Homing verses Tracking

[John Bell]

I got interested in the effects of homing on a waypoint as opposed to
tracking. I have seen the illustrations and have understood the concept for
some time, but I have never seen any numbers. If you are interested here is
the results of my playing around with Excel:

http://www.cockpitgps.com/other_articles/homing/homing_cross_track_error.htm

John Bell
www.cockpitgps.com
www.smallboatgps.com

[Bob Gardner]

Maybe the recent spate of posts about cross-posting has made me sensitive,
but since homing/tracking is an IFR exercise, why post anywhere other than
rec.aviation.ifr?

Bob Gardner

"John Bell" > wrote in message
...
>I got interested in the effects of homing on a waypoint as opposed to
> tracking. I have seen the illustrations and have understood the concept
> for
> some time, but I have never seen any numbers. If you are interested here
> is
> the results of my playing around with Excel:
>
> http://www.cockpitgps.com/other_articles/homing/homing_cross_track_error.htm
>
> John Bell
> www.cockpitgps.com
> www.smallboatgps.com
>
>

[Steven P. McNicoll]

"Bob Gardner" > wrote in message
...
>
>Maybe the recent spate of posts about cross-posting has made me sensitive,
>but since homing/tracking is an IFR exercise, why post anywhere other than
>rec.aviation.ifr?
>

Homing/tracking is a navigational exercise, navigation is not limited to IFR
operations.

[Casey Wilson]

"Steven P. McNicoll" > wrote in message
ink.net...
>
> "Bob Gardner" > wrote in message
> ...
> >
> >Maybe the recent spate of posts about cross-posting has made me
sensitive,
> >but since homing/tracking is an IFR exercise, why post anywhere other
than
> >rec.aviation.ifr?
> >
>
> Homing/tracking is a navigational exercise, navigation is not limited to
IFR
> operations.
>
Oh Geez! I'm trapped into agreeing with Mr. McNicoll on an issue.
Tracking is just as important in VFR as IMC. It saves gas, and time between
waypoints.

[Peter Duniho]

"Casey Wilson" > wrote in message
news:qGI3d.3087$C8.2963@trnddc05...
> Oh Geez! I'm trapped into agreeing with Mr. McNicoll on an issue.
> Tracking is just as important in VFR as IMC. It saves gas, and time
> between
> waypoints.

That still begs the question as to why you posted to r.a.student and
sci.geo.satellite-nav.

I agree with Bob...you "over-cross-posted".

Remember, when it comes to posting on Usenet, less is more.

[[email protected]]

On Mon, 20 Sep 2004 11:48:14 -0700, "Bob Gardner" >
wrote:

>Maybe the recent spate of posts about cross-posting has made me sensitive,
>but since homing/tracking is an IFR exercise, why post anywhere other than
>rec.aviation.ifr?

Obviously a single newsgroup does not provide sufficient scope
for adequate adulation of certain types of genius.

>
>Bob Gardner
>
>"John Bell" > wrote in message
...
>>I got interested in the effects of homing on a waypoint as opposed to
>> tracking. I have seen the illustrations and have understood the concept
>> for
>> some time, but I have never seen any numbers. If you are interested here
>> is
>> the results of my playing around with Excel:
>>
>> http://www.cockpitgps.com/other_articles/homing/homing_cross_track_error.htm
>>
>> John Bell
>> www.cockpitgps.com
>> www.smallboatgps.com
>>
>>
>

[Kevin Black]

> >Maybe the recent spate of posts about cross-posting has made me
sensitive,
> >but since homing/tracking is an IFR exercise, why post anywhere other
than
> >rec.aviation.ifr?
>
> Obviously a single newsgroup does not provide sufficient scope
> for adequate adulation of certain types of genius.

<snip>

pleeaaassse!!!!!! I for one use navaids flying VFR and the homing/tracking
is at worst interesting and at best very useful. Further, I don't subscribe
to the IFR newsgroup or the satellite nav news group, but I do to RAS and
RAP so I got the info if I choose to follow it up. I guess there's people
using GPS that aren't aviators so I can see why John posted to the GPS NG so
what's the problem?

Further, for no cost (donationware actually) John has produced a couple of
damned fine e-books on the use of GPS in the air (and small boats). I think
this sort of effort (whether you like the content or not), and the obvious
interest and enthusiasm he displays, shows a committment far and above most
that subscribe to any of the RA... newsgroups. We should be encouraging
people like John (and others like Gene Whitt for example) at every
opportunity not sniping with snide comments.

And no, I didn't cross-post:)

Just my $0.02c worth....

Kevin

[Ron]

Slightly off this thread topic, but what formula do you use to calc the XTE?

I've used a variation of Ed Williams' formula "XTD
=asin(sin(dist_AD)*sin(crs_AD-crs_AB))" but if I run my calcs in parallel
with a GPS they are consistently different with the GPS numbers varying
considerably more than mine.

"John Bell" > wrote in message
...
>I got interested in the effects of homing on a waypoint as opposed to
> tracking. I have seen the illustrations and have understood the concept
> for
> some time, but I have never seen any numbers. If you are interested here
> is
> the results of my playing around with Excel:
>
> http://www.cockpitgps.com/other_articles/homing/homing_cross_track_error.htm
>
> John Bell
> www.cockpitgps.com
> www.smallboatgps.com
>
>

[John Bell]

> but since homing/tracking is an IFR exercise, why post anywhere other than
> rec.aviation.ifr?
>
> Bob Gardner

Bob,

I have read the some of the complaints about cross posting and debated
whether or not to do it. However, I decided that it was appropriate. In
fact, I am not sure that I didn't leave some appropriate groups out in my
cross posting.

Homing can happen if you steer towards a point without properly correcting
for a cross current, as I am sure you understand. Where I will disagree
with you is that it is exclusively an IFR exercise (Instrument Flying
Regulations for the non-aviation cross-posting of my response). While
trying to use an ADF (Automatic Direction Finder) is one of the more common
examples, there are many other cases. One case is steering to a point
visually whether flying or boating. This can also happen when steering a
heading as indicated by a GPS bearing, whether in an airplane or boat. Thus
the case of homing verses tracking is not limited to IFR flying at all.

Anyway, I had never seen any numbers as to just how much one can get off
course with homing, so I spent a little time with Excel for my own curiosity
and thought that I would post it to my site (
http://www.cockpitgps.com/other_articles/homing/homing_cross_track_error.htm
) and share it on the newsgroups where I thought people might find it
interesting and relevant to the nature of the newsgroup.

John Bell
www.cockpitgps.com

[John Bell]

> Slightly off this thread topic, but what formula do you use to calc the
XTE?
>
> I've used a variation of Ed Williams' formula "XTD
> =asin(sin(dist_AD)*sin(crs_AD-crs_AB))" but if I run my calcs in parallel
> with a GPS they are consistently different with the GPS numbers varying
> considerably more than mine.

For anybody on the cross post response list, this refers to Ed William's
Aviation Formulary page. There are some things directly related such as
airspeed and altimetry issues. However, there are also some useful general
navigation formulas with more general applicability:
http://williams.best.vwh.net/avform.htm

Ron,

The way that I did the spreadsheet, I never had to use this formula.
Without checking, here is a guess: I think crs_AB would refer to the GPS
value of course and crs_AD would refer to the GPS value of BRG.

If you go to the very top of the text, Ed talks about using radians to
measure distance:

Great circle distance can be likewise be expressed in radians by defining
the distance to be the angle subtended by the arc at the center of the
earth. Since by definition, one nautical mile subtends one minute (=1/60
degree) of arc, we have:

distance_radians=(pi/(180*60))*distance_nm
distance_nm=((180*60)/pi)*distance_radians

Note: the nautical mile is currently defined to be 1852 meters - which to be
consistent with its historical definition implies the earth's radius to be
1.852 * (180*60/pi) = 6366.71 km, which indeed lies between the currently
accepted ( WGS84) equatorial and polar radii of 6378.137 and 6356.752 km,
respectively. Other choices of the earth's radius in this range are
consistent with the spherical approximation and may for some specialized
purposes be preferred.

Since 1 radian = 180/pi degrees, you can use distance_degrees=
distance_nm/60.

I keep some of Ed's formulas on my Palm PDA. For more info:
http://www.cockpitgps.com/palm/index.htm

John

[Ed Williams]

"John Bell" > wrote in message >...
> I got interested in the effects of homing on a waypoint as opposed to
> tracking. I have seen the illustrations and have understood the concept for
> some time, but I have never seen any numbers. If you are interested here is
> the results of my playing around with Excel:
>
> http://www.cockpitgps.com/other_articles/homing/homing_cross_track_error.htm
>
> John Bell
> www.cockpitgps.com
> www.smallboatgps.com

Curiously enough, my very first posting to Compuserve's AVSIG forum,
almost twenty years ago, was on exactly this subject, in response to a
discussion between Bob Dubner and Barry Schiff.

Suppose an airplane flying at unit speed starts homing on the origin
of the (x,y) plane, starting at (1,0) in a crosswind of u. The
equations of motion are

dx/dt = -x/sqrt(x^2 + y^2)
dy/dt = -y/sqrt(x^2 + y^2) + u

with x-1, y=0 at t=0

so

dy/dx = (y - u sqrt(x^2 - y^2))/x

You can verify the the solution of this ODE is:

y =(x/2) * (x^(-u) - x^u)
and that for the homing to succeed, we must have u < 1 (less
crosswind than airspeed!)

From this we can derive a couple of interesting results:

(1) The time to home is 1/(1-u^2), which we can compare to the time
to track, which is 1/sqrt(1-u^2). Reverting to dimensional units, we
can say that it takes longer by 1/sqrt(1 - (xwind/TAS)^2) to home than
to track in a direct crosswind.

(2) The maximum cross-track displacement (where dy/dx=0) is

y_max = (1/2) ( ((1-u)/(1+u))^(1/2u -1/2) - ((1-u)/(1+u))^(1/2u
+1/2) )


A great deal more numerical resolution is required to get accurate
results from your spreadsheet for other than small u, particularly
near the origin (homing point), where the track ends up coming in at
right angles to the course, however small u (but non-zero) may be.

Ed

http://williams.best.vwh.net

[Stan Gosnell]

(Ed Williams) wrote in
om:

> Curiously enough, my very first posting to Compuserve's AVSIG forum,
> almost twenty years ago, was on exactly this subject, in response to a
> discussion between Bob Dubner and Barry Schiff.

It's good to see you here, Ed. Your Aviation Formulary is one of the
treasures of the internet, IMO. I've used it many times. Thank you for
providing it.

Followups set to rec.aviation.ifr.

--
Regards,

Stan