The Numbers Game of the N-Prize, Quick and Dirty Feasibility Overview/Simulator, and a $1000 Challenge!

Those of you who’ve read my earlier blog entry “Overview of the LMR N-Prize Approach”  (www.littlemonsterrocket.com/news/overview-of-the-lmr-n-prize-approach/) might be interested in the details of how my decisions and estimates were arrived at. I'm going to cover some of that thought process here; this will hopefully (also) shed some insight into the basic first-pass design of a multistage rocket system.

 

This is informal, and there are many ways to approach the problem. The thought methodology I've outlined here happens to lend itself well to the constraints of the N-Prize (and the constraints of a blog).

 

I'm also going to talk a bit about my Quick and Dirty Feasibility Overview of Microscale Launch Vehicles (and adjunct Simulator), and our $1000 Challenge(!).

 

As a note (and to the best of my knowledge) I'm the first (and only) person to do such a detailed analysis in regards to microscale launch vehicles (going on decades now) – so, you simply can't get this information anywhere else.

 

 

 

The Numbers Game of the N-Prize

 

Any coverups aside, there is only one technology we (as Earthlings) popularly know of (and only one that has actually worked) to get us into orbit: rockets. No technological embodiment popularly known to mankind has gone from Earth to orbit, other than rockets. So, if you're going to send something into orbit, the logical choice would therefore be rockets.

 

Physics is the same for all of us (at least in this realm). This means that a conventional rocket system designed to reach space with a 20 g payload and $2000 budget constraint is going to have particular parameters. And, unless you're Merlin (that's the “Magician,” not the “Engine”) or perhaps Xantu of Ceti Alpha-5, you're stuck with all that.

 

But, we do have a background in engineering, physics, and a wide variety of other disciplines – this supposedly helps us know what we're doing. So, let's start...

 

The limited budget means you need to make the smallest rocket possible (and feasible) which is applicable to the task; this is largely because of the labor and materials costs. You obviously can't make it smaller than possible for the task because it wont work (duh). The constraints also mean that you're going to be limited in materials options; probably nothing too exotic: copper, aluminum, perhaps thin stainless and limited fiber over-wrap structures. Electronics are cheap if you can design and build the systems yourself (which luckily, I can do).

 

Launch is really two parts: lower atmosphere and upper atmosphere (vacuum). Air resistance (drag) is a big deal, and a lot of ideas have been thrown around to fix it. This includes things like balloons and air launch with the idea that the higher you launch, the easier the atmospheric portion of the flight. Not only have these systems not worked out very well (so far); there is no evidence that they are any simpler to implement (overall) than a rocket booster. In addition, rocket boosters have many important advantages such as providing a stable platform, being able to reach much higher altitudes, and providing a substantial delta V at staging – these things are critical aspects (I'll talk more about balloon launch in a later post). So conservatively, the entire system becomes rocket based.

 

So, we know that reaching any orbit is (practically speaking) going to need two or three stages (lower atmosphere + upper atmosphere) – single stage to orbit (SSTO) is theoretically possible, but probably too technical for the budget (and it's never been demonstrated in any scale domain). Given the potential issues with scaling, we take the conservative approach and choose three stages.

 

We know that solids won't do it because they typically have short burn times (especially in smaller scale) and we need long burn times to get through the atmosphere and align ourselves for orbit; solids are also relatively low performance and difficult to steer. Hybrids are an option but have relatively low performance and have the same types of steering issues as solids, so we choose liquids, and bi-propellants because of the higher performance and flexible propellant options.

 

Now, we have a three stage liquid rocket; since we can gimbal the engines (which is, in the current crop of known steering methods, the most effective steering method overall), we do it. We're set! Now what?

 

We estimate our engine capabilities; we have plenty of examples and data for doing this. We initially choose LOX as an oxidizer because of availability, performance, and reams of existing technical information. We consider hydrocarbon (HC) based fuels: kerosene because it's dense, propane because it's energetic and clean burning, butane because of a potentially favorable vapor pressure depending on engine design, and possibly heavier fuels due to density and other aspects. All of these will have reasonably similar performance; so we just term them “hydrocarbons” (HCs) for the first pass and move on.

 

We also consider alcohol based fuels because of the favorable cooling properties, and note that WFNA is a possible oxidizer alternative with both advantages and disadvantages. H2O2 is too difficult to get, store, and handle; N2O requires sub-cooling to be even moderately effective (or your stuck with heavy tanks). All options perform worse than LOX; we stick with LOX/HC for now.

 

We then choose a feed system. Pumps are generally too complex if not needed. Because we plan extremely low pressure upper stages (vacuum exhaust conditions allow this to be practical), upper stages won't benefit so much from them; the booster could benefit, but we can run this fairly low pressure as well. As a compromise, electromechanical pumps appear viable (analysis shows roughly the same performance as open-cycle gas generator engines). But, we'll keep it simple and opt for pressure-fed systems as a first go-around.

 

Now we can proceed one of two ways: a) figuring out what we need and then determining if we can realistically build it (the logical way), or b) figuring out what we can realistically build and then evaluating if that meets the requirements (the practical way). We're going to choose plan “B” (just because I'm in that mood right now and the N-Prize has well defined constraints). Let's do it...

 

We estimate the performance that we can attain. We know that low-pressure upper stages perform nearly as well as their high-pressure counterparts due to favorable exhaust conditions (vacuum); low-pressure means lower tank weights (tanks can be made thinner), so the stages are made as low-pressure as possible to be as lightweight as possible. Thus, we want both upper stages to be super-thin low-pressure structures designed for vacuum operation. This means our booster needs to get up out of the atmosphere (at least ~45 km or thereabouts) while also protecting both upper stages; this implies a studier booster with suitable payload bay and release mechanism for both upper stages (an exposed second stage is an unlikely option because the mass fraction would probably be too low if built to handle the atmospheric loads). A clam-shell type nosecone is suitable for this purpose; it can break away at altitude, exposing the upper stages when required. Such nosecones have been used and work fine, so we'll choose that for now.

 

Modern upper stages running LOX/HC usually have a specific impulse of >310 s; we'll choose a conservative value we are certain to reach with our materials and construction techniques. Based on our experience we determine 290 s, but choose a lousy 270 s to make the engineering easier (also because that puts us within the range of WFNA, if we decide to go there). Thus, we target both upper stages at an industry-dismal 270 s specific impulse.

 

We look at our prior experience in building LOX/HC engines which have given us >250 s at sea level; we know that modern high performance LOX/HC engines can do better than this. We consider taking the easy road and picking 240 s (sl) for the booster, but we want the super-simple road and choose 220 s (sl) – this also gives some additional buffer.

 

We estimate the size of the vehicle by looking at the payload requirement – we want the smallest vehicle possible (lower cost in materials and propellant, potentially easier to machine).

 

We can focus on well designed upper stages; we already know we're going to get reasonable mass fractions (MFs) due to the ultra-low pressures. Plus, they're smaller – so making them better (lighter) is less costly overall. We know that 0.9 stage mass fractions are common in industry; a quick evaluation suggests 0.85 is a reasonable target – we choose 0.8 overall MF with payload for our upper stages (to give us some wiggle room).

 

Now we go for the mass estimate. We're going to use rough ballparks as a first pass – if they seem reasonable, we'll go with them; if not, well revise and iterate until we get something that makes sense. The initial estimates are based on research and experience with existing multistage rockets.

 

The payload is taken as the maximum 20 g (we can shave off a couple if we need to save some weight for launch). You're obviously not going to pick a structural mass too close in size to the payload, nor are you going to pick something supremely gargantuan. For this stage, we'll start with an estimate of either 20x the payload in wet mass or more conservatively 5x the payload mass in structure. We can really start with anything that makes sense, but experience suggests that these are reasonable figures for the lightweight structures we're using. Since we're dealing with such a small stage here (thin gauge), we'll choose the more conservative figure. That yields 100 g of structure, 120 g with payload – 600 g for the upper stage wet mass.

 

We then take a glance at the 100 g structure and evaluate if we can actually make the stage with existing materials. We roughly estimate weights of tanks, pressurant, engine size (assuming a 1:1 T/W ratio), electronics, control system, interconnects, wiring, release mechanism, valves/plumbing, and other odds and ends. We jot all that down and after checking it out... Yes, 100 g seems reasonable in first pass; this then becomes a target (see the LMR-A/S3-HG overview slide*).

 

The second stage is the same as first stage, 0.8 MF. We could make it really easy and simply scale up the third stage to second stage size – we know for certain this would work (for our intents and purposes, scaling up directly will always work, and actually improve the MF somewhat). However, this appears a bit too conservative; research and experience suggests that a reasonable wet mass for a second stage in small scale would be ~5-10x the payload. Because of the thin materials, we'll use 20x and see how that works out in the calculations (still conservative, but not as extreme as the third stage).

 

This gives us 12 kg total: 11.4 kg stage GLOW; 9.6 kg of propellant, 1.8 kg in structural mass – structural mass is about 3x the payload which is reasonable. Again, do the above quick evaluation with components... And, after checking it out... Yes, 1.8 kg seems reasonable in a first pass; this then becomes another target.

 

The booster is more difficult; it needs a nosecone and a method to protect both upper stages – the upper stages are clearly too thin to survive the atmospheric flight. As noted earlier, a clam-shell nosecone or other suitable system is needed; we'll opt for the clam-shell (for the time being) as it's relatively simple and serves both purposes. In addition, we're going to need higher pressures because of less favorable exhaust conditions (lower atmosphere); this means heavier tanks and lower mass fractions. We select 0.6, knowing from experience and research we could reach perhaps 0.7 with some effort (given a pressure-fed stage).

 

Thus, we're going to have a fairly sturdy booster with relatively low MF; from the discussion above, you've probably already guessed what we'll choose as a first-pass. We select 5-10x the payload mass as wet mass or 60-120 kg GLOW. We choose 120 kg conservatively: 72 kg in propellant, 36 kg structure, 12 kg payload. We again do the evaluations of components... And, after checking that out... Yes, this can be built – but, 36 kg in structure appears to be overkill (possibly too conservative).

 

What about 60 kg? 36 kg in propellant, 12 kg structure, 12 kg payload. Do the evaluations... And, after checking it out... Yes, this can be built – but a 12 kg structure doesn't give much margin.

 

Although we want the smallest rocket because we want to minimize cost, 60 kg might be pushing it a bit with our constraint of meager materials. Besides, going a bit larger can't hurt unless we break the budget. 90 kg is between the two estimates and gives us some margin; that's 54 kg propellant, 24 kg structure and 12 kg payload.

 

 

Yay! We now have our first-pass, rough-cut rocket system ready for further analysis. We're looking at an approximate 90 kg GLOW, three-stage, pressure-fed, liquid bi-propellant rocket system with ultra-low pressure upper stages, gimbaled engines, and a relatively beefy booster with clam-shell nosecone.

 

 

Now, I don't care who you are (maybe even Xantu himself), if you're trying to design the smallest three stage rocket which can carry 20 g into orbit, and you select reasonable mass fractions, and intend on reasonably low-cost (and readily available) Earth materials, and have N-Prize style budget constraints overall, this is about what you're going to come up with: somewhere around 60 kg to 120 kg GLOW; perhaps a bit less or more, but fairly close to this range.

 

You don't want to go much bigger because it becomes more costly. On the flip side, you can't build the upper stages much lighter because the materials are not readily available – to go much smaller with the already lightweight ultra-low pressure tanks, you'd probably need to electroform the structures; while not a difficult process (it's done all the time) it's another layer of complexity for this project. Because of that, you can't build the booster much smaller; as noted, already at 60 kg it was getting harder to find commonly available materials that could make the structural mass budget, the cost budget, and also meet the mechanical requirements.

 

As a side note, I prefer smaller rockets because it means I can build smaller engines, have lower materials cost, use less propellant in testing, and all kinds of other great stuff. So, my choice here would be to shoot closer to the 60 kg mark – and if you've read my earlier blog entry “Overview of the LMR N-Prize Approach” you'll see I selected 75 kg.

 

 

Now that it's “built” (and assuming we've made our targets) the rocket either works (mathematically) or it doesn't; if it doesn't we iterate on the design until it does. We know for a fact it will eventually work (at least theoretically) because we know that three stage rockets do work (we could simply keep scaling it and improving it until it functioned). But, the real question is whether it will it work in a reasonable microscale embodiment that also meets our criteria and constraints.

 

So, we still need to answer that feasibility question – does the rocket just designed work or not? Well, to determine that, we run the calculations....

 

And... And... And...

 

Well, does it work??? You bet it does!!! Our first pass is good enough that we can now refine it as we see fit.

 

 

 

Quick and Dirty Feasibility Overview and Launch Simulator

 

“But, wait a minute Chris, or Sage, or whatever your name is!!! Where are all those calculations??? Certainly, a rocket this small can't do it!!! You're definitely WRONG!!! Show me how you determined feasibility!!! Show me the numbers!!! Everybody – professors and industry professionals – everyone I know says it simply CAN'T work. Until you show me the numbers, I think this is bunk!!! There's just too much drag loss and all the other kinds of barriers that I've heard about!!! What about all that?!”

 

Oh yeah, “those” things. They were all considered. But, do you really want those “minor” details anyway? You don't take my word for it, huh?

 

Alright then, I'll give you more information. But first, how about giving a small symbol of support for this great cause?

 

With just $20 of support to LMR you can request both the “Quick and Dirty Feasibility Overview of Microscale Launch Vehicles” and the “Quick and Dirty Launch Simulator” which demonstrate (definitively) that such a rocket can indeed make it into orbit.

 

What are these things??

 

 

“Quick and Dirty Feasibility Overview of Microscale Launch Vehicles”

It's a rough, off-the-cuff, relatively brief (~50 page) summary/recap/overview document of several larger efforts which spanned thousands of pages documentation, along with countless hours of research, design, calculations, simulations, analysis, and testing; it covers the salient points of the feasibility analysis.

 

Several of my previous efforts on this topic have culminated in fairly extensive research papers, the most recent wrapping up in a February 2009 document: “Feasibility Analysis of Micro-Scale Launch Vehicles.” This “Quick and Dirty” document is basically a repackaged informal overview of the results of several earlier investigations.

 

The Quick and Dirty document covers microscale launch feasibility from an overall perspective; it's definitely not encyclopedic on external reference material nor is it any template for formatting detailed equations – but there's certainly plenty there to keep the mind occupied. In addition, I have included a works cited list from a larger document for the reader to have additional study material. If/when I add to this document (and/or include excepts from my other documents) some additional sources may come from the included list. Note that it's a rough, living document completely subject to change – it's Quick, and it's Dirty. Updates/additions/revisions to this document will be provided without further donation.

 

 

An except from my February 2009 paper that sums up the available literature on this particular topic:

 

“Prior to this analysis, there was practically zero literature on the topic; a search found no similar studies with the exception of one conducted by Lawrence Livermore National Laboratory by Dr. John Whitehead (Whitehead). Although interesting, Whitehead's investigation was relatively limited in scope, and more focused on micro-pumps and Mars ascent vehicles than general purpose micro-scale launchers. Some informal commentary (by this author) [Granger] on Mr. Whitehead's study can be found in Appendix A.

 

As will be shown in this feasibility analysis, launch vehicles can indeed be made far smaller than the current state-of-the-art – in fact, they can be made nearly two orders of magnitude less massive than those now existing – without resorting to exotic, outlandish, or otherwise prohibitive engineering techniques.”

 

 

 

 

I've heard claims that the idea of a lightweight launcher has sometimes come up in industry. But, other than my own studies, I have yet to see a single piece of credible feasibility literature on microscale launch systems at the scale sizes I'm referring to. Certainly, people have talked about 100 kg and sometimes even 10 kg payload launchers – but these are relatively giant machines; I've never seen anything at the scale level I'm referring to.

 I've encountered a few brief (sometime one-liner) ad hoc arguments over the years which claim “impossibility” (usually in response to my posts, and usually claiming drag or fabrication considerations or such), but have not seen anything indicative of an actual feasibility study whatsoever (other than my own research).

 

 

I have not made the larger February 2009 feasibility document available, but I will likely be posting excerpts from time to time (and/or possibly including them in future document versions – for instance, the Appendix A mentioned above); the Quick and Dirty version itself is more than enough for a feasibility treatment.

 

 

 

 

“Quick and Dirty Launch Simulator”

A numerical simulator that runs the entire launch into orbit. Executes on Windows OS. Only 57 kB – it's been stripped-down to the essentials and adapted specifically for this feasibility treatment.

 

While it's certainly not the most accurate simulator (such as our advanced 6-DOF LMR OVAL validation suite, which is highly accurate) it's plenty accurate for the purposes of demonstrating feasibility; it includes the necessary physics models to validate a launch.

 

 

How do I know it works?

 

Well, after running thousands of test cases through it, including many hundreds of Saturn V parking orbit variants (which it computes quite well, including reasonable estimates of drag loss and remaining tank propellant), I'm confident it works more than well enough for determining purposes of feasibility. But, if you think I'm wrong and my feasibility conclusions are bunk, then you're after the $1000 challenge below.

 

The simulator is NOT general-purpose for the end-user; it was designed NOT to be (on purpose); it's a fixed output simulation. You'll get two of them: one with the LMR N-Prize mission and one with a Saturn V Earth Parking Orbit mission.

 

Remember, the validation runs are the important part. Virtually no amount of code review/analysis can give you anywhere near an indication of simulator functionality as compared to simulator output evaluated against empirical data; the simulation is either going to produce reasonable results or not.

 

The output includes a complete time history of the launch (and orbit), including altitude, velocity, vehicle and propellant masses, computed losses, attitude tracking data (such as pitch attitude and in-plane central angles), staging events, and other information.

 

 

 

IMPORTANT: Want to test your own rockets through the simulator? A version that will allow end-user modifications of the rocket parameters and GNC/ACS commands (via external scripting) may become available upon request (if there's enough interest) with a small additional donation (perhaps $50-$100). After seeing the simulator output, let me know if you would like something like this and I'll consider it (your original donation will be applied to the subsequent donation in this case).

 

Source code is NOT included (in any version), but can be requested with a $5000 donation (like the compiled software itself, it's also protected by copyright and may not be distributed – it's available for review only (not commercial use)).

 

 

 

Note again that you cannot get this information anywhere else, period. To the best of my knowledge, I am the first (and only) person (on this planet at least) who has done such a detailed, in-depth study on the subject of microscale launch vehicles and their feasibility (going on decades now since I first did it). To the best of my knowledge, I am also the first (and only) person to have shown such feasibility mathematically. And, to the best of my knowledge, I am also the first (and only) person making source code (that's adequate for such a feasibility analysis) available to the general public.

 

While others have thrown out all manners of hand-waving, pie-in-the-sky figures, wild-ballparks and hypothetical speculations on possibility, impossibility, or whatnot, I've actually done the numbers and the hard grinding.

 

Bottom line... If you're the least bit interested in microscale spacecraft and launch vehicles, you need to examine this feasibility treatment.

 

 

And remember, when you donate, you're supporting the decades of research, calculations, experimentation, simulation, analysis, and testing which has gone into building the experience and knowledge base necessary to succeed in this effort – and that's in addition to all the ongoing work happening every day.

 

Each and every penny of your donation will be used to further our efforts; this includes our education and outreach programs as well as the LMR launch vehicle and satellite. So, you'll really get a lot of societal return for a little support.

 

Please show the world that this kind of independent research and development work is important and support our cause. Your symbol of support will go a long way.

 

 

 

 

The $1000 Challenge!

 

Challenge:

The first person who can prove clearly and to my satisfaction that a 120 kg GLOW launcher cannot put a 20 g payload into orbit (no matter how well it's built) will get $1000 cash.

 

Eligibility:

Open to all individuals who have obtained the feasibility treatment via an LMR donation.

 

No gimmicks:

This must comprise a technical/scientific proof (not one of logistics, monetary, and/or legal considerations); it may be informally written (similar to my feasibility summary document) and of any length (but as short as possible). Please don't try tricks to wrangle the $1000, it won't work. For instance, it cannot be some typo in my calculations, some bug in the simulator, or some obvious, non-fundamental mistake or whatnot, it must be a clear proof (and to my satisfaction).

 

Comments:

Though I'm confident no one can do this (because I've obviously already done the analysis and such a launcher can certainly be built), if someone does find something I've overlooked (or otherwise some fundamental error) which invalidates the overall feasibility of such small scale launchers, present your proof to me before anyone else does and collect your $1000 (and save me a ton of money in additional R&D over the next year (while also proving me wrong, if you're into that sort of thing)).

 

Oh yeah, I also reserve the right to make any and all final decisions, change/modify the challenge in any way and/or at any time, and/or cancel it at any time. I'm certainly not intending to do any of that, but thought I should note it.

 

 

~Sage

 

*LMR-A/S3-HG overview slide available upon request with a $20 donation

 

 

 

 

 

By the way (and I really hate to do this):

 

Important Notice and Legal Disclaimer

 

Neither LMR, it's affiliates, nor I guarantee the accuracy, adequacy, completeness or availability of any information; this includes any errors or omissions or for the results obtained from the use of such information. WE PROVIDE NO EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, ANY WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE OR USE. In no event shall LMR, it's affiliates, nor I be liable for any indirect, special or consequential damages in connection with the use of our information and/or software.

 

Please note that the information contained in the Quick and Dirty Feasibility Treatment (including the overview, simulator, and/or any supporting documentation, software, and/or other materials, herein collectively referred to as the “Quick and Dirty Materials” or the “materials”) is informal and based on my own personal research and experimentation; there are no guarantees as to the completeness and/or accuracy of the information contained therein and there are no guarantees nor warranties of any kind (express or implied); this includes (but is not limited to) errors and/or omissions in the documentation (and/or software) or any warranties of merchantability or fitness for a particular purpose.

 

The informal Quick and Dirty Materials are strictly for informational purposes only; LMR (and it's affiliates) and I shall in no event and under no circumstances by liable for anything you do with the information, simulator, or other materials; this includes any special, indirect, consequential and/or other damages that may result form the use and/or misuse of the information, simulator, and/or other materials (this includes anything and everything, without limitation, including items such as lost data or otherwise). Your use of the information, simulator, and/or other materials is completely AT YOUR OWN RISK.

 

Although I've done due diligence to insure that the simulator is safe for use, if you run it and some bug trashes your hard drive, you've been warned – use it completely at your own risk and peril.

 

In addition, these materials may not be leased, sold, rented, exposed, or otherwise distributed in any format whatsoever (including hard-copy and/or electronic formats), nor may any derived works be produced from these materials, without the express written consent of the author (that would be me). All works are protected under copyright.