Coriolis force and predicted effects?

> I have a few questions that I hope you won't mind answering,
> relating to Coriolis force, and how it would affect normal
> activities that people carry out.

[...]

In late July last year there was a thread concerning the Coriolis force. To save you the trouble of mining the ssi_list archives, and to exploit this grand opportunity to repeat the responses crafted by my genius ---
--- I'll copypaste my contributions to that thread here.

> 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...

> Coriolis is a facinating thing, that will make life on the High
> Fronteir interesting in new and challenging ways. Is there a unit of
> measurement for the Coriolis effect? There certainly should be. If
> I have weak bones, it's good to know if the habitat I'm visiting is
> 0.5 G or 1.5 G. It would be nice to know if it is 0.5 C (or whatever
> it would be called) or 1.5 C (or whatever it would be called).
The Coriolis force (pseudoforce) is given as -2m multiplied by the cross product of the vector of rotation and the velocity vector of the object moved. That is, an object moving parallel to the spin axis feels no Coriolis force - which intuitively makes sense, since the intuitive explanation of the Coriolis force is that when an object moves from a high-velocity region (far from the spin axis) to a low-velocity region (closer to the axis) or vice versa, it will feel a "tug" to accomodate it to the velocity of the new surroundings.
The magnitude of the Coriolis force on an object being moved vertically in a rotating habitat is then 2*m*v*w: 2 times the product of the object's mass, its velocity, and the angular velocity of the habitat measured in radians per second. Divide out the mass, and you get a Coriolis "acceleration", which for an Island One type habitat (with rotation rate = 2 RPM = 0.21 radians/second) is 0.42 multiplied by the velocity, in SI units.
So if you stand in an elevator car that rises by one meter per second, you will feel a sideways acceleration of 0.42 meters/square second, or about 4.3% of your weight at the 1 g level. If that elevator car goes all the way to the spin axis, the Coriolis force that you feel will remain constant, but since your weight will go down the Coriolis force will eventually dominate. If that elevator car simply passes the spin axis and descends on the other side, then as you pass the axis you will weigh 4% of your normal weight; and that weight will press you towards the wall of the elevator car. Then, of course, unless the elevator car is rotated, you will feel an increasing weight due to centrifugal force towards the original ceiling of the elevator car, but the Coriolis force will remain constant at 4% of your 1 g weight.
An Island Three type habitat rotates at a quarter of the rate of an Island One. Therefore the Coriolis force will also be a quarter as strong.
Now, if you rise from a chair, what is the upward speed of your torso? A rough estimate is this: my thighs, from knees to pelvis, are about 45 cm long. The chair that I'm sitting on right now is tall enough that my knees are bent at roughly right angles; therefore, when I stand up from it, my torso moves 45 centimeters vertically. I estimate that I can easily stand up from this chair in half a second, if I'm in a hurry.
That means that my torso moves with a mean vertical speed of roughly a meter per second.
So if my house were located at the 1 g level of an Island One, I would experience a sideways tug upon my upper body of about 4% of my weight. How much my upper body weighs, from pelvis and up (neglecting the Coriolis force upon my thighs), I don't know, but let's say 70 kg or not much less.
So the Coriolis force that I would experience would be like to someone pushing me with a force equivalent roughly to 3 kg, or six pounds. The weight of three cartons of milk. Noticeable, but not enough to make me tumble across the room unless I were dead drunk.

If we want to make a unit for the Coriolis force, we must specify what vertical velocity this Coriolis force is calculated for. One meter per second would be a good choice, both to simplify calculations and because this speed lies right in the range of vertical speeds that inhabitants would be likely to experience: the characteristic Coriolis force in a habitat is specified as the pseudoforce exerted upon an object being moved vertically at a meter per second. Since the Coriolis force scales linearly with the mass of the object, like centrifugal force and gravity, we can easily subtract the mass out and get the Coriolis acceleration, just as we have the centrifugal acceleration, and we can compare the Coriolis acceleration with the standard 1 g. Thus, an Island One space habitat has a Coriolis force of 0.042 m/s^2, or about 4% gee. An Island Three has 1% Coriolis; a small habitat of a quarter of Island One's radius spun up to one gee has 16% Coriolis.

> Also, does it act the same on objects of different mass, like
> gravity does? I mean, if I drop a 10 Kg object from ten metres, and
> it is displaced 1 metre while falling, would a 100 Kg object dropped
> from the same hight in the same habitat also be displace 1 metre?
S.

> So will we have to redesign many fixtures and processes to
> accomodate the coriolis effect?
Rapid elevators come to mind. And trampolines and ski jumps. Archery and sports involving throwing, hitting and kicking things such as baseball and javelin.

> Will the drain hole in a sink be offset an inch from the faucet?
Only if it is required that the faucet drip right into the drain hole. As long as the sink is large enough to receive the water from the faucet, no problem.

> Will you (as a man) still be able to go pee in the middle of the
> night and know that you're hitting the bowl :)))
As for myself, I generally turn on the light if it's dark outside. However, even though I'm living alone, I prefer to reduce the noise by peeing on the side of the bowl rather than into the water in the middle. So I would be more susceptible to missing the toilet bowl altogether.
Of course, as soon as I aquire my space legs, I can redirect my aim properly. In a habitat with noticeable Coriolis effect, it should be easy to determine which way the habitat spins (notice which way you're pushed when rising from a chair, or make a small jump). But if you forget the direction of the spin - such as if you're using another toilet than your own, and this toilet is pointed the opposite way from yours - you could end up correcting in the wrong direction. Then you won't miss by one inch, but by two.
There may be signs above toilet bowls, saying "Male Guests, Please Sit Down To Pee" or arrows painted in the toilet bowl indicating the spin direction.

> Will you have to pay particular attention when you're pouring you
> hot coffee.
Not if you keep the spout of the coffee can a few inches above the cup.

> Will the aim on kid's squirt guns have to be tinkered with?
That's for the kids to work out. I should prefer to tinker with their squirt guns such that they backfire when the kids try to squirt at *me*.

> What kind of turbulence will occur in the Habitat's water mains and
> sewer pipes?
Nothing much, I think. Unless you move large volumes of water rapidly in a vertical direction, or horizontally downspin. Then the pipe might be torn loose if you haven't fastened it properly. Not so nice if it's a big sewer pipe.

> Will birds and bees be able to adjust?
That will have to be seen. Birds probably will adjust, at least those that are not migratory. Bees might be confused by the fact that the sun doesn't move - ISTR that bees not only use the sun to navigate, but they correct for its motion across the sky. In neither case do I think that the Coriolis effect should be a problem. Flying things are already adapted to wind and gusts. If they can correct for wind, they can correct for Coriolis.
Birds might be confused by varying gravity, though being more intelligent and therefore more adaptive than bees, they might be well able to learn to cope with this. Bees are so small and therefore so localized in their flight routes that I suppose this won't be a problem for them.

Hope this helps.

> Is Coriolis the only force that would act on people in a space
> colony? Would it or any other 'force'(effect of rotation) act in
> different ways depending on the size of the space habitat?

Well, there is obviously the pseudogravity itself, the centrifugal force (or pseudoforce). The larger the habitat, for a given rate of rotation, the stronger the pseudogravity. The larger the habitat, for a given pseudogravity that is desired, the slower the rate of rotation. And in a very small habitat, or near the axis of a larger one, you can change your pseudogravity noticeably by running upspin or downspin. Running upspin (against the direction of the spin) you will appear to weigh less than when standing still; running downspin the opposite.
If the habitat serves as a large space ship, with some sort of engine tacked onto it, then of course there will be an added component to the pseudogravity, which disappears again when the engine is idle. Though only if the habitat rotates slowly enough to create only a small fraction of a g, or if the engines are very powerful, will this added component be felt by the inhabitants.

Jon Lennnart Beck.