Practical Maths

[Caspar Hauser]

Not being sure where to post this I plumped for here.

In another thread, sketchup was used to determine the radius of camber that Mr Strasil prefers on his plane irons. The information given being the width of the iron and the height of the camber from shoulder to apex, a chord of a circle.

What is the formula to determine this? It's the kind of thing that is quite useful on the job site.

What other formulae/practical mathematical approaches etc have you for the various layout, measuring issues your practice deals with?

May I ask that pencils only are allowed

Thanks

CH

[Daniel Kennedy]

I don't know about pencils only, but here is one that you don't need a formula for. You will need a compass though. If you need me to elaborate a little bit more let me know.

140120

[Walter Plummer]

One half the width squared plus the height squared divided by two times the height. I found it in an old book.

[Nick Laeder]

Here's a solution swiped from the interwebs (dr. math) that has awesome ASCII artwork to go with it.

Total ASCII fail. The board must not allow a bunch of spaces.

I'll do a sketch later, but essentially, the equation is:

r= (d^2 + h^2)/2h

Where:
r= radius
d= half of the chord length. i.e. half of the width of the blade in the blade camber issue.
h= the greatest value of the distance from the chord to the arc. i.e. the distance from the curved edge of the blade to a straight-edge held from corner to corner of the blade, taken at the center of the blade.

Which is exactly what Walter Plummer said.

[harry strasil]

1/2 the chord squared, Chord = a straight line from one side of the circular depression to the other, + the height squared, height equal the distance from from the chord line to the center of the depression or camber, divided by the height ='s the diameter.

Source, 3rd Edition 1920 revised edition of The American Machinists Handbook.

[Jeff Hallam]

Caspar,

I found a wealth of practical math for woodworking in a book by Ken Horner, called "Woodworkers' Essential". With a pencil and a calculator you can do pretty much all the math you need in the workshop/jobsite.

I recommend checking it out, maybe pick up a used copy for cheap.

http://books.google.ca/books?id=22INAQAACAAJ&dq=woodworkers%27+essential+ken+horner&cd=3

[Caspar Hauser]

Thank you all for the responses.

The problem was matching two antique arch topped windows, I had looked up and used a formula but being cautious did the sums twice and got different results (before and after the first cuppa of the day). I then drew it out on the floor using a stick and nail.

It all worked out just fine. However clients don't always like it when I draw on the floor, hence the quest for a simple (i.e. yours truly can use and remember it) mathematical solution.

Thanks again

CH