Bending It Like Bernoulli

The colored "strings" you see represent air flow around the soccer
ball, with the dark blue streams behind the ball signifying a
low-pressure wake. Computational fluid dynamics and wind tunnel
experiments have shown that there is a transition point between
smooth and turbulent flow at around 30 mph, which can dramatically
change the path of a kick approaching the net as its speed
decreases through the transition point. Players taking free-kicks
need not be mathematicians to score, but knowing the results
obtained from mathematical facts can help players devise better
strategies. The behavior of a ball depends on its surface design as
well as on how it.s kicked. Topology, algebra, and geometry are all
important to determine suitable shapes, and modeling helps
determine desirable ones. The researchers studying soccer ball
trajectories incorporate into their mathematical models not only
the pattern of a new ball, but also details right down to the
seams. Recently there was a radical change from the long-used
pentagon-hexagon pattern to the adidas +TeamgeistTM. Yet the
overall framework for the design process remains the same: to
approximate a sphere, within less than two percent, using
two-dimensional panels.