# NavList:

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

**Re: Distance off useing a hand held compass**

**From:**Richard M Pisko

**Date:**2003 Mar 25, 19:42 -0700

Back before the dawn of time (on Tue, 25 Mar 2003 13:50:42 -0500, to be exact), David Weilacherwrote: >So you are arguing that if I can measure the distance I travel... > >If I were to take a bearing on an object then wait till the bearing changed by one degree, my distance off would be 360 times my distance travelled? > Not exactly, but close in principle. For a circle, there are 2pi radians or 360 degrees, so one degree would be (2 x 3.14)/360 = .0175 radians. Walking around the 360 degree circle of (say) 1000 yards radius would cause you to travel about 6290 yards. Each degree you walked would be (6290/360) = 17.47 yards approximately. If you walked ten times as far,175 yards, and the compass bearing to the center would change ten degrees, you would still be the same distance from the object , but only 6.3 times the amount you walked instead of 63 times. The mil (possibly short for approximately miliradian, possibly short for the one to one thousand ratio common usage) works well because the because the angle subtended by one mil has a tan of 1/1000 using army math. The short base line of the walk, divided by the long distance to the object, is the tan of that 1 mil angle, and the math is easy. Distinguishing one mil is hard, 10 mils is possible. >At 2 degrees, I could multiply my distance traveled by 360 and divide by 2 for distance off? > Multiply by 62.9 and divide by 2, yes. The mil is smaller than the degree, and the army has 6400 mils around the circle instead of the more accurate but awkward 6283.14 miliradians. So my example of walking ten mils for the 100:1 ratio is about 34 minutes or half a degree. Ten mils is 3.4 inches at 100 yards, not a lot of angle to see with the naked eye. One hundred mils (34 inches) would be easier, one thousand mils (340 inches or about ten yards) easiest if the estimated inaccessible point is 100 yards away. Something a mile away would deserve more careful reading and less walking. >This is strictly a question. In no way is it meant as a comment or criticism. > Well, my conversions from degrees are off the top of my head and with a calculator illuminated by a monitor screen, so I make no guarantees as to the particulars; but the general idea is correct. Remember that you will be walking in a slight curve with a hand compass; not taking chord distances with an EDM and angles with a theodolite. My standard walking step is 30 inches, so I pace off counting by five feet per left foot. -- Richard ...