# What's the best device for measuring angles?

• Dorea
In summary, the instructor is looking for a device or method to measure angles with high accuracy. They are considering a Machinist's sine bar, a Vernier Caliper, a Micrometer, and a Spherometer. They are also considering a Theodolite, but are worried about the cost. They are also considering a Machinist's sine bar, a Vernier Caliper, a Micrometer, and a Spherometer. They are also considering a Theodolite, but are worried about the cost. They are also considering a Sextant, but are worried about the accuracy.

#### Dorea

<< Moderator Note -- Dorea is an instructor asking about their physics lab >>

The first experiment in our fundamental physics lab is "Measuring & Measurement errors". Currently we have four devices:
- rule (0.5 mm)
- Vernier Caliper (0.02 mm)
- Micrometer (0.01 mm)
- Spherometer
We're seeking for a method/device to find angles with high accuracy (=>for example: for example: 40 degree 25' 36"). There are some complicated optical devices/methods as in theodolites, but we want it to be economical and freestanding: Something with an obvious physics/mathematics basic for training aims.

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Where will the angles be? ( Are you going to draw the angles on a piece of paper? )

Dorea said:
economical and freestanding: Something with an obvious physics/mathematics basic for training aims.
Machinist's sine bar will get you into minutes of angle, and isn't too horribly expensive. Throw in a surface plate, and the cost goes up, but it can't walk off that easily.

The method is trigonometry.

(Mentor note: we are currently discussing where this thread should go, it might get moved soon)

Angles of what? Do the measurements have to be absolute, or is a relative measurement (e. g. "we started at 40°, now we are at 25' 36'' more") in a smaller range sufficient?

Reflections of laser beams are nice methods to convert small angles to large displacements.

Stephen Tashi said:
Where will the angles be? ( Are you going to draw the angles on a piece of paper? )
I'd like to know that, too. Pencil lines on paper are way too fat for that sort of accuracy. Would you not need a good table to work on, with a long throw. Are we talking Astronomy here?

Stephen Tashi said:
Where will the angles be? ( Are you going to draw the angles on a piece of paper? )
On real objects!
For example: A triangle shaped wood/iron

Bystander said:
Machinist's sine bar will get you into minutes of angle, and isn't too horribly expensive. Throw in a surface plate, and the cost goes up, but it can't walk off that easily.
This seems great. But it needs a set of http://www.insize.com/products/tools/pdf/plate-l/4150.pdf [Broken] which is expensive! However I'm working on brands to find a low price gauge block. thank you.
Do you know what's the application of holes on the body of sine bar?!

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Dorea said:
Do you know what's the application of holes on the body of sine bar?!
Intuitive response: weight reduction, and that's about as stupid as I can get. Real purpose(s) for clamping in assorted set-ups on mill tables.

The problem is you have not specified an accuracy tolerance.

There are many tools to measure angles, but I use something called an inclinometer for measuring real objects. You can get accurate ones and less accurate ones depending on your budget.

http://www.electro-medical.com/product_images/large/baseline-digital-inclinometer-0600190.jpg [Broken]

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If you have two or three decent rules (long straight edges) and a square can you set them up in contact with the object to form a large right angled triangle and then apply trig. Perhaps experiment with shims to calculate the likely error/accuracy.

The sextant is the time honored device for measuring angles without touching the objects. Contrary to popular belief, they can be easily used to measure non-heavenly angles.

It could be a fun and instructive project to build a sextant adapted for classroom use. Everybody can intuitively see how they workm and construction needs only everyday materials. Any divide that uses mirrors to view and align split images can claim to be a form of sextant.

You could get started by using an ordinary mariner's sextsnt to measure apparent angles to things such as the corners of the classroom.

Dorea said:
On real objects!
For example: A triangle shaped wood/iron

For precision work, "Real objects" is too general a category to be useful. Different real objects require different set-ups.

Simple lab experiments concerning precision in measurement assume the thing being measured exists. Most real objects around the house (or lab) do not have angles formed by precisely straight surfaces. For example, in measuring "the" angle at the corner of a table top, the first problem is to define what we mean by "the" angle since the edges of tabletop are not precise lines. If you press different length straightedges against the sides of the table top, they may lie along lightly different tangent lines.

I you create a real piece triangular shaped piece of wood or iron that has precise angles at the corners, the corners will be sharp enough to stick people and in ordinary handling they will get worn off. You can set the task as measuring the angle formed where lines parallel to the surfaces or edges of such objects meet. A taught piece of string can be used to approximate a line (as is often done with "chalk lines" in building construction). If you can run two strings along the edges of something you can extend the lines of the edges a considerable distance and use trigonometry on measurements of length on the strings to deduce angles.

The Cavendish experiment to measure gravitational attraction is an example of extending the lines of the angle to be measured. Perhaps that technique can be applied to some of your real objects.