Get your own Free Home Page
"Space is big. Really big." We've heard the joke, but when you think about space travel, you discover the truth inside the joke. Interplanetary travel involves distances of hundreds and thousands of millions of kilometers between moving objects. As an example, Earth is moving around its sun at an average velocity of nearly 30 km/sec, Mars is moving at 24 km/sec (a difference of about 20,000 kilometers per hour, or almost 13,000 miles per hour), and the distance between them is millions of kilometers. How do your characters get from here to there?
The first step is getting into space. For most purposes, that means getting into a low orbit. The second step is most of the distance of getting from here to there (and back). The third step is getting out of space again; this is the same problem as step one, but in reverse, so we'll deal with both together.
The legal definition of space is 50 kilometers up, but for our purposes, "space" starts about 200 kilometers up. There's still a lot of atmosphere ("lot" being a relative term) there, but a satellite can stay in orbit for weeks before the atmospheric friction slows it enough so it falls out of orbit.
In our current space missions, we use rockets for all three steps, but that's not the way it has to be in your campaign.
We currently use rockets, simple reaction engines that act according to Newton's Third Law of Motion: For every action, there is an equal and opposite reaction. That is, if you're throwing stuff out the back of your space ship, your space ship will move forward. It doesn't need anything to push against; you just need to throw enough stuff fast enough.
There are lots of ways to "throw stuff out" -- you could use chemicals, electricity (or "ion engines"), fission or fusion, or even antimatter.
Modern rockets are usually designed like artillery, to be disposable. The reason they're designed as disposable is because the farther and faster you want your payload to go, the more fuel you need -- the more stuff you have to throw out the back. Pretty soon, your rocket is 99% fuel, 1% payload, or worse. Mathematically, this is hidden in the rocket equation, the equation that describes the change in a rocket's velocity based on how much its mass is propellant and how fast that propellant is shot out the nozzle.
| (Initial mass/final mass) = e(deltav/ve) | |
| deltav | the final velocity you want the rocket to achieve |
| ve | the exhaust velocity of the propellant relative to the rocket |
[This can also be expressed as: deltav = ve ln(initial mass/final mass)]
If your rocket is 90% fuel (initial mass/final mass is 10), the final velocity will be 2.3 times the exhaust velocity. If it's 99% fuel, the final velocity will be 4.6 times the exhaust velocity. If it's 99.9% fuel, final velocity will be 6.9 times the exhaust velocity.
That's a lot of fuel for not very much result. The Hydrogen-Oxygen mix used for the space shuttle has a specific impulse of 460 seconds, for an exhaust velocity of a little over 4500 m/s. Using the same mix to achieve a speed of [velocity required to reach Mars] would require a single rocket that is ??% fuel.
The specific impulse is the measure of a rocket's efficiency. It's the exhaust velocity divided by the constant g, the acceleration due to earth's gravity, or about 9.81 m/s. This means that the exhaust velocity of the space shuttle rockets is 460*9.81, or a little over 4500 m/s.
The answer we've used in the past is multi-stage rockets. Here's the idea: After you've burned off 90% of your mass as fuel, all of the stuff that was holding it is just dead weight, so why not throw it away? If the 10% that's left over is a rocket all by itself, it launches as a smaller rocket already moving at a good speed.
For those who want the equation: if the ratio of propellant to payload is R and it remains constant with each stage and each stage has the same exhaust velocity, you can find the final velocity for a rocket with n stages using:
deltav = n[ve ln(R)]
Since R is effectively the same as (initial mass/final mass), this equation says that a two-stage rocket gives you double the final velocity of a one-stage rocket, a three-stage rocket gives you triple the final velocity of a one-stage, and so on. The final velocity is great, but the overall mass ratio is terrible:
(Total initial mass/disposed mass) = Rn
And no matter how many stages you have:
Rn = e(deltav/ve)
Staging is a great technique for one-shot attempts, but it's very expensive in terms of constant, economical use.
Most of the rockets built have been chemical rockets, but they top out somewhere around an Isp of 500 or so (though there was speculation that monatomic hydrogen would give an Isp of over 2,000). Basically, chemical rockets have their limits in terms of efficiency, but they're great for getting off the ground.
For leaving a planet, you need sufficient thrust. The thrust of a rocket is very different from its specific impulse. Thrust is a measure of the rocket's total power; thrust is usually measured in pounds or newtons (?). Thrust is mostly about how big the engine is; specific impulse measures how efficiently it uses its fuel.
For example, the F-1 engine of the Saturn V produced 1.5 million pounds of thrust, but it had a specific impulse of only 265 seconds. The main engine of the Space Shuttle produces only 470,000 pounds of thrust but has a specific impulse of about 460 seconds. (This relatively low thrust explains why the Space Shuttle needs the boosters...which each have a thrust of 2.6 million pounds and a specific impulse of about 260 seconds.)
The problem with thrust, however, is that it leads to human complications: People are soft and squishy and accelerations of more than 3 earth gravities are something of a problem if maintained for too long.
So there are two problems with the current design of rockets: One is that they're very expensive bullets we throw away, and the second is that they require a great deal of thrust, which affects the types of payloads we can send up.
The answer to the first problem is to use something other than giant artillery shells.
Have a reusable mechanism that can be easily maintained and quickly turned around. The shuttle was supposed to be one of these, but it's more expensive (in dollars per pound of payload) than a Saturn V. It takes quite a while to get the shuttle refurbished for launch; for example, every heat tile is unique and they must be checked and possibly replaced.
This is part of the idea of the SSTO (single-stage-to-orbit) vehicle. It is a single vehicle that's reusable and easily maintained. Because it's a single stage, there aren't parts thrown away. Other concepts have involved two-stage vehicles that were both manned; the Dark Horse concept is along this line...the orbital vehicle flies to a certain altitude, is refueled, and completes its trip to space.
I don't know of a trivial way to calculate the benefit that wings give in achieving orbit; if someone does, please contact me.
(A quirky one I like is to use a real cannon. There really was an engineer who worked out the problems of building a cannon that would shoot small payloads into orbit. (I believe it was an expatriate Canadian named Bull, but I may be wrong.) The propellant stays on the ground, and most of the casing is in a mile-long barrel buried in the earth. The payload must be able to sustain hundreds (if not thousands) of gees of acceleration. The numbers may make it economical on a per-pound basis.)
Another popular idea is the beanstalk or skyhook. This is a flexible tower (or cable) that extends from the ground out...so far out that it extends past that orbit where an orbit takes 24 hours (the geostationary orbit); it extends far enough out that the part outside that geostationary point balances the part inside it. The total length in current designs is 146,000 kilometers...well beyond current materials technology.
The beauty of the beanstalk or the skyhook is that you take an elevator into space. Sure, it takes a day or two to ride up, but there's never any significant acceleration. Very delicate items can be sent up that way.
A variation on the beanstalk is the "space fountain." Essentially, the space fountain shoots pellets into space; they are deflected by the space platform and sent back to earth. While a huge project, at least one design for a space fountain can be built with modern-day materials. You could ride an elevator into space.
Here are two comparative costs in 1995 dollars for getting a kilogram of payload into orbit. They're derived from figures in Space Travel by Bova & Lewis.
| Delivery | cost/kilogram |
|---|---|
| Saturn V | $7253 |
| Shuttle | $22000 |
This is based on 2 Saturn V launches a year and 5-7 Shuttle launches. Forward claims the current cost to orbit is $5000/kg (in the discussion of the space fountain, he mentions that the cost to get a kilogram into orbit by fountain elevator is $2/kg).
In landing, you have the reverse problem. How do you slow down enough to hit the surface without splashing? Our technology is very good at slowing down from speeds of two or three times the speed of sound, but how to get from that orbital velocity of ?? meters per second to a mere Mach 3?
One technique that is used is atmospheric braking, using friction with the atmosphere to slow down the vehicle. This creates tremendous amounts of heat, however.
Once we're in low-earth orbit, it's a lot easier to get someplace. For one thing, we don't need all that thrust. The difference between earth orbit and interplanetary orbit can be as low as 2 meters per second.
Already built with Isp ranging from 2,500 - 10,000 seconds. Values of up to 400,000 seconds have been extrapolated. Specific impulse for an ion engine is calcuated by:
Isp = 1/g * (2 * (q/m) * va)0.5
where:
| g | acceleration due to gravity |
| q | charge of individual ion |
| m | mass of individual ion |
| va | voltage through which ions are accelerated |
There was a nice use of ion engines in the story "The Grand Tour" by Charles Sheffield. I found it in the Project Solar Sail anthology. In this story, they have bicycle-powered ion engines.
An ion engine has a high Isp but a low thrust: It may provide a reasonable alternative for automated missions launched from orbit to orbit, but it's not something you'd use to leave a significant gravity well.
These are the nuclear engines I'm aware of: pulsed, fission, fusion, and MHD. (I'm ignoring cases where the nuclear reactor provides the electricity for an ion engine.)
Nuclear pulsed propulsion is the Project Orion style, throwing bombs out the back and letting a giant hemispherical "pusher plate" absorb the force. Project Orion estimated specific impulse 2000-6000 seconds, possibly up to 10,000 - 20,000. Bombs would be exploded at intervals of 1 - 10 seconds, depending on the mission, and would be of a size between 0.01 to 10 kilotons.
Dyson proposed using fusion bombs for an interstellar vehicle; one of his designs accelerated for 10 days at 1 g, required 3 x 105 (or 300,000) bombs, and reached a velocity of 10,000 km/sec. (It would reach Alpha Centauri in 100 years.)
Orion was scuttled by political problems and the Outer Space Treaty of 1967, which forbade nuclear explosions in space.
Fission rockets (such as NERVA, Kiwi, and Rover) were built and tested, but have never been flown. Essentially hydrogen gas is passed through the center of a fission reactor to heat it and expelled through the nozzle.
Specific impulse ranges are:
| Type | Isp range |
|---|---|
| pulse | 2000-20000 |
| solid core | 500-1100 |
| liquid core | 1300-1600 |
| gas core | 3000-7000 |
| fusion | 2500-200,000 |
Fusion rockets are essentially a fusion reaction in a magnetic plasma confinement bottle that leaks.
Remember that the maximum speed of a ship depends upon the specific impulse of the rocket exhaust. Plasma (the fourth stage of matter, superheated matter) is very hot and can be very fast. You want the fastest exhaust you can get, but fast exhaust is usually hot exhaust: there's a problem with engines melting. Furthermore, although nuclear reactors can turn nearly any propellant into plasma, the plasma is usually radioactive. These are two problems that the MHD (magnetohydrodynamic) engine tries to overcome.
The MHD engine uses a fission reactor circuit connected to a heat exchanges. The fission reactor heats up a propellant (such as water) to plasma. Unlike most designs, the plasma isn't radioactive, because it hasn't come from the reactor directly. The fission reactor also generates the energy to contain the plasma in a magnetic bottle.
The light from the sun has pressure; the sunlight falling on a football field has a pressure about the same as a small pebble. (It's about 1400 watts/square meter.) Konstantin Tsiolkovskii and F. A. Tsander came up with this this back in the 1920s, after Einstein suggested that photons had momentum.
The pressure of sunlight can be used to move spacecraft, with a constant acceleration. (Constant acceleration significantly cuts down the length of time a trip takes.) (BTRC's Vehicle Design System assumes that all sails produce 10w of power per square kilometer of sail, at the same position as the earth's orbit.)
The effectiveness of a solar sail depends upon its reflectivity, its area, and its mass: high reflectivity and area and low mass give the best results. However, the pressure of sunlight decreases the farther one gets from the sun (as the square of the distance, in fact). Another limit is the strength of the materials for the tethers. If humans are aboard the ship, the maximum acceleration tolerance would also be important. (A red giant makes an excellent launch system for an interstellar solar sail because the star itself is so huge.)
Although there are theoretical maneuvers to send a solar sail at several gees of acceleration (a perihelion boost, for example), for the most part a solar sail is a low-acceleration craft. (Again, that doesn't mean the overall velocity won't be high.)
For a sail that does not transmit sunlight, with a reflectivity k, the pressure on the sail is:
p = (1+k)S/c
Where S is the solar irradiance (for our sun, that's about 3.04E25/(r2) watt/m2, where r is the separation in meters between the sail and the Sun's center.
Stephen W. Soliday kindly sent me these equations for calculating this as a relationship to luminosity, which means that you can apply this to other stars:
L = 3.09 +/- 0.004 x 1033 ergs/sec for the sun x 1026 J/sec 1 J/sec = 1 watts your irradiance number S = 3.04 x 1025 watt/r2 is found by
S = L/(4 Pi r2) inverse square law for the propagation of light. All radiated energies including gravity fall off at 1/(4 Pi r2) 4 Pi r2 being the area of a sphere at radius (r)
Thanks, Stephen.
Some people think you can't move in-system with a solar sail, it can only move out; that's not true. For every velocity there is an orbit (although sometimes the "orbit" is "falling into the sun"). Tilting the sail creates a component of the force that either adds or subtracts to the vector of the orbital velocity. You can increase or decrease your orbital velocity (orbital velocity is v=(GM/r)0.5) to move into an orbit that is closer to the primary or farther from the primary.
For a circular sail craft whose total mass is M and whose sail radius is R, the acceleration outward from the sun is:
a = (1+k)(6.3E17)(R2)/(2M(r2))
The parameter 6.3E17 will vary for another star, of course.
From a practical standpoint, solar sails require no external fuel and are very reusable; they can be slow, but might be well-suited to automated deliveries and courier runs for materials that have no time limit. For example, solar sails would be a good bet for a regular shuttle of raw materials from one location to another (to and from a colony? sending refined ores back from the asteroid belt?). They're unlikely to be much use in the earth-moon corridor (too much traffic), and will probably need to be built in space.
A certain amount has been written about using sails for interstellar flight (especially by Robert Forward). A couple of things are worth noting: First, the designs for anything large enough to carry a colony (an ark) are high performance sails that look like parachutes; they have to be rotated to maintain the curve. (It's been suggested that the rotation be used for energy storage that can be tapped during the middle of the mission.)
Incidentally, for an interstellar flight, the final interstellar departure velocity, Vinf, in meters/sec with a velocity of Vo at its closest approach to the center of the sun ro is:
Vinf = [[0.5(1+k)(1.26E17)(R2)]/(Mro + Vo2)]0.5
(A related vehicle is the magnetic sail but it requires superconductors to work.)
Although some speculation has been described here, there's nothing in this so far that contradicts any laws of physics. In fact, the pellet fountain and the Orion pulsed engine could both be built today.
Bashing this out I've referred to:
Get your own Free Home Page