Pegboard - a poor man’s Parf system

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If you want to make lots of worktops with 20mm dogholes, accurately aligned, at 96mm centres, a commercial jig for making them is the Parf system.

I have enjoyed the videos by the inventor on YouTube, but I am never going to make any more work benches.

About 40 years ago, I salvaged a lot of pegboard from a shop refurbishment. I put 3 sheets over my first workbench. This was not an original idea, since it was first published in “Fine Woodworking.” Reprinted in “Proven Shop Tips” The contributor was Dennis J. Teepe.
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At the time I was going to night classes at Reading Tech college, training in Carpentry & Joinery, especially interested in roofing geometry, where sometimes the pitches are given in Rise and Run, where rise is the Opposite, Run the adjacent and the rafter is the hypotenuse.

Purely as a intellectual exercise, I drew up a table of all degrees from 1- 44. The angle formed by the straightedges above is 23 degrees, having a rise of 14 & a run of 33.

I have never used this chart. All the fractions are within 0.002 of the tangent. Is it actually of any use to anybody?

Here it isAttachment 43569

I do not really want to type it up, unless I get a few requests, but if you wanted to do it for a particular angle, what I did was to strike the angle on graph paper, using a cheap protractor, which showed the line passing through a number of intersections, which gave me fractions to resolve on the calculator, to choose the closest to the tangent.

I sent this to “The Woodworker” and was rewarded with a tool token which I used to buy a set of wood boring augers.

Years ago I wrote a program to produce a rational fraction approximation to any decimal number accurate to a user input accuracy.

Below is shown what it produces when I input tan(23) = 0.424475 and a desired accuracy of 0.1 %.

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RATIONAL FRACTION APPROXIMATION

Number to approximate [3.14159] ? 0.44275
Desired approximation accuracy [0.01 %] ? 0.1

Number = 0.424475
0 & 14/33 = 14/33 = 0.424242424
Approximation Error = -0.0547914 %

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OTOH, if we ask for 0.01% accuracy, we get...

Number = 0.424475
0 & 59/139 = 59/139 = 0.424460432
Approximation Error = -0.00343209 %

The price we pay for this much better approximation is larger integers in both numerator and denominator.

The program is available on my page although I suspect (haven't checked) that less sophisticated programs are available on the interweb.