Heavy Haul

Each contact patch is a Pacejka Magic Formula evaluation — the same sigmoid used for lateral force against slip angle and longitudinal force against slip ratio:

The second line is the one that matters. Peak friction falls as vertical load rises — here at k = 0.22 per unit of relative overload, from a peak of 0.85 at a nominal 26 kN per tire position, against 1.05 and k = 0.12 for the passenger cars sharing the road. Doubling the weight on a tire therefore gives noticeably less than double the grip. A 200,000 lb rig does not merely stop slowly because of its inertia; its tires are also working further down their own friction curve. It is also the modelled reason duals exist: a dual splits its position’s load across two patches, so each sits lower on the curve and keeps more of its coefficient.

Longitudinal and lateral demand then compete inside a friction ellipse, capped at μF_z in the combined direction. That single constraint is why braking mid-corner in a loaded rig pushes the nose wide, and it is why the tire-scrub sound is gated on how saturated the patches actually are rather than on steering angle — the noise arrives exactly when grip is running out.

Three properties of an air brake system change how the rig has to be driven, and all three are modelled. Application lag means air takes time to reach the trailer, so a long combination starts braking from the front and gets pushed from the back — that lag is the trailer-swing mechanism in a panic stop. Reservoir depletion means fanning the brakes outruns the compressor; below about 60 psi you get a warning, and below 35 psi the spring brakes drop and cannot be released, so the rig stops wherever it happens to be. And drum brakes hauling 200,000 lb down a grade heat fast and lose a large fraction of their torque.

That last one is why the compression brake is not optional equipment on the −9% descent off Prospect Hill, which has a signalised junction at the bottom of it: 244 °C in the drums on the pedal against 181 °C with the engine doing the work. The descent is the one place on the route where the correct technique is a gear and a valve rather than a pedal, and the scorecard measures whether you found it.

Pulling away is its own problem. Driveline inertia is reflected to the wheels through the square of the gear ratio, which in a crawler gear is roughly 1,000 kg·m² per wheel against the wheel’s own 32 — that is what lets a loaded rig feed torque in smoothly on a grade instead of instantly lighting up its drives, and clutch heat is what punishes launching a superload in too tall a gear. For the dual-lane move there are four engines on the combination, and they are deliberately not modelled as four times one engine. Each pushes through its own tires, capped at what a loaded drive tandem can actually hold, because 328 tonnes needs 205 kN on a six percent grade and one tandem cannot put that down however much torque the engine makes. Multiply the tractor’s torque instead and you get spinning drives. With the push trucks the combination holds 13.8 mph up the hill; without them it stops on it.

The route is 8.4 miles from a terminal to a substation, and the centreline is written the way a survey describes a road — a run of so many metres at so much grade, then a turn of so many degrees at so much radius. It used to be forty-eight control points read off a sketch, and stated that way nobody could see that seven and a half miles of it contained three corners. You cannot see a radius in a list of coordinates. Stated as turns, the corner becomes the unit of design, and a tool walks the finished centreline and reports every one of the twenty-one of them with its radius and an advisory speed.

Everything else on the route is placed at a named mark on that survey rather than at a number — every junction, bridge, grade, ramp and change of cross-section — so moving a corner moves what stands on it instead of leaving a bridge in a field. The cross-section is a first-class part of the world too: sections are declared at arc lengths and blended across a taper, so a lane opens the way a real one does. The pavement widens first, and the lane is only usable once the taper has finished. The 320-metre acceleration lane onto the interstate is that same mechanism used forwards, and the three-to-one drop at the exit is it used backwards.

The pavement is widened through each of the six junctions the load turns at, and that is where Figure 1 comes back. A city intersection is built to a fifteen-metre kerb radius; a combination between 64 and 249 feet long swinging through it traces sixty metres on the centreline and puts its rear axles well inside the tractor’s path. The widening is the swept path. The lane paint is geometry rather than a texture for the same reason — edge lines that follow the pavement wherever it goes, a double yellow that becomes a turn lane’s markings where there is a turn lane, and no yellow at all on the interstate, where what is down the middle is a barrier.

The escorts are a behavioural system, not scripted animation. Two police units run ahead, take a light or park across the mouth of a side road, hold it until the whole combination is clear, then release and run up the closed lane past you to take the next junction nobody is covering. Done properly the load never stops and it looks like every light in the city happens to be green. A pilot car sits 140 m out front carrying a height pole set just above the load, calling bridges, corners, ramps and grades over the radio before you can see them; a chase car sits behind the tail — and where the tail is comes from the trailer, so it stations 70 m behind a step deck’s tailboard and 70 m behind the tip of a 72-metre blade rather than inside it.

Ambient traffic runs an Intelligent Driver Model and treats the load and every escort as solid: it follows them, queues behind them, and cannot pass through them. What those cars do then falls out of the road’s cross-section rather than from a rule about escorts. Where there is one lane each way, a 3.66 m load in a 3.7 m lane leaves oncoming traffic nowhere to be except the kerb, stopped, until the whole formation is past — not just the load, because that lane is what the police units leapfrog up. Where there are two or three lanes, the same traffic simply moves over one and carries on. The convoy test measures both: 83% of oncoming traffic pulls over and stops on the single-lane roads, against 0% on the multi-lane ones.

The signals are simulated rather than drawn, because a signalised junction changes the escort job completely. At a stop-sign side road the officer has to physically cross the carriageway and park across the mouth, shutting the highway down for the seconds that takes. At a signal he takes the light from the kerb on his own side and never crosses in front of anybody. Ten of the sixteen junctions on the route are signalised, each running a real fixed cycle with yellow and all-red clearance intervals that no two conflicting approaches ever overlap. Preemption freezes the controller at the top of the mainline green and restarts the cycle on release, so the cross street gets a full green afterwards rather than the tail of one. The mission test asserts the load never arrives at a signal that is not green for it, and the convoy test asserts nothing is ever in the intersection box as the load goes through.

American Truck Simulator’s look is a studio-scale asset problem — years of modelled trucks, scanned highways, licensed brands — and none of that can be produced from code. So every model here is generated procedurally at load time and every sound is synthesised rather than sampled: the engine note is built from its own firing frequency plus harmonics behind a lowpass that opens under load, so it lugs and shifts because the engine does, not because a clip was crossfaded. The result is readable rather than photoreal, and that is the trade being made on purpose.

Ambient vehicles are not simulated with the rig’s physics either — they are an arc length along the route and a lane offset. Their pose is reconstructed for rendering so they yaw into a lane change before they get there, keep their front wheels turned for as long as they are turning, and pitch with the grade. Without that reconstruction a kerbside pull-off is a box being slid sideways across the road, which is what it looked like for a while.

One more admission, because it cost the project twice. Three.js is right-handed: with +Y up and the rig facing +Z, the driver’s right-hand side is −X, and a right turn is a negative rotation about +Y. The axis labels suggest otherwise. Getting it backwards mirrors the entire simulation, so the right arrow steers left and the load drives up the oncoming lane. Two named constants now carry the convention, every steer angle below the steering box is stored as the raw rotation, and a test suite asserts the observable end of it — which way the rig goes when you press the right arrow, and which side of the paint the permitted lane is on.