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I need some trig help. I need to create a bending form but I need the
diameter (or radius, it doesn't matter) based on the following

The diameter of a circle formed by an arc with a 1/8" apex over a 1 5/16" base length. Yeah, I know some of the terms are wrong, but I'm a long way removed from Mr. Cole's high school trig class.

tia

jc

Joe wrote:

Before I go too far, to be sure...

You mean find a circle whose diameter will yield an 1/8" projection above the chord subtending a length of 1-5/16"?

--

There's those terms I can't remember!

Yes, that's exactly what I was trying to say.

Joe

Don't have AutoCad; so did about the same calculation as you did. In your last formula, it should be "+h^2". Then the result matches AutoCad's. Kerry

The diameter would be 3.570". Thank God for AutoCAD.

todd

Well, the last bit should be r=(x^2 + h^2)/2h. Plug those numbers in and it works out.

todd

Todd It***IS*** a well-known fact that -you- don't make mistakes.

When a 'oopsie!' is committed by someone of your gender, it's a mister-stake.

It's been a while for me too, but I think a diameter of 3 9/16 is close to what you want. It seems small to me, but I did it twice and checked, so like I said it should be close (I got 3.57 inches for the diameter, which is just a hair over 3 9/16.)

The setup is to draw the chord and radii from each endpoint and one from the center of the chord - that gives four right triangles, two big ones with a radius as hypotenuse and two little ones. Solve the small triangle (you know the two sides, 1/8 and 21/32), then figure out how the little triangle is related to the larger one with which it shares a side. I figured out that the central angle of the larger right triangle is just twice the smaller angle in the little triangle. I got r sin 2(arctan ) = 21/32 and solved for r. You can check me on this, but I think it's right.

Drawing that on AutoCAD that comes to a diameter of 3-9/16 rounded to the nearest 1/16th.

#### Site Timeline

- posted on October 8, 2007, 5:37 pm

The diameter of a circle formed by an arc with a 1/8" apex over a 1 5/16" base length. Yeah, I know some of the terms are wrong, but I'm a long way removed from Mr. Cole's high school trig class.

tia

jc

- posted on October 8, 2007, 5:40 pm

Before I go too far, to be sure...

You mean find a circle whose diameter will yield an 1/8" projection above the chord subtending a length of 1-5/16"?

--

- posted on October 8, 2007, 5:48 pm

There's those terms I can't remember!

Yes, that's exactly what I was trying to say.

Joe

- posted on October 8, 2007, 6:04 pm

Joe wrote:

That's easier than a couple of alternatives... :)

No real way for ASCII art for the circle, so I'll try just the algebra from a verbal description. Consider the triangle of the radius perpendicular to the chord and another radius to one end of the chord. That's a right triangle whose hypotenuse is R, one leg is your desired L/2 and the other side is the radius R-1/8.

So, letting x = L/2, r = R and h the projection desired, Pythagorus says

x^2 + (r-h)^2 = r^2

x^2 + r^2 - 2rh + h^2 = r^2

x^2 - 2rh + h^2 = 0

r = (x^2 - h^2)/2h

Substituting in your values I get r = 6.828 --> 6-53/64", approx.

--

That's easier than a couple of alternatives... :)

No real way for ASCII art for the circle, so I'll try just the algebra from a verbal description. Consider the triangle of the radius perpendicular to the chord and another radius to one end of the chord. That's a right triangle whose hypotenuse is R, one leg is your desired L/2 and the other side is the radius R-1/8.

So, letting x = L/2, r = R and h the projection desired, Pythagorus says

x^2 + (r-h)^2 = r^2

x^2 + r^2 - 2rh + h^2 = r^2

x^2 - 2rh + h^2 = 0

r = (x^2 - h^2)/2h

Substituting in your values I get r = 6.828 --> 6-53/64", approx.

--

- posted on October 8, 2007, 6:26 pm

Don't have AutoCad; so did about the same calculation as you did. In your last formula, it should be "+h^2". Then the result matches AutoCad's. Kerry

- posted on October 8, 2007, 6:08 pm

The diameter would be 3.570". Thank God for AutoCAD.

todd

- posted on October 8, 2007, 6:14 pm

todd wrote:

Dang! I'll have to check the calculator, then...

Oh, I forgot to divide the chord length...but I get 3.32", not 3.57"

Wonder where the difference is coming from?

--

Dang! I'll have to check the calculator, then...

Oh, I forgot to divide the chord length...but I get 3.32", not 3.57"

Wonder where the difference is coming from?

--

- posted on October 8, 2007, 6:23 pm

Well, the last bit should be r=(x^2 + h^2)/2h. Plug those numbers in and it works out.

todd

- posted on October 8, 2007, 6:27 pm

todd wrote:

Yeah, I saw I didn't transpose the one sign when I did the copy and paste from one line to the next after I too briefly looked at it earlier...dang bifocals! (Got to blame something, can't be I just made a misteak! :) )

--

Yeah, I saw I didn't transpose the one sign when I did the copy and paste from one line to the next after I too briefly looked at it earlier...dang bifocals! (Got to blame something, can't be I just made a misteak! :) )

--

- posted on October 8, 2007, 6:58 pm

dpb wrote:

Following this thread has reminded my why I was a liberal arts major.

Following this thread has reminded my why I was a liberal arts major.

- posted on October 9, 2007, 2:16 pm

Charlie M. 1958 wrote:

Well, we were allowed to count any math theory course as a liberal arts elective... :)

Of course, that was in the era when a programming language qualified as the foreign language requirement in a PhD program, too...

--

Well, we were allowed to count any math theory course as a liberal arts elective... :)

Of course, that was in the era when a programming language qualified as the foreign language requirement in a PhD program, too...

--

- posted on October 10, 2007, 9:12 am

Todd It

When a 'oopsie!' is committed by someone of your gender, it's a mister-stake.

- posted on October 11, 2007, 2:37 am

wrote:

I'm not sure I'm inferring the intended tone of this post. What I am sure of, however, is that I did not write the part above that you attributed to me. That was written by dpb. Clip with care!

todd

I'm not sure I'm inferring the intended tone of this post. What I am sure of, however, is that I did not write the part above that you attributed to me. That was written by dpb. Clip with care!

todd

- posted on October 8, 2007, 6:08 pm

http://www.ts-aligner.com
Home of the TS-Aligner

- posted on October 8, 2007, 6:28 pm

Thank you everyone for the answer. I have a bending form to make.

be well, work wood

jc

be well, work wood

jc

- posted on October 8, 2007, 6:59 pm

It's been a while for me too, but I think a diameter of 3 9/16 is close to what you want. It seems small to me, but I did it twice and checked, so like I said it should be close (I got 3.57 inches for the diameter, which is just a hair over 3 9/16.)

The setup is to draw the chord and radii from each endpoint and one from the center of the chord - that gives four right triangles, two big ones with a radius as hypotenuse and two little ones. Solve the small triangle (you know the two sides, 1/8 and 21/32), then figure out how the little triangle is related to the larger one with which it shares a side. I figured out that the central angle of the larger right triangle is just twice the smaller angle in the little triangle. I got r sin 2(arctan ) = 21/32 and solved for r. You can check me on this, but I think it's right.

- posted on October 8, 2007, 7:06 pm

Jim Willemin wrote:

...

...

You got the answer (and I didn't until somebody pointed out the algebraic error in sign I made, so take this for what that's worth :) ), but in this particular case you can solve for the radius directly from one of the large (right) triangles as two sides are known in terms of one unknown (the radius) without even having to solve the quadratic as the quadratic terms end up canceling...

--

...

...

You got the answer (and I didn't until somebody pointed out the algebraic error in sign I made, so take this for what that's worth :) ), but in this particular case you can solve for the radius directly from one of the large (right) triangles as two sides are known in terms of one unknown (the radius) without even having to solve the quadratic as the quadratic terms end up canceling...

--

- posted on October 8, 2007, 9:12 pm

Drawing that on AutoCAD that comes to a diameter of 3-9/16 rounded to the nearest 1/16th.

- posted on October 8, 2007, 10:37 pm

"Joe" wrote:

the

5/16" > base length.

Life is short, the problem is very straight forward using a graphical camber layout using the info given.

I'm reminded of the time I took the PE exam oh those many years ago.

I'm a young, pimple faced, smart assed engineering guy with the fastest slide rule on the planet.

Seated at a desk a few rows in front of me was a gray haired man, perhaps 50, with a small drafting board complete with triangles, pencils and scales.

This old man was going to try to compete with the fastest slide rule on the planet using graphical solutions.

Never heard if he passed the exam or not, but he completed the exam before I did.

The older I get, the more respect I gain for that man and his approach. He has has probably long since departed.

Lew

the

5/16" > base length.

Life is short, the problem is very straight forward using a graphical camber layout using the info given.

I'm reminded of the time I took the PE exam oh those many years ago.

I'm a young, pimple faced, smart assed engineering guy with the fastest slide rule on the planet.

Seated at a desk a few rows in front of me was a gray haired man, perhaps 50, with a small drafting board complete with triangles, pencils and scales.

This old man was going to try to compete with the fastest slide rule on the planet using graphical solutions.

Never heard if he passed the exam or not, but he completed the exam before I did.

The older I get, the more respect I gain for that man and his approach. He has has probably long since departed.

Lew

- posted on October 9, 2007, 1:42 pm

Lew Hodgett wrote:

Decartes proved, oh so many years ago, that geometry and algebra were mathematically equivalent - anything doable in one was doable in the other.

Decartes proved, oh so many years ago, that geometry and algebra were mathematically equivalent - anything doable in one was doable in the other.

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