Planimeter

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planimeter

[plə′nim·əd·ər]
(engineering)
A device used for measuring the area of any plane surface by tracing the boundary of the area.

Planimeter

a mathematical instrument for measuring the areas of plane figures of arbitrary shape. The most widespread type is the polar planimeter, which was invented by the Swiss mathematician J. Amsler in 1854.

Figure 1

The principle of operation of such a planimeter is shown in Figure 1. When the oriented line segment AB moves in the plane, the area of the figure swept out by it is equal to the product of the length of AB and the length of the arc described by the segment’s midpoint. The quantity σ is equal to the length of the arc of rotation of the integrating wheel if the wheel is placed at the midpoint of AB and its axis coincides with the segment. The polar planimeter (Figure 2) has a polar arm and a tracing arm, which are pivoted at the point B. The polar arm can be rotated about the pole pivot O. The integrating wheel and the counting mechanism are located on a special carriage that can slide along the tracing arm, thereby changing the length of the arm.

Figure 2. Polar planimeter: (O) pole, (OB) polar arm, (A) tracing pointer, (AB) tracing arm, (C) carriage, (W) integrating wheel, (M) counting mechanism

In every planimeter the function of the sweeping line segment is performed by the tracing arm, at one end of which is fastened a pointer for tracing out the figure’s outline and the other end of which moves along a “directrix.” The directrix is a straight line in a linear planimeter, a circle in a polar planimeter, and a point in a radial planimeter. Linear and polar planimeters are used to compute areas bounded by curves given graphically and to calculate integrals of the form

Radial planimeters permit integrals of the form

to be found if the curve r = f (ϕ) is drawn in polar coordinates.

planimeter

A mechanical integrator for measuring the area of a plane surface usually within a given perimeter on a map.
References in periodicals archive ?
On the graphs in Figure 5 the planimetric (using 10 x 10 cm grid) and altimetric RTK positions based on the RAP network registered at GRND test point in session 1, 2 and 3 are plotted.
Larsgaard assessed overall mapping progress at the start of the 1980s to that date and found that some 1,000 planimetric maps had been published since IGY activities commenced.
In all of these studies, planimetric measurements were used.
d) It is easy to note that the reconstruction of the city began with the most important of them, and above all, with the former Turkish raias, old port and important medieval defensive strategic points on the Danube (Giurgiu, Braila) the most interesting planimetric compositions of Giurgiu.
By using the aerial photography, planimetrics, and the RTK GPS valve and hydrant data, the water dataset was populated in GIS.
To support this, an investigation was constructed for certain public hospitals in Turkey to classify the planimetric design efficiency of their nursing floors.
This only differs 13-25 metres from our initial georeferencing and is well within the 40-metre planimetric accuracy of this part of Wardenaar's ground plan (see Figure 5).
For example, the results achieved for the composition of a planimetric transition curve with the following input data give a rise to a single solution:
3) With respect to planimetric construction exercises Klein emphasizes that they are important for applying the acquired skills in geometry, but that they also bear the danger to become just a useless drill in an over-formalized setting: Die Art jedoch, die darauf hinauskommt, dass sich der Schuler nur eine gewisse Rutine erwirbt,--ich meine das Verfahren, dafi aufden verschiedenen Stufen wochenlang Dreiecke aus irgendwelchenfernliegenden Bestimmungsstiicken theoretisch konstruiert werden--das muss uns doch als verfehlt erscheinen.
A large-scale planimetric map is a great aid in co-ordinating this advance planning and very useful to the tactical troops both prior to and after the landing has been made.
The Precision products offer industry-leading planimetric accuracy for precise measurements, uniformity and consistency with other datasets and the ability to derive the most accurate information.
The ATOMI project (Eidenbenz, Kaeser, and Baltsavias 2000; Niederost, 2000) was aimed at detecting changes and enhancing planimetric accuracy from the 5-meter level to the 1-meter level based on colored aerial photos, a digital elevation model (DEM), and a DSM.

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