A driver braking hard at 120 km/h stops in about 80 metres. A train at the same speed needs about ten times that, even with every brake applied correctly. The usual explanation is that trains are heavy, but weight is not the main reason. The limit is how much grip a steel wheel has on a steel rail, and the arithmetic that turns that grip into distance is short enough to do by hand.
Grip comes from friction, not from weight
A braking vehicle can slow down only as fast as its wheels can push against the surface. The most force that contact can give is the weight pressing on it multiplied by the coefficient of adhesion. Weight appears on both sides of the sum: a heavier vehicle presses harder, but also has more mass to slow. They cancel, so the maximum deceleration is simply the coefficient times g, about 9.81 m/s².
- Rubber on dry road: about 0.7, so at best about 7 m/s². Tyres on a real road give somewhat less, but the order of magnitude holds.
- Steel on steel: typically 0.1 to 0.3, which is a ceiling of about 1 to 3 m/s². Wet rail, frost or crushed leaves can push it towards the bottom of that range.
The smooth, hard contact that lets a locomotive pull a long load with little effort, which is also part of why railways follow rivers and gentle gradients, is the same contact that limits braking. Rolling resistance is low and so is grip.
Service braking uses only part of that
A train does not brake at its adhesion ceiling in normal running. Passengers standing in a carriage would be thrown about, and a wheel that locks and slides loses grip and can grind a flat onto itself. Typical service braking is therefore around 0.5 to 1 m/s², with emergency braking often a little higher. The figures below use constant deceleration, which is a simplification, so treat them as a pattern rather than a timetable for any particular train.
The sum: d = v² ÷ 2a
For constant deceleration a from speed v, the stopping distance is d = v² ÷ 2a. Speed must be in metres per second, so divide km/h by 3.6. For 120 km/h that is 33.3 m/s, and v² is about 1,111.
- At 0.5 m/s²: 1,111 ÷ 1 = about 1,111 m, taking about 67 seconds.
- At 0.7 m/s²: 1,111 ÷ 1.4 = about 794 m.
- At 1.0 m/s²: 1,111 ÷ 2 = about 556 m, taking about 33 seconds.
- A car at 6.9 m/s² (0.7 × g): 1,111 ÷ 13.8 = about 81 m, taking under 5 seconds.
The curve bends upwards because speed is squared. Double the speed and the distance quadruples, which is why the lines for trains pull away from the car so quickly. At 200 km/h the 0.7 train needs about 2,205 m, over two kilometres. That is also why railways cannot rely on a driver seeing a hazard in time, a problem that signals and blocks exist to solve.
In Valley Rail: Train Tycoon you buy a train, choose where it goes and it runs the route on its own, and rail crossings have automatic signals. The app is in closed testing.
Why the number is worse in practice
The sum gives the distance once the brakes are working at full strength. Real trains add three delays.
- Reaction time. The driver must notice, decide and act. At 120 km/h each second of delay covers about 33 metres.
- Brake build-up. Brake force does not appear at once. On a long train, the signal to brake travels along the train and takes time to reach the last vehicle, so the full rate is reached after a few seconds, longer on a heavy freight train.
- Poor adhesion. If the rail is contaminated, the grip available drops, and brakes that would be fine on a clean dry rail make the wheels slide. Drivers and systems use sand and wheel-slide protection to limit it, but the safe rate is lowered.
Add a few seconds of delay to the 0.7 case at 120 km/h and the stop moves from about 800 m towards 900 m or more. A railway has to design for the bad day, not the clean dry one.
A train is slow to stop because steel grips steel weakly, not because it is heavy. A lighter train on the same rail would need nearly the same distance.
What to take from it
- Maximum braking is the adhesion coefficient times 9.81 m/s²: about 7 for rubber on dry road, about 1 to 3 for steel on steel.
- Normal train braking is gentler, around 0.5 to 1 m/s², which keeps passengers safe and wheels from sliding.
- Distance is v² ÷ 2a, so 120 km/h needs about 556 to 1,111 m and 200 km/h needs about 1,543 to 3,086 m.
- Reaction and brake build-up add to the figure, which is why long blocks, early warnings and level-crossing barriers matter.
Valley Rail: Train Tycoon lets you build railways, run trains and watch small towns grow into busy cities. It has six train models for passengers and freight, and rail crossings with automatic signals. Any money in the game is in-game only and has no cash value. Valley Rail is in closed testing and not yet publicly available.