Transcript Douglas Brown`s explanation

Jackknife Planimeter
to Calculate Area
Tools:
Jackknife
Ruler – one with decimal divisions of inches makes the math easier (Many
compasses have a 1/20 inch scale)
Triangle – Something to draw a right angle or just use you compass body
Map or paper with a polygon of unknown area drawn on it
Doug Brown, Lowman R.D., Boise N.F., USFS – 5/24/10
Set up your knife like this – angles are not
important but it helps with the math later
if the distance between the pointer “A”
and the place where the blade touches the
paper “B” is a whole number or an easy
fraction like ½.
A
B
On your polygon select and mark a starting place on the polygon’s perimeter then draw a horizontal
line. Next place the knife on the horizontal line with pointer “A” on the starting place and “B” on
the horizontal line. Mark the place on the horizontal line where the blade touches the line. It might
help to mark the blade – precision = accuracy.
The knife should be held by the pointer and kept perpendicular to the surface of the paper so there
is little interference with the travel of the blade end.
Trace the perimeter in a counter-clockwise direction from the starting point around to the start. The
knife blade will trace a sort of “Z” and end up close to the mark
Mark
After completing the trace of the perimeter make a 2nd mark where the blade touches the paper.
2nd Mark
Mark
Draw a line from the starting point to the 2nd mark (call it “X”) and draw a line perpendicular to the
line just drawn extending to the horizontal line (call it “Y”). The right triangle formed by X, Y and
the horizontal line has an area ½ the area of the polygon.
X
90
degrees
Y
Mark
2nd Mark
X * Y = the Area of the Polygon
Example:
We set the jackknife so its “open” length is 5 inches and we measured the Y distance – the
displacement of the blade as 5/20
5”*0.25” = 1.25 square inches
At our location here in Idaho 1 square inch on a 1:24000 USGS quad equals about 92 acres
92*1.25 = 115 acres
Note:
The polygon’s general diameter should
be less than half the jackknife’s span (A
to B). Large polygons may need to be
divided into smaller parts.
You can see that the use whole numbers
in setting up the jackknife and the use of
decimal equivalents when measuring the
“Y” length makes the math easier – here
are some other values which may be
useful 1/8 = 0.125 and 1/16 = 0.0625.
Conversion of twentieths
5
/2 = 2.5
________
20
_________
/2 = 10
OR
0.25