Night Fog, an Unlit Lorry, and the Arithmetic You Should Have Done Earlier
It is 02:15 on a straight two-lane desert highway outside Al-Qassim, with no street lighting. You are driving a fully loaded sedan at an indicated 100 km/h on high beam. Patches of ground fog reduce visibility in places to about 60 metres; between patches you can see 200 metres. The surface is dry asphalt with a braking capability of about 0.7 g. Ahead, a heavy lorry is parked half on the hard shoulder with its rear corner overhanging your lane; its rear reflectors are caked in dust, there are no hazard lights, and the only warning is a faint red glow. You first pick it out at about 55 metres. Your reaction time tonight, at this hour and after four hours of driving, is realistically about 1.5 seconds.
1. Calculate whether you can stop from 100 km/h within the distance at which you first see the lorry.
Read the worked answer
Step 1 - distance covered before the brakes do anything: 100 km/h = 27.8 m/s. Reaction distance = 27.8 × 1.5 = 41.7 m.
Step 2 - braking distance at 0.7 g: Braking distance = v² / (2 × 0.7 × 9.81) = 771.6 / 13.73 ≈ 56.2 m.
Step 3 - total: 41.7 + 56.2 ≈ 98 m.
Step 4 - compare with the 55 m at which you actually saw the lorry. You need 98 m and you have 55 m. You stop about 43 m past the lorry - that is, you do not stop at all.
The conclusion that matters: at 55 m detection distance, no braking technique and no reflexes save this. The collision was created roughly two minutes earlier, when you chose 100 km/h for a road where you could see 60 m. The remaining distance only determines how hard the impact is.
Sanity check on the reaction time: at 4 a.m. after four hours of driving, 1.5 s is generous, not pessimistic. A drowsy driver's reaction time routinely doubles, which would add another 40 m and make the outcome worse still.
2. What speed would let you stop within the 60 metres you can actually see to be clear?
Read the worked answer
Set the stopping distance equal to 60 m and solve for speed. In m/s (call it v):
1.5v + v² / (2 × 0.7 × 9.81) = 60 1.5v + v² / 13.73 = 60 v² + 20.6v − 824 = 0 v = (−20.6 + √(424 + 3296)) / 2 = (−20.6 + 61.0) / 2 ≈ 20.2 m/s ≈ 73 km/h
Check the answer by substitution:
- At 70 km/h (19.4 m/s): reaction 29.2 m + braking 27.4 m = 56.6 m - stops inside 60 m, with about 3 m spare. Acceptable.
- At 80 km/h (22.2 m/s): reaction 33.3 m + braking 35.9 m = 69.2 m - overruns 60 m by 9 m. Not acceptable.
So the answer is about 70 km/h, and that is a ceiling, not a target. The 3 m of spare margin at 70 km/h disappears the moment the surface is damp, the tyres are worn, or the driver is slower than 1.5 s - all of which are likely at 02:15 in a fog patch.
The principle: you must be able to stop within the distance you can see to be clear. Fog does not change the limit; it changes the speed. Note also that the visibility is patchy - 200 m then 60 m - which is the worse case, because the fast sections tempt you back up to a speed you cannot use in the next patch.
3. Fog closes in and you are now inside the 55 m window with the lorry filling the lane. What do you do with the last two seconds?
Read the worked answer
Three actions, in this order:
- Brake hard and straight. Maximum pressure, both hands on the wheel, keep the car in its lane. Braking is the only thing that reduces the energy of the impact, and it works immediately.
- Do not swerve into the unknown. On a two-lane desert highway at night, the alternative to the lorry is a head-on with whatever is in the opposite lane, or a rollover on soft shoulder. A controlled impact with the lorry's rear corner at 40 km/h is survivable; an offset head-on at a combined 150 km/h is not. If a swerve is unavoidable, aim to clip the corner rather than take the rear squarely, so the passenger cell is not the crush zone.
- The instant you stop, become visible. Hazard lights on, engine off, and get out on the side away from traffic - not into the lane you have just been driving in. Put a warning triangle out only if it is genuinely safe to walk back up the road, ideally 50 m or more behind, and wear something reflective.
Then: call for help on the unified emergency number 911 or the traffic police on 999, and give the kilometre marker or the last exit name - on a desert highway 'near Al-Qassim' is useless to a patrol.
Judgement note on the first decision in this case: the high beam was the wrong setting inside the fog. High beam reflects off the water droplets and gives you a wall of white at 25 m. Low beam, fog lamps if fitted, and a speed matched to the 60 m visibility were the correct combination from the moment the first patch appeared.