# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Manual calculation of compass variation
From: Richard B. Langley
Date: 2004 Oct 19, 09:58 -0300

```On Sat, 16 Oct 2004, Fred Hebard wrote:

>Richard,
>
>That was a very informative article for this non-expert navigator, not
>to mention a reminder of how much I don't know.
>
>I was surprised that a vessel needs to be going 5-10 km/hr to get a GPS
>track accurate to better than one degree, and am wondering what the
>accuracy of the track is for low speeds, which might easily be
>encountered in a sailing vessel; I suppose this information is included
>in GPS manuals, but I don't have one.

the one for the Garmin eTrex Vista, which I own, doesn't). But it is not too
difficult to show, using a back-of-the-envelope propagation of error
calculation, that the heading accuracy is roughly inversely proportional to
the speed. The heading is determined by taking the arcsine of the ratio of the
east component of the velocity to the speed (the magnitude of the velocity
vector) (arcosine of north component over speed or arctangent of the ratio of
the east and north components could also be used -- although the latter will
have problems near 90 and 270 degrees).

As an approxixmation (making assumptions that the east component is
approximately equal to the total speed; i.e. the receiver is heading nearly
due east), we end up with

delta-A = 1/v delta-v

that is, the error in the heading (as an azimuth) equals the error in the
speed divided by the speed (result is in radians which can then be converted
to degrees). A typical GPS receiver determines speed to an accuracy of about
0.05 metres per second or 0.2 km per hour. So the heading error will be
roughly:

(km/hr)     (degrees)
-----------------------
100         0.1
10         1.0
1         10.

And that is why for GPS receivers which include an electronic magnetic
compass, an option is included to switch to the compass when the speed drops
below a certain user-specified value as the compass (if properly calibrated)
will be more accurate.

-- Richard

>Thanks,
>
>Fred
>

===============================================================================
Richard B. Langley                            E-mail: lang---.ca
Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506 453-5142
University of New Brunswick                   Fax:      +1 506 453-4943
Fredericton?  Where's that?  See: http://www.city.fredericton.nb.ca/
===============================================================================

```
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