Mark Wilson (mmwilson2@earthlink.net)
Tue, 7 Nov 2000 20:15:19 -0500


The tangential velocity component (how fast the outside of the cylinder
would spin to a stationary observer) is calculated by w*r (where w is the
rotational rate in radians/s), not gravity*r. For a 500m radius, rotating
at 3.924E-5 rad/s, its tangential velocity would be 0.0196 m/s (or 0.044
mph). For a 500 m station with a circumference of 2*Pi*r = 3141 m, it
would take 44.47 hours for it to complete one rotation.

If a MS flew into a 500 m radius colony cylinder and did not touch the
surface, the ground would not exactly be flying by. For that matter, the
"surface" air flow wouldn't exactly cool you on hot day either!

Make it a 250 m radius colony (This is still HUGE!!) and the ground
velocity only speeds up to 0.078 m/s or 0.176 mph.

Would you jump off a car going a tenth of a mile per hour? Not exactly
that dramatic.

For a "dangerous" rotational speed (say ~20 mph) the radius of the colony
would have to be reduced to ~ 80 m, or it would be a bit shy of 2 football
fields in diameter (not including the end zone!).

> [Original Message]
> From: Vince Leon <vleon@email.arizona.edu>
> To: gundam@aeug.org <gundam@aeug.org>
> Date: 11/7/00 7:12:52 PM
> Subject: RE: [gundam] Gravity within a colony (was: Funnels and flying MS)
>
> 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-----
> From: Mark Wilson [SMTP:mmwilson2@earthlink.net]
> 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.
>
>
> -
> Gundam Mailing List Archives are available at http://gundam.aeug.org/

Mark Wilson

-
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