When the light turns yellow, every driver makes a snap decision: stop, or go. The engineer’s job is to make sure that for every car on the road, at least one of those choices is safe — that nobody is ever so close they can’t stop, yet so far they can’t clear. The gap where neither works is called the dilemma zone, and it’s where right-angle crashes are born. The fix isn’t a longer yellow because it feels safer; it’s a yellow timed to the speed, plus an all-red long enough for a car that entered late to physically clear the box before the cross street gets the green.
Set the speed and the width of the intersection below. Pick a yellow and an all-red. Then run the light and watch the worst-case car — the one that hit the yellow at the exact wrong distance — either slide clean through, or get stranded in the middle when the cross movement goes. Hit Use ITE timing to see what the formula says it should be.
The red band on the pavement is the dilemma zone — cars caught there at yellow onset can neither stop nor clear. A correctly-timed yellow makes that band disappear (the distance you need to stop equals the distance you cover during the yellow). The all-red then buys time for any car that entered the box late to get all the way across before the conflicting movement’s green. Two intervals, both kinematics, zero guessing.
🐧 NULL watched ten thousand cars cross the Arkadelphia light in a day, not one of them knowing a number was holding them apart. NULL said nothing. NULL knew the number, and who first worked it out, two finger-typed lines at a time.
The yellow-and-all-red is a life-safety calculation, not a courtesy. Get it right and a driver who commits at the worst possible instant still makes it across before anyone else moves. Get it wrong — a yellow a half-second too short for the speed — and you manufacture a dilemma zone, where the only choices are slam the brakes (rear-end crash) or run the red (right-angle crash). It is one of the few places in civil engineering where a single number, set by a kinematic formula, directly decides whether people walk away from an intersection.
It’s also where engineering meets ethics. Shortening a yellow below the ITE value raises red-light-running rates — and red-light-camera revenue. Communities have been caught doing exactly that. So the honest engineer doesn’t time the light to feel safe or to raise money; they time it to the physics, document it, and defend it. That’s the whole spirit of this place: the number is the number, and you can show your work.
This lab is the transportation cousin of the rest of the suite — the Static Beam sizes a beam so it doesn’t fail, the Moment Frame keeps a building up long enough to evacuate, and The Crossing keeps two streams of traffic from occupying the same box at the same instant. Same job, different scale: engineer the thing so the worst case still ends safe.
The kinematics are real. The yellow change interval here uses the standard ITE form — Y = t + v / (2a) on the flat, with reaction time t = 1.0 s and deceleration a = 10 ft/s² — and the all-red clearance uses R = (W + L) / v, with intersection width W and a 20-ft vehicle L. The dilemma zone is the gap between the distance needed to stop and the distance covered during the yellow. These are the equations in the FHWA MUTCD / FHWA Signal Timing Manual and ITE practice.
The theory has a famous origin. The dilemma-zone problem was first formalized in Gazis, Herman & Maradudin (1960), “The Problem of the Amber Signal Light in Traffic Flow,” Operations Research 8(1), 112–132 — the paper that proved a too-short yellow leaves drivers with no safe option.
Stylized here: the intersection geometry, the single “worst-case” car, and the timing are an illustrative teaching model tuned for legibility — representative numbers, not a signed timing sheet. Real designs account for grade, multiple approach speeds, pedestrian intervals, and a yellow capped between ~3 and 6 seconds. No values here are certified for a real signal.
The field site is real, the rest is the universe. US-78 & Arkadelphia is a real Birmingham interchange near 900 Arkadelphia Road. Mike Thornton, Moaz, Bobby B, Kai and his carp tacos are THE NET. This lab grew out of a student’s own first traffic model — a made-up-volumes practice run on an intersection a town over — and the program that computes this very clearance. Built to teach, not to scare.