Dynamic Planet B/C

[EileenofSD]

Haha! I'm quite excited for this event. Last year, I was able to participate during state, but I had a schedual conflict at nationals and decided that I would rather do Enviormental Chem. Now that E.C. is gone from Division B, I wish I had stuck with Dynamic, but oh well.

Does anyone know of any good sites that give an explanation on how to find the epicenter of a quake? I have a hard time with that...

[Celeste]

Does anyone know of any good sites that give an explanation on how to find the epicenter of a quake? I have a hard time with that...

It sort of explains it at this site. (Click on the link at the side that says Epicenter & Magnitude.)

You need the distances away from the epicenter at 3 different stations. If you don't know those distances, you may need to use the P/S wave travel time graph to find them. You need a map with the 3 stations on it. Take the distance away from one station and use the map scale to set your compass to draw a circle with a radius of the distance. Do that with the remaining stations and where the circles intersect should be your epicenter.

[winneratlife]

I've heard that some people had to go without compasses last year, and I thought about a while. Eventually I realized that if you find the equation of the circle by treating longitude as x coordinates and latitude as y coordinates, and solved the three circles, it could be done. One glitch: The radius has to be in terms of longitude and latitude. So, can somebody tell me how many miles are in a degree longitude or latitude? (Also, if they aren't the same, does anybody know how to compensate for that to make sure that the graph is still a circle? Maybe the equation for an ellipse?)

EDIT: Oh geez, never mind, I just looked it up. I forgot that longitude varies in distance, so unless I could find some sort of formula expressing the length of a degree of longitude in terms of the latitude, I won't even be able to use longitude, let alone making a circle. At best, I could find the formula (which would just be an approximation, which would probably assume that the Earth is a sphere), try to make an ellipse with the degrees, then find the intersection of three ellipses, and hope that an ellipse was accurate in the first place. Anyone have a better way to do it without a compass?

[Celeste]

If you don't have one, you can sort of make your own compass with the edge of a paper. You would need a ruler, though. You mark the radius on the edge of the paper, one end being the corner and the other a pencil mark. You then put the corner where the station is, and put a pencil mark on the map where the mark on the paper is. Then rotate the paper a little and mark it again, and keep doing that until you have a circle of dots around the station. Connect the dots and you have a somewhat circular circle! I hope I explained that well enough, if not, just ask and I'll try to rephrase it!

[winneratlife]

I guess that would work, but what is the margin of error allowed at most events?

[smartkid222]

I've heard that some people had to go without compasses last year, and I thought about a while. Eventually I realized that if you find the equation of the circle by treating longitude as x coordinates and latitude as y coordinates, and solved the three circles, it could be done. One glitch: The radius has to be in terms of longitude and latitude. So, can somebody tell me how many miles are in a degree longitude or latitude? (Also, if they aren't the same, does anybody know how to compensate for that to make sure that the graph is still a circle? Maybe the equation for an ellipse?)

EDIT: Oh geez, never mind, I just looked it up. I forgot that longitude varies in distance, so unless I could find some sort of formula expressing the length of a degree of longitude in terms of the latitude, I won't even be able to use longitude, let alone making a circle. At best, I could find the formula (which would just be an approximation, which would probably assume that the Earth is a sphere), try to make an ellipse with the degrees, then find the intersection of three ellipses, and hope that an ellipse was accurate in the first place. Anyone have a better way to do it without a compass?

Would the fact that most maps are Mercator projection make the longitude values the same?

[gneissisnice]

You can still do it without a compass. Just take a piece of paper, put the corner on the city, mark the length you need, and rotate it around. It's more difficult and not as accurate as a compass, but it works fine.

[winneratlife]

I've heard that some people had to go without compasses last year, and I thought about a while. Eventually I realized that if you find the equation of the circle by treating longitude as x coordinates and latitude as y coordinates, and solved the three circles, it could be done. One glitch: The radius has to be in terms of longitude and latitude. So, can somebody tell me how many miles are in a degree longitude or latitude? (Also, if they aren't the same, does anybody know how to compensate for that to make sure that the graph is still a circle? Maybe the equation for an ellipse?)

EDIT: Oh geez, never mind, I just looked it up. I forgot that longitude varies in distance, so unless I could find some sort of formula expressing the length of a degree of longitude in terms of the latitude, I won't even be able to use longitude, let alone making a circle. At best, I could find the formula (which would just be an approximation, which would probably assume that the Earth is a sphere), try to make an ellipse with the degrees, then find the intersection of three ellipses, and hope that an ellipse was accurate in the first place. Anyone have a better way to do it without a compass?

Would the fact that most maps are Mercator projection make the longitude values the same?

Unfortunately, I don't think so. Actually, that would mean the map scale would be off by a bit at different points. Although...CRAP! Doesn't that mean that when you draw a circle with the compass, it won't really be a circle, because the distortion on the projection might make the circle more of an ellipse? Will Sci-O really care?

[smartkid222]

im pretty sure it would be a circle. If a map key says. 1in=600miles, it means it any direction, so if you follow the map key they give you and make the circles, you'll be fine. I think you're overthinking it. If you need practice ask an earth science teacher at your school and im sure they'll gladly give you stuff to practice on. Or you can look online or on the test exchange.

and yeah gneiss, that what we did at regionals.

[winneratlife]

im pretty sure it would be a circle. If a map key says. 1in=600miles, it means it any direction, so if you follow the map key they give you and make the circles, you'll be fine.

Sadly, no. The problem is that with the mercator projection, if a map key says 1 in=600 miles, that's something like an overall average, and not always true. At some points, an inch may be 590 miles, and at some, 610 miles. Case in point: If one looks at a mercator projection of a world map, all of the longitude lines are parallel. However, at the pole, all of the lines touch. Therefore, at the pole, the scale is 1 inch=0 miles. Then, if one makes the scale uniform, such that the north-south scale equals the east-west scale, and the scales are the same everywhere, one achieves the result that Earth is a point, not a sphere. Also, if the horizontal scale is uniform, but not the vertical, that in itself causes any circle drawn to be an ellipse, yet that assumes that the Earth is a vertical line. Therefore, to compensate, mapmakers distort both the north-south and east-west scales at different points while keeping them equal, preserving the angles, but not the distances.