Determine Arc Based on Perimeter?

[trashcan]

I have a scale drawing from client and the only information they've provided is: the arc is 55'

 

Is there a way that I can determine the arc based on perimeter? I got pretty darn close with some proportional algebra, but I'd love for it to be exact. Any ideas? 

 

[Pat Stanford]

No, you don't have enough information. There are three main items for an arc.  Radius, Arc Angle and Arc Length (or Chord Length).  Given any two you can calculate the third.

 

Given you only have one, you can not calculate the other two. Best you can do is come close.

 

There are an infinite number of arcs that will give you a length of 55' between the two end points. You have to guess which is closest to what you need.

[trashcan]

Thanks @Pat Stanford

 

If I had the depth of the arc would that do the trick? 

[bcd]

Yep, any 2 variables will fix it for you.

But depending what it's describing your 55' may only be approximately 55' and might be made up of an even number of 1m sections for example.

[michaelk]

I think it depends on if 55' is the arc length, chord length, or radius.  (I just worked on a problem that dealt with arc formulas.  And I bugged Pat about it, too).

 

If I remember correctly:  If you know the chord length and the arc length you can't solve for the radius directly because you end up solving for a value that appears both inside a sin function and outside a sin function. There is an approximation method that gets you an answer, but I've completely forgotten how to do it.

 

I think if you know the sagitta (distance from the chord to the arc along the radius that bisects the chord.  That name was gone from my memory.  Had to look it up 🙂 ) then you can get the radius.

[trashcan]

@bcd yessir! I got close enough with proportional algebra, so I'm good for now. 54'11.996" is good enough fo me 🙂