In the old days, they took a reading as to where they were on a map. Then they looked at the place they wanted to go. Then they took out a straight edge and drew a line between the two. Using a protractor, the measured the direction from magnetic north and that determined their course.
In general, on the old sailing ships, they took new readings at least once a day, sometimes three of four. The ships were susceptible to drift because of wind and tides. Hence, the more often they pulled out the sextant and took readings, the more accurate their journey.
In my mind, I figured that was sort of the way they do it today. However, when I started flying my MS flight simulator, did I get a surprise. I set my plane to make a flight from one point to another and put it on autopilot, using GPS. As I watched the compass, I realized the autopilot was making small changes on a regular basis.
That didn’t make sense to me. I mean, everyone knows that the shortest distance between to points is a straight line, not curved.
I did a little research into it. If you use a flat map to do the navigation, the straight line does appear to be the shortest distance. However, if you work with a globe, instead of a flat map, you can easily see that the shortest distance line will be a curve, at least in most cases.
Hence, when a pilot takes off from San Fran to the City of Lights, he will likely start off flying north-east instead of east. He will gradually change his course to eastward until flying east. Then he will start turning southward. His final course will likely be south-east. If you draw the course on a flat map, it will look like an arc. If you draw the course on a globe, it will make perfect sense.
For shorter distances, it will make no measurable difference. However, ignoring roads, the shortest route to the store you regularly make, would be curved. You are going just a little farther by going straight. Ideally, you would be making course changes about every second. I wouldn’t suggest trying it though. First you need to stay on the roads and, of course, neither of us will be able to tell the difference.
However, the fact that we navigate a globe instead of a plane does create some oddities. For instance, if you go 50 miles north, 100 miles east, 100 miles south, 100 miles west, and finally 50 north, the assumption would be that you traveled in a square. As such, you should end up in the same place as you started. However, that would only happen if you start on the equator.
One thought on “When Straight Isn’t Straight”
I sort of get what you’re saying.
Back in my surveying days we worked out ‘plane’ distance by knocking out elevation (slope distance) between points measured as that sorted out pesky things like mountains, and valleys. There was a calc you could do to figure out distance differences regards curvature but stuffed if I can remember that one.
I haven’t had to think about that for a few years now.