An investigation Begins
Posted: Sun Jun 12, 2016 2:32 pm
Following my discussion with Ian Anderson in a separate thread concerning the finding of backing cuts on a curved hip rafter, I was reacquainted with one of my French Layout texts, a volume dealing with advanced cabinetmaker's drawing, La Menuiserie.
I thought it would be worthwhile to start going through the book, and make the models and examples contained within, as double circular work remains a frontier I have yet to explore in depth. You've gotta study if you want to advance in this field, at least that is how it seems to me.
The preliminary section is called Éléments de géométrie plane, and contains a series of standard exercises for producing parallel lines, perpendicular lines, and then moves to drawing various angles, using compass and straightedge. I was intrigued to come across a different method than I had seen before for producing a desired angle, Fig. 19:
So, I opened SketchUp and drew it out, but the angle produced by the intersection of a line projected from point C through D to produce D' was not exactly 29˚, as advertised. Puzzled, I set Sketchup to a higher number of facets (360) per circle, thinking the coarse faceting of the arc initially might have led to the obvious inaccuracy. However, I still got the same result after a redraw.
So, then I turned to calculation - you can see some of my numbers pencilled in on the drawing - using the Law of Sines to work out angle D'OC (which was 119.49209...˚), then, subtracting 90˚ from that obtained the angle AOD', at 29.492˚. It supposed to be 29.0˚, so this method, for that angle at least, produces an inaccuracy of nearly half a degree.
One can argue about how accurate is accurate enough, but I would say that half a degree of error is too much. For rough framing, perhaps okay, but that is far from what this text is all about.
This is a modern text by Les Compagnons Du Devoir, so I was surprised to find a method shown so early in the book which is not anything more than capable of producing a rough angle. I read through the textual description for that Figure, thinking I might find some sort of comment to the effect that the method was only approximate, but no. Surprising.
I thought it would be worthwhile to start going through the book, and make the models and examples contained within, as double circular work remains a frontier I have yet to explore in depth. You've gotta study if you want to advance in this field, at least that is how it seems to me.
The preliminary section is called Éléments de géométrie plane, and contains a series of standard exercises for producing parallel lines, perpendicular lines, and then moves to drawing various angles, using compass and straightedge. I was intrigued to come across a different method than I had seen before for producing a desired angle, Fig. 19:
So, I opened SketchUp and drew it out, but the angle produced by the intersection of a line projected from point C through D to produce D' was not exactly 29˚, as advertised. Puzzled, I set Sketchup to a higher number of facets (360) per circle, thinking the coarse faceting of the arc initially might have led to the obvious inaccuracy. However, I still got the same result after a redraw.
So, then I turned to calculation - you can see some of my numbers pencilled in on the drawing - using the Law of Sines to work out angle D'OC (which was 119.49209...˚), then, subtracting 90˚ from that obtained the angle AOD', at 29.492˚. It supposed to be 29.0˚, so this method, for that angle at least, produces an inaccuracy of nearly half a degree.
One can argue about how accurate is accurate enough, but I would say that half a degree of error is too much. For rough framing, perhaps okay, but that is far from what this text is all about.
This is a modern text by Les Compagnons Du Devoir, so I was surprised to find a method shown so early in the book which is not anything more than capable of producing a rough angle. I read through the textual description for that Figure, thinking I might find some sort of comment to the effect that the method was only approximate, but no. Surprising.