A senior engineer at 3M(Earl Hoyne)once explained how to use a
two-bladed pocket knife as a planimeter, an idea from someone in
Finland. You need a knife that has one blade pivoting from each end of
the handle. If the blades both come from a common pivot point, it won't
work.

Here's how to use it:

Setup:
-Get a scale plan view of the surface whose area needs to be determined.

-On that plan, draw, in scale, a rectangle of some size whose area you
do know. The area of this rectangle should be about the size of the
surface to be evaluate. Plus or minus 50% is fine.

Now you are ready to determine the area of the unknown shape.

Example:
I want to measure the area of a farm field. It is irregular in
shape. The Farm Service Agency has given me an aerial printout of the
section that contains my field.
It is easy to see on the printout, the perimeter a 40 acre field.

I can also see the boundaries of the field of interest to me.

-Open the large blade of the pocket knife completely.

-Open the smaller blade so it makes an obtuse angle of about 100° with
the handle of the knife.


-The tip of the small blade will become the pointer to be used in
tracing the outline of the shape whose area is to be measured.

Calibrating the setup:
-Now stand the knife up on that point, with the point touching a corner
of the scaled rectangle (it has a known area, right?).

-The cutting edge of the large blade will be contacting the printout.
With a sharp pencil, make a single point on the printout, exactly at the
at the tip of the large blade.

NOTE: During the rest of this process, it is important that the blades
don't pivot at all, so hold the tool lightly.

-Now slowly move the pointer end of the knife along the perimeter of the
rectangle. As you do so, the cutting edge of the large blade will go
back and forth, but not sideways. Go all the way around the perimeter.
You will see that the ANGLE of the back and forth motion of the large
blade changes the direction that the end of that blade moves.

-So, when you have returned to the starting point of the rectangle,
having traced around the whole shape, the tip of the large blade will
have come to rest in a different location. Mark this point with the
sharp pencil. Carefully measure this distance. This is the calibration
of the printout.

-Now, do the same thing, this time marking, tracing and then marking the
begin/endpoint of the outline of the field whose area is to be measured.
Carefully measure the distance between those 2 dots.

-The difference between the two distances is directly proportional to
the areas of the two shapes.

-So, if the distance between my calibration marks was 1/4" (for a known
40 acre field) and the distance between marks on the subject field was
3/16", then my subject field has an area of 30 acres.

Boy, I hope I got this right, I haven't done this for 25 years,
Pete Stanaitis

spaco wrote:
A senior engineer at 3M(Earl Hoyne)once explained how to use a
two-bladed pocket knife as a planimeter, an idea from someone in
Finland. You need a knife that has one blade pivoting from each end of
the handle. If the blades both come from a common pivot point, it won't
work.

Here's how to use it:

Setup:
-Get a scale plan view of the surface whose area needs to be determined.

-On that plan, draw, in scale, a rectangle of some size whose area you
do know. The area of this rectangle should be about the size of the
surface to be evaluate. Plus or minus 50% is fine.

Now you are ready to determine the area of the unknown shape.

Example:
I want to measure the area of a farm field. It is irregular in
shape. The Farm Service Agency has given me an aerial printout of the
section that contains my field.
It is easy to see on the printout, the perimeter a 40 acre field.

I can also see the boundaries of the field of interest to me.

-Open the large blade of the pocket knife completely.

-Open the smaller blade so it makes an obtuse angle of about 100° with
the handle of the knife.


-The tip of the small blade will become the pointer to be used in
tracing the outline of the shape whose area is to be measured.

Calibrating the setup:
-Now stand the knife up on that point, with the point touching a corner
of the scaled rectangle (it has a known area, right?).

-The cutting edge of the large blade will be contacting the printout.
With a sharp pencil, make a single point on the printout, exactly at the
at the tip of the large blade.

NOTE: During the rest of this process, it is important that the blades
don't pivot at all, so hold the tool lightly.

-Now slowly move the pointer end of the knife along the perimeter of the
rectangle. As you do so, the cutting edge of the large blade will go
back and forth, but not sideways. Go all the way around the perimeter.
You will see that the ANGLE of the back and forth motion of the large
blade changes the direction that the end of that blade moves.

-So, when you have returned to the starting point of the rectangle,
having traced around the whole shape, the tip of the large blade will
have come to rest in a different location. Mark this point with the
sharp pencil. Carefully measure this distance. This is the calibration
of the printout.

-Now, do the same thing, this time marking, tracing and then marking the
begin/endpoint of the outline of the field whose area is to be measured.
Carefully measure the distance between those 2 dots.

-The difference between the two distances is directly proportional to
the areas of the two shapes.

-So, if the distance between my calibration marks was 1/4" (for a known
40 acre field) and the distance between marks on the subject field was
3/16", then my subject field has an area of 30 acres.

Boy, I hope I got this right, I haven't done this for 25 years,
Pete Stanaitis

Pete, I am having trouble picturing this. How do you move the the knife
around 4 sides of the rectangle without it moving sideways?
And why would the tip not wind up in the exact same spot?

Go to youtube and type in "planimeter". That video shows one with
wheels, but just imagine the wheels being replaced by the knife's large
blade cutting edge.

--I'd do a youtube on this if I had the capability.

Pete Stanaitis
------------------

RBnDFW wrote:



Pete, I am having trouble picturing this. How do you move the the knife
around 4 sides of the rectangle without it moving sideways?
And why would the tip not wind up in the exact same spot?

On Thu, 08 Oct 2009 14:41:32 -0500, spaco wrote:
RBnDFW wrote:
Pete, I am having trouble picturing this. How do you move the the knife
around 4 sides of the rectangle without it moving sideways? And why
would the tip not wind up in the exact same spot?

Very much like parallel parking your car. When you begin the process,
the rear wheels (the large blade's cutting edge) are out in the street.
As you manuever the front end of the car, going back and forth, the
rear wheels, because of the constant changing of the angle of the car
body, move sideways toward the curb.
If this doesn't do it, I can take a couple of pix.

I don't understand just where you are holding on to the knife
and whether you align the little blade in any particular
direction as you move it along the contour.

I assume that "the blades don't pivot at all" means that they
don't turn on their hinges during the process, ie, the knife
with its two open blades is moving as a rigid unit.

You say the "edge of the large blade will go back and forth, but
not sideways". What constrains it?

Is this a process that can be done with a caliper like on the back wall in
http://homepage.ntlworld.com/stevenson.engineers/lsteve/files/caliper.jpg
? Or does the flatness of the blades have some effect?

Also, have you got a web link for it?

--
jiw