Diesel-Electric Locomotive Traction Lab (3D)

Loading the locomotive...

Presets

Camera

Layers

Force arrows (green: tractive effort, red: resistance) Exhaust smoke (scales with throttle) Scenery motion Distance haze

Parameters

Live readouts

Graphs

Tractive effort F (blue) and resistance R (red) versus speed; white dot: now, green dot: equilibrium

Speed versus time (last 10 minutes of simulated time), dashed: equilibrium speed

Power at the rail (blue) and available power (dashed), MW

Numerical checks

running...

What to try

Press Mountain grade: the train settles to a much lower speed because the grade force m g sinθ eats the power.
Choose Wet rail: the adhesion plateau on the first graph drops, so the locomotive cannot use its full power until it is moving faster.
Raise the wagon count and watch the equilibrium speed fall; set the brake to 1000 kN after Start at 80 km/h to see the stopping distance.
Use the camera buttons for the bogie close-up (watch all six wheelsets turn) or drag to orbit, wheel to zoom. Space pauses, R resets.

The locomotive, wagon, track, signal, poles and trees (named parts such as Bogie_F_ws0, RoofFan, Wagon, TrackSeg) were modelled and baked in Blender; Three.js r160 animates the wheels, fan, smoke and scenery from the same physics module as the 2D companion.

The science

Tractive effort. With every axle driven the adhesion limit is F_adh = μ M g where M is the locomotive mass. The engine delivers power at the rail P_rail = η P (notch / 8), η = 0.9 so at speed v the pulling force cannot exceed P_rail/v: F_t = min( μ M g, η P_notch / v ) The two limits cross at v_c = η P_notch / (μ M g): below it the wheels are the limit, above it the engine is.

Resistance. For total mass m (tonnes) at speed v (m/s) the model uses R = 20 m + 5.5 v² + m g sinθ rolling resistance of about 20 N per tonne, a lumped aerodynamic term and the grade force (θ = atan(grade/100)).

Motion. 1.06 m dv/dt = F_t − R − F_brake with the 1.06 factor for rotating inertia. The equilibrium speed is the root of F_t(v) = R(v). Wheel angle is x / r with r = 0.5 m.

Simplifications. Constant-power engine with no lag, no wheel-slip dynamics (traction is clamped at the adhesion limit), no curve resistance, no coupler slack, constant adhesion although real μ varies with speed and rail condition, and only the nearest 14 wagons are modelled in 3D (the rest of a long train is drawn as one long body). Time can be accelerated, so the picture is a time-lapse. Educational model, not a training tool.