Tired of seeing ads? Click here to upgrade to Elite Membership!

Mathematics Forum

Tired of seeing ads? Click here to upgrade to Elite Membership!

Author	Message / Information
BobG This message was updated on 4/30/2004 9:22:07 AM by BobG	Arc Length and Chord Length replied on: 4/29/2004 11:18:07 AM If you do this a lot, I've got something that can help you. If you have a computer with Microsoft Excel, do the following: (Oops, somehow I got my rows and columns mixed up! - this will probably work better) In Cell B1 enter: =A1SIN(4/A1)-3 (A1 is where you'll enter your first guess. If your guess is right, the radius times the sine of the angle will equal 3; subtracting 3 will give you zero or an indication of how far off your guess was) In Cell C1 enter: =A1COS(4/A1) (This is the derivative of Cell A2 with respect to theta - this basically tells you how much your result will change in response to a change in r) In Cell D1 enter: =B1/C1 (This is how much you need to adjust your next guess by - note the ratio between how far off your guess was and how much your result will change if r is increased by 1) In Cell A2 enter: =A1-D1 (This is your second guess) Highlight cells B1 through D1, copy them, and paste them into cells B2 through D2 Highlight cells A2 through D2, copy them, highlight a bunch of rows (columns A through D), and paste them Now as soon as you enter your first guess in A1, column A of the last row should give you your answer. You can tell if it worked by looking at column B and column D of the last row. They should both be zero or pretty darn close to it. If you were generous in the number of rows you decided to make, you'll probably notice your guesses stopped changing after around 15 to 23 tries depending on how many digits you're displaying. Since you're already playing in the spreadsheet.... In Cell F1 enter: =4/A40 (IMPORTANT: I didn't mess around - Row 40 was the last row I pasted to. In place of A40, you should put Axx where xx is the last row of your guesses) In Cell G1 enter: =F12 (This is your actual angle in radians) In Cell H1 enter: =G1180/PI() (Your buddies will get real annoyed with you if you give the angle in radians, so convert it to degrees so they won't make fun of you) You can also do this on a good hand-held graphing calculator by entering: x-var sin(4/x)-3 as your equation, graphing it, and using the ROOT function to find where the graph crosses zero.
BobG	Arc Length and Chord Length replied on: 4/29/2004 10:52:08 AM Try a radius of 3.135538 and a half angle of 73.0921 degrees (1.275698 radians). That means the angle of the entire arc/chord is about 146.2 degrees. Divide the chord and arc in half so you have a right triangle to work with. r(theta) = s where s is the arc length, or 4 so: theta = s/r or 4/r c = r sin(theta) theta = 4/r c = 3 Now, you can solve for 4 numerically. Newton-Raphson method is best. My first guess was way off (4.5), so it took me about 9 guesses to get the error less than 0.1 and about 23 tries to get the answer I gave you (of course, if you use a spreadsheet, you don't care near as much about how many tries it takes - it's as quick to make 25 guesses as one guess)
GlitchCog This message was updated on 4/28/2004 11:18:16 PM by GlitchCog	Arc Length and Chord Length replied on: 4/28/2004 10:48:51 PM Yeah, I'm sitting here with the same problem... I'm doing work on plate buckling and I need some formula for radius based only on arc length and chord length. Thinking about it you'd guess it'd be possible, but I just can't figure it out. If you've got either the angle or R it's easy, but with just arc length and chord length... I'm about to give up. I've been searching for an answer for hours. Hey... found the answer... but it seems it must be done numerically. http://mathforum.org/library/drmath/view/51797.html c=chord length, s=arc length, A=angle, r=radius (c/s)=sin(x)/x, A=2x r=c/(2sinx) Not much help for me, but if you've got measurements it'll do you.
george	Need Trig Formula Please replied on: 10/25/2003 11:28:49 PM I read with interest your reply to squishy concerning the problem of finding the radius of a circle given an arc length and chord length. After working on it I got a similar result, but not the same. I got sin(4/r)=3/r. I agree that it appears that the solution is a numerical one, not that of an equation. You would think that a circle would be uniquely determined given those measures and thus would yield to a solution not requiring numerical approximations. Do you know of any web sites that discuss this particular problem?
HallsofIvy	Need Trig Formula Please replied on: 9/5/2003 10:54:37 PM If the arclength is 8,then the central angle is 9/r where r is the radius. Drop a perpendicular from the center of the circle to the chord and you have a right triangle with leg opposite the angle of length 3 (half the length of the chord), angle 9/2r and so hypontenuse r given by 3/r= sin(9/2r). there is no "algebraic" way of solving that equation, you will need to solve that equation
dmoran	Need Trig Formula Please replied on: 9/3/2003 7:54:52 AM Use the formula s=r(theta) where s is the arc length, r the radius, and theta the angle. However, I don't know how the chord is drawn so I can't tell you how to find the radius. David Moran
squishy	Need Trig Formula Please replied on: 9/2/2003 8:19:37 PM Hi, I don't have an algebra background; I'm a machinist who uses trig to program a CNC machine. My question is: I have a segment of a circle; the length of arc is 8 inches; the chord is 6 inches. Please give me the formula to figure out the radius, the diameter, or the angle.

Tired of seeing ads? Click here to upgrade to Elite Membership!

ChatArea.com Help & News Forums | Terms of Use | Contact ChatArea.com | Advertising

Powered By ChatArea.com - Get your free Society today! © Copyright 2003 Wewp!