arc length formula

[woodzilla]

I need some help from the math types out there for writing a formula for arc length. I have several formulas for calculating radius and springback. I build curves for wood molding.
I wanted to input the varibles,chord and height, of radius to get the arc length. The formulas I have involve the degree of angle. I haven't figured out how write a formula using chord and height.

 

[Jay Petrulis]

Hi,

Try...

Chord length in B1, Height in B2
=SQRT(B2^2+(B1/2)^2)*ATAN(B1/2*B2)*2

Report back your results.

Bye,
Jay

 

[woodzilla]

I tried a few times and checked the answer with a cad program, and it is a mismatch.

A 60" chord with 16" rise on the excel program comes up as 106.67" and on cad its 70.8".. I'm still looking for the error.
What do you get?

Thanks alot for your help.

 

[Jay Petrulis]

On 2002-06-07 22:36, woodzilla wrote:
I tried a few times and checked the answer with a cad program, and it is a mismatch.

A 60" chord with 16" rise on the excel program comes up as 106.67" and on cad its 70.8".. I'm still looking for the error.
What do you get?

Thanks alot for your help.

I think we are miscommunicating on the terminology here. In addition, I missed one set of parentheses.

A 60" chord with a 16" rise gives two right triangles with base of 30 and height of 16.

Taking one of the trinagles, the radius of the circle in the above is 34
=SQRT(16^2+30^2)

If that agrees with what you have, then we need to find the angle and multiply it by the radius to find the chord length for one half the full segment.

We should have tan x = 30/16, so x = ATAN(30/16) = 1.0808 radians

34*1.0808*2 = 73.5 or so.

=SQRT(B2^2+(B1/2)^2)*ATAN(B1/(2*B2))*2

In the ATAN calc, I messed up the divisor.

Please let me know what I am missing here. Our numbers should jibe with the CAD program.

Bye,
Jay

 

[woodzilla]

Arc length
chord height arc length
60 16 73.49705204 =SQRT(B12^2+(A12/2)^2)*ATAN(A12/(2*B12))*2
I'm working off row 12.

cad program has this arc as 70.8"



chord height Arc length
60 32 66.07158855 somthing a little odd, if height is increased, the arc should get longer.

cad program has this as 98.32"

the length of the arc is what I'm after. I tried to paste in the drawing, didn't work.

 

[Jay Petrulis]

Hi,

If the height is increased, the arc should get *smaller* if I am thinking correctly. I will try to match the program results and report back.

Thanks for the specific feedback. It helps to know exactly what the target is.

Based on your replies, I am thinking that this chord is a tangent line to the circle, not a line segment joining two points on the circle (effectively splitting the circle into two pieces). Am I on the right track?

If this is a tangent line, then the formula above will not work, as you undoubtedly found out already.

I will post back when I get a solution.

Bye,
Jay

 

[woodzilla]

I think you are on track Jay.
I am working with a radius arc. The chord being a line that connects the 2 ends of the arc. And the height or rise being the farthest distance between the line and radius. The goal is to figure out how long a strip of wood needs to be to bend around a radius.


In my reading various forum notes here, excel uses radians instead of degrees with trig formulas. Thats something I have never used. So maybe a degree conversion needs to be put in somewhere.
I'm also working on a compound miter formula, I got a good one from a website, but putting it into a spreadsheet formula is kinda hard.

 

[woodzilla]

To Jay and all other readers,cabinet makers and woodworkers that might build curves.
I plowed my way through, and came up with my own formula for arc length. Not pretty, but it seems to work, and I checked the results with CAD.
my arc formula

cell 1 - varible chord length

cell 2 - varible height length or rise

cell 3 - ATAN(B12/(A12/2))*2

cell 4 - TAN(1.5708-C12)*(A12/2)

cell 5 - SQRT((D12^2)+(A12/2)^2) this gives the radius

cell 6 - E12*C12*2 arc length

I am working on a compound miter formula and some others that I will be posting on Woodweb and cabinetmaker online sometime in the future.

 

[Lori_M]

Assuming 1.5708 is an approximation PI()/2, I think the arc-length formula simplifies to:

=ATAN(2*B12/A12)*(A12^2/(2*B12)+2*B12)

This was just using a bit of algebra, I'm not sure geometrically why this should be the case?