City buses are surprisingly very bad for roads

Turns out, a city bus can do a LOT of damage, and per-passenger, it does over twice the damage of even a single-occupancy SUV. A plan-loaded city bus is almost as bad for roads as a fully loaded semi truck, and a crush-loaded city bus is worse. Whether you calculate it as marginal damage per passenger, or average damage per passenger, a bus passenger is hundreds of times more damaging to the road than even a fully-loaded cargo bike, and thousands of times more damaging than someone merely carrying themselves on a bicycle. Even the marginal road-damage cost of the first passenger to board a bus is a little bit worse than the road-damage cost of a single-occupancy SUV.

It may be wrong to assume that the cubic cost metric scales all the way down to vehicles as light as a bicycle, or even an SUV.  The cubic damage figure was computed for trucks; it’s possible that here is a quadratic or linear term with a much larger term that matters more for lower wheel loads, just as a bicycle is affected more by rolling resistance at low speeds and by wind resistance at high speeds. I haven’t been able to find anything published on this, however.

I’m not at all sure that these costs are rolled into the published “costs” of transit. Note that these are not the only costs; there are congestion costs, parking space costs, fuel costs, risk-to-others costs, risks-to-rides costs. But the road damage costs are really large.
(And if someone knows more about this than I do, do please check my math, I am working from published sources and conservative estimates. This was surprising to me.)

Pasted from Calca, lightly edited to remove irrelevant decimals and in one place line-wrapped.

First, data, sources, and assumptions:

In a comment exchange on some random liberal blog, a transit advocate was mysteriously opposed to bicycles-as-transit. He never completely explained why, but I think he was making assumptions about road damage and congestion that assumed a linear relationship to weight. However, that’s just not so. Damage-per-wheel is at least proportional to the cube of the weight on the wheel, if not the fourth power. It’s very non-linear, and non-intuitively a heavy vehicle with many wheels can do less road damage than a lighter vehicle with just a few.

http://mpta-transit.org/pdf/roadeo/New_Flyer_40Ft_Competition_Bus.pdf
Flyer_empty_weight = 28,880
http://en.wikipedia.org/wiki/File:SEATNewFlyer.jpg (picture showing paired rear wheels)
Flyer_wheels = 6
http://www.mbta.com/uploadedfiles/documents/Bluebook%202010.pdf (p. 64)
Flyer_plan_capacity = 54
Flyer_crush_capacity = 75

Passenger_weight = 150
Flyer_weight(passengers) = Flyer_empty_weight + Passenger_weight * passengers

Semi_weight = 80000
Semi_wheels = 18

http://en.wikipedia.org/wiki/Honda_civic
Compact_weight = 2500
Car_wheels = 4

http://en.wikipedia.org/wiki/Lincoln_Navigator
SUV_weight = 5500

Bike_weight = 250
Bike_wheels = 2

Cargo_bike_weight = 500
Light_bike_weight = 175

Road_damage(weight, wheels) = weight * (weight/wheels) * (weight/wheels) / 1,000,000,000
Bus_damage_pp(passengers) = Road_damage(Flyer_weight(passengers), Flyer_wheels) / passengers

Comparing damage per vehicle:

Road_damage(Semi_weight, Semi_wheels) => 1,580

Road_damage(SUV_weight, Car_wheels) => 10.4
Road_damage(Compact_weight, Car_wheels) => 0.98

Road_damage(Cargo_bike_weight, Bike_wheels) => 0.0313
Road_damage(Bike_weight, Bike_wheels) => 0.0039
Road_damage(Light_bike_weight, Bike_wheels) => 0.0013

Road_damage(Flyer_weight(0), Flyer_wheels) => 669
Road_damage(Flyer_weight(Flyer_plan_capacity), Flyer_wheels) => 1,405
Road_damage(Flyer_weight(Flyer_crush_capacity), Flyer_wheels) => 1,795

Bus damage, average per passenger at various loads, and ratios with bikes:

Bus_damage_pp(5) => 144.5
Bus_damage_pp(10) => 78
Bus_damage_pp(20) => 45
Bus_damage_pp(30) => 34.5
Bus_damage_pp(40) => 29.5
Bus_damage_pp(Flyer_plan_capacity) => 26
Bus_damage_pp(Flyer_crush_capacity) => 24

Bus_damage_pp(Flyer_crush_capacity)/Road_damage(Cargo_bike_weight, Bike_wheels) => 766
Bus_damage_pp(Flyer_crush_capacity)/Road_damage(Bike_weight, Bike_wheels) => 6,127
Bus_damage_pp(Flyer_crush_capacity)/Road_damage(Light_bike_weight, Bike_wheels) => 17,864

Marginal road damage; if the bus is running anyway, does it really matter that much if I take the bus? Yes, it does — even the first passenger to board a bus does more damage to the road than if they were driving an SUV. The heavier the bus, the greater the marginal cost per passenger, and it is always hundreds-to-thousands of times more damaging than riding a bicycle.

Bus_marginal_damage_p(passengers) = Road_damage(Flyer_weight(passengers + 1), Flyer_wheels) - 
                                    Road_damage(Flyer_weight(passengers), Flyer_wheels)

Bus_marginal_damage_p(0) => 10.48
Bus_marginal_damage_p(10) => 11.6
Bus_marginal_damage_p(Flyer_plan_capacity) => 17
Bus_marginal_damage_p(Flyer_crush_capacity) => 20

Bus_marginal_damage_p(0)/Road_damage(Cargo_bike_weight, Bike_wheels) => 335
Bus_marginal_damage_p(0)/Road_damage(Bike_weight, Bike_wheels) => 2,683
Bus_marginal_damage_p(0)/Road_damage(Light_bike_weight, Bike_wheels) => 7,822

Bus_marginal_damage_p(Flyer_plan_capacity)/Road_damage(Cargo_bike_weight, Bike_wheels) => 549
Bus_marginal_damage_p(Flyer_plan_capacity)/Road_damage(Bike_weight, Bike_wheels) => 4,394
Bus_marginal_damage_p(Flyer_plan_capacity)/Road_damage(Light_bike_weight, Bike_wheels) => 12,810