Polar Planimeter quantifies the area by plotting the perimeter

polar planimeter featured


These days it’s hard to bear the label “maker” or “hacker” without also being proficient in some sort of CAD, even if the C is for Cardboard. But before there was CAD, there was Drafting and the arts associated with it, and you couldn’t just select a shape and see its area in the square unit of your choice. So how could an old-fashioned draftsman figure out the realm of complex shapes? [Chris Staecker] introduce us to the polar planimeter, a measuring instrument created especially for this purpose and fully explained in the video below the break.

The polar planimeter under discussion is a more expensive unit from the 1960s. Interestingly, the first polar planimeters were invented in the early 1800s, even before the math describing their function was complete. At one end a lever is placed in a fixed position and at the other in the planimeter. The planimeter itself has another arm with a reticle on it. The unit is zeroed with a button and the outline of the shape in question is traced clockwise with the reticle.

What allows the pole planimeter to measure in multiple dimensions is the fixed arm. The fixed arm rotates, allowing the planimeter to track angular changes that affect the output. So the planimeter measures not only the length of the circumference, but also the size of the circumference. The final measurement is taken in square inches.

Overall, it’s a really handy tool that we didn’t know existed, and it’s fascinating to see how issues like this were solved before anything could be done with a mouse click. Be sure to check out this 100+ year old reference set to supplement your knowledge of previous knowledge. Thanks to [Zane] for the good tip!

Leave a Reply

Your email address will not be published.