How To Travel Really Far

[shintashi]

Greetings!

 

Some time ago, I began thinking about different methods of getting around the acceleration issues of long distance space travel. As you know, when a rocket is traveling through space, it's mass is depleting every second of acceleration, and every second of course course correction. That's because the fuel has mass, and when it's gone, it's gone for good. Most of us interested in exploring the solar system have noticed there's lots of asteroids and they probably have the materials we need to make more rocket fuel, but that's not an easy endeavor at this time, since those rocks are huge, fast, and often rotating, and we really don't have what it takes to build something like an asteroid mining facility at this time, without creating a global super-depression.

 

So I thought, well, how can we get something going faster, without assuming there's going to be more "stuff" on the way?

 

The answer is very similar to the parallax and lunar tide manifestations. As anyone who's got some understanding of astronomy might recall, the distance from the sun to the earth is actually not so great that it has less gravitational effect than the moon. In fact, it has more. The reason we notice the lunar tides more than the solar is because the sun's distance is so great that the difference between the light side and the dark side of the earth is approximately the same. That means on a sunny day in Hawaii, the sun's pull on the Atlantic Ocean is like 99.9...% the pull on the Pacific, so the dinky gravity of the Moon has much more wobble producing power, because the moon is so close that the difference between the Atlantic and pacific oceans have a noticeable difference.

 

This is also similar to the laser like quality of sunlight when compared to something like an incandescent bulb or candle. The light from the sun is also radial, but the sunlight that hits us is already a slice of that pie- a sliver in fact. That sliver is so thin - it's angle is so sharp that you could reflect it all the way around the world with mirrors and it would hardly get much "fatter".It's practically a laser beam.

 

So what do does this all have to do with space exploration?

 

Fuel.

 

When you go up in space with a 100 ton rocket, and a crew with supplies, you might be lucky if 50 tons are dedicated to fuel. Most of the time, with rockets, the fuel weighs considerably more than the capsule. The real problem with this is the fact that the fuel has to move itself too. So the whole time you are blasting off into space, you are also losing your mass, which means you can go faster, but you are also losing fuel to fight against the weight of the fuel + you.

 

So what I came up with is the idea of a big triangle, or deformed tetrahedron or diamond point. The tip of the "blade" where the lines of the triangles meet, is way out in space. The rendezvous point. One of these rockets is the crew and their base supplies, while the other rockets are full of extra fuel and/or supplies. The spacecraft link up at such great distances that the angles needed to line up become negligible. Thus while a bunch of fuel is spent getting each rocket that far and fast in space, when they converge, the craft has an entirely new set of fuel to either keep going or to slow down.

 

Other factors can be taken into account to improve overall performance, including using the gravitational pull of large objects to slow down or make sharp turns, or using asteroids etc. for new fuel. It's also possible, if your focus isn't raw acceleration, to send up unmanned rockets that are transporting a lot of fuel and supplies very slowly, but far in advance of the live crew, and then intercept these at a later point, by spending a portion of your fuel to accelerate there, and a lesser portion of your fuel to slow down to their speed, you can still link up to a monstrous amount of reserve fuel and supplies.

 

You could even use this technique to create massive space stations at remote regions of the solar system, by launching at different times of the year with different rates of acceleration. You could also set up the supply ships to automatically, and remotely assemble into some kind of super-tanker like space base.

 

 

So the basic idea is exploiting the fact that at extreme distances, the amount of 'course correction' needed to line up and dock is nearly zero, and the fact that you can put more fuel on something that doesn't need people or research equipment (etc.) and send it great distances without completely exhausting itself, and by doing this in numbers greater than 1, implies your human occupied space craft, accelerating merrily at 1G could end up with more fuel to spend on arrival than even when it first left - this all means space exploration can go much, much further, without having to create unrealistic or prohibitively expensive technologies.

[CraigD]

So what I came up with is the idea of a big triangle, or deformed tetrahedron or diamond point. The tip of the "blade" where the lines of the triangles meet, is way out in space. The rendezvous point. One of these rockets is the crew and their base supplies, while the other rockets are full of extra fuel and/or supplies.

...

So the basic idea is exploiting the fact that at extreme distances, the amount of 'course correction' needed to line up and dock is nearly zero, and the fact that you can put more fuel on something that doesn't need people or research equipment (etc.) and send it great distances without completely exhausting itself, and by doing this in numbers greater than 1, implies your human occupied space craft, accelerating merrily at 1G could end up with more fuel to spend on arrival than even when it first left - this all means space exploration can go much, much further, without having to create unrealistic or prohibitively expensive technologies.

The idea of launching fuel separately from payload – human or otherwise – is a pretty promising, but not nearly enough to suggest that a chemical reaction powered rocket could sustain 1 g (about 10 m/s/s) acceleration for long periods. Most discussion I’ve encountered, such as the Zubrin and Baker’s Mars Direct proposal, involves refueling at key points where large forces are needed, such as in orbit around Earth, on the surface and in orbit around the Moon or Mars.

 

You could in principle greatly increase the fuel available to a rocket by carefully planning rendezvouses with pre-launched “tankers” (given that high-performance rocket motors are somewhat “used up” by a single firing, it might be more practical to launch fuel and motor, and just dock the payload module with a new booster module, analogous to a post rider changing horses). However, I think this would be, as you put it, “prohibitively expensive”, cost increasing by about the original vehicle cost for each additional “tanker/spare horse” vehicle flown.

 

I think what’s really need to greatly increase the performance of a spacecraft using practical near-future technology it either:

• a rocket-propelled vehicle with many times greater power than a chemical fuel, and little additional mass, such as an antimatter rocket;
  
• a vehicle doesn’t carry its main fuel and reaction mass at all, such as solar or artificial beam propelled light sail (an especially interesting design for this is Forward’s light-sail system).
  

[shintashi]

The long term equations are still going to boil down to 1g/s being the optimal acceleration for human beings over a long period of time, assuming essentially near luminal accelerants like some over powered ion cannon. I created this theory based on the absolute limits of propulsion technology and biology. While human beings can survive 4 Gs, and some don't black out at 9+, it is a fact most would not enjoy anything over 1 G. But it is also a fact that in low gravity over long periods of time human bone marrow decays and then the tissues decay on the microscopic level, even if the astronauts are practicing isometrics. By consistently accelerating the craft at 1G, our hypothetically optimized spacecraft can reach extremely high velocities in a short period of time. Naturally, craft today can accelerate a vehicle much faster, but for only short periods of time.

 

My principle doesn't fail in either case - whether we have high acceleration, low acceleration, gradual acceleration or sporadic acceleration - the point is to create a distant - potentially moving target, and then have the technical equipment and researchers transported to a new concentration of fuel and supplies. This system is ideal for ranges exceeding several astronomical units. Mainly, the system accounts for the fact that spacecraft at extreme ranges use fuel or other gases to maneuver through verniers, and that substance used for maneuvering, docking, slowing down, speeding up, etc., can be optimized by minimizing the amount of changes in angles, velocities, and position in space used for rendezvous.

 

If we are clever, we would send these convergent craft to a place where they approximated synchronized or parallel motion with a large fuel supply, depending on what materials are used for fuel, such as a moon or asteroid belt. The flaws of this system are as follows:

 

 

• the more vehicles you send out, the more likely something will go wrong with some of them
  
• the greater the distance, the more precise the calculations have to be and the greater the correct necessary if in error
  
• limited man, or unmanned fuel transports would collectively increase the total cost of the project far beyond a single craft
  

 

Nevertheless, this is a proven way for a craft with limited mass and limited fuel to achieve much greater acceleration potentials and thus much longer range.

[CraigD]

The long term equations are still going to boil down to 1g/s being the optimal acceleration for human beings over a long period of time, assuming essentially near luminal accelerants like some over powered ion cannon. I created this theory based on the absolute limits of propulsion technology and biology. While human beings can survive 4 Gs, and some don't black out at 9+, it is a fact most would not enjoy anything over 1 G. But it is also a fact that in low gravity over long periods of time human bone marrow decays and then the tissues decay on the microscopic level, even if the astronauts are practicing isometrics. By consistently accelerating the craft at 1G, our hypothetically optimized spacecraft can reach extremely high velocities in a short period of time. Naturally, craft today can accelerate a vehicle much faster, but for only short periods of time.

The benefits to human (or most other terrestrial animals) passenger of a spacecraft that accelerates at 1 g (about 9.8 m/s/s) for extended periods would, as you say sintashi, be great. We’ve all spent our whole lives experiencing 1 g, by virtue of living on Earth, and are happy and hale. The engineering of such a thing using technology resembling present day, however, is daunting, because the required energy is many times greater than ever achieved in a rocket ship. Let’s look at the details of how daunting later.

 

There is a much more practical way for the crew of a spaceship to spend time in 1 g than for the ship to constantly accelerate at 9.8 m/s/s: the ship can contain, or be configured to be, a centrifuge. There’s a lot of literature on this subject, including Kirk Sorensen’s 2005 paper A Tether-Based Variable-Gravity Research Facility Concept (PDF format).

 

Nevertheless, this [rendezvousing with other spacecraft to refuel] is a proven way for a craft with limited mass and limited fuel to achieve much greater acceleration potentials and thus much longer range.

I wouldn’t call this approach “proven”, because it’s never been done, or even, to the best of my knowledge, designed in even a preliminary manner.

 

So, let’s make a preliminary model of this system, using the specifications of a well-know, throttleable rocket motor, a shuttle main engine (SME). For example, here’s what I get for a single-motor spacecraft that sustains 1 g acceleration:

SME min thrust: 1400300 N

SME max thrust: 2280000 N

SME average propellants consumption rate: 1069 kg/s

Spacecraft empty (no propellant) mass = SME min thrust * 9.8 = 13722940 kg

Propellant mass = SME max thrust * 9.8 -13722940 = 8621060 kg

Time until propellant exhausted: 8621060 / 1069 = 7967 s

 

So, for this configuration (about 11 times the mass of the full Space Shuttle stack), you need to “refuel” (however that can be done) about every 2 hours. Take an example distance of 78341251000 m (the closest Earth-Mars distance), we get a 1 g travel time (with 0 velocity at origin and destination) of

[math]2 \sqrt{\frac{78341251000}{2} \frac{2}{9.8}} \dot = 178818 \,\mbox{s}[/math]

 

This trip, then, would require 178818 / 7967 = 22 refuelings.

 

Shintashi (or anybody else), can you repeat and check my work, and design a mission like this in more detail?

[JMJones0424]

You asked for someone to check your work...

 

Spacecraft empty (no propellant) mass = SME min thrust * 9.8 = 13722940 kg

Propellant mass = SME max thrust * 9.8 -13722940 = 8621060 kg

Time until propellant exhausted: 8621060 / 1069 = 7967 s

 

Shouldn't you be dividing by 9.8m/s² in order to go from Newtons to kilograms? If so...

 

Spacecraft empty = 142888 kg

Propellant mass = 89765 kg

Time until propellant is exhausted = 83 s

 

Changing rockets every minute and a half is of course absurd, so unless I am incredibly wrong, the Space Shuttle Main Engines are an inappropriate device to use if one wishes to maintain 9.8m/s² of acceleration for extended periods of time.

[CraigD]

You asked for someone to check your work...

I did, and thank you! :thumbs_up

 

Shouldn't you be dividing by 9.8m/s² in order to go from Newtons to kilograms? If so...

 

Spacecraft empty = 142888 kg

Propellant mass = 89765 kg

Time until propellant is exhausted = 83 s

You’re right! I messed up spectacularly. :doh:

 

Multiplying by about 10 instead of dividing means my key calculation of time until propellant exhausted is overstated by about a factor of 100, as your correct calculation shows.

 

Changing rockets every minute and a half is of course absurd, so unless I am incredibly wrong, the Space Shuttle Main Engines are an inappropriate device to use if one wishes to maintain 9.8m/s² of acceleration for extended periods of time.

I agree 83 s is uselessly short. To get a greater duration, we need to increase the ratio of max to minimum thrust , which we can do by adding motors. Unfortunately we get only modest gain this way, as this little MUMPS calculation program shows (N is the number of SMEs the ship uses, the next numbers fuel mass, average burn rate, and time ‘til empty):

f  r "N:",N,"  " s MF=N*2280000/9.8-286024,CA=N+1/2*1240*.98,D=MF/CA  w $j(MF,0,0)," / ",$j(CA,0,0)," = ",$j(D,0,0),!
N:3  411935 / 2430 = 169
N:4  644588 / 3038 = 212
N:5  877241 / 3646 = 241
N:6  1109894 / 4253 = 261
N:7  1342547 / 4861 = 276
N:8  1575200 / 5468 = 288
N:20  4367037 / 12760 = 342
N:100  22979282 / 61368 = 374
N:1000  232367037 / 608208 = 382
N:10000  2326244588 / 6076608 = 383

 

As you can see from these preliminary calculations, shintashi, maintaining a 1 g acceleration with essentially the best conventional rocket motor available today requires an impractical number of refueling – from 2208 for any a 1 SME ship to 586 for a 10 SME one for the shortest possible, ignoring gravity, trip from Earth to Mars. So SMEs, and, since no conventional rocket motor is much better than a SME, any conventional rocket motor, isn’t feasible for the scheme you propose.

 

What’s needed is a much higher specific impulse rocket, for which you need a much higher energy density fuel. This is where antimatter rockets, a physically reasonable, even simple concept, yet at this time unfeasible because of the tremendous cost and low rate at which antimatter can be manufactured, look so attractive - you can't get better power density than antimatter!

[shintashi]

in the far future, you will see we are still going to be able to use these basic limitations as guidelines until something dramatic changes the way we perceive the laws of physics. In the mean time, the same system - triangulating the end point of a moving vehicle and sending fuel/supply ships to converge, at different speeds and times, is something we can do even if the passengers are stuck in a giant rotating donut. I am well aware of the limited acceleration capabilities of our current rocket designs, and also understand a slow stream/ion engine is probably going to be the mainstream in this century.

 

This system is meaningless if you are thinking about a bunch of people firing off rockets from the same point simultaneously, or even to relatively stationary points in LEO or nearby satellites. It's designed to keep high speed vehicles from spending too much energy to avoid crashing into each other or to otherwise 'catch up' or 'slow down'. Thus it becomes more efficient when we have even higher durations of sustained acceleration at extreme ranges. It's essentially a fix for several problems we don't even have the technology to reach yet.

 

But it's also a simple principle for colonization. You can use low G for long periods of time, and drift, and you could use a toroid full of passengers drifting at high speeds then dock with several other craft, if you had their maximum velocity stair cased in a sequence of release. Thus the first vehicle would be the slowest, while the others would be subsequently higher velocity. At some point one of these vehicles, be it the slowest, the fastest, or somewhere in the middle, meets up with the others, and they all dock simultaneously. The best case scenario would launch solar satellite stations at different points where the new craft would be assembled and then launch all craft simultaneously. I think factoring in extreme distances, however, can help reduce the amount of change in velocity a staggered release would produce. That's because the extreme distances would drag out the time to the extreme, so even the slightest difference in velocity between ship A and ship B would mean the faster ship would inevitably catch up, even if it was only 0.1 meters/second faster.