I was really trying to avoid this thread but can't ignore a direct invite
First, here's some material I've written on the the coriolis effect:
Spin and Coriolis Drift
Handwritten examples are linked at the bottom that will allow you to calculate both horizontal and vertical effects. It's the exact math used in ballistics programs.
Unfortunately the above text doesn't directly address the 'why' of the effect.
First let's consider the vertical component because it's the easiest.
Facts about the vertical component of coriolis:
It causes you to hit high when shooting east.
It causes you to hit low when shooting west.
The closer you are to the equator, the stronger the effect is.
At the poles, there is no effect (because there is no east or west).
So,
why do you hit high when firing east?
Think about something we're all familiar with; a sunrise. When you're looking at a sunrise, it looks like the sun is rising out of the ground. However, as we all learned in grade school, the sun is (relatively) stationary, and it's the earths rotation that makes it look like the sun is 'rising'. With this understanding, we can revise the description of a sunrise to be: a sunrise is when the horizen 'falls down'. This is an oversimplification, but will serve the purpose of understanding intuitively how the coriolis affect works.
Now that you're envisioning the horizon falling down when you face east (this happens all day long by the way, not just in the morning
, imagine your target is on the horizon and you're aiming at it. The bullet starts out flying straight for the aim point, but what you don't know is that the target is actually a moving target. As the bullet flies, the target is falling down with the horizon (in an inertial frame, which manifests itself as an apparent alteration in gravity). So your bullet strikes the target high because the apparent affect of gravity was weakened, but it's actually because the target was falling down with the eastern horizon.
If the above makes sense to you, then the rest will follow easily.
Shooting west has the opposite affect. Another way to say the sun sets in the west is to say the western horizon rises. Again this happens all day long. If you have a target on the western horizon, it will 'rise' while your bullet's flying to it, and the bullet will strike low. To an observer, it looks like gravity is stronger, but it's actually because the western horizon is moving.
When you shoot north or south, there is no vertical deflection because the northern and southern horizon are fixed. There are no inertial reference points that rise and set in the north and south, in other words, the northern and southern horizon's are neither rising or falling. So you can count on your bullet finding the vertical center of it's target.
The earth is fattest at it's equator. A consequence of this is that the surface of the earth at the equator is moving faster (in the inertial frame) than on a point away from the equator. (think of the equator as the tread of the tire, and the poles as the hub). Since the surface of the earth at the equator is moving the fastest, and your target is attached to it, the vertical coriolis effect is at a maximum there.
That about covers vertical.
Horizontal is much harder.
Imagine you're standing on the equator facing north. Remember that the land you're standing on is moving east faster than the land you're looking out over. If you could put your 'inertial glasses' on, you would see the land to the north
drifting west, and drifting faster in the distance. So when you pick a point to shoot at, without your 'inertial glasses' it looks stationary, but the bullet will hit a point to the east of the target (to the right) because the land is 'drifting' west.
Now if you're standing in Canada looking south, you're standing on slow moving ground compared to what you see to the south of you. In this case, the inertial glasses would show the landscape drifting to the east (because it's moving east faster than you are). Fire in that direction, and the bullet will strike to the west of your aim point (which is still to the right).
The cause of horizontal coriolis drift when firing east and west is much harder to visualize (even with the 'inertial glasses'), but it works the same way. Remember that you're on the northern hemisphere of a rotating sphere, and look east (the direction you're moving). Look at the landscape in relation to the stars behind it. The stars should reveal that the landscape is moving to the left (in the northern hemisphere). Now turn around and face west. The stars should still reveal that the landscape is drifting to the left. Both of these scenarios will result in a bullet striking to the right of the aimpoint. The landscape appears to move that way because it's attached to a rotating sphere. As it turns out, the bullet will strike to the right by the same amount as the north and south shots as it does for east/west shots.
In the southern hemisphere, the landscape appears to move to the right (compared to an inertial reference) so the bullet appears to drift to the left.
I'm sure an academic professor would have my *** for the above description, but I think it serves to illustrate the coriolis effect for our purposes.
-Bryan
