Estimating the distance across a lake, river, stream, or even a canyon is a snap with the proper tools:
Here is the basic formula:
- A magnetic compass
- A scientific calculator, one that has the TRIG function of TANGENT.
Distance = abs(tan((a - b) + 90) x l)
abs means the absolute value--if the answer turns out to be negative, simply disregard the negative sign and make it positive.
The formula is simple to use.
- Pick out a landmark straight ahead of you on the other side, such as a tree or rock; using the compass, take a magnetic bearing (a).
- At a right angle to (a), measure off a distance in strides or double paces, along the shore (l); the longer this distance is, the more accurate will be the result.
- From here take a second bearing (b) to the same landmark.
As an example, say the first bearing (a) is 112º. Turn and walk say 50 strides (l) to get (b), we'll say it's 107º.
Substituting these numbers in the formula:
Distance = tan((112 - 107) + 90) x 50)) or tan(95) x 50 = -11.4301 x 50 = -571.5 or the absolute value = 571.5.
Thus, the answer is approximately 572 strides to the other side of the lake.
To convert to distance in feet or meters, you will need to know the average length of your stride.
This can easily be done by measuring off a distance of say, 50 feet, and dividing this by the number of strides you take to walk it.
As the stride of the average person has been estimated at 66 inches (5.5 feet), this brings the answer to approximately 2860 feet (572 strides x 5.5)
Estimating without a Calculator
- As above begin by taking a magnetic bearing to a prominent landmark.
- Now do one of two things:
- If you turn to the left then add 45º to the bearing, and set the compass to this new bearing.
- If you turn to the right, then subtract 45º from the bearing and set the compass to this new bearing.
- Keeping the compass pointed at the landmark, walk until the needle is once again aligned with the north end of the arrow. The distance between the point where you are now standing and the point where you first took the bearing is equal to the distance across.
- Counting the number of paces back to the first position will give the answer.