What is Leonardo DaVinci's Power Factor Correction Capacitor?

Not many people realize that Leonardo DaVinci came up with the first (as far as I've found) power factor correction capacitor. It's mechanical, but it clearly solves a power efficiency problem created by the power source and the power load being in quadrature.

In a most un-Leonardo-like goof, he missed a much simpler mechanical solution to the problem.

Leonardo DaVinci - Codex Atlanticus
I came across this sketch from DaVinci's Codex Atlanticus while browsing through some old books in the U.C. Berkeley library. A is a piece of wood being sawn (or, more correctly, ripped -- the cut appears to be along the grain, not across it). The frame saw B is conventional; in Leonardo's day, it would have typically been used as a pit saw, with one man standing in a pit below the rough wood, and another standing above. The man below would use his weight to haul the saw down; the man above would return the saw to its top position, and advance the rough wood. In the original sketch, it's clear the the teeth of the saw are set properly for cutting in this direction.

Leonardo's contribution is the handle C; by pulling and pushing horizontally on this handle, one man can do the work of two, and no pit has to be dug.

But there's a problem: notice that the saw blade velocity is zero at the top and bottom of its stroke, and that the maximum effort is required midway through its stroke. In contrast, the man at the horizontal handle C can contribute maximum effort when the crank is at the top and bottom, but can't deliver any effort when the crank is horizontal -- just when the maximum effort is needed. The input power available and output power required are in quadrature.

Leonardo's solution is to add a flywheel D, apparently modelled on a grindstone (widely used at the time for sharpening agricultural implements and weapons). The flywheel stores and releases the input power twice per cycle, effectively correcting the phase angle between the input power and the output power.

If that isn't a power factor correction capacitor, I don't know what is.

(The simpler solution that Leonardo missed was to have two cranks, an input crank and an output crank, at 90 degrees to each other. Of course, some energy storage would have still been useful to cut through knots and to carry the cranks past the 90°/270° dead spots, but the requirement would have been far smaller.)

One efficiency solution to the quadrature nemesis would be to add a second hand crank to the other (left-hand?) side of the wheel in a ninety degree leading offset. This would add a second, but out of phase, power pulse. As in poly-phase versus single phase, one could reduce the size, but not the need for correction. A side benefit would be the control of start direction without external influence.

The old steamer reference (below) comes from my involvement in stationary and mobile boilers, Corliss and Locomotive prime movers, old and not so old. And yes, the quadrature solution dates back some two hundred years, now. If you were to put a piston at the 0 or 180 degree position, no motiion is possible. If, however, a second assembly were added to the common shaft at a ninety degree lead or lag, that piston could apply maximum torque to the shaft, thus relieving the locked position of the first assembly. By controlling the position of the valve system (called the "chest") letting steam into the double-acting cylinder, start torque and direction is controlled. this handle is named the "Johnson Bar."

Some external combustion engines have single-acting cylinders, though. Mostly, these are marine. This arrangement requires three or more cylinders to compete with two double-acting cylinders, which equate to four singles.

If you have any model or toy train engines around, examine the drive system. Make that a toy steamer; a diesel won't do this job. By the way, the Brits were the ones who developed the technology, and it has not changed one bit from the git-go.

Chuck Leppert superlec@nivets.com
An old steamer - 9 March 1999

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