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Planimeters have been used in pretty much every area (pun fully intended) of science and engineering for millennia, until CAD came around.? In my case in an earlier career, they were used for calculating the cross-sections of ship hulls at each transverse ¡°frame¡± in naval architecture.? The areas of cross sections for each frame are then multiplied by the distances between frames to calculate the volumes between frames, then those volumes are added to calculate the total volume of a hull. Planimeters can also be used to calculate the longitudinal cross-sections between frames where they¡¯re not rectangular, e.g., toward the bow and stern, or highly hydrodynamically efficient military combatants (especially submarines), racing craft, and so forth. Of course, it¡¯s an approximation, but ¡°close enough for government work¡±, as well as commercial shipbuilding, etc.? In fact, it¡¯s a mechanical form of integral calculus for calculating the area under a curve, where???(Greek letter ¡°del¡±, lower-case delta,?¦¤) is the value of the maximum accuracy (minimal incremental value) that the planimeter can measure in distance in a given dimension (similar to how typical slide rules can be used to calculate to about three decimal places of accuracy). ? Jim ?KJ7JHE On Wed, Nov 30, 2022 at 2:08 PM jjpurdum via <jjpurdum=[email protected]> wrote:
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