Vince Leon (vleon@email.arizona.edu)
Tue, 7 Nov 2000 17:12:30 -0700

Actually -Z- is the author of that web page I was just referring readers to
it, and some of what you described was already mentioned by him in one of
his previous post.

A little more info, my example of on object being "pushed" down by the air
referred to an object that was not previously in contact with the surface
of the cylinder. Over a couple of years ago I had assumed that an object
not in contact with the surface of the colony at anytime would be
weightless as long as it did not come in contact with the surface. For
example: after watching the Kampfer flying only inches of the road in 0080;
I had thought that a mobile suit could fly in through the dry dock, into
the colony and fly up to the inside surface of the colony only inches away
and hover there without having to waste extra fuel.
But as -Z- pointed out, the air inside a colony will also begin to rotate
around due to the spinning of the colony and this is what would "push" an
object "down" or towards the surface of the colony.

So in calculated a colonies' rotation with a radius of 500 meters I would
do it as so:
Calculate circumference (2 * Pi * 500 meters) = 2 * 3.14 * 500m = 3,149.59
meters

then velocity if colony surface^2 (gravity * radius) = 9.8m/s * 500m =
4,900m^2/s

then take the sq root of the velociy = 4,900m^2/s = 70 m/s

so the time for one revolution would be (circumference / velocity) =
3,149.6m / 70m/s

this comes to 44.88 seconds for one revolution. Is this incorrect?

--- --- --- --- --- --- --- --- --- --- --- ---
Vince Leon
vleon@u.arizona.edu

-----Original Message-----
Sent: Monday, November 06, 2000 11:01 PM
To: gundam@aeug.org
Subject: RE: [gundam] Gravity within a colony (was: Funnels and flying MS)

Hi;

There are a number of items on your page that are either somewhat incorrect
or unclear. For one, since the gravity is due to centripedal acceleration
(w*r^2, where w is the rotational velocity in radians/s), it drops off
exponentially, not logarithmically.

Secondly, "centrifugal force" is a layman's term which isn't used in
science. There is no such thing. Take a horizontally spinning carnival
ride. It spins up, you get squished to the outside of the seat. What you
are experiencing when spun is an acceleration, or centripedal acceleration.
Centripedal acceleration is the acceleration a body must have towards the
inside of a circle for it to stay on a circular path. Since you have mass
and inertia, your body resists the acceleration, causing you to press into
the outside of the seat.

If you jump up from a spinning colony cylinder, you are not "pushed down"
by the air. Since you are travelling at the same velocity as the cylinder
when you jump up and leave the colony surface, you are in essence flung
back down to the surface due to you velocity and acceleration. When you
jump on the colony, you appear to go up and down. But actually, you are
also traveling sideways due to the spin. Lets say you are standing along
the colony axis, facing along the axis. When you jump, if you jump up at 5
ft/s, you are still traveling sideways at the same speed as the colony
spin, and this combined velocity, part up, part sideways due to spin, is
what pushes you back into the colony. You simply re-collide--there is no
attraction involved.

So, if you jump, the colony also will not spin out from under you very
much--relatively speaking, you and it are travelling at the same speed. If
you jump straight up in a moving school bus, does it drive out from under
you? Nope. Same idea on the colony--relative velocity (except that the
rotational component of velocity does kick in a bit).

BTW, A colony cylinder that has a 500m radius ( a 1 km diameter) would need
to rotate as follows:

earth g = 9.81 m/s^2 = colony g =w*r^2

Solving for w, w= 9.81/(r^2) = 9.81/250000 = 3.924*10(-5) rad/s

In more common terms, to convert rad to degrees, multiply rad by 180/Pi.
Therefore, 3.924E-5 rad/s is 0.0022 degrees/s. or 0.1349 degrees per
minute. Or, 2668 minutes per revolution, or one turn every 44.5 hours.
Make the colony 250 m in diameter, and the rotation rate increases to:

w = 0.0002 rad/s = 0.009 deg/s = 0.5396 degs/min -> 667.2 minutes per
revolution, or 11.11 hours per revolution.

What about if you are at the axis of the colony, where the radius is zero,
and you are pushed towards the outer wall? Well, the only way you would
have motion is if something pushed you towards the wall. As you came
closer to the spinning wall, you would have NO attraction to the wall. If
there is an atmosphere, the air being dragged along with the cylinder wall
would create a wind relative to you, which you slowly speed you up in the
direction of the colony spin and pull you further out to the wall until you
schmacked into it. Depending on how much drag you have, the air can speed
you up tangentially a lot, causing you to smack nearly vertically into the
wall as if you fell from a height. If there were no air in the colony, you
would travel straight out to the wall, which to you would look like a huge
moving wall. Depending on the colony size, it could be moving quite fast.
Your impact would then be more like jumping out of a moving car than
dropping from a height.

Yeah, I have a couple degrees in this stuff--I'm not making it up.

-
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