Jeff Woolf was riding down a narrow London street when an irate driver clipped his bike. The car’s fender snagged Woolf’s pedal, flinging him headlong into a curb. As ambulance workers triaged Woolf’s broken body, they marveled that his skull had remained in one piece; his helmet, they said, had saved his life. Twenty years later, Woolf saw few London bike share riders wearing helmets, so he invented a model that’s as handy as a bike itself. Called the Morpher, his creation is a full-scale helmet that folds to the size of a textbook.

Woolf’s timing couldn’t be better. The duration of bike rides in the U.S. has more than doubled since 2001, trips are up 25 percent, and cities around the world—Chicago, Dublin, Montreal, and more—are launching or expanding bike share programs.