Problem No. 1: From a given point on the map, you walk one mile due North, then turn East and walk one mile, then turn South and walk one mile. Your companion says, "Hey, we're exactly where we started from!" Where are you?
Problem No. 2: You are standing at an intersection of county roads. One says, 1050 N, and the other, 325 E. You are heading for where CR 200 W meets Baseline Rd. Assuming a perfectly rectangular grid of roads, and further assuming that you will walk only on the road, how far do you have to walk?
Problem No. 3: You are out in the wilds of Philmont Scout Ranch. You've been told that "declination" out here is approximately 10 degrees. You have just taken a bearing on Baldy Mountain, and your compass reads 250 degrees. In order to transfer that to your map and determine your actual position, what do you need to adjust your compass to read for the true bearing?
Answer to Problem No. 1
Answer to Problem No. 2
Answer to Problem No. 3
For answers, click here:
1. You are standing at the South Pole.
2. The roads are named according to the base-and-range system used in surveying the old Northwest Territory (which includes Indiana). Each 100 = 1 mile. So the distance between 325 E and 200 W is 5 1/4 miles, straddling the north-south line from which the county is surveyed. 1050 N would be 10 1/2 miles north of the baseline. So the distance between the two points indicated would be 15 3/4 miles.
3. Declination is the difference between True North and Magnetic North. Out in New Mexico, the compass points about 10 degrees to the right (clockwise) from True North. Which means that although your compass says 250 degrees, the true bearing is 10 degrees off. So after shooting the bearing, you would turn your compass housing 10 degrees to the left (counter-clockwise), ending up with a true bearing of 260 degrees. This allows you to then lay your compass on the map, aligning the housing arrow with the map grid. Your direction of travel arrow on the compass plate is then pointing directly at Baldy Mountain, and you can strike a line from there along the straight edge of the compass plate back towards your position.
Take a second bearing on another recognizable point, correct for declination, and strike a line on the map. Where the two lines intersect is your exact position, your "fix."
If your compass has declination markings on it, you can simply sight your landmark, then turn the housing until the magnetic needle points to 10 degrees E declination, rather than lining up with the housing arrow. Then your compass will read accurately as is, and you can strike your line on the map without doing anything complicated in your head or changing the reading of the compass.