Monday Math Quiz - circulator saw blade size

February 22, 2021, 01:38 PM

In 2018 I curb-snatched half a dozen boards from a pile in front of an 1880s building. They were bottoms from built-in drawers. It looks like one side was mill-planed, the other leveled by hand plane. A bevel was hand-planed along three sides to fit into a groove in the drawer sides. Only after 320-grit sanding did I find these blade marks (I've made two shelves so far; this one will be the best, and I still have three untouched boards).

What size saw blade would made these markings? Across 140mm there is 4mm "rise" to the arc.

I date the boards 1885 - 1920, leaning towards the earlier number. Thoughts?

February 22, 2021, 01:46 PM

old dino

Gonna take a stab at this ... but figuring about 48.4 inch diameter circular blade.

February 22, 2021, 01:57 PM

StarTraveler

old dino has it. R=24.2", Dia=48.4"

Chord c = 140
Rise b = 4

Radius R = (4 b^2 + c^2)/(8b)
=614.5 mm = 24.2"

February 22, 2021, 02:02 PM

Rey HRH

I think you need three points to determine the radius of the saw.

First, you have to mark 2 points at either end of the arc.

Then you draw a straight line between the two points and bisect the line between the two points to find the midpoint of the cord. Then draw a perpendicular line from the midpoint to where it intersects the arc.

Connect the midpoint at the arc to both endpoints. Now you have two paths:

Path A: without having to calculate: Bisect each line between the arc midpoint and the ends. Draw a line perpendicular from the two midpoints. Measure from the arc to where the two lines intersect and that's the radius of the saw.

Path B: Measure the height of the arc midpoint to the cord. Transfer the drawing to a piece of paper and do the work on the paper.

"It did not really matter what we expected from life, but rather what life expected from us. We needed to stop asking about the meaning of life, and instead to think of ourselves as those who were being questioned by life – daily and hourly. Our answer must consist not in talk and meditation, but in right action and in right conduct. Life ultimately means taking the responsibility to find the right answer to its problems and to fulfill the tasks which it constantly sets for each individual." Viktor Frankl, Man's Search for Meaning, 1946.

February 22, 2021, 02:18 PM

Woodman

Thanks, guys. I figure the largest blade a local mill would have would be 4', but did imagine both bogger and smaller. That 140mm / 4mm is inacurate enough for the blade to be 47" with wear, tear, sharpening. Could be closer to 140mm / 3.85mm

February 22, 2021, 02:49 PM

Jim Shugart

Fuck.

I could have done that radius of curvature calculation but I was off getting my 2nd China virus shot.

Anyway this math shit is RACIST. Haven't y'all heard?

February 22, 2021, 03:04 PM

Woodman

OK, but there is still Part-B. When would 48"-bladed mills turning out S3S pine for build-in-place drawers have gone the way of the Edsel? When multiple band saws were used to cut board?

Is there anything to suggest blade was water-powered? This pine would have been cut and milled within 50 miles of Philadelphia. Post '73 Depression (1873).

quote:
Originally posted by StarTraveler:
old dino has it. R=24.2", Dia=48.4"

Chord c = 140
Rise b = 4

Radius R = (4 b^2 + c^2)/(8b)
=614.5 mm = 24.2"

ST, can you give us the text translation of the equation? I wanna look smart in front of my 16 year old nephew

February 22, 2021, 03:51 PM

StarTraveler

Steam-powered sawmills were in operation in some areas by the 1830s and were quite common by the 1880s. I found an article by Popular Mechanics that says 77 steam-powered ones were operational in Oregon and Washington by 1880. Unless water-power was readily available, I'd suspect it was steam.

https://www.popularmechanics.c...red-sawmill/?slide=1

Still, many people used the cheapest source of power available so it's possible that it could have been water-powered. My grandfather and great-uncle ran a small gasoline-powered sawmill out in the country in the 1930s using (I believe) a Farmall F30 tractor. I think it was with a flywheel band-belt, but Grandpa, who told me about it, died in 1975, so I may not remember that correctly.

Regarding the forumla, it's from properties of circle. I could try to derive it but I don't want to bore anyone to death. In English,

The Radius equals four times the Rise squared plus the Chord squared all divided by eight times the Rise.

Good luck with your nephew!

February 22, 2021, 04:08 PM

Woodman

quote:
Originally posted by StarTraveler:
The Radius equals four times the Rise squared plus the Chord squared all divided by eight times the Rise.

Sounds good to me! Thanks, and thanks for the saw history.

Here's what they looked like in August 2018 ... Damn, I should have taken the sides too!

February 22, 2021, 11:32 PM

Watergoat

I just bought some rock maple from a local wood supplier, and it was sawn with a blade at least that big. I was surprised, would have thought even the very rural sawmills up in the mountains had band mills by now.
When my late FIL retired in the 70's. he bought an ancient 0 Frick to have a sawmill as a hobby. Powered by an engine from an old RR track tamper. Started on gas, ran on kerosene. His youngest son did something similar, but bought a new band mill.

February 23, 2021, 04:33 AM

sns3guppy

Curb-snatched sounds a lot like "stole."

February 23, 2021, 05:29 AM

Woodman

quote:
Originally posted by sns3guppy:
Curb-snatched sounds a lot like "stole."

Yep, it sure does. And it was. The number of artsy ex-students, contractors, DIY'ers, etc, driving past that point is huge. The West Philly house restorers love this stuff. It was white-glove trash-picking. Like curb-picking. Except I was first when the college maintenance folks dumped the refuse out on the curb.

I few years back their shop had to trim the rails on several 1 ¾" solid oak doors. Guess who spied the cut-offs in a Dumpster from 40 yards?

It was during rush hour but I still stopped a line of traffic and maneuvered into a No Parking Zone.

Another time driving by a different college there was a load of 5/4" x 12" clear sugarpine planks in a Dumpster. Some of them 10'-12' long. A few had cut-outs in them but there was plenty of good wood. I used them to panel a customer's tiny 1st floor bathroom ceiling (built in the alley between two houses). After insulating with super-dense yellow panel insulation pulled from another Dumpster by City Hall. The hits just keep on coming!

February 23, 2021, 06:14 AM

smlsig

quote:
Originally posted by Woodman:
quote:
Originally posted by sns3guppy:
Curb-snatched sounds a lot like "stole."
Yep, it sure does. And it was. The number of artsy ex-students, contractors, DIY'ers, etc, driving past that point is huge. The West Philly house restorers love this stuff. It was white-glove trash-picking. Like curb-picking. Except I was first when the college maintenance folks dumped the refuse out on the curb.

I few years back their shop had to trim the rails on several 1 ¾" solid oak doors. Guess who spied the cut-offs in a Dumpster from 40 yards? It was during rush hour but I still stopped a line of traffic and maneuvered into a No Parking Zone.

Another time driving by a different college there was a load of 5/4" x 12" clear sugarpine planks in a Dumpster. Some of them 10'-12' long. A few had cut-outs in them but there was plenty of good wood. I used them to panel a customer's tiny 1st floor bathroom ceiling (built in the alley between two houses). After insulating with super-dense yellow panel insulation pulled from another Dumpster by City Hall. The hits just keep on coming!

I like your style!

February 23, 2021, 08:01 AM

cne32507

In the 1950's, the sawmill in Ellisville, MS was steam-powered. It just made sense: they burned the scrap. Temporary sawmills, known as peckerwood sawmills, were located near forests and were gas-powered. My dad said Buick engines were preferred. I remember watching the steam engine and the rapid travel of the carriage. The stream whistle at noon.

February 23, 2021, 08:58 AM

lyman

quote:
Originally posted by Woodman:
quote:
Originally posted by sns3guppy:
Curb-snatched sounds a lot like "stole."
Yep, it sure does. And it was. The number of artsy ex-students, contractors, DIY'ers, etc, driving past that point is huge. The West Philly house restorers love this stuff. It was white-glove trash-picking. Like curb-picking. Except I was first when the college maintenance folks dumped the refuse out on the curb.

I few years back their shop had to trim the rails on several 1 ¾" solid oak doors. Guess who spied the cut-offs in a Dumpster from 40 yards? It was during rush hour but I still stopped a line of traffic and maneuvered into a No Parking Zone.

Another time driving by a different college there was a load of 5/4" x 12" clear sugarpine planks in a Dumpster. Some of them 10'-12' long. A few had cut-outs in them but there was plenty of good wood. I used them to panel a customer's tiny 1st floor bathroom ceiling (built in the alley between two houses). After insulating with super-dense yellow panel insulation pulled from another Dumpster by City Hall. The hits just keep on coming!

a friend worked for a while for a guy that owned a handful of rentals in downtown RVA,

near the VCU VUU Area north of Broad St,

friend worked in a warehouse the guy used to store stuff for the rentals, they basically had to redo the rentals every spring after the students moved out (some trashed the place)

he would pick up furniture, parts, etc out of the trash on the curb or alley and repurpose them as needed,

some were nice enough to sell for decent cash, most were used to fix something else