Formula for Spiral Around Cone - Get Your Answer Here

[eli_lied]

I am looking for the formula to describe a spiral formed around a conical shape. If any particular details are needed, please make them variables and define them.

Thanks to all for the help!

 

[tiny-tim]

Hi eli_lied!

Do you mean a shortest-possible-distance spiral, as if a string was pulled tight around the cone?

If so, then remember a cone's "own" geometry (as opposed to embedded geometry) is flat Euclidean …

so just cut the cone along a generator, unfold it, draw a straight line on it, and then join it up again.

 

[eli_lied]

Thanks for the reply Tiny Tim :)

What I'm specifically looking for is the equation for a "spring-like" spiral that is, for lack of a better term, 0 at one end and infinity at the other. As though a spring were wrapped around a conical formation with a varying height that increases over time.

 

[blkqi]

The simplest method would be to use a parametric equation

$$r(t)=(x(t), y(t), z(t)): x(t)=t \sin t, y(t)=t \cos t, z(t)=t$$

or something like that.