-0146 engine to the butt end of a Space Shuttle SLWT and magicked it into space you'd get an "ideal delta-v" of 15.43 km/s thanks to the SLWT's 27.7:1 hydrolox propellant fraction and the RD-0146's stupidly high specific impulse. Doing something useful with it is a different matter.

Vulcain 1 is no longer in use, so I'll use Vulcain 2 instead. It has a sea level specific impulse of 318 seconds and a dry mass of 811 kg, and it develops 939.5 kN of thrust at sea level. Using two of those would give a liftoff thrust of 1,879 kN. Building a frankenrocket with two of those on a JAVE-less Ariane 5 core stage the Ariane 4 H10 upper stage would give a liftoff mass of 181.6 tonnes, for a painfully anemic liftoff T/W ratio of 1.05:1. That's woefully insufficient, and we haven't even added payload or strengthened the LH₂ tank enough to get off the ground. Decreasing the propellant (on either stage) would only make your mass fractions worse and decrease your total Δv.

Add a third Vulcain 2 and we might be getting somewhere. Now our liftoff mass is 182.4 tonnes and our liftoff thrust is 2,818 kN, giving us a respectable T/W ratio of 1.58:1. Let's target 1.4:1 after we account for payload and strengthening the core stage (a lower liftoff T/W ratio will help reduce the amount of core stage strengthening we need to do anyway). At 1.4 gees, those three Vulcain 2s are using 393.2 of their 2,818 kN to lift themselves, the hydrogen tank, and its contents, leaving  2,424.8 kN of force to be transferred through the hydrogen tank into the LOX tank.

That's a whopping eight times greater than the amount of force that the Ariane 5 LH₂ tank transferred to the LOX tank and JAVE element at liftoff. Fortunately, physics allows us to take the square root here, in order to account for the circumferential change in skin thickness. We'll need to bulk up the hydrogen tank from 1.3 mm to 3.68 mm, raising its dry mass to 12.2 tonnes. Add three Vulcain 2 engines and the LOX tank and the dry mass of our first stage now comes to 20.3 tonnes, giving us a propellant fraction of 7.8:1. That's about the same as the propellant fraction of a Delta IV common booster core stage.

Hydrogen can be useful in a sustainer stage architecture but it simply is not very good for a single-stick first stage. The engine needs to be overweight in order to get you off the ground quickly and the tank is going to be overweight because it must be both bulky (due to hydrogen's low density) and strong (to transmit loads).

Assuming a small 800 kg fairing, Silverbird gives an estimated 7.3 tonnes to LEO from the French Guiana launch site, but that's probably an overestimate because Silverbird isn't using a large enough sea level thrust penalty.

So we've built a completely new hydrogen tank, dusted off a retired upper stage, and bought three times as much engine per launch, all to get less than ten tonnes to LEO? Just for the sake of avoiding SRBs?

Payload fraction doesn't matter. Price matters. If you need to send 5 tonnes to GTO, and you can do the job with a 250 tonne rocket for $40 million or a 120 tonne rocket for $90 million, you'll pick the 250 tonne rocket every time, even though the 120 tonne rocket has twice the payload fraction.

But for the record, the LEO payload fraction of our all-liquid Ariane 6-5-4 frankenrocket is 4%, which is only 1.3% better than the 2.7% payload fraction of the Ariane 5 ES. And, again, customers aren't chasing payload fractions; they're chasing price.

 

 ATK, now Northup Grumman, partnering with Astrium proposed a  modification of the Ares 1 that would use a Shuttle derived SRB for the first stage and an Ariane 5 core for the upper stage called the Liberty rocket. The Astrium engineers would remove the JAVE attachment at the top of the core without the SRB’s of the Ariane 5:

Liberty.

A single Vulcain 2 engine powers the stage, providing 136 tonnes of thrust for about 540 seconds.  It also provides roll control during the main propulsion phase. At shut down, EPC separates from Ariane's upper stage and reenters.    

On Ariane 5, the EPC is topped by a forward skirt named JAVE ("Jupe AVant Equipée") that transmits thrust from the two solid boosters to the core vehicle.   This structure will not be needed on Liberty.

Araine 5 launchers are topped by a Vehicle Equipment Bay (VEB) that houses guidance and control systems, along with sets of hydrazine fueled roll and pitch thrusters.  The VEB, which is usually positioned atop the Ariane 5 second stage, is 5.4 meters in diameter, is 1.56 meters tall, and weighs 1.9 tonnes.

EPC will be modified for use on Liberty.  The tank walls will have to be strengthened, but some or all of the added mass would likely be offset by the elimination of the JAVE.  Vulcain 2 would have to perform an air start, but since it is a gas generator engine modifications are expected to be managable.   Snecma and Astrium have already been working on air start designs.  Ground test firings of an air-start Vulcain 2 would occur in mid 2013 if Liberty won a NASA contract.
https://web.archive.org/web/20160301144316/http://www.spacelaunchreport.com/liberty.html

 I agree with you the ballon tank structure of the Ariane 5 core was a key reason why it was able to achieve high propellant mass ratio. But remember the  famous Centaur upper stage also uses ballon tank structure and has been in use over 50 years, with very high reliability.

 About the payload estimates using the SilverbirdAstronautics.com estimator, as described in its documentation you have to use the vacuum values of both the thrust and ISP even for the first stage engines.  The reason is the calculator already takes into account the diminution at sea level.

  Robert Clark

 

[sevenperforce]

11 hours ago, Exoscientist said:

ATK, now Northup Grumman, partnering with Astrium proposed a  modification of the Ares 1 that would use a Shuttle derived SRB for the first stage and an Ariane 5 core for the upper stage. . . . The Astrium engineers would remove the JAVE attachment at the top of the core without the SRB’s of the Ariane 5:

On Ariane 5, the EPC is topped by a forward skirt named JAVE ("Jupe AVant Equipée") that transmits thrust from the two solid boosters to the core vehicle.   This structure will not be needed on Liberty.

[snip]

EPC will be modified for use on Liberty.  The tank walls will have to be strengthened, but some or all of the added mass would likely be offset by the elimination of the JAVE.

What you're quoting here matches what I said. The tank walls would have to be strengthened. And even for the Liberty concept, it was still "likely" that only "some" of the added mass would be offset by the removal of the JAVE, so the stage would likely be heavier than the Ariane 5 version with the JAVE. So the notion of a 16.3:1 propellant fraction remains a pure fiction.  

I never suggested that you wouldn't remove the JAVE for a liquid-only Ariane; I said that the necessary tank strengthening would make a liquid-only Ariane heavier than the stage with the JAVE.

In the case of the Liberty rocket concept, the vehicle was envisioned to send 20 tonnes to LEO, with a 5-segment Shuttle SRB and the Ariane 5 core as the upper stage. The Ariane 5 core is 12.2 tonnes plus 158.1 tonnes of propellant, and a five-segment SRB masses 725.7 tonnes at liftoff with 14.4 MN of thrust. So the T/W ratio of this rocket would have been 1.6 gees at liftoff. The SRB would be spending 11.8 MN pushing itself, the Vulcain 1, and the hydrogen tank at 1.6 gees, leaving 2,600 kN of thrust that the hydrogen tank would need to transfer to the LOX tank and everything above it: about 7% more than in the three-Vulcain 2-case above. So the fact that the engineers at Astrium knew that they would need to strengthen the tank makes perfect sense.

You're certainly not gonna get the 16.3:1 propellant fraction you've been talking about.

11 hours ago, Exoscientist said:

 I agree with you the ballon tank structure of the Ariane 5 core was a key reason why it was able to achieve high propellant mass ratio. But remember the  famous Centaur upper stage also uses ballon tank structure and has been in use over 50 years, with very high reliability.

Reliability is great and all, but that's not really relevant here because we're talking about the basic constraints of physics. The Centaur upper stage is much smaller and it's not carrying first-stage acceleration loads, so it's not a good comparison.

11 hours ago, Exoscientist said:

 About the payload estimates using the SilverbirdAstronautics.com estimator, as described in its documentation you have to use the vacuum values of both the thrust and ISP even for the first stage engines.  The reason is the calculator already takes into account the diminution at sea level.

I already used the Vulcain 2's vacuum thrust and vacuum specific impulse in the calculation which showed that your three-Vulcain-2 all-liquid Ariane frankenrocket wouldn't be able to get more than 7 tonnes to low earth orbit.

However, as I explained above, the calculator is overestimating here because it isn't using a large enough sea level thrust penalty for the architecture we're contemplating. Most first-stage engines are optimized for low altitudes and increase slightly in specific impulse at high altitudes only due to the pressure differential from underexpansion, and so the calculator assumes that the difference between sea level and vacuum specific impulse (for a first-stage engine) is relatively meager. For example, the RS-68A goes from 3.14 MN at sea level to 3.56 MN in a vacuum: a 16% increase. Silverbird will therefore apply a ~13.8% thrust and specific impulse penalty at liftoff to the first stage engines. But the Vulcain 2 is designed as a sustainer engine, so it is very overexpanded at sea level. As a result, its specific impulse (and, correspondingly, its thrust) increases by 36% from sea level to space.

The Silverbird calculator is overestimating because it is applying the ~13.8% thrust penalty typical for a first-stage engine, rather than the ~26.5% thrust penalty appropriate for a sustainer architecture like Vulcain 2. And remember that this thrust penalty is a double-edged sword because it impacts the usable Δv of the stage AND increases gravity drag on the stage.

[sevenperforce]

21 hours ago, sevenperforce said:

On 7/6/2023 at 3:13 AM, Exoscientist said:

on the Ariane 5 core the JAVE on the forward skirt of the Ariane 5 core is specifically to transmit the high thrust of the two side boosters

From the link you provided:

"This element . . . transmits thrust from the two solid boosters to the launcher in order to lift the fully loaded EPC."

Just an added note on this.

At booster burnout for the Ariane 5G, the total thrust of the stack was 13.96 MN and the total mass of the stack was 238.48 tonnes with 20% of the core stage propellant expended. That is a T/W ratio of almost 6. Even assuming that some sort of propellant shaping is used to limit that T/W ratio (let's say 5:1 for example), that means the hydrogen tank would have an effective weight of 1.1 MN, greater than the 1.015 MN vacuum thrust of the Vulcain 1. This means that at booster burnout, the hydrogen tank is actually in tension rather than compression, with the JAVE being used to lift a portion of its weight. 

[Exoscientist]

3 hours ago, sevenperforce said:

What you're quoting here matches what I said. The tank walls would have to be strengthened. And even for the Liberty concept, it was still "likely" that only "some" of the added mass would be offset by the removal of the JAVE, so the stage would likely be heavier than the Ariane 5 version with the JAVE. So the notion of a 16.3:1 propellant fraction remains a pure fiction.  

I never suggested that you wouldn't remove the JAVE for a liquid-only Ariane; I said that the necessary tank strengthening would make a liquid-only Ariane heavier than the stage with the JAVE.

In the case of the Liberty rocket concept, the vehicle was envisioned to send 20 tonnes to LEO, with a 5-segment Shuttle SRB and the Ariane 5 core as the upper stage. The Ariane 5 core is 12.2 tonnes plus 158.1 tonnes of propellant, and a five-segment SRB masses 725.7 tonnes at liftoff with 14.4 MN of thrust. So the T/W ratio of this rocket would have been 1.6 gees at liftoff. The SRB would be spending 11.8 MN pushing itself, the Vulcain 1, and the hydrogen tank at 1.6 gees, leaving 2,600 kN of thrust that the hydrogen tank would need to transfer to the LOX tank and everything above it: about 7% more than in the three-Vulcain 2-case above. So the fact that the engineers at Astrium knew that they would need to strengthen the tank makes perfect sense.

You're certainly not gonna get the 16.3:1 propellant fraction you've been talking about.

Reliability is great and all, but that's not really relevant here because we're talking about the basic constraints of physics. The Centaur upper stage is much smaller and it's not carrying first-stage acceleration loads, so it's not a good comparison.

I already used the Vulcain 2's vacuum thrust and vacuum specific impulse in the calculation which showed that your three-Vulcain-2 all-liquid Ariane frankenrocket wouldn't be able to get more than 7 tonnes to low earth orbit.

However, as I explained above, the calculator is overestimating here because it isn't using a large enough sea level thrust penalty for the architecture we're contemplating. Most first-stage engines are optimized for low altitudes and increase slightly in specific impulse at high altitudes only due to the pressure differential from underexpansion, and so the calculator assumes that the difference between sea level and vacuum specific impulse (for a first-stage engine) is relatively meager. For example, the RS-68A goes from 3.14 MN at sea level to 3.56 MN in a vacuum: a 16% increase. Silverbird will therefore apply a ~13.8% thrust and specific impulse penalty at liftoff to the first stage engines. But the Vulcain 2 is designed as a sustainer engine, so it is very overexpanded at sea level. As a result, its specific impulse (and, correspondingly, its thrust) increases by 36% from sea level to space.

The Silverbird calculator is overestimating because it is applying the ~13.8% thrust penalty typical for a first-stage engine, rather than the ~26.5% thrust penalty appropriate for a sustainer architecture like Vulcain 2. And remember that this thrust penalty is a double-edged sword because it impacts the usable Δv of the stage AND increases gravity drag on the stage.

 Below are the input page I used and results page for the Silverbirdastronautics.com calculator.  For the Vulcain  engine, I took the vacuum thrust as  1,350 kN. So for three Vulcains I input 4050 kN in the thrust field for the first stage. I took the vacuum ISP as 434 s.

 Since it had higher thrust than two Vulcains  I used the later, larger version Ariane 5 “E” core at 170 ton propellant load and 14 ton dry mass. I added ~4 tons for two additional Vulcains and another ~2 tons for strengthening the tank for the higher thrust, but also subtracted ~2 tons for removing the JAVE. The resulting dry mass I used was ~ 18 tons for the first stage.

 For the second stage, the higher thrust enabled a larger upper stage. So I took it comparable to the Centaur V at a 50 ton propellant load and 5 ton dry mass. For the engines I used three Vinci engines at 180 kN vacuum thrust each for a total of 540 kN, but I mentioned I assumed a larger nozzle to reach the highest 465.5 s Isp of the RL10. 

 The result was 19.6 tons to LEO. This is nearly 3 times your result of 7 tons. May I see the input page you used to the Silverbirdastronautics.com since the inputs you used must have been very different from the ones I used?

  Robert Clark

 

 

[sevenperforce]

19 minutes ago, Exoscientist said:

Below are the input page I used and results page for the Silverbirdastronautics.com calculator.  For the Vulcain  engine, I took the vacuum thrust as  1,350 kN. So for three Vulcains I input 4050 kN in the thrust field for the first stage. I took the vacuum ISP as 434 s.

As discussed above, the Silverbird calculator will overestimate the result because it does not provide a sufficiently large sea level thrust penalty.

To get an engine that is properly expanded at sea level and also boasts a 434 second vacuum specific impulse, you would need something like the RS-25 powerhead with a smaller sea-level sized nozzle. And even then you'd probably still have to crank up the chamber pressure.

19 minutes ago, Exoscientist said:

 Since it had higher thrust than two Vulcains  I used the later, larger version Ariane 5 “E” core at 170 ton propellant load and 14 ton dry mass.

Well now we have an entirely different first stage. I can do the math for that stage, but different inputs mean different outputs.

19 minutes ago, Exoscientist said:

I added ~4 tons for two additional Vulcains and another ~2 tons for strengthening the tank for the higher thrust, but also subtracted ~2 tons for removing the JAVE.

The JAVE only has a mass of 1.7 tonnes, and you're going to need a lot more than 2 additional tonnes to strengthen the hydrogen tank.

19 minutes ago, Exoscientist said:

 For the second stage, the higher thrust enabled a larger upper stage. So I took it comparable to the Centaur V at a 50 ton propellant load and 5 ton dry mass.

So we also have an entirely different second stage too.

19 minutes ago, Exoscientist said:

For the engines I used three Vinci engines at 180 kN vacuum thrust each for a total of 540 kN, but I mentioned I assumed a larger nozzle to reach the highest 465.5 s Isp of the RL10.

The Vinci engines have a nozzle extension that is 2.15 meters in diameter and makes the entire engine 4.2 meters long. How are you going to fit those -- with room to gimbal -- inside a 5.4-meter interstage? And the RL10B2's 465.5 second specific impulse already comes from a 2.15 meter wide nozzle, so what makes you think you can squeeze out more specific impulse from the Vinci? Just use the Vinci's actual specific impulse. And you can really only fit two of them on the stage anyway.

19 minutes ago, Exoscientist said:

 The result was 19.6 tons to LEO. This is nearly 3 times your result of 7 tons.

That's to be expected because you used a different first stage and a different second stage.

[Ultimate Steve]

You know, this is why I love this forum so much. You two have been debating for at least a page with giant posts of several paragraphs in length, and there's been no shouting or insulting. That doesn't seem to happen many other places these days. Good job, keep it up!

[darthgently]

9 minutes ago, Ultimate Steve said:

You know, this is why I love this forum so much. You two have been debating for at least a page with giant posts of several paragraphs in length, and there's been no shouting or insulting. That doesn't seem to happen many other places these days. Good job, keep it up!

+1 on this.  As it should be

[AckSed]

Science fight! Science fight!

Edit: Say we have a thrust-augmented nozzle that injects extra oxygen to increase thrust. Not looking for anything special, just a bit more mass-flow at the start for a O/F ratio of say 13:1 for 30 seconds. Does that do anything for the lift-off mass?

Edited July 9, 2023 by AckSed
Adding question

[magnemoe]

1 hour ago, AckSed said:

Science fight! Science fight!

Edit: Say we have a thrust-augmented nozzle that injects extra oxygen to increase thrust. Not looking for anything special, just a bit more mass-flow at the start for a O/F ratio of say 13:1 for 30 seconds. Does that do anything for the lift-off mass?

It should if TWR is low and therefore its more important to increase TWR than high ISP at liftoff. 
Probably not burning oxygen rich but rather not burning hydrogen rich at liftoff, With SRB you would then switch to more hydrogen rich and then throttle down as TWR get high enough. 
 

[sevenperforce]

18 hours ago, magnemoe said:

20 hours ago, AckSed said:

Science fight! Science fight!

Edit: Say we have a thrust-augmented nozzle that injects extra oxygen to increase thrust. Not looking for anything special, just a bit more mass-flow at the start for a O/F ratio of say 13:1 for 30 seconds. Does that do anything for the lift-off mass?

It should if TWR is low and therefore its more important to increase TWR than high ISP at liftoff. 
Probably not burning oxygen rich but rather not burning hydrogen rich at liftoff, With SRB you would then switch to more hydrogen rich and then throttle down as TWR get high enough. 

Bumping up thrust at the beginning definitely helps. Liftoff thrust is a big problem on the first stage. Of course the more you increase thrust, the more you have to strengthen the LH₂ tank, but the improvement is better.

The thrust improvements in the Vulcain 2 came from going to a less fuel-rich mixture ratio. Similarly (but in history), the Saturn V's increased lift margins to be able to send the rover to the lunar surface came from adjusting the F1 engine to be able to change the mixture ratio in flight, from high thrust and lower isp at liftoff to lower thrust and higher isp at altitude.

Spoiler

Specifically (for anyone interested) this increased capacity was the result of a LONG sequence. Higher thrust at liftoff meant lower gravity drag, and lower gravity drag meant a faster climb and a more rapid increase in F1 specific impulse. Then the increased specific impulse and subsequent mixture ratio change meant the first staging happened at a higher speed. This meant that the second stage got closer to orbit, which meant the third stage had less work to do to get into orbit and had more propellant left over for the lunar burn. This not only meant that the third stage could throw the added weight of the rover, but also that the third stage could place the whole stack in a more optimal higher-energy lunar trajectory, which meant fewer correction burns and a shorter insertion burn by the CSM. The CSM then had more propellant left to place the lunar module in a lower lunar orbit, reducing the amount of propellant that the lunar module would need to burn in order to reach the lunar surface.

Going up to a 13:1 O/F ratio would probably eat the engine -- that's way too oxygen-rich. However, the thrust-augmented nozzle could work with some sort of boundary layer film cooling.

I could calculate the actual change in thrust but it would depend on choices like injection pressure and set figures like turbopump capability.

[tater]

Maybe a handful of Arianespace employees can work some of these issues—it will give them something to do for the next year/whatever while they are not launching rockets.

Course the ones who would actually do this work are working on a slow-follower version of the F9, and no such changes to Ariane 6 will ever happen or even be considered—just as frankenrocket changes to SLS will never happen.