# Radius of curvature along a spring

Hello friends,

I am working on a design project for my capstone course in my engineering curriculum. Part of the design involves a cord consisting of wires tightly wrapped helically (à la a spring) around a nylon rope core. An important specification of this design is the radius of curvature of the wires under various tensions at various angles.

To measure this, my group and applied various tensions at various angles to the cords and then taking pictures of the cord. From there we could plot points on the picture along the cord to model the cord, then used groups of 3 consecutive points to approximate the radius of curvature of the cord as a whole. In other words, we already know the radius of curvature of the cord as a whole.

My question is twofold:
1. Clearly when the cord is untensed and unbent the radius of curvature of the wires is constant and equal to slightly more than the radius of the nylon rope. Is it reasonable to assume that the radius remains constant even under tension and bending?
2. If the answer to question 1 is no, is there any way I can go about calculating or estimating the radius of curvature of this "spring" under bending? The tensile force is taken up by the nylon rope so there is no direct axial compression on the spring.
I have attached a picture of our setup to help aid your understanding (note that the area of interest is only about the first inch coming out of the C-clamp). You can kind of see the helical wrap through the heat shrink.

#### Attachments

• IMG_1530.JPG
93.8 KB · Views: 493

A.T.
1. Clearly when the cord is untensed and unbent the radius of curvature of the wires is constant and equal to slightly more than the radius of the nylon rope. Is it reasonable to assume that the radius remains constant even under tension and bending?

I don't think the radius of curvature of the wire is just slightly more than the radius of the nylon rope. Given the high pitch of wrapping seen in the picture it can be much more.

1. If the answer to question 1 is no, is there any way I can go about calculating or estimating the radius of curvature of this "spring" under bending? The tensile force is taken up by the nylon rope so there is no direct axial compression on the spring.

http://en.wikipedia.org/wiki/Helix#Arc_length.2C_curvature_and_torsion

radius of curvature = 1 / curvature

BiGyElLoWhAt
Gold Member
If I understand the question, these should make sense:
1: Will, under any tension, the helix unravel?
2: Maybe read into hamiltons principle of least action, along with applying Youngs stress equations. (Youngs Modulus)