Re: (TFT) Math of Demon Towers --> Too expensive!

["Quite Confused" <Confused3141@hotmail.com>]

> Hello,
> Here is my take at the demon tower.
>
> acceleration = 9.8 m / (s*s)
>
> The velocity with constant acceleration is:
>
> velocity at a given time
> = starting velocity + acceleration * time
>
> Assuming that the escape velocity is 11.2 km / s and
> converting everything into meters we get:
>
> 11200 m / s = 0 m/s + 9.8 m / (s * s) * ? s
>
> Solving for ? gives us:
>
> (11200 m/ s) / 9.8 m/(s*s) = ? s  = 1142.9 s

at least we all agreed on this!

> (This is ignoring air resistance and changes in the
> gravitational field between the top and bottom of
> the tower.)
>
> Now how far would you fall in the 19 odd minutes
> above?
>
>
> The distance equation is:
>
> distance (in a time) = starting distance +
> ( starting velocity * time ) +
> ( 1/2 (acceleration) * time squared)
>
> d( t ) = 0 + 0 + 1/2 * (9.8 m/(s*s) ) * 1142.9 s * 1142.9 s
>
> d( t ) = 6,500,480 m
>
> Assuming the gates are 1,000 meters apart
> I calculate it will pass thru the gates at least 6,501
> times.

Not shabby so far excepting that the original problem gives the seperation
at 1000ft (304+m) not 1km. I see why you set that limit from your remarks
later on though. I did it as a differential equation as follows;

M * A = F
where force is the resultant of the forces acting on the Demon at any
instant
these forces are the weight (W) of the Demon (I used 5 slugs or 160lbs) and
the air resistance (U)

the weight is W = mg where g is gravitional acceleration at earths surface
and m is the Demons mass so we get something like;

W - U = mg - bv^2

acceleration (a) is the time derivative of v a = dv/dt so by Issacs second;

m * dv/dt = mg - bv^2

which is a differential and we want v(t) satisfying the initial condition
v(0) = v sub 0 = 10 try dividing m to start

> The first time the gate fails, it will flicker
> for 1 minute before collapsing.  (In my campaign
> it lasts for an AVERAGE of 1 minute but might fail
> after 5 seconds or might last a maximum of 1 minute
> and 55 seconds (but that is just because I'm a mean
> GM)).  However if a gate fails a second time while it
> is flickering I rule that it fails instantly cutting the
> person in half.  (I do it this way because it make
> going thru failing gates much more interesting
> and because I'm mean.)
>
> Now just before launching the demon into
> orbit, they are passing thru 11 gates per second.  It
> takes 5 seconds to cast the spell to stabilize the gate.
> I believe a gate fails on a 17 or an 18.  This is a 4/216
> chance or 0.0185... or just more than 1.85 %.

I had this at 53.5 transits a second or 107 gates. But again that was for
300m. I didn't bother with the failure rate because that wasn't part of the
problem given. That'd WAY up the required number of pairs as you point out

> Now assuming an average velocity of
> 11 km / s just before orbit insertion our demon
> will pass thru 55 gate transitions before the gate
> can be repaired.  The probability of a second
> gate failure given that one happens in the last
> 5 seconds or so is:
>
> P(2nd gate failure) = 1 - ((1 - 0.0185 ) to the 55th power).
>    =  64.2 % (approximately)
>
> Of course this could happen on an earlier
> 5 second group of time, but many fewer gates would
> be transited so the odds are much better that the
> wizards could repair the gates.

Now why would I wanna have to repair them? Arn't gates 2 dimensional? If so
I could stack them one on top of the other at either end and as it was
originally stated the gate underneath would take over should a higher gate
fail.

> Therefore, I wouldn't send any demon
> I want to see alive again, into this device...
>
> Note that the demon would hit like a meteor
> against the floor so any wizards standing around
> to repair the gates are quite likely to be blown up.
> That would increase the cost of such a device by a
> significant fraction.

Uh yeah.
Well over 160,000lbs per square foot. Make the collision inelastic and 99+%
goes to heat. Quite a little pop.

> A smaller version of this where a rock
> only falls for 30 seconds or so could be safer and
> would still make a powerful artillery piece for
> bombarding castle walls.  Such a device would
> have the rock pass thru 5 or so gate and would
> fire rocks at around 300 meters per second
> (neglecting air resistance).  Of course the wizard
> would have to get close enough to the castle wall
> to cast the final targeting gate.
>
> One thing people have not considered
> is the difficulty of hitting a 3m square target
> after falling 1000 meters.  How would we steer
> our demon or rock while it is falling this
> distance?  If our missile touched the side of
> the tube it would rattle back and forth wiping
> out the tube, and if we make the fall a much
> smaller distance (say 15 meters) then the
> number of gate passages increases sharply
> greatly increasing the cost.
>

The frictionless Demon is no problem. Rocks are another matter entirly but
if we use srydzews' vaccum plan then we're okay there too.

Jay
<<I am depriving a village somewhere of an idiot>>
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