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 Pivskid June 28th, 2013 03:25 AM

Circle segment area

Hi there
Problem:
Of a circle segment is known: Area and radius.
Wanted:
Height from the circle circumphere ot the chord.

I know the formula for the circle segment it is to found everywhere.

But how do I resolve it to return the height ?

NOTE: the angle is NOT known.

 agentredlum June 28th, 2013 04:08 AM

Re: Circle segment area

You can find the angle in radians using

$A \= \ \frac{1}{2}r^2 \theta$

Then use that angle to find the height of the isosceles triangle

Then subtract that from the radius.

:)

 Pivskid June 30th, 2013 12:03 AM

Re: Circle segment area

It is a circle segment not sector.

How do I get the radians out ?

 agentredlum June 30th, 2013 03:00 AM

Re: Circle segment area

Quote:
 Originally Posted by Pivskid It is a circle segment not sector. If I: A/0.5*r^2= (radians-Sin(radians) How do I get the radians out ?
If you know A and you know r then $\ \theta \$ is in radians automatically.

:)

 Pivskid June 30th, 2013 11:35 PM

Re: Circle segment area

But radians from a area of a circle sector not a segment.

The result is that I get a redicously narrow angle.

 agentredlum July 1st, 2013 11:20 AM

Re: Circle segment area

If i now understand you correctly ,

$\frac{2A}{r^2} \= \ \theta \ - \ sin{\theta}$

You have A , you have r so now you want to solve for $\ \theta \$ in radians.

Is that right?

If that's right , you can only get an approximation , there is no way i know of to get an exact solution.

There may be a different approach to get the height that i don't know about , you don't have the length of the chord , do you?

:)

 Pivskid July 1st, 2013 10:31 PM

Re: Circle segment area

It is a "real life" scenario where a horizontal positioned vibrating tube is filled with a product, could be flour, or sugar.
The tube transports the product, such as conveyour belt.

I'm the programmer of the controling device.

I know the dimenion of the tube.
I know how much is poured into the tube.
Due to regulations no sensors alowed in the setup.

I have to provide a "gauge" that tells the height of the product in the tube.

Since I know the amount of of product in the tube, I know the area of the circle segment.
Since I know the dimensions of the tube I know the radius.
Chord is unknown.

I wanted to calculate the height of the product. Present to the operator.
Not at a high accuracy.

For the "curiosity" ...the height is required since experienced has learned us that above and below a certain productheight the product is changed in homogeniousity.
This is to be avoided.

 agentredlum July 1st, 2013 11:39 PM

Re: Circle segment area

1 Attachment(s)
Well since you don't need high accuracy then it's easy to get a result using trial and error. Here is an approach. First calculate

$\frac{2A}{r^2}$

Get a number for that. Then use the graph of $\ y \= \ \theta \ - \ sin{\theta}$

[attachment=0:1j832pdu]MSP2201f207geaebfh4f1800003f19938gg2h3h8c8.GIF[/attachment:1j832pdu]

That number you calculated? Locate it on the vertical axis , then move horizontally accross till you hit the graph , then drop vertically down to the horizontal axis and read the value. That is your $\theta$ and it is in RADIANS.

Confirm your work by substituting that value into the formula to see how accurate it is. Make sure your calculator is in RADIANS mode. Accuracy will depend on how well you have read the graph. If you can get $\theta$ to within 2 to 3 decimal places it may be adequate to use that value to calculate the height to within reason.

Post your calculations so that we may do them as well , in particular, post A and r.

:)

 Pivskid July 2nd, 2013 03:54 AM

Re: Circle segment area

Urgh.. :(

I will need a sharp chisel to get this into a PLC.

 Denis July 2nd, 2013 08:52 AM

Re: Circle segment area

Well, why don't you go here:
http://www.ajdesigner.com/phpcircle/cir ... _theta.php

Easier that typing back and forth here :wink:

Another good place:
http://mathworld.wolfram.com/CircularSegment.html

 Pivskid July 3rd, 2013 04:21 AM

Re: Circle segment area

Well, I have been there before but did not see any answer to my question.

Maybe you can point out where you see the solution in those links, Denis ?

I could expect a integration would to the trick. But Integration is out of the question in the computing devices at hand.

 Denis July 3rd, 2013 08:25 AM

Re: Circle segment area

$\frac{2A}{r^2} \= \ \theta \ - \ sin{\theta}\$

Solving that type cannot be done directly: numeric method required.
A bit like solving x - a/(1 + a)^n = 0 for a

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