Wednesday, December 28, 2005

Hohman Transfer Calculator

Here's a little thing I put together a few nights ago. Nothing profoundly useful or complicated about it, though it may come in handy. It's an excell spreadsheet used to calculate the total delta v and transit time to make a hohman transfer between two circular orbits.

Hohman Transfer Calculator

Tuesday, December 20, 2005

The Moon-Comet Run

The need for Hydrogen

One of the main problems with living on the moon is a lack of hydrogen. The moon doesn't lack in oxygen (in the form of various metal oxides, not to mention sand). It doesn't lack in carbon (various carbonates). Nitrogen should be easy enough to obtain from Earth's upper atmosphere if it's not already present in lunar minerals. But the moon is almost entirely devoid of hydrogen. Without hydrogen, you don't get water, you don't get nuclear thermal rocket fuel, you don't get engine grease, adhesive, oil, ect. That’s why NASA is looking for polar ice deposits so hard.

The moon has a very very small trace amount of hydrogen in the regolith (parts per million). All the rest of it has boiled away. It may be possible to microwave that hydrogen out of the soil and collect it by covering a lot of surface area. This would definitely be a non-renewable limited resource: not the type of thing you want to blow away by the ton as rocket fuel. This can probably be enough to support a base in the early phases of settlement, assuming an efficient extraction vehicle is developed. However, the primary attraction of setting anything up on the moon at all is as a way-station and shipyard for expansion further out in the solar system. Without a source of rocket fuel, the moon is about as useful as a space station – not very.

Note -- the moon probably can function as a source of rocket fuel for nuclear electric ion engines. Ion drives usually can be designed for a wide variety of ions. Because no direct thermal expansion is involved, ion engines don’t need to use low-molecular mass fuels. In fact, heavier ions are easier to ionize. However, the type of engine I had in mind for fueling was a nuclear thermal engine. Nuclear thermal engines produce moderately high thrusts (much more than you’ll ever get out of an ion engine) at very nice Isps (800-1100 sec or so). But they need hydrogen for fuel, or their Isp and thrust quickly spiral down the toilet. (Exhaust velocity (hence Isp) scales roughly with the square root of molecular mass) For manned missions, a NERVA engine can get you where you need to go blazingly fast at nice mass fractions.

One of the suggested sources of hydrogen for the moon is to mine near Earth comets. In this post, I want to take a look at the logistics of making a moon to near Earth comet run.

Delta V Requirements to get there from the Moon
Or, more poetically: Catching the Comet

First of all, one of the things about the inner solar system is that, unless you are under an atmosphere, water sublimes away. That’s why the moon doesn’t have ice covering its surface like the outer solar moons do. So “near Earth” comets don’t stay near Earth for very long – or they would be gas clouds. They usually orbit the sun at very high eccentricity (having their source in the Kupier belt at 30+ AU from the sun). This means that any mining that takes place is not going to be a fixed base operation. A ship will have to go to a comet, do it’s business, then get back to the moon, and wait until another comet passes by. (Unless you feel like waiting 300 years for your equipment to come back into the inner solar system.) That’s okay though, because there are thousands of near earth objects, one is bound to be in the neighborhood any given year or so.

The dv requirements for meeting up with a high eccentricity comet are quite high however.
- The Earth-moon system orbits the sun at 1 AU. (1 AU is about 1.496E11 meters).
- The sun’s mass is 1.99E30 kg.
- Newton’s Gravity constant is 6.67E-11 Nm^2/kg^2

Suppose a comet happens to be passing by Earth’s orbit (1AU) from it’s home of 30 AU. Semimajor axis is 15.5 AU. Eccentricity is 0.935. Earth is going sqrt(G*Msun/Rearth) = 29786 m/sec tangent to the sun in it’s orbit. The comet, on it’s close approach will be going sqrt(G*Msun/Semimaj*(1+eccin)/(1-eccin)) = 41439 m/sec. This means to catch the comet, an increment of 11650 m/sec in your velocity is required with respect to earth. This is only part of the dv requirements though.

Let’s suppose our hypothetical comet miner is nuclear thermal powered itself (so that it can use the fuel it mines, among other things), and its mission is to take off from the moon (1600 m/sec), break Earth orbit (1439 m/sec from the moon), rendezvous with the comet, then use it’s nuclear engines in a power producing mode to power a hydrogen electrolysis factory. (Water is only 11% hydrogen by mass. It’s far more efficient to transport only the hydrogen). The hydrogen is liquefied and stored in fuel tanks onboard the vessel. Then the fuel miner accelerates back towards earth, re-enters the earth-moon system, and lands back at the moon. Also throw in 800 m/sec for maneuvering.

For the outbound leg, about 15500 m/sec dv is required. For the inbound leg, another 15500 m/sec dv is required. This is an extremely fuel expensive mission, even though we’re not leaving the inner solar system. (We could, assuming we get stranded near the comet on a trajectory out past Pluto). This is another reason why the high fuel efficiency of nuclear thermal is preferred over chemical propulsion.

Iteration 1 Vehicle IdeaThis vehicle will be sized according to the inbound leg. Since no one’s yet built a nuclear thermal rocket ship before, I’ll have to pull a few numbers out of my head.

The NERVA program back in the 60’s created and tested a series of nuclear rocket engines. These engines vastly outperformed even modern chemical engines in terms of fuel efficiency. They were intended as part of a program for upper stage and in-space vehicles to expand our presence in the solar system. A Saturn V with a NERVA upper stage could deliver a whopping 500 tons to LEO, and similarly massive amounts of cargo throughout the solar system. Unfortunately, the program was canceled in 73.

The NERVA engine weighs 30 tons. (I use metric tons btw. I’m using at as an abbreviation for 1000 kg). Even though NERVA 2’s Isp was 820 sec, recent material advances could probably push the operating temperature way up (uranium carbides, or other uranium ceramics could operate hotter without melting). This could lead to 1000 sec Isps in theory. I’m going with that, because it makes the final rocket look nicer.

Let’s also throw on a 10 ton computer/communications/hydrogen electrolysis payload.

Let’s say that since these fuel tanks will primarily operate under low acceleration – the weightlessness of space, or landing/launching from the moon, that they won’t need to be as structurally robust as our launch vehicles. A fuel tank propellant mass fraction of 0.95 will be used.

The Mass ratio required for the return leg is 0.2058. The payload fraction is 0.1640.

Let’s assume, for initial estimation’s sake, that we’re going to mine 500 tons of hydrogen off the comet as payload, and the rest as fuel. The rocket needs to mine a great enough weight in hydrogen off a comet to make up for it’s reactor and vehicle mass on a trip returning to a comet. Since it will use the very fuel it mines to get back to the moon, unload a fraction of it’s payload, and use the rest to get back to another comet, the percentage of payload that it can unload on the moon is proportional to the hydrogen payload to rocket systems mass ratio.

That 500 tons of hydrogen will also require 2615 tons of hydrogen to push it to the moon. It will also require 137 tons of tanks and structure.

The rocket, upon arriving and landing back on the moon can afford to unload 306 tons of hydrogen to a lunar base. It will need 194 tons of it’s payload to take back off and go chase another comet. 61% of the payload can be unloaded to the moon for other uses.

Looking at this vehicle more closely:

This rocket is a massive construction. It would make sense to invest in it only if you intend to run multiple missions from the moon to refuel interplanetary rockets. The nuclear reactor and the rest of the complex equipment would have to be launched direct from Earth. Hopefully there will be a way to construct the tanks and other structure (the “dumb” inert mass) using native lunar materials. This would require some sort of metal processing plant and construction yard present on the moon. A serious space effort would be needed to justify the moon comet runs.

On the positive note – if your space program is large enough to accommodate a moon-comet run, then it will become far easier to fuel your spacecraft. Hydrogen fuel from the moon can be used to power Earth-moon system tugs, and re-usable cargo vessels to Mars and elsewhere in the system. The moon can get not only hydrogen from comets, but also nitrogen and carbon, materials that should also be present in the ‘dirty snowballs’.

The file I used to play with the variables: Comettrip.xls

Thursday, December 15, 2005

Why Colonize Space? Part 2 of 2

3. What do we have to gain from humans in space?

Short term – not much beyond basic research

I’ll be the first to admit that, in the short term, it’s a daunting task to find a compelling reason to go. Economically, even the best prospects seem incredibly inefficient compared with developing an equivalent industry here on earth to serve earth’s population.

The argument that we’re running out of resources here on Earth is not a very convincing one. In terms of material resources, such as metals and rock, the type of resources we are likely to find in space, Earth has thousands of tons per capita available in readily extractable deposits. We simply are not going to run out of these. Rarer metals can be recycled quite easily from scrap (in fact, more easily recycled in some cases, than mined and refined). We may run out of oil, but we aren’t going to find oil in space anyway. We have sufficient deposits of uranium for the forseeable future. In terms of biological resources – we, the breadbasket of the world, aren’t using the majority of potential farmland available to us, and if we wanted to we could increase yields many times over using genetically modified crops, or farming more efficiently. Using crop rotations, we can harvest any reasonable quantity of wood needed and have it grow back in a decade or so. Pine trees are a type of weed anyway. And how are you going to do any of this better inside a space-limited dome on the moon or Mars?

The planets and moons available to us are stark barren wastelands. In the inner solar system, in terms of material resources available to a colony, you have variations on the theme of rock. Antarctica presents a friendlier face for would be colonists.

There are some methods that a space colony might have of generating income. These aren’t necessarily business-plan quality economic justifications of a space colony, but they can generate some cash and begin to pay back the earth for shelling out the resources to colonize.

A moon colony could build reflective mirrors out of the silicon and titanium in the lunar soil, run giant solar thermal plants, and beam the energy back to earth via a microwave or radio pulse. This would probably require relay satellites in geosynchronous orbit. Even though you could generate energy more efficiently by just building nuke plants on Earth, the Earth will never have a shortage in demand for energy. It will always be something that pays, for as long as civilization does industrial work. At present average prices (8 cents per kW-h), 10 GW of electricity would give you $200/sec. Of course, the inefficiencies involved in transmission might necessitate that a 10GW antenna on earth equate to a 100GW plant on the moon. But hey, $7 billion/year wouldn’t be anything to sneeze at. Already half NASA’s budget.

There are some interesting small-scale things we can do in zero gravity. We can reliably produce metal foams with small bubble geometry and no directional bias. We could conceivably produce some sort of biological products. That was the intent of some of the ISS experiments. If we could find something that we could only accomplish in zero-g, we could then justify a lunar colony on the basis of providing raw material to orbital factories. But I haven’t heard of anything yet. We need to get up there and start tinkering.

Medium Term

What is the purpose of running? It expends your body’s resources. It tires you. It requires your best efforts and exertion. But afterwards, you become fit. You learn to tolerate pain. You learn what you are capable of and what is required of you to perform. You are less prone to deteriorating health due to lack of exercise.

My argument is that in the medium term, exerting ourselves nationally to overcome the obstacle of space colonization will make our air and space capabilities fit, innovative, diverse (if the funding given meritocratically, which is going to be a bit of a challenge, in light of history). It will drive progress. It will also ensure that we maintain the ability to perform as we do. It’s harder to backslide technologically while pushing ahead. Basically, this is a rehash to my response to question 2.

Long Term:

In the long term, assuming that civilization confines itself to Earth, it will eventually (more distantly than in the immediate future, or even this century, but eventually) enter a zero sum situation. Probably not in terms of resources, but in terms of culture, in terms of what individuals can hope to build and achieve without stepping on each other’s toes. It would become a zero sum game in terms of what the best and brightest, most motivated could apply their efforts to. One company’s engineering achievement, say, a new jet-liner, could put thousands of aero engineers out of business for decades – because eventually in such a world, only one would be required to fill the entire niche. Without new industries being generated, or new products agitating the market, it would become a zero sum game in terms of the diversity of products and services. Expanding societies are healthy societies. Those that lose momentum tend to start caving inwards. There’s nowhere left for innovation to go, to grow to, away from the established society and culture, but up.

The solar system has the advantage of being absolutely huge. If we begin to develop a civilization that expands there, it will be long before we run up against similar boundaries.

Eventually, the probabilities are very small, and yet eventually, there may be another major asteroid strike on Earth. There are thousands of asteroids that orbit within the inner solar system. Our rather shell-shocked moon provides a myriad of examples of what a collision can do. 100 mile wide craters, the works. Defending Earth would be the ideal response to such a situation. Without a competently space-faring civilization capable of finding such asteroids on time, and sending enough H-bombs their way to vaporize them, we’ll probably end up being caught by surprise with minimal response time, and with no long distance launcher like the Saturn V to lob anything at it. We’d have to hope in a last minute explosion breaking the object up enough for our atmosphere to absorb the matter. It could still cause widespread damage (1000 1-mile wide craters vs 1 100 mile wide crater + massive secondary effects from shockwaves/tsunamis/ect).

A space faring civilization, one that has developed the capability to survive on bare rock and raw materials, that has refined it’s construction to the point where it can operate independently of nature, is a far more resilient civilization than exists at present, just as our civilization is a far more resilient civilization than the ancient Mycenians – who were forced into mass migration and invasion because of a climate change. Our technological development has enabled us to deal with more and more situations and disasters, and to inhabit and thrive in greater and greater regions of our world (not to mention thrive to greater and greater degrees). The ability to colonize space would mark a turning point in that, given raw material, we could conceivably survive anywhere. We would become, not just conquerors of new environments, but builders of our own environments. (Of course, we still have to do the work of getting to this point).

For that matter, we would also have the capability to expand to just about anywhere as well. Anything that could conceivably happen to Earth would not destroy a space-faring civilization.

(An additional, though somewhat odd point: a space-faring civilization would be immune from cultural nihilism and civilization collapse. Any degradation below a minimum competence in dealing with the environment, as well as any philosophy bent on opposing or destroying man’s constructive nature would result in death, hence would engage people’s survival instincts in preserving civilization. Perhaps this wouldn’t be total immunity, but I’d be surprised if a country run like Soviet Russia or North Korea could survive in space given that their people have or had a hard enough time surviving on Earth!)

Finally, in terms of the larger universe as a whole: While I hope life is abundant – that it resides wherever it possibly could reside, and that planets like Earth aren’t so very rare around other stars, we still have to face the fact that most of our own solar system is inhospitable to life, and that there is likely a large ratio of the wider universe that is also absolutely barren. Life has managed to conquer many niches, from high altitude mountain peaks, to hydrothermal vents in the ocean, to the interiors of volcanoes. So far, only mankind has managed to set foot and survive in space. All the ingenuity of life so far has only managed to allow it to survive beneath the thin envelope of our atmosphere, or the (comparative to the radius) thin oceans coating the surface of our planet. If we can accomplish our expansion into space, perhaps we will be doing it in the name of life on earth as well as human civilization.

(And doesn’t that sound like a sappy sound-byte that would go at the back of a documentary? :-P Oh well. I mean it.)

Why Colonize Space? Part 1 of 2

This is a tough question. It’s one that I’ve been sort of sliding around as well in terms of my posting so far on this blog. But it’s also a very important one.

There are some halfway decent arguments against spending resources on a space program of any sort, much less one that puts the resources to sustain humans into the works – what with the endless list of requirements to keep them alive, to sustain them in the space environment, to subject them to the extraordinary dangers of space-flight. Several questions are posed regularly by those of this camp.

1. Couldn’t these resources be spent elsewhere on better things?

Space is expensive. It requires a lot to build rockets, and it requires a lot of rocket to get a small bit of matter where you want it to go in space. There are still people starving in Africa. People still die of malaria and bacteriological illnesses.

If we pose the question which should we be spending our resources on, space, or saving starving people? – the expected answer is saving starving people. But there’s a serious assumption there – that spending resources on “starving people” is actually going to alleviate starvation. There are many countries in the world that still have starvation, malnutrition, rampant disease, and that have populations that die like flies. They usually also receive upwards of 30% of their GDP in terms of resources designed to keep them from these very ills. They also usually have one other element in common: They are ruled by tribal or authoritarian despotisms which take that aid money and either burn it, leave piles of food to rot, or buy weapons with our charity and use them to terrorize their populations. The problem has never been one of “resources”. People who are free – who have their able bodies at their own disposal, usually never starve. There are instances where natural disaster or infirmity occasionally prevails. But they, under normal circumstances, never fail to at least feed themselves. Taiwan is a resource-less rock in the middle of the ocean – the Taiwanese don’t starve. South Korea is a harsh piece of terrain, yet South Koreans don’t starve. North Koreans do.

If we posed this question another way – would you rather, given circumstances favorable to doing so, spend your resources on either space colonization, or liberating people from tyrannies - I’d cheerfully divert the funding from my lifelong dream and spend my engineering talents, for part of my life, designing the new and improved despot-seeking-missile. (In fact, that’s what I hope to do). What mankind stands to gain, medium term, from eradicating tyranny is much greater than from a space program.

But there’s another problem with this question – it’s a false dichotomy. We spend $16 billion on NASA per year. We spend $2.5 trillion dollars on everything else. NASA is only 0.1% of our total federal spending. In contrast, we spend $400 billion per year in interest on our national debt! If we were going to trim something, there’s no shortage of places to start. Why cut the space program? Why challenge increases in the space program with starving children in Africa, but not federal highway maintenance pork? ($35 billion, most of which is probably pork, unleashed and running wild. BTW, we’re spending more to maintain the highways than we did to build them – figure that one out).

If we were the United States of NASA, and we spent 80% of our federal budget on space exploration, I’d want to cut the space program back down to a reasonable size too. I’d probably be blogging my discontent from an internet café on Mars, but even so – then starving children in Africa would be a valid point to raise.

2. Wait for Technology to Develop

The second argument that’s often raised against it is that we don’t have the technology to colonize space. We should wait until we have the ability to do it before making any serious efforts at climbing this mountain.

This argument is in error for the following reason: It assumes that Technology Just Happens, that men have a passive role to play in the development of technology, and that they do what they can when it becomes possible to do it. That’s not how it works. Capital T Technology doesn’t solve problems for us. Men develop technology to solve problems. I believe that our greatest technological advancements happened, not while we were waiting for them to happen, but when we were striving to overcome an obstacle. The oceangoing technology of our millennia of sailing was not invented, refined, or developed by abstract theorists in a land-locked university. Conversely, our knowledge of fluid dynamics came first to the Romans and the ancient Persians, who had to plumb their cities and irrigate their deserts. The steam engine wasn’t built for amusement. James Watt’s efforts to regulate the device were not born of abstractions, but practical experience and experimentation. Our greatest bursts of applied invention and innovation, of technological advancement, came first when we had the world to explore and understand, second when we had the continents to tame, and more recently when we needed to fight our wars and overcome the enemy.

To make no effort towards conquering space means that we will develop no technology making it any easier to do so. Our expertise in other fields may advance arbitrarily. But we will remain precisely in the position we are in now in terms of being able to put humans on other planets and moons and enabling them to live there. Having made no efforts to make this work, we will have no technology to help them. We can see the outlines of this in the frustrated question that many space-enthusiasts have asked of late: “Why could send men to the moon in the 70s, and yet can’t send men reliably into orbit today?” The answer is that we haven’t been pushing ourselves to go the distance. The Saturn V was developed by engineers who had practical experience pushing the boundary of our aerospace knowledge. They had designed rockets, rocket planes, and innovative supersonic airplanes before. They had practical experience building the things. The Saturn V wasn’t just a rocket – it was a culture that enabled it to exist. Today, the blueprints to build that rocket are in storage somewhere, the engineers are retired or deceased, and the companies that built the parts are out of business. Even the people who engineered the shuttle are spending their efforts holding the fleet together, and retiring. Most of the engineers in charge today have never had the opportunity to design and build a new rocket.

It ultimately doesn’t matter when we start – the technology won’t happen until we do. If we develop a moral paradigm now to put this off to a future generation, then as long as the paradigm persists, we will make no progress towards accomplishing the goal.

Tuesday, December 13, 2005

Basic Sizing of a Rocket

Now – how big does your rocket have to be to get there? The following are pertinent equations for sizing a rocket:

For a rocket stage with a certain payload mass, propellant mass fraction, delta v, and engine Isp, the mass of the fuel, inert mass, and everything else falls into place. Tsiolkovsky’s (spelling on slide – I are engineer) rocket equation relates the mass ratio of the rocket stage to the amount of dv needed.

Isps (specific impulses) are typically around 300-420 sec for liquid propellants, and around 300 or below for solid propellants. Hydrogen/Oxygen – the best chemical propellant usable (there are better ones involving fluorine – but they produce poisonous gas as an exhaust!) has around 420 sec. 440 sec in vacuum with a good engine. The specific impulse, as a measurement, is defined as the total impulse (integral of thrust with time – the total change in momentum of the spacecraft) divided by the total weight of the propellant on earth. Neglecting atmospheric effects, it ends up being equal to the exhaust velocity * earth gravity. The faster your exhaust velocity is, the less fuel mass you need to make a certain change in momentum. (Thrust = mass flow rate * exhaust velocity, Impulse = mass expended * exhaust velocity).

Propellant Mass fraction is the ratio of fuel mass to the mass of the full stage – the payload. Chemical rocket stages have propellant mass fractions ranging from 0.7 to 0.9. It is a good idea to conservatively estimate 0.8, even though some rockets may achieve better performance when all is said and done. If you don’t end up having enough mass budgeted for your engines, you’ll have to iterate your calculations again.

For multi-stage rockets, one of the things that must be decided is what fraction of the total delta v each stage will take.

MRstage1 * MRstage2 * MRstage3 = exp((dv1/Isp1 + dv2/Isp2 + dv3/Isp3)/g0).

For stages of equal capability (equal Isp and propellant mass fraction), the lightest rocket is the one that has equal mass fractions (and equal fractions of total delta-v) for each stage.

The payload to total mass ratio helps round out the equations to find the total mass. Note – if the mass ratio is too low (dv too high) and the pmf is too great, it means the rocket stage can’t carry enough fuel to loft both the payload and the structural mass to the delta v. The payload fraction goes to zero, and then negative. This means you’ll have to stage your rocket further, or slim down on structural mass.

Example – you want to loft a 10000 kg payload to geostationary orbit. You decide to use a two stage rocket to accomplish this – both stages use hydrogen and oxygen propellant and a decent engine (420 sec Isp). Because you want your rocket to have minimized mass requirements, you equalize the dv required between stages.

Total mission dv = 9000+3580 = 12580 m/sec.
Dv for stage 2 = 6290 m/sec
Dv for stage 1 = 6290 m/sec
Propellant mass fraction for each stage = 0.8
Isp for each stage is 420 sec

The massfraction for each stage is 0.2169.
The payload fraction for each stage is 0.02116. This means that payload is only 2.1% of the weight of each stage!

The payload mass for the second stage is 10000 kg. The total mass of the first stage is 472546 kg. The fuel mass is 462546 kg. The inert mass is 92509 kg.

The payload mass for the first stage is the fully loaded mass of the second stage. The total mass of the first stage (payload included) is 22332000 kg. The fuel mass is 1717496000 kg. The inert mass is 4373000 kg.

So your total rocket mass is 22,332 tons. Umm, how realistic is this exactly? If you needed it to accelerate at 1.1 g forces (for takeoff purposes) you would need 241 MN of thrust. That equates to 129 space shuttle main engines. This is one gigantic rocket! I don’t think we would want to build anything this big. If you were constrained to a propellant mass fraction of 0.8, you would have to use more stages.

Let’s start over with a 3 stage rocket:

Dv for each stage = 4193 m/sec
Propellant mass fraction = 0.8
Isp = 420
MR = 0.361
Payload fraction = 0.20125

Notice that now your payload is 20% of the mass of each stage, and 8% of the total rocket mass. This is far better than the previous case, where your payload fraction was only 0.04%. Your rocket is going to end up being much smaller.

Stage 3:
Total Mass: 49689 kg
Fuel: 31,751 kg
Inert Mass: 7937 kg

Stage 2:
Total Mass: 246901 kg
Fuel: 157700 kg
Inert Mass: 39442 kg.

Stage 1:
Total Mass: 1,226,837 kg
Fuel: 783,949 kg
Inert Mass: 195,987 kg

A 1226 ton rocket is 20 times smaller than our previous 22332 ton rocket. To take off at 1.1 g forces, this rocket will only have to generate 13 MN of thrust. It would only take the equivalent of 7 SSMEs (52360 kg of engine there, leaving 143 tons left over for 1st stage structure).

This is still a sizeable rocket, but that is because 10 tons to GEO is a large payload for that sort of orbit.

Navigation in Spaaaaaace!

How do you size a rocket for a mission? This is actually not very difficult to do if you know the pertinent equations. One of the first things you need to know is where you are going. This determines your delta v, the total change in velocity that your rocket makes as it accelerates the payload. To get into orbit, for example, you need to know how fast your payload ends up going.

Circular Orbits:

The velocity at which objects orbit a planet is determined by gravity and the altitude of the orbit. Orbits can be circular, elliptical, or hyperbolic (with a boundary case of a parabolic orbit). Hyperbolic orbits are escape trajectories, or trajectories which don’t involve capture by a planet. The orbital energy in these cases is greater than the escape energy of the system.

For circular orbits, if you use Newton’s gravity and balance it with centrifugal acceleration, you can solve for the velocity which an object has to attain to orbit.

For a low earth orbit (from about 100km to 1500 km), (100 km for this example) you rotate at a rate of 7840 m/sec. This is blazingly fast – one of the reasons why it takes so much fuel to get into orbit. But this isn’t the totality of the delta v which the rocket must expend. Part of it is drag loss. The rocket ascends through the atmosphere faster than any aircraft could hope to go, and drag wastes some of your propellant, usually around 1000 m/sec or so. Gravity loss is also an issue. If your rocket didn’t produce enough thrust to overcome gravity, it would go nowhere, but expend tons of propellant, hence effective delta v loss. Delta v losses for gravity are between 500m/sec and 1000 m/sec usually. They are equal to the effective gravitational acceleration on your rocket multiplied by the amount of time that it’s burning fuel to fight it.

Altogether, about 9000 m/sec delta v is required to get into low earth orbit.

Maneuvering in space:

To go beyond low earth orbit, additional burns must be made. Gravity and drag loss don’t factor in as much (for short burns) when you are beyond earth’s atmosphere and already in orbit. If you burn in your orbital direction, you will raise your orbital eccentricity, and enter an elliptical orbit. If you burn against your orbital direction, you will enter another elliptical orbit that oscillates between where you are and a lower altitude.

One of the simplest maneuvers to raise or lower your orbital altitude is the hohman transfer. For short burns, it is also the most fuel efficient trajectory for changing orbital altitude. It involves burning once to enter an elliptical transfer orbit. You then travel from the perigee of the elliptical transfer orbit to the apogee, where you burn again in the orbital direction to circularize your orbit. Then you are at a circular orbit with a higher altitude.

To transfer from low earth orbit to geosynchronous orbit – 35786 km – we first have to increment our velocity to get into the transfer ellipse. Our current orbital velocity is 7840 m/sec. The eccentricity of the transfer ellipse is 0.6934. The semi-major axis is 21132 km. The velocity at perigee needs to be 10201 m/sec. You have to burn to increment your orbital velocity by 2361 m/sec. Then you coast until you reach apogee, where your velocity is 1847 m/sec. The circular orbit velocity at a radius of 35786 km is 3336 m/sec. You have to burn again to increment your velocity by 1489 m/sec. The total delta v for this transfer is 3850 m/sec.

Saturday, December 10, 2005

The program itself: Rocketcalc.cpp

This post isn't working yet. I can't get the program to post in plain text. Does anyone know how to do that?

I'll get this program posted eventually. I've discovered a few more bugs, though, and need to make sure it isn't spitting out gibberish for more than 4 stage rockets.

I'll find a way to post the source file after I get back from my bug-hunting safari.

Rocket Sizing Software:

The following is a description and some code for a piece of rocket sizing software that I'm programming. It takes a bunch of input variables that the user supplies and optimizes the dv distribution, and calculates the stage masses for a multi-stage rocket.

Have you ever wondered how large a rocket would have to be to launch a specific payload? What the effects of staging are? My C program answers some of these questions by providing a preliminary mass budget for a multi-stage rocket.

pmf (propellant mass fraction) = m_inert/m_fuel. A rocket is primarily a giant fuel tank. The amount of structure is roughly proportional to the amount of fuel. The propellant mass fraction is a number (usually between 0.7 and 0.9 for liquid rockets) that defines the ratio of fuel to (fuel+structure) mass. It neglects the payload. Any lighter than 0.9 and your rocket usually doesn't have enough structure to hold the fuel tank together, or withstand the forces of launch. In space vehicles may be able to get away with higher pmfs, but not launch vehicles. The pmf coupled with the limited Isp of chemical propulsion is also the primary reason why we don't do Single Stage to Orbit. Try it for a pmf of 0.8 and an Isp of 420, and see what you get.

The Isp (specific impulse) is the fuel efficiency of the engines for a rocket stage. Typical numbers are around 340 for kerosene/LOX engines and 420-440 for hydrogen/oxygen engines.

Any extra inert mass is included in the payload of each stage. Things like extra systems or structure can be directly added in to ensure that there is enough of a mass budget to attach them to the rocket.

The dv is the total change in velocity that the rocket can make. Missions in space are usually defined by the amount of dv necessary to perform them. Launching cargo into LEO typically requires 9000+ m/sec of dv. Going to the moon requires another 3200 m/sec or so. Landing on it or takeing off requires 1600 or so m/sec dv. Anyway, all of this stuff adds for your total mission.

My program was compiled as a command line executable with DevCPP. I don't know how to do makefiles. I'm an engineer, not a unix wizard.

Saturday, December 03, 2005

Why send people?

Human space exploration is the type of space exploration that I am most interested in. However, I don't think the primary purpose of human space "exploration" is exploration, as much as it is an attempt at colonization and expanding our capabilities to travel and live in outer space.

The probe people are probably right that it will usually require less mass to send machinery and instruments to a remote location than people. People radically complicate any space travel involved, with increased mass and specialized equipment required just to keep them alive. Furthermore, with modern computing technology, our probes can have a good degree of autonomy in what they do, and time delays for communicating become less of a problem. Probes do have drawbacks - they're usually limited to doing only the types of exploration that they're designed for, they're physically clumsy and can run into obstacles that a human being would just step over or shoulder aside, and they can only deal with problems that the programmers anticipate. However, they have succeeded in getting the basic exploration of the inner solar system done.

If a human being is going to another planet, odds are that a probe has gotten there first, mapped the surface, located deposits of useful materials such as ice and various metals. On mars, our surface rovers are drilling samples from rocks near to their landing area at fractions of the payload mass required to send people. If we only wanted to explore mars, we could send a spacecraft with equivalent payload absolutely jam-packed with sensors, bus sized rovers and robots, drill rigs, ect, all without the life support, water, and living space that people require.

But then again, why are we exploring space? Exploring extremely distant galaxies and other stellar objects gives us a picture of the universe, how it came about, ect, satisfies some curiosity and hones our physics. Exploring the inner solar system holds the long-shot chance of discovering life that may have developed independently of Earth based life, and thus dramatically raise the guessed-at chances of life existing in other star-systems, as well as giving microbiologists something to study. However, I think the main reason we explore space is to see if there's something out there that we can use, to see if there's somewhere new to expand our human presence to. When we began having inklings that the other planets were worlds just like the earth, getting people there was one of the first things to come to mind, no matter how impossible it seemed at the time.

Why bother knowing whether or not the moon has ice? So that when we start building bases there we can drink the water and grow our food (unfortunately the moon doesn't have a whole lot of hydrogen or ice). Why try to determine the effects of zero gravity on frogs? So that we know what sorts of precautions we have to take when we send people on interplanetary trips.