Direction of TravelDate: 10/18/96 at 16:41:0 From: Aldon Hynes Subject: Finding direction given Lat. Long. I have read through Web pages and found how to find the distance between two locations using latitude and longitude. I even got it to work. Now I have the next question. How do I find direction? If I want to go from San Francisco (37 37' N 122 22' W) to Paris (48 44'N 2 23' E), I know just from looking at a map that I should head mostly east and a little north. How would I calculate the exact compass heading? Aldon Hynes Date: 10/18/96 at 19:13:43 From: Doctor Anthony Subject: Re: Finding direction given Lat. Long. In fact, if you go the shortest route (along a great circle) from one point to the other, your direction will be changing all the time. You would need spherical trig to calculate the exact heading at each stage. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 10/22/96 at 9:30:29 From: Anonymous Subject: Re: Finding direction given Lat. Long. That doesn't make sense! From my time on a boat, I know that if I want to go from one place to another, I set a heading and stay on that heading. And I get there (I believe in the shortest path). Is there no way to calculate this? I can see this being a problem if I go over a pole. - Aldon Date: 10/22/96 at 11:41:47 From: Doctor Ceeks Subject: Re: Finding direction given Lat. Long. Hi, Doctor Anthony's comment is true. For example, suppose you are in the Northern hemisphere and you want to travel due east. So you set your boat along an easterly heading. Then, in fact, you are travelling along a line of latitude, but lines of latitude are not great circles (except at the equator), and do not provide the shortest distance between two points on the same latitude line. It's very easy to see this if you are near the North Pole, where traveling due east will make you walk in a circle around the North Pole, whereas it may be much faster just to walk right over the North Pole. On the other hand, if you do not care to travel the shortest distance, then you can find a single compass heading which you can stick to for the entire journey, although it isn't easy to compute this heading without a computer. Also, if you're not travelling far, then the earth is flat enough that all the problems discussed above become practically irrelevant. So if you travel less than 10 miles on a boat, it's likely that you can just use a flat map and compute a single compass heading by drawing a straight line on the map. The errors will probably be comparable to the errors in reading the actual compass heading anyway. (Okay, if you blindly stick to a fixed compass heading using this method, you might crash into the dock instead of run alongside it!) But for the example you give, the roundness of the earth is very important to take into account. -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/