This page tries to summarize the algorithm used for realistic train acceleration. What follows is a description of the formulas listed at the bottom of this page.

• acceleration = (force – friction) / 4m
  • where m is the mass of the train

• force = 2.2 * power / velocity = 2.2 * time * power / distance

• friction = 4 * (1.3m + 60n + μmv*10^-3 + Adv²/10,000 + q)
  • where n is the number of cars
  • and v is the velocity.

• μ is the coefficient of friction, which is set to 35 for OpenTTD.

• A is the area of mumble, mumble 120.

• d = 20+3n
  • This is the drag coefficient, although it does not depend on velocity as one would expect.

• q = Σ 60s_im_i
  • where s_i is the slope of car i
  • and m_i is the mass of car i.

This is incline of the train as a whole (or the sum of the inclines of each car), where 60s_im_i is the incline of a single car i.

• The slope of a car is one of the following:
  • 1 if the car is ascending
  • 0 if the car is level
  • -1 if the car is descending

Units used

velocity [v] = mph

power [P] = W

mass [m] = t

Formulas

F = 22P / 10v [N]

n — number of cars

μ = 35 (eq. 1e-3 ?) — coefficient of friction

A = 120 — area (units?)

d = 20+3n — drag coefficient

q = Σ 60s_im_i — incline term, summed over cars

s_i — slope, -1 (going down), 0, or 1

m_i — mass of the car

Fr = 4(13m / 10 + 60n + μmv / 1000 + Adv²/10000 + q) [N]

a = (F - Fr) / (m * 4) [m s^-2]