Week 5: Human perception and reaction time at dusk

Why "the driver should have seen it" assumes a detection distance nobody measured — and how far a stopping-distance model can travel once you give it one.

22 March 2027

Open the slides

You Cannot Brake for What You Have Not Seen.

Week 4 built a stopping-distance model and was honest about one thing it assumed rather than calculated: that the driver notices the animal at the moment the clock starts. This week removes that assumption. Every metre Week 4 calculated is still correct — it just doesn’t start counting until something upstream of the physics happens first.

Last week’s number, this week’s question#

At 80 km/h, Week 4’s model put total stopping distance at 71.3 m: 33.3 m of reaction distance plus 38.0 m of braking distance, using a 1,500 kg vehicle, 1.5 s reaction time and 6.5 m/s² deceleration. That number answers “how far does the vehicle travel once the driver starts responding.”

Now ask a different question: what if the animal only becomes detectable 50 metres ahead? The stopping distance hasn’t changed — it still takes 71.3 m to stop. What’s changed is whether 71.3 m of road was ever available in the first place.

Five stages, one boundary#

A roadside encounter has more stages than “the driver saw it or didn’t”:

1. the animal is present near the road;
2. it becomes visible — detectable in principle, given the driver’s position, speed and sightline;
3. the driver recognises it as a hazard, not a shadow or a road sign;
4. the driver responds — foot moves, brake pedal is pressed;
5. braking actually begins.

Week 4’s “reaction time” is a single number standing in for stages 3 and 4 together — recognition and response, bundled. That bundling is a modelling choice, not a hidden extra step. If you ever add a separate “recognition delay” on top of the stated reaction time, check first whether the stated reaction time already includes it — double-counting the same interval under two different names is the most common way to get this calculation wrong, the same way mixing up km/h and m/s was Week 4’s.

Stage 2 — becoming visible at all — is what this week is actually about. Everything from stage 3 onward is Week 4’s territory.

What changes when something is harder to see#

Detection distance is not a fixed property of an animal; it’s a joint property of the animal, the road, the light and the driver. Four factors worth naming separately, because popular accounts collapse them into a single word — “dark”:

• contrast — how much an animal’s colour and shape stand out against what’s behind it. A kangaroo against an open paddock and a kangaroo against roadside scrub are different detection problems at the same light level;
• glare — an oncoming headlight or a low sun doesn’t just reduce brightness, it temporarily degrades the eye’s ability to resolve anything near it, and recovery from that isn’t instantaneous;
• roadside vegetation — scrub, long grass and tree lines can hide an animal’s outline or delay the moment it’s separable from its background, independent of how much light is available;
• attention and fatigue — a driver looking at a dashboard, a passenger, or simply tired, can fail to register something that was, in principle, visible the whole time.

Resist tidying these into one story. Dusk is not universally worse than full night — headlights provide a consistent contrast baseline that changing twilight light levels don’t, and a well-lit night stretch can be easier to read than an unlit one at dusk. Nor does every road present the same combination of these four factors: a straight, open highway and a scrub-lined back road are different detection problems even at identical light levels. The honest version of this section names four separate, road-specific and condition-specific variables — it does not rank “times of day” against each other in general.

A short note from Dr Beaumont. Every detection-technology claim you’ll meet in week 6 is making an implicit promise about exactly the stage this week names as stage 2 — becoming visible. A sensor that “detects wildlife” is claiming to move that boundary earlier than a human driver’s own eyes would. Whether it actually does, under what conditions, and by how much, is the entire subject of next week.

Distance margin#

Once you have a detection distance — however it was established — it plugs directly into Week 4’s model as a boundary the stopping distance either clears or doesn’t:

Distance margin = assumed detection distance − modelled stopping distance

A positive margin means the simplified model leaves distance to spare between where the animal became detectable and where the vehicle would stop. A negative margin means stopping before the assumed, stationary hazard is not possible under those particular assumptions. Neither result is a guarantee about a real encounter: a positive margin doesn’t promise a safe outcome (the animal might move into the vehicle’s path after the calculation ends, exactly as Week 4’s limitations list already warned), and a negative margin doesn’t promise a collision (a driver might still avoid it by steering, or the animal might move away). The margin describes what a simplified model can say about a boundary condition — nothing about what actually happens next to a particular animal on a particular night.

Four illustrative scenarios#

These four scenarios are invented teaching inputs, built to isolate one variable at a time — not measurements of real fatigue, glare or dusk conditions, and not a claim about any real detection distance. All four use Week 4’s same 1,500 kg vehicle and 6.5 m/s² braking deceleration.

Bars above the line have distance to spare; bars below it don’t clear the modelled stopping distance under those particular assumptions.

Each pair of adjacent scenarios isolates one changed input:

• A → B changes only speed (60 → 80 km/h, same 70 m detection distance): the margin flips from comfortably positive to slightly negative. Speed moved twice — it lengthens reaction distance directly and braking distance by its square, so the same detection distance stops being enough.
• B → C changes only detection distance (70 m → 50 m, same speed and reaction time): the margin gets 20 m worse, one-for-one with the 20 m lost from detection distance, because nothing about the vehicle’s own stopping distance changed at all.
• B → D changes only reaction time (1.5 s → 2.0 s, same speed and detection distance): the margin gets 11.1 m worse — the same additional reaction distance Week 4’s own extended scenario produces at 80 km/h, because reaction distance scales linearly with reaction time.

That last comparison is worth sitting with: reaction time adds distance linearly, one extra half-second always costing the same 11.1 m at 80 km/h, while speed affects both terms at once — a genuinely different kind of lever on the same margin.

What this exercise cannot establish#

A calculation using an assumed detection distance is not a measurement of any real driver’s, or any real road’s, actual detection distance. It cannot tell you whether a specific stretch of road is safe at a specific time of day, whether a specific driver would notice a specific animal, or what detection distance to expect on a road nobody has actually tested. It shows you how sensitive a stopping-distance model is to an input Week 4 held fixed — nothing stronger than that.

Where this goes next#

A distance margin is only as good as the detection distance fed into it, and so far that number has just been assumed. Next week asks where a real detection distance might actually come from — a sensor, a warning sign, an automatic braking system — and what it would take to trust a vendor’s number for it. The braking system cannot respond to an animal that is still classified as “probably a shrub.” Your confidence is not an additional headlight.

Physics starts counting after detection. The kangaroo has already been there for some time.

Reading#

Wood, J. M., Tyrrell, R. A., & Carberry, T. P. (2005). “Limitations in drivers’ ability to recognize pedestrians at night”, Human Factors, 47(3), 644–653. A closed-course study of pedestrian recognition distance at night — not kangaroos, but the same perceptual mechanism this week teaches: measured recognition distances ranged from 0 m to 220 m across clothing contrast, headlamp beam and glare conditions alone, with the same driver and the same road. Detection distance is not a fixed number; it moves by orders of magnitude with exactly the factors this week names.