Direction of Travel

Date: 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/