Homing verses Tracking

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
m...
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_arti...rack_error.htm

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

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_arti...rack_error.htm

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

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_arti...rack_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

On Tue, 21 Sep 2004 00:22:04 GMT, "Steven P. McNicoll"
wrote:


"Bob Gardner" wrote in message
...

Can't say that I never used VOR for VFR navigation but I can't recall ever
using the ADF for that purpose.


It works just as well as it does under IFR. Some years ago a booklet
listing AM radio stations by frequency and location was available for just
that purpose. Some years earlier than that they were depicted on
sectionals.

FWIW, the NY sectional has the humbolt NDB (next to Hazleton, PA) on
it and is marked "VFR use only".

On Tue, 21 Sep 2004, Steven P. McNicoll wrote:


"Bob Gardner" wrote in message
...

Can't say that I never used VOR for VFR navigation but I can't recall ever
using the ADF for that purpose.


It works just as well as it does under IFR. Some years ago a booklet
listing AM radio stations by frequency and location was available for just
that purpose. Some years earlier than that they were depicted on
sectionals.

On Canadian sectionals, some AM commerical stations still are depicted,
esp. in areas where actual navaids are thin on the ground.

Brian.

Roy Smith wrote:
In article ,
"Bob Gardner" wrote:


Your thinking that a VFR pilot crabs to maintain a track over the ground, I
guess. Hard to imagine how the same pilot would home to the same end point.
Ican track a radial, a localizer, or a bearing, but of the three I can only
home to an NDB. Homing/tracking just brings NDB/ADF to my mind.


I guess GPS has brought technology full circle. You can home to a GPS
waypoint. Just do "direct" and make your heading match the bearing.

I do agree with you that you can't home to a localizer, and homing to a
VOR would require an RMI (an instrument which I've never had the
opportunity to fly behind).
Isn't the idea that you can _track_ a ground reference path but you
_home_ to a point. So tracking a VOR radial makes sense as does homing
to an NDB. If you want some fun, try tacking one balloon from your
balloon -- "fox and hound".

"Brian Burger" wrote in message
ia.tc.ca...
On Tue, 21 Sep 2004, Steven P. McNicoll wrote:

On Canadian sectionals, some AM commerical stations still are depicted,
esp. in areas where actual navaids are thin on the ground.


They are still depicted on US sectionals as well

Stan

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

My pilotage skills never deteriorated to that extent, Roy. In VFR conditions
I use eyeballs, and teach accordingly.

Bob

"Roy Smith" wrote in message
...
"Bob Gardner" wrote:

Can't say that I never used VOR for VFR navigation but I can't recall
ever
using the ADF for that purpose.

Why not? If the airport you're going to has an NDB on the field, it's
the obvious way to find it.

None of my club's planes have ADFs anymore, but when they did, I would
often tune in nearby NDB's depicted on sectionals while on VFR trips, to
confirm my pilotage.

"John Bell" wrote in message m...
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_arti...rack_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