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> Arc Radius, How to calculate the radius from an arc
blackman
Posted: November 21, 2010 11:17 am
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Hey guys. This has always bothered me, I could never work out how to calculate the radius of an arc with the dimentions.

I never thought to find out until now, as I need it for a project.

I need to work out the radius of a concave bowl, I have its diameter and its depth.

Any help would be appreciated.

Thanks in advance.
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MacFromOK
Posted: November 21, 2010 11:35 am
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Calculator for radius of an arc... beer.gif


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GPG
Posted: November 21, 2010 11:43 am
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As long as the bowl is circular....
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MacFromOK
Posted: November 21, 2010 11:47 am
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QUOTE (GPG @ November 21, 2010 04:43 am)
As long as the bowl is circular....

Even if it isn't, he could take a depth/width measurement where he wants the radius calculated (well below the rim if necessary). Or are you talking about radius of the bowl's rim rather than depthwise? huh.gif


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GPG
Posted: November 22, 2010 01:51 am
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The arc first mentioned. ie not parabolic etc.
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MacFromOK
Posted: November 22, 2010 02:52 am
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Ah, ok. Sorry, I thought perhaps you meant an elongated bowl or trough. doh.gif


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AdamO
Posted: November 25, 2010 02:56 am
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QUOTE (blackman @ November 21, 2010 11:17 am)
I have its diameter

You also have the radius, in that case, unless I am missing something.

-Adam O.
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MacFromOK
Posted: November 25, 2010 03:26 am
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I assume the diameter mentioned is the width of the arc section, measured across the bowl's inside at some depth (and thus the bowl's diameter at that depth, not the desired arc's diameter).


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iamthemik3
Posted: November 25, 2010 06:01 am
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Worked it out by drawing a few triangles inside a circle:
r=radius
w=width of bowl
d=depth of bowl

r=(d^2+(w/2)^2)/2d


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AdamO
Posted: November 26, 2010 03:28 am
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iamthemik3, I got the same result, but that's only good for a spherical bowl. I worked it out for a paraboloid bowl and got:

w = width
d = depth
P = vertical distance between the bottom of the bowl and focus

P = (w^2)/8d

I figured that finding the distance between the vertex and focus of a paraboloid is analogous to finding the radius of a sphere.

-Adam O.
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Georgia
Posted: November 04, 2011 01:19 pm
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QUOTE (blackman @ November 21, 2010 12:17 pm)
Hey guys. This has always bothered me, I could never work out how to calculate the radius of an arc with the dimentions.

I never thought to find out until now, as I need it for a project.

I need to work out the radius of a concave bowl, I have its diameter and its depth.

Any help would be appreciated.

Thanks in advance.

he blackman, i would tell how to calculate radius of an arc. There is a very simple way to calculate it....Calculates the radius of an arc when the width and height of the arc are given. The length of the arc and the angle subtended by the arc (not shown in figure) are also calculated. To draw the arc: 1)Swing arcs (using the calculated radius) below the width using as center the endpoints of the width thus creating the intersection point of the arcs. 2) Set the point of the compass at this intersection point (which now becomes the centerpoint of the arc) and swing an arc thru the endpoints of the width thus creating the arc. Take note that if the angle subtended by the arc (not shown in figure) is greater than 180 degrees then the arc length is greater than the arc length of a semi-circle. In this case, the centerpoint of the arc must be created above the width instead of below and the arc is drawn as before. Check out also the Calculator for Radius of an Arc #2 that calculates radius when the width and length of the arc are given. For a complete analysis of a circular arc please check out The Complete Circular Arc Calculator.

he blackman, i would tell how to calculate radius of an arc. There is a very simple way to calculate it....Calculates the radius of an arc when the width and height of the arc are given. The length of the arc and the angle subtended by the arc (not shown in figure) are also calculated. To draw the arc: 1)Swing arcs (using the calculated radius) below the width using as center the endpoints of the width thus creating the intersection point of the arcs. 2) Set the point of the compass at this intersection point (which now becomes the centerpoint of the arc) and swing an arc thru the endpoints of the width thus creating the arc. Take note that if the angle subtended by the arc (not shown in figure) is greater than 180 degrees then the arc length is greater than the arc length of a semi-circle. In this case, the centerpoint of the arc must be created above the width instead of below and the arc is drawn as before. Check out also the Calculator for Radius of an Arc #2 that calculates radius when the width and length of the arc are given. For a complete analysis of a circular arc please check out The Complete Circular Arc Calculator.
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CWB
Posted: November 04, 2011 11:50 pm
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well , that was certainly redundant . dry.gif


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