Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

bill_cunningham · 2002-02-18 17:32:28

I'm working on a hard science fiction comic book that has an inhabited Solar System as it's setting, and I'm trying to play by the rules.

However, I don't have a solid background in math.

In the story, there is a passenger ship that makes regular transit between Earth, Mars and Saturn. The story involves the Mars to Saturn leg, as some of the characters are on their way to Titan.

I'm using nuclear fusion as the propulsion of the passenger liner, and I'm trying to figure out how long the trip would take.

I based my figuring on these quotes from Robert Zubrin's "Entering Space":

"a rocket using the D-He3 reaction could theoretically produce an exhaust velocity of 26,400 km/s"

and,

"practical spacecraft can be designed to reach a speed about twice their engine's exhaust velocity"

So, to be conservative I set the maximum exhaust velocity of the fusion engines of my fictional spaceship at 10,495.8 km/s. I figure they have the technology, but haven't developed it to it's fullest potential yet.

From what I can figure, the mean distance from the orbit of Mars to the orbit of Saturn is about 1199.1 million km.

For a one way trip, at 10,495.8 km/s, it would take 31.736176 hours to travel 1199.1 million Km.

(Figure at 10,495.8 km/s, if you divide 1 million by that number, it comes to about 95.28 seconds to travel 1 million km. Multiply that 95.28 by 1199.1 (that's how many million km are in the mean distance between the orbits of the planets in question) and you get about 114,250.24 seconds. Divided by 60 gives you 1,904.1706 minutes. Divided by 60 again gives you 31.736176 hours.)

Is this right? 31 hours and 45 minutes? Did I figure it wrong?

It's much quicker than I was expecting.

Some caveats:

My idea is that the ship is under acceleration to the halfway point of the trip, where it makes a flip and then decelerates the rest of the way, in order to keep the passengers under "acceleration gravity" the whole way. I haven't taken this into account yet. How long would it take to accelerate to 10,495.8 km/s if you needed to make sure you didn't pull more than .4 g the whole way? I don't know how to begin to figure this out.

Also, I figured the distance to travel as the mean distance from the orbit of Mars to the orbit of Saturn, but of course the actual planets could be much farther apart from each other. The frequency of interplanetary travel in this story is greater than I imagine waiting for near passeges would allow. Does anyone know where I can find out practical information on how far apart the planets might be from each other at any given time?

Any help you folks can give me would be greatly appreciated! I don't want to short change the details in this story.

If you're interested, I have some pencil work and development sketches for the project up on this free Geocities website.

Thanks for your kind attention! -Bill

Shaun Barrett · 2002-02-19 02:54:43

Congratulations bill on having the courage to launch into writing. A lot of us like to imagine we have the talent and the tenacity to try it but few of us ever do!
My grasp of orbital mechanics is tenuous, to say the least, but I may be able offer some small assistance.
I note you have chosen an exhaust velocity of 10,495.8 kms/sec for your ship, and then you set this as your ship's velocity. ( I'm not sure why you don't set the ship's velocity closer to twice this level, in accordance with Zubrin's figures?) In any event, you ask how long it would take, at an acceleration of 0.4g, to reach 10,495.8 kms/sec. Using an equation I remember from highschool: s = ut + 1/2 at*2 (where s = distance, u = initial velocity, t = time, and
a = acceleration), and with a little judicious transposition of terms, and inserting your values of velocity and acceleration, I came up with a time of 8 weeks, 5 days, and some 22 hours!!
At first I thought I must have made an error. It seemed like too long a time to accelerate to 10,495.8 kms/sec. Then I realised just how fast that speed really is: it's 3.5% the speed of light!
I think from this you will see the problem. If you could instantaneously attain a speed of 0.035c (where c = light speed in vacuo), you might very well get from Mars to Saturn in not much more than 31 hours and 45 minutes. However, even at the very respectable acceleration of 0.4g, you have no hope of reaching that velocity in a reasonable (from your story's point of view) timeframe. In other words, its going to take a lot longer than you'd hoped.
Even if we assume you can maintain a constant acceleration of 1g, it's still going to take you about 3.5 weeks to reach 10,495.8 kms/sec.
Another problem may be how much reaction mass you can carry and how long you can keep on pushing it out at these high velocities. Although a fusion powered rocket is going to be far more efficient than any chemical (or fission powered) rocket, it is still a rocket. It still relies on throwing something backwards in order to go forwards! How much reaction mass does it take to keep accelerating at 0.4g for so long? How much can you reasonably expect to carry?
I regret I don't know the answers to these questions but I hope I've at least thrown some light on the limitations of the situation. I think, bill, it's more complicated than you thought and it would be best to seek the advice of someone with some real "smarts" in this department.
Incidentally, this whole topic gives you an appreciation of authors like Sir Arthur C. Clarke, who do all the arithmetic for their stories and make them sound so plausible by including just enough fact to hide the fiction!!
A fascinating topic, bill. But is there anybody out there who can really "flesh out" the mathematics and set this comic book story on its rightful path to publication?
:0

bill_cunningham · 2002-02-19 03:31:07

Thanks alot Shaun, that's exactly the kind of info I was looking for!

Actually, the fact that the travel time has gotten longer is a good thing! I had plotted the story with the idea that a trip from Mars to Saturn would be more along the lines of a transatlantic voyage in the days of sail power only. It happens regularly, but it's still not a casual commitment to take this trip. The passenger liner I've been designing is like a giant cruise ship, with all kinds of recreation built in, to keep people amused for what I was thinking would be a trip of a couple months at least.

So it was to my dismay that my math gave me only 31 hours!
(I didn't figure the doubling in the quote because the time was already way too fast, and I recoiled in horror!)

I didn't know where to find the equation to keep the acceleration within the .4 g tolerance, but I figured that would stretch my time a bit. Plus there's still the fact that it's much more likely Saturn will actually be further from Mars than the mean distance.

Your darn tootin' it gives one a new respect for Messers Clarke et. al., and I'm lucky enough that the comic book format doesn't really require that such a depth of detail be revealed mathematically, but I really do want everything to be plausable.

To write science fiction and not be a scientist seems to require that you at least have some friends who are!

Anyway, thanks! And if anyone knows of any other info along these lines, please send me a post...

Shaun Barrett · 2002-02-19 20:59:40

Hi again bill!
I've been doing more thinking about your spaceflight and I think I may be able to offer a little more help.
Although your ship is capable of 0.035c, we obviously don't need to get it to that sort of speed for this relatively short(!) journey.
Let's ignore Mars' and Saturn's orbital velocities, and let's ignore the fact that we're all orbiting the Sun. So, in fact, I'm relieving us of the complications of orbital mechanics entirely
.... and, with the raw power of your fusion engines, I think we can do this legitimately.
I've done some more arithmetic and found that, at the shortest Mars-Saturn distance, and at 0.4g acceleration, it will take you 6.4 days to get to the half-way mark, and then another 6.4 days to decelerate to meet Saturn. Interestingly, even at the maximum Mars-Saturn distance, it will only take 7.52 days to the half-way mark, and the same again to arrive at Saturn.
So as far as your story goes, there'll be little difference in journey times no matter when you leave Mars; it's roughly a two week trip, regardless. This, of course, is due to the sheer brute force of your propulsion system! I'm still not sure about the reaction-mass you'd need to carry in order to maintain such accelerations for so long. For that you'd need to find out some more figures on the efficiency of the engines; things like the specific impulse, which basically measures how long one pound of propellant can maintain one pound of thrust (which is dependent on the exhaust velocity, I believe).
Hoping this is useful!

bill_cunningham · 2002-02-21 01:30:24

I'd love to learn more about orbital mechanics and, well heck, all of this stuff. This is all fascinating.

It's much more fun to write this way than to just say "hyperspace!" and pop - everybody's where they want to be just like that! The problem itself sends the story in different directions.

Yeah, I need to figure out reaction mass and all that. I think I have some notes on that part of the problem somewhere.

I was also pulling info on fusion reactors off the internet, but i haven't sifted through it all yet.

I've got a bit more time than I thought to get this all right. I sat down and worked out the details on the rest of the script for the book this last couple of days, and the trip to Saturn won't occur until issue #2. My target to finish issue #1 is June, #2 by the end of the year.

If you don't mind, I may try to bounce some of the other technical problems I'll be dealing with off you. This has been very helpful.

Shaun, you are da man.

I'll give you a Technical Advisor nod in the comic when I get it done.

Shaun Barrett · 2002-02-21 05:49:53

It's a great pleasure to offer any assistance I can, bill. The best of luck to you in your work on this comic book.
May it be a runaway success! (I can't wait to read it!)

Karl Evans · 2002-03-06 00:37:02

More potential help: Dr. Arthur I Berman wrote a really accessible primer on orbital mechanics called Space Flight (ISBN 0-385-02754-0) that you may find informative. (Well, it sure got ME started.)

bill_cunningham · 2002-03-17 23:56:54

Thanks Karl, I'll check it out.

I also printed out some stuff related to the voyager trajectories (I think) from the JPL website. I'll find that link and post it here in a bit.

thunder · 2002-04-01 20:41:10

Hi, I just read this post and thought I'd add my 2 cents in.

If we assume that the total mass of the ship (Mo) ( = mass of fuel (Mp) + the mass of the ship & cargo (Mi)) is a nice even 1 million kg (roughly 1100 tons), then it turns out that Mp = 995570 kg and Mi = 4430 kg That's right. The ship is 99.5% fuel. And it gets worse as the ship gets heavier.

Another problem is that your 4430 kg is the weight of the ship and the cargo (i.e passengers). 4430 kg is only 4.88 tons. I hope you have a superlight material to build your ship with. For comparrison, the Space Shuttle is roughly 125 tons empty.

Sorry to paint such a grim picture for you.

ED

thunder · 2002-04-01 21:02:52

Ok, it's even worse than that, I had the metric to English conversion backwards. 1 million kg IS 1100 tons, but 4430 kg of payload isn't 5 tons, its just one ton.

thunder · 2002-04-01 21:21:16

grrr. Never post after bedtime, it makes you look stupid. 1 million kg is 227 tons, NOT 1100 tons. So a rocket accelerating at +/- .4g for 12.8 days is going to require ~99.6% of it's take off mass to be it's Deuterium and Helium-3 fuel no matter how big it is. So now you can make the ship as big as you want, but remember 99.4% of it is going to be fuel. If you want a ship whose empty weight is 1000 tons, it's going to require 25 000 tons of fuel

Shaun Barrett · 2002-04-02 03:50:07

By way of clarification, 1kg is equal to 2.204lbs. A million kilograms is therefore equal to 2,204,000lbs.
Of course, before we can convert that into tons, we have to decide what kind of tons we're talking about. An Imperial ton equals 2240lbs while a U.S. ton equals 2000lbs. Let's assume we mean U.S. tons, since America is the leading space power at the moment (though with their present lack of direction, that situation may be quite temporary!).
Dividing 2,204,000lbs by 2000 gives us 1102 tons (U.S.). And, using the same arithmetic, 4430kgs is equal to 4.88 tons (U.S.).
As for the rest of your figures, I'm not really in a position to comment since my grasp of how propulsion-system efficiency affects payload percentages is vague, to say the least! However, having read about the enormous Isp (specific impulse) of the Orion fission-bomb propulsion system, and being under the impression that fusion propulsion is even more efficient, I can't help but suspect that your analysis is overly pessimistic.
Besides, Bill's comic book propulsion system doesn't really have to stick precisely to the rules. We can always cut him some slack and allow him a little poetic licence, can't we?

thunder · 2002-04-02 19:05:15

Your right on the conversion; like I said, bad things happen when posting after bedtime.

As for the actual equations, I checked them 3 times. The only source of error is if I misunderstand the actual basis of nuclear propulsion. The D-He3 equation D + "3"He -> "4"He(3.7MeV) + p(14.2MeV)

It gives you 3.7 million electronVolts of energy in standard helium and 14.2 million electronVolts of energy in the form of protons. I based my equations of an example using a D-D reaction; the products were only .8 million electronVolts in He3 and a bunch of radioactive neutrons. In the example, only the He3 was utilized (thrown out the rear end of the rocket nozzle). So my numbers only involved the energy of the He4. So I don't really know if the protons can be used. If they can, the system has nearly 5 times as much energy. In that case, only 90% of the ship's mass is fuel instead of 99.6%
So the real problem isn't the efficiency of the engine, but the length of time it's being used and how hard it's worked. You've got to spit an aweful lot of little helium atoms, or helium atoms and leftover protons, to get eleven hundred tons accellerating at .4 g By the original numbers, it's ejecting nearly 5 kg of propellant per second. And 12.8 days is over a million seconds.

But I definately agree that poetic liscence can give the ship an added boost of efficiency

Michael Bloxham · 2002-04-03 14:52:24

Shaun, did you say an Imperial ton was not equal to a US ton? I thought an Imperial ton was a US ton. How 'bout we all just work in metric Tonnes from now on?

Shaun Barrett · 2002-04-04 01:54:38

By Imperial ton, I mean the UK ton, which is 2240lbs. As far as the US is concerned, it is actually more complicated than my post would indicate!
The US has two different tons: The US long ton and the US short ton; the former being 2240lbs while the latter is 2000lbs.
To the best of my knowledge and belief, when an American talks about a ton, s/he is talking about 2000lbs. Any reference by an American to a ton weighing 2240lbs would include the prefix "long" or "Imperial" in order to distinguish it from the regular 'ton' as used in everyday parlance. If there are any Yankees out there who can be bothered with this topic, would you please confirm this so we can all sleep easy in our beds!
In the meantime, Michael, I'm with you! Let's all use the metric tonne (1000kg) and save ourselves a lot of confusion!

Aaron Chester · 2002-04-04 10:45:39

Yes we should use the metric ton. However, as an American I must admit I have a hard time thinking in metric measurements. I wish we would actually make the switch to metrics rather than just talk about it!

I must agree that studying orbital mechanics is interesting, even if it is complicated.

bill_cunningham · 2002-04-06 16:08:09

Please, please, cut me no slack!

I'll grant that any science fiction projection of technology, if it sticks exclusively to known principals, is going to come up short as a prediction because certainly when such things as interplanetary fusion driven spacecraft are common enough that there is something like a regular passenger run between Mars and Saturn, all sorts of efficiencies which we haven't discovered yet (as the detailed engineering work hasn't been attempted yet) will probably make the whole thing work better, or at least differently, than our strict projection might conclude.

However, if I do take any sort of artistic license, I'd prefer it to be taken with some real knowledge of what I'm departing from. So keep being literal and specific, this discussion is of enormous help to me!

Shaun Barrett · 2002-04-06 19:03:05

The sun is constantly spewing out a stream of charged particles called the solar wind. In effect, this constitutes an electric current; weak though it is due to the attenuation of spreading out over huge volumes of space. Nevertheless it is a current and is accompanied, inevitably, by the magnetic field always associated with a current.
I'm going out on a speculative limb here and fully expect to be shot down by a physicist, but how do we know Bill's interplanetary passengers won't be wafted through the solar system by some ingenious use of this magnetic field? (I'm sure I've read something about such a scheme somewhere, so I don't claim any originality at all in this! ) And what if the enormous power of Bill's fusion engines are used in conjunction with advanced superconductors to create colossal currents and monstrous magnetic fields which can interact with the solar wind to produce thrust? This may be a way to get away from the old "propellant tossed out the back of the craft" type set-up and avoid the fuel/payload ratio difficulty.
The actual mechanism of Bill's propulsion system is not vitally important in terms of its details, as long as it's based on fundamentally sound principles; which is what I think he just said in his last post. But, of course, he wants it to be as realistic as possible to add plausibility to the storyline.
I hope at least some of this is relevant to the discussion! Any comebacks on it?

thunder · 2002-04-10 05:43:04

Yes, the magsail approach has great potential for crossing vast distances in a "short" time. I don't claim to know as much as I should about this type of propulsion but this is what I do know. Depending on the configuration, the maigsail is going to produce an accelleration of about 0.1 g This gives you Earth to Mars in approximately 8 weeks.
If you want the people in the ship to live in a higher gravity field than .1 g then your goign to have to produce artifical gravity in a way other than thrust. A rotating hub format being the most favored method for this.

Canth · 2002-04-30 21:20:51

A rotating hub with a fusion engine which is smaller and produces less thrust allowing for less fuel and a longer trip might work. You don't have to use the max speed of your propulsion system, it is often more effecient if you don't, double the payload and halve the speed for any given acceleration device.

Tom Jolly · 2002-05-24 09:47:38

Here are two useful formulas for you to work with.
v=at ; Given your final velocity (10 million meters per second) and your acceleration (0.4 G's, or 3.92 m/sec^2), you can easily figure the number of seconds it'll take you to get to that speed. I get about 29 days.
deltaV = (v.e * ln(MR)) ; This looks worse than it is. (v.e) is just your exhaust velocity. MR is your vehicle mass without fuel divided by your vehicle mass with fuel. "ln" is natural log, a button on your calculator. Since you know your exhaust velocity and the delta-v you want (your final velocity), you can work the equation backwards to get your mass ratio. This comes out to;

(deltaV/v.e)= ln(1/MR)

This is the same as;

e^(deltaV/v.e) = 1/MR; "e" is the physical constant e = 2.718, which you are taking to the power of (deltaV/v.e), a number you can easily calculate. Thus, if your end-velocity is the same as your exhaust velocity, you get an MR of .37. This means your ship is only about 2/3 fuel, which isn't bad at all. Aerospace engineers would kill for an MR like that for Earth-launch. Usually MR is about 0.05 for Earth launch.

On the other hand, that only ACCELERATES you. If you have to decelerate, too, then your overall deltaV is twice as much, and you have e^2 in the formula above. This reduces your payload mass to 0.135 of your overall mass so you can slow down at your destination. And, of course, you have to refuel when you get there.

New Mars Forums

Announcement

#1 2002-02-18 17:32:28

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#2 2002-02-19 02:54:43

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#3 2002-02-19 03:31:07

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#4 2002-02-19 20:59:40

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#5 2002-02-21 01:30:24

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#6 2002-02-21 05:49:53

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#7 2002-03-06 00:37:02

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#8 2002-03-17 23:56:54

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#9 2002-04-01 20:41:10

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#10 2002-04-01 21:02:52

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#11 2002-04-01 21:21:16

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#12 2002-04-02 03:50:07

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#13 2002-04-02 19:05:15

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#14 2002-04-03 14:52:24

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#15 2002-04-04 01:54:38

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#16 2002-04-04 10:45:39

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#17 2002-04-06 16:08:09

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#18 2002-04-06 19:03:05

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#19 2002-04-10 05:43:04

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#20 2002-04-30 21:20:51

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

#21 2002-05-24 09:47:38

Re: Mars to Saturn in 31 hours and 45 minutes!? - Question about fusion propulsion

Board footer