If you're carrying a folded umbrella and it starts raining, you just pop that umbrella open and keep walking. The Italian-designed BikerTop is designed to work in much the same way, although it's made for use by cyclists.
When not in use, the BikerTop sits folded down in a bag on the handlebars. That bag attaches to the bars via a quick-release mounting bracket, although it can also be key-locked in place when the bike is parked in public.
Once it starts raining, the rider stops, folds out the BikerTop's two aluminum vertical support arms, then extends those telescoping arms along with the flexible rain shield. That shield is made of waterproof nylon with a transparent polyurethane windshield, plus it has PVC mesh "wings" on either side.
The whole setup process reportedly takes just 10 to 15 seconds, and the shield is claimed to withstand winds of up to 35 km/h (22 mph). There is no windshield wiper, but as the designers point out, most scooter windshields don't have wipers, either.
Reflective glass beads in some parts of the shield help make it visible to drivers at night, plus it features a space where a third-party magnetic headlight can be attached to the mount (even when the shield is still in the bag). The whole rig weighs a claimed 3 kg (6.6 lb), and features an inner cargo pocket for carrying items such as smartphones or water bottles.
Should you be interested, the BikerTop is currently the subject of an Indiegogo campaign. A pledge of €167 (about US$198) will get you one, when and if they reach production. The planned retail price is €279 ($331). You can see the device in use, in the following video.
Potential backers might also want to check out the existing Dryve and Veltop systems.
It appears they have a prototype available for study, so I guess concerns for bicycling with a sail through rain while riding on wet streets is safe enough. A sudden gust from the side, especially if you are leaning into a turn away from the wind - would it add to your moment of inertia and raise your effectiev center of gravity higher than you are used to? I mean, if you do turn, and lean, and a gust pushes the sail in the same time forcefully - could you unexpectedly eat pavement?
I think it is a great idea, not great enough to back it, but a decent idea. And I don't think the Tour de France riders would utilize such a device except for training as they want every cornering and speed advantage. In rain your cornering angle diminishes as tire/road friction decreases and riding with a sail could create a tremendous "headwind" or drag. As I type this - maybe they would use it during training for the muscular development. You could ride shorter distances and still achieve the same level of work (except in physics where work = distance from starting point - hence the test question - Ben ran once around a track of X length and crossed the finish line directly over the start line - how much work did Ben do? with the answer NONE since he ended where he started). That one got me back in physics in high school.
2) The packed up mode is surprisingly inelegant - a big flat air brake on the front of the bike.
3) US$330 seems too high to generate any volume.