No doubt people have noticed the new green bike boxes at a number of locations in Madison. This is what the Bike Madison web site has to say about them
Bike boxes are rectangles, painted on the pavement at intersections, which move car traffic back several feet from the crossing and allow space for bicyclists to position themselves in front of waiting traffic. Bike boxes are intended to reduce bicycle and car collisions, especially those between drivers turning right and bicyclists going straight by providing greater visibility.
They also have a PDF that goes into it a bit farther
In general it does improve things. The biggest reason appears to be that it gives vehicles a clear view as to where to stop. I live close to a bike box and have noticed that most vehicles do now stop behind the green box while before nearly all cars pulled right up to the pedestrian crosswalk. It was not uncommon for cars to stop in the crosswalk, seemingly oblivious to pedestrians having to walk around their vehicle.
It also improves things for bikes in several other ways. On the left side of the box is an arrow for turning left. With the green box bikes are not forced to the center of the road when wanting to turn left. It also places bikes in front of vehicles so drivers have a much clearer view as to what’s about to happen.
One other thing the boxes improve on not mentioned in the PDF is for bikes positioning themselves for a left turn who prefer not to cut across traffic. The photos above are for the corner of Dayton and Park. When traveling on the bike lane on Park Street many bikers would rather not try to cut across two lanes of traffic from the bike lane on Park Street to position themselves for a left turn onto Dayton. I would include myself among those. Much better to continue on the bike lane on Park, cross Dayton, and then get positioned at the light to cross Park. With the green bike box there is more room for bikers to get themselves in position. Before the green box appeared bikes where forced to try and turn themselves around with very little room. Throw in vehicles who have edged up to close to the pedestrian crossing, and of course pedestrians crossing the street, and it makes for a very congested and confusing corner. The green bike box has created a better situation for bikes, pedestrians, and vehicles by pushing back vehicles and giving everyone more room. The subjective safety for bikers is certainly improved.
So is this an ideal situation for bikers? Given the current situation it is clearly an improvement with a relatively small investment, but it is a long way from ideal. If Madison ever wants to get the bike commuting level up to the 20% the city claims it wants it’s going to have to do a lot better.
Let's take a look at what other countries have done to dramatically improve the real and subjective safety of bicyclist. Here and here are good examples of a much more advanced way to handle busy intersections.
The above example really works best with bike paths that are separated from vehicles as they should be anyway. The current system in Madison (and most other cities in the USA) of painting a white line a few feet from the curb, or worse yet parked cars, or a mix with buses and right turning vehicles, and calling it a bike lane does not a good bike infrastructure make. There is no way Madison will ever reach a high level of bike commuting, or even much higher then we already have, until we get serious about an infrastructure that treats all forms of transport equally. For bicyclist that means bike paths with a physical separation from vehicles. The current bike infrastructure is only slightly better then an afterthought.