Accurate angle measurement

[mklotz]

In a Tool Talk thread, I talked about the need to measure the angle of a planer gauge accurately...

http://www.homemadetools.net/forum/h...7175#post85187

While this has more to do with how to use the tools you have rather than the construction of a new tool, like my taper measurement method, I feel it's a tool in the conceptual sense of the word, hence its presence in the tool forum.

The basic idea of this method is to use a sine bar to "cancel out" the angle to be measured and, having done this, the stack height under the sinebar becomes an indirect, accurate measure of the angle in question.

As the photo shows, the object is placed on a sine bar in such a way that raising the end of the sine bar can make one side of the object horizontal.

How do we determine when it's horizontal? A DTI is swept across the top of the object; when it shows no change in value from one end of the object to the other the top of the object is parallel to the surface plate on which the work is done. A surface plate is essential; for this scheme to be accurate the surface must be flat and featureless.

The DTI is supported on one of my height gauges. The height gauge plays no part in the measurement; it's simply a convenient way to adjustably support the DTI and slide it over the surface plate.

Purists may note that I used an adjustable parallel rather than Jo blocks to create the stack for the sine bar. It's easier and the effect on accuracy is negligible.

So, what were the results?

After the DTI showed no slope of the gauge, the adjustable parallel miked to be 1.136" high. With the 2.5" sine bar I was using this translates into an angle of...

ang = arcsin (1.136/2.5) = 27.03 deg

That's only 0.01 deg = 0.6 arcmin difference from the value I obtained in the referenced thread using a no sinebar method of measurement.

You'll only rarely need to measure angles with this degree of accuracy but, should you need to, now you know how to do it.

[Frank S]

I was wondering it the angle could possibly have originated based off half of the Old British 55° Whitworth the 27.03° being quite close to 27.5°

[mklotz]

I was wondering it the angle could possibly have originated based off half of the Old British 55° Whitworth the 27.03° being quite close to 27.5°

I doubt that an American manufacturer would be making anything to Whitworth standard.

If you read post #12 in my other thread on this subject...

http://www.homemadetools.net/forum/h...7175#post85187

you'll learn that there appears to be no consistency whatever among manufacturers regarding the angle they use. Thus my notion that the angle serves some measurement purpose seems to be just plain wrong.

I do find it interesting though that, by picking some useful angle, they could have, without cost to them, created a "feature" of their tool to trumpet over the competition in their advertising even if that feature was of dubious utility.

[Toolmaker51]

In light of variety, it probably was established by means of henway.

[Frank S]

Yep just how much does a henway anywayj

[DIYer]

Thanks mklotz! We've added your Angle Measurement Method to our Measuring and Marking category,
as well as to your builder page: mklotz's Homemade Tools. Your receipt:

Angle Measurement Method by mklotz

tags: angle, measurement

[mklotz]

As long as the picture showing the setup is there, I should mention that it is exactly the same setup used to calibrate a sinebar.

Normally, the roll-to-roll distance of a sinebar is some simple value. 2.5, 5 and 10 inches are common values; the one shown in the picture is 2.5. But the roll distance can be any value SO LONG AS WE KNOW WHAT IT IS. If you make your own sinebar or inherit one of unknown accuracy, you'll want to measure the roll distance so it can be used when setting the sinebar to a desired angle.

One tool is needed - an accurate angle plate. They typically come in the form of 30-60-90 or 45-45-90 triangles. Every serious metalworking hobbyist should have one, preferably both.

If we replace the part shown in the picture with the known-to-be-accurate 30-60-90 triangle and adjust the stack height so the hypotenuse of the plate is parallel to the surface plate, we will know that the angle of the sinebar is 30 degrees to the same accuracy as the triangle.

The sinebar equation is:

sin(A) = S / L

A = angle
S = stack height
L = roll-to-roll distance

Solving for L then yields

L = S / sin(30) = S / (1/2) = 2 * S

Once the L value is calculated, it's worth writing it on the bottom of the sinebar with a Sharpie.

Speaking of Sharpies, they now make paint pens...

https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1

which make a more permanent mark than the ordinary Sharpie marker. Since they don't make an ordinary one with white ink, the white paint pen is a boon. It's especially useful when marking dark metals.

[PJs]

Normally, the roll-to-roll distance of a sinebar is some simple value. 2.5, 5 and 10 inches are common values; the one shown in the picture is 2.5. But the roll distance can be any value SO LONG AS WE KNOW WHAT IT IS. If you make your own sinebar or inherit one of unknown accuracy, you'll want to measure the roll distance so it can be used when setting the sinebar to a desired angle.

One tool is needed - an accurate angle plate. They typically come in the form of 30-60-90 or 45-45-90 triangles. Every serious metalworking hobbyist should have one, preferably both.

If we replace the part shown in the picture with the known-to-be-accurate 30-60-90 triangle and adjust the stack height so the hypotenuse of the plate is parallel to the surface plate, we will know that the angle of the sinebar is 30 degrees to the same accuracy as the triangle.

The sinebar equation is:

sin(A) = S / L

A = angle
S = stack height
L = roll-to-roll distance

Solving for L then yields

L = S / sin(30) = S / (1/2) = 2 * S

Once the L value is calculated, it's worth writing it on the bottom of the sinebar with a Sharpie.

Speaking of Sharpies, they now make paint pens...

https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1

which make a more permanent mark than the ordinary Sharpie marker. Since they don't make an ordinary one with white ink, the white paint pen is a boon. It's especially useful when marking dark metals.

Thanks Marv for this adjunct to your above and finding out exactly what you have or build. To me it's an excellent thing to do because of the difficulty in making these exact lengths. Even the big names in metrology spend considerable time on this aspect, which is part of the high cost of theirs. Being somewhat leery of imports after my experience, these tests and some math will tell you what you have as best as your equipment will let you.

Also thanks for the link to the Oil based pens from Sharpie...makes sense they would jump on the band wagon. Have you tried them? Added them to my want list. Agreed about a choice of white but find Yellow contrasts on a lot of backgrounds too...the key is contrast I believe.

[mklotz]

Also thanks for the link to the Oil based pens from Sharpie...makes sense they would jump on the band wagon. Have you tried them? Added them to my want list. Agreed about a choice of white but find Yellow contrasts on a lot of backgrounds too...the key is contrast I believe.

Yes, I bought the set of Sharpies pictured in the URL.

I have a bunch of those cheapy free screwdrivers from HF. I throw them in all my toolboxes and bags. Don't care if I wreck them through misuse and sometimes even drive screws with them. The problem is the slot and Phillips have identical handles. I don't like wasting time sorting through to find the style I want. I took the white Sharpie and drew straight lines on the slot drivers and crosses on the Phillips handles. The marks are on each side and on the top so, no matter how they're lying (or even stuck in tool bag side pockets) at least one of the marks is visible. Saves me a lot of frustration.

I've always been curious why Sharpie never made a conventional white marker. Before the paint pens I used the metallics, gold, silver and bronze, on dark materials. That works but white is more visible.

Yes, it's all about contrast. Yellow is arguably better than white. Millions of years of evolution have made the sensitivity of our retinas peak exactly at the peak output frequency of the sun and that's in the yellow part of the spectrum.

[Ed ke6bnl]

Yes, I bought the set of Sharpies pictured in the URL.

I have a bunch of those cheapy free screwdrivers from HF. I throw them in all my toolboxes and bags. Don't care if I wreck them through misuse and sometimes even drive screws with them. The problem is the slot and Phillips have identical handles. I don't like wasting time sorting through to find the style I want. I took the white Sharpie and drew straight lines on the slot drivers and crosses on the Phillips handles. The marks are on each side and on the top so, no matter how they're lying (or even stuck in tool bag side pockets) at least one of the marks is visible. Saves me a lot of frustration.

I've always been curious why Sharpie never made a conventional white marker. Before the paint pens I used the metallics, gold, silver and bronze, on dark materials. That works but white is more visible.

Yes, it's all about contrast. Yellow is arguably better than white. Millions of years of evolution have made the sensitivity of our retinas peak exactly at the peak output frequency of the sun and that's in the yellow part of the spectrum.

I also have a lot of HF screw driver and use a hack saw to put an X or - on the top for the same reason, and I am going to start heating the shaft to remove the shaft from the plastic and use the handles for my files without the handle.
PS good write up and do like the idea of the parallels for the height of the sine bar.