radius question, math guru's

larry merlau

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ok how do you folks determine your radius's for a preselected arch,,

example need a arch that is 13.375 long and 1.75 high.. i am sure there is a formula to do it out there but this old noggen has forgotten it and the string trick is getting old..:) help also need the radius for a 15.375 arch as well:)
 
Do you know the arc angle? I'm not sure that table will solve the problem unless another variable is known, i.e. the arc angle. In Larry's example I think he's referring to the arc length rather than the chord length, but.......?
 
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Do you know the arc angle? I'm not sure that table will solve the problem unless another variable is known, i.e. the arc angle. In Larry's example I think he's referring to the arc length rather than the chord length, but.......?

Yeah good point, a more complete calculator that tries to solve all of the cases is at: http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry
it will solve either the arc length or the chord length given one or the other and the height.
 
thanks guys after i saw the arc swing marks my dusty brain woke up:) will make me a example and hang it up for later dates:) as for laying the spring stick down aqnd tracing it ryan my spring stick doesnt flex equally along its length so that didnt work for me i tried that first.. so that stick can become kindling..
 
thanks guys after i saw the arc swing marks my dusty brain woke up:) will make me a example and hang it up for later dates:) as for laying the spring stick down aqnd tracing it ryan my spring stick doesnt flex equally along its length so that didnt work for me i tried that first.. so that stick can become kindling..


Try the following. I have not tested it out.

H = height of arch

L = length of arch at the base, not arc length

radius = (H² + 1/4L²)/2H
 
Or:

L=Arc Length = 13.375
A=Arc Angle = 12.47481
P=Pi=3.1416
R=Radius

L=(R*A*P)/180 or R=(180*L)/A*P

R=(180*13.375)/(61.43030*3.1416)=12.475
 
Ryan, thanks for the handy tables. Didn't know they existed. I saved as a favorite place.

Any others that are as useful? I had to did into my old Machinist Handbook that I bought new in 1960 (16th Edition) to find the formula.

Al
 
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Or:

L=Arc Length = 13.375
A=Arc Angle = 12.47481
P=Pi=3.1416
R=Radius

L=(R*A*P)/180 or R=(180*L)/A*P

R=(180*13.375)/(61.43030*3.1416)=12.475

hey al, where did you come up with the arc angle? the 61.43030 i understand pi but all i have to work with is the width of arc and the hieght.. which threw ryan's link i can do mathematically or geometrically with a set of long compass arms.
 
I use a strip of 1/8" polycarbonate instead of wood, it is more consistent and uniform when bending and will not break.

would any plastic work, roger.. i got some abs plastic that i can try.. it bends easy and doesnt break like styrene does.. i also have some plexi glass but that will break if you go to far..
 
Larry, I am missing some notes from the class I took. I need to contact Jim Tolpin and see if he will email me the missing notes, or maybe I will just wait until this spring when his new book on the subject comes out. I did find this following link to a method that avoids using a compass or bending a stick. It is suppose to be an old boat builders technique. Check it out.
 
Ryan, thanks for the handy tables. Didn't know they existed. I saved as a favorite place.

Any others that are as useful? I had to did into my old Machinist Handbook that I bought new in 1960 (16th Edition) to find the formula.

Al

I just used Google for "arc radius calculator" and first link.

You can also find ~many math formulas for simple trig up to basic calc (which if like me you've long forgotten all of) at http://www.mathopenref.com/
 
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