Help, properties of a curve/circle

[Noel]

Is there a way of finding out the radius or any other properties of a circle with only the following information:

(very technical drawing of flexible rod pulled into a curve with string)

 

[novocaine]

https://www.dummies.com/education/math/ ... -an-arc-2/

 

[doctor Bob]

Do you know the height of the segment?

If you do there is a formula.

 

[Eric The Viking]

Pythagoras's Theorem, sines and cosines will get you there.

The black line is your string. The red line you haven't told us yet, but you need to measure it.

Crucially, the shape of the triangles A and B is the same, but the sizes are different. This is because wherever a triangle from the diameter of a circle touches its edge, the angle is always 90 deg. (the triangle made by the green and blue lines). The big triangle is also the same shape, as it shares the same angles with the other two.

So work out the missing distance in triangle A (the green line of it). That can be dropped into the big triangle, allowing you to work out both the other green line and eventually getting you to the diameter of the circle (blue).

Note that this is an approximation, because the "bowstring" method actually makes a bit of a parabola or a catenary (a proper engineer will be along in a minute...), NOT an arc of a circle. But it's probably close enough for your needs.

You need a calculator that can do sines, cosines and arcsines, etc. as you'll be swapping between angles and distances. It also probably needs to do degrees (at least I find them easier than radians!).

HTH, E.

 

[doctor Bob]

If you know A above, then it's a simple formula with no sins, cosines etc.

 

[Noel]

Thanks Bob, Novo and Eric, knew I was missing something.

 

[Yojevol]

This is a difficult problem to solve with the info given, but not impossible if you have the relevant mathematical software available. Fortunately it is available at https://planetcalc.com/1421/
This screenshot gives the answers with your data fed in:-

Brian

 

[Sheffield Tony]

I'm fairly sure a rod tensioned by a string will not be a circular arc.

 

[gasman]

No it will be a parabola which doesn't have a radius. It wont be too far away from an arc if it is 'shallow' though so the formulae above will be a reasonable approximation
cheers mark

 

[ColeyS1]

If you've got the rise of the curve -

Sent from my SM-G900F using Tapatalk

 

[MikeG.]

Is there a way of finding out the radius or any other properties of a circle with only the following information:

(very technical drawing of flexible rod pulled into a curve with string)

7816mm diameter

As an aside, the distance "A" from ErictheViking's diagram is approx 120mm.

 

[Tasky]

I'm fairly sure a rod tensioned by a string will not be a circular arc.

No, it won't.
More importantly, people have been hand-making bloody good and accurately sized Longbows for centuries, without having a clue who Pythagoras even was... So there must be some even simpler tricks!!

 

[Eric The Viking]

If you know A above, then it's a simple formula with no sins, cosines etc.

Quite right - just pythagoras as they are all right-angled triangles. I was being a twit... ;-)

 

[Johnboy]

Using CAD to draw it the radius is 3900. The rise is 120.254.

John

 

[niagra]

handymath.com/cgi-bin/arc18.cgi

This site calculates several parameters. Radius 3900mm with the assumption that the shape is an arc.

 

[Noel]

Thanks again to everybody who has posted, all have been useful and educational.
Ta.