finding area of a spring

[qwertypunk]

how do i find the area of a spring?
can anyone tell me the formula to find it??
thanks

[HallsofIvy]

how do i find the area of a spring?
can anyone tell me the formula to find it??
thanks
What do YOU mean by "area" of a string? Mathematically a spring is modeled by a helix which is a one dimensional object has "length" not "area".

Perhaps you are thinking of a wire of a given radius shaped into a helix. In that case, the surface area of the wire would be its circumference (2pi r) multiplied by the length of the helix. How you would calculate that depends on exactly how the helix is specified.

Let's say you are given a helix of radius R which rises a distance h in one revolution. Then a point on the helix can be specifice by the vector z(theta)= (R cos(theta), R sin(theta),(h/2 pi) theta) where theta is the angle or rotation of the helix. The tangent vector to that helix at given theta is (-R sin(theta), R cos(theta), h/2pi) and the length of the tangent vector is sqrt(r^2+ h^2/4pi^2), a constant. The length of the helix between two angles is just the integral of that which, since it is a constant, would be that number times the difference in two the two angles. In particular, its lenth in one complete loop of the helix is 2pi sqrt(R^2+ h^2/4pi) and so the surface area of a spring made of wire with radius r is given by 4 pi^2 r sqrt(R^2+ h^2/4pi)

[jeremyparker10]

The only thing I can say is, for a volume can you model this as a cylinder? Then V = \pi r^2 L where L is the distance along the helix's axis.

Or is the pipe wrapped around in a helical shape?

[Cell.Phone]

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