We hear complaints that bike lanes are underutilized.

This might be true, or it might appear to be true and not be true.

Let’s think about the traffic physics of this.

Imagine there is a lane of traffic full of cars, say a flow (Q) of 500 vehicles per hour, going very slowly, an average speed (V) say 5 km/h because of congestion, traffic signals, unloading trucks, and the like. The lane will appear full, because the density is high. Density (K) is vehicles per km, and the relationship between flow, density, and speed is given by Q=KV or K=Q/V. In this example, the density is 100 vehicles per km, or about 10 vehicles every 100 m, or 10 m between vehicles, which is a pretty high density. Not quite jam density (minimum vehicle spacing, maximum vehicles per km, on the order of 150), but close.

Imagine there is a parallel lane for bicycles. They are traveling at 20 km/h. The spacing is one bicycle every 40 m, or a density of 25 bicycles per km. Yet the flow is an identical 500 vehicles per hour (Q=KV). The lane looks one fourth as full (even less, because bicycles take up much less space than cars), but serves just as many vehicles as the crowded lane.

Now of course the bike lane is narrower than the car lane, so if we were to look at bicycles per square meter, accounting for a car lane of 3 m (typically 3.65m, but narrower in cities) and a bike lane of 1.5 m, we only need a density of one bicycle every 80 m to get the same flux (flux is flow accounting for the width of the lanes and vehicles). One bicycle every 80 m is about 1 bicyclist per block at a given time. In contrast that congested lane of cars has at least 8 vehicles in it for the same length block.

(I realize I should evaluate person throughput rather than vehicle throughput. For illustration, I am assuming 1 person per motor vehicle, which is a bit pessimistic, in practice it is closer to 1.1 for work trips and 1.5 all day).

Now, I am not saying the bike lane has 500 bicyclists per bike lane per hour (or the road has 500 vehicles per lane per hour). Most have fewer. Your kilometerage may vary. It doesn’t have to. The alternative use of the lane may have been storing cars. They have a speed of zero and a flow of 0, and a pretty high density (roughly 150 vehicles/km) for being unproductive.

Furthermore performance in terms of flow (or flux) isn’t the only question at hand. Safety is important too, and bike lanes are typically safer for bicyclists than riding in traffic, and sure feel safer.