[simpits-tech] GPS craziness and "desired track"

Wed Apr 9 12:16:26 PDT 2014

> Date: Tue, 8 Apr 2014 19:15:46 -0500
> From: dabigboy at cox.net
> To: simpits-tech at simpits.org
> Subject: Re: [simpits-tech] GPS craziness and "desired track"
> 
> On Sat, 5 Apr 2014 20:13:02 +0200
> Jeroen Huijben <jeroen_huijben at hotmail.com> wrote:
> 
> > Your method of finding where you should be sounds right.
> > But if you want to fly straight to this point you will have to fly
> > perpendicular to the desired track and if you do this until you reach
> > it you will overshoot and end up snaking along the desired track. So
> > you should add something to start the turn before reaching the
> > desired track and make a smooth transition.
> 
> This "intermediate" point isn't something I would navigate to, its sole
> purpose would be to find a bearing solution from this point to my next
> waypoint, so that I would get the correct desired-track value for that
> point in the Great Circle route.

Picture: http://imgur.com/gEmLOo7
Plane P flies from A to B.
All possible courses are divided into five sectors:
A course in sector a will be the best option as this will bring you to the desired track before reaching the destination.
In sector b you will fly towards the desired track but you will pass by the destination before reaching the desired course.

Courses in sectors c, d and e will take you away from the desired track, the destination or both.

Which specific course you take depends on what you want most.
If you want to stay on the desired track then the course a/e will take you there quickest.
This is the perpendicular intercept course.
If you want to get to the destination the quickest then the course a/b is a direct route.
Any course between a/e and a/b is a compromise between the two.

> > You could add a warning to start a standard rate turn when you are
> > one turn radius away from the desired track. That should place you on
> > the track while flying along it. Then you can switch to a course
> > deviation indicator to show how far away from the track you are.
> 
> I am actually tied to the operation of the old 1990s Trimble GPS units,
> as I am basically re-implementing the Trimbe "OS" in Python (so that
> it can be interfaced to X-Plane, or even FSX/FlightGear/et al).
> The CDI is always available. I'm pretty sure the only "help" it's
> suppose to give the pilot is a fly-to heading, which I already have
> written into my software. I do not yet have it set up for course
> corrections, but I'm thinking I will simply make it a percentage of the
> course error.
>
> One thing I'm not sure about is if the CDI/heading corrections are
> based on bearing, or cross-track error. I'm assuming it's bearing, as
> this is how a VOR works. Otherwise, you could be almost past the
> waypoint, but have only a small CDI deflection because your actual
> cross-track distance might be fairly small (a couple miles or so, for
> instance). But then maybe a real GPS works this way, I'm not sure.

This is what I would do, without knowing the methods used by any particular real GPS.

Another picture: http://imgur.com/Fykzipp 
Again, P wants to fly from A to B and wants to intercept AB at point I.
To do this it flies intercept course PI. (see above)

First the GPS will indicate the distance from the line PI on the CDI.
By keeping the CDI centered the plane will fly along PI towards I.
The course to steer is the course from P to I.

When the plane gets within distance d from the line AB the CDI will start indicating the distance from the point T.
By keeping the CDI centered the plane will fly an arc around point T and transfer from the course PI to the course AB.
The course is perpendicular to the direction of T and will rotate as you fly along the arc.

When the plane gets beyond distance d from the line PI the CDI will start indicating the distance from the line AB.
By keeping the CDI centered the plane will fly along AB towards B.
The course to steer will any course in sector a, as explained above.

As an extra you can calculate the difference between the heading and the groundtrack (=wind drift) and add that to the course to steer to get the right heading that will yield the right ground track.

Turns when flying through a waypoint can be handled in a similar fashion.
Picture: http://imgur.com/Flx2Vub 
First the CDI indicates the distance from one leg, then the distance from a turning point T and then the distance from the next leg.
Except here the GPS would switch between the three phases when it flies to specific radials from point T.

> I'm tempted to yank the Trimble antenna off the Sabreliner, rig up a
> portable power unit for the GPS, and take it up in a real plane so I
> can see how it behaves in the air. :)

Or reprogram it's database with the local roads and put it in your car :)

> > You could even seamlessly integrate each part and present only a CDI
> > to the pilot. To reach the desired track you will first fly a great
> > circle perpendicular to it. Then you fly along a small circle that
> > touches the intercept track and the desired track. Finally you fly
> > along the great circle that is the desired track. In each case the
> > CDI would show the distance from the active great or small circle.
> 
> By "small circle" are you referring to something other than a Great
> Circle, or do you mean just a shorter Great Circle? :)

A small circle is any circle on the surface of a sphere that is not a great circle:
http://www.mathworks.nl/help/map/great-circles-rhumb-lines-and-small-circles.html

> Matt
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I hope that clarifies things.

Regards,
Jeroen.

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