Coriolis

> By how many centimetres is an object dropped from a height of one
> metre displaced? Assuming Island One, 1 G, 1 RPM, etc. This could
> be valuble information for traveling athletes.
If my calculations are correct, then for objects dropped from altitudes that are very small compared to the habitat radius (which permits me to assume constant gravity, simplifying integration; I haven't done this in years) the displacement is 2/3*sqrt(2)/sqrt(g)*w*h^(3/2). Here g is the pseudogravity of the habitat, w is the angular speed, and h is the height that the object is dropped from. Plugging in the numbers for Island One (w = 0.21) and the object dropped from a height of one meter, I get a displacement of a little more than six centimeters. That's nearly two inches in a one yard fall. For an object dropped from two meters (eg. water from a shower pointing directly downwards) I get a displacement of 18 centimeters.
So remember that when peeing in a toilet bowl: you will miss by an inch or two. :-)
Assuming g = 9.8, the formula simplifies to 0.3*w*h^(3/2), or 0.3*w*h*sqrt(h). Of course, you can calculate the displacement at a different altitude by plugging in a different value of g. At half the radius, gravity is half of the standard. Since this factor of one half goes into the denominator of the fraction, it is seen that the displacement increases: the higher up you are, the further a falling object is displaced from point zero. If, at the 0.1 gee swimming pool, you drop a ball from one meter above the water, it will hit the water at slightly more than thrice six centimeters from the place immediately below: twenty centimeters. Jump from a diving board of three meters, and you will land a meter away from where your Flatlander reflexes expected you to (twenty centimeters multiplied by three to the power 1.5). Jump from an even higher diving board, and the assumption of constant gravity is broken, so the formula is no longer reliable. But a five meter diving board should land you more than two meters off your Flatlander-intended target.

> Xenophile (there should be computer games with Coriolis being one
> thing that has to be taken into account... it could be built into the
> game engine... would make baseball or archery interesting)
There should be computer games la SimCity: SimHabitat. Given a certain amount of machinery, manpower (specified in skill profiles), and raw materials, you build a space colony. Succeeding at that, you build several, revenue from sales of habitats and powersats going into building more habitats, which you may sell for a profit or retain in order to grow. And treat those colonists well, or they may invite you over for a nice cuppa tea...

Jon Lennart Beck.