Bulge Calculation

[jimandi5000]

Hi all,

Looking for some help. before I do the deep dive on spending a bunch of time, I would ask... I am looking for the formula to calculate arc bulge. Anyone out there crossed that bridge?

This is what I have so far:

Code: Select all

function BulgeCalculator (Rad, Ang)
   return math.tan (math.rad(Ang) * Rad)
end

[jimandi5000]

Hi,

I wrote this and ran 30 to 40 test. I am thing it is working.

Code: Select all

function Arc2Bulge (p1, p2, Rad)
    local chord = math.sqrt(((p2.x - p1.x) ^ 2) + ((p2.y - p1.y) ^ 2))
    local seg = (Rad - (0.5 * (math.sqrt((4.0 * Rad^2) - chord^2))))
    local bulge = (2 * seg) / chord
    return bulge
end


[vgraves]

Not exactly sure what you mean by bulge, but I interpreted it to refer to circular segments. This may help you validate the results of your existing function.

https://en.wikipedia.org/wiki/Circular_segment

Van

[jimandi5000]

Hi Van,

Thanks for the reply. Here is what the SDK states on page 95.

[armbrusterco]

In geometry, the "bulge" is called a sagitta. Surveyors sometimes calculate the sagitta to use when staking out arcs.

If you know the radius and chord length of the arc, here are two links with the formula to calculate the length of the sagitta.
https://www.mathopenref.com/sagitta.html https://www.liutaiomottola.com/formulae/sag.htm

If you know the radius and the angle of the arc, here is a link with a formula to calculate the length of the sagitta.
https://planetcalc.com/1421/

[jimandi5000]

Hi armbrusterco,

Not sure I agree. the SDK states

The bulge represents a ratio between the chord length of an arc and its height (bulge = (2*arc_height) / chord_length).

So you are somewhat correct we do need the sagitta but we need the ratio to the chord to the sagitta.

Thoughts?

[armbrusterco]

You are correct. I missed the ratio. Oooops.

[jimandi5000]

No Problem... I am just trying to learn as much as I can...