coriolis bicycle question

--- In spacesettlers, "Ian Woollard" wrote:
> In a rotating frame of reference, there's two pseudoforces that
> appear, centrifugal force that pushes you outwards with a g-force
> proportional to your distance from the spin axis, and Coriolis force
> that kicks in when you start to move.

OK, centrifugal I pretty much get. After all, it's what will give
space dwellers weight.

> Coriolis only kicks in though when you climb up/down or go
> upspin/downspin. Going along the axis (north/south or whatever you
> want to call it) doesn't do anything per se.

Think I get this too. If my student lives due north or south from
school (and doesn't have to go uphill or downhill), she can ignore
Coriolis while biking to and from Gerard O'Neill High.

> Coriolis acts at 90 degrees to your speed in the plane your spinning
> in. So if you run downspin, coriolis pushes you harder into the
> deck.
> If you run upspin it lightens you. If you drop something it pushes
> it upspin, if you raise it up, it pushes downspin.
>
> Hope you're with me so far.

I think so. We'll call the direction of spin "west" and the anti-spin
direction "east" and assume them to be left and right of a person
facing north, respectively (it is on Earth). With the several hundred
KmPH that a habitat spins, the gains and losses in weight would hardly
be noticeable, unless you are a champion racer or something.

But if I drop a shot-put, it won't fall (from my POV) straight down.
It will move slightly to the west. How much depends on how high the
drop is and how fast the habitat is spinning. If I care about the
condition of my toes, I'll take this into account (or just not drop
the danged thing). If I toss it straight up, it moves to the east...
until it starts back down, at which time it starts curving to the west.

> The bottom line is that cycling on the 'flat' (i.e. constant radius
> from spin axis, for example going equatorially around a Bernall
> sphere) does nothing more than make you heavier or lighter, but for
> example, going downhill or uphill along the spin axis (north/south)
> will mean you will have to lean the bike to compensate for Coriolis,
> and yes, it does depend whether you're going up or downhill- it will
> be opposite directions!

OooooooK. I think I get this. If our high school bicyclist is going
uphill and north, she will feel a force pushing her west (left, from
her POV). However, if she then turns around and rides downhill and to
the south, she will feel pushed to the east (still left, for her). In
both cases, she leans RIGHT to compensate.
If she then rides over a section where she neither gains nor loses
altitude (a cylindrical section near the equator?) she feels no force
to the side, and rides upright, like on Earth.
But, if she continues to the south and starts going uphill again, she
will feel pushed to, um... to the west again, only now this is right
to her. Coming back downhill, she will be pushed east again, which
again will be right. In both cases, she leans LEFT to compensate.

WHEW!!
So it isn't "lean right going to school and left coming home," it's
"lean east going uphill and lean west going downhill."
I'm pretty sure I've got this, now. And yes, I'm writing a scene of a
high school girl riding her bike to school. I'll post it here when I'm
done, if anybody wants to read it.