Great circle formulae, True cource and actual heading

"John Bell" writes:

I agree that a GPS will not tell you an absolute heading to fly, but it will
tell you a relative heading. The GPS will give you a value of TRACK and it
will give you a value for BEARING. The idea is to adjust your heading so
that TRACK matches BEARING. Many GPS receivers have a data field called
TURN --this is just the difference between TRACK and BEARING. If the GPS
indicates a TURN of 5 degrees left, adjust your heading 5 degrees left. If
you follow TURN or match TRACK and BEARING, you should track directly to the
active waypoint.

That's correct, with a couple of caveats.

The first is that in an aircraft at least, you normally fly a heading
based on the directional gyro, since it gives you a stable reading. The
GPS TRACK doesn't reflect heading changes instantly, while the DG does.
So you maintain a heading, then see what happens to the track, then
possibly adjust the heading.

The second is that this method takes you directly to the destination,
no matter where you are now, no matter how much you've drifted off your
original course. Sometimes that's fine, but sometimes you want to
regain your originally-planned ground track (e.g. it takes you between
mountains, or avoids submerged rocks, or avoids a restricted area).
For these cases, what you really want is to look at cross-track error
(the deviation from your planned route) and get back on the planned
track.

The method that you describe of adjusting your heading to manage cross track
is not incorrect. However, I thing that the ability to get an exact heading
that compensates for wind or currents by comparing the TRACK to BEARING is
one of the most powerful features that GPS has to offer aviators and
boaters.

Why is it not correct? Keeping the cross-track error zero takes you
directly to your next waypoint, factoring in any wind or current
correction that is necessary, and it lets you follow your originally-
planned ground track. It's the best you can do. It's like following a
VOR radial, except that the virtual "VOR" can be placed anywhere (it's
just a waypoint), and the "needle deflection" vs. track error has
constant gain all along the route.

The method of matching track to bearing will also take you directly to
the destination if you never get off course. But once you do get off
course, this method takes you along a new "direct" path to the next
waypoint. This is *faster*, but it isn't always safe. Navigating to
minimize cross-track error is safer, but potentially slower. Both
result in exactly the same ground track if you never get off the planned
route. You can say that either is better than the other, depending on
circumstances. I don't see how you can say one method is "not
correct".

Dave

Dave,

I actually agree with your points. In fact, many of the points that you
make are ones that I make in my chapters on navigation in both of my texts
at www.cockpitgps.com.

The only thing that I substantially disagree with you is in that I disagreed
with you in the first place. In answer to the comment: "I don't see how
you can say one method is 'not correct'." I had actually written that your
original post was "not incorrect." I apologize for the double negative, but
my intent was to emphasize that I was not contradicting your original post
so the double negative seemed appropriate in context. I feel confident in
my ability to navigate with a GPS. However, I have never bragged about my
writing abilities.

My point is that although old methods of navigation based on cross track
error are still correct, the GPS gives a unique capability to more
accurately find a very precise heading to compensate for winds and cross
currents because of its ability to sense an actual track.

I think that cross track error is a very useful and at times essential piece
of data. I see the method that you describe and the method that I describe
as being complimentary, not contradictory.

--John Bell, www.cockpitgps.com

"John Bell" writes:

The only thing that I substantially disagree with you is in that I disagreed
with you in the first place. In answer to the comment: "I don't see how
you can say one method is 'not correct'." I had actually written that your
original post was "not incorrect."

Oops. I was in a hurry, and misread that as "not correct". My fault.

Dave