zondag 16 maart 2014

Expanding on my SpaceX BFR napkin estimates

Postage stamp sized picture of what some dude on NSF
thinks the BFR family might possibly look like. 
Some time ago, I drew up some napkin level concepts to look at what a SpaceX super heavy lift vehicle could look like. These concepts were based on what we knew about Raptor (1 million pounds of thrust, 380s vac isp) as well as Falcon 9 figures. However, in the meantime, new figures have been coming out further expanding on what we know about Raptor. Also, the original scratchings did not assume reusability, even though that is undoubtedly something this BFR will have to be capable of being, if they ever wish to colonize Mars without government support.

Disclaimer: All "tons" are metric tons in here. Also, all these figures are estimates. While the figures are given as specific, one should take them with a grain of salt, and remember they're estimates.

Creating a "reference vehicle"

First, a starting point from which we can expand on the concept. As a starting point, I'll take the Falcon 9v1.1 rocket, with the numbers provided from Spacelaunchreport.com's article about F9. The performance figures for Raptor are taken from this NSF article. At sea level, the vehicle has a specific impulse of 321 seconds, and a specific impulse of 363 seconds in vacuum. The thrust in vacuum is 4500 kN, which translates into 3979 kN (or 406 metric tons) of thrust at sea level. The upper stage version of Raptor is assumed to have an Isp of 380 seconds, which would translate into a thrust of 4711 kN.

The first step is to scale up the Falcon 9 stages to fit with these new thrust levels. From spacelaunchreport.com, we take the estimates of 404 tons for the first stage and 99 tons for the upper stage, and multiply them by the ratio between the Raptor thrust and the Merlin 1D thrust. Doing so, we get stage GLOWs of 2452 tons for the first stage, and 582 tons for the second stage. Falcon 9's stages have a propellant mass fraction of about 0.95-0.96, but this would be slightly lower because of the lower density of methane. The density of a mixture of methane/oxygen is about 80% of that of RP-1 and oxygen, meaning that these stages would have a propellant mass fraction of about 0.94. Which is pretty darn high, mind you.

Using these numbers, we get the following values for our hypothetical "Falcon Mars":

Stage 1:
GLOW: 2452 tons
Total propellant: 2305 tons
Empty mass: 147 tons
Thrust in vacuum: 40500 kN
Thrust at lift-off: 35811 kN (3654 tons)
Specific impulse: 363 vac, 321 sl, ~349 avg.

Stage 2:
GLOW: 582 tons
Total propellant: 547 tons
Empty mass: 35 tons
Thrust: 4711 kN
Isp: 380 

Vehicle total: 
Payload fairing: 10 tons (10 meter fairing)
GLOW (without payload): 3044 tons
Payload to LEO: 145.4 tons
Payload to TMI (C3=15): 21.8 tons
Total TWR at lift-off: 1.15

So, 145.4 tons to LEO, with a low TWR at lift-off of 1.15. This low TWR is a bit of a bummer, as it restricts a lot of upper stage upgrades to the vehicle. The estimate assumes that 1% of propellant is unusable and is added to the empty mass to become burnout mass.

The simplest upgrade from here would be to add an engine to the upper stage, as the current one might get underpowered, as we shall see later. If we take the Raptor TWR as 75:1, similar to RD-180 and RS-25, the engine mass becomes about 6.4 tons. Adding this to the upper stage and increasing the thrust increases payload to an even awesomer 153.6 metric tons, which is a 5.6% increase in payload. While it would further reduce lift-off TWR to 1.14, it would still be sufficient to take off.

Making the vehicle reusable

How much would making this BFR reusable cost in terms of payload? For Falcon 9, first stage reuse would cost about 30%. We could just say, well, let's cut 30% for first stage reuse. But that would be easy, wouldn't it?

In order to get a 30% reduction in payload from Falcon 9v1.1 the first stage would need to hold about 50 metric tons of propellant upon separation. Using the F9 estimates I used earlier, I get about 15.7 tons to LEO without reuse. Increasing the first stage's burnout mass by 40 tons and reducing propellant mass by 40 tons reduced this to 11 tons, which is a roughly 30% decrease.

Using a 311 second isp and 19 ton burnout mass, this translates into about 3450 m/s to return to the launch pad. Plugging this back into the BFR estimates, the core burnout mass would have to be increased to 387 metric tons, and propellant mass reduced to 2065 tons. This in turn reduced payload to 109.5 metric tons. This is a 29% reduction in payload, so this was completely pointless. But math is fun, so why would it matter?

Upper stage reuse is harder to estimate. I believe Elon estimated reduction in payload per stage as about 30%, meaning upper stage reduction would reduce payload by another 30%, or about half of what it was originally. But because I have no idea how much a PICA heat shield 10 meters in diameter would weigh, I don't think I can really do any math on this one. Simply assuming 30% off, the payload would drop to 76.7 tons to LEO, which is still pretty high. SLS-class payloads for very little. Mehr Nutzlast zum Spotpreis!

How about making it bigger?

We have already created a monster rocket. 153.6 tons to LEO, or 109.5 tons to LEO if partially reusable. But SpaceX has hinted at getting 100 tons directly to Mars, not 100 tons to LEO. So, we need to make it even bigger. And the easiest way to do that is by looking at what SpaceX has already chosen to do, which is making a tri-core variant like Falcon Heavy. 

Using identical cores, like originally planned for Falcon Heavy, we can increase the payload by quite a lot: assuming perfrect cross-feed, and doubled propellant left in the central core, the total LEO payload becomes 230.8 tons to LEO, with all three first stages reused. The payload to Mars is a meager 38 tons though. Surely that can be higher?

The most obvious way to increase the payload would be to scale up the boosters and reduce the propellant load left in the core stage upon booster separation. It could still be reused, but would have to land on an ocean platform, or maybe a small island in the Atlantic. While this would reduce turnaround time, it's a spacecraft to Mars. There's only one launch window every two years anyway.

Using an ocean platform increases TMI payload by a lot; from 38 to 57.7 metric tons to a C3=15 trajectory. Without fairing, this would be about 58 tons, though this could cause changes to MCT's design. Also, the boosters can be made a lot bigger, similar to Falcon Heavy, because of the much higher thrust at lift-off. The total thrust at lift-off would be 10962 tons. Limiting TWR to 1.14 and assuming a 100 ton payload, the boosters could be scaled up to be a total of 3236 metric tons, or almost 1000 tons bigger than the core.

These boosters, with flyback ability, could hold about 2724 tons of propellant, and would have a separation mass of 511 tons. Using these figures, the TMI payload goes up again, to 67.8 metric tons. But it's still not 100.

However, the LEO payload becomes a staggering 327.4 metric tons. Using a third stage to do TMI, however, one could increase the usable payload to Mars to 101 metric tons. We did it!

It now also becomes clear how important it would be to use two engines on the upper stage rather than one. With a 327 ton payload, the TWR of the upper stage with two engines is 1.03. With one engine, however, it would be a TWR of only 0.52. As the upper stage still has to do quite the burn to LEO, having such a high thrust stage is useful in reducing gravity losses. Not having one would reduce payload by about 5-10%.

Then what could MCT look like? Maybe something like this. All I know is that in order for the vehicle to get to Mars from LEO, it's going to have to hold a heck of a lot of propellant.

Highly technical sketch of what MCT, the BFR's payload, could look like.

zaterdag 1 februari 2014

Ariane 6: Where does it come from, and can it compete?

Recent Ariane 6 concept. Credit: CNES
The launch vehicle market is rapidly evolving. While Europe has been in a comfortable position over the past 20 years, with Ariane 4 and later 5 dominating the commercial launch market, this has been changing over the past few years. First the Russian Proton rocket took the market by storm, capturing a large part of the market, now emerging launch vehicles from China, India and new commercial ventures like SpaceX are posing a threat to Europe's lead in the commercial market.

While Ariane 5 has so far had little trouble keeping up with Proton, this has always required a significant amount of government subsidies. Currently, an Ariane 5 costs about €150 millions for 10 tons to a Geostationary Transfer Orbit, and receives on average €120 million in subsidies per year. For comparison, a Proton costs less than €80 million per launch with a payload of 6.5 tons. In addition to this, Ariane 5 launches two satellites at a time, one big one (in the range of 6 tons) and a small one, in the range of 3 tons. This means that any customer will have to wait until a suitable second customer is found for a launch, and as satellites are getting heavier, this is becoming more and more difficult. This can be seen in the design of many new vehicles; with the exception of the SpaceX Falcon Heavy, most commercial launch vehicles like Proton or GSLV have payloads to GTO in the range of 4 to 7 tons.

While Europe is currently developing Ariane 5 ME, which will reduce costs per kg to GTO by 20% and remove the need for subsidies, but even though the payload increase alleviates it somewhat the dual launch problem will remain. This is a problem the European Space Agency ESA has realized and the reason they decided on the development of a new launch vehicle, the Next Generation Launcher, recently dubbed Ariane 6. For the first time, Europe is designing a launcher with low cost in mind, with the goal of reducing the cost for both commercial, military and scientific payloads.

The current baseline design is a surprising design that has little similarity to previous concepts. It uses four common rocket stage carrying 135 tons (newer sources indicate 145 tons) of solid rocket propellant, with two or three of these "cores" making up the first stage and a single one making up the second stage. An upper stage would use a single cryogenic Vinci engine and use hydrogen and oxygen to propel the payload into the target orbit. The payload to GTO is 6.5 tons for the full configuration, and a version using two solids in the first stage would bring 3.4 tons to GTO (the two solid configuration was originally claimed by CNES but hasn't been mentioned for some time now). The goal is to cost only €70 million, or about $95 million dollars.

During a recent tweetup, the French Space agency CNES claimed that Ariane 6 could evolve to lift between 4 and 8 tons to GTO, with the 8 ton version using five solid boosters as a first stage. A 4 ton version might use two solids or three solids as first stage, as this wasn't specified. However, the vehicle would likely be evolvable, like SLS, rather than modular like the EELVs. A six-solid configuration would require modifications to the current design which would reduce performance on the current four solid configuration.

How the design came to be

The design of Ariane 6 is quite unusual, with no previous vehicle concepts looking anything like it. This is reflected in the way it was received, with reactions ranging from "brilliant" to "the end of European access to space". It might look like it was clumped together, but you can't be more wrong about that. It was a result of a long series of trade studies, and the advantages of the design are less obvious than you might think.

In 2012, ESA started the NELS study: New European Launch Service. This study evaluated over 700 launch vehicle concepts on several different factors including cost, payload, reliability, development cost and risk. The main concepts were:

  • KH: Kerosene first stage with NK-33 engines.
  • HH: Three Vulcain-3 engines on the first stage, no boosters.
  • HH-PPB: Two Vulcain-3 engines, small P20 boosters.
  • PPH: P340 first stage, P110 second stage.
  • Multi-P: Solid common cores (the later selected design).
  • PPH-PPB: P180 first stage, P110 second stage, P40 boosters
  • KH-CCB/HH-CCB: Hydrogen or Kerosene first stage using common core boosters to reach the 6.5 ton requirement.
All of these concepts used a hydrogen upper stage with a single Vinci engine.

Out of these concepts, the PPH concept was the cheapest, especially at low flight rates. However, it had significant development risk because the P340 solid first stage would be the biggest and most powerful monolithic solid motor ever made by a very large margin. 

Below that, KH, HH and Multi-P all had very similar cost, slightly higher than PPH. However, HH and KH were not configurable like Multi-P, meaning that they were more expensive and less flexible with smaller payloads. On top of that, KH required the use of Russian engines rather than European ones if the design was to make the 2020 first launch mandate, which made it a political dead end. 

At the bottom where the strap-on and common core designs. While these vehicles were cheaper for small payloads in the 3.5 ton range, they proved to be slightly more expensive than the concepts above them. Strap-on boosters cause a large increase in fixed cost and common cores are a lot more expensive than simply stretching the core.

From this, the advantages of Multi-P become clear. The vehicle combines the low cost of an in-line concept with the versatility of the modular designs, with moderate development risk and a lower cost increase at low flight rates. On top of that, the common core also allows to function as the first stage of Vega, which would increase Vega's payload and reduce the cost of the small launcher. 

Later, ESA further down selected Ariane 6 concepts. However, because both ESA and CNES usually have payloads in the smaller range, the modular concepts gained an upper hand again. Currently, European nations have to rely on the Russian Soyuz for these smaller payloads, and independence is an important requirement for Ariane 6. In fact, it is the main reason Ariane exists in the first place: Independent access to space for Europe. For these reasons, the eventual choice came down to three concepts: H2C, P1B and P7C, which were HH-PPB, PPH-PPB and Multi-P from the previous study, as these allowed for full independence at lower cost than any of the kerosene hydrogen CCB concepts.

With these concepts, the choice became a lot easier. P7C, or Multi-P, provided the synergies with Vega and a lower cost than the other designs, even if it was slightly less flexible. Combine this with Italy's and France's love for solid boosters, and the winner is clear.
The final three Ariane 6 configurations. Credit: Aviation Week

Can it compete?

Disclaimer: This part is slightly opinionated.

Whether Ariane 6 can compete with the other upcoming competitors will depend on a lot of different factors. The first one is whether they can reach the €70 million goal with 6.5 tons to GTO. This is a rather aggressive cost goal as this is 30% lower in cost per kilogram than the current Ariane 5. Most preliminary studies showed this to be difficult to reach, and in order to reach this, ESA has decided to throw the conventional development structure out of the window.

""Unlike past ESA development projects, Ariane 6 is being designed by industry to meet cost and technical requirements without regard for where the work is conducted. ESA’s contract pillar — geographic return guaranteeing governments that the money they spend at ESA will be returned in the form of contracts to their national industry — has been tossed aside for Ariane 6."

In an interview with lesechos, ESA director General Jean Jacques Dordain claimed that while it was going to be difficult, the cost goal was possible. Later, it was also announced that the supplier base was being cut by two-thirds. All of these things together mean that the €70 million cost goal is definitely not impossible, even if it might become hard to reach.

It will also depend on what the competition will be capable of doing. The most dangerous looking competitor at the moment seems to be SpaceX. They have already managed a significant reduction in cost, at least they advertise as such. These figures should be approached with slight skepticism, as Falcon 9 is not yet a mature system, but they are very low and they are already starting to capture a large customer base and full manifest.
The SpaceX Falcon 9 is one of the biggest competitors Ariane might face. Credit: SpaceX

However, Ariane 6 should be competitive with their current vehicles at a reasonable launch rate of 9 per year. While the claimed payload to GTO for Falcon 9, 4.85 tons, would imply a much lower cost per kg, it should be remembered that this Falcon 9 GTO requires the satellite to perform 1800 m/s of velocity change by itself, while the Ariane 6 GTO requires only 1500 m/s. The equivalent payload of Falcon 9 to the same orbit, which was also used by SES-8, is only about 3.5 metric tons. This results in a price per kg which is almost identical to Ariane 6.

But then there is another issue. SpaceX has set a goal of making Falcon 9 and Falcon Heavy fully reusable launch vehicles. And they have been making steady progress on this front. On the first flight of Falcon 9v1.1, with the launch of CASSIOPE, they successfully landed the Falcon 9 first stage in the ocean, with only a small roll problem causing the engine to shut down too early.

While full reusability is likely many years away, first stage reuse might be just around the corner, as an attempt to fly the first stage with legs is planned for early March. Reuse of the first stage will cause a large payload decrease however, of about 30%. For Falcon Heavy it is likely more as the first stage will separate much later than on Falcon 9, and for GTO, this is likely even more, as the upper stage will have to do even more work with the first stage's earlier separation. This means that it is possible the cost/kg reduction for GTO is not huge, or maybe non-existant.

Falcon 9 first stage coming in for landing. Credit: SpaceX
Nonetheless, it's a danger to Ariane's competitiveness. With Ariane 6 not expected before 2021, the chance that Ariane's market share might wither away as Ariane is developed is very high. If Europe wants to remain competitive, reusability should at least be looked at and payed attention to. It's a good thing they currently are doing so, with ESA studying and investing in Skylon, as well as the IXV reentry demonstrator, and it's follow-on, the PRIDE innovative space vehicle, which are supposed to test critical technologies for reusable upper stages.
PRIDE reusable demonstrator servicing a satellite. Credit: ESA

IXV reentry demonstrator reentering the atmosphere. Credit: ESA

The option to replace the second and third stage of Ariane 6 with an IXV/PRIDE derived cryogenic upper stage is an attractive one and hopefully one ESA are looking into. Currently though, the Ariane 6 design appears to show little interest in partial reusability, which it definitely should. 

Ariane 6 has the potential to be a very competitive launch vehicle and it's aggressive cost target, versatility and responsiveness make it a very welll-rounded option. However, as long as the threat of reusability looms around the corner, it should be payed attention to. The option of implementing reusability into Ariane 6 should be available, and the current design appears to keep little of this in mind. If this doesn't happen, it's very well possible Europe in 10 years might no longer be in the comfortable position it is in now.