Jackknife Planimeter to Calculate Area

Tools:JackknifeRuler – 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

Mark

2nd Mark

After completing the trace of the perimeter make a 2nd mark where the blade touches the paper.

Mark

2nd 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.

90 degrees

XY

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 inchesAt our location here in Idaho 1 square inch on a 1:24000 USGS quad equals about 92 acres

92*1.25 = 115 acres

Conversion of twentieths5 /2 = 2.5________ _________ OR

20 /2 = 10 0.25

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.