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# sine bar setting height

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#### norton8

##### Plastic
Why when figuring the gage block stack to get a given angle on a sine plate, you cannot use the sum of two angles sine numbers to get the correct height? For instance, if you want to get the stack height for 45 degrees, you cant add the stack height for 5 degrees and the stack height for 40 degrees. Their sum will be different than the stack height for 45 degrees. Why?

A graphical explanation. Literally back-of-envelope!

Sine is pretty linear up to about 45 degrees, good enough for mental math. If you use a Sine of .017/inch per degree, you are still within 10% at a 45 angle.

I wouldn't call 10% "pretty linear". At 45 degrees, 10% if 4.5 degrees.

If you are going to use such loose tolerances, why not just use a dime store, protractor scale. In addition to being more accurate for that 45 degrees, they cost less than half a dollar as compared to a sine bar which will cost at least ten no a hundred times as much.

I have \$5 calculators which will give me a sine value as fast as I can punch the buttons. From there getting the stack height is easy.

1. Get the sine value on your calculator.
2. Multiply it by the size of your sine bar.
3. Your calculator is now displaying the size of the stack in the same units as the sine bar's size.
DONE!

If you are working from a printed table of sine values, there are some tricks.
First, look up the sine value (as above with a calculator).
If you have a 10 inch sine bar, move the decimal place to the right one place. That is your stack value.
If you have a 5 inch sine bar, move the decimal place to the right one place and then DIVIDE by 2. That is the stack value for a 5" sine bar.

This explains why 5" is the most popular size for sine bars. The math can be done in your head after finding the sine value. Ten inches is probably the second most popular size and the math is easier, but it is too large for many set-ups. Those old time machinists knew a thing or two.

Sine is pretty linear up to about 45 degrees, good enough for mental math. If you use a Sine of .017/inch per degree, you are still within 10% at a 45 angle.

sin 1* = .0175
sin 45* = .7071

10%? Don't think so. I do use the .0175"/inch for very small angles.

BTW, the sin and tangent are very close for small angles.

@norton8 try sketching  all problems. A picture is worth a thousand words, and will really help with understanding. Once you have a grasp you can back off the sketching a bit.

Trig functions are simply a ratio of the length of side of right trangles. SohCahToa is a great mnemonic tool to help you remember what goes where!

Way back in the dark ages when I was in engineering school, we were told the linear approximation was good up to 10 degrees. Actually the approximation was (in radians) sin a= tan a= a. for small angles. and cos a= 1 but that is less interesting.

Aka the small angle approximation used in physics (mechanics). It makes the differential equation of a pendulums motion much easier to solve ( sin x = x ).

Sine 45/45=.01571, close enough to .017 for mental math.

I think the sine A = tangent A in radians is only about 5% off at 20 degrees, 1% at 10 degrees.

Sine 45/45=.01571, close enough to .017 for mental math.

I think the sine A = tangent A in radians is only about 5% off at 20 degrees, 1% at 10 degrees.
Help me please. I don't understand why knowing sin45/45 is close to sin1 is useful to know.

Because sine and cosine functions are not linear, that's why.
Or to be even more precise:

Help me please. I don't understand why knowing sin45/45 is close to sin1 is useful to know.
Now, not so much. There was a time when we didn't have scientific calculators with us at all times.

Now, not so much. There was a time when we didn't have scientific calculators with us at all times.
we used tables or pencils and paper. As someone as else said if you are going to use an approximation use a protractor or a vernier protractor for a little better accuracy

What year is it now?
Just ask any kid nearby to punch it into his/her cell phone.
Or- tap the microphone icon and ask goggle. 10 seconds max.
Bob

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Just ask any kid nearby to punch it into his/her cell phone.
Bob
OK, I'll take that bet.

I say less than 25% of those "any kids" would pass the test of handing him/her a sine bar, say it's a 5" version, and then ask him/her to set it to 37.25 degree.
I'll even double down by saying on some college campuses you'll get less than 5% to get it right.
All without some Chat GPT bullshit though!

Interesting.
If you ask google "What is the the sine of 37.25 times 5" it solve in radians.
If you ask for the sine of 37.25 degrees times 5 it gives the right answer.
Pretty sure if you ask the kid to put in 37.25, press the sin button and multiply by five most could do it.
Of course way less than the 25% know what a sine bar is, much less how to use it.
Maybe it is understanding how to ask the question.

If I ask you for the height of a 1/2 inch triangle insert with a .032 radius how fast can you answer?
Everybody knows it is 1.5 times the IC - the rad size, right?
Bob

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Pretty sure if you tell the kid to put in 37.25, press the sin button and multiply by five most could do it.

There, I've fixed it for you.
If you don't know what I mean, you certainly have more faith in the current upcoming generation than I, or either of my two millennial offsprings do. ( one of them actually works in the education system )

Do you think that the current upcoming generation is worse than those before?
I've been teaching many people with no knowledge about it how to do machining for a long time. (since the 70s)
I do not see a real difference.

I remember before the days of scientific calculators.
Making a part and I want 30 degrees on it.
Okay, easy, touch off the endmill, move over 5 inches and touch again. Check the rise number against the handy book for a 5 inch sine.
"Dad, something is not right with the markings on the rotary table" .

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OK, I'll take that bet.

I say less than 25% of those "any kids" would pass the test of handing him/her a sine bar, say it's a 5" version, and then ask him/her to set it to 37.25 degree.
I'll even double down by saying on some college campuses you'll get less than 5% to get it right.
All without some Chat GPT bullshit though!
There are a fair number of people in general society as evidenced by some of the stupid questions on this site who would be rooted if the internet wasn't available.

twas written on a cave wall"youth is going to the dogs"
as the blinders tighten.
Gw

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