Thursday, June 10, 2010

Spaceship Design 103: Quick & Dirty

Reader JP emailed to ask about the practical sequence of spaceship design, where 'practical' means suited for created settings, stories or games, not spaceworthy for actual travel. In other words, do not try these tricks anywhere but at home.

And if you haven't done so already, this is a good time to consult relevant sections of Atomic Rockets, including the handy page of equations (from which I also swiped the image above).

JP writes:

I get the feeling that there's a specific order that I have to go in in order to determine the following:

-Propulsion system specific impulse
-Available payload capacity
-Propulsion system mass flow
The short answer is there is no one 'right' way to attack this interlinked web of performance traits. Acceleration (thrust), specific impulse, and propellant flow are all very closely tied together, along with propellant fraction, which in turn constrains payload. Drive power density is also in this mix, constraining acceleration on the one hand and payload fraction on the other.

Define one parameter and all the others can vary around it. Define two parameters and the rest become much more constrained. Each defined parameter reduces the degrees of freedom for the remaining ones, until you lock it down. Great in principle, not so helpful in practice. I have my own approach and rules of thumb, shaped by my workflow habits and biases as well as mission requirements. But I gotta say something, so here goes:

The first parameter of all is mission delta v - how fast you want the ship to go - because that will drive everything else. After that, start is with parameters that are fixed by your techlevel, because that sets the ground rules that possible designs have to play by. And the parameters that are most fixed by techlevel are specific impulse and drive power density (power/mass ratio).

For chemfuel, both of these are sharply defined. Specific impulse (for H2-O2) is about 450 seconds, or 4.5 km/s exhaust velocity, and power density is on order of 1 MW/kg. Chemfuel engines put out such prodigious thrust relative to their weight that you can pretty much ignore drive power density (and therefore engine mass) unless you intend multi-g acceleration.

Example 1: Suppose an orbital 'gunship' with 5 km/s mission delta v, and an H2-O2 chemfuel drive. Total mass is an arbitrary benchmark (you can have big ships or small ones), but let us say 100 tons full load mass.

Right off the bat we know that full load mass ratio must be 3.04, a value determined by mission delta v, specific impulse, and the basic rocket equation. This means that out of our 100 tons departure mass, 67 tons will be propellant, the remaining 33 tons everything else - engines, fuel tankage, ship structure and equipment (including crew), plus payload.

Old Sir Isaac tells us that 1 kg of propellant burned in these engines in a second produces 450 kg of thrust (~4500 Newtons, for the picky), with a thrust kinetic energy of 10.125 MJ. Suppose we want a maximum acceleration of 2 g, requiring 200,000 kg or 2 MN of thrust. We need to burn 444 kg/second of propellant to get, which will produce 4.5 GW of effective thrust power. By my simple rule of thumb the engines will have a mass of 4.5 tons.

This performance requirement happens to be very close to that of a Space Shuttle Main Engine, SSME, now verging on retirement. It has a mass of 3.2 tons, but turned out much less rugged than hoped, so I'd stick with 4.5 tons for a combat capable engine.

That leaves 28.5 tons for the rest of your ship. Say 7 tons for fuel tankage and fittings and 5 tons each for overall structure, equipment, and crew pod including the crew, leaving 6.5 tons for additional payload such as a weapon pod.

A couple of things to note. As you burn off propellant, performance increases. Once this ship has burned off half its fuel, acceleration is 3 g, and the ship has about 3 km/s of delta v remaining. Assuming your mission involves going somewhere, blowing someone up, and returning, your combat acceleration will be higher than full load acceleration, something to remember in design.

The other thing to note is that you cannot overload a ship in space. It will not sink, crash at the end of the runway, or even bottom out its suspension. It will merely be sluggish. Thus full load, maximum load, or whatever you call it, are all really terms of art, and for some ships will be almost meaningless - for example a drive bus, that can be mated to a small payload section for fast travel or a big payload for slow hauling.

Example 2: Now suppose a deep space ship, such as the one I outlined last post for travel to Titan. In that case I first specified a 'travel speed' of 100 km/s, corresponding to a mission delta v of 200 km/s.

I assume some sort of 'plausible midfuture' nuclear-electric plasma drive, without going into details, even fission v fusion. Drives of this type need not have a fixed exhaust velocity (specific impulse). The maximum is very high, hundreds or even thousands of km/s, but these drives lend themselves to VASIMR style variable specific impulse. The key techlevel parameter is power density, how much oompf you can fit into a given mass.

But for this discussion I leave techlevel itself a bit open. Instead I pick an exhaust velocity of 200 km/s (~20,000 seconds Isp), equal to mission delta v, and specify an average acceleration of 1 milligee. Departure mass is, arbitrarily, 1000 tons.

Since mission delta v and exhaust velocity are the same, we know that the mass ratio is e, 2.72. Thus our ship departs with 632 tons of propellant, and the ship itself (plus payload) has a mass of 368 tons. Acceleration will increase as fuel is burned off, so let us say that full power delivers 600 kg of thrust, or 6 kilonewtons. Departure acceleration is thus 0.6 milligee, while acceleration at fuel exhaustion is 1.63 milligee.

Burning 1 kg/second in the engine described produces 20 tons of thrust, and requires 20 GW of power. So to meet our requirement we will burn 0.03 kg/second, and our drive engine puts out 600 megawatts of thrust power. (Last post I said 10 GW, because I was working really quick & dirty.)

Suppose that our drive tech can develop 10 kw/kg - much less than chemfuel rockets, but comparable to jet engines, and about 100 times better than a first generation nuke electric drive might put out. Thus our drive engine must have a mass of 60 tons, including shielding and radiators, leaving 308 tons for the rest of the ship. Hydrogen propellant is bulky, and you'll need a cryo system for long missions, so let the fuel tankage be 20 percent of fuel mass or 74 tons, leaving 234 tons. Say 34 tons for structure, 50 tons for equipment and fittings, 100 tons for the hab, including crew/passengers, leaving 50 tons for additional payload.

We can also cross check a few numbers. With fuel consumption of 0.3 kg/second it will take 2.11 million seconds to burn through all the propellant and reach 200 km/s, and our actual average acceleration is 0.95 milligee. Close enough for quick & dirty!

I previously wrote about spaceship design in general, and life support. (Connoisseurs of SEO spam may note that this last post gets more spam comments than any other - perhaps the combination of design and life.)

Update: Commenter nqdp did some head scratching about my deep space ship's drive engine, and when I checked I found I'd committed multiple brain dead errors, adding or dropping zeroes, that ended up with a correct result - so long as you didn't check too closely. I have fixed the errors in the main text, but for the sake of completeness here is the original section, with errors lined out:

Since mission delta v and exhaust velocity are the same, we know that the mass ratio is e, 2.72. Thus our ship departs with 632 tons of propellant, and the ship itself (plus payload) has a mass of 368 tons. Acceleration will increase as fuel is burned off, so let us say that full power delivers 6 tons of thrust, or 6 meganewtons. Departure acceleration is thus 0.6 milligee, while acceleration at fuel exhaustion is 1.63 milligee.

Burning 1 kg/second in the engine described produces 20 tons of thrust, and requires 20 GW of power. So to meet our requirement we will burn 0.3 kg/second, and our drive engine puts out 6 GW of thrust power. (Last post I said 10 GW, because I was working really quick & dirty.)

Suppose that our drive tech can develop 10 kw/kg - much less than chemfuel rockets, but comparable to jet engines, and about 100 times better than a first generation nuke electric drive might put out. Thus our drive engine must have a mass of 60 tons, including shielding and radiators, [and miraculous save, dropping a zero to end up with the correct result] leaving 308 tons for the rest of the ship ....

Well, I did say only to try these tricks at home!


Unknown said...

Another route to quick and dirty designs - The GURPS Spaceships PDF series. Very well thought out, designed by a guy with a degree in physics, and simple to use. You can design a realistic and fairly detailed craft in less than half an hour. It also talks about how to tweak the rules to better reflect your own setting. For those of use with the math skills of squirrely roadkill, it's a great tool.

Sabersonic said...

And for the exemptionally lazy and/or time limited, there's always the Online GURPS Spaceship Calculator. Granted, it helps to have the PDF (and in my case, the softcover core book) to know exactly what you're adding onto your spacecraft.

But back to the topic at hand, nearly all realistic spacecraft designs are dictated by the DeltaV the spacecraft is expected to perform, the power to mass ratio to calculate exactly how much of the mass is "payload" over propellant and/or fuel, and the ISP of the drive(s) themselves. Everything else, arguably, are secondary and naturally flow from those corner stones. Well, at least as far as I can figure.

But as for "pratical" designs as JP inquires. Well, for the really lazy one can go the Hollywood route and havie the ship do whatever is neccessary for the plot and/or setting with the ratio of realistic to handwavianism depending upon how much one is able to keep the tension of suspense. Granted, such a design philosophy has earned the ire of the rest of the scientific community, but it did work for a majority of the visual media entertainment industry.

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Citizen Joe said...

One of the things I've noticed is the way everything can be bootstrapped and worked backwards. For example: If you want to put a beacon on the Moon. Start with the mass of the Beacon, that is the payload. Now create a means to place that on the moon, which would be some sort of lander. Lander plus beacon would be payload prime or pl'. Now you need to get from Earth orbit to lunar orbit, so that gets you pl'', etc.

To paraphrase:
"A journey of a [billion] miles [ends] with a single step."

Byron said...

I have to agree with Joe. Actually, I'd take it a step farther and say that you have to define what you want to do first. That includes deltaV and payload, along with any acceleration requirements. The rest of the numbers flow from there. Deciding on loaded mass first is putting the cart before the horse in a big way.
On the other end of the spectrum from "quick and dirty" I spent the whole of last semester designing a spaceship for an independent study. This included a paper and a video.
The paper is available here and the video can be found here.
I would not advise doing something like this unless you're comfortable with basic calculus and a CAD program.

Anonymous said...

Quick and dirty spacecraft design? OK! I always start with what the spacehip will do; after all, you'll have different basic assumptions about a rocket passenger ferry for Earth surface to orbit and back than you would for a spaceship capable of going from Earth to Saturn orbit and supporting a long-term scientific exploration of Titan. I'll use an example of an auxilary light cruiser (a part-time warship that is normally used as a civilian transport). Now, I have a starting point. This ship needs to beable to go from orbit to orbit; it needs to have a long crew endurace, so needs a spin hab; it has to have a large/multiply power plant (I'll use a small reactor, two solar panels, and an emergency fuel cell system); It needs several redundent heat radiators; armor and heavy radiation protection; high proformance, rugged engines (I'll use VASIMR-type plasma engines); a larger-than-usual electronics/sensor suite; twice as many manuvering thrusters as minimumly needed; several 'plug-in' slots for weapons (they can be used for cargo during normal operations). Now, does this ship need to be able to go from Earth orbit to Mars orbit and back, or does it need to be able to go from Venus orbit to Earth orbit to Mars orbit and back to Venus orbit before it needs to be refueled? During war-time should it be a lone cruiser, a convoy escort, or operate in a wolf pack? Should it operate alone or in a convoy during peace time? Answer those questions and you know where to start as far as capabilities.
Engines and manuvering, heat-management, hab-command-life-support, propellent stores, power plant(s), and mission modules; assmble those and you've got a spaceship. Whether it works or not is in the details.
From the others who post here, they all start with the engines/Delta V/propultion; I, personally, think that what the ship is supposed to do is what should be the starting point.


Byron said...

I'm not sure that said auxiliary cruiser is practical. Any armor added to a civilian ship is just less payload mass. My Aurek, despite being a good candidate for warship conversion, and designed to allow it, has no armor.
My steps to quick-and-dirty starship design.
1. Decide on payload and mission deltaV.
2. Figure out empty dry mass.
3. Mass ratio.
4. Engine mass.
5. Other masses.
Most masses can be approximated fairly quickly. When I was in initial design, I used a lot of "rules of thumb" to guess at the mass. I assumed 500 tons payload, 250 tons dry mass (100 tons engine, 50 tons structure, 100 tons other), and an 8-hour brachistone from Luna to Earth. That, along with engine calcs, gave me the needed engine specs, which then allowed me to nail down the others.
It's odd, but for 90% of a ship's systems, it doesn't matter what they do or how they work, all that matters is the mass. The only things that require more thought are structure, engine, radiation shielding, and possibly weapons.

Anonymous said...

The armor is added on, along with the weapons...sorry I didn't make that clear.
However, I still think that figuring out what a spaceship can do before you decide what that spaceship is going to be used for, is putting the cart before the horse...your Aurek is an amazing example of workmanship and practical design, but I'm sure that you didn't design the ship and then decide what you'd use it for. I'm just sayin':)


nqdp said...

It might be plausible to say that in some situations, total mass could be a limiting factor. For example, we can only lift 500 tons to orbit before the next Martian transfer window closes.

In the spreadsheet that this post inspired me to make, though, you have to enter cargo mass, ship empty mass, and delta-v before you get fuel mass and total mass. I figure my numbers work because they match Rick's in both examples.

I didn't really follow how Rick estimated engine mass, though. Actually, I think I'm just confused because he seems to be mixing units with reckless abandon, and I gather that higher acceleration = fuel burned faster = bigger engine. Could anyone explain it a bit better?

Rick said...

Cool paper and video!

The GURPS geeks have evidently done a lot of homework on a range of subjects. I seem to recall looking at their galley rules, and while I could find some quibbles, they were a pretty good guide to oared ships.

Byron's design sequence is not unlike mine, and anyone who does this a few times will come up with a number of rules of thumb.

nqdp, your problem in following my engine mass calculation is very simple: My calculation was bogus.

It had multiple bonehead factor of 10 errors that managed to offset to produce a correct final result for engine mass and ship acceleration, but misstated thrust and drive power.

I said to only try these tricks at home!

Now I'm off to correct my work on the front page! :-)

Byron said...

Ferrell - No, it was designed as a high-speed armed freighter, initially in a period of pirate issues.
nqdp- Yes, that could happen, but 90% of the time, you can start with payload and dry mass. Honestly, one of the biggest problems is estimating dry mass.
Rick - Yes, I can see and find said rules of thumb. The difference is that I went all the way through with them. I'm actually working (slowly) on other ships now.

Rick said...

Dry mass is tricky, because it is basically an engineering consideration - how much structure you need, plus auxiliary equipment. It doesn't have a theoretically elegant solution like the rocket equations.

Citizen Joe said...

Dry mass should still be calculable. You would still need a configuration decided ahead of time, for example spherical or cylinder. But you just factor in much of the "can't be any smaller" components (like computers) into the payload. Then engines, skin and structure are based on proposed acceleration and thus would be some proportion of total mass.

If I were to spreadsheet something like that, I'd run a couple of columns so that there would be calculated mass and then dictated mass. That way you can plug in actual real world components into the model if you know those values.

Byron said...

The problem is that finding those values takes time, and most people just want numbers. It depends on the level of detail involved in the design, and the level of realism desired. For example, I basically made up a number for the Aurek's electronics, as I was tired of trying to wrestle new fields into submission, and didn't want to try to learn communication theory as well.

Albert said...

Citizen Joe said:
"Dry mass should still be calculable."

I am struggling to make up some decent approximations for a personal project. So far I had a look at modern rockets and they are all around 0.05 Kg of structure per kg of total mass (propellant included).
Shuttle's external tank (no thrusters, avionics and little non-structural mass) is 0.036 kg of structure per kg of total mass.

A quick look at the Apollo command module revealed that about one third of its 5 tons is structural mass. But I haven't looked a lot into the habitat module businnes yet.

These things must resist a lot more stress (a liftoff at around 2 Gees and a reentry for Apollo) than the average space-only ship with milligee acceleration, but they can be considered a "higher limit" imho.


Rick said...

Welcome to another new commenter!

Repeating my comment on SFConsim-l, space boosters are extreme designs, which is why the whole business remains so dicey.

That said, I wouldn't be surprised if the pure structural shell comes out to perhaps 10 percent of load mass. In my example I came up with 108 tons structure plus fuel tankage for a deep space ship of 1000 tons load mass. But I also allow 100 tons for the hab, mostly for structure and equipment.

Thucydides said...

Atomic Rockets has several sections which delve into design, a person with some time and the various tables can design a suitable spaceship for almost any purpose (extreme designs like exploring the surface of Venus and boosting back to orbit or hypersonic ramscoops for mining Helium3 from gas giants excepted).

The nice (or annoying) thing about spaceship design is that in one sense it almost does not matter what you do. Your payload will get there sooner or later, either by a blaze of gamma radiation from the antimatter drive or drifting along the various gravitational fields between planets. Most of your other decisions are bound by your time frame, a manned spaceship using gravitational highways would have to devote a huge mass to life support, while the antimatter drive might need a similar amount of lead shielding to protect the crew.

An extreme example is from an old Jerry Pournelle story, where the hero uses a hot water heater to boost from one asteroid to another in a cloud of steam and ice crystals. Try doing something like that on Earth outside of an episode of Mythbusters!

I would expect that spacecraft, like cars, ships and aircraft, will settle on some sort of common design factor based on a combination of cost and utility. There may be a few extreme examples outside the box for special purposes, but just as jetliners follow the form factor poineered by the Boeing 707, or cars have evolved from the Ford Model T, the spaceliners and cargo pods of Uranus will be very similar to the ones built around Mars

Albert said...

Thucydides said...
"Atomic Rockets has several sections which delve into design, a person with some time and the various tables can design a suitable spaceship for almost any purpose"

I beg to disagree. AR talks a lot and is quite informative, but the numbers needed to actually design things are scarce. With very limited tinkering capability.

"the spaceliners and cargo pods of Uranus will be very similar to the ones built around Mars "
If they are both meant to travel between inner and outer system you are probably right.

I think that there will be 3 kinds of ships:
-Inner system, they use solar power and are overall optimized for inner-system use. Maybe better particle shielding.
-Outer system, nuke-powered, and overall optimized for outer system.
-Multitask, nuke-powered, very long endurance and able to cope with both inner and outer system.

I think the inner system ships will be the cheaper, outer system ones are middle ground, and the multitasking ones are pretty expensive.

Mostly due to bigger weight and more expensive hardware needed.

If we add "moonhopper" class, meant for use in a planet-moon route only (so it will be very probably a rocket) that's probably the cheapest kind.


Byron said...

I have to agree with Albert on this. Atomic Rocket is a great site, but honestly, I used it more for the links then the actual data. It's a good starting point if you're trying to create a realistic ship for a story, but less so if you're trying to actually design one.
On common standards, I sort of agree. Though in Duel of the Buffoons, my private universe, it doesn't quite work that way, I expect that standard containers will be used for just about everything, and that ships will be built to carry them.
The problem with the "common form factor" is that the constraints that push towards those are largely absent. Airliners use that layout because it's the best for high-subsonic cruise. There is no stuff like that in space. Still, ships of the same class will probably look similar, with an engine, a central spine, and container anchors.

Byron said...

Also, if you wish to see the Aurek report, I've replaced the document, so you can link to it from my blog.

Anonymous said...

It might become common for spacecraft to be moduler; choose a suitible hab/command module, power/propulsion module, and a mission module...just mix and match for whatever mission profile you need; most commercial spacecraft would be multi-modular. Only special purpose spacecraft would be "unibody" construction.


Citizen Joe said...

Spacecraft assembled in orbit will very likely be modular. Reentry vehicles will not be modular.

Rick said...

Per Albert's remark, not enough attention is paid to the importance of solar distance. Solar electric has big advantages in the inner system, but fades out much past Mars. Hab sections will also have different design considerations - especially if you're operating inward of 1 AU, and keeping the hab from overheating becomes a serious issue.

My bias has long been toward modular or at least semimodular construction, but not for atmospheric entry vehicles! (Or ships that use aerobraking/aerocapture.)

But in a lot of respects you have much more freedom with spacecraft than with terrestrial vehicles. Compare Apollo and Soyuz as early examples of how much outward configuration can vary. I think of spaceship design as rather akin to architecture.

Another possible historical example is the bridge and mast structures of big-gun era battleships. Overall requirements were similar, but designs were not significantly constrained by aerodynamic factors, and national styles became very distinct - British tripods, US cage masts, Japanese pagoda masts, etc.

Albert said...

Somewhat humorous how-to. :)


VonMalcolm said...

Nothing to say: I am just 'bookmarking' as to be notified for future comments via Gmail!