I Don't Understand Sweep Numbers

[Whit AndersonIL]

I'm not an experienced carver. I've got a question about how the sweep of gouges are related. I'm using Pfeil gouges. I thought that I understood that all #9 sweep gouges were different size portions of the same diameter circle.

I thought that if I did a stop cut straight down with say a #9/10 gouge that I could then fit the cutting edge of a #9/6 gouge into that arc.

I now see that is not correct. Below I have a section of a chart showing the sweep of Pfeil #9 gouges. I have superimposed another version of that same section of the chart where I have changed the colors so that I can distinguish the two charts. I offset the chart so that the #9/50 and the #9/35 line up at the bottom. I previously thought that they would line up perfectly with each other, just that the #9/35 would be a shorter segment than the #9/50.

http://www.whitanderson.com/wood/carving/sweep/PfeilChartNumberNine.jpg

What is the relationship of the different size gouges within a family of sweeps (say the #9 sweep gouges)?

Thanks.

--Whit

[Mike Henderson]

As far as I know, there is no relationship. Each manufacturer makes his own. So when you need a certain curve, you have to match the gouge to the curve (or circle).

Also, one company's #9/20 (for example) will not have the same sweep as another company's #9/20. I suppose that's why carvers have so many gouges - to make sure they can match any curve.

Mike

[Whit AndersonIL]

As far as I know, there is no relationship. Each manufacturer makes his own. So when you need a certain curve, you have to match the gouge to the curve (or circle).



But within the gouges of one manufacturer, Pfeil in this case, what is the relationship between the gouges that have the same sweep number? What is it that makes one gouge a #8 sweep and another a #9 sweep? I see that a #8 is flatter than a #9, but what similarity is there between a 9/2, 9/4, 9/8, 9/12, etc. ?

--Whit

[Derek Cox]

G'Day Whit,
My understanding is that the number of the gouge indicates the fraction of a total circle that the edge of the gouge forms. For example, in most systems, the No 9 is exactly half a circle - you can test this by putting a stop cut in some wood and then swinging the edge of the gouge around and you will need only one more stop cut to inscribe a full circle. As you get a larger or smaller No 9 gouge, the radius of the half circle will change. Lower number gouges, a number 3 for example, are correspondingly smaller segments of a full circle - you need an increasing number of stop cuts to inscribe a full circle, maybe something like 8-10 for a No 3. Because the number nine is a half circle, the size of the gouge (i.e. 20mm for a Pfeil No 9/20 gouge) will equate to the diameter of the circle. Of course it doesn't work out so nicely for gouges that are smaller fractions of a circle.

Hope this helps and isn't confusing.

Derek

[Mel Fulks]

I read (don't remember where) that the Addis company was the first to use a number system and it was widely copied.

[mike holden]

First, using the same sweep number and increasing the width will allow you to create a spiral, not a circle.

This chart may help.

289082

Note that one can obtain the radius by multiplying the width by the multiplier (which is the radius for a one inch wide gouge of a given sweep)

So there is a system, but it is not very important.

Even though some gouges may have the same radius, the differing width keeps them from being interchangeable.

Also, the chart is only one manufacturers list of what they attempt to make. There is so much variation in manufacturing that even gouges made in the same batch, by the same operator, will vary slightly.

Carving is part art, and part "carve by number" and so the variation means little.

Hope this helps some.
Mike

[Whit AndersonIL]

Thanks to all the people who posted responses. I'm still struggling to understand this.

I think that what Derek and Mike posted are different ways of saying the same thing. In either case, it doesn't seem to apply to my Pfeil gouges. I made a high resolution scan of a single imprint from a few of my gouges. The relationship within a family of sweeps does not seem to remain constant to either the diameter or the radius.

I think if Derek's supposition applied to my Pfeil gouges, the 3/20 and the 3/12 gouge imprints would both fill the triangle from left to right.


http://www.whitanderson.com/wood/carving/sweep/sweep3circlesb.jpg
If I understand correctly, if Mike's chart applied to my gouges (but with my numbers), I should be able to calculate the radius of the 3/12 gouge from that of the 3/20 gouge as follows:

12 * 2.14 = 25.68

Maybe I have misunderstood the math.

I also tried this with an 8/20 and and 8/7 gouge without finding the relationships I hoped for. There is some room for error in my measurements, but I think there is more deviation than can be accounted for by errors in measurement. Maybe there is that much error. I don't know.

My original idea had been to draw patterns on the computer, fudging to make curves that matched the gouges I have. Or, if fudging wasn't feasible, to know what gouge I needed to acquire.


--Whit

[Mike Henderson]

This is a very interesting thread. I just always assumed the sweeps were based on history and did not have any pattern. Thanks for bringing this up and pursuing it.

Mike

[Whit AndersonIL]

I just always assumed the sweeps were based on history and did not have any pattern.

Mike

You may be right. I don't see a pattern yet. I just wrote to Pfeil, asking them if there is a pattern to sweeps. I hope that they answer me.

--Whit

[mike holden]

"If I understand correctly, if Mike's chart applied to my gouges (but with my numbers), I should be able to calculate the radius of the 3/12 gouge from that of the 3/20 gouge as follows:

12 * 2.14 = 25.68

Maybe I have misunderstood the math."

The chart requires one to start from the ONE INCH width radius for a multiplier. That multiplier is the value for that particular sweep. Multiply times the width of the gouge to get the radius of the gouge in that sweep and width.

Pfeil tools are in metric, and the chart is not from them, so for metric tools I do not know what is the "multiplier width" i.e. the width that corresponds to "one inch". And NO you cannot assume that the 25.6mm width is the multiplier width, the multiplier width is an arbitrary selection that is used to create the radiuses from. A manufacturer can just as easily choose 10mm or 32mm as their multiplier width.

Also, remember that gouge widths are chord lengths not arc lengths.

It is an interesting topic, but perhaps akin to asking how may angels can dance on the head of a pin. Interesting, but not useful.

Also, variation in production makes any intended radius a target, not a certainty.

Mike

[Whit AndersonIL]

The chart requires one to start from the ONE INCH width radius for a multiplier. That multiplier is the value for that particular sweep. Multiply times the width of the gouge to get the radius of the gouge in that sweep and width.

Pfeil tools are in metric, and the chart is not from them, so for metric tools I do not know what is the "multiplier width" i.e. the width that corresponds to "one inch". And NO you cannot assume that the 25.6mm width is the multiplier width, the multiplier width is an arbitrary selection that is used to create the radiuses from.

Also, variation in production makes any intended radius a target, not a certainty.

Mike

If I am following the math of the chart, then for a given sweep you take the width of a gouge x the multiplier for that sweep and you get the radius of that gouge:

width * multiplier = radius

If that is true, then isn't the following also true:

radius / width = multiplier

for the first example from the chart that would be

15/32 divided by 1/8 = 3 3/4" (which agrees with the chart)

For my Pfeil gouges, I took the radius that I measured from my scan divided by the width of the gouge (units not a factor as long as they are all the same units) to get the multiplier for that sweep.

Starting with a 3/20 gouge:

42.8 divided by 20 = 2.14

With a multiplier of 2.14 for my #3 gouges, I then calculated the radius of a 3/12 gouge:

(width * multiplier = radius)
12 * 2.14 = 25.68

But when I measured the radius of my 3/12 gouge, instead of a radius of 25.68 mm I get a radius of 31.8 mm.

My point is that the math of the chart doesn't apply to the Pfeil gouges (or there is so much error in my measurements and/or Pfeil's manufacturing to make the whole exercise useless).


how may angels can dance on the head of a pin

This is too deep for me. First we would need to know what brand of pin...

Just kidding.

--Whit

[mike holden]

Yep, did say that the chart was ONE manufacturer's listing.

Re: pins - have you read any Terry Pratchett? Specifically "Going Postal" ? (grin)

Mike