## Bulge Calculation

jimandi5000
Vectric Wizard
Posts: 330
Joined: Wed Mar 11, 2015 6:50 pm
Model of CNC Machine: Home Made 60 x 120
Location: North Houston Tx.

### Bulge Calculation

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)
end``````
Thanks,
Jim

jimandi5000
Vectric Wizard
Posts: 330
Joined: Wed Mar 11, 2015 6:50 pm
Model of CNC Machine: Home Made 60 x 120
Location: North Houston Tx.

### Re: Bulge Calculation

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
``````
Thanks,
Jim

vgraves
Vectric Craftsman
Posts: 122
Joined: Sat Sep 29, 2012 2:04 am
Model of CNC Machine: CNC Router Parts PRO4848 w/LinuxCNC
Location: Knoxville, TN

### Re: Bulge Calculation

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
Vectric Wizard
Posts: 330
Joined: Wed Mar 11, 2015 6:50 pm
Model of CNC Machine: Home Made 60 x 120
Location: North Houston Tx.

### Re: Bulge Calculation

Hi Van,

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

armbrusterco
Vectric Craftsman
Posts: 128
Joined: Tue Feb 14, 2012 5:26 am
Model of CNC Machine: Roland MDX-40A
Location: Lake Barrington, IL
Contact:

### Re: Bulge Calculation

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/
Bob Armbruster
www.ArmbrusterCo.com

jimandi5000
Vectric Wizard
Posts: 330
Joined: Wed Mar 11, 2015 6:50 pm
Model of CNC Machine: Home Made 60 x 120
Location: North Houston Tx.

### Re: Bulge Calculation

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?
Thanks,
Jim

armbrusterco
Vectric Craftsman
Posts: 128
Joined: Tue Feb 14, 2012 5:26 am
Model of CNC Machine: Roland MDX-40A
Location: Lake Barrington, IL
Contact:

### Re: Bulge Calculation

You are correct. I missed the ratio. Oooops.
Bob Armbruster
www.ArmbrusterCo.com

jimandi5000
Vectric Wizard
Posts: 330
Joined: Wed Mar 11, 2015 6:50 pm
Model of CNC Machine: Home Made 60 x 120
Location: North Houston Tx.

### Re: Bulge Calculation

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