I agree with Cletus about chords being shorter than arcs. I would try his method of testing the
distance of a GPS unit at a High School track.
My Garmin GPS III+ takes readings when I change speed or direction. The following excerpt from
one of my journeys (this was in an uphill portion of the route) shows how frequently it will mark
a point on a track. When I change direction or speed it stores a "Trackpoint", provides the
latitude and longitude of the point, shows the time it created the point, then shows the
distance, elapsed time, speed, and heading to the next "Trackpoint" Trackpoint N47 48 39.4 W122
00 44.8 3/15/03 9:10:33 AM 36 ft 00:00:02 12.2 mph 278° true Trackpoint N47 48 39.4 W122 00 45.1
3/15/03 9:10:34 AM 17 ft 00:00:01 11.7 mph 270° true Trackpoint N47 48 39.0 W122 00 46.2 3/15/03
9:10:39 AM 88 ft 00:00:05 12.0 mph 242° true Trackpoint N47 48 38.8 W122 00 46.6 3/15/03 9:10:41
AM 39 ft 00:00:02 13.2 mph 227° true Trackpoint N47 48 38.6 W122 00 46.8 3/15/03 9:10:42 AM 20 ft
00:00:01 14.0 mph 220° true
The following excerpt shows the frequency when I am in flat and straight sections of a ride
Trackpoint N47 50 18.4 W122 04 25.5 3/15/03 9:24:04 AM 570 ft 00:00:18
21.6 mph 326° true Trackpoint N47 50 21.2 W122 04 30.4 3/15/03 9:24:17 AM 438 ft 00:00:13
22. mph 310° true Trackpoint N47 50 23.9 W122 04 36.1 3/15/03 9:24:32 AM 476 ft 00:00:15
23.7 mph 306° true Trackpoint N47 50 26.2 W122 04 39.6 3/15/03 9:24:41 AM 332 ft 00:00:09
24.1 mph 313° true Trackpoint N47 50 26.7 W122 04 41.0 3/15/03 9:24:44 AM 113 ft 00:00:03
25.6 mph 300° true Trackpoint N47 50 29.8 W122 04 47.1 3/15/03 9:24:58 AM 520 ft 00:00:14
26.3 mph 307° true Trackpoint N47 50 30.8 W122 04 49.4 3/15/03 9:25:04 AM 188 ft 00:00:06
27.3 mph 302° true
As you can see it does a fairly good job of reporting the changes in direction and speed. If my
direction and speed remain constant, the frequency of reporting get stretched out. Most roads have a
fairly large radius curves. If you have an 11.5 degree arc with a 500 foot radius the difference
between the arc length and the chord length is about 0.16 feet. This is in a nominal 100 section of
road. Most roads that I work with and ride on have a radius that is usually measured in the
thousands of feet. In cases like that the difference becomes even less.
Having said something about the theoretical side I would advise a person to use the approach
suggested by Cletus. That should give you a good reference for the accuracy of the unit you use.
William Higley, Sr. Vision R-50 RANS Rocket
"Cletus D. Lee" <
[email protected]> wrote in message
news:[email protected]...
> In article <
[email protected]>,
>
[email protected] says...
> >
> > "Cletus D. Lee" <
[email protected]> wrote in message
> >
news:[email protected]...
> > > In article <
[email protected]>,
> > >
[email protected] says...
> > > >
> > > > "Cletus Lee" <
[email protected]> wrote in message
> > > > >> Another choice, a Garmin Geko. uses GPS for speed and distance.
No
> > wheel
> > > > magnet. It does under report speed by about 1.5% over a well
calibrated
> > > > wired computer.
> > > >
> > > > My Garmin Geko doesn't under report speed--it's right on.
> > >
> > > I am sorry, You are correct about the speed. Mine is accurate to the .10 mph. Except for the
> > > time it registered 888 mph in downtown
Houston
> > > while I was stopped at a traffic light. It is distance that is under reported by ~1.5%. The
> > > reason the distance is off is because the Geko measures distance from point to point. A route
> > > with a lot of turns
will
> > > be in error. Also I have found that false signals are causing route track errors in city
> > > canyons.
> > >
> > > --
> > > Cletus D. Lee Bacchetta Giro Lightning Voyager
http://www.clee.org
> > > - Bellaire, TX USA -
> >
> > Well, I'm not so sure about the trip distance being under-reported.
When I
> > first bought it, just for an experimentation I brought it along and
watched
> > it update while my wife was driving down the freeway. Assuming the
survey
> > mile markers were correct, I didn't see any noticeable error at all. I
also
> > used it when I rode a century (actually a 108 mile ride), every rest
stop
> > was exact on my Garmin, as was the final distance when compared to the cheat-sheet. It was not
> > 1.5 miles off, it wasn't even .15 miles off.
But
> > heck, I guess you could also argue that they probably used some kind of
GPS
> > to calculate and make the cheat sheet to start with.
> >
> > Maybe you know for sure, but I theorize the Garmin does not simply triangulate between points
> > (thus cutting corners as you indicate). I believe the Garmin somehow integrates velocity, and
> > thus doesn't
necessarily
> > cut off corners. The reason I believe this is I've seen the Garmin
continue
> > to update trip distance for a several seconds (at least) after the GPS signal is lost.
>
> What I know is from observation. Take a look at the track produced by your Garmin. Compare on a
> map against the roads actually taken. I think you will find the route is a series of chords. The
> distance along those chords is the distance measured and reported by the GPS. The Chord is always
> (by definition) shorted than the curve that it spans. This is the error that I refer to. It is not
> much but it accumulates. More accurate on straight roads, less so on routes with lots of turns.
>
> As for your 108 mile Century, if the sponsors did anything other than actually chain off the
> actual distance, then it is an approximation.
>
> If you want to really see how accurate your Garmin really is at distance, take it to a High School
> track. At cycle speeds, do several miles of a known distance (caution the track may be metric).
> See how that compares to the known distance.
>
> I did this with my Magellan once and was lucky to get three points per lap. I would have sampled
> more often if I had been walking.
> >
>
> --
> Cletus D. Lee Bacchetta Giro Lightning Voyager
http://www.clee.org
> - Bellaire, TX USA -