Math Is Fun Forum

DocBoom

Member

Registered: 2008-02-25

Posts: 3

need help laying out an arc

I am working in construction and laying out a radius wall for a hospital that we are building.  I have to provide several points along this radius for the formwork to be built.  I know the raduis of the wall (108m), I know the distance between columns [(represented by 'b' in the image provided)9.114m].  Now what I want to do is create a value for 'a' and find 'c' from that. 

I'm hoping I have explained concisely enough

I am also hoping there is a simple formula that I can use to figure this out.  Any help will, needless to say, be appreciated!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: need help laying out an arc

Sorry, I'm not sure what you want to do. The picture looks like it might help, but when I click it to make it a bigger size, it doesn't load.

Could you maybe upload it to imageshack (or equivalent) and post it using the [img] tags?

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Why did the vector cross the road?
It wanted to be normal.

DocBoom

Member

Registered: 2008-02-25

Posts: 3

Re: need help laying out an arc

trying to uplaod image again

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: need help laying out an arc

there seems to be a problem with the site atm for images having been uploaded.

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The Beginning Of All Things To End.
The End Of All Things To Come.

DocBoom

Member

Registered: 2008-02-25

Posts: 3

Re: need help laying out an arc

image not uploading well or I'm diong it wrong.  Let me explain better...

I have a circle with a radius of 108m.

I have points along the perimeter of this circle which have a chord length of 9144mm.

what i want to do is, every say 500 mm along this chord, turn 90 degrees and plot a point along the arc.

I dont know how to find the distance from this cord at these particular points.

Does this clarify the problem any?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: need help laying out an arc

Ah, that makes more sense.
If I'm right, this can be solved entirely using Pythagoras.

First you work out how far your chord is from the centre of the circle.
The point on the chord that touches the circle is 4.572m away from the circle's centre, horizontally.
It's also 108m away in total.

So using Pythagoras, it is √(108² - 4.572²) = 107.903m away, vertically (to 3 decimal places).
The chord is horizontal, so the same is true for all points on the chord.

You can use the same technique to find the height above the centre for any point on the circle, by specifying how far it is horizontally from the centre. Then for each point, you can take the height of the chord away from the height of the point to find the distance from the point to the chord.

So, if a point on your circle is x metres horizontally away from the centre, then its height above the chord would be:

(Note that x has to be between 0 and 4.572 for this formula to apply)

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Why did the vector cross the road?
It wanted to be normal.

DocBoom

Member

Registered: 2008-02-25

Posts: 3

Re: need help laying out an arc

I very much appreciate the help... If this proves to work it will save me mucho time, effort and stress manually plumbing up lines from the existing slab below.

Love that pathagoras too by the way,  I don't know how buildings would be constructed square and now apparently round without him!