Digital Compass

Date: 08/23/2002 at 11:34:09
From: Josh
Subject: Digital compass

Dr. Math -

I'm not sure if you can answer questions like this, but I was just 
wondering how a digital compass works. I've looked everywhere and I 
cannot find any information on it. Any help would be appreciated.

-Josh

Date: 08/23/2002 at 16:04:54
From: Doctor Rick
Subject: Re: Digital compass

Hi, Josh.

I'm not up on all the latest technology, but I looked around the Web 
a bit, and one commercial site mentioned Hall-effect technology. If 
that's what they use, I can tell you the basics of how it works.

The Hall effect works like this. You make an electric current flow 
through a metal bar or film of some sort - something that has width as 
well as length. A magnetic field (such as the earth's) deflects the 
electrons sideways in their travel along the metal film, toward one 
side of the film. This makes the electrons sort of pile up on the side 
they are pushed toward, and when there are more electrons in one place 
than another, you can measure a voltage between the two places. The 
voltage, called the Hall voltage, is proportional to the current in 
the film, and it is also proportional to the magnetic field strength.

What I've said is a bit too simple. If the magnetic field is 
perpendicular to the film then what I said is true. But if it is not, 
it is the *component* of the field perpendicular to the film that 
matters. If you've seen anything about vectors, you'll probably know 
what I mean; if not, you can ask and I'll try to explain more. In any 
case, you can set up two (or better, three) Hall-effect sensors, 
perpendicular to one another. Then the ratios of the Hall voltages in 
the sensors can be used to reconstruct the direction of the magnetic 
field. If you know about vectors, you can work out exactly how the 
direction would be determined from these ratios.

One tricky thing is that we don't really want to know the angle 
between the direction we're headed and the magnetic field. That's 
because the magnetic field isn't just pointed north, it's also 
pointed down (has a downward component) in the northern hemisphere 
(up in the southern hemisphere). In vector terms, we want to know the 
angle between the horizontal component of our direction and the 
horizontal component of the magnetic field. I suppose this is why I 
saw ads for hand-held digital compasses that had bubble levels to 
help you hold the compass horizontal.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/