Carpentry/ woodworking mathematics

[mseries]

My general answer would be: geometry - and specifically trigonometry and circles/arcs. I don't know what the syllabus is like these days, but in the mid-nineties I learned everything I've ever used in woodwork at GCSE; if the syllabus is the same these days I don't think there's any real reason to learn anything more advanced. (I did Maths and Further Maths A-Levels, then went on to a Computer Science degree that was full of maths, and the only geometry I encountered outside of GCSEs was a long way from practically applicable!)

I agree, school geometry and trig. is all we really need. It's nice to be able to develop a formula for something without having to look it up though.

 

[mseries]

As an aside, do you know a ruler-and-compass way to find the radius of an arch segment, given a rise and a span? Algebraically it's quite easy, and has been discussed here before.

BugBear

Here's my thoughts, not proven.

Imagine three points on the arc, A,B, C where A-C is the span, and the distance from B to the chord A-C is the rise. Drop a perpendicular ((Do you want me to tell you how to do this ?).) from B through A-C, the centre of the arc is on this line somewhere - call this line 1.
Join A-B and bisect this chord. (Do you want me to tell you how to do this ?). WHere this new line intersects line 1 is the centre of the arc, the radius is the distance from here to one of the points A, B or C

 

[Jacob]

Yep. Euclid. The perpendicular bisectors of any chords to a circle will cross at the centre.

But Euclid or algebra aren't necessarily part of the use of a rod as a graphical calculator and the idea could put someone off.
Things you do on a rod are often dead simple such as taking marks direct from an object to the rod (or "story stick" if it's a staircase) and then manipulating them on the rod - dividing, adding other components, clearance gaps etc etc.
It gets (a bit) more Euclidean with complicated non rectangular "projections" - roofs etc. but still no algebra or other computation required http://owdman.co.uk/howto/howto2.htm

 

[Random Orbital Bob]

This is a fascinating conversation. I recall viewing one of Matthias Wandel's you tubes a while back where he took a digital photo of an actual arch. I think he then imported the image into his print programme that you can download off his website. He had measured the span and he inputted those actuals into the software. His algorithm then laid out the arch with all the appropriate curves etc and he was able to print it on multiple pieces of A4 which when taped together provided an actual template to cut what he wanted. I think he was making a wooden arch from memory but I haven't the time now to dig it out. I remember thinking what an ingenious method it was if you didn't want the brain ache of having to dredge through all the maths.

Having said that though, some of the explanations here have been very useful and I'll bookmark this thread for future head scratch avoidance

 

[Jacob]

This is a fascinating conversation. I recall viewing one of Matthias Wandel's you tubes a while back where he took a digital photo of an actual arch. I think he then imported the image into his print programme that you can download off his website. He had measured the span and he inputted those actuals into the software. His algorithm then laid out the arch with all the appropriate curves etc and he was able to print it on multiple pieces of A4 which when taped together provided an actual template to cut what he wanted. I think he was making a wooden arch from memory but I haven't the time now to dig it out. I remember thinking what an ingenious method it was if you didn't want the brain ache of having to dredge through all the maths.....

There you go!
Ingenious? Quite the opposite: :roll:
A modern man using more computing power than the brains of the whole of ancient Greece, slowly and complicatedly on expensive machines (with all the learning curve that would entail), to solve a problem which an ancient Greek schoolboy could do with a piece of string and a ruler, with hardly any maths at all, in a fraction of the time. Q.E.D!

 

[Random Orbital Bob]

LOL....here we go.....so just nipping down to ye olde Tesco on me penny farthing..back in about.....10 hours

 

[Jacob]

I couldn't find the video - was it this arch? https://www.youtube.com/watch?v=bQce6QNfEkc
Compound curve so not simple.
Personally I would have done it the brass rubbing way - hanging a sheet of stiff brown paper over it and picking up the curve with a crayon. Perhaps then to make up a template from hardboard, to be adjusted by offering up etc.

His moulding system is complicated. Router is the wrong tool for the job. I've done similar curved mouldings (bigger and more complicated than his architrave) on a spindle with home made cutters, ring fences and vertical curved jig (mostly mdf). Cheaper, faster, easier, more repeatable than Wandel's complicated router fiddling.

It's like sharpening - just because someone gets a good result fiddling about with great difficulty and a lot of expensive kit doesn't mean that there aren't easier ways (thank god :roll: )!

 

[JakeS]

His moulding system is complicated. Router is the wrong tool for the job

It may be, but if one owns a router and doesn't own a spindle moulder, it's probably still more efficient/economical to do a one-off fiddly job with a router!

(Wandel is quite aware that he goes over the top and makes lots of things more complicated than they need to be - he makes fun of himself for it quite often, but he seems to be enjoying himself.)

 

[riclepp]

I watched that and fell asleep with his boring narration

 

[mseries]

it's just demonstating his tilting router lift, using something else wouldn't fulfil his requirement

 

[Random Orbital Bob]

I couldn't find the video - was it this arch? https://www.youtube.com/watch?v=bQce6QNfEkc
Compound curve so not simple.
Personally I would have done it the brass rubbing way - hanging a sheet of stiff brown paper over it and picking up the curve with a crayon. Perhaps then to make up a template from hardboard, to be adjusted by offering up etc.

His moulding system is complicated. Router is the wrong tool for the job. I've done similar curved mouldings (bigger and more complicated than his architrave) on a spindle with home made cutters, ring fences and vertical curved jig (mostly mdf). Cheaper, faster, easier, more repeatable than Wandel's complicated router fiddling.

It's like sharpening - just because someone gets a good result fiddling about with great difficulty and a lot of expensive kit doesn't mean that there aren't easier ways (thank god :roll: )!

It might have been...I'm so short of time today....hospital stuff....I've just scan read it and it does look like the one I remember.

I'm not going to get dragged into the boxing ring on this Jacob. I'm enjoying the discussion. I like the old methods, those classic techniques are fabulous and I have the utmost respect for them. Amazingly, they can also co-exist with modern and alternate approaches. This isn't a binary discussion, it's not an either or, it can be quite reasonably an...."as well as".

All discussion on woodworking methods doesn't have to be relegated to a value judgement about which technique "trumps" another one. So in the words of the ancient Greeks my response is Mu....."it is neither yes nor no, you should un-ask the question"