LESSON 3.3 · 2:34 · CHAPTER 3 · PATHS ON CURVED SURFACES
Two curvatures
A curve's bending on a surface splits into normal curvature (into the surface: it presses a taut fibre in) and geodesic curvature (sideways: it tries to slide the fibre). A geodesic has no sideways part. A helix on a cylinder is a geodesic with k_n = sin²α/R; on a surface of revolution k_g = (1/R) d(R sin α)/dm.
Predict · at 0:53 in the video
A helix on a straight cylinder. Does it curve sideways at all?
No. Unroll the cylinder, and the helix becomes a straight line. Straight on the flat means no sideways bend.
Further reading
This course is our own. These books go deeper.
- Composite Filament Winding, S. T. Peters (ed.), ASM International, 2011
- Filament Winding: a Unified Approach, S. Koussios, Delft University Press, 2004
About the numbers
Simulations in this lesson are our own. Where a number rests on an assumption, the video marks it with an asterisk and says where it comes from.
Up next · 3.4 · 2:27The friction budget