Somebody Explain the Coriolis Effect to me

[borschevsky]

At some point in my life I heard the "fact" that water drains one way in the northern hemisphere and the other way in the southern. I might have heard this from a teacher somewhere, or from that Simpsons episode about Australia . Anyway, I had this idea in my head for a while, and then somebody pointed out that the Coriolis effect is too small to really affect draining water in a normal sink. So I looked it up, and I found what I guess is the normal diagram: a guy standing at the north pole, and shooting a bullet south. As the bullet goes further south, the earth "moves out of the way," because the earth is rotating east while the bullet is not. So the bullet appears to be "deflected" to the right. Fine.

But this explanation implies to me that the Coriolis effect only operates on the north/south component of the bullet, and would not have any effect on a bullet fired due east or west. Now this guy says that's not true, that the effect is the same regardless of the direction the projectile is moving. I don't understand his explanation, but that may be because I have the old explanation stuck in my head. Anybody have a good explanation or diagram for this?

[Logain]

The Coriolis effect is real according to literature I read on it, but definitely too small to observe in real life. Only under perfectly controlled conditions in a lab could you possibly witness the draining phenomenon.

[Dr. Borodog]

The mathematical term that describes the coriolis force involves the negative of the cross-product of the Earth's angular velocity vector and the velocity vector of the moving object. Hence a projectile fired east or west will be subject to the coriolis force. However . . . the resultant vector points south and up (for an eastward-moving projectile in the northern hemisphere, for example). The component that points south vs. the component that points up depends upon your lattitude. If you are on the equator, it points completely upward. Just off the north pole it points almost completely south.

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You will respect my philosophai.

[This message has been edited by Dr. Borodog (edited 03-15-2004 12:13 PM).]

[Quailman]

Here's a site with some reasonably good explanations.

When I had astronomy (There were only about four named constellations back then), I tried to reconcile the effect on an east-west vector by imagining what it would be if the earth were flat. By that I mean if the earth was a spinning disk. Then if it had some thickness at the center, and this gets wider until it's a sphere.

And while the effect on draining water is not nearly enough to offset even the slightest movement in that water, it does affect the rotation around high and low pressure systems. In the northern hemisphere, budding meteorologists use the left-hand rule to remember which way the air circulates around a high or low. Point your left thumb up for a high or down for a low. Then curl your fingers like you're making a fist. The air circulates this direction.

[wordcross]

So then why does the water swirl into sink drains, if not because of the Coriolis Effect?

[Dr. Borodog]

Because it is nearly impossible for the fluid to remain irrotational as it drains. The slightest rotation of the water is increased (by the conservation of angular momentum) as the water approaches the drain.

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You will respect my philosophai.

[borschevsky]

Originally posted by Quailman:

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Here's a site with some reasonably good explanations.

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Thanks for that; it's a good explanation.

Originally posted by Dr. Borodog:

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However . . . the resultant vector points south and up

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So just conceptually, is a bullet fired east trying to get into something like a "higher orbit"? In the north, it could go south to a longer line of latitude, or else up further off the earth?

Does this mean that bullets fired east take longer to land than bullets fired west? Since easterly bullets would have a component of the coriolis vector pointing up.

[Quailman]

And in the case of toilets, they are designed to drain with a swirling action that will facilitate the movement of movements over the trap that forms the bottom of the bowl and down the drain.

oh, and we should never forget to consult Cecil on such weighty matters as this.

[Dr. Borodog]

[Pablo]

I remember doing an experiment with a pendulum in college. It was set up so that the tip of the pendulum dragged lightly through some sand at the bottom of its arc. The line that it traced slowly moved around and if you measured the displacement over some known time, you could calculate your latitude on the earth.....as I recall.

I think this was discovered by Charles or Boyle.

(I think this thing is called a Fucault pendulum, but then I'm reaching back to the late 60's)

[Dr. Borodog]

It's Foucault, and oddly enough, I think it was shown by Foucault. A pendulum on the equator will not rotate, and one on the pole will rotate once a day. You can indeed use a formula and the local rate of rotation to calculate your latitude. Of course, this requires building a giant pendulum. It's much easier to just measure the altitude of the north star above the horizon, which is identical to your latitude.


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You will respect my philosophai.

[This message has been edited by Dr. Borodog (edited 03-15-2004 01:00 PM).]

[Pablo]

[Vinny]

So theoritically, what does really happen if every Chinese in China jump up in the air at the same time, holding hands?

[Dr. Borodog]

Nothing. Assume one billion chinese massing an average of 100 kg (which is MUCH too large, but makes my math easy). That's 100 billion kg of chinamen, 10¹¹kg. The Earth masses about 6x10²⁴kg, or almost 10¹⁴ times as much as our chinamen. Compretry negrijabber.

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You will respect my philosophai.

[This message has been edited by Dr. Borodog (edited 03-15-2004 01:20 PM).]

[Courk]

You know, Pablo, two wrongs don't make a right, but even I would expect you to know that two Wrights made a plane. *dodges tomatoes*

[One Skunk Todd]

<worthless trivia>I'm fairly certain that the force exerted on small arms projectiles is so small as to be negligible. However, I remember reading once that very long range artillery and naval guns used to have to take the effect into account when calculating range and bearing to the target.</worthless trivia>

[Mikko]

I've read that in the Falklands during WW1 the English navy kept fireing left of their targets because they had calibrated their guns on the north hemisphere, where the Coriolis effect is in the opposite direction.

[Dr. Borodog]

OST,

I think that ultra-long-range (of order a mile) sniper rifle fire has to take the coriolis effect into account, but I haven't run the numbers.

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You will respect my philosophai.

[Samadhi]

That reminds me of a demonstration they had for a dependants cruise on my brother's ship (Nimitz). The sea was fairly choppy, not affecting the carrier much, but the other ships were rocking quite a bit. The accompanying cruiser was firing it's large gun repeatedly into the ocean just shy of the horizon (around 10 - 15 miles from the flight deck of a carrier). There were plenty of binoculars to use, even the "big eyes" (mounted 20x). The splash from each shot was in the same spot each and every time despite the rough seas and the winds. Impressive to see.

[jadesmar]

Dr. Borodog:

I don't understand this part.

1. If a coriolis force involves the negative of the cross product of two vectors, why not make it easy on yourself and reverse the order of the cross product

-(A X B) = (B X A) no?

2. If a bullet is fired at the equator due east, from the moment of firing, it should have a downward acceleration, this would produce a downward component of the velocity. The cross product should produce a result that is mutually perpendicular to the West/East motion of the earth and the East/Down motion of the bullet. Why does it not produce a North or South result?

[Dr. Borodog]

quote:

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1. If a coriolis force involves the negative of the cross product of two vectors, why not make it easy on yourself and reverse the order of the cross product

-(A X B) = (B X A) no?

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You could do that. It's just traditionally written the other way, with the w terms written first in the cross products:

ma = F_grav - mw x (w x r) - 2mw x v.

[Will]

yes it does effect water drainage out of a toliet or a sink. I also noticed something else with a toy i have. This toy you hang from the cieling on a piece of string. The toy is a bird that flaps its wing it will only go one direction and that direction is the same as the water drainage.

[Dr. Borodog]

Wrong.


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You will respect my philosophai.

[Lucky Wizard]

Will, as has been pointed out in this thread, sinks, toilets, and the like are too small to be affected by the Coriolis effect. If a certain toilet or sink always drains one way, it's not because of what hemisphere it's in, it's because of the shape of the toilet or sink. Read the links in this thread, and while you're at it, you might consider taking a look at the second chapter of Phil Plait's Bad Astronomy.

As for the toy, maybe the bird's mechanism is specifically designed so that it'll always move the bird in one direction, and that direction coincidentally happens to be the same as the water drainage direction?

[Dr. Borodog]

So I wrote a computer program to work out the effect of the centrifugal and coriolis forces on a rifle bullet. The assumptions:

The muzzle velocity is 700 m/s.
The bullet is fired due east, from a height of 1.5 meters, at an altitude of zero degrees above the horizon.
Wind resistance is neglected.
Curvature of the Earth is neglected.

The bullet travels about 390m, as is easily verified. The bullet is deflected only 1cm to the south.

I could include air resistance, which is necessary for a longer range, elevated shot, but I can't find anywhere that lists what a proper drag coefficient should be.




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You will respect my philosophai.

[Dr. Borodog]

Okay,

I made a back-of-the-envelope calculation to approximate a drag coefficient.

I found with a 10 degree elevation, my round travelled 600 meters, and was deflected a whopping 1.6 meters south. So I'd say that the centrifugal and coriolis forces must be taken into account for long range rifle fire.



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You will respect my philosophai.

[Dr. Borodog]

Whoops. Bug. Make that about 500 meters, and only 20cm of deflection. Still significant, though.

[yeahgirl:-?]

Yeah..so I read up on the Coriolis Effect and it sounds pretty neat...but the question is:Is it true that the water in sinks of the NH spins clockwise while the water in the SH sinks? Why??

[Guest]

Uh... are you serious?

The water spins, but the Coriolis Force is too small to cause this. In most cases, the water spins because toilets and sinks are designed to create some vorticity in the water flow. The higher-vorticity water washes away clingy poo better than lower-vorticity water.

[Leptonn]

^me

[Beartalon]

[extro...]

[Guest]

I'm confused. And I read this puzzle somewhere, can someone...

[Leptonn]

Instead of dwelling on the surface of the earth, take the questions inside a closed railroad train that is moving at a steady clip.

If you jump up, will you land several feet down the car?
no

If you throw two paper airplanes, one in the direction of travel and one against, will the former travel less far? (note: if your answer is "yes" consider what would happen in a much faster train... would the forward-thrown airplane travel backwards compared to where you are standing?)
no, and no

The third question, however, is interesting in a way that I doubt you envisaged. Kepler's second law of planetary motion tells us that low-altitude satelites (the ISS, for example) orbit the earth in much less than a single day. Therefore, from some fictional "rest" frame in which the earth is rotating, a rocket must gain a lot of rotational velocity. Thus, rockets should be launched in the direction of earth's rotation.

[LGB*]

Boundary Layers and ragged trousered philanthropists