In larger cities such as Lyon or even Dublin, bikeshare schemes are quite successful. In smaller ones like Limerick they struggle. I am convinced the problem is critical mass. As a scheme gets bigger, it provides disproportionately more possible useful journeys (as long as there is the population density to support it).

I want to model this. Let’s start by imagining cities that are big enough to sustain a square grid of bike stations, and let’s count the number of possible A-B journeys it provides (of different distances).

A 5 by 5 grid contains 25 stations, and 600 possible A-B journeys (25 by 24). I believe the ideal distance between stations is taken to be about 300m: if the stations are thus located, the distances of the 600 possible trajectories are distributed as follows:

5×5 distances | Freq. | Percent | Cumulative |
---|---|---|---|

(metres) | Percent | ||

300 | 80 | 13.33 | 13.33 |

424 | 64 | 10.67 | 24.00 |

600 | 60 | 10.00 | 34.00 |

671 | 96 | 16.00 | 50.00 |

849 | 36 | 6.00 | 56.00 |

900 | 40 | 6.67 | 62.67 |

949 | 64 | 10.67 | 73.33 |

1082 | 48 | 8.00 | 81.33 |

1200 | 20 | 3.33 | 84.67 |

1237 | 32 | 5.33 | 90.00 |

1273 | 16 | 2.67 | 92.67 |

1342 | 24 | 4.00 | 96.67 |

1500 | 16 | 2.67 | 99.33 |

1697 | 4 | 0.67 | 100.00 |

Total | 600 | 100.00 |

### 7 by 7 grid

If we (almost) double the size of the scheme to a 7 by 7 grid (49 stations), the number of possible journeys (almost) quadruples to 2,352:

7×7 distances | Freq. | Percent | Cumulative |
---|---|---|---|

(metres) | Percent | ||

300 | 168 | 7.14 | 7.14 |

424 | 144 | 6.12 | 13.27 |

600 | 140 | 5.95 | 19.22 |

671 | 240 | 10.20 | 29.42 |

849 | 100 | 4.25 | 33.67 |

900 | 112 | 4.76 | 38.44 |

949 | 192 | 8.16 | 46.60 |

1082 | 160 | 6.80 | 53.40 |

1200 | 84 | 3.57 | 56.97 |

1237 | 144 | 6.12 | 63.10 |

1273 | 64 | 2.72 | 65.82 |

1342 | 120 | 5.10 | 70.92 |

1500 | 152 | 6.46 | 77.38 |

1530 | 96 | 4.08 | 81.46 |

1616 | 80 | 3.40 | 84.86 |

1697 | 36 | 1.53 | 86.39 |

1749 | 64 | 2.72 | 89.12 |

1800 | 28 | 1.19 | 90.31 |

1825 | 48 | 2.04 | 92.35 |

1897 | 40 | 1.70 | 94.05 |

1921 | 48 | 2.04 | 96.09 |

2012 | 32 | 1.36 | 97.45 |

2121 | 16 | 0.68 | 98.13 |

2163 | 24 | 1.02 | 99.15 |

2343 | 16 | 0.68 | 99.83 |

2546 | 4 | 0.17 | 100.00 |

Total | 2,352 | 100.0 |

A 10 by 10 scheme offers 9,900 journeys, with a mean length of 1.572 km and a max of 3.818 km.

Clearly there is a really big return to scale. Even in the 10 by 10 grid, the longest journey is less than 4km, which is not long enough to put people off. Correspondingly, in the small 5 by 5 grid, 24% of journeys are less than 500m, which is possibly too short to bother checking out a bike.

Since there is no point putting a station in an area with low population density, city size (and possibly shape, topography) puts a hard limit on the size of the scheme. This is the hard reality facing bike schemes in Limerick.