S-curves tire cords Foster 1986

R&D Productivity for tire cords: cotton, rayon, nylon, and polyester (Foster, 1986)

S-curve (S-shaped curve) is a graph commonly encountered when plotting various aspects of technological developments. For example, growth of knowledge in a newly opened field (Isenson and Hartman models), adoption of a new technology are often very well described by an S-curve.

The illustration shows how successive technologies for tire cords (cotton, rayon, nylon and polyester) outperformed older ones and replaced them in the marketplace. After a certain point spending money on research in the old field is simply pointless and the old technology dies out.

Similar graphs can be made for generational changes in various areas, with new products starting small, gaining momentum, quickly winning the marketplace and then slowly reaching the saturation.

S-curve can be modelled by a logistic function.

"One adaptation of the S-curve is known as the envelope S-curve, which takes into consideration successive generations of technologies that provide the same benefits. The term "envelope" refers to the curve that connects the tangents of the successive individual S-shaped curves." [1] A combination of successive S-curves can produce linearly or exponentially growing graph. For example, many successive paradigms in computing, taken together produce exponential growth in computational capacity over 100 years (Kurzweil, 2001, 2003).