Mathematical angles?

[Justin Cavender]

I need to make a three degree shim for a neck pocket on a guitar and I don't have a protractor How can I go about figuring this out mathematically?I know it is rise over run but I dont know exactly how much

[Jamie Buxton]

For a run of 1, the rise is .0524.

[Jim Koepke]

Sounds like you need to find some trig tables and do a little consultation with our Native American woodworker SOH CAH TOA.

For 3° that is:

sin
.0523

cos
.9986

tan
.0524

jim

[Sam Takeuchi]

Mathematically impaired me's short cut (http://www.csgnetwork.com/righttricalc.html)

You just have to supply two of three and calculate! Angle A is 3 degrees, and then the length of your shim. That's all. You then make a shim of appropriate height, taper it and that's it.

[Phillip Pattee]

Justin,

I don’t know how accurate you need your angle to be so this might not work. For small angles, there is virtually no difference between the sine and the tangent. What you need is the tangent to calculate a rise over run. In the navy we used an approximation to calculate sine for small angles of dividing the angle by 60. This works pretty well up to about 30 degrees. In your case 3/60, so there you are for a run of 60 a rise of 3 is an approximation for the tangent of 3 degrees. So try a rise of 1 inch over 20 inches.

[Justin Cavender]

Thanks everyone it doesnt have to be exact there is room for adjustment at the bridge but I have it figured as 3/16 over 3.5 run I got the shim cut about to glue it in .

[Wilbur Pan]

Just out of curiosity, why not just go get a protractor? They sell them at Staples for only about $2.

[Justin Cavender]

Wilbur I live in the boonies.

[Wilbur Pan]

Just out of curiosity, I took a look at Google maps. There's a Staples in Crosslanes, WV, which is about 20 minutes from Saint Albans.

But any place that sells school or office supplies should have a protractor, too -- Walmart, Target, K-mart, your average drug store, etc. Overall, I've found these places really good for getting a lot of measuring and marking supplies: regular and mechanical pencils, rulers (mainly for straightedge use), compasses, protractors, French curves, drafting supplies, etc. I got a basic set of colored pencils from the local Walgreen's that I've found really useful for color coding plans and workpieces. You'd be surprised what you'll find in the school supply section that is useful in a woodworking environment.

[Justin Cavender]

How acurate is a dollar protractor? I have one of those but refuse to use it I was talking about the metal woodworking kind I don't have. If you are telling me they are accurate enough cool I will use it. because all that math hurts my head.

[Brian Kent]

You can try it out, Justin. Draw a triangle using the 60° mark at each corner. Then measure the sides and see if they are all he same length. If they are, then the protractor is probably accurate.

Brian

[Wilbur Pan]

The better office supply stores will carry drafting supplies for architects and other folks that need to make those types of technical drawings. The ones by me have a Staedtler section. Their rulers and protractors are very accurate.

But I've found that the average schoolkid's protractor is accurate enough for woodworking tasks. It's at least as accurate as this protractor (http://www.leevalley.com/wood/page.aspx?c=2&p=32581&cat=1,43513,51657) that all the woodworking stores sell. I have that protractor as well. In your case of making a shim for the neck pocket of a guitar, I'm sure you'll be fine tuning the fit by hand anyway, so all you need to do is get reasonably close. I know that every time I needed to make a piece with some prescribed angle, I always wound up doing some sort of fine tuning.

Brian's calibration method is a very good one, by the way.

And if you still want to get a metal protractor (http://www.leevalley.com/wood/page.aspx?c=2&p=32582&cat=1,43513,51657) that woodworkers use, Lee Valley has a free shipping offer going on right now. ;)

[Malcolm Tibbetts]

There’s a simple way of figuring this without measuring any angles. If your shim were thought of as a segment in a 360-degree ring, then 3-degrees would equal 120th of the circumference (360/3). The length of the shim, from zero to whatever, can be thought of as the radius of a segmented ring (or disc). So if your shim length needs to be 3 ½” long, then the diameter is 7” (2*R). 7” times pi (3.1416) equals 22” (the circumference). 22” divided by 120 (# of segments) equals .183333 or 3/16” as you’ve determined. There’s a lot that can be calculated by just having a clear understanding of the relationship between diameter, circumference, and pi.

[Justin Cavender]

You got to be crazy not to buy something from lee valley right now.

[David Keller NC]

Justin - While I think most shops should have a protractor and bevel gauge as standard equipment, you're correct to make this shim by measuring and cutting rise over run. While something like an Incra Protractor is very accurate, it's still quite difficult to get a very small acute angle from such a gauge - the simple reason is that the angle is very small, the protractor's circumference is also relatively small and the width of a pencil line comprises a substantial fraction of what you're trying to measure.

That's why I usually do what you did to make a precise shim with a small acute angle.

[John Keeton]

There’s a simple way of figuring this without measuring any angles. .....There’s a lot that can be calculated by just having a clear understanding of the relationship between diameter, circumference, and pi. And, that is why our present day teaching methods for math are inadequate!! Malcolm, I don't know your age, but it sounds like you were educated a few decades back when we really were required to think through these problems. Sadly, today that is not the case.

Don't want to divert this thread, but it has been an interesting commentary. Most mathematical problems are overcomplicated by a failure to understand the basic fundamentals.

[Bob Strawn]

A 19 to 1 slope is about 3.01278750418334 degrees. So if you take a bit of graph paper, draw a line with a straight edge that goes up one square and over 19, you will have a template for the angle that will do pretty well. Especially considering that most wood will swell and change angle way more than the margin of error, depending on humidity.

Bob

[Jim Koepke]

For a lot of things like this, just making a piece from trial and error often works better than measuring and layout.

Another old trick I didn't think about is a clock face is good for estimating angles. Each minute mark is 6°. I have used this for a "poor man's" micrometer using a 4-40 screw and nut. Each full revolution is 0.025". Figuring the gap for partial revolutions is simple math.

In my old job, where setting gaps by adjusting threaded fasteners was common, this was handy to know. 32 threads per inch equals 0.03125" per revolution. 5 minutes of turn is a little less than 0.003".

Having the tools to lay things out accurately is fine, but often seat of the pants reasoning is just as good.

jim

[Billy Chambless]

Having the tools to lay things out accurately is fine, but often seat of the pants reasoning is just as good.

jim

And sometimes, even better. It's easy to forget that measurement is a means to an end.

[Jim Koepke]

I need to make a three degree shim for a neck pocket on a guitar...

What ever you do, watch this before you put your guitar through checked baggage:

http://www.msnbc.msn.com/id/31836977/ns/travel-news/?GT1=43001

jim

[Richard Magbanua]

Google protractor in google images. Find a decent image, print it out and use that. That's assuming you have a printer.

[Jim Foster]

Rise: .01746" per inch on one degree angle.


I need to make a three degree shim for a neck pocket on a guitar and I don't have a protractor How can I go about figuring this out mathematically?I know it is rise over run but I dont know exactly how much

[Johnny Kleso]

Just remember this......

One Degree is .017 high on a 1" long popcicle stick..

If you need three degrees, times it by three..
If you need 1* at 3" long also times it by three..

If you need 3* at 4" long times by 3 and then 4 ...
.
IE: 3* angle x 4" long

3x.017=.051 is 3 degree height (sine)
4x.051=.204 is the height of 3 degrees shim at 3" long popcicle stick

Also 1/64=.015 might be close enough for what your doing......