[Runequest] Fact check

Styopa styopa1 at gmail.com
Wed Mar 27 09:38:43 EST 2013

On Tue, Mar 26, 2013 at 4:32 PM, Asher Royce Yaffee
<ashersensei at gmail.com>wrote:

> Hi, All,
>    One thing to remember about a ringworld or spinning space station or
> other such structure that gets "gravity" by rotation.  When you drop an
> object inside the environment -- ring, station, what have you -- the object
> does not continuously accelerate.  Ringworld's "gravity" is just about the
> same as Earth's, in that we would be the same weight on Ringworld as we
> would be on Earth.  But that is where the similarity ends.
> ...

>   On the Ringworld, if I jump off a tall building, I fall at about 32
> feet/second or 9.8 meters/second -- and that's it.  There is no further
> acceleration due to gravity.  So I watch the sidewalk below approach at a
> more leisurely pace.

Great point.

IANARE (I am not a Ringworld Engineer), but what we're talking about is
(essentially) a fast spinning wheel, from which something teeny near the
rim separates and becomes an independent body.

First, your point is well-taken that the moment the Troll separates from
the wall, he's no longer part of the ring.  Where on earth, there would be
a constant force of gravity operating, this acceleration wouldn't be
happening.  That made me pause for a second.
Of course: he doesn't become an 'independent body in space' by any means.
Assuming http://www.alcyone.com/max/reference/scifi/ringworld.html has done
his homework correctly, to generate 0.99g gravity, it's spinning
fast...CRAZY fast.  It completes one circuit in 9 days. (!)

Now remember, he's NOT really feeling gravity.
The ring is simulating it by spinning fast - crazy fast, like 1220 km/s -
and essentially what he feels is 'gravity' is the curvature of the ring
coming up under his feet (because his body, as anything spinning in a
circle, is trying really hard to fly off on a straightline tangent to where
it is right now).  When he steps off the edge, both he and the ring are
still going 1220 km/s laterally - his body is just free to follow the
straight line path it really wants to.
He will NOT be accelerating toward the ground.  In essence, the curvature
of the ground will be coming up to greet him somewhere ahead on his linear
path.  What forces ARE acting on him at the moment?

1) his momentum - carrying him forward in a straight line at 1220 km/s, the
same speed as the ring rolling under him in the same direction.
2) air pressure - working in 2 directions:
 - first, it's pushing him laterally.  The entire multi-gigaton airmass of
the ring is spinning along with the ring.  So he's like a bug in stream of
water being pushed forward, essentially (I'd guess) keeping his speed up to
the ring, as there's really nothing slowing him down either.
- second, like any earthbound object, the air is going to resist his fall
by not getting out of his way (drag).  Every particle of this airmass is
trying also to go in straight lines, and being intercepted by the curve,
just like he will be. Which means it's going to be denser near the ground,
and pushing harder spinward as he approaches the surface.

So my guess is that if we plot his position at t1, t2, t3, t4, t5, ... from
a fixed external viewpoint, we'll see him go in a straight tangential line
from his point of departure, POSSIBLY curving spinward a little as
increased air density is hitting him as his aspect approaching the ring
surface gets more and more toward the perpendicular.

(Just for fun, I did manually plot this with him at an exagerrated height -
using graph paper, a circle of radius 15, a troll jumping from a height of
10.  Plotting his heights from the ground at t1, t2, t3, t4, t5, ...it sure
looks like this heights decrease linearly over time.)

FWIW, NASA apparently doesn't agree with me, as their java model shows
things differently, but I genuinely feel their model is intuitively wrong.
 Yes, I'm disagreeing with Rocket Scientists. :(  I suspect they assumed a
frictionless environment, which at this scale is significant.

Fun thought experiment, I'm going to submit it to xkcd's "what if" and see
what he determines.  He IS a rocket scientist and he likes solving things
like this.
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