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Trying to figure out math on circular metal bender

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Swerdk

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#1
Is there a method to laying out spirals so that holes get wider the further out you go? Does someone have a stencil cheat sheet?







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Bob Korves

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#2
Use a center point that is the correct diameter to move the radius of your spiral by the desired distance per revolution. Pi X D, 3.14 times the diameter, give you the distance increment per full revolution. If you wanted one inch between the lines of the spiral, you would divide that one inch by 3.14 and use that number for the diameter. I don't know how accurate this needs to be, but a piece or string wrapping around a center point of the correct diameter with the other end attached to a pencil or scribe would certainly do the job for ordinary work.
 

Bob Korves

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#3
Looking at the hidden photo, my idea will not work as stated for that job, but the concept does not change.
 

Swerdk

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#4
I am not understanding [emoji848]this device (overpriced to buy but easy to make) allows me to make clean repeatable scrolls. It looks like the holes are spaced more widely as each of the 3 spirals move away from center. I do not understand your first statement use centerpoint that is correct diameter to move the radius of your spiral by desired distance per revolution. Is there another way to say it?


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Bob Korves

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#5
The spiral I was describing increases by the same amount per revolution:

In the photo you posted the rate of diameter change increases with clock position. It is a logarithmic spiral:

This relationship is that equal angles correspond to exponential changes in arc length. Thus, an increase of the angle by "n" increases the corresponding arc length by the "nth" power. (For example, a change in position measured by a doubling of an angle corresponds to squaring of the arc length along the spiral path.)
 

Swerdk

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#6
That's exactly what I'm trying to figure out so let me ask again what is the calculation I use to determine the length between X and x2 and so on through the spiral? You are being extremely helpful and I appreciate your patience - angles is not my strong suit


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Bob Korves

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#7
That's exactly what I'm trying to figure out so let me ask again what is the calculation I use to determine the length between X and x2 and so on through the spiral? You are being extremely helpful and I appreciate your patience - angles is not my strong suit


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That depends on the increase you are looking for. You must decide how fast you want it to expand. Here is the source:
http://www.wlym.com/antidummies/part62.html
However they are using the increase of the length of the arc to the change in angle by multiplying by an exponential factor to define the spiral. The bigger the exponent the faster the spiral opens up. If you look at "spiral maker software" you will find programs to meet your needs, some free, some pay.
 

Swerdk

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#8
Thank you for all your expertise I have it figured out now I so appreciate everything you did --have a good night


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chips&more

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#9
You guy’s please stop this, change the subject. You are hurting my head, I thought I didn't need to go back to college:confused:. But on a serious note, good for you! My brain is too far gone for that kind of math thinking. I can barely get the fork from plate to mouth.
 
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Swerdk

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#10
There is a math equation for that too but then a physics lecture would evolve. I got it Bob- thank you for stepping up and helping me.


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Blackjackjacques

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#11
You are describing what is known as a golden or fibonacci spiral. It occurs naturally in nature -- manifesting in examples such as nautilus shells or the stems of fiddlehead greens. You can read about them here ; https://www.intmath.com/blog/mathematics/golden-spiral-6512
and if you are comfortable in programming, can write some code to implement the formula detailed in the above or :

The Golden Spiral has the special property such that for every 1/4 turn (90° or π/2 in radians), the distance from the center of the spiral increases by the golden ratio φ = 1.6180.
 
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