# Planimeter



## dnalot (May 22, 2013)

Didn't know these existed now I have one. Is it of any use to a machinist? It came with a lathe mixed in with a bunch of old micrometers and such. Played around with it for a few hours before I figured out what it does. What it does is measure the area of an irregular shape. The round block has a sharp point in the center and acts as an anchor. Now you just trace around the shape you want to measure and then read the dials. 

Mark T


----------



## jwcnc1911 (May 22, 2013)

That is awesome!  I've never seen one of these used.  If you ever get into anodizing or electroplating surface area becomes important.  Outside of that I've never seen an "area" call-out on a print.


----------



## enfieldbullet (May 22, 2013)

that's amazing! please get more pictures!

sounds like a physical integrating(as in calculus) engine. those are somewhat rare.


----------



## mu38&Bg# (May 22, 2013)

Used by people who worked with maps. The mechanism sounds interesting, I'll have to look up how it works.


----------



## thayer (May 22, 2013)

My father still has the one that I borrowed while in college for a class in yacht design. We used them to generate areas of the hull cross sections which we then integrated to find total displacement, righting moments, etc.  Fun to have and know how to use, but with CAD so prevalent I expect they are less practical than a slide rule these days.

Thayer


----------



## albertorc19 (May 22, 2013)

Wonderful instrument, it was used to calculate areas in maps and plans. I've just seen one in a pawn shop, they wanted about 100 dollars for it. It has not any use for me but I really like those fine instruments.


----------



## RonGinger (May 22, 2013)

No steam engineer could be without one. You 'took a card' with an indicator, then measured the area of the curve to determine horsepower. You did one on each end of the cylinder to tell if the valve was adjusted right.

I was at the last running of a BIG 3 cylinder rotary sewerage pumping engine years ago and we were taking cards then- that was the only time I have ever actually seen it done.


----------



## Tin Falcon (May 22, 2013)

Yep the area under a curve is power.You can calculate with calculus or get a good estimate with a planimeter. great for calculating the area of a lake or pond on a map. 
Tin


----------



## jwcnc1911 (May 22, 2013)

I was having tool envy, already bidding on one on eBay.


----------



## Mainer (May 22, 2013)

Someplace I have a writeup of the mathematical theory of their operation. We used planimeters in one of my engineering classes, maybe thermodynamics.

We always used the dial reading as a relative value only. We'd "calibrate" the planimeter by tracing a square of known area on the graph -- maybe a 10x10 block -- and using the resultant dial reading to figure out a scale factor to use when measuring the actual area of interest.


----------



## rodw (May 24, 2013)

I had one of these and used it on maps. I twas built in the 50's and I gave it to a young Surveyor. He said he thought he knew what it was as everything he did was digital and that was over 10 years go. Very cool bit of gear. I always thought of them as being used for cartography, never machining.


----------



## Mosey (May 24, 2013)

Great old tool, you are fortunate to have. Enjoy it.
There is an old thread here that shows old devices like that.
Soon, analog clocks will be turning up at flea markets, and we can explain to the youngins how they worked in the day to tell time. And, handwritten or drawn objects as well.
CAD programs do a nice job of calculating areas under a p-line.
Mosey


----------



## rickhann (May 24, 2013)

Prior to the digital age, it was a common instrument in any Civil Engineering office or public works office that dealt with road construction.  It was used to determine the individual areas of roadway cross sections, at usually 50 or 100 hundred foot intervals.  Each cross section would be either a cut section or a fill section or a combination of both.  Knowing the areas of each section and the distance between sections, the quantities of earth needed to construct a roadway could be determined.  Back in the early 60's during the peak of the Interstate road construction boom, I was a construction engineer for the Illinois Highway Dept.  When construction on the highways was shut down for the winter, the construction personnel would be reassigned to the design office.  We would be given stacks of plan sheets, a planimeter, and told to "buggy" them.   Don't know the origin of the term "buggy", but after a few weeks of  "buggying" cross sections for 8 hours a day, we would become buggy!  Rick


----------



## Gedeon Spilett (May 24, 2013)

An other way to estimate areas is to copy the design onto cardboard, cut out the shape, weigh and compare it with a standard, I did that when I was student ! 

this one is the planimeter of Oppikofer (1827). The point p follows the perimeter of the curve and the counter V measures the area drawn by p. The clever point is the cone. the x dimension remains linear while the y dimension is coupled with the cone to the counter, hence measuring the product xy.


----------



## Mainer (May 24, 2013)

Here's a picture of the Dietzgen I bought years ago. I think I may have used it once in the past 20 years. It looks to be newer than the K&E that dnalot has, but basically the same thing.  It was for sale, used, for $35 and I couldn't resist.


----------



## Shopguy (May 24, 2013)

Very nice example.  But as mentioned kind of obsolete in this day of computers.
Haven't seen one of these in years.  I recall they were used for calculating cut and fill on road engineering and  in my world  for calculating the area of pressure volume diagrams in engine testing.


----------



## jwcnc1911 (May 24, 2013)

Gedeon Spilett said:


> An other way to estimate areas is to copy the design onto cardboard, cut out the shape, weigh and compare it with a standard, I did that when I was student !
> 
> this one is the planimeter of Oppikofer (1827). The point p follows the perimeter of the curve and the counter V measures the area drawn by p. The clever point is the cone. the x dimension remains linear while the y dimension is coupled with the cone to the counter, hence measuring the product xy.



Great. Now I gotta make one of these!


----------



## hilij (May 25, 2013)

John from Malta, I agree with RonGinger the planimeter was used to calculate IHP on steam engines after you took a card with the indicator. I do have a Dobie Macinnes indicator still in original box and also a planimeter. The first I bought in a car boot sale the other I bought on Ebay. I would post a photo when my children show me how))


----------



## Hopper (May 25, 2013)

Of course it is of use to a machinist. For impressing your mates no-end when they visit your shop. 
Nice piece of kit just to look at and play with!


----------



## rickhann (May 25, 2013)

hilij said:


> John from Malta, I agree with RonGinger the planimeter was used to calculate IHP on steam engines after you took a card with the indicator. I do have a Dobie Macinnes indicator still in original box and also a planimeter. The first I bought in a car boot sale the other I bought on Ebay. I would post a photo when my children show me how))



I am a bit confused as to what you are saying.  By stating that you agree that the planimeter was used to calculate IHP infers that it is a single use instrument.  It is an instrument used to find the approximate area from a scale drawing.  Using it to find the indicator diagram area is but one of a myriad of uses for the planimeter.  Rick


----------



## va4ngo (May 25, 2013)

I have used a planimeter extensively in the Hull Drawing office for cakculating areas of scaled drawings in order to allow us to calculate c.g. Etc. Particularly useful for complex curved shapes.


----------



## hilij (May 26, 2013)

Rickhann please don't be confused, I know that a planimeter has lots of other uses in measuring areas. As an ex engine fitter in a shipyard I was talking about its use for measuring IHP on steam engines!


----------



## Tin Falcon (May 26, 2013)

Wow how easily things can be misunderstood on the web.. 
I do not think anyone is implying a single use. 
I am enjoying this thread.  
There was actually two original questions .
how it works and what application it has for a machinist. 

I think a better question it what application  it has to a model engineer. 
so lets focus on that. 

and what does the indicator look like that draws the card. 
Tin


----------



## rodw (May 26, 2013)

I think all of the applications referred to above are simply measuring area. It sounds like sometimes it was the area of a nomagraph for steam calculations but most of the time it is either the area on a plan or map or the area of a given cross section as in hull design or dam design. I am pretty sure the hull designer would use the same trapezoidal rule we dam designers used them for to calculate the total volume or displacement of a 3 dimensional shape.

Some of the cheap ones (which I used as a student) were calibrated so that 1 revolution was 100 square centimetres (at 1:1) but others had a vernier scale on one of the arms that allowed you to vary the calibration to agree with the scale of a map or plan. So if you had a scale of 1:5000, you could read the value based on the scale in use rather than having to do your own scaling maths.

I will say there was a bit of an art in deciding where to position the fixed base so the tool could trace the whole area under consideration and to watch out for wheels fouling the edge of the map, plan or photo.

In a real life example, I used them for water way design when surveying contour banks. Starting with aerial photos and looking at them through a stereograph (similar to binoculars mounted on a stand above the photos) , we would manipulate the overlapping photos until we got a stereoscopic view. Then we would draw in the ridgelines on one photo with a brown chinagraph pencil and the streams and waterways in on blue. Once this was done, we could site the waterways contour banks would flow into. Then we could measure the catchment area with a planimeter and calculate the estimated runoff for a given rainfall intensity return period depending on what we were designing. Once this was done, we should know the design parameters to use to design the size of the waterway . 

If we were designing a dam, we could site the dam wall and measure each contour (which generally involved doing a grid survey and interpolating values to draw our own contours from) and use the trapezoidal rule to calculate the dam volume. We would also measure the catchment area determined maximum design runoff to ensure the spillway was designed to have sufficient capacity to handle the overflow without gouging big gullys or the dam overtopping and the wall breaching. 

Civil engineeers might use the same procedures to size culverts under a road to handle the runoff which they would determine from nomographs. I remember while at college in the early 80's getting the bookshop to order in copies of a book of nomographs from the US. It cost us a fortune for about 50 pages. I kept this book for ages but one day I opened it up while packing up  to move and could not understand even one of the diagrams so I finally gathered up the courage to ditch it.

Now everything is done with Satellite photos and GPS units.

*To use a planimeter,* set it on your plan with the two arms at roughly 90 degrees. Lift the mechanism and rotate the wheels to zero the scale and put the mechanism down again. Then trace your shape (which must be enclosed so you finish where you started and read the scales. If you don't know the 1:1 scaling, draw a square of known dimensions (eg 100mm x 100mm or 4" x 4") and compare the device reading with the known area. Some came with a little metal part you could trace to calibrate the device to a known standard. From memory, we would do it about 3 times and average the result if precision was required.

So the challenge now for those who have a planimeter is to find the stereoscope that was so often used in conjunction with one. See http://en.wikipedia.org/wiki/Stereoscopy and there is a picture at the top right of a small one.


----------



## deverett (May 28, 2013)

thayer said:


> My father still has the one that I borrowed while in college for a class in yacht design. We used them to generate areas of the hull cross sections which we then integrated to find total displacement, righting moments, etc.  Fun to have and know how to use, but with CAD so prevalent I expect they are less practical than a slide rule these days.
> 
> Thayer



Simpson's Rules by any chance?  Would have come in handy for 2nd Mates stability when I was but a simple sailor.

Dave
The Emerald Isle


----------



## stew (May 29, 2013)

HI,
Interesting and a very useful device, thanks for posting.


----------



## thayer (May 29, 2013)

deverett said:


> Simpson's Rules by any chance?




Sounds about right, but it was quite a while ago and not used since.


----------

