Navigation - things aren't always as simple as they seem

Salty

Salty

Touchdown! Greaser!
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Salty
So, maybe I'm alone on this tunnel vision, but probably not, so I'll share what just dawned on me.

It will NOT always be the case that if you plot a direct route, the heading you need to fly at the end of the route is the same as it is in the beginning. You can't just set out at 289 degrees and fly that to your destination. Sometimes your heading at the destination will be different than it was when you started out. And I'm not talking about wind effects, or magnetic variation changes either.

It never occurred to me before that, taking the extreme example, if you fly over the pole, you'll start out heading north and end up heading south all while still going direct to your destination.

It is possible to fly direct to a destination on the other side of the pole while using the same heading throughout, but it means flying a spiral around the globe slowly changing your latitude as you go. As an example, this flight to Cheremshanka Russia from Tampa FL flies a constant 289 heading for 7500 NM on a spiral course.

IMG_0182.PNG

But flying it direct you begin with a 005 heading and end with 172. And you save almost 2000 miles.
IMG_0181.PNG

The same is true of any long flight, the closer to the poles, the bigger the effect.

Anyway, I'm sure a lot of you knew all this already, but I had always naively thought, "if I'm going direct, I fly a heading and get there (minus corrections for variation and wind)". Not true.
 
Walboy said:
Those points were then transferred to mercator projection chart which resulted in what appeared to be a curved path. A curved path on that type of projection would result in continually changing courses.
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That's right. A straight line on a Mercator-projected map is a line of equal track (rhumb lines, a.k.a. loxodromes), whereas a straight line on a Labert-projected map (e.g. our VFR sectionals) is a close approximation of the great circle route.

- Martin
 
Salty said:
It will NOT always be the case that if you plot a direct route, the heading you need to fly at the end of the route is the same as it is in the beginning. You can't just set out at 289 degrees and fly that to your destination. Sometimes your heading at the destination will be different than it was when you started out. And I'm not talking about wind effects, or magnetic variation changes either.
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That's a correct observation. I would go even further and say the track along a great circle line is almost never constant. The only exceptions are flying east or west over the equator, or precisely north or south along any meridian.

- Martin
 
MauleSkinner said:
It takes a pretty significant leg length for he course change to be big enough for most of us to notice.
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No argument there. And wind and mag variance are going to be as big or bigger, unless you're flying very, very far north (or south), but it's still true.

On the other hand, a 1 tank trip in my Mooney from Tampa to Memphis the heading changes 8 degrees.
 
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Right, most of this is more exciting for math geeks than for pilots.
Spherical geometry is not everybody's favorite subject. :)

- Martin
 
Martin Pauly said:
Right, most of this is more exciting for math geeks than for pilots.
Spherical geometry is not everybody's favorite subject. :)

- Martin
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It's definitely not mine, but it is mildy interesting to me. lol
 
Martin Pauly said:
Right, most of this is more exciting for math geeks than for pilots.
Spherical geometry is not everybody's favorite subject. :)

- Martin
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To show you how ignorant I was when I started thinking about this, I thought I could "get close" to a distance between lat/lon coords by using Pythagoras. Oh how wrong I was.
 
But the old intercontinental airlines didn't even fly great circle. They pressure flew. And to a certain extent......the oceanic tracks change daily......they still do.
 
Salty said:
To show you how ignorant I was when I started thinking about this, I thought I could "get close" to a distance between lat/lon coords by using Pythagoras. Oh how wrong I was.
Click to expand...

You'll need to use the spherical law of cosines to get close.
 
Walboy said:
Sounds like good material for one of your videos.
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Ha - I think I'll save this topic for when one day I'll make videos to intentionally cure insomnia (as opposed to doing it unintentionally these days). :)

- Martin
 
Walboy said:
In the good old days of the U.S. Navy, to plot courses for oceanic crossings you pulled out a great circle chart and drew a line between the origin and destination. You then selected a series of points on the great circle chart and determined the latitude and longitude using the scale on the side of the chart.

Those points were then transferred to mercator projection chart which resulted in what appeared to be a curved path. A curved path on that type of projection would result in continually changing courses.

Now, GPS navigators plot courses using great circle routing automatically.

I don't even know if the Navy uses paper charts anymore. Back in the day, there was a chart house adjacent to the bridge where Quartermasters spent their days updating navigation data changes by hand. And when I say back in the day, that was in the 1980s.
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We did 10 years ago anyway. I imagine it’s the same as wanting paper VFR charts even when flying with legal iPad VFR charts...2 is 1, 1 is none.
 
kgruber said:
But the old intercontinental airlines didn't even fly great circle. They pressure flew. And to a certain extent......the oceanic tracks change daily......they still do.
Click to expand...
I managed to fly most of a leg in a Hawker that way once from SOCAL to Michigan...explained to the controller(s) that I was doing a “navigation exercise” that might have me a little bit off of the actual direct route that I filed. Apparently not a big deal for them, as they really don’t know when I’m on that direct route anyway. ;) I had a printout of magnetic courses along the route, and added a constant wind correction For the pressure differential at my altitude to those courses.

Amazed me how close I came.
 
Walboy said:
What do you mean by "pressure flew"?
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Single wind correction angle based on the pressure difference between departure and destination. You’ll “deft” left and right due to the pressure patterns, but end up in the right place. It also results in close to minimum flight time, as you’re not “fighting” crosswinds as hard.
 
Walboy said:
Interesting, this is a concept I haven't heard about before. Not surprising given the typical distances flown by single engine piston airplanes. But you still had to know a series of magnetic courses from a great circle chart to apply the wind correction to?

Any online resources that you know of about this would be much appreciated.
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Yes.

“pressure pattern flying “ or “Bellamy drift” should be good terms to search.
 
In addition to "pressure" navigation there was/is grid navigation for the polar regions. Ah, the good old days…
 
sextant.JPG Don't forget about the window / port on top of the cockpit area where the navigator took star sightings / sextant sightings.
 
MauleSkinner said:
It takes a pretty significant leg length for he course change to be big enough for most of us to notice.
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Not as long as you might think.

The way the instrumentation works on Boeings, the heading bug doesn't move as you (or the autopilot) tracks LNAV. You want to keep the heading bug close to the airplane's current heading so that when ATC gives you a heading assignment the airplane doesn't start turning the wrong when when you hit the heading-select button. The airplanes have no "sync" function on the heading bug, for some reason. The result is, airline procedure has us reaching up frequently to resync the heading bug to our slowly changing heading.

When the distance between fixes is more than 80-100 miles, or so, I won't set the bug on the exact current heading. The bug is 4° wide. I set the edge of the bug on our current heading with the body of the bug on the SOUTH side of our course. As we track the course, the aircraft heading will gradually changing toward south so now I won't have to resync the bug until the heading has changed 4°.

kgruber said:
But the old intercontinental airlines didn't even fly great circle. They pressure flew. And to a certain extent......the oceanic tracks change daily......they still do.
Click to expand...
The software that the dispatcher's use plot routings based on the forecast winds. The routing for a city-pair can change for each flight based on those winds. We'll file, and fly, a route that is quite a bit longer than the direct route but, with the wind, is actually fewer air-miles. The difference can be so significant that if we take a more direct routing that offsets us more than 100 nm from the filed course we have to have the dispatcher run the new route to ensure that fuel burn on the new route isn't significantly higher. There have been cases where an airliner, even on a domestic route, took a big shortcut only the end up with a fuel emergency before reaching their destination.
 
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