8 · Trucks Fool the Loop

A single loop detector estimates speed by assuming every vehicle is a car. Add trucks and watch it go wrong

A single lane at a steady 72 km/h passes a 1.8 m loop. The loop flashes while a vehicle is over it. Every 30 seconds it reports what a real detector would: a count, an occupancy, and a speed estimated by assuming every vehicle is a 5 m car.

viewof loopTrucks = Inputs.range([0, 40], {value: 20, step: 1, label: "Share of trucks (%)"})

loopLive = {
  const v = 20, L = 360, x0 = 200, d = 1.8, dt = 1 / 30, rate = 0.45, p = loopTrucks / 100, period = 30;
  let veh = [], t = 0, nextArrival = 0, occTime = 0, count = 0, periodStart = 0;
  const reports = [];
  while (true) {
    for (let s = 0; s < 4; s++) {
      if (t >= nextArrival) {
        const len = Math.random() < p ? 18 : 5;
        const last = veh[veh.length - 1];
        if (!last || last.x - last.len > 8) veh.push({x: 0, len, truck: len > 5});
        nextArrival = t - Math.log(1 - Math.random()) / rate;
      }
      let over = false;
      for (const c of veh) {
        const xn = c.x + v * dt;
        if (c.x < x0 && xn >= x0) count++;
        c.x = xn;
        if (c.x >= x0 && c.x - c.len <= x0 + d) over = true;
      }
      if (over) occTime += dt;
      veh = veh.filter(c => c.x - c.len < L);
      t += dt;
      if (t - periodStart >= period) {
        const o = occTime / period, q = count / period * 3600, kEst = o / (5 + d) * 1000;   // veh/h and veh/km, so q / kEst is in km/h
        reports.unshift({time: Math.round(t), count, occ: o, q, vEst: kEst > 0 ? q / kEst : NaN});
        if (reports.length > 5) reports.pop();
        occTime = 0; count = 0; periodStart = t;
      }
    }
    yield {veh: veh.map(c => ({...c})), over: veh.some(c => c.x >= x0 && c.x - c.len <= x0 + d), reports: reports.slice(), L, x0};
  }
}

{
  const W = plotW < 640 ? plotW : 720, left = 20, right = W - 20, sc = (right - left) / loopLive.L;
  return htl.svg`<svg width="100%" viewBox="0 0 ${W} 70">
    <rect x=${left} y="20" width=${right - left} height="28" fill="#8882" />
    <rect x=${left + loopLive.x0 * sc - 3} y="16" width="6" height="36" fill=${loopLive.over ? "#ff9f1c" : "#ff9f1c55"} />
    ${loopLive.veh.map(c => htl.svg`<rect x=${left + (c.x - c.len) * sc} y="26" width=${Math.max(3, c.len * sc)} height="16" rx="3" fill=${c.truck ? "#6c757d" : "#2a9d8f"} />`)}
    <text x=${left + loopLive.x0 * sc} y="66" font-size="11" text-anchor="middle" fill="#c77700" font-weight="bold">loop</text>
    <text x=${right} y="12" font-size="11" text-anchor="end" fill="gray">green: 5 m cars · grey: 18 m trucks</text>
  </svg>`;
}

loopLive.reports.length
  ? md`| Report at | Occupancy | Flow (veh/h) | Estimated speed (true: 72 km/h) |
|---:|---:|---:|---:|
${loopLive.reports.map(r => `| ${r.time} s | ${(r.occ * 100).toFixed(1)}% | ${r.q.toFixed(0)} | **${isNaN(r.vEst) ? "—" : r.vEst.toFixed(0) + " km/h"}** |`).join("\n")}`
  : md`*The first 30-second report is on its way…*`

What it shows

Nobody slows down, yet the reported speed falls as the share of trucks rises. Real systems use pairs of loops or radar to measure speed directly. Lecture 2 shows where the error comes from.

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