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Computing Magnetic Declination

If you're going to be doing much map-and-compass work it's very important that you understand the concept of magnetic declination. It sounds scary but it's really just the difference between True North (what maps use) and Magnetic North (what your magnetic compass uses.) Magnetic North will usually be different from True North because your compass needle aligns itself to the local magnetic field lines of the earth, not the geographical north pole. The directions these field lines point are different for every place on earth and tend to drift slowly as the earth's molten core moves around. Most good maps will tell you what the declination was when the map was printed but because the declination changes over time it's best if you calculate it yourself.

To calculate declination for your area all you have to do is shoot a compass bearing to some landmark from a known location and compare the resulting reading to what your map says it should be. For my little test I used my compass to take a bearing from the NAU Sky Dome to the Mt. Elden Lookout towers, both of which are readily apparent on my map. In the below picture I was standing at the northeast side of the Sky Dome looking towards Mt. Elden. The compass bearing of 26° was an average of three compass shots.

When I got home I used my Flagstaff Trails Map, a ruler, and my nifty new Silva Ranger compass to determine what the True North angle between the Sky Dome and Elden Lookout really is. To do this I first oriented my map to magnetic north so that I could use the compass as a protractor:

 

Orienting the map to magnetic north is easy. Simply set the compass to 0° and then position the compass so the edge of it lines up with a couple of UTM markers on the map (the two smaller red arrows in the above pic). Once you've done that all you need to do is turn the entire map and compass together so the red "North" arrow on the dial aligns with 0° and you're set. The large red arrow above shows that the compass is pointing to north (0°).

Now that the map was oriented to magnetic north I used the compass to measure the angle between the NAU Sky Dome and Elden Lookout. This is most easily done with a plain old ruler or other long straightedge:

 

In the above picture I've positioned a ruler between the NAU Sky Dome (red arrow) and Elden Lookout (blue arrow). All that was left to do was measure the angle of the ruler:

 

The angle of the ruler, which you can't really make out in the above jpeg image, is 37°. This angle (37°) is the True North bearing to the Elden Lookout as viewed from the NAU Sky Dome. I then compared this True North bearing to the Magnetic North bearing that I took in the field at the dome.

True North Bearing to Elden Lookout from the map: 37°
Magnetic North Bearing to Elden Lookout using the compass in the field: 26°

Hhhmmm. They're not the same, are they? The True North bearing is 11° more (37° - 26° = 11°) than the one the compass gave us. This means that in order to convert a compass bearing taken in Flagstaff to one usable on a map we need to add that 11°. In other words, we need to shift all of our magnetic compass readings +11° East to work with them on the map. This adjustment, normally just written 11°E, is the magnetic declination for Flagstaff!

Okay, so I experimentally determined Flagstaff's magnetic declination using my compass, ruler, and map. To check my results I got a second opinion from the NOAA Magnetic Declination calculation web page:

NOAA says Flagstaff's magnetic declination is a tad over 11°, which is pretty darned close to my experimentally determined value. Not bad!

In the age of the Internet, manually computing declination isn't a strict requirement because of NOAA's spiffy web application, but it's still worth doing if only to gain practice and confidence using your compass and map together.

Can you use a pedometer in orienteering?

The other day I was trying to figure out how I could measure distance walked in the field without carrying a GPS or manually counting paces. Knowing how far you've traveled is useful in orienteering for several reasons. If you know how far you've walked you can guesstimate where you are on a trail without resorting to taking compass bearings. The same goes for estimating your position along a compass bearing (as long as you've walked in a fairly straight line!). And, last but not least, if you know how far you've walked then you know how much farther you need to go to reach your destination, i.e. the next trail intersection, lunch, the trailhead, etc.

Now, if you're like me, counting paces doesn't work very well for distances longer than a few hundred feet. Mostly this is because counting is a very dull activity and invariably you'll spot a flock of birds or some other distraction and lose the count. This is bad. So what you really need is something that will mechanically count those paces for you and that's where the pedometer comes in.

Pedometers are usually used for keeping track of how far you've walked as part of an exercise regimen. They don't cost much and can be purchased at any sporting goods store or Mega Lo Mart in your area. I got mine, an Omron HJ-112, for $20 at Amazon on a whim just to see if it'd work for orienteering purposes. I was expecting a chintzy piece of plastic crap but I was pleasantly surprised: the Omron is actually a compact and well constructed little bit of kit.

Pedometers compute distance walked by counting your steps, usually via a pendulum or other mechanical/electronic mechanism, and then multiplying the result by your stride length. Therefor, the first thing you have to do is measure your average stride length and input it into the pedometer. This is the most important thing to get right: if you enter a bad measurement the pedometer won't be able to compute distance accurately and you'll have problems. For example, getting your average stride wrong by even one inch will result in an error of 200 feet over the course of a mile. That's not a lot but compounded over several miles and that error begins to add up to real distance. Better to get it right.

The manual that came with the Omron recommended that you take ten steps, measure the distance, and then divide by ten to get your average stride length. I did this in my living room and got an average of 26 inches so that's what I used initially. Of course that was on a flat surface and wearing different shoes than my hiking boots so I was expecting to have to adjust it once in the field.

Some things that can affect your stride length:

• Terrain - Climbing or descending a steep hill will alter your stride length in relation to your stride length on flat ground.
• Footwear - Your stride length may change based on whether you're wearing heavy hiking boots or running shoes.
• Pack weight - A heavy pack should force you to take shorter steps than when carrying a lighter one.
• Exertion level - Walking faster should increase your stride length versus a calm stroll.
• Exhaustion level - A tired hiker near the end of a long day should take smaller steps versus the same hiker at the beginning.

To test the Omron pedometer in the field I took it along with me on the Brins Mesa and Jim Thompson trails in Sedona. I hiked the trails normally and compared the computed distances with the (supposedly) more accurate ones listed on my trail map. For the first leg of the test I walked from Midgely Bridge on Highway 89A along the Wilson Canyon trail to the Jim Thompson trail and then to the Brins Mesa trailhead. On the map this is a 2.9 mile walk over mixed terrain. Surprisingly, the Omron pedometer showed 2.95 miles -- very close!

Thinking that my simple stride length calculation from my living room was spot-on I reset the pedometer and hiked the 2.1 miles on the Brins Mesa trail to where the Soldier Pass trail branches off. To my disappointment I saw that the pedometer had measured 1.8 miles, a pretty large error of about a quarter mile. Hmmmm. What happened?

This part of the Brins Mesa trail includes a quarter-mile section of very steep and rocky climbing up the eastern edge of the mesa. The only thing I can think of is that the slower and uneven walking pace during the climb caused the pedometer to fail to register most of the steps I took. This would in turn cause the computed distance to be lower than the true distance. Because the "missing" distance is so close to the distance that the trail spends climbing the steep mesa I strongly suspect this to be the underlying cause of the error.

The next leg of the hike was down the western side of Brins Mesa to the far west trailhead, a shorter distance of 1.5 miles and, except for one steep section, was mostly a gradual downhill descent along a sandy drainage bottom. This time the pedometer computed a distance of 1.45 miles; still a little low but not too bad and within acceptable error levels. It's also entirely possible that the mapmaker rounded off the distance for that leg of the trail, too: the pedometer may have been dead on.

So this led me to develop some rules for using the pedometer to estimate trail mileage:

1. The pedometer will underestimate distance traveled if it fails to count steps due to a slow or uneven walking pace. If you feel your normal walking pace slowing down significantly due to a steep climb then you need to be aware that the pedometer may "drop" that whole section of the trail!
2. The pedometer will overestimate distance traveled if your stride length shortens for some reason, as when taking shorter steps over broken ground or while descending extremely steep sections of the trail.
3. If you're walking on even or mixed terrain the pedometer will be very accurate, especially if the distance is longer than a mile or two. Miscounted steps or variations in stride length will tend to balance out over a longer distance.

The lesson here appears to be that yes, a cheap pedometer can be useful in orienteering but you need to be careful with steep climbs and descents as they will cause the unit to under or over estimate distance traveled. Climbing seems to be the major culprit for causing inaccurate readings.

Determine your location using multiple compass bearings

In my last post on orienteering I explained how to use a single compass bearing to find your location on a trail or road. With this post I'll show how to use multiple bearings to triangulate your location anywhere, whether you're on a trail or not. This is a useful technique if you're hiking off-trail or have become lost.

Here is a panoramic photo I took from somewhere up on the San Francisco Peaks with three compass bearings in red:

From left to right the bearings are to Freemont Peak, Humphreys Peak, and Aubineau Peak. To determine your location using the compass bearings you first have to convert them to back-bearings and then adjust for magnetic declination. Remember, to convert to a back-bearing you add/subtract 180° to obtain the bearing as it would be for someone standing on Freemont/Humphreys/Aubineau back to your current location. Finally, you add the magnetic declination as determined from your map's legend. This gives you the True North back-bearing which can be used on a topographic map:

Freemont Peak = 223-180+13 = 56°TN
Humphreys Peak = 298-180+13 = 131°TN
Aubineau Peak = 334-180+13 = 167°TN

With the True North back-bearings you can then plot course lines on the map as I've done in the Topo! screenshot below (click for full size version):

The intersection of the three back-bearings points to my location, which turns out to be the Doyle Saddle (no surprise there). The topographic maps all have Doyle Saddle and Freemont Saddle swapped so ignore the label next to the location. When I made the panoramic photo I walked downslope a little to avoid getting too much of the ground in the shot so that's why my location is not precisely in the center of the saddle.

I made the above plot using my copy of National Geographic Topo!, which is very nice software if you're an outdoorsy sort of geek, but not exactly practical in the field. Instead, you'd use a protractor or else orient the map to magnetic north and then use your compass to plot the course lines as I discussed in my previous post. With some practice you can get very close to what Topo! will give you.

This example used three compass bearings but it's perfectly acceptable to use only two bearings. Your accuracy won't be quite as precise but you should be close enough. The third bearing acts as a check on the other two: if instead of converging to a tight point on the map you get a big triangle then you know that one (or more) of the bearings is off.

Determine your location using a compass bearing

Here's a picture of the compass I sometimes use on hikes:

It's a model-27 military-grade lensatic compass that I bought before I got out of the Army about <mumble mumble> years ago. The Army had two kinds of lensatic compasses when I was in: one with radioactive tritium paint on the dial that would permanently glow for use at night and another with phosphorescent paint on the dial. The tritium dial compass was not available at the PX so I ended up with the one with phosphorescent paint. It's a rugged design and makes for a very cool (if a little heavy) piece of kit.

Unlike the clear plastic Silva navigation compasses you normally see people using, the lensatic compass is designed for taking bearings quickly and easily. The folding rear site allows you to look down through the lens and see the dial without needing to move the compass away from your face. This increases accuracy, which is a good thing if you're going to be calling in an air strike based off your reading.

If you're like me and mostly stay on established trails then a compass is most useful for estimating your current location using a single bearing measurement. Off-trail bushwhackers can also use a compass to follow a bearing toward some destination. Both skills are pretty easy to master but for this post I'm just going to show how to find your location on a trail or road using a compass bearing.

Okay, so let's say you've been hiking up the Weatherford Trail on the San Francisco Peaks for a couple of hours and while you know you're still in Weatherford Canyon you want to know exactly where you are. To do this you look across the canyon and take a compass bearing to a prominent location, which in this case would be Schultz Peak:

The compass tells you that Schultz Peak is at bearing 95° from your current location on the trail. If someone standing atop Schultz Peak were to shoot a compass bearing back to you the angle would be 275°(95°+ 180°). This is called the "back-bearing". With the back-bearing and a map you can determine the location on the Weatherford Trail that intersects with that angle, i.e. your current location!

Now, there's a slight complication with that 275° angle. Because you used a magnetic compass to obtain it the angle is in relation to magnetic north, which is not the same as the true north your map uses. Magnetic north drifts around slowly and depending where you are on the Earth the difference between magnetic and true north can be quite large. So you must correct for this difference, otherwise your calculations will be off. Fortunately, all good maps will tell you what the difference is, called magnetic declination, somewhere on them, usually in the map's legend. My map's legend tells me that magnetic declination for Flagstaff is 13° east, which we then add to the 275° magnetic back-bearing to get 288° true north bearing (275°MN + 13° = 288°TN).

So now that you've converted your magnetic back-bearing to map bearing it's time to find the location on the Weatherford Trail that intersects with that angle. To do this get out your map and orient it to magnetic north. This allows you to make angle measurements directly on the map with the compass, negating the need to carry a protractor along with you on the hike. Lay the map on the ground, align the compass with a north-south line on the map, and then turn the entire thing (both compass and map) until the compass needle reads zero degrees:

In the above example I aligned the compass to three UTM markers on the map but any north-south line will do, even the edge of the map.

Once you've oriented the map to magnetic north all that remains is to find Schultz Peak on the map and then shoot a 288° back-bearing from it to find your location on the Weatherford Trail. Because you know you're on the Weatherford Trail you know your location has to be where the bearing line intersects with the trail on the map:

 

In the above picture I placed the lower edge of the compass's straight edge on top of Schultz Peak and then rotated the compass until the dial read 288° below the hairline. This places the intersection of the green line (the 288°back-bearing) with the Weatherford Trail about here:

 

The black circle denotes my estimated location, which happened to be where I stopped for lunch on this particular hike. Checking with my GPS and Topo! show that the location determined via compass and back-bearing from Schultz Peak was about 200 feet off. My true location as given by the GPS was actually a little further down the trail near the southern edge of the black circle. Not perfect but also not too bad for someone without a lot of experience doing this sort of thing.

So what did we learn from this exercise?

1. How to use the lensatic compass to take a magnetic bearing reading to a distant location (Schultz Peak was 95°).
2. How to convert the bearing to a back-bearing (added 180° to bearing to get the back-bearing of 275°).
3. How to convert the back-bearing from magnetic north to true north as used on the topographic map. Flagstaff's magnetic declination is 13° so we added that to 275° and got 288°.
4. We then oriented the map to magnetic north so we could use the compass to measure angles instead of a protractor.
5. And finally, we placed the edge of the compass straight edge on Schultz Peak and rotated the compass to 288° to find our location on the Weatherford Trail.

As I said, this didn't give perfect results but it was close enough for me to know that I was only a half mile or so from the Doyle Saddle. I'm pretty sure the error was due to inexperience shooting bearings and not with the map or the compass.

My dad's mad orienteering skills

One day when I was a teenager my dad, who worked for the Forest Service and whose job it was to mark off timber sale boundaries, brought me to work with him. I don't remember why, but I guess it was one of those "take your kid to work" days or something. At the time I was more interested in reading Heinlein and thinking up new adventures for our role-playing game club at school than tromping around the forest with my father. So, needless to say, I was a less-than-enthusiastic ride-along partner.

After an hour of paperwork and office talk we loaded up a bunch of gear into a green Forest Service truck and drove out into the middle of the forest on a network of seemingly random logging roads. When we finally got to the proposed timber sale, which looked like any other patch of impenetrable eastern arizona forest, we set off into the tangle of trees on foot. Keep in mind that this was raw, virgin forest filled with huge old-growth douglas fir and spruce. The canopy overhead was so thick you couldn't see through it to the sky and the forest floor was such a tangle of brush and downed trees that it was impossible to walk ten feet in a straight line without having to veer around some obstacle. Think of the forest around the Humphreys Trail on the San Francisco Peaks and you'll have a pretty good idea of what I'm talking about.

It was then that my dad showed me the most amazing feat of old-school orienteering that I've ever seen.  Even the land-nav instructors I met in the Army could never have matched it. We spent the rest of the day navigating through this impenetrable mess to precisely predefined locations specified by the timber sale prescription, measuring off various distances down to the foot, and marking trees with spray paint and ribbons. Not once did we get lost. And at the end of the day after hours of transecting the sale back and forth in big loops and figure-eights we not only found our way back to the truck but we did so from a different angle and were only off by a few feet or so.

All of this was done without the aide of a GPS receiver, which, if they existed at all at the time, would've been the size of a jeep and decidedly not portable. My dad's tools were a map, a compass, and sometimes a really long tape measure, although mostly he just counted paces. Hours later, when I saw that green Forest Service truck appear like magic out of the thick trees exactly where my dad said it would I was just floored. It was incredible and maybe a little uncanny, too. To modify Clarke's famous saying: Any sufficiently advanced skill is indistinguishable from magic.

So, Sunday when I noted that my Garmin eTrex GPS had lost its satellite lock yet again in the trees I decided that I wasn't going to carry the damned thing on my birding expeditions anymore. Not only is its battery seemingly always dead but in all the many hikes I've been on this year and last I can't think of a single instance when I really needed to know my location down to ten foot accuracy. Also, it's utility has diminished somewhat since I don't geocache any longer. Instead, in the future I'll do as my dad did: use my mind, a map, and a simple compass to find my route. Maybe I'll get lost, maybe I won't. But it'll be interesting and maybe we'll learn something.