Two Stage Rocket, One Stage Design

JoshNH4H · 2013-10-31 00:25:17

In most branches of engineering and manufacturing, it's considered a good idea to reuse components where possible. This lowers development cost and cuts the number of production lines that need to be operating to produce the product. It also increases safety by making it possible to concentrate more closely on improving manufacturing accuracy of a smaller number of components. It also lowers the development cost because (assuming you're not trying to make some kind of reverse Frankenstein Monster, whereby the same component is used for far too many things) you don't have to develop as many separate items. This ultimately results in higher safety and lower cost. SpaceX pursues this strategy in (for example) their Merlin engines which are to be found on both the upper and lower stages of their Falcon rockets.

I think that it makes sense to apply this strategy more generally to the design of the entire rocket: Taking SSTO (Single Stage to Orbit) designs off the table for the moment, I propose that it is not just possible but feasible and a good idea to design a TSTO (Two Stage To Orbit) rocket where the first and second stage are, as much as possible, the same hardware. I contend that this is has benefits both for reusable and non-reusable rockets.

First of all, the math: I put this stuff in a spreadsheet, which you can download from Google drive if you would like.

The basic results are rather simple but pretty appealing. The best fuel combination to use, by far, is H2/LOX. If payload is to be 1% of GLOM (Gross Lift Off Mass), dry/structural mass in each stage can amount to 19.2% of the mass of the fuel in that stage (16.1% of fully fueled stage mass). My spreadsheet assumes that the exhaust velocity is constant, which is a poor assumption but simplifies the math greatly. I used a trajectory averaged exhaust velocity of 4,200 m/s for Hydrogen, 3,600 m/s for Methane, and 3,100 m/s for Kerosene. A table of various important quantities is as follows:

Fuel Combination    Exhaust Velocity*   Structural Mass Fraction**  Lower Stage ΔV**   Upper Stage ΔV**

H2/LOX                    4,200 m/s                0.161              2,253 m/s        7,247 m/s
Methlox                   3,600 m/s                0.110              2,091 m/s        7,409 m/s
Kerolox                   3,100 m/s                0.068              1,918 m/s        7,582 m/s

*Trajectory averaged.  Compare to expected maximum for H2/LOX of 4,500 m/s, for Methlox of 3,750 m/s,
 and for kerolox of 3,350 m/s.  
**All figures ignore variation in exhaust velocity during flights.  Numbers shown are for payload fraction
 of 0.01.  Structural mass fraction is the mass of structure/total stage mass.  9,500 m/s is used for the
 total delta-V required to achieve orbit.

Note that the actual delta-Vs will be split even less evenly between the two stages, because the entirety of the atmospheric flight will be at the beginning of first stage firing, and thereafter the rocket can fire in effectively vacuum conditions. This suggests that the first stage will be moving fairly slowly and fairly close to the ground at the staging point, which leads to the possibility of recovery-- especially for the H2/LOX stages, which have a relatively high structural mass fraction and could be built to be more resilient than the stages built with other fuels (specifically kerolox, whose small structural mass fraction makes me question if it can survive even a single launch). The unfueled rocket would be able to slow down by a significant amount just by falling back through the atmosphere. The low density of Hydrogen would actually make this even more practical.

And what of the second stage? Well, it will have achieved orbit. This means that it can reenter as is convenient, perhaps at the end of its first orbit. The high structural mass fractions and low density of H2/LOX fuel (specifically) mean that the rocket stage will have a low ballistic coefficient and will therefore slow down more in the upper atmosphere leading to lower maximum heating rates and perhaps enabling the use of a simple metal heat shield, or metal coated in a thin layer of ceramic.

Even for disposable rockets, the simplicity gained by near-complete commonality of parts would likely override the increase in payload that could come from more even staging.

Another plus is that there's a lot of room for improvement: Compared to my baseline H2/LOX rocket, if you can decrease the mass of the structure by just 10%, the payload will increase by 90%, to 1.9% of GLOM.

RGClark · 2013-10-31 01:59:05

Thanks for that. This is known as a bimese arrangement. To get more accurate payload estimates you might want to try Dr. John Schilling's Launch Performance Calculator, http://www.silverbirdastronautics.com/LVperform.html .
You might want to try also cross-feed fueling to improve your payload.

Bob Clark

Last edited by RGClark (2013-10-31 02:00:30)

JoshNH4H · 2013-10-31 09:02:54

I took a look at that calculator and it's useful in some ways but doesn't allow you to optimize for a given structural mass fraction and so is less useful than Excel, imo.

My proposal is different from the bimese proposal because I'm proposing serial vertical staging, instead of parallel horizontal staging. I'm arguing for s real two stage rockery rather than a one and a half stage rocket with drop tanks.

JoshNH4H · 2013-10-31 14:12:46

By the way, that calculator suggests (using 390 s as the trajectory-averaged lower stage Isp and 450 as the upper stage Isp) that with that same 16.1% structural mass fraction, the payload will increase to 2.2% of GLOM, or that payload can be retained at 1% of GLOM by increasing the structural mass fraction in both stages to 17.9%. This is still a pretty conservative approach: The RS-24 (Space Shuttle Main Engine) gets 363 s at 1 atmosphere, but I would expect this to rise very quickly because the SSME is designed to run in a vacuum. By changing the expansion ratio to one more suitable to atmospheric firing it should be possible to get the trajectory averaged Isp higher.

For vacuum firings, the Isp is affected more by the expansion ratio than by the chamber pressure, and increasing the chamber pressure will only increase the flow rate and therefore the thrust. This is desirable, but less important than having a high Isp.

This approach has the most benefits to reusable rockets, because the staging time makes reusability (in the form of flyback) more feasible. These rockets could also have the high structural mass fractions that would enable reusability. The payload limit (e.g. the point at which payload drops to zero) is at around structural fractions of 20%.

The characteristics of a rocket, designed using RGClark's calculator to have a payload mass of 1% of GLOM, suggest that the first stage will have a delta V just under 2 km/s. This says to me that the staging will likely occur at a speed of about 1.3 km/s and a height of about 40 km. It will be about 35 km downrange. I calculated this based on the fact that the Space Shuttle Solid Rocket boosters contribute the vast majority of the thrust (and therefore delta-V) until their separation at 124 s, and their total delta-V contribution is 1.8 km/s. Accounting for the fact that the Space Shuttle Main Engines also do contribute to the delta-V, I used the information about its trajectory to be found here at 110 seconds after launch. Information on shuttle components was found on astronautix.

This would suggest that the return trajectory for the first stage would be to first attain as much altitude as possible, then to turn around and slow down for landing. This, in turn, suggests a winged design would be a good idea for the lower stage. The relatively slow speeds make the aerodynamics much less challenging. I'm not suggesting a fully winged craft, just a rocket with rather large fins. Kind of like a V-2, but the fins would have the ability to contribute lift instead of just being used for steering.

By the way, cross-feeding of propellant would be fairly pointless in this application because the two stages would not be burning simultaneously.

Terraformer · 2013-10-31 14:58:09

If you're adding wings and a different engine to the lower stage, how is it still a one stage design? Surely better to adopt a full triamese system, like Falcon without an upper stage? Or maybe even a Pentese system, with a core stage surrounded by four - two are drained and dropped, leaving three full tanks, then two of those drop away leaving a core stage that's full and travelling fast at high altitude. You might be able to reuse the first two...

Or just go full out Otrag. Personally, I'm leaning towards a combination of a reusable lower stage and mass produced disposable upper stages.

JoshNH4H · 2013-10-31 22:09:35

Well, ideally the wings would be a simple strap-on kind of affair. I'd point out that extra heat shield area would be beneficial on the upper stage too, but I would certainly not go so far as to suggest that they could be the same profile. The two stages could use substantially the same architecture.

I don't like OTRAG in the long run because it gets really expensive to throw away all those stages each launch. In terms of the specific OTRAG design I think their rocket modules were too small and larger modules would have resulted in the ability to use a higher Isp fuel and significant savings from economies of scale.

Terraformer · 2013-11-01 06:09:39

But if you're producing these stages in the quantity you'd be wanting to, would it really make sense to make them have the same tanking? Is making 50 tanks the same that much harder than making 25 of two different types?

Why not biamese or triamese, though? It's been demonstrated multiple times, it's an understood technology.

JoshNH4H · 2013-11-01 13:37:16

With a high launch rate, it would ideally be possible to have a fairly small number of rockets. Let's say you have three different classes of rockets, one each at the 2, 15, and 60 tonne payload class (Small satellite launch, human ferry, and manned mission classes respectively). Let's say you have 10 2 tonne rockets, 5 15 tonne rockets, and 2 60 tonne rockets. Assuming a turnaround time of one month (If we're allowing for reusable rockets instead of refurbishable ones like the shuttle) you have a total of 17 rockets and an annual launch capacity of over 2500 tonnes.

This is a massive launch capacity, and it would be able to support a massively robust colonization program. That's not even to speak of other firms with rocket lines that presumably have similar capacities (monopoly is bad, after all; even duopoly and oligopoly is undesirable). This gets back to an oft-overlooked detail of the EtO (Earth to Orbit) industry: We haven't even begun to really touch the massively huge cost savings available from mass production. If you want to support this massive colonization program and only have this one line of rockets, assuming each can fly 12 times (e.g. one year service life) and each is composed of two totally different stages, you have to produce 34 stages per year; however, because there are six different types that becomes 6 per type per year, or approximately one every two months. This is certainly not mass production. If you can halve the number of stage designs by simply specifying strap-on aerodynamic surfaces that is an improvement. The extreme of this is the OTRAG design, which is very cheap but not extremely practical because their rocket modules have a very minimal performance.

Please note that one ever two (or one) month is a very optimistic estimate for the rate at which stages will need to be produced. Near-term, SpaceX's very busy launch manifest is for 2014 is under 200 tonnes to LEO. This will grow in 2015 to 225 tonnes to LEO (subject to their usual "Year indicates arrival at launch site" disclaimer). At this launch rate, say perhaps one 60 tonne launcher, 10 15 tonne launchers, and 10 2 tonne launchers for a total of 230 tonnes, and continuing to assume a 12 launch lifetime, it will be necessary to make a total of between zero and 6 stages per year total, or an average of 3.5 total per year. If there are six different stages, each type of stage will be built on average every 21 months; if there are 3 then on average every 10.

21 months is closer to every two years than every year. There could be significant cost savings from getting the frequency down, ideally to more than once per month per stage.

What this also shows is that reusable rockets probably don't make sense for launch rates below about 1000 tonnes per year, but they become feasible sooner the more commonality of parts you have.

Why not a bimese or trimese configuration?

Well, to start with, my original intent with this thread was to investigate a rocket made of two identical stages . To address your point more directly, a biamese configuration would in this case be more like a one-and-a-half stage vehicle with drop tanks. That's a perfectly good design, even if drag were higher. In that case, you would probably want to go with a vehicle that is only partially reusable, and make the drop tanks dirt cheap. It's a pretty good rocket design, all-told. Perhaps worth its own thread. I would note that this design is somewhat better optimized for a low launch rate. However it would seem to me that disposable drop tanks indicate that you would want to use a denser fuel, perhaps methlox, kerolox, or even keroperox. High density, storability, and the like. These don't agree well with the high structural mass fractions that can be attained using Hydrolox fuel. You start to get into the region where you're dropping engines, and since engines are by far the most complicated and expensive part of a rocket (I believe I saw figures somewhere that 30% of the end user cost of the Delta-IV heavy rocket can be accounted for just by the cost of the three RS-68 engines, even though these engines are considered cheap for their performance and capabilities).

It's an interesting concept, but it needs more consideration.

In closing, I would like to add that for this configuration the per-unit cost is less important than it is for disposable rockets because one would expect it to be reused a good number of times before failure.

GW Johnson · 2013-11-01 15:03:34

I'm not sure what the terminology biamese, triamese, etc, means. I looked at the link for the OTRAG article, and there is merit in that idea; it's quite similar in fundamental concept to what I posted over at "exrocketman" for using simplified ramjet missile technology as a first stage. Production savings often does overcome technological shortfalls, even in rocket work (although logistical tail is the real cost driver). Otherwise, I'm not "up" on what y'all are really discussing here.

But here's a thought anyway. Why not think modular like OTRAG, but not quite the same way he did. More like what I proposed for the Mars manned mission vehicles.

Come up with some sort of a common engine design, with mix-and-match bell extensions. Come up with a common engine "module" that is just a mounting frame for anywhere from 1 to maybe 10 of those common engines. Then come up with a common propellant module (both sets of tanks), that can be linked end-to-end or side-by-side (or both), and plumbed together easily. (BTW, these will not turn out to be 5% inert. More like 10+%.)

A bigger stack of propellant modules and more engines in the engine module, is your first stage. A smaller stack of propellant modules and maybe just 1 or 2 engines in the engine module, that's your second stage. Vertical launch on a typical rocket fast ascent trajectory leaves the sensible air at around Mach 2 at near 60-80,000 feet. Cluster drag is really not much of an issue, and neither is ascent heating. You can use that "textured" lithium-aluminum panel that folks like so well.

Plus, any dropped stage is easily split into individual modules for the best chances of successful recovery and reuse. Smaller is better as far as chutes are concerned. Same for deployed parasails or wings. Just remember, adding recoverability could double inert weight. Or worse.

Just an hunch on my part that something like that could be somewhat-tailored to any payload you want to launch, up to the max TO thrust your design allows. That kind of modular thing has been working for me up to know, far better than any of the "classic" ideas.

GW

Last edited by GW Johnson (2013-11-01 15:04:29)

JoshNH4H · 2013-11-01 15:15:45

GW-

It's not explained well really anywhere, so far as I can tell, but a so-called "Triamese" system would be rather like the Falcon 9 Heavy, without engines on the side boosters. In effect, biamese is the same thing as a drop tank, so far as I can tell. There's more discussion of the topic on the Selenian Boondocks blog.

Also, what do you think of my dry mass fractions for reusability, specifically in the case of the Hydrogen rocket? Up to 17.9% dry mass seems like you're getting to the point where reusability is an option.

Your concept is actually probably what OTRAG would have turned into if it were developed to completion, which geopolitics seems to have made impossible.

Terraformer · 2013-11-01 17:59:14

What? Falcon Heavy *is* a triamese system, using propellent cross-feeding (much like Shuttle) to ensure that the core stage is fully fueled at separation. The engines on the boosters mean you have enough thrust to launch the whole assembly. Drop tanks are a separate thing.

GW, that sounds like what Armadillo Aerospace were working on, before they hibernated. I like that idea. Especially if it could be made to work with the same sort of stages that would be needed for the Scootaloo or Rainbow Dash systems. Just have one fuel tank system, one engine design, and several frameworks to construct the stages. Run it all on Methlox, probably. It would certainly solve the issue of launching large (>1 tonne) cargo...

JoshNH4H · 2013-11-01 20:01:11

Can you point me towards a reference that talks about about biamese and triamese rockets a bit more? I haven't really heard the term before and am not really sure what is meant.

Also, what propellant cross feeding hhappened in the shuttle? Each of its three propellant systems used different fuels.

Terraformer · 2013-11-02 06:23:57

What I mean is, the SSMEs were fueled by an external tank. So yeah, it's a drop tank system. Cross feeding isn't really the right word, but it would be the we attached rocket engines to the main tank...

Biamese rockets are explained in the link you posted. But here's an Encyclopedia Astronautica entry on the triamese concept.

I'm not particularly a fan of it - I'm most a fan of the TSTO system we've been discussing in the other thread, actually - but if it can be combined with an OTRAG like system? We'll need to launch big payloads anyway...

RGClark · 2013-11-02 16:42:34

JoshNH4H wrote:

Can you point me towards a reference that talks about about biamese and triamese rockets a bit more? I haven't really heard the term before and am not really sure what is meant.
Also, what propellant cross feeding happened in the shuttle? Each of its three propellant systems used different fuels.

You can find several refs on the bimese or trimese concept by doing a web search. Here's one trimese proposal from the 60's I find interesting:

Weird Wings - BAC MUSTARD
http://www.unrealaircraft.com/wings/bac_mustard.php

For cross-feed fueling on the shuttle, it was actually used between the two Orbital Maneuvering System (OMS) pods:

STS-133: Crossfeed flange seal R&R complete – OMS reload in work.
October 22, 2010 by Chris Bergin

http://www.nasaspaceflight.com/2010/10/ … l-rr-task/

Bob Clark

RGClark · 2013-11-02 17:17:46

Bimese, var. biamese, means two copies of the same stage using parallel staging, not serial staging. Trimese, var. triamese, means three, also in parallel.
Strictly speaking, the Falcon Heavy is not trimese, because it has a smaller stage up top. For the same reason, the Delta IV Heavy also is not trimese.

Triamese shuttle models.
Posted on September 4, 2012 by admin

http://www.aerospaceprojectsreview.com/blog/?p=655

Bob Clark

JoshNH4H · 2013-11-02 19:21:48

Well in that case, as I said, drop tanks are a good system but it really depends what launch volume you're designing for. Biamese (or triamese) rockets seem like a good idea, but I question if you would really want the thrust to decrease after staging-- the T/W of rockets at liftoff is typically below 1.5, sometimes as low as 1.1, and if both of your modules are the same size your acceleration still won't be that high at staging. You start to approach a drop tank concept, and I discussed the reasons why I think that's less preferable than my proposed design in my last post.

Also, the aerodynamics of that triamese rocket really do look like a nightmare.

Terraformer · 2013-11-03 03:49:51

Not unmanageable though. We launch rockets like that regularly...

JoshNH4H · 2013-11-03 06:55:38

The aerodynamics would be somewhat worse than the Shuttle for equally sized components.

I will admit that parallel staging is a pretty attractive option, though.

SpaceNut · 2018-12-28 12:30:56

Just found the topic again and its one that Space x has embraced in its past and current design methods. Unfortunately it leaves a vehicle waiting on orbit to be refuled via its simple design concept.

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#1 2013-10-31 00:25:17

Two Stage Rocket, One Stage Design

#2 2013-10-31 01:59:05

Re: Two Stage Rocket, One Stage Design

#3 2013-10-31 09:02:54

Re: Two Stage Rocket, One Stage Design

#4 2013-10-31 14:12:46

Re: Two Stage Rocket, One Stage Design

#5 2013-10-31 14:58:09

Re: Two Stage Rocket, One Stage Design

#6 2013-10-31 22:09:35

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#7 2013-11-01 06:09:39

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#8 2013-11-01 13:37:16

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#9 2013-11-01 15:03:34

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#10 2013-11-01 15:15:45

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#11 2013-11-01 17:59:14

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#12 2013-11-01 20:01:11

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#13 2013-11-02 06:23:57

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#14 2013-11-02 16:42:34

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#15 2013-11-02 17:17:46

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#16 2013-11-02 19:21:48

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#17 2013-11-03 03:49:51

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#18 2013-11-03 06:55:38

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#19 2018-12-28 12:30:56

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