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Chord & Rise

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Time stops for a pile of century-old wood

 

old-wood-a.jpg.1b50a0fa91498d4099d037f99e384ea1.jpg

 

Wanting to know what size blade cut these markings, I did some research. Then a bit of math using a formula. The straight line is called the chord and the other, the rise.


[(rise-squared x 4) + chord-squared] ÷ (8 x rise) = radius

I used millimeters for accuracy; chord = 140mm, rise = 4mm; 19600/32 = 612.5 x 2 = 1225mm = 48”

 

The whole story:

 

This pile of wood looked interesting. It had remained curbside for a few days. Eventually I stopped. With a little more forethought I wood have taken the pile. But only grabbed the drawer bottoms. And they sat in my basement until Mid-Covid ... I found images of the boards on my blog from August 2018.
 

1978254960_westphillycurbfindbuiltindrawers.jpg.816d7fe8ba9134f982158004c312ad85.jpg

 

775308005_wphillycurbfinddrawerbottoms.jpg.fc76c1a42fb081f5bec66d04c6f88b34.jpg

 

In the rough, and a few projects. The fourth board chosen had these blade markings. After online sleuthing this morning, I find the phrase kerf marks and kerfs (term confirm please).

 

1249251306_wphillyoldboards1.jpg.68c0397d44f1fe32c1d47e8acb7ee1e8.jpg

 

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2138966237_wphillyoldboards8.jpg.7d29fa95bd6bc232da3574c1af1aba46.jpg

 

The slat shelf is my favorite; I use it every day as a pillow shelf. Radiator closed (it usually is off), linens and blankets put on hooks, pillows on the pillow shelf, window opened, door closed, the whole compartment aired out daily.

 

440177872_20210423spruceshelf.jpg.f8ff2778529fa128ae543cda1912cb0f.jpg

 

799262873_20210306spruceframe.jpg.e423df06428d5860166a3fdcf8fe198f.jpg

 

Hope you enjoyed the tour!  - jim

Good save and great use of the material.  Too bad you couldn't/didn't salvage the whole pile ;)

 

Kerf & kerf marks - IMHO, the kerf is the gap left when the saw blade cuts through the board.  In my mind a gap doesn't leave marks, the saw blade did.

***Notice when I typed the word "kerf" that it became underlined?  Supposed to take you to a TPW dictionary for the word - but it doesn't seem to do that, or maybe I don't know how to access it... hey @John Morris, what's the key here?  May just be semantics, but I've never heard or used the term kerf marks.

 

Getting to your formula, I'm sure our resident "math guy" @kmealy  could join in here with some commentary.  My first question is whether the speed the log was carried by the blade, or with a bandsaw the speed of the carrier by the log would make any difference?  Or blade speed, or tooth size...

 

**Edit, kerf was underlined when I typed it, but the underline went away once I posted.  Obviously I need a course in the TPW dictionary :)

Edited by Cal

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19 minutes ago, Cal said:

Too bad you couldn't/didn't salvage the whole pile

Yes. I get nauseous recounting my ignorance that summer of 2018. Clear aged 5/4 sugar pine, likely. A few blocks away, '00 or so, I found a table outside a church covered with contact paper. Its top was 5/4" x 22" sugar pine.  

 

These bottoms were 1/2" stock, hand-planed on three sides to fit a slot on the drawer sides and back, tacked on the front. Back before closets, before folks own twelve coats and enough clothes for a family of fifteen, when masonry structural walls interrupted modern flow, nooks would have been filled with whatever method was favored by the carpenters. These were built-in-place to size drawers. I've seen them before but never realized their architectural significance. 

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I've salvaged some old wood and was never sorry I did.  Takes some work and can be hard on blades but I have never been disappointed with it.  I like what you have done with your nice find.

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Good reuse of otherwise landfill.

 

:TwoThumbsUp:

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Thank you! One plank left but no table saw for now (time to hand-rip?). The previous project, a shelf with vertical board beneath for belt / shirt hooks, is in the basement joist bay awaiting the authentic period hooks.  [I've gotten to the point finished items are underfoot]. Can you believe a plumber buddy SCRAPPED the perfect nickel-plated brass hooks removed from a series of c.1925 apartments undergoing renovation?

 

Otherwise down to scraps; it's brittle so this little project will take all week. Then back to heart pine. 

IMG_3397.JPG

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10 hours ago, Cal said:

 

Getting to your formula, I'm sure our resident "math guy" @kmealy  could join in here with some commentary. y :)

 

Easier for me to derive the formula that find it.  See the diagram, chord is 2a, rise is b, unknown radius is r

2022_02070003.JPG.da096e5a4bb0e3149fb23a3244d25ddf.JPG

Using the Pythagorean theorem

a^2 + (r-b)^2 = r^2

simplifying this to solve for unknown r,

a^2 +r^2 - 2rb + b^2 = r^2

a^2 + b^2 = 2rb

(a^2 + b^2) / 2b = r

 

Which, if my mental math is working is the same as your result, but a little simpler because I took the cord length / 2 as my known.

 

If you have a compass and straightedge, you can find the center of the arc, and thus the radius without any arithmetic.

 

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1353131896_TractorFest2019sawmill.JPG.02bc4e1341dfb3c763d57bd11ed5d9c3.JPG

There is this one down in West Liberty, OH...

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Note the size of the saw blade...and..this was the SMALLER of the 2 in the shed..

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28 minutes ago, steven newman said:

Note the size of the saw blade...and..this was the SMALLER of the 2 in the shed..

:JawDrop::JawDrop::JawDrop:

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3 hours ago, kmealy said:

(a^2 + b^2) / 2b = r

Hey! It works!

4916/8 = 615mm = a little more than a 24” radius 

 

 

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image.png.4eefcaca7a6d21c26506fb29714bcccd.png

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Now, that's a conundrum!

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5 minutes ago, Gene Howe said:

Now, that's a conundrum!

 

I always called them comics :D

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Always thought most of these sawmill blades were similar size, but irregardless bigger than I want to get close to. 

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This comic reminds me of a problem.  I took the GRE (Graduate Record Exam), sort of the ACT or SAT for grad school and took the 2 general sections, then the math advanced section.  I got a chuckle out of the two women in front of me in the morning line who said something like "Ok, now the area of a circle is pi R squared, right?"  and I'm thinking, "Well, what am I supposed to do with the verbal half of the general exam, memorize the dictionary?"   Anyway, the general 2 parts were OK.  Then I got to the advanced math part.  To make matters worse, it was the weekend before term finals, so I had a lot of studying to review 4 years of math notes plus my current classes before the exam.  I decided that if I didn't know a question in a section (usually 15-20 questions at a time), I'd skip it and answer the ones I knew, then come back.  There were several sections where I just skipped them all and frustrated, started over to try to solve some of them.   It was the hardest exam I ever had and thought I'd just blew my chances to get into grad school.  One of the questions was like this record, it was a tape spool with a certain diameter, rotating at a rpm certain speed, with a film thickness of so much.  How fast was the film coming off?  I did my best on it and later that evening, it occurred to me that I could figure out the answer, but I had gotten it wrong.  I got my results in a few weeks, and lo and behold, I had gotten a 91 percentile on the math part.  I guess it was really tough for everyone.

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15 minutes ago, Gerald said:

bigger than I want

Nine feet, according to one resource:

 

After 1813 or 1822 saw mills use large circular saws, up to 3 meters (9 ft) in diameter.

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