Tractive effort at the rail follows the standard locomotive-engineering formula, using boiler pressure P, cylinder bore d and stroke s, and driving-wheel diameter D (all converted to inches/psi internally, matching the historical formula's units):
TE_start = 0.85 · P[psi] · d²[in²] · s[in] / D[in] (lbf)
The 0.85 factor is the mean-effective-pressure fraction of two double-acting cylinders averaged over a full wheel revolution — the standard constant used to size real locomotives. At low speed the valve gear can admit steam for the full cutoff each stroke, so TE stays essentially flat at this starting value. Past a "corner speed" the boiler can no longer refill each cylinder in the shrinking time per stroke, so available power caps out and effort falls off as TE(v) = P_max / v — the classic constant-power region of a real steam-locomotive performance curve.
Boiler saturation temperature comes from the real water Antoine-equation vapour-pressure relation (valid ~100–210 °C), so raising the pressure slider genuinely raises the temperature the boiler water must reach to produce that pressure of steam:
log10(P[mmHg]) = 8.14019 − 1810.94 / (244.485 + T[°C])
Net force on the train is TE(v) minus rolling resistance (≈0.3% of weight) and grade force (mg·sinθ); acceleration a = F_net / m is integrated each frame, so speed genuinely responds to every slider — a heavier train or a steeper grade measurably cuts both acceleration and top speed, while a bigger boiler, bigger cylinders or bigger driving wheels raise or lower the starting effort exactly as the formula predicts.