Finding the integral for coil width given wire length and diameter

[willib]

i am looking for an equation (integral) , so that i can predict what width to make a coil of wire , of certain length ,and thickness, so that it comes out to an outer diameter of 1.5" with an inner diameter of .5"..
i usually spend my time in the engineering section , but i thought that i would come to you , with this question..

 

[HallsofIvy]

Here's what I would do: The volume of the "hollow" cylinder of inner radius r₁ and outer radius r₂ and height W (it's really the width of the coil) is $$\pi W(r_2^2-r_1^2)$$ which with r₂= 1.5 and r₁= 0.5 is $$\pi W(2.25- .25)= 2\pi W$$. The volume of a length of wire of radius R and length L (a very thin cylinder) is $$\piLR^2$$. Set those equal and solve for W: $$W= \frac{R^2L}{2}$$.

 

[willib]

thats not close to what i am getting ... by your equation , it comes out to .44376 " ...
i started winding with a width of 0.6" , and due to the tightness of my winding , it bulged out to 0.7 " tward the outer windings..
My wire diameter is 0.043 " , pretty thick wire..
and the reason i need to calculate the width is because my wire comes in certain lengths , specificly 480" .. and i would like to use all the wire for each coil that i am winding..and the inner & outer diameter have to be 0.5" & 1.5" respectively, so the only thing i can vary is the width..