Helpful physicist needed

Hi,

We need someone with a strong physics background to settle an argument for
us. I apologise for blundering into your newsgroup and please ignore this
if you're not interested. We have some gross mis-education going on in our
own newsgroup though and could do with some help.

We're a role-playing game forum (anyone stll reading?) for a
game called Shadowrun which has a sci-fi setting with fantasy elements.
The game is "hard" sci-fi so real world physics is important to it. We now
have a seven page argument about travelling to Mars and back in two days
which some people consider feasible. Myself and another are insistent that
this is silly. It matters to us because the believer is one of the new
game designers and we don't want the setting to be turned into Star Wars
etc. Also, he seems to be carrying other people along with this belief and
spreading bad physics all over the shop. Now I know that we're humble
role-playing gamers, so if I'm bugging your newsgroup, please do ignore
this and I hope I haven't interrupted too many discussions on "The Lorentz
Transformation for Velocity" (whatever *that* is). If anyone wants to show
off their physics knowledge though, I'll lay out the argument below and
you can have a look. Many thanks for any help you can offer and happy
physicing, cheers for all the power-stations, and telecommunications etc,
you guys.

-K. Nasser.

The setting for the game is cyberpunkish in 2070AD. Established cannon for
the setting includes fusion power and advanced but plausible space
technology - a small manned base on Mars, an orbital habitat. There's no
revolutionary warp-drives or crap like that, just hand-waving of some of
today's technological sticking points.

The initial proposal from the designer was that it would be reasonable to
accelerate a craft at a constant 1g half way to Mars, decelerate at 1g the
other half, take a few hours to do some stuff and then do the same
journey in reverse. For when Mars is at it's closest, which was stated as
78million kilometres, it was said that this is a weekend trip. The
designer's rationale for this acceleration was that with fusion power, you
can generate as much energy as you like. He seems to think that the plasma
generated by the fusion reaction will shoot the craft forward like a
rocket (I mean that literally - the heat produces pressure which expels
the plasma which drives the craft). Probably the best thing to do is quote
directly from the argument to give you a taste.

***begin quote***

Let's step-by-step it:

Our reaction produces 18.4 MeV. That's a tremendous lot. We whip out our
Conversion Factors and find that that is equivalent to 21340000000 Kelvin.
Ouch.

Now we put these temperatures into the Kinetic Temperature Equations for
our products (80% He-4 and 20% H) and find that our most probable speeds
are 29787994 for He-4 and 59575988 for the H - an average mass speed of
35745592 m/s.

Now, this is all plasma, so it's magnetically active, we can bounce it
off of magnets. It's already super-fast so we don't need a magnetic
accelerator, just a magnetic bottle with a hole in it for the plasma jet
to shoot out of. Assuming that it shoots out the back at its current
speed, we are now caught up in the wild world of Conservatin of Momentum.
See, if part of the original mass is going out the back at an average of
35745592 m/s, then remaining vehicle will have to go forward at a speed
proportional to its mass so that the momentums (velocity times mass) sum
to zero.

Or to put it another way, we now have the magic equation:

9.8 m/s * (100,000 kg - N) + -35745592 m/s * (N) = 0

Where N is the mass of the ejecta out the back. I assume we can all do
basic algebra, and we are left with an N being .002798 kilograms. For the
first second

Now as the vehicle continues to hurl mass out the back, it will have to
throttle down some or the acceleration will increase. Our ratio stays
constant each second. .000027 % of the total mass every second, for 187200
seconds round about.

So we now have a compound interest problem, where we have
..9999997258^187200 and we have 94.9978% of our original mass at the end.
Since our original mass was 100 tonnes, will still have about 95 tonnes
left, so we've shot out about 5 tonne of ejecta out the back.

OK, now that we've done all the math with the actual inputs instead of
just made up stuff, can we call it a day? Or rather, 2 days?

***End Quote***

I think you can sort of see my problem from that. It's the ultimate case
of "A little knowledge." If anyone can throw some numbers back at him, or
point out the disconnections in what he's saying, then please help. The
100,000kg, by the way, was suggested as the smallest reasonable mass of a
craft you'd bother to send to Mars. The original thread is at:

[Only registered users see links. ]

should anyone actually want to see the argument. You'll see me in there
too letting the side down. You'll also see a lot of weird crap about
spirits, etc. As I said, it's a role-playing game, but it's *supposed* to
at least have internal consistency which means not re-writing physics.

I don't expect to necessarily convince this guy that he's wrong (or at
rather admit it), but I'd at least like to stop this idea from taking hold
in a game that I love. I doubt many people care about role-playing games
here, but it's important to a few of us. I guess that the ideal
response from anyone here would be:
1. Pointing out what's wrong with the physics above in ways that utter
non-physicists will find convincing.
2. Possibly a quote I can use from someone with established
science qualifications.

Note that there's a certain amount of handwaving, such as allowing the
Helium-3 process rather than D-T, a fairly generous efficiency in
converting heat into electricity, etc. Basically, we allow an
extrapolation of technology from today's, but no radical overhaul of
the laws of physics. You could post a comment on the thread above, but I'd
more appreciate replies here as unless you know the setting,
you're going to get some very irritating and confusing replies.

And sincere thanks to anyone who's read this far or bothered to post a
response!

Cheers,

-K.

Khadim Nasser (nospam) wrote:

Shadowrun is a good game system. It is also fiction. The secret to a
good game system is to find a balance between simplicity for the
purpose of facilitating game play and complexity to command interest
and credibility. Remember that this is fiction fo *SOME* rational
suspension of disbelief is in order.

To paraphrase R.A. Butler, the game mechanics should be "like a lady's
dress - long enough to cover the subject and short enough to be
interesting."

Having said that, look at the physics ot getting to Mars, stopping, and
returning.

You are interested in the fastest round-trip travel time between Earth
and Mars

Using the maximum acceleration (a) at all times will insure the minimum
travel time (t) over a fixed distance (x):

x = (1/2) a * t^2

Accelerating flat out all the way to Mars would get you there with too
much speed to stop. You have to accelerate at maximum *half* of the
way there, and then decelerate at the same rate for the rest of the
trip. [The midpoint of such a journey used to be called the *turnover
point* back in the 50's in the sci-fi pulp stories because the imagined
rockets had uni-directional thrust, and would have to literally flip
over to complete the journey while decelerating.]

So when we insert *half* the distance to Mars as x, and half the time
we wish to spend on a one-way trip as t, we can calculate the
acceleration required from the ship's drive:

a = 2 * x / t^2

For the absolute minimum distance between Earth (at aphelion) and Mars
(at perihelion) we get 54,546,844 km. One could cover this distance in
12 hours (43,200 seconds) at a constant acceleration of 0.05846 km/sec,
or about 5.95 gees. The whole trip would take 24 hours one-way and 2
days for the round trip.

[Under adverse alignments the distance could increase to as much as
396,326,804 km.]

One could not survive travel at 6 gees for very long, regardless of the
training and real-world technology involved, because at 6 gees the
brain gets compressed against the inside of the cranium, reducing blood
circulation to the point of eventual unconsciousness.

Military fighter pilots can survive brief spells (a few *SECONDS*) of 6
to 10 gees without losing consciousness because special equipment
(pneumatic pants to squeeze blood up towards the upper body), training
techniques (exercises to squeeze blood from the andomen towards the
head), and physical conditioning (cardiovascular fitness).

Anything else encroaches on 'Star Trek"-style anything-goes physics.

Tom Davidson
Richmond, VA

Tom,

Thank you very much for this. It's good you know the game too!

I was actually more interested in disputing the idea of generating a
constant 1g acceleration on a space craft for two days solid, but you've
actually pointed out something simpler in that the initial calculation of
how much acceleration would be needed is wrong. The maximum g that
humans can stand is also very useful. I'll take all this back to the forum
which will help.

Unfortunately, this will probably just shift the
argument to how it's easy to make a four day trip to Mars and back
instead, which is still absurd. I think the only thing that will close
this is to take apart the argument about driving the ship forward. For
example, I'm fairly sure you can't just take the 18.4MeV from the He3
fusion reaction, use "heat equations" to turn it into a thrust.

The designer's science goes something like:

***Begin Quote***
Our reaction produces 18.4 MeV. That's a tremendous lot. We whip out our
Conversion Factors and find that that is equivalent to 21340000000 Kelvin.
Ouch.

Now we put these temperatures into the Kinetic Temperature Equations for
our products (80% He-4 and 20% H) and find that our most probable speeds
are 29787994 for He-4 and 59575988 for the H - an average mass speed of
35745592 m/s.

Now, this is all plasma, so it's magnetically active, we can bounce it
off of magnets. It's already super-fast so we don't need a magnetic
accelerator, just a magnetic bottle with a hole in it for the plasma jet
to shoot out of. Assuming that it shoots out the back at its current
speed, we are now caught up in the wild world of Conservatin of Momentum.
See, if part of the original mass is going out the back at an average of
35745592 m/s, then remaining vehicle will have to go forward at a speed
proportional to its mass so that the momentums (velocity times mass) sum
to zero.

***End Quote***

I'm sure this is wrong, but I'm not qualified to describe how. I'm
concerned that this logic is carrying the day over there, and I'd hate to
see it pop-up in published material. Any help with this is much
appreciated.

Dear Khadim Nasser:

"Khadim Nasser" <K(nospam)@knasser.me.uk> wrote in message
newsan.2006.11.12.15.05.30.776365@knasser.me.uk. ..
....

I'd be interested in how they got a conversion from MeV to K,
without specfying the products being heated. Not that this
number is wrong... only unsupported here.


I'd be interested in how they arrived at this average.


(M + m)v0 = Mv1 + mv2
remembering that velocity is a vector, and you pick a frame that
is interesting / easy for v0. Let some small amount of mass (m)
sneak out, and see what "specific impulse" you might get.

Google search
"specific impulse"
" fusion engine"
"project orion"

David A. Smith

David,

Thanks for this. I'm now googling the terms you recommended. I don't know
how easy or hard it is to calculate this sort of stuff, but I've answered
the questions you had below, so it might be possible to go further in
saying whether it's right or wrong. Again, your help is really appreciated.


I presume the products are Helium-4 and Hydrogen. It's supposed to be a
fusion reaction of Helium-3 and Deuterium. I'm not a physicist, but I make
excellent use of Google, and Wikipedia gives me 3.7 MeV for the Helium and
14.7 MeV for the Hydrogen. I don't know if the division between them is
significant. I also have no idea how this translates to heat or even if
the formulas he's using are appropriate here. The guy is saying that all
these super-heated particles are going to propel the craft like a rocket.


Your guess is as good as mine. What is the process for getting from heat
to kinetic energy like this? This is one of the bits I'm doubtful about
but don't know enough to dispute. And I think he believes it will all be
useful because it's contained in a "magnetic bottle" which will propel the
whole plasma in one direction. There's a question about whether this
magnetic bottle is powered in any way, or just consists of big magnets. I
don't know if there's a possible issue with that, also.




Can you just tell me if I've understood this correctly?

If M is the ship, say 100,000kg, and m is the plasma going at 35745592m/s,
and we assume accelerating at 1g from 0, then it's:

100,000kg + m kg = (100,000kg * v m/s) + (35745592m/s * m)

m = 0.024kg. I think that's right, but it's been a while since I solved
equations.

So in order to get an acceleration of 9.8m/s/s he would need to spew out
0.024kg of this plasma every second. Is that correct? Assuming that his
average mass speed was correct which I only have his word and your
"Hmmmmm" for? You can see the problem I'm having now, at any rate. This
guy's throwing around a lot of numbers thrown at me that I distrust but
I need to be able to say what they should be.

Again, thanks for your help. This is already very useful (assuming I have
my sums right, which I may not).

-K.

Dear Khadim Nasser:

"Khadim Nasser" <K(nospam)@knasser.me.uk> wrote in message
newsan.2006.11.12.18.18.30.82224@knasser.me.uk.. .
....

If you set v0 = 0, and use the first second where 1g acceleration
gets you 16.6 m/sec for the ship...
100000 * 16.6 = m * 35745592, m = 0.046 kg


Close enough.
[Only registered users see links. ]

.... but I think they have attributed far too little reaction mass
that does not take part in their reaction. This lowers the bulk
temperature, and consequently, the exhaust gas temperature.

David A. Smith

David,

You are being an immense help. I hope I'm not taking up too much of your
time, or that someone else is willing to share the burden of my ignorance
with you.


One of the points that my friend has put to this guy is that the ship will
need to carry a large amount of reaction mass. The response has been that
no reaction mass is needed as the enormous velocity of the plasma leaving
the ship is sufficient to achieve 1g acceleration. Your equation shows
that this would require 0.046kg per second if I have understood. Or a
total of nearly 8,000kg for a two day journey of constant acceleration and
deceleration. That's a huge amount of Helium-3, I know that. This is
the sort of stuff that I've been saying, but unable to put numbers on and
thus unable to convince anyone.

Three questions if you (or anyone else) can help. How would I go about
calculating the effect of adding reaction mass into the mix. Are there
usable formula for averaging out the temperature, can I just apportion the
temperature between the elements according to their atomic weights?
Secondly, I've taken on trust that the full velocity of the the particles
produced in this fusion reaction is being applied for directional thrust.
I have no idea if this is acceptable, but it seems to me that it may not
be. Third question would be about focusing the plasma with an
electromagnetic field. Is it possible to give me any sort of idea about
how much energy is required to sustain a field that is directing energy of
this magnitude? I would guess that it is a lot, but I don't know.

And sorry I suppose there is a fifth question ("four, sir.") - is
that the speed of the particles is correct? I believe that the guy used
KE = (3/2) k T to determine their speeds and then averaged them. Is this
actually the correct way to get thrust for a plasma rocket?

Again, thank you for all of your help.

-Khadim.

Dear Khadim Nasser:

"Khadim Nasser" <K(nospam)@knasser.me.uk> wrote in message
newsan.2006.11.12.21.30.29.833259@knasser.me.uk. ..

It OK. And please forgive the mixed unit systems I applied
before, and the fact that I conflated how far something moves in
the first second (16 feet), with its velocity (32 feet/sec or ~10
meters/sec).


Ideally, no. But in practice, yes. Most of an atomic bomb stays
as fissible material, only a very small percentage is actually
"downconverted" to more stable forms.


Double that (my error). Yes. As an absolute minimum, for a
perfect process, with assumed average velocity.


I would guess that 10 times that would be required, were we to
attempt this process today.


"kinetic theory of gasses". You are liberating, and you must
spread that uniformly across what is being spewed out the rear.


Rocket engines are *extremely* efficient in doing their job.
Consider that you will do a control volume around the engine.
Inputs are the reactants. Outputs are hot gas, and whatever
propagates through the mechanism.


"tokamak"
.... it has been more energy than is liberated in our attempts at
controlled fusion. Not by much, but...
It is the neutrons that is the real problem. A real bevy of
neutrons are created, and they are not containable.


Do the thing, and ask forgiveness later. I would revel at the
miracle of arriving at any temperature first. "kinetic theory of
gasses" will get from temperature to average velocity.

David A. Smith

As this is a game, you don't need to stick to current physics. You can
posit an advance that makes your game possible. Make your assumptions
consistant and stick to them. Robert Heinlein's "Fifth Column" relies on
this technique.

For example, I've been toying with some ideas that make the systems used
by David Drake and Daved Webber in their novels possible.

The trick is to make only one or two assumptions that aren't precluded
by modern physics and follow them to their logical conclusion.

Khadim Nasser wrote:

Charles,

Thanks for replying. The problem is not "making it work" as such though.
The problem is that the game already exists, has a fairly established
level of science and technology and a new designer hired for the setting
is utterly convinced that flying a ship to Mars in two days is a small
task. This sort of discarding of science undermines a well-constructed
setting and shatters the internal consistency you're talking about. The
problem I'm having is more "pointing out that it doesn't work" in a
desperate bid to preserve that setting.

Anything you can do to show that accelerating a ship at 1g for 2 days
without melting it is not "near future" technology, is what I urgently
need.

But good luck with the Drake and Webber systems.

Regards,

-Khadim.