Calculate Arc Width by having length and rise

[ravetunes]

Hi there, is it possible to calculate the Arc width by only having the Arc Length and Rise?

Rise is the height of arc

Arc length = 1525

rise = 230

width = ?

 

[ravetunes]

someone told me it is impossible but surely not??

 

[ravetunes]

is it possible that its impossible? even in excel....

 

[ravetunes]

check this out any 2 inputs gives the answer im looking for but how can this be done in excel.... it seems the impossible is possible....

http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry

 

[CircuitsMan]

This is more of a math problem than an Excel question.
http://mathworld.wolfram.com/ArcLength.html

From what I know, Excel does not have built-in integral/derivative functions but there may be some macro routines that can calculate approximations.

 

[CircuitsMan]

Although, having a fixed-radius arc makes things easier.

check this out any 2 inputs gives the answer im looking for but how can this be done in excel.... it seems the impossible is possible....

http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry

 

[CircuitsMan]

http://mathforum.org/dr.math/faq/faq.circle.segment.html

 

[wsjackman]

this is a math question which can be done in Excel

Arc length divided by the radius is some angle in radians

the cosign of half this angle = 1-the rise divided by the radius

therefore
1-Rise/radius=cos(length/(2*radius)

the arc width is 2 times the radius times the sine of (length/(2*radius))

the clue is to solve for radius

there is no direct way to solve for the radius so you can use solver to make 1-Rise/radius-cos(length/(2*radius) =0

or you can do it by entering different values of radius until the equality is there

once you know the radius you can calculate the width.

 

[ravetunes]

im not sure what you mean, i just had 2 inputs for the calculator and it gave me the answer i was looking for i checked it on autocad.... so there must be a formula cant find it anywhere online tho... thanks for the website ill check it out...

 

[CircuitsMan]

From the link I posted:

Case 3: You know s and h. Then solve
2h/s = (1-cos[x])/x,
for x, which must be done numerically (see below). Then
theta = 2x,
r = s/theta,
c = 2r sin(x),
d = r - h,
K = r2[theta-sin(theta)]/2.

s is arc length, h is height, and c is chord length (width)