Science!

[dvandom]

Well, more like science, not SCIENCE!. But still. Back in grad school I worked out an explanation of the Coriolis force that didn't require using all sorts of complicated principles. It had holes, and I found a better explanation. That has stood until recently, when a guy in Germany started emailing me about a problem with it. I'm still not totally sure what he's getting at, but clearly it's time for another revision. And here it is! The part I need to re-explain in the most depth isn't done yet, I'm still building the props.

Edit: I borrowed a basketball from the lab equipment room and used it and some micro-Gundam figures to finish up my explanation.

Comments

[foomf.livejournal.com]

But there's no preferred north in this case - with a two-point problem, you never have to move off the equator no matter where it is.

And with regards to coriolis force, all this geometry serves only to identify the vectors involved. And the amusing thing about that: there's a right-hand-rule governing the expansion of a triangle to a sphere. The bulge will always be to the outside, which (standing at any vertex and facing out) will map the points to the right of where they would be on the planar view.

[dvandom.livejournal.com]

Part of defining an arbitrary north is that you're establishing a great circle upon which you're standing. If you say you're shooting something north on a non-spinning sphere, it will keep going north. If you say, "That's north, now I will shoot this east" and turn 90 degrees before firing, your shot will start to curve to the right as it follows a great circle rather than following the arbitrary line you draw on the ground.

I doubt this issue will bother the target audience, but I'll put in an aside anyway. :)

[foomf.livejournal.com]

The arbitrary line you draw on the ground is also a great circle segment. It's illusionary to think it's flat; on a sphere, there is no flat. You can demonstrate it by drawing all this on a balloon, then inflating it.

If you have a transparent bowl and the balloon is too opaque to see through, you can demonstrate the 'flat' part by showing the flat balloon under the bowl, then inflate the balloon and draw the line on the outside. The curve becomes immediately obvious when you look from the 'start.


Yeah, I figured all this out in third grade when the teacher was trying to explain parallel lines and that they don't ever meet, except of course in a curved space-time, and she didn't understand that. This is what happens when you teach new math before you teach arithmetic - the kids can grasp really interesting concepts but cannot perform simple calculations in reasonable time.

[foomf.livejournal.com]

AHA! I just spotted the problem.

No, if you shoot east and are facing east, the shot will not curve. The curve, as mapped to your planar view, is still entirely vertical and thus appears to be a line.

Now if you are facing North and shoot something to the northeast, and manage to keep the trajectory visible, you will see the rightwards bulge, of course, since the center of the translation is north. And it will arc back in again.

[foomf.livejournal.com]

And incidentally, you can see this effect in jet contrails.