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Back before the dawn of time (on Tue, 25 Mar 2003 13:50:42
-0500, to be exact), David Weilacher
 wrote:

>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 ...

   

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