I'm trying to work out an equation for the combined value of circumferences of a set of concentric circles.
For example - if we start with a circle of say, 5mm Dia, the Circumfence would be 15.71. If there was then
a circle placed outside of this at a 4mm distance it would have a dia of 13mm - the circumference of this
would be 40.83. Another one at 4mm offset from that would be 21mm (Circumference 65.96). Clear so far?
Well, if you add the above three figures, you get a value (15.71+40.83+65.96) = 122.5. What I want to get is
a simple equation where I can start with a Circle of 5mm, with 2 more Concentric Circles at an offset of 4mm
each time and arrive at the 122.5 I'm looking for. I would want this equation to work for any size circle, with
any number of concentrics and a delta offset (obviously a constant delta, though!). Hopefully I haven't lost you
now...
So for example if you had a circle of 25mm with 15 Concentric circles at an offset of 4mm
(so 25mm, 33mm, 41mm, 49mm) etc. - What would the total value of circumferences be for those 15 circles???
I am doing this so I can work out what the outside diameter a reel of webbing will be after a certain amount of
webbing has been wrapped onto a shaft of a particular diameter.
(Although I guess in reality the pure answer would actually be based on a helix.......)
2007-01-09
19:55:40
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5 answers
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asked by
Miss M R Cook
1
in
Mathematics