LESSON 4.2 · 2:28 · CHAPTER 4 · DOMES AND THE POLE
Where the curve turns
The isotensoid's meridian curvature changes sign where tan²α = 2, i.e. at α = 54.74°, at a radius of √1.5 times the turnaround radius. Near there the metal boss takes over.
Predict · at 0:53 in the video
At what winding angle does the ideal dome stop curving one way, and start curving the other?
54.74 degrees. With Clairaut, that's at a radius of root one and a half times the turnaround radius. The same angle as the balanced pipe, for the same reason: right there, the net carries two to one.
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 · 4.3 · 2:33Fibres pile up at the pole